// Lute - 一款结构化的 Markdown 引擎，支持 Go 和 JavaScript
// Copyright (c) 2019-present, b3log.org
//
// Lute is licensed under Mulan PSL v2.
// You can use this software according to the terms and conditions of the Mulan PSL v2.
// You may obtain a copy of Mulan PSL v2 at:
//         http://license.coscl.org.cn/MulanPSL2
// THIS SOFTWARE IS PROVIDED ON AN "AS IS" BASIS, WITHOUT WARRANTIES OF ANY KIND, EITHER EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO NON-INFRINGEMENT, MERCHANTABILITY OR FIT FOR A PARTICULAR PURPOSE.
// See the Mulan PSL v2 for more details.

package test

import (
	"testing"

	"github.com/88250/lute"
)

var html2MdTests = []parseTest{

	{"240", "<dl>\n<dt>描述架构</dt>\n<dd>对组件进行高层次的整体概括，它们如何相互作用、各种情况下的控制流程是什么样的……简而言之 —— 代码的鸟瞰图。有一个专门用于构建代码的高层次架构图，以对代码进行解释的特殊编程语言 <a href=\"http://wikipedia.org/wiki/Unified_Modeling_Language\">UML</a>。绝对值得学习。</dd>\n<dt>记录函数的参数和用法</dt>\n<dd>有一个专门用于记录函数的语法 <a href=\"http://en.wikipedia.org/wiki/JSDoc\">JSDoc</a>：用法、参数和返回值。</dd>\n</dl>", "**描述架构**\n\n对组件进行高层次的整体概括，它们如何相互作用、各种情况下的控制流程是什么样的……简而言之 —— 代码的鸟瞰图。有一个专门用于构建代码的高层次架构图，以对代码进行解释的特殊编程语言 [UML](http://wikipedia.org/wiki/Unified_Modeling_Language)。绝对值得学习。\n\n**记录函数的参数和用法**\n\n有一个专门用于记录函数的语法 [JSDoc](http://en.wikipedia.org/wiki/JSDoc)：用法、参数和返回值。\n"},
	{"239", "<div class=\"hyc-common-markdown__table-wrapper isDark\" data-has-scroll=\"false\"><table><thead><tr><th>用例编号</th><th>TC-F-01-01</th></tr></thead><tbody><tr><td>​<strong>​用例标题​</strong>​</td><td>成功绑定一张新的储蓄卡</td></tr><tr><td>​<strong>​优先级​</strong>​</td><td>P0（最高）</td></tr><tr><td>​<strong>​测试目标​</strong>​</td><td>验证绑定银行卡的核心正向流程是否通畅、有效。</td></tr><tr><td>​<strong>​前置条件​</strong>​</td><td>1. 微信已登录且已完成实名认证。<br>\n2. 准备一张未绑定过的、有效的储蓄卡及对应的身份证号和银行预留手机号。<br>\n3. 网络连接正常。</td></tr></tbody></table></div>", "| 用例编号                   | TC-F-01-01                                                                                                              |\n| ---------------------------- | ------------------------------------------------------------------------------------------------------------------------- |\n| \u200b**\u200b用例标题\u200b**\u200b | 成功绑定一张新的储蓄卡                                                                                                  |\n| \u200b**\u200b优先级\u200b**\u200b   | P0（最高）                                                                                                              |\n| \u200b**\u200b测试目标\u200b**\u200b | 验证绑定银行卡的核心正向流程是否通畅、有效。                                                                            |\n| \u200b**\u200b前置条件\u200b**\u200b | 1. 微信已登录且已完成实名认证。<br/>2. 准备一张未绑定过的、有效的储蓄卡及对应的身份证号和银行预留手机号。<br/>3. 网络连接正常。 |\n"},
	{"238", "<figure class=\"p-2 mb-2\"><video class=\"sm:w-[60%] mx-auto w-full rounded-lg\" autoplay=\"\" controls=\"\" loop=\"\" playsinline=\"\" preload=\"auto\"><source src=\"https://zed.dev/img/post/crdts/divergence.webm\"></video><figcaption class=\"sm:w-[60%] mx-auto bg-[#212220] text-center w-full\">存在并发时, 天真的复制操作会导致分歧</figcaption></figure>", "<video src=\"https://zed.dev/img/post/crdts/divergence.webm\" controls=\"controls\"></video>\n存在并发时, 天真的复制操作会导致分歧\n"},
	{"237", "<ul _ngcontent-ng-c60218225=\"\" class=\"ng-star-inserted\"><ms-cmark-node _ngcontent-ng-c60218225=\"\" _nghost-ng-c60218225=\"\"><li _ngcontent-ng-c60218225=\"\" class=\"ng-star-inserted\"><ms-cmark-node _ngcontent-ng-c60218225=\"\" _nghost-ng-c60218225=\"\"><p _ngcontent-ng-c60218225=\"\" class=\"ng-star-inserted\"><ms-cmark-node _ngcontent-ng-c60218225=\"\" _nghost-ng-c60218225=\"\"><strong _ngcontent-ng-c60218225=\"\" class=\"ng-star-inserted\"><ms-cmark-node _ngcontent-ng-c60218225=\"\" _nghost-ng-c60218225=\"\"><span _ngcontent-ng-c60218225=\"\" class=\"ng-star-inserted\">阶段一：需求分析</span></ms-cmark-node></strong></ms-cmark-node></p><ul _ngcontent-ng-c60218225=\"\" class=\"ng-star-inserted\"><ms-cmark-node _ngcontent-ng-c60218225=\"\" _nghost-ng-c60218225=\"\"><li _ngcontent-ng-c60218225=\"\" class=\"ng-star-inserted\"><ms-cmark-node _ngcontent-ng-c60218225=\"\" _nghost-ng-c60218225=\"\"><p _ngcontent-ng-c60218225=\"\" class=\"ng-star-inserted\"><ms-cmark-node _ngcontent-ng-c60218225=\"\" _nghost-ng-c60218225=\"\"><span _ngcontent-ng-c60218225=\"\" class=\"ng-star-inserted\">收集用户反馈</span></ms-cmark-node></p></ms-cmark-node></li><li _ngcontent-ng-c60218225=\"\" class=\"ng-star-inserted\"><ms-cmark-node _ngcontent-ng-c60218225=\"\" _nghost-ng-c60218225=\"\"><p _ngcontent-ng-c60218225=\"\" class=\"ng-star-inserted\"><ms-cmark-node _ngcontent-ng-c60218225=\"\" _nghost-ng-c60218225=\"\"><span _ngcontent-ng-c60218225=\"\" class=\"ng-star-inserted\">定义产品规格</span></ms-cmark-node></p></ms-cmark-node></li></ms-cmark-node></ul></ms-cmark-node></li></ms-cmark-node></ul>", "* **阶段一：需求分析**\n\n  * 收集用户反馈\n  * 定义产品规格\n"},
	{"236", "<section><p></p><section data-formula=\"\\dfrac{1}{a}(1-\\ln \\dfrac{1}{a})=\\dfrac{1}{b}(1-\\ln \\dfrac{1}{b})\n\"></section><p></p></section>", "$$\n\\dfrac{1}{a}(1-\\ln \\dfrac{1}{a})=\\dfrac{1}{b}(1-\\ln \\dfrac{1}{b})\n$$\n"},
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120 180 104T199 61Q199 36 182 18T139 0T96 17T78 60Z\" style=\"visibility: visible;\"></path></g></g></g></g></g></g><g style=\"visibility: visible;\"></g></svg></section></span></section>", "$$\n\\begin{aligned}\na_{n+1}&=\\frac{6}{5}a_n-\\frac{3}{5}b_n\n-a_n(a_n^2+b_n^2),\\\\\nb_{n+1}&=\\frac{3}{5}a_n+\\frac{6}{5}b_n\n-b_n(a_n^2+b_n^2).\n\\end{aligned}\n$$\n"},
	{"234", "<ms-text-chunk _ngcontent-ng-c1183478193=\"\" _nghost-ng-c3238036794=\"\" class=\"ng-star-inserted\"><ms-cmark-node _ngcontent-ng-c3238036794=\"\" class=\"cmark-node v3-font-body ng-star-inserted\" _nghost-ng-c60218225=\"\"><h1 _ngcontent-ng-c60218225=\"\" class=\"ng-star-inserted\"><ms-cmark-node _ngcontent-ng-c60218225=\"\" _nghost-ng-c60218225=\"\"><!----><!----><!----><!----><!----><!----><!----><!----><!----><!----><span _ngcontent-ng-c60218225=\"\" class=\"ng-star-inserted\">购物清单</span><!----><!----><!----><!----><!----><!----><!----><!----><!----><!----><!----><!----><!----><!----><!----><!----><!----></ms-cmark-node></h1><!----><!----><!----><!----><!----><!----><!----><!----><!----><!----><!----><!----><!----><!----><!----><!----><!----><!----><!----><!----><!----><!----><!----><!----><!----><!----><!----><!----><!----><!----><!----><!----><!----><!----><!----><!----><!----><!----><!----><!----><!----><!----><ul _ngcontent-ng-c60218225=\"\" class=\"ng-star-inserted\"><ms-cmark-node _ngcontent-ng-c60218225=\"\" _nghost-ng-c60218225=\"\"><!----><!----><!----><!----><!----><!----><!----><!----><!----><!----><!----><!----><!----><li _ngcontent-ng-c60218225=\"\" class=\"ng-star-inserted\"><ms-cmark-node _ngcontent-ng-c60218225=\"\" _nghost-ng-c60218225=\"\"><!----><!----><!----><!----><!----><!----><!----><p _ngcontent-ng-c60218225=\"\" class=\"ng-star-inserted\"><ms-cmark-node _ngcontent-ng-c60218225=\"\" _nghost-ng-c60218225=\"\"><!----><!----><!----><!----><!----><!----><!----><!----><!----><!----><span _ngcontent-ng-c60218225=\"\" class=\"ng-star-inserted\">牛奶</span><!----><!----><!----><!----><!----><!----><!----><!----><!----><!----><!----><!----><!----><!----><!----><!----><!----></ms-cmark-node></p><!----><!----><!----><!----><!----><!----><!----><!----><!----><!----><!----><!----><!----><!----><!----><!----><!----><!----><!----><!----></ms-cmark-node></li><!----><!----><!----><!----><!----><!----><!----><!----><!----><!----><!----><!----><!----><!----><!----><!----><!----><!----><!----><!----><!----><!----><!----><!----><!----><!----><li _ngcontent-ng-c60218225=\"\" class=\"ng-star-inserted\"><ms-cmark-node _ngcontent-ng-c60218225=\"\" _nghost-ng-c60218225=\"\"><!----><!----><!----><!----><!----><!----><!----><p _ngcontent-ng-c60218225=\"\" class=\"ng-star-inserted\"><ms-cmark-node _ngcontent-ng-c60218225=\"\" _nghost-ng-c60218225=\"\"><!----><!----><!----><!----><!----><!----><!----><!----><!----><!----><span _ngcontent-ng-c60218225=\"\" class=\"ng-star-inserted\">面包</span><!----><!----><!----><!----><!----><!----><!----><!----><!----><!----><!----><!----><!----><!----><!----><!----><!----></ms-cmark-node></p><!----><!----><!----><!----><!----><!----><!----><!----><!----><!----><!----><!----><!----><!----><!----><!----><!----><!----><!----><!----></ms-cmark-node></li><!----><!----><!----><!----><!----><!----><!----><!----><!----><!----><!----><!----><!----><!----><!----><!----><!----><!----><!----><!----><!----><!----><!----><!----><!----><!----><li _ngcontent-ng-c60218225=\"\" class=\"ng-star-inserted\"><ms-cmark-node _ngcontent-ng-c60218225=\"\" _nghost-ng-c60218225=\"\"><!----><!----><!----><!----><!----><!----><!----><p _ngcontent-ng-c60218225=\"\" class=\"ng-star-inserted\"><ms-cmark-node _ngcontent-ng-c60218225=\"\" _nghost-ng-c60218225=\"\"><!----><!----><!----><!----><!----><!----><!----><!----><!----><!----><span _ngcontent-ng-c60218225=\"\" class=\"ng-star-inserted\">鸡蛋</span><!----><!----><!----><!----><!----><!----><!----><!----><!----><!----><!----><!----><!----><!----><!----><!----><!----></ms-cmark-node></p><!----><!----><!----><!----><!----><!----><!----><!----><!----><!----><!----><!----><!----><!----><!----><!----><!----><!----><!----><!----></ms-cmark-node></li><!----><!----><!----><!----><!----><!----><!----><!----><!----><!----><!----><!----><!----><!----><!----><!----><!----><!----><!----><!----><!----><!----><!----><!----><!----><!----><li _ngcontent-ng-c60218225=\"\" class=\"ng-star-inserted\"><ms-cmark-node _ngcontent-ng-c60218225=\"\" _nghost-ng-c60218225=\"\"><!----><!----><!----><!----><!----><!----><!----><p _ngcontent-ng-c60218225=\"\" class=\"ng-star-inserted\"><ms-cmark-node _ngcontent-ng-c60218225=\"\" _nghost-ng-c60218225=\"\"><!----><!----><!----><!----><!----><!----><!----><!----><!----><!----><span _ngcontent-ng-c60218225=\"\" class=\"ng-star-inserted\">水果</span><!----><!----><!----><!----><!----><!----><!----><!----><!----><!----><!----><!----><!----><!----><!----><!----><!----></ms-cmark-node></p><!----><!----><!----><!----><!----><!----><!----><!----><!----><!----><!----><!----><!----><!----><!----><!----><!----><!----><!----><!----><!----><!----><!----><!----><!----><!----><!----><!----><!----><!----><!----><ul _ngcontent-ng-c60218225=\"\" class=\"ng-star-inserted\"><ms-cmark-node _ngcontent-ng-c60218225=\"\" _nghost-ng-c60218225=\"\"><!----><!----><!----><!----><!----><!----><!----><!----><!----><!----><!----><!----><!----><li _ngcontent-ng-c60218225=\"\" class=\"ng-star-inserted\"><ms-cmark-node _ngcontent-ng-c60218225=\"\" _nghost-ng-c60218225=\"\"><!----><!----><!----><!----><!----><!----><!----><p _ngcontent-ng-c60218225=\"\" class=\"ng-star-inserted\"><ms-cmark-node _ngcontent-ng-c60218225=\"\" _nghost-ng-c60218225=\"\"><!----><!----><!----><!----><!----><!----><!----><!----><!----><!----><span _ngcontent-ng-c60218225=\"\" class=\"ng-star-inserted\">苹果</span><!----><!----><!----><!----><!----><!----><!----><!----><!----><!----><!----><!----><!----><!----><!----><!----><!----></ms-cmark-node></p><!----><!----><!----><!----><!----><!----><!----><!----><!----><!----><!----><!----><!----><!----><!----><!----><!----><!----><!----><!----></ms-cmark-node></li><!----><!----><!----><!----><!----><!----><!----><!----><!----><!----><!----><!----><!----><!----><!----><!----><!----><!----><!----><!----><!----><!----><!----><!----><!----><!----><li _ngcontent-ng-c60218225=\"\" class=\"ng-star-inserted\"><ms-cmark-node _ngcontent-ng-c60218225=\"\" _nghost-ng-c60218225=\"\"><!----><!----><!----><!----><!----><!----><!----><p _ngcontent-ng-c60218225=\"\" class=\"ng-star-inserted\"><ms-cmark-node _ngcontent-ng-c60218225=\"\" _nghost-ng-c60218225=\"\"><!----><!----><!----><!----><!----><!----><!----><!----><!----><!----><span _ngcontent-ng-c60218225=\"\" class=\"ng-star-inserted\">香蕉</span><!----><!----><!----><!----><!----><!----><!----><!----><!----><!----><!----><!----><!----><!----><!----><!----><!----></ms-cmark-node></p><!----><!----><!----><!----><!----><!----><!----><!----><!----><!----><!----><!----><!----><!----><!----><!----><!----><!----><!----><!----></ms-cmark-node></li><!----><!----><!----><!----><!----><!----><!----><!----><!----><!----><!----><!----><!----><!----></ms-cmark-node></ul><!----><!----><!----><!----><!----><!----><!----><!----><!----><!----><!----><!----><!----><!----><!----><!----><!----></ms-cmark-node></li><!----><!----><!----><!----><!----><!----><!----><!----><!----><!----><!----><!----><!----><!----><!----><!----><!----><!----><!----><!----><!----><!----><!----><!----><!----><!----><li _ngcontent-ng-c60218225=\"\" class=\"ng-star-inserted\"><ms-cmark-node _ngcontent-ng-c60218225=\"\" _nghost-ng-c60218225=\"\"><!----><!----><!----><!----><!----><!----><!----><p _ngcontent-ng-c60218225=\"\" class=\"ng-star-inserted\"><ms-cmark-node _ngcontent-ng-c60218225=\"\" _nghost-ng-c60218225=\"\"><!----><!----><!----><!----><!----><!----><!----><!----><!----><!----><span _ngcontent-ng-c60218225=\"\" class=\"ng-star-inserted\">蔬菜</span><!----><!----><!----><!----><!----><!----><!----><!----><!----><!----><!----><!----><!----><!----><!----><!----><!----></ms-cmark-node></p><!----><!----><!----><!----><!----><!----><!----><!----><!----><!----><!----><!----><!----><!----><!----><!----><!----><!----><!----><!----></ms-cmark-node></li><!----><!----><!----><!----><!----><!----><!----><!----><!----><!----><!----><!----><!----><!----></ms-cmark-node></ul><!----><!----><!----><!----><!----><!----><!----><!----><!----><!----><!----><!----><!----><!----><!----><!----><!----></ms-cmark-node><!----><!----><!----><!----><!----><!----></ms-text-chunk><!----><!----><!----><!----><!----><!----><!----><!----><!----><!----><!----></body></html><!--EndFragment-->", "# 购物清单\n\n* 牛奶\n* 面包\n* 鸡蛋\n* 水果\n\n  * 苹果\n  * 香蕉\n* 蔬菜\n"},
	{"233", "<pre class=\"prettyprint linenums prettyprinted\" style=\"\"><i class=\"iconfont iconfuzhi\" title=\"点击复制代码\"></i><ol class=\"linenums\"><li class=\"L0\"><code class=\"lang-shell\"><span class=\"pln\">ip route show</span></code></li><li class=\"L1\"><code class=\"lang-shell\"><span class=\"pln\">    </span><span class=\"kwd\">default</span><span class=\"pln\"> via </span><span class=\"lit\">1.1</span><span class=\"pun\">.</span><span class=\"lit\">1.254</span><span class=\"pln\"> dev ens192 onlink</span></code></li><li class=\"L2\"><code class=\"lang-shell\"><span class=\"pln\">    </span><span class=\"lit\">0.0</span><span class=\"pun\">.</span><span class=\"lit\">0.2</span><span class=\"pln\"> dev wg0 scope link</span></code></li><li class=\"L3\"><code class=\"lang-shell\"><span class=\"pln\">    </span><span class=\"lit\">2.2</span><span class=\"pun\">.</span><span class=\"lit\">2.2</span><span class=\"pln\"> dev wg0 scope link</span></code></li><li class=\"L4\"><code class=\"lang-shell\"></code></li><li class=\"L5\"><code class=\"lang-shell\"><span class=\"pln\">ip route show table </span><span class=\"lit\">51820</span></code></li><li class=\"L6\"><code class=\"lang-shell\"><span class=\"pln\">    </span><span class=\"com\">#此时为空</span></code></li></ol></pre>", "```shell\nip route show\n    default via 1.1.1.254 dev ens192 onlink\n    0.0.0.2 dev wg0 scope link\n    2.2.2.2 dev wg0 scope link\n\nip route show table 51820\n    #此时为空\n```\n"},
	{"232", "<pre class=\"prettyprint linenums prettyprinted\" style=\"\"><i class=\"iconfont iconfuzhi\" title=\"点击复制代码\"></i><ol class=\"linenums\"><li class=\"L0\"><code class=\"lang-shell\"><span class=\"pln\">ip </span><span class=\"pun\">-</span><span class=\"lit\">4</span><span class=\"pln\"> route add </span><span class=\"lit\">0.0</span><span class=\"pun\">.</span><span class=\"lit\">0.0</span><span class=\"pun\">/</span><span class=\"lit\">0</span><span class=\"pln\"> dev wg0 table </span><span class=\"lit\">51820</span></code></li></ol></pre>", "```shell\nip -4 route add 0.0.0.0/0 dev wg0 table 51820\n```\n"},
	{"231", "<ul style=\"box-sizing: border-box;border-width: 0px;border-style: solid;border-color: rgb(229, 229, 229);list-style: circle;margin: 0px;padding: 0px 0px 0px 1em;text-align: left;line-height: 1.75;font-family: -apple-system-font, BlinkMacSystemFont, &quot;Helvetica Neue&quot;, &quot;PingFang SC&quot;, &quot;Hiragino Sans GB&quot;, &quot;Microsoft YaHei UI&quot;, &quot;Microsoft YaHei&quot;, Arial, sans-serif;font-size: 14px;color: rgb(63, 63, 63);\" class=\"list-paddingleft-1 js_darkmode__90\"><li style=\"box-sizing: border-box;border-width: 0px;border-style: solid;border-color: rgb(229, 229, 229);text-align: left;line-height: 1.75;font-family: -apple-system-font, BlinkMacSystemFont, &quot;Helvetica Neue&quot;, &quot;PingFang SC&quot;, &quot;Hiragino Sans GB&quot;, &quot;Microsoft YaHei UI&quot;, &quot;Microsoft YaHei&quot;, Arial, sans-serif;font-size: 14px;text-indent: -1em;display: block;margin: 0.2em 8px;color: rgb(63, 63, 63);\" class=\"js_darkmode__91\"><section><span leaf=\"\">• ⚡ REST APIs</span></section></li><li style=\"box-sizing: border-box;border-width: 0px;border-style: solid;border-color: rgb(229, 229, 229);text-align: left;line-height: 1.75;font-family: -apple-system-font, BlinkMacSystemFont, &quot;Helvetica Neue&quot;, &quot;PingFang SC&quot;, &quot;Hiragino Sans GB&quot;, &quot;Microsoft YaHei UI&quot;, &quot;Microsoft YaHei&quot;, Arial, sans-serif;font-size: 14px;text-indent: -1em;display: block;margin: 0.2em 8px;color: rgb(63, 63, 63);\" class=\"js_darkmode__92\"><section><span leaf=\"\">• ⚡ NocoDB SDK</span></section></li></ul>", "* ⚡ REST APIs\n* ⚡ NocoDB SDK\n"},
	{"230", "<span class=\"container-YQu5sM math-inline single-afuC4w\" data-custom-copy-text=\"E\"><span class=\"katex\"><span aria-hidden=\"true\" class=\"katex-html\"><span class=\"base\"><span style=\"height:0.6833em;\" class=\"strut\"></span><span style=\"margin-right:0.05764em;\" class=\"mord mathnormal\">E</span></span></span></span></span>为<strong>能量本征值</strong>，表示粒子处于定态时的能量。", "$E$ 为\u200b**能量本征值**\u200b，表示粒子处于定态时的能量。\n"},
	{"229", "<div class=\"auto-hide-last-sibling-br paragraph-Oc488D paragraph-element br-paragraph-space\"><span class=\"container-YQu5sM math-inline\" data-custom-copy-text=\"\\(G_{\\mu\\nu} = 8\\pi G \\frac{T_{\\mu\\nu}}{c^4}\\)\"><span class=\"katex\"><span aria-hidden=\"true\" class=\"katex-html\"><span class=\"base\"><span style=\"height:0.9694em;vertical-align:-0.2861em;\" class=\"strut\"></span><span class=\"mord\"><span class=\"mord mathnormal\">G</span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span style=\"height:0.1514em;\" class=\"vlist\"><span style=\"top:-2.55em;margin-left:0em;margin-right:0.05em;\"><span style=\"height:2.7em;\" class=\"pstrut\"></span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span style=\"margin-right:0.06366em;\" class=\"mord mathnormal mtight\">μν</span></span></span></span></span><span class=\"vlist-s\">&ZeroWidthSpace;</span></span><span class=\"vlist-r\"><span style=\"height:0.2861em;\" class=\"vlist\"><span></span></span></span></span></span></span><span style=\"margin-right:0.2778em;\" class=\"mspace\"></span><span class=\"mrel\">=</span><span style=\"margin-right:0.2778em;\" class=\"mspace\"></span></span><span class=\"base\"><span style=\"height:1.3307em;vertical-align:-0.345em;\" class=\"strut\"></span><span class=\"mord\">8</span><span style=\"margin-right:0.03588em;\" class=\"mord mathnormal\">π</span><span class=\"mord mathnormal\">G</span><span class=\"mord\"><span class=\"mopen nulldelimiter\"></span><span class=\"mfrac\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span style=\"height:0.9857em;\" class=\"vlist\"><span style=\"top:-2.655em;\"><span style=\"height:3em;\" class=\"pstrut\"></span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\">c</span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span style=\"height:0.7463em;\" class=\"vlist\"><span style=\"top:-2.786em;margin-right:0.0714em;\"><span style=\"height:2.5em;\" class=\"pstrut\"></span><span class=\"sizing reset-size3 size1 mtight\"><span class=\"mord mtight\">4</span></span></span></span></span></span></span></span></span></span></span><span style=\"top:-3.23em;\"><span style=\"height:3em;\" class=\"pstrut\"></span><span style=\"border-bottom-width:0.04em;\" class=\"frac-line\"></span></span><span style=\"top:-3.5073em;\"><span style=\"height:3em;\" class=\"pstrut\"></span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\"><span style=\"margin-right:0.13889em;\" class=\"mord mathnormal mtight\">T</span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span style=\"height:0.1645em;\" class=\"vlist\"><span style=\"top:-2.357em;margin-left:-0.1389em;margin-right:0.0714em;\"><span style=\"height:2.5em;\" class=\"pstrut\"></span><span class=\"sizing reset-size3 size1 mtight\"><span class=\"mord mtight\"><span style=\"margin-right:0.06366em;\" class=\"mord mathnormal mtight\">μν</span></span></span></span></span><span class=\"vlist-s\">&ZeroWidthSpace;</span></span><span class=\"vlist-r\"><span style=\"height:0.2819em;\" class=\"vlist\"><span></span></span></span></span></span></span></span></span></span></span><span class=\"vlist-s\">&ZeroWidthSpace;</span></span><span class=\"vlist-r\"><span style=\"height:0.345em;\" class=\"vlist\"><span></span></span></span></span></span><span class=\"mclose nulldelimiter\"></span></span></span></span></span></span></div>", "$$\nG_{\\mu\\nu} = 8\\pi G \\frac{T_{\\mu\\nu}}{c^4}\n$$\n"},
	{"228", "<pre tabindex=\"0\" class=\"prism-code language-tsx relative py-3 outline-none\" style=\"color: var(--lb-color-text-code);\"><code class=\"block min-w-full font-mono\"><span class=\"token-line CodeHighlight_line__ki_1l relative select-none table-row [counter-increment:line-count]\" style=\"color: var(--lb-color-text-code);\"><span class=\"sticky left-0 z-10 table-cell w-[1%] select-none break-normal px-4 text-right text-marketing-subtler before:content-[counter(line-count)] CodeHighlight_gutter__Z7nD6\"></span><span class=\"block h-full select-text pr-[1em]\"><span class=\"token comment\" style=\"color: var(--lb-color-text-code-comment); font-style: italic;\">// Adding some pre-built extensions</span><span class=\"token plain\"></span></span></span><span class=\"token-line CodeHighlight_line__ki_1l relative select-none table-row [counter-increment:line-count]\" style=\"color: var(--lb-color-text-code);\"><span class=\"sticky left-0 z-10 table-cell w-[1%] select-none break-normal px-4 text-right text-marketing-subtler before:content-[counter(line-count)] CodeHighlight_gutter__Z7nD6\"></span><span class=\"block h-full select-text pr-[1em]\"><span class=\"token plain\"></span><span class=\"token keyword\" style=\"color: var(--lb-color-text-code-tag);\">const</span><span class=\"token plain\"> editor </span><span class=\"token operator\" style=\"color: var(--lb-color-text-code-tag);\">=</span><span class=\"token plain\"> </span><span class=\"token function\" style=\"color: var(--lb-color-text-code-constant);\">useEditor</span><span class=\"token punctuation\" style=\"color: var(--lb-color-text-code-punctuation);\">(</span><span class=\"token punctuation\" style=\"color: var(--lb-color-text-code-punctuation);\">{</span><span class=\"token plain\"></span></span></span><span class=\"token-line CodeHighlight_line__ki_1l relative select-none table-row [counter-increment:line-count]\" style=\"color: var(--lb-color-text-code);\"><span class=\"sticky left-0 z-10 table-cell w-[1%] select-none break-normal px-4 text-right text-marketing-subtler before:content-[counter(line-count)] CodeHighlight_gutter__Z7nD6\"></span><span class=\"block h-full select-text pr-[1em]\"><span class=\"token plain\">  extensions</span><span class=\"token operator\" style=\"color: var(--lb-color-text-code-tag);\">:</span><span class=\"token plain\"> </span><span class=\"token punctuation\" style=\"color: var(--lb-color-text-code-punctuation);\">[</span><span class=\"token plain\"></span></span></span><span class=\"token-line CodeHighlight_line__ki_1l relative select-none table-row [counter-increment:line-count]\" style=\"color: var(--lb-color-text-code);\"><span class=\"sticky left-0 z-10 table-cell w-[1%] select-none break-normal px-4 text-right text-marketing-subtler before:content-[counter(line-count)] CodeHighlight_gutter__Z7nD6\"></span><span class=\"block h-full select-text pr-[1em]\"><span class=\"token plain\">    </span><span class=\"token maybe-class-name\" style=\"color: var(--lb-color-text-code-class);\">StarterKit</span><span class=\"token punctuation\" style=\"color: var(--lb-color-text-code-punctuation);\">,</span><span class=\"token plain\"> </span><span class=\"token comment\" style=\"color: var(--lb-color-text-code-comment); font-style: italic;\">// Adds standard features, e.g. styles, quotes, lists</span><span class=\"token plain\"></span></span></span><span class=\"token-line CodeHighlight_line__ki_1l relative select-none table-row [counter-increment:line-count]\" style=\"color: var(--lb-color-text-code);\"><span class=\"sticky left-0 z-10 table-cell w-[1%] select-none break-normal px-4 text-right text-marketing-subtler before:content-[counter(line-count)] CodeHighlight_gutter__Z7nD6\"></span><span class=\"block h-full select-text pr-[1em]\"><span class=\"token plain\">    </span><span class=\"token maybe-class-name\" style=\"color: var(--lb-color-text-code-class);\">Typography</span><span class=\"token punctuation\" style=\"color: var(--lb-color-text-code-punctuation);\">,</span><span class=\"token plain\"> </span><span class=\"token comment\" style=\"color: var(--lb-color-text-code-comment); font-style: italic;\">// Adds smart typography, e.g. curly quotes, fractions</span><span class=\"token plain\"></span></span></span><span class=\"token-line CodeHighlight_line__ki_1l relative select-none table-row [counter-increment:line-count]\" style=\"color: var(--lb-color-text-code);\"><span class=\"sticky left-0 z-10 table-cell w-[1%] select-none break-normal px-4 text-right text-marketing-subtler before:content-[counter(line-count)] CodeHighlight_gutter__Z7nD6\"></span><span class=\"block h-full select-text pr-[1em]\"><span class=\"token plain\">    liveblocks</span><span class=\"token punctuation\" style=\"color: var(--lb-color-text-code-punctuation);\">,</span><span class=\"token plain\"> </span><span class=\"token comment\" style=\"color: var(--lb-color-text-code-comment); font-style: italic;\">// Adds realtime collaboration, comments, mentions</span><span class=\"token plain\"></span></span></span><span class=\"token-line CodeHighlight_line__ki_1l relative select-none table-row [counter-increment:line-count]\" style=\"color: var(--lb-color-text-code);\"><span class=\"sticky left-0 z-10 table-cell w-[1%] select-none break-normal px-4 text-right text-marketing-subtler before:content-[counter(line-count)] CodeHighlight_gutter__Z7nD6\"></span><span class=\"block h-full select-text pr-[1em]\"><span class=\"token plain\">  </span><span class=\"token punctuation\" style=\"color: var(--lb-color-text-code-punctuation);\">]</span><span class=\"token punctuation\" style=\"color: var(--lb-color-text-code-punctuation);\">,</span><span class=\"token plain\"></span></span></span><span class=\"token-line CodeHighlight_line__ki_1l relative select-none table-row [counter-increment:line-count]\" style=\"color: var(--lb-color-text-code);\"><span class=\"sticky left-0 z-10 table-cell w-[1%] select-none break-normal px-4 text-right text-marketing-subtler before:content-[counter(line-count)] CodeHighlight_gutter__Z7nD6\"></span><span class=\"block h-full select-text pr-[1em]\"><span class=\"token plain\"></span><span class=\"token punctuation\" style=\"color: var(--lb-color-text-code-punctuation);\">}</span><span class=\"token punctuation\" style=\"color: var(--lb-color-text-code-punctuation);\">)</span><span class=\"token punctuation\" style=\"color: var(--lb-color-text-code-punctuation);\">;</span></span></span></code></pre>", "```tsx\n// Adding some pre-built extensions\nconst editor = useEditor({\n  extensions: [\n    StarterKit, // Adds standard features, e.g. styles, quotes, lists\n    Typography, // Adds smart typography, e.g. curly quotes, fractions\n    liveblocks, // Adds realtime collaboration, comments, mentions\n  ],\n});\n```\n"},
	{"227", "<ol class=\"ReferenceList\">\n    <li id=\"ref_1\" tabindex=\"0\"><a class=\"ReferenceList-backLink\"\n                                   href=\"https://www.zhihu.com/question/563718496/answer/1900558338183393316#ref_1_0\"\n                                   aria-label=\"back\" data-reference-link=\"true\">^</a><span>WebP2 Diff 1251ca748c17278961c0d0059b744595b35a4943</span>&nbsp;<a\n            href=\"https://chromium.googlesource.com/codecs/libwebp2/+/1251ca748c17278961c0d0059b744595b35a4943%5E%21/\"\n            class=\"external\" target=\"_blank\" rel=\"noopener noreferrer\">https://chromium.googlesource.com/codecs/libwebp2/+/1251ca748c17278961c0d0059b744595b35a4943%5E%21/</a>\n    </li>\n    <li id=\"ref_2\" tabindex=\"0\"><a class=\"ReferenceList-backLink\"\n                                   href=\"https://www.zhihu.com/question/563718496/answer/1900558338183393316#ref_2_0\"\n                                   aria-label=\"back\" data-reference-link=\"true\">^</a><span>AVIF Supported Software (Wikipedia)</span>&nbsp;<a\n            href=\"https://en.wikipedia.org/wiki/AVIF#Support\" class=\"external\" target=\"_blank\"\n            rel=\"noopener noreferrer\">https://en.wikipedia.org/wiki/AVIF#Support</a></li>\n    <li id=\"ref_3\" tabindex=\"0\"><a class=\"ReferenceList-backLink\"\n                                   href=\"https://www.zhihu.com/question/563718496/answer/1900558338183393316#ref_3_0\"\n                                   aria-label=\"back\" data-reference-link=\"true\">^</a><span>HEIF Supported Software (Wikipedia)</span>&nbsp;<a\n            href=\"https://en.wikipedia.org/wiki/High_Efficiency_Image_File_Format#Support\" class=\"external\"\n            target=\"_blank\" rel=\"noopener noreferrer\">https://en.wikipedia.org/wiki/High_Efficiency_Image_File_Format#Support</a>\n    </li>\n    <li id=\"ref_4\" tabindex=\"0\"><a class=\"ReferenceList-backLink\"\n                                   href=\"https://www.zhihu.com/question/563718496/answer/1900558338183393316#ref_4_0\"\n                                   aria-label=\"back\" data-reference-link=\"true\">^</a><span>JXL Supported Software</span>&nbsp;<a\n            href=\"https://jpegxl.info/resources/supported-software.html\" class=\"external\" target=\"_blank\"\n            rel=\"noopener noreferrer\">https://jpegxl.info/resources/supported-software.html</a></li>\n    <li id=\"ref_5\" tabindex=\"0\"><a class=\"ReferenceList-backLink\"\n                                   href=\"https://www.zhihu.com/question/563718496/answer/1900558338183393316#ref_5_0\"\n                                   aria-label=\"back\" data-reference-link=\"true\">^</a><span> JPEG XL decoding support (image/jxl) in blink (tracking bug)</span>&nbsp;<a\n            href=\"https://issues.chromium.org/issues/40168998\" class=\"external\" target=\"_blank\"\n            rel=\"noopener noreferrer\">https://issues.chromium.org/issues/40168998</a></li>\n    <li id=\"ref_6\" tabindex=\"0\"><a class=\"ReferenceList-backLink\"\n                                   href=\"https://www.zhihu.com/question/563718496/answer/1900558338183393316#ref_6_0\"\n                                   aria-label=\"back\" data-reference-link=\"true\">^</a><span>Request: Re-open JPEG XL issue</span>&nbsp;<a\n            href=\"https://issues.chromium.org/issues/40270698\" class=\"external\" target=\"_blank\"\n            rel=\"noopener noreferrer\">https://issues.chromium.org/issues/40270698</a></li>\n    <li id=\"ref_7\" tabindex=\"0\"><a class=\"ReferenceList-backLink\"\n                                   href=\"https://www.zhihu.com/question/563718496/answer/1900558338183393316#ref_7_0\"\n                                   aria-label=\"back\" data-reference-link=\"true\">^</a><span>APNG (CANIUSE)</span>&nbsp;<a\n            href=\"https://caniuse.com/apng\" class=\"external\" target=\"_blank\" rel=\"noopener noreferrer\">https://caniuse.com/apng</a>\n    </li>\n    <li id=\"ref_8\" tabindex=\"0\"><a class=\"ReferenceList-backLink\"\n                                   href=\"https://www.zhihu.com/question/563718496/answer/1900558338183393316#ref_8_0\"\n                                   aria-label=\"back\" data-reference-link=\"true\">^</a><span>Skia: Use libjpeg-turbo for YUV-&gt;RGB conversion in jpeg encoder</span>&nbsp;<a\n            href=\"https://github.com/google/skia/commit/c7d01d3e1d3621907c27b283fb7f8b6e177c629d\" class=\"external\"\n            target=\"_blank\" rel=\"noopener noreferrer\">https://github.com/google/skia/commit/c7d01d3e1d3621907c27b283fb7f8b6e177c629d</a>\n    </li>\n</ol>", "1. [^](https://www.zhihu.com/question/563718496/answer/1900558338183393316#ref_1_0)WebP2 Diff 1251ca748c17278961c0d0059b744595b35a4943 [https://chromium.googlesource.com/codecs/libwebp2/+/1251ca748c17278961c0d0059b744595b35a4943%5E%21/](https://chromium.googlesource.com/codecs/libwebp2/+/1251ca748c17278961c0d0059b744595b35a4943%5E%21/)\n2. [^](https://www.zhihu.com/question/563718496/answer/1900558338183393316#ref_2_0)AVIF Supported Software (Wikipedia) [https://en.wikipedia.org/wiki/AVIF#Support](https://en.wikipedia.org/wiki/AVIF#Support)\n3. [^](https://www.zhihu.com/question/563718496/answer/1900558338183393316#ref_3_0)HEIF Supported Software (Wikipedia) [https://en.wikipedia.org/wiki/High\\_Efficiency\\_Image\\_File\\_Format#Support](https://en.wikipedia.org/wiki/High_Efficiency_Image_File_Format#Support)\n4. [^](https://www.zhihu.com/question/563718496/answer/1900558338183393316#ref_4_0)JXL Supported Software [https://jpegxl.info/resources/supported-software.html](https://jpegxl.info/resources/supported-software.html)\n5. [^](https://www.zhihu.com/question/563718496/answer/1900558338183393316#ref_5_0) JPEG XL decoding support (image/jxl) in blink (tracking bug) [https://issues.chromium.org/issues/40168998](https://issues.chromium.org/issues/40168998)\n6. [^](https://www.zhihu.com/question/563718496/answer/1900558338183393316#ref_6_0)Request: Re-open JPEG XL issue [https://issues.chromium.org/issues/40270698](https://issues.chromium.org/issues/40270698)\n7. [^](https://www.zhihu.com/question/563718496/answer/1900558338183393316#ref_7_0)APNG (CANIUSE) [https://caniuse.com/apng](https://caniuse.com/apng)\n8. [^](https://www.zhihu.com/question/563718496/answer/1900558338183393316#ref_8_0)Skia: Use libjpeg-turbo for YUV->RGB conversion in jpeg encoder [https://github.com/google/skia/commit/c7d01d3e1d3621907c27b283fb7f8b6e177c629d](https://github.com/google/skia/commit/c7d01d3e1d3621907c27b283fb7f8b6e177c629d)\n"},
	{"226", "<table style=\"width: 656px; border-color: #000000; margin-left: auto; margin-right: auto;\">\n<tbody>\n<tr>\n<td style=\"width: 76px;\">\n<p><strong>Burn Degree</strong></p>\n</td>\n<td style=\"width: 215px;\">\n<p><strong>How to Recognize</strong></p>\n</td>\n<td style=\"width: 363px;\">\n<p><strong>How to Treat</strong></p>\n</td>\n</tr>\n<tr>\n<td style=\"width: 76px;\">\n<p><span style=\"font-weight: 400;\">First Degree</span></p>\n</td>\n<td style=\"width: 215px;\">\n<ul>\n<li style=\"font-weight: 400;\"><span style=\"font-weight: 400;\">Redness of the skin</span></li>\n<li style=\"font-weight: 400;\"><span style=\"font-weight: 400;\">Itchiness</span></li>\n<li style=\"font-weight: 400;\"><span style=\"font-weight: 400;\">Potentially some minor swelling</span></li>\n<li style=\"font-weight: 400;\"><span style=\"font-weight: 400;\">Not a major problem in most cases</span></li>\n</ul>\n</td>\n<td style=\"width: 363px;\">\n<ul>\n<li style=\"font-weight: 400;\"><span style=\"font-weight: 400;\">Run cool (NOT COLD) water over the affected area for five minutes</span></li>\n<li style=\"font-weight: 400;\"><span style=\"font-weight: 400;\">Apply aloe vera as needed</span></li>\n</ul>\n</td>\n</tr>\n<tr>\n<td style=\"width: 76px;\">\n<p><span style=\"font-weight: 400;\">Second Degree</span></p>\n</td>\n<td style=\"width: 215px;\">\n<ul>\n<li style=\"font-weight: 400;\"><span style=\"font-weight: 400;\">Painful blisters</span></li>\n</ul>\n</td>\n<td style=\"width: 363px;\">\n<ul>\n<li style=\"font-weight: 400;\"><span style=\"font-weight: 400;\">Run cool water over the affected area for fifteen minutes</span></li>\n<li style=\"font-weight: 400;\"><span style=\"font-weight: 400;\">Keep blisters clean, especially if they pop.</span></li>\n</ul>\n</td>\n</tr>\n<tr>\n<td style=\"width: 76px;\">\n<p><span style=\"font-weight: 400;\">Third Degree</span></p>\n</td>\n<td style=\"width: 215px;\">\n<ul>\n<li style=\"font-weight: 400;\"><span style=\"font-weight: 400;\">Minimal pain. Nerve damage has been done</span></li>\n<li style=\"font-weight: 400;\"><span style=\"font-weight: 400;\">Waxy white pigment to the skin</span></li>\n<li style=\"font-weight: 400;\"><span style=\"font-weight: 400;\">A dark brown or charred appearance</span></li>\n</ul>\n</td>\n<td style=\"width: 363px;\">\n<ul>\n<li style=\"font-weight: 400;\"><span style=\"font-weight: 400;\">Seek medical assistance IMMEDIATELY. Do NOT attempt to heal on your own.</span></li>\n</ul>\n</td>\n</tr>\n</tbody>\n</table>", "| **Burn Degree** | **How to Recognize**                                                                                                    | **How to Treat**                                                                                            |\n| ----------------------- | ------------------------------------------------------------------------------------------------------------------------------- | ------------------------------------------------------------------------------------------------------------------- |\n| First Degree          | \\* Redness of the skin<br />\\* Itchiness<br />\\* Potentially some minor swelling<br />\\* Not a major problem in most cases    | \\* Run cool (NOT COLD) water over the affected area for five minutes<br />\\* Apply aloe vera as needed            |\n| Second Degree         | \\* Painful blisters                                                                                                           | \\* Run cool water over the affected area for fifteen minutes<br />\\* Keep blisters clean, especially if they pop. |\n| Third Degree          | \\* Minimal pain. Nerve damage has been done<br />\\* Waxy white pigment to the skin<br />\\* A dark brown or charred appearance | \\* Seek medical assistance IMMEDIATELY. Do NOT attempt to heal on your own.                                       |\n"},
	{"225", "<span>其中，<span>&nbsp;</span></span><span class=\"ztext-math\" data-eeimg=\"1\" data-tex=\"\\[{g_{me}} = {g_m} + {g_{mb}}\\]\"><span></span><span><span class=\"MathJax_Preview\"></span><span class=\"MathJax_SVG\" id=\"MathJax-Element-6-Frame\" tabindex=\"0\" data-mathml=\"<math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;><mrow class=&quot;MJX-TeXAtom-ORD&quot;><msub><mi>g</mi><mrow class=&quot;MJX-TeXAtom-ORD&quot;><mi>m</mi><mi>e</mi></mrow></msub></mrow><mo>=</mo><mrow class=&quot;MJX-TeXAtom-ORD&quot;><msub><mi>g</mi><mi>m</mi></msub></mrow><mo>+</mo><mrow class=&quot;MJX-TeXAtom-ORD&quot;><msub><mi>g</mi><mrow class=&quot;MJX-TeXAtom-ORD&quot;><mi>m</mi><mi>b</mi></mrow></msub></mrow></math>\" role=\"presentation\"><svg xmlns:xlink=\"http://www.w3.org/1999/xlink\" width=\"15.763ex\" height=\"2.21ex\" viewBox=\"0 -650.3 6786.6 951.6\" role=\"img\" focusable=\"false\" aria-hidden=\"true\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><use xlink:href=\"#MJMATHI-67\" x=\"0\" y=\"0\"></use><g transform=\"translate(477,-150)\"><use transform=\"scale(0.707)\" xlink:href=\"#MJMATHI-6D\" x=\"0\" y=\"0\"></use><use transform=\"scale(0.707)\" xlink:href=\"#MJMATHI-65\" x=\"878\" y=\"0\"></use></g><use xlink:href=\"#MJMAIN-3D\" x=\"1806\" y=\"0\"></use><g transform=\"translate(2862,0)\"><use xlink:href=\"#MJMATHI-67\" x=\"0\" y=\"0\"></use><use transform=\"scale(0.707)\" xlink:href=\"#MJMATHI-6D\" x=\"675\" y=\"-213\"></use></g><use xlink:href=\"#MJMAIN-2B\" x=\"4283\" y=\"0\"></use><g transform=\"translate(5284,0)\"><use xlink:href=\"#MJMATHI-67\" x=\"0\" y=\"0\"></use><g transform=\"translate(477,-150)\"><use transform=\"scale(0.707)\" xlink:href=\"#MJMATHI-6D\" x=\"0\" y=\"0\"></use><use transform=\"scale(0.707)\" xlink:href=\"#MJMATHI-62\" x=\"878\" y=\"0\"></use></g></g></g></svg><span class=\"MJX_Assistive_MathML\" role=\"presentation\"><math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mrow class=\"MJX-TeXAtom-ORD\"><msub><mi>g</mi><mrow class=\"MJX-TeXAtom-ORD\"><mi>m</mi><mi>e</mi></mrow></msub></mrow><mo>=</mo><mrow class=\"MJX-TeXAtom-ORD\"><msub><mi>g</mi><mi>m</mi></msub></mrow><mo>+</mo><mrow class=\"MJX-TeXAtom-ORD\"><msub><mi>g</mi><mrow class=\"MJX-TeXAtom-ORD\"><mi>m</mi><mi>b</mi></mrow></msub></mrow></math></span></span></span></span><span><span>&nbsp;</span>，我们</span>", "其中， ${g_{me}} = {g_m} + {g_{mb}}$ ，我们\n"},
	{"224", "<figure style=\"border-width: 0px;border-style: solid;border-color: hsl(var(--border));margin: 1.5em 8px;color: rgb(63, 63, 63);\"><span leaf=\"\"><img data-src=\"https://mmbiz.qpic.cn/sz_mmbiz_jpg/icMUEqOiagpkg9R13r4OhF9gM0sJNF7e1wZsWL5mkog7SWX8CccxyrkjGXvZNM3IJLQ3aIwibqMjAsKibdDiaYbBlNA/640?wx_fmt=jpeg&amp;from=appmsg\" alt=\"节点整合\" class=\"rich_pages wxw-img\" data-ratio=\"0.562962962962963\" data-type=\"jpeg\" data-w=\"1080\" style=\"border-width: 0px; border-style: solid; border-color: hsl(var(--border)); display: block; vertical-align: middle; margin: 0.1em auto 0.5em; border-radius: 4px; height: auto !important; visibility: visible !important; width: 661px !important;\" title=\"null\" data-imgfileid=\"100012968\" data-original-style=\"border-width: 0px;border-style: solid;border-color: hsl(var(--border));display: block;vertical-align: middle;margin: 0.1em auto 0.5em;border-radius: 4px;height: auto !important;\" data-index=\"19\" src=\"https://mmbiz.qpic.cn/sz_mmbiz_jpg/icMUEqOiagpkg9R13r4OhF9gM0sJNF7e1wZsWL5mkog7SWX8CccxyrkjGXvZNM3IJLQ3aIwibqMjAsKibdDiaYbBlNA/640?wx_fmt=jpeg&amp;from=appmsg&amp;tp=webp&amp;wxfrom=5&amp;wx_lazy=1&amp;wx_co=1\" _width=\"677px\" crossorigin=\"anonymous\" data-report-img-idx=\"3\" data-fail=\"0\"></span><figcaption style=\"border-width: 0px;border-style: solid;border-color: hsl(var(--border));text-align: center;font-size: 0.8em;color: rgb(136, 136, 136);\"><span leaf=\"\">节点整合</span></figcaption></figure>", "![节点整合](https://mmbiz.qpic.cn/sz_mmbiz_jpg/icMUEqOiagpkg9R13r4OhF9gM0sJNF7e1wZsWL5mkog7SWX8CccxyrkjGXvZNM3IJLQ3aIwibqMjAsKibdDiaYbBlNA/640?wx_fmt=jpeg&from=appmsg&tp=webp&wxfrom=5&wx_lazy=1&wx_co=1 \"节点整合\")\n"},
	{"223", "<div class=\"language-math\" data-math=\"A = QR\"><span class=\"katex-display\"><span class=\"katex\"><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"strut\" style=\"height:0.6833em;\"></span><span class=\"mord mathnormal\">A</span><span class=\"mspace\" style=\"margin-right:0.2778em;\"></span><span class=\"mrel\">=</span><span class=\"mspace\" style=\"margin-right:0.2778em;\"></span></span><span class=\"base\"><span class=\"strut\" style=\"height:0.8778em;vertical-align:-0.1944em;\"></span><span class=\"mord mathnormal\" style=\"margin-right:0.00773em;\">QR</span></span></span></span></span></div>", "$$\nA = QR\n$$\n"},
	{"222", "<span><span>&nbsp;</span></span><span class=\"language-math\" data-math=\" m \\times n \"><span class=\"katex\"><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"strut\"></span><span class=\"mord mathnormal\">m</span><span class=\"mspace\"></span><span class=\"mbin\">×</span><span class=\"mspace\"></span></span><span class=\"base\"><span class=\"strut\"></span><span class=\"mord mathnormal\">n</span></span></span></span></span><span><span>&nbsp;</span></span>", "$m \\times n$\n"},
	{"221", "<a href=\"https://github.com/Siunami/Latticework\">Latticework <span class=\"badge badge-notification clicks\" title=\"2 次点击\">2</span></a>", "[Latticework 2](https://github.com/Siunami/Latticework)\n"},
	{"220", "<p><strong>foo </strong>bar</p>", "**foo \u200b**bar\n"},
	{"219", "<ul><li>Via a distributed file system such as a<span>&nbsp;</span><a href=\"https://en.wikipedia.org/wiki/Network-attached_storage\">NAS server</a>,<span>&nbsp;</span><a href=\"https://en.wikipedia.org/wiki/Network_File_System\">NFS</a>,<span>&nbsp;</span><a href=\"https://en.wikipedia.org/wiki/File_Transfer_Protocol\">FTP</a>, or<span>&nbsp;</span><a href=\"https://linux.die.net/man/1/rsync\">rsync</a>;</li></ul>", "* Via a distributed file system such as a [NAS server](https://en.wikipedia.org/wiki/Network-attached_storage), [NFS](https://en.wikipedia.org/wiki/Network_File_System), [FTP](https://en.wikipedia.org/wiki/File_Transfer_Protocol), or [rsync](https://linux.die.net/man/1/rsync);\n"},
	{"218", "<p>好的，我这里有一个比较复杂的数学公式：</p>\n<p>$$\\oint_C \\left( \\nabla \\times \\mathbf{F} \\right) \\cdot d\\mathbf{r} = \\iint_S \\left( \\nabla \\times \\mathbf{F} \\right) \\cdot \\mathbf{n} , dS = \\iint_S \\mathbf{curl}(\\mathbf{F}) \\cdot \\mathbf{n} , dS$$</p>\n<p>这是斯托克斯定理(Stokes' Theorem)的表达式，它表明闭合曲线C的线积分等于以该曲线为边界的曲面S上旋度的面积分。这在电磁学、流体动力学和矢量场理论中有广泛应用。</p>", "好的，我这里有一个比较复杂的数学公式：\n\n$$\n\\oint_C \\left( \\nabla \\times \\mathbf{F} \\right) \\cdot d\\mathbf{r} = \\iint_S \\left( \\nabla \\times \\mathbf{F} \\right) \\cdot \\mathbf{n} , dS = \\iint_S \\mathbf{curl}(\\mathbf{F}) \\cdot \\mathbf{n} , dS\n$$\n\n这是斯托克斯定理(Stokes' Theorem)的表达式，它表明闭合曲线 C 的线积分等于以该曲线为边界的曲面 S 上旋度的面积分。这在电磁学、流体动力学和矢量场理论中有广泛应用。\n"},
	{"217", "<ul style=\"padding-left: 1em;outline: 0px;line-height: 1.75;list-style: circle;color: rgb(63, 63, 63);visibility: visible;\" class=\"list-paddingleft-2\"><li style=\"margin: 0.2em 8px;outline: 0px;text-align: left;line-height: 1.75;text-indent: -1em;display: block;visibility: visible;\"><p style=\"outline: 0px;visibility: visible;\"><span leaf=\"\" style=\"visibility: visible;\">• 集群信息</span></p></li><li style=\"margin: 0.2em 8px;outline: 0px;text-align: left;line-height: 1.75;text-indent: -1em;display: block;visibility: visible;\"><p style=\"outline: 0px;visibility: visible;\"><span leaf=\"\" style=\"visibility: visible;\">• Pod 诊断</span></p></li><li style=\"margin: 0.2em 8px;outline: 0px;text-align: left;line-height: 1.75;text-indent: -1em;display: block;visibility: visible;\"><p style=\"outline: 0px;visibility: visible;\"><span leaf=\"\" style=\"visibility: visible;\">• 服务诊断</span></p></li><li style=\"margin: 0.2em 8px;outline: 0px;text-align: left;line-height: 1.75;text-indent: -1em;display: block;visibility: visible;\"><p style=\"outline: 0px;visibility: visible;\"><span leaf=\"\" style=\"visibility: visible;\">• 部署诊断</span></p></li><li style=\"margin: 0.2em 8px; outline: 0px; text-align: left; line-height: 1.75; text-indent: -1em; display: block; visibility: visible;\"><p style=\"outline: 0px; visibility: visible;\"><span leaf=\"\" style=\"visibility: visible;\">• 网络诊断</span></p></li><li style=\"margin: 0.2em 8px; outline: 0px; text-align: left; line-height: 1.75; text-indent: -1em; display: block; visibility: visible;\"><p style=\"outline: 0px; visibility: visible;\"><span leaf=\"\" style=\"visibility: visible;\">• 持久卷和持久卷声明诊断</span></p></li><li style=\"margin: 0.2em 8px;outline: 0px;text-align: left;line-height: 1.75;text-indent: -1em;display: block;\"><p style=\"outline: 0px;\"><span leaf=\"\">• 资源使用情况</span></p></li><li style=\"margin: 0.2em 8px;outline: 0px;text-align: left;line-height: 1.75;text-indent: -1em;display: block;\"><p style=\"outline: 0px;\"><span leaf=\"\">• 安全和授权</span></p></li><li style=\"margin: 0.2em 8px;outline: 0px;text-align: left;line-height: 1.75;text-indent: -1em;display: block;\"><p style=\"outline: 0px;\"><span leaf=\"\">• 节点故障排除</span></p></li><li style=\"margin: 0.2em 8px;outline: 0px;text-align: left;line-height: 1.75;text-indent: -1em;display: block;\"><p style=\"outline: 0px;\"><span leaf=\"\">• 其他诊断命令：文章还提到了许多其他命令，如资源扩展和自动扩展、作业和定时作业诊断、Pod 亲和性和反亲和性规则、RBAC 和安全、服务账号诊断、节点排空和取消排空、资源清理等。</span></p></li></ul>", "* 集群信息\n* Pod 诊断\n* 服务诊断\n* 部署诊断\n* 网络诊断\n* 持久卷和持久卷声明诊断\n* 资源使用情况\n* 安全和授权\n* 节点故障排除\n* 其他诊断命令：文章还提到了许多其他命令，如资源扩展和自动扩展、作业和定时作业诊断、Pod 亲和性和反亲和性规则、RBAC 和安全、服务账号诊断、节点排空和取消排空、资源清理等。\n"},
	{"216", "<ol style=\"/* padding-left: 1em; */: ;/* white-space: normal; *//* background-color: rgb(255, 255, 255); *//* font-size: 14;/* letter-spacing: normal; */ormal;/* text-align: left; *//* line-height: 1.75; *//* font-family: -apple-system-font, BlinkMacSystemFont, 'Helvetica Neue', 'PingFang SC', 'Hiragino Sans GB', 'Microsoft YaHei UI', 'Microsoft YaHei', Arial, sans-serif; *//* color: rgb(63, 63, 63); */\" class=\"list-paddingleft-1\"><li style=\"margin: 0.2em 8px;outline: 0px;text-align: left;line-height: 1.75;/* text-indent: -1em; *//* display: block; */\"><p style=\"outline: 0px;\"><span leaf=\"\">1. 显示 Kubernetes 版本：</span><code style=\"padding: 3px 5px;outline: 0px;white-space: pre-wrap;line-height: 1.75;font-size: 12.6px;color: rgb(221, 17, 68);background: rgba(27, 31, 35, 0.05);border-radius: 4px;\"><span leaf=\"\">kubectl version</span></code></p></li><li style=\"margin: 0.2em 8px;outline: 0px;text-align: left;line-height: 1.75;text-indent: -1em;display: block;\"><p style=\"outline: 0px;\"><span leaf=\"\">2. 显示集群信息：</span><code style=\"padding: 3px 5px;outline: 0px;white-space: pre-wrap;line-height: 1.75;font-size: 12.6px;color: rgb(221, 17, 68);background: rgba(27, 31, 35, 0.05);border-radius: 4px;\"><span leaf=\"\">kubectl cluster-info</span></code></p></li><li style=\"margin: 0.2em 8px;outline: 0px;text-align: left;line-height: 1.75;text-indent: -1em;display: block;\"><p style=\"outline: 0px;\"><span leaf=\"\">3. 列出集群中的所有节点：</span><code style=\"padding: 3px 5px;outline: 0px;white-space: pre-wrap;line-height: 1.75;font-size: 12.6px;color: rgb(221, 17, 68);background: rgba(27, 31, 35, 0.05);border-radius: 4px;\"><span leaf=\"\">kubectl get nodes</span></code></p></li><li style=\"margin: 0.2em 8px;outline: 0px;text-align: left;line-height: 1.75;text-indent: -1em;display: block;\"><p style=\"outline: 0px;\"><span leaf=\"\">4. 查看一个具体的节点详情：</span><code style=\"padding: 3px 5px;outline: 0px;white-space: pre-wrap;line-height: 1.75;font-size: 12.6px;color: rgb(221, 17, 68);background: rgba(27, 31, 35, 0.05);border-radius: 4px;\"><span leaf=\"\">kubectl describe node &lt;node-name&gt;</span></code></p></li><li style=\"margin: 0.2em 8px;outline: 0px;text-align: left;line-height: 1.75;text-indent: -1em;display: block;\"><p style=\"outline: 0px;\"><span leaf=\"\">5. 列出所有命名空间：</span><code style=\"padding: 3px 5px;outline: 0px;white-space: pre-wrap;line-height: 1.75;font-size: 12.6px;color: rgb(221, 17, 68);background: rgba(27, 31, 35, 0.05);border-radius: 4px;\"><span leaf=\"\">kubectl get namespaces</span></code></p></li><li style=\"margin: 0.2em 8px;outline: 0px;text-align: left;line-height: 1.75;text-indent: -1em;display: block;\"><p style=\"outline: 0px;\"><span leaf=\"\">6. 列出所有命名空间中的所有 pod：</span><code style=\"padding: 3px 5px;outline: 0px;white-space: pre-wrap;line-height: 1.75;font-size: 12.6px;color: rgb(221, 17, 68);background: rgba(27, 31, 35, 0.05);border-radius: 4px;\"><span leaf=\"\">kubectl get pods --all-namespaces</span></code></p></li></ol>", "1. 显示 Kubernetes 版本：`kubectl version`\n2. 显示集群信息：`kubectl cluster-info`\n3. 列出集群中的所有节点：`kubectl get nodes`\n4. 查看一个具体的节点详情：`kubectl describe node <node-name>`\n5. 列出所有命名空间：`kubectl get namespaces`\n6. 列出所有命名空间中的所有 pod：`kubectl get pods --all-namespaces`\n"},
	{"215", "<pre class=\"prism-code language-bash border bg-muted overflow-x-auto p-6 text-sm rounded-xl scrollbar-thin scrollbar-track-transparent scrollbar-thumb-primary/10 hover:scrollbar-thumb-primary/20 glass-effect\" style=\"background-color:hsl(220, 13%, 18%);color:hsl(220, 14%, 71%);text-shadow:0 1px rgba(0, 0, 0, 0.3)\"><div class=\"token-line\" style=\"color:hsl(220, 14%, 71%);text-shadow:0 1px rgba(0, 0, 0, 0.3)\"><span class=\"token plain\"># Using Homebrew</span></div><div class=\"token-line\" style=\"color:hsl(220, 14%, 71%);text-shadow:0 1px rgba(0, 0, 0, 0.3)\"><span class=\"token plain\">brew install uv git sqlite3</span></div><div class=\"token-line\" style=\"color:hsl(220, 14%, 71%);text-shadow:0 1px rgba(0, 0, 0, 0.3)\"><span class=\"token plain\" style=\"display:inline-block\">\n</span></div><div class=\"token-line\" style=\"color:hsl(220, 14%, 71%);text-shadow:0 1px rgba(0, 0, 0, 0.3)\"><span class=\"token plain\"># 或者直接下载：</span></div><div class=\"token-line\" style=\"color:hsl(220, 14%, 71%);text-shadow:0 1px rgba(0, 0, 0, 0.3)\"><span class=\"token plain\"># uv: https://docs.astral.sh/uv/</span></div><div class=\"token-line\" style=\"color:hsl(220, 14%, 71%);text-shadow:0 1px rgba(0, 0, 0, 0.3)\"><span class=\"token plain\"># Git: https://git-scm.com</span></div><div class=\"token-line\" style=\"color:hsl(220, 14%, 71%);text-shadow:0 1px rgba(0, 0, 0, 0.3)\"><span class=\"token plain\"># SQLite: https://www.sqlite.org/download.html</span></div></pre>", "```bash\n# Using Homebrew\nbrew install uv git sqlite3\n\n\n# 或者直接下载：\n# uv: https://docs.astral.sh/uv/\n# Git: https://git-scm.com\n# SQLite: https://www.sqlite.org/download.html\n```\n"},
	{"214", "<p>foo<span class=\"zhushi\">content1<span class=\"tip\">content1 memo</span></span>    <span class=\"zhushi\" title=\"content2 memo\">content2</span>bar</p>", "foo<span data-type=\"inline-memo\" data-inline-memo-content=\"content1 memo\">content1</span><span data-type=\"inline-memo\" data-inline-memo-content=\"content2 memo\">content2</span>bar\n"},
	{"213", "<div id=\"readability-page-1\" class=\"page\">\n    <div class=\"Post-RichTextContainer\">\n        <div class=\"css-1od93p9\">\n            <div class=\"css-376mun\">\n                <div class=\"RichText ztext Post-RichText css-ob6uua\" options=\"[object Object]\"><p data-pid=\"rfr-9chG\">\n                    foo</p>\n                    <p data-pid=\"JHk7pnaF\"><span class=\"ztext-math\" data-eeimg=\"1\"\n                                                 data-tex=\"\\mathbf{C}_{i,j,k}=\\mathbf{R}^{n}\\cdot\\mathbf{I}^{-1}\\cdot\\mathbf{\\hat{P}}_{i, j,k}+\\mathbf{T}^{n}, \\tag{1}\"><span></span><span><span\n                            class=\"MathJax_Preview\"></span><span class=\"MathJax_SVG_Display\"><span class=\"MathJax_SVG\"\n                                                                                                   id=\"MathJax-Element-12-Frame\"\n                                                                                                   tabindex=\"0\"\n                                                                                                   data-mathml=\"<math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot; display=&quot;block&quot;><mtable displaystyle=&quot;true&quot;><mlabeledtr><mtd><mtext>(1)</mtext></mtd><mtd><msub><mrow class=&quot;MJX-TeXAtom-ORD&quot;><mi mathvariant=&quot;bold&quot;>C</mi></mrow><mrow class=&quot;MJX-TeXAtom-ORD&quot;><mi>i</mi><mo>,</mo><mi>j</mi><mo>,</mo><mi>k</mi></mrow></msub><mo>=</mo><msup><mrow class=&quot;MJX-TeXAtom-ORD&quot;><mi mathvariant=&quot;bold&quot;>R</mi></mrow><mrow class=&quot;MJX-TeXAtom-ORD&quot;><mi>n</mi></mrow></msup><mo>&amp;#x22C5;</mo><msup><mrow class=&quot;MJX-TeXAtom-ORD&quot;><mi mathvariant=&quot;bold&quot;>I</mi></mrow><mrow class=&quot;MJX-TeXAtom-ORD&quot;><mo>&amp;#x2212;</mo><mn>1</mn></mrow></msup><mo>&amp;#x22C5;</mo><msub><mrow class=&quot;MJX-TeXAtom-ORD&quot;><mrow class=&quot;MJX-TeXAtom-ORD&quot;><mover><mi mathvariant=&quot;bold&quot;>P</mi><mo mathvariant=&quot;bold&quot; stretchy=&quot;false&quot;>&amp;#x005E;</mo></mover></mrow></mrow><mrow class=&quot;MJX-TeXAtom-ORD&quot;><mi>i</mi><mo>,</mo><mi>j</mi><mo>,</mo><mi>k</mi></mrow></msub><mo>+</mo><msup><mrow class=&quot;MJX-TeXAtom-ORD&quot;><mi mathvariant=&quot;bold&quot;>T</mi></mrow><mrow class=&quot;MJX-TeXAtom-ORD&quot;><mi>n</mi></mrow></msup><mo>,</mo></mtd></mlabeledtr></mtable></math>\"\n                                                                                                   role=\"presentation\"><span\n                            class=\"MJX_Assistive_MathML MJX_Assistive_MathML_Block\" role=\"presentation\"><math\n                            xmlns=\"http://www.w3.org/1998/Math/MathML\" display=\"block\"><mtable displaystyle=\"true\"><mlabeledtr><mtd><mtext>(1)</mtext></mtd><mtd><msub><mrow\n                            class=\"MJX-TeXAtom-ORD\"><mi mathvariant=\"bold\">C</mi></mrow><mrow class=\"MJX-TeXAtom-ORD\"><mi>i</mi><mo>,</mo><mi>j</mi><mo>,</mo><mi>k</mi></mrow></msub><mo>=</mo><msup><mrow\n                            class=\"MJX-TeXAtom-ORD\"><mi mathvariant=\"bold\">R</mi></mrow><mrow class=\"MJX-TeXAtom-ORD\"><mi>n</mi></mrow></msup><mo>⋅</mo><msup><mrow\n                            class=\"MJX-TeXAtom-ORD\"><mi mathvariant=\"bold\">I</mi></mrow><mrow class=\"MJX-TeXAtom-ORD\"><mo>−</mo><mn>1</mn></mrow></msup><mo>⋅</mo><msub><mrow\n                            class=\"MJX-TeXAtom-ORD\"><mrow class=\"MJX-TeXAtom-ORD\"><mover><mi mathvariant=\"bold\">P</mi><mo\n                            mathvariant=\"bold\" stretchy=\"false\">^</mo></mover></mrow></mrow><mrow\n                            class=\"MJX-TeXAtom-ORD\"><mi>i</mi><mo>,</mo><mi>j</mi><mo>,</mo><mi>k</mi></mrow></msub><mo>+</mo><msup><mrow\n                            class=\"MJX-TeXAtom-ORD\"><mi mathvariant=\"bold\">T</mi></mrow><mrow class=\"MJX-TeXAtom-ORD\"><mi>n</mi></mrow></msup><mo>,</mo></mtd></mlabeledtr></mtable></math></span></span></span><script\n                            type=\"math/tex;mode=display\" id=\"MathJax-Element-12\">\\mathbf{C}_{i,j,k}=\\mathbf{R}^{n}\\cdot\\mathbf{I}^{-1}\\cdot\\mathbf{\\hat{P}}_{i, j,k}+\\mathbf{T}^{n}, \\tag{1}</script><span\n                            class=\"tex2jax_ignore math-holder\">\\mathbf{C}_{i,j,k}=\\mathbf{R}^{n}\\cdot\\mathbf{I}^{-1}\\cdot\\mathbf{\\hat{P}}_{i, j,k}+\\mathbf{T}^{n}, \\tag{1}</span></span></span>\n                    </p>\n                    <p data-pid=\"4lABtjNu\">bar</p></div>\n            </div>\n        </div>\n    </div>\n    <div role=\"button\" tabindex=\"0\" class=\"ContentItem-time\"><p>编辑于 2024-01-10 10:41</p><!-- --><p>・IP 属地上海</p>\n    </div>\n    <div class=\"PostIndex-Contributions\"><h3 class=\"BlockTitle\">内容所属专栏</h3>\n        <ul class=\"css-zein01\">\n            <div>\n                <div class=\"ContentItem Column-ColumnItem\">\n                    <div class=\"ContentItem-main\">\n                        <div class=\"ContentItem-image\"><a class=\"ColumnLink\"\n                                                          href=\"https://www.zhihu.com/column/c_1722981294831661056\"><p>\n                            <img class=\"Avatar css-1u7r5c9\"\n                                 src=\"https://pic1.zhimg.com/v2-f111d7ee1c41944859e975a712c0883b_l.jpg?source=172ae18b\"\n                                 srcset=\"https://pic1.zhimg.com/v2-f111d7ee1c41944859e975a712c0883b_l.jpg?source=172ae18b 2x\"\n                                 alt=\"自动驾驶与多模态大模型\"></p></a></div>\n                        <div class=\"ContentItem-head\">\n                            <h2 class=\"ContentItem-title\"><span><a class=\"ColumnLink ColumnItem-Title\"\n                                                                   href=\"https://www.zhihu.com/column/c_1722981294831661056\"><p>自动驾驶与多模态大模型</p></a></span>\n                            </h2>\n                            <p>介绍自动驾驶与多模态大模型结合的文章</p></div>\n                    </div>\n                </div>\n            </div>\n        </ul>\n    </div>\n    <div class=\"Post-topicsAndReviewer\">\n        <div class=\"TopicList Post-Topics\">\n            <div class=\"Tag Topic css-ch8ocw\" data-za-detail-view-path-module=\"TopicItem\"\n                 data-za-extra-module=\"{&quot;card&quot;:{&quot;content&quot;:{&quot;type&quot;:&quot;Topic&quot;,&quot;token&quot;:&quot;25824334&quot;}}}\">\n                <p><span class=\"Tag-content\"><a class=\"TopicLink\" href=\"https://www.zhihu.com/topic/25824334\"\n                                                target=\"_blank\"></a></span></p>\n                <p><a class=\"TopicLink\" href=\"https://www.zhihu.com/topic/25824334\" target=\"_blank\">自动驾驶技术</a></p>\n                <p></p></div>\n            <div class=\"Tag Topic css-ch8ocw\" data-za-detail-view-path-module=\"TopicItem\"\n                 data-za-extra-module=\"{&quot;card&quot;:{&quot;content&quot;:{&quot;type&quot;:&quot;Topic&quot;,&quot;token&quot;:&quot;26637029&quot;}}}\">\n                <p><span class=\"Tag-content\"><a class=\"TopicLink\" href=\"https://www.zhihu.com/topic/26637029\"\n                                                target=\"_blank\"></a></span></p>\n                <p><a class=\"TopicLink\" href=\"https://www.zhihu.com/topic/26637029\" target=\"_blank\">BEV感知</a></p>\n                <p></p></div>\n        </div>\n    </div>\n</div>", "foo\n\n$$\n\\mathbf{C}_{i,j,k}=\\mathbf{R}^{n}\\cdot\\mathbf{I}^{-1}\\cdot\\mathbf{\\hat{P}}_{i, j,k}+\\mathbf{T}^{n}, \\tag{1}\n$$\n\n\nbar\n\n\n\n\n\n编辑于 2024-01-10 10:41\n\n・IP 属地上海\n\n\n### 内容所属专栏\n\n[![自动驾驶与多模态大模型](https://pic1.zhimg.com/v2-f111d7ee1c41944859e975a712c0883b_l.jpg?source=172ae18b)](https://www.zhihu.com/column/c_1722981294831661056)\n\n## [自动驾驶与多模态大模型](https://www.zhihu.com/column/c_1722981294831661056)\n\n介绍自动驾驶与多模态大模型结合的文章\n\n\n[自动驾驶技术](https://www.zhihu.com/topic/25824334)\n\n\n[BEV 感知](https://www.zhihu.com/topic/26637029)\n"},
	{"212", "<p>foo <img draggable=\"false\" class=\"emoji\" alt=\"❓\" src=\"https://twemoji.maxcdn.com/v/14.0.2/72x72/2753.png\"> bar</p>", "foo ❓ bar\n"},
	{"211", "<pre><textarea></textarea><span class=\"copyTooltip\" style=\"display: inline;\"><img src=\"https://learnblockchain.cn/css/default/copy.svg\"></span><code class=\"language-go hljs\"><span class=\"hljs-keyword\">type</span> PurchaseOrder <span class=\"hljs-keyword\">struct</span> {  \n     Id      <span class=\"hljs-type\">uint</span>      <span class=\"hljs-string\">`json:\"id\" gorm:\"primaryKey\"`</span>  \n     UserId  <span class=\"hljs-type\">string</span>    <span class=\"hljs-string\">`json:\"userId\"`</span>  \n     Product []Product  <span class=\"hljs-string\">`json:\"product\" gorm:\"foreignKey:Id\"`</span>  \n     Date    time.Time <span class=\"hljs-string\">`json:\"date\"`</span>  \n}\n</code></pre>", "```go\ntype PurchaseOrder struct {  \n     Id      uint      `json:\"id\" gorm:\"primaryKey\"`  \n     UserId  string    `json:\"userId\"`  \n     Product []Product  `json:\"product\" gorm:\"foreignKey:Id\"`  \n     Date    time.Time `json:\"date\"`  \n}\n```\n"},
	{"210", "<pre><textarea></textarea><code class=\"language-go hljs\">this is code</code></pre>", "```go\nthis is code\n```\n"},
	{"209", "<figure> <img alt=\"c03f001.eps\" class=\"center\" src=\"https://www.w3schools.com/tags/pic_trulli.jpg\"> <figcaption><p><a id=\"figure3-1\" href=\"#figureanchor3-1\"><b>Figure 3-1:</b></a> If you try to design an automobile that pleases every possible driver, you end up with a car with every possible feature that pleases nobody. Software today is too often designed to please too many users, resulting in low user satisfaction. <a id=\"figureanchor3-2\" href=\"#figure3-2\">Figure 3-2</a> provides an alternative approach.</p></figcaption> </figure>", "![c03f001.eps](https://www.w3schools.com/tags/pic_trulli.jpg \"Figure 3-1: If you try to design an automobile that pleases every possible driver, you end up with a car with every possible feature that pleases nobody. Software today is too often designed to please too many users, resulting in low user satisfaction. Figure 3-2 provides an alternative approach.\")\n"},
	{"208", "foo<h1>bar</h1>", "foo\n# bar\n"},
	{"207", "foo<ul><li>bar<ul><li>baz</li></ul></li></ul>", "foo\n* bar\n  * baz\n"},
	{"206", "<p class=\"el-h4\"><h4 data-heading=\"foo\" dir=\"auto\" class=\"publish-article-heading\"><span class=\"heading-collapse-indicator collapse-indicator collapse-icon\"><svg xmlns=\"http://www.w3.org/2000/svg\" width=\"24\" height=\"24\" viewBox=\"0 0 24 24\" fill=\"none\" stroke=\"currentColor\" stroke-width=\"2\" stroke-linecap=\"round\" stroke-linejoin=\"round\" class=\"svg-icon right-triangle\"><path d=\"M3 8L12 17L21 8\"></path></svg></span><br data-added-by-siyuan=\"true\">foo <span class=\"clickable-icon\" aria-label=\"Copy link\"><svg xmlns=\"http://www.w3.org/2000/svg\" width=\"24\" height=\"24\" viewBox=\"0 0 24 24\" fill=\"none\" stroke=\"currentColor\" stroke-width=\"2\" stroke-linecap=\"round\" stroke-linejoin=\"round\" class=\"svg-icon lucide-link\"><path d=\"M10 13a5 5 0 0 0 7.54.54l3-3a5 5 0 0 0-7.07-7.07l-1.72 1.71\"></path><path d=\"M14 11a5 5 0 0 0-7.54-.54l-3 3a5 5 0 0 0 7.07 7.07l1.71-1.71\"></path></svg></span><br data-added-by-siyuan=\"true\"></h4></p>", "#### foo\n"},
	{"205", "<div style=\"margin-top: 20px; text-indent: 0px; color: black;\">如果换到<img class=\"ma-tex-img\" alt=\"\\rho-\\theta\" src=\"\" style=\"max-width: 100%; margin: 0px 2px; vertical-align: middle; display: inline-block;\">坐标系下：</div>", "如果换到 $\\rho-\\theta$ 坐标系下：\n"},
	{"204", "<p>在物理学中，牛顿的第二定律可以用如下公式表示：</p><span class=\"katex-display\"><span class=\"katex\"><span class=\"katex-mathml\"><math xmlns=\"http://www.w3.org/1998/Math/MathML\" display=\"block\"><semantics><mrow><mi>F</mi><mo>=</mo><mi>m</mi><mi>a</mi></mrow><annotation encoding=\"application/x-tex\">F = ma</annotation></semantics></math></span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6833em;\"></span><span class=\"mord mathnormal\" style=\"margin-right: 0.13889em;\">F</span><span class=\"mspace\" style=\"margin-right: 0.2778em;\"></span><span class=\"mrel\">=</span><span class=\"mspace\" style=\"margin-right: 0.2778em;\"></span></span><span class=\"base\"><span class=\"strut\" style=\"height: 0.4306em;\"></span><span class=\"mord mathnormal\">ma</span></span></span></span></span><p>其中 <span class=\"katex\"><span class=\"katex-mathml\"><math xmlns=\"http://www.w3.org/1998/Math/MathML\"><semantics><mrow><mi>F</mi></mrow><annotation encoding=\"application/x-tex\">F</annotation></semantics></math></span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6833em;\"></span><span class=\"mord mathnormal\" style=\"margin-right: 0.13889em;\">F</span></span></span></span> 表示力，<span class=\"katex\"><span class=\"katex-mathml\"><math xmlns=\"http://www.w3.org/1998/Math/MathML\"><semantics><mrow><mi>m</mi></mrow><annotation encoding=\"application/x-tex\">m</annotation></semantics></math></span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.4306em;\"></span><span class=\"mord mathnormal\">m</span></span></span></span> 是物体的质量，<span class=\"katex\"><span class=\"katex-mathml\"><math xmlns=\"http://www.w3.org/1998/Math/MathML\"><semantics><mrow><mi>a</mi></mrow><annotation encoding=\"application/x-tex\">a</annotation></semantics></math></span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.4306em;\"></span><span class=\"mord mathnormal\">a</span></span></span></span> 是物体的加速度。这个公式描述了物体所受外力与其加速度之间的关系。</p>", "在物理学中，牛顿的第二定律可以用如下公式表示：\n\n$$\nF = ma\n$$\n\n其中 $F$ 表示力，$m$ 是物体的质量，$a$ 是物体的加速度。这个公式描述了物体所受外力与其加速度之间的关系。\n"},
	{"203", "<div class=\"highlight\"><div class=\"chroma open\"><div class=\"code-header language-fallback\"><span class=\"code-title\"><i class=\"arrow fas fa-chevron-right fa-fw\" aria-hidden=\"true\"></i></span><span class=\"ellipses\"><i class=\"fas fa-ellipsis-h fa-fw\" aria-hidden=\"true\"></i></span><span class=\"copy\" data-clipboard-text=\"2020-08-29 支出 100 CNY ; 购买日用品\n\" title=\"Copy to clipboard\"><i class=\"far fa-copy fa-fw\" aria-hidden=\"true\"></i></span></div><div class=\"table-wrapper\"><table class=\"lntable\"><tbody><tr><td class=\"lntd\"><pre tabindex=\"0\" class=\"chroma\"><code><span class=\"lnt\">1\n</span></code></pre></td><td class=\"lntd\"><pre tabindex=\"0\" class=\"chroma\"><code class=\"language-fallback\" data-lang=\"fallback\"><span class=\"line\"><span class=\"cl\">2020-08-29 支出 100 CNY ; 购买日用品\n</span></span></code></pre></td></tr></tbody></table></div></div></div>", "```\n2020-08-29 支出 100 CNY ; 购买日用品\n```\n"},
	{"202", "<p>foo<u>bar</u><b><u>baz</u></b>bazz</p>", "foo<u>bar</u>**<u>baz</u>**bazz\n"},
	{"201", "<figure data-size=\"normal\"><div><div class=\"GifPlayer css-1isopsn\" data-size=\"normal\" data-za-detail-view-path-module=\"GifItem\"><img class=\"ztext-gif\" width=\"480\" role=\"presentation\" src=\"https://pica.zhimg.com/v2-454df793026c3018d1f047d9bbf2aefe_b.jpg\" data-thumbnail=\"https://pica.zhimg.com/v2-454df793026c3018d1f047d9bbf2aefe_b.jpg\" data-size=\"normal\" alt=\"动图封面\" style=\"display: block;\"><div class=\"GifPlayer-icon css-d39tw7\"><svg width=\"50\" height=\"50\" viewBox=\"0 0 60 60\" xmlns=\"http://www.w3.org/2000/svg\"><g stroke=\"none\" stroke-width=\"1\" fill=\"none\" fill-rule=\"evenodd\"><ellipse fill=\"#000\" opacity=\"0.45\" cx=\"30\" cy=\"30\" rx=\"30\" ry=\"30\"></ellipse><ellipse stroke=\"#FFF\" stroke-width=\"2\" stroke-linecap=\"round\" stroke-linejoin=\"round\" opacity=\"0.5\" cx=\"30\" cy=\"30\" rx=\"26\" ry=\"26\"></ellipse></g><svg x=\"16\" y=\"18.5\"><g fill=\"#fff\"><path x=\"100\" y=\"100\" d=\"M12.8422852,12.9814453 L12.8422852,11.3994141 L7.63916016,11.3994141 L7.63916016,13.0517578 L10.9086914,13.0517578 L10.9086914,13.3242188 C10.8911133,15.2050781 9.46728516,16.4707031 7.39306641,16.4707031 C5.01123047,16.4707031 3.51708984,14.625 3.51708984,11.6367188 C3.51708984,8.70117188 5.00244141,6.84667969 7.34912109,6.84667969 C9.08056641,6.84667969 10.284668,7.68164062 10.7768555,9.2109375 L12.7543945,9.2109375 C12.3237305,6.64453125 10.2319336,5.00976562 7.34912109,5.00976562 C3.79833984,5.00976562 1.50439453,7.61132812 1.50439453,11.6542969 C1.50439453,15.75 3.77197266,18.3076172 7.36669922,18.3076172 C10.6889648,18.3076172 12.8422852,16.2246094 12.8422852,12.9814453 Z M17.5180664,18 L17.5180664,5.31738281 L15.5493164,5.31738281 L15.5493164,18 L17.5180664,18 Z M22.659668,18 L22.659668,12.7441406 L28.1088867,12.7441406 L28.1088867,11.0039062 L22.659668,11.0039062 L22.659668,7.11035156 L28.6098633,7.11035156 L28.6098633,5.31738281 L20.690918,5.31738281 L20.690918,18 L22.659668,18 Z\"></path></g></svg></svg></div></div></div></figure>", "![动图](https://pica.zhimg.com/v2-454df793026c3018d1f047d9bbf2aefe_b.webp){: style=\"width: 480px;\"}\n"},
	{"200", "<section><span><strong><span>foo</span></strong></span></section>\n<section><span>bar</span></section>\n<section><span>baz</span></section>", "**foo**\n\nbar\n\nbaz\n"},
	{"199", "<pre style=\"background-color: rgb(246, 248, 250);border-radius: 6px;padding: 4px;margin-bottom: 15px;overflow: auto;line-height: 1.45;color: rgb(68, 68, 68);font-size: 14px;letter-spacing: normal;text-align: start;border-width: initial !important;border-style: none !important;border-color: initial !important;\" class=\"js_darkmode__22\"><em style=\"cursor: pointer;font-size: 12px;color: rgb(51, 102, 153) !important;\"> 复制代码</em><em style=\"cursor: pointer;font-size: 12px;color: rgb(51, 102, 153) !important;\"> 隐藏代码<br></em><code style=\"font-family: SFMono-Regular, Consolas, &quot;Liberation Mono&quot;, Menlo, monospace;background: rgb(0, 0, 0);color: rgb(248, 248, 248);padding: 1em;display: block;overflow-x: auto;\" class=\"js_darkmode__23\">public <span style=\"color: rgb(255, 255, 182);\">Object</span> <span style=\"color: rgb(255, 255, 182);\">Index</span>(<span style=\"color: rgb(255, 255, 182);\">Object</span> functionObject, <span style=\"color: rgb(255, 255, 182);\">Object</span> newTarget, <span style=\"color: rgb(255, 255, 182);\">Index</span> <span style=\"color: rgb(198, 197, 254);\">this</span>, <span style=\"color: rgb(255, 255, 182);\">Object</span> arg0, <span style=\"color: rgb(255, 255, 182);\">Object</span> arg1, <span style=\"color: rgb(255, 255, 182);\">Object</span> arg2, <span style=\"color: rgb(255, 255, 182);\">Object</span> arg3, <span style=\"color: rgb(255, 255, 182);\">Object</span> arg4, <span style=\"color: rgb(255, 255, 182);\">Object</span> arg5) {<br>&nbsp; &nbsp;&nbsp; &nbsp;&nbsp;&nbsp;<span style=\"color: rgb(150, 203, 254);\">if</span> ((<span style=\"color: rgb(255, 115, 253);\">0</span> == arg3 ? <span style=\"color: rgb(255, 115, 253);\">1</span> : <span style=\"color: rgb(255, 115, 253);\">0</span>) != <span style=\"color: rgb(255, 115, 253);\">0</span>) {<br>&nbsp; &nbsp;&nbsp; &nbsp;&nbsp; &nbsp;&nbsp; &nbsp;arg3 = -<span style=\"color: rgb(255, 115, 253);\">1</span>;<br>&nbsp; &nbsp;&nbsp; &nbsp;&nbsp;&nbsp;}<br>&nbsp; &nbsp;&nbsp; &nbsp;&nbsp;&nbsp;<span style=\"color: rgb(150, 203, 254);\">if</span> ((<span style=\"color: rgb(255, 115, 253);\">0</span> == arg4 ? <span style=\"color: rgb(255, 115, 253);\">1</span> : <span style=\"color: rgb(255, 115, 253);\">0</span>) != <span style=\"color: rgb(255, 115, 253);\">0</span>) {<br>&nbsp; &nbsp;&nbsp; &nbsp;&nbsp; &nbsp;&nbsp; &nbsp;arg4 = <span style=\"color: rgb(198, 197, 254);\">null</span>;<br>&nbsp; &nbsp;&nbsp; &nbsp;&nbsp;&nbsp;}<br>&nbsp; &nbsp;&nbsp; &nbsp;&nbsp;&nbsp;<span style=\"color: rgb(255, 255, 182);\">Object</span> obj = <span style=\"color: rgb(198, 197, 254);\">super</span>(arg0, arg2, arg3, arg5);<br>&nbsp; &nbsp;&nbsp; &nbsp;&nbsp;&nbsp;<span style=\"color: rgb(150, 203, 254);\">if</span> ((<span style=\"color: rgb(168, 255, 96);\">\"function\"</span> == <span style=\"color: rgb(255, 255, 182);\">typeof</span>(arg4) ? <span style=\"color: rgb(255, 115, 253);\">1</span> : <span style=\"color: rgb(255, 115, 253);\">0</span>) != <span style=\"color: rgb(255, 115, 253);\">0</span>) {<br>&nbsp; &nbsp;&nbsp; &nbsp;&nbsp; &nbsp;&nbsp; &nbsp;obj.paramsGenerator_ = arg4;<br>&nbsp; &nbsp;&nbsp; &nbsp;&nbsp;&nbsp;}<br>&nbsp; &nbsp;&nbsp; &nbsp;&nbsp;&nbsp;obj.__userInput = <span style=\"color: rgb(255, 255, 182);\">ObservedPropertySimplePU</span>(<span style=\"color: rgb(168, 255, 96);\">\"\"</span>, obj, <span style=\"color: rgb(168, 255, 96);\">\"userInput\"</span>);<br>&nbsp; &nbsp;&nbsp; &nbsp;&nbsp;&nbsp;obj.secretKey = <span style=\"color: rgb(168, 255, 96);\">\"[f#fLw)??Pz?#9w)Du[ks[q[#w4D?4P4UJf,kU[f.rDkfwrDtq...)?J.#rP4[qrPDJkkJ|.9J|qffU?k|D4P4P[wkk.)k?JUJ[k#9kww[r??wUfw|PkrPUf.P#f.P#.PwJ4f4q.PU4UPDr9.[9fJ#PqP)cDDffJPDrJ.J4qPP[r[.JfJ4f|?U9#\"</span>;<br>&nbsp; &nbsp;&nbsp; &nbsp;&nbsp;&nbsp;obj.<span style=\"color: rgb(255, 255, 182);\">setInitiallyProvidedValue</span>(arg1);<br>&nbsp; &nbsp;&nbsp; &nbsp;&nbsp;&nbsp;obj.<span style=\"color: rgb(255, 255, 182);\">finalizeConstruction</span>();<br>&nbsp; &nbsp;&nbsp; &nbsp;&nbsp;&nbsp;<span style=\"color: rgb(150, 203, 254);\">return</span> obj;<br>&nbsp; &nbsp; }</code></pre>", "```\npublic Object Index(Object functionObject, Object newTarget, Index this, Object arg0, Object arg1, Object arg2, Object arg3, Object arg4, Object arg5) {\n        if ((0 == arg3 ? 1 : 0) != 0) {\n            arg3 = -1;\n        }\n        if ((0 == arg4 ? 1 : 0) != 0) {\n            arg4 = null;\n        }\n        Object obj = super(arg0, arg2, arg3, arg5);\n        if ((\"function\" == typeof(arg4) ? 1 : 0) != 0) {\n            obj.paramsGenerator_ = arg4;\n        }\n        obj.__userInput = ObservedPropertySimplePU(\"\", obj, \"userInput\");\n        obj.secretKey = \"[f#fLw)??Pz?#9w)Du[ks[q[#w4D?4P4UJf,kU[f.rDkfwrDtq...)?J.#rP4[qrPDJkkJ|.9J|qffU?k|D4P4P[wkk.)k?JUJ[k#9kww[r??wUfw|PkrPUf.P#f.P#.PwJ4f4q.PU4UPDr9.[9fJ#PqP)cDDffJPDrJ.J4qPP[r[.JfJ4f|?U9#\";\n        obj.setInitiallyProvidedValue(arg1);\n        obj.finalizeConstruction();\n        return obj;\n    }\n```\n"},
	{"198", "<p><strong><span class=\"katex\"><span class=\"katex-mathml\"><math xmlns=\"http://www.w3.org/1998/Math/MathML\"><semantics><mrow><mi>E</mi></mrow><annotation encoding=\"application/x-tex\">E</annotation></semantics></math></span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6833em;\"></span><span class=\"mord mathnormal\" style=\"margin-right: 0.05764em;\">E</span></span></span></span></strong>：表示能量（Energy），单位是焦耳（J）。这是物体或系统所拥有的能量。</p>", "\u200b**$E$**\u200b：表示能量（Energy），单位是焦耳（J）。这是物体或系统所拥有的能量。\n"},
	{"197", "<span>代码用<span>&nbsp;</span></span><code class=\"notranslate\">``</code><span><span>&nbsp;</span>包裹。</span>", "代码用 ` `` ` 包裹。\n"},
	{"196", "<picture class=\"relative w-full mx-auto decoration-primary/6 max-w-3xl page-api-block:ml-0\"><div class=\"relative overflow-hidden rounded straight-corners:rounded-none after:block after:absolute after:-inset-[0] after:border-dark/2 after:border after:rounded straight-corners:after:rounded-none dark:after:border-light/1 dark:after:mix-blend-plus-lighter after:pointer-events-none mx-auto\"><div><div><div style=\"left: 0; width: 100%; height: 0; position: relative; padding-bottom: 56.25%;\"><iframe src=\"https://cdn.iframe.ly/H0TV8Ps\" style=\"top: 0; left: 0; width: 100%; height: 100%; position: absolute; border: 0;\" allowfullscreen=\"\" scrolling=\"no\" allow=\"accelerometer *; clipboard-write *; encrypted-media *; gyroscope *; picture-in-picture *; web-share *;\"></iframe></div></div></div></div><figcaption class=\"text-sm text-center mt-2 text-dark/7 dark:text-light/6\">Double Fine PsychOdyssey · EP08: “A Couple Years of a Lot of Work” <a class=\"underline underline-offset-2 text-primary hover:text-primary-700 transition-colors \" href=\"https://www.youtube.com/watch?v=eaA0P2dDHSg&amp;list=PLIhLvue17Sd70y34zh2erWWpMyOnh4UN_&amp;index=9\">(via YouTube)</a> uploaded 11 Feb 2023</figcaption></picture><h2 id=\"example-dishonored-2-clockwork-mansion\" class=\"text-3xl font-semibold group relative grid w-full mx-auto decoration-primary/6 max-w-3xl page-api-block:ml-0\"><div class=\"grid grid-area-1-1 relative -ml-6 w-7 border-0 opacity-0 group-hover:opacity-[0] group-focus:opacity-[0] md:group-hover:md:opacity-[1] md:group-focus:md:opacity-[1] [margin-top:_1em]\"><a href=\"#example-dishonored-2-clockwork-mansion\" aria-label=\"Direct link to heading\" class=\"inline-flex h-full items-start dark:text-light/3 dark:shadow-none dark:ring-0 leading-tight\"><svg class=\"gb-icon w-3.5 h-[1lh] transition-colors text-transparent group-hover:text-dark/6 dark:group-hover:text-light/5 lg:w-4\" style=\"mask-image: url(&quot;https://ka-p.fontawesome.com/releases/v6.6.0/svgs/regular/hashtag.svg?v=2&amp;token=a463935e93&quot;); mask-repeat: no-repeat; mask-position: center center;\"></svg></a></div><div class=\"grid-area-1-1 z-[1] [margin-top:_1em]\">Example: Dishonored 2, \"Clockwork Mansion\"</div></h2>", "<iframe src=\"https://cdn.iframe.ly/H0TV8Ps\" style=\"top: 0; left: 0; width: 100%; height: 100%; position: absolute; border: 0;\" allowfullscreen=\"\" scrolling=\"no\" allow=\"accelerometer *; clipboard-write *; encrypted-media *; gyroscope *; picture-in-picture *; web-share *;\"></iframe>\n\n\n\n\n\n\nDouble Fine PsychOdyssey · EP08: “A Couple Years of a Lot of Work” [(via YouTube)](https://www.youtube.com/watch?v=eaA0P2dDHSg&list=PLIhLvue17Sd70y34zh2erWWpMyOnh4UN_&index=9) uploaded 11 Feb 2023\n\n## Example: Dishonored 2, \"Clockwork Mansion\"\n"},
	{"195", "<div class=\"w-full mx-auto decoration-primary/6 max-w-3xl page-api-block:ml-0 flex flex-row gap-3 justify-center\"><picture class=\"relative\"><div class=\"relative overflow-hidden rounded straight-corners:rounded-none after:block after:absolute after:-inset-[0] after:border-dark/2 after:border after:rounded straight-corners:after:rounded-none dark:after:border-light/1 dark:after:mix-blend-plus-lighter after:pointer-events-none w-fit mx-auto\"><img alt=\"\" loading=\"lazy\" fetchpriority=\"low\" class=\"block ZoomImage_zoomImg__teSyL\" src=\"https://book.leveldesignbook.com/~gitbook/image?url=https%3A%2F%2F1666186240-files.gitbook.io%2F%7E%2Ffiles%2Fv0%2Fb%2Fgitbook-legacy-files%2Fo%2Fassets%252F-LtVT8pJjInrrHVCovzy%252F-MVOe7gOtBO2fR1OaIjJ%252F-MVOeNGkYd_XvSwlSxn7%252FLDB_Sniper_Rebellion_BlockoutArtpass.gif%3Falt%3Dmedia%26token%3Da10f1d36-1367-4304-b106-8253f9b9ee1a&amp;width=768&amp;dpr=4&amp;quality=100&amp;sign=14064be0&amp;sv=1\" srcset=\"https://book.leveldesignbook.com/~gitbook/image?url=https%3A%2F%2F1666186240-files.gitbook.io%2F%7E%2Ffiles%2Fv0%2Fb%2Fgitbook-legacy-files%2Fo%2Fassets%252F-LtVT8pJjInrrHVCovzy%252F-MVOe7gOtBO2fR1OaIjJ%252F-MVOeNGkYd_XvSwlSxn7%252FLDB_Sniper_Rebellion_BlockoutArtpass.gif%3Falt%3Dmedia%26token%3Da10f1d36-1367-4304-b106-8253f9b9ee1a&amp;width=400&amp;dpr=1&amp;quality=100&amp;sign=14064be0&amp;sv=1 400w, https://book.leveldesignbook.com/~gitbook/image?url=https%3A%2F%2F1666186240-files.gitbook.io%2F%7E%2Ffiles%2Fv0%2Fb%2Fgitbook-legacy-files%2Fo%2Fassets%252F-LtVT8pJjInrrHVCovzy%252F-MVOe7gOtBO2fR1OaIjJ%252F-MVOeNGkYd_XvSwlSxn7%252FLDB_Sniper_Rebellion_BlockoutArtpass.gif%3Falt%3Dmedia%26token%3Da10f1d36-1367-4304-b106-8253f9b9ee1a&amp;width=400&amp;dpr=2&amp;quality=100&amp;sign=14064be0&amp;sv=1 800w, https://book.leveldesignbook.com/~gitbook/image?url=https%3A%2F%2F1666186240-files.gitbook.io%2F%7E%2Ffiles%2Fv0%2Fb%2Fgitbook-legacy-files%2Fo%2Fassets%252F-LtVT8pJjInrrHVCovzy%252F-MVOe7gOtBO2fR1OaIjJ%252F-MVOeNGkYd_XvSwlSxn7%252FLDB_Sniper_Rebellion_BlockoutArtpass.gif%3Falt%3Dmedia%26token%3Da10f1d36-1367-4304-b106-8253f9b9ee1a&amp;width=400&amp;dpr=3&amp;quality=100&amp;sign=14064be0&amp;sv=1 1200w, https://book.leveldesignbook.com/~gitbook/image?url=https%3A%2F%2F1666186240-files.gitbook.io%2F%7E%2Ffiles%2Fv0%2Fb%2Fgitbook-legacy-files%2Fo%2Fassets%252F-LtVT8pJjInrrHVCovzy%252F-MVOe7gOtBO2fR1OaIjJ%252F-MVOeNGkYd_XvSwlSxn7%252FLDB_Sniper_Rebellion_BlockoutArtpass.gif%3Falt%3Dmedia%26token%3Da10f1d36-1367-4304-b106-8253f9b9ee1a&amp;width=400&amp;dpr=4&amp;quality=100&amp;sign=14064be0&amp;sv=1 1600w, https://book.leveldesignbook.com/~gitbook/image?url=https%3A%2F%2F1666186240-files.gitbook.io%2F%7E%2Ffiles%2Fv0%2Fb%2Fgitbook-legacy-files%2Fo%2Fassets%252F-LtVT8pJjInrrHVCovzy%252F-MVOe7gOtBO2fR1OaIjJ%252F-MVOeNGkYd_XvSwlSxn7%252FLDB_Sniper_Rebellion_BlockoutArtpass.gif%3Falt%3Dmedia%26token%3Da10f1d36-1367-4304-b106-8253f9b9ee1a&amp;width=768&amp;dpr=1&amp;quality=100&amp;sign=14064be0&amp;sv=1 768w, https://book.leveldesignbook.com/~gitbook/image?url=https%3A%2F%2F1666186240-files.gitbook.io%2F%7E%2Ffiles%2Fv0%2Fb%2Fgitbook-legacy-files%2Fo%2Fassets%252F-LtVT8pJjInrrHVCovzy%252F-MVOe7gOtBO2fR1OaIjJ%252F-MVOeNGkYd_XvSwlSxn7%252FLDB_Sniper_Rebellion_BlockoutArtpass.gif%3Falt%3Dmedia%26token%3Da10f1d36-1367-4304-b106-8253f9b9ee1a&amp;width=768&amp;dpr=2&amp;quality=100&amp;sign=14064be0&amp;sv=1 1536w, https://book.leveldesignbook.com/~gitbook/image?url=https%3A%2F%2F1666186240-files.gitbook.io%2F%7E%2Ffiles%2Fv0%2Fb%2Fgitbook-legacy-files%2Fo%2Fassets%252F-LtVT8pJjInrrHVCovzy%252F-MVOe7gOtBO2fR1OaIjJ%252F-MVOeNGkYd_XvSwlSxn7%252FLDB_Sniper_Rebellion_BlockoutArtpass.gif%3Falt%3Dmedia%26token%3Da10f1d36-1367-4304-b106-8253f9b9ee1a&amp;width=768&amp;dpr=3&amp;quality=100&amp;sign=14064be0&amp;sv=1 2304w, https://book.leveldesignbook.com/~gitbook/image?url=https%3A%2F%2F1666186240-files.gitbook.io%2F%7E%2Ffiles%2Fv0%2Fb%2Fgitbook-legacy-files%2Fo%2Fassets%252F-LtVT8pJjInrrHVCovzy%252F-MVOe7gOtBO2fR1OaIjJ%252F-MVOeNGkYd_XvSwlSxn7%252FLDB_Sniper_Rebellion_BlockoutArtpass.gif%3Falt%3Dmedia%26token%3Da10f1d36-1367-4304-b106-8253f9b9ee1a&amp;width=768&amp;dpr=4&amp;quality=100&amp;sign=14064be0&amp;sv=1 3072w\" sizes=\"(max-width: 640px) 400px, 768px\" width=\"1272\" height=\"703\" style=\"max-width: 100%; height: auto;\"></div><figcaption class=\"text-sm text-center mt-2 text-dark/7 dark:text-light/6\">animated GIF of development process for a snowy military dock level in Sniper Elite</figcaption></picture></div><h3 id=\"id-8.-release\" class=\"text-2xl font-semibold group relative grid w-full mx-auto decoration-primary/6 max-w-3xl page-api-block:ml-0\"><div class=\"grid grid-area-1-1 relative -ml-6 w-7 border-0 opacity-0 group-hover:opacity-[0] group-focus:opacity-[0] md:group-hover:md:opacity-[1] md:group-focus:md:opacity-[1] [margin-top:_0.75em]\"><a href=\"#id-8.-release\" aria-label=\"Direct link to heading\" class=\"inline-flex h-full items-start dark:text-light/3 dark:shadow-none dark:ring-0 leading-snug\"><svg class=\"gb-icon w-3.5 h-[1lh] transition-colors text-transparent group-hover:text-dark/6 dark:group-hover:text-light/5 lg:w-4\" style=\"mask-image: url(&quot;https://ka-p.fontawesome.com/releases/v6.6.0/svgs/regular/hashtag.svg?v=2&amp;token=a463935e93&quot;); mask-repeat: no-repeat; mask-position: center center;\"></svg></a></div><div class=\"grid-area-1-1 z-[1] [margin-top:_0.75em]\">8. <a class=\"underline underline-offset-2 text-primary hover:text-primary-700 transition-colors \" href=\"/process/release\">Release</a></div></h3>", "![](https://book.leveldesignbook.com/~gitbook/image?url=https%3A%2F%2F1666186240-files.gitbook.io%2F%7E%2Ffiles%2Fv0%2Fb%2Fgitbook-legacy-files%2Fo%2Fassets%252F-LtVT8pJjInrrHVCovzy%252F-MVOe7gOtBO2fR1OaIjJ%252F-MVOeNGkYd_XvSwlSxn7%252FLDB_Sniper_Rebellion_BlockoutArtpass.gif%3Falt%3Dmedia%26token%3Da10f1d36-1367-4304-b106-8253f9b9ee1a&width=768&dpr=4&quality=100&sign=14064be0&sv=1){: style=\"width: 1272px;\"}\n\n\nanimated GIF of development process for a snowy military dock level in Sniper Elite\n\n\n### 8. [Release](/process/release)\n"},
	{"194", "<div id=\"readability-page-1\" class=\"page\"><div class=\"rich_media_content js_underline_content\n                       autoTypeSetting24psection\n            \" id=\"js_content\"><section data-tool=\"mdnice编辑器\" data-website=\"https://www.mdnice.com\"><p data-tool=\"mdnice编辑器\">有很多可用项目，当然厨子直接RC4解密也可以，解密后的base64解码保存为zip，直接字典跑rockyou即可得到解压密码</p><h3 data-tool=\"mdnice编辑器\"><span data-lazy-bgimg=\"https://mmbiz.qpic.cn/mmbiz_png/crOK73kjDuiakkEF9Ljib1mqEjCy7CLMmNtmk1xgQWkZlaWSqGOpPKRoOHOwH5Y3X6hhcicdAD0vbAoDVwHEwwGbA/640?wx_fmt=png&amp;from=appmsg\" class=\"\" data-fail=\"0\"></span><span>[WEEK1]拜师之旅①</span></h3><blockquote data-tool=\"mdnice编辑器\"><p>相关知识请自行搜索了,也是老题目了</p></blockquote><span data-tool=\"mdnice编辑器\"><section data-formula=\"leak = pr-qt-tmp\n\"></section></span><p data-tool=\"mdnice编辑器\">上述式子模上t，则有</p><span data-tool=\"mdnice编辑器\"><section data-formula=\"leak+tmp \\equiv pr \\space mod \\space t\n\"></section></span><p data-tool=\"mdnice编辑器\">此时，r已知，也就说当我们确定tmp的时候，计算出r对于t的逆元，就可以求出p，而tmp只有15bit，可以很快的遍历出来。</p></section></div></div>", "有很多可用项目，当然厨子直接 RC4 解密也可以，解密后的 base64 解码保存为 zip，直接字典跑 rockyou 即可得到解压密码\n\n### [WEEK1]拜师之旅 ①\n\n> 相关知识请自行搜索了,也是老题目了\n\n\n$$\nleak = pr-qt-tmp\n$$\n\n上述式子模上 t，则有\n\n\n$$\nleak+tmp \\equiv pr \\space mod \\space t\n$$\n\n此时，r 已知，也就说当我们确定 tmp 的时候，计算出 r 对于 t 的逆元，就可以求出 p，而 tmp 只有 15bit，可以很快的遍历出来。\n"},
	{"193", "<div class=\"table-wrapper\"><table>\n<thead>\n<tr>\n<th style=\"text-align: center\">输入</th>\n<th style=\"text-align: center\">显示</th>\n<th style=\"text-align: center\">输入</th>\n<th style=\"text-align: center\">显示</th>\n</tr>\n</thead>\n<tbody>\n<tr>\n<td style=\"text-align: center\">black</td>\n<td style=\"text-align: center\"><span class=\"math inline\"><span class=\"MathJax_Preview\" style=\"color: inherit;\"></span><span id=\"MathJax-Element-278-Frame\" class=\"mjx-chtml MathJax_CHTML\" tabindex=\"0\" style=\"font-size: 119%; position: relative;\" data-mathml=\"<math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;><mstyle mathcolor=&quot;black&quot;><mi>t</mi><mi>e</mi><mi>x</mi><mi>t</mi></mstyle></math>\" role=\"presentation\"><span id=\"MJXc-Node-5719\" class=\"mjx-math\" aria-hidden=\"true\"><span id=\"MJXc-Node-5720\" class=\"mjx-mrow\"><span id=\"MJXc-Node-5721\" class=\"mjx-mstyle\" style=\"color: black;\"><span id=\"MJXc-Node-5722\" class=\"mjx-mrow\"><span id=\"MJXc-Node-5723\" class=\"mjx-mi\"><span class=\"mjx-char MJXc-TeX-math-I\" style=\"padding-top: 0.391em; padding-bottom: 0.262em;\">t</span></span><span id=\"MJXc-Node-5724\" class=\"mjx-mi\"><span class=\"mjx-char MJXc-TeX-math-I\" style=\"padding-top: 0.197em; padding-bottom: 0.262em;\">e</span></span><span id=\"MJXc-Node-5725\" class=\"mjx-mi\"><span class=\"mjx-char MJXc-TeX-math-I\" style=\"padding-top: 0.197em; padding-bottom: 0.262em;\">x</span></span><span id=\"MJXc-Node-5726\" class=\"mjx-mi\"><span class=\"mjx-char MJXc-TeX-math-I\" style=\"padding-top: 0.391em; padding-bottom: 0.262em;\">t</span></span></span></span></span></span><span class=\"MJX_Assistive_MathML\" role=\"presentation\"><math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mstyle mathcolor=\"black\"><mi>t</mi><mi>e</mi><mi>x</mi><mi>t</mi></mstyle></math></span></span><script type=\"math/tex\" id=\"MathJax-Element-278\">\\color{black}{text}</script></span></td>\n<td style=\"text-align: center\">grey</td>\n<td style=\"text-align: center\"><span class=\"math inline\"><span class=\"MathJax_Preview\" style=\"color: inherit;\"></span><span id=\"MathJax-Element-279-Frame\" class=\"mjx-chtml MathJax_CHTML\" tabindex=\"0\" style=\"font-size: 119%; position: relative;\" data-mathml=\"<math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;><mstyle mathcolor=&quot;grey&quot;><mi>t</mi><mi>e</mi><mi>x</mi><mi>t</mi></mstyle></math>\" role=\"presentation\"><span id=\"MJXc-Node-5727\" class=\"mjx-math\" aria-hidden=\"true\"><span id=\"MJXc-Node-5728\" class=\"mjx-mrow\"><span id=\"MJXc-Node-5729\" class=\"mjx-mstyle\" style=\"color: grey;\"><span id=\"MJXc-Node-5730\" class=\"mjx-mrow\"><span id=\"MJXc-Node-5731\" class=\"mjx-mi\"><span class=\"mjx-char MJXc-TeX-math-I\" style=\"padding-top: 0.391em; padding-bottom: 0.262em;\">t</span></span><span id=\"MJXc-Node-5732\" class=\"mjx-mi\"><span class=\"mjx-char MJXc-TeX-math-I\" style=\"padding-top: 0.197em; padding-bottom: 0.262em;\">e</span></span><span id=\"MJXc-Node-5733\" class=\"mjx-mi\"><span class=\"mjx-char MJXc-TeX-math-I\" style=\"padding-top: 0.197em; padding-bottom: 0.262em;\">x</span></span><span id=\"MJXc-Node-5734\" class=\"mjx-mi\"><span class=\"mjx-char MJXc-TeX-math-I\" style=\"padding-top: 0.391em; padding-bottom: 0.262em;\">t</span></span></span></span></span></span><span class=\"MJX_Assistive_MathML\" role=\"presentation\"><math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mstyle mathcolor=\"grey\"><mi>t</mi><mi>e</mi><mi>x</mi><mi>t</mi></mstyle></math></span></span><script type=\"math/tex\" id=\"MathJax-Element-279\">\\color{grey}{text}</script></span></td>\n</tr>\n<tr>\n<td style=\"text-align: center\">silver</td>\n<td style=\"text-align: center\"><span class=\"math inline\"><span class=\"MathJax_Preview\" style=\"color: inherit;\"></span><span id=\"MathJax-Element-280-Frame\" class=\"mjx-chtml MathJax_CHTML\" tabindex=\"0\" style=\"font-size: 119%; position: relative;\" data-mathml=\"<math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;><mstyle mathcolor=&quot;silver&quot;><mi>t</mi><mi>e</mi><mi>x</mi><mi>t</mi></mstyle></math>\" role=\"presentation\"><span id=\"MJXc-Node-5735\" class=\"mjx-math\" aria-hidden=\"true\"><span id=\"MJXc-Node-5736\" class=\"mjx-mrow\"><span id=\"MJXc-Node-5737\" class=\"mjx-mstyle\" style=\"color: silver;\"><span id=\"MJXc-Node-5738\" class=\"mjx-mrow\"><span id=\"MJXc-Node-5739\" class=\"mjx-mi\"><span class=\"mjx-char MJXc-TeX-math-I\" style=\"padding-top: 0.391em; padding-bottom: 0.262em;\">t</span></span><span id=\"MJXc-Node-5740\" class=\"mjx-mi\"><span class=\"mjx-char MJXc-TeX-math-I\" style=\"padding-top: 0.197em; padding-bottom: 0.262em;\">e</span></span><span id=\"MJXc-Node-5741\" class=\"mjx-mi\"><span class=\"mjx-char MJXc-TeX-math-I\" style=\"padding-top: 0.197em; padding-bottom: 0.262em;\">x</span></span><span id=\"MJXc-Node-5742\" class=\"mjx-mi\"><span class=\"mjx-char MJXc-TeX-math-I\" style=\"padding-top: 0.391em; padding-bottom: 0.262em;\">t</span></span></span></span></span></span><span class=\"MJX_Assistive_MathML\" role=\"presentation\"><math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mstyle mathcolor=\"silver\"><mi>t</mi><mi>e</mi><mi>x</mi><mi>t</mi></mstyle></math></span></span><script type=\"math/tex\" id=\"MathJax-Element-280\">\\color{silver}{text}</script></span></td>\n<td style=\"text-align: center\">white</td>\n<td style=\"text-align: center\"><span class=\"math inline\"><span class=\"MathJax_Preview\" style=\"color: inherit;\"></span><span id=\"MathJax-Element-281-Frame\" class=\"mjx-chtml MathJax_CHTML\" tabindex=\"0\" style=\"font-size: 119%; position: relative;\" data-mathml=\"<math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;><mstyle mathcolor=&quot;white&quot;><mi>t</mi><mi>e</mi><mi>x</mi><mi>t</mi></mstyle></math>\" role=\"presentation\"><span id=\"MJXc-Node-5743\" class=\"mjx-math\" aria-hidden=\"true\"><span id=\"MJXc-Node-5744\" class=\"mjx-mrow\"><span id=\"MJXc-Node-5745\" class=\"mjx-mstyle\" style=\"color: white;\"><span id=\"MJXc-Node-5746\" class=\"mjx-mrow\"><span id=\"MJXc-Node-5747\" class=\"mjx-mi\"><span class=\"mjx-char MJXc-TeX-math-I\" style=\"padding-top: 0.391em; padding-bottom: 0.262em;\">t</span></span><span id=\"MJXc-Node-5748\" class=\"mjx-mi\"><span class=\"mjx-char MJXc-TeX-math-I\" style=\"padding-top: 0.197em; padding-bottom: 0.262em;\">e</span></span><span id=\"MJXc-Node-5749\" class=\"mjx-mi\"><span class=\"mjx-char MJXc-TeX-math-I\" style=\"padding-top: 0.197em; padding-bottom: 0.262em;\">x</span></span><span id=\"MJXc-Node-5750\" class=\"mjx-mi\"><span class=\"mjx-char MJXc-TeX-math-I\" style=\"padding-top: 0.391em; padding-bottom: 0.262em;\">t</span></span></span></span></span></span><span class=\"MJX_Assistive_MathML\" role=\"presentation\"><math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mstyle mathcolor=\"white\"><mi>t</mi><mi>e</mi><mi>x</mi><mi>t</mi></mstyle></math></span></span><script type=\"math/tex\" id=\"MathJax-Element-281\">\\color{white}{text}</script></span></td>\n</tr>\n<tr>\n<td style=\"text-align: center\">maroon</td>\n<td style=\"text-align: center\"><span class=\"math inline\"><span class=\"MathJax_Preview\" style=\"color: inherit;\"></span><span id=\"MathJax-Element-282-Frame\" class=\"mjx-chtml MathJax_CHTML\" tabindex=\"0\" style=\"font-size: 119%; position: relative;\" data-mathml=\"<math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;><mstyle mathcolor=&quot;maroon&quot;><mi>t</mi><mi>e</mi><mi>x</mi><mi>t</mi></mstyle></math>\" role=\"presentation\"><span id=\"MJXc-Node-5751\" class=\"mjx-math\" aria-hidden=\"true\"><span id=\"MJXc-Node-5752\" class=\"mjx-mrow\"><span id=\"MJXc-Node-5753\" class=\"mjx-mstyle\" style=\"color: maroon;\"><span id=\"MJXc-Node-5754\" class=\"mjx-mrow\"><span id=\"MJXc-Node-5755\" class=\"mjx-mi\"><span class=\"mjx-char MJXc-TeX-math-I\" style=\"padding-top: 0.391em; padding-bottom: 0.262em;\">t</span></span><span id=\"MJXc-Node-5756\" class=\"mjx-mi\"><span class=\"mjx-char MJXc-TeX-math-I\" style=\"padding-top: 0.197em; padding-bottom: 0.262em;\">e</span></span><span id=\"MJXc-Node-5757\" class=\"mjx-mi\"><span class=\"mjx-char MJXc-TeX-math-I\" style=\"padding-top: 0.197em; padding-bottom: 0.262em;\">x</span></span><span id=\"MJXc-Node-5758\" class=\"mjx-mi\"><span class=\"mjx-char MJXc-TeX-math-I\" style=\"padding-top: 0.391em; padding-bottom: 0.262em;\">t</span></span></span></span></span></span><span class=\"MJX_Assistive_MathML\" role=\"presentation\"><math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mstyle mathcolor=\"maroon\"><mi>t</mi><mi>e</mi><mi>x</mi><mi>t</mi></mstyle></math></span></span><script type=\"math/tex\" id=\"MathJax-Element-282\">\\color{maroon}{text}</script></span></td>\n<td style=\"text-align: center\">red</td>\n<td style=\"text-align: center\"><span class=\"math inline\"><span class=\"MathJax_Preview\" style=\"color: inherit;\"></span><span id=\"MathJax-Element-283-Frame\" class=\"mjx-chtml MathJax_CHTML\" tabindex=\"0\" style=\"font-size: 119%; position: relative;\" data-mathml=\"<math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;><mstyle mathcolor=&quot;red&quot;><mi>t</mi><mi>e</mi><mi>x</mi><mi>t</mi></mstyle></math>\" role=\"presentation\"><span id=\"MJXc-Node-5759\" class=\"mjx-math\" aria-hidden=\"true\"><span id=\"MJXc-Node-5760\" class=\"mjx-mrow\"><span id=\"MJXc-Node-5761\" class=\"mjx-mstyle\" style=\"color: red;\"><span id=\"MJXc-Node-5762\" class=\"mjx-mrow\"><span id=\"MJXc-Node-5763\" class=\"mjx-mi\"><span class=\"mjx-char MJXc-TeX-math-I\" style=\"padding-top: 0.391em; padding-bottom: 0.262em;\">t</span></span><span id=\"MJXc-Node-5764\" class=\"mjx-mi\"><span class=\"mjx-char MJXc-TeX-math-I\" style=\"padding-top: 0.197em; padding-bottom: 0.262em;\">e</span></span><span id=\"MJXc-Node-5765\" class=\"mjx-mi\"><span class=\"mjx-char MJXc-TeX-math-I\" style=\"padding-top: 0.197em; padding-bottom: 0.262em;\">x</span></span><span id=\"MJXc-Node-5766\" class=\"mjx-mi\"><span class=\"mjx-char MJXc-TeX-math-I\" style=\"padding-top: 0.391em; padding-bottom: 0.262em;\">t</span></span></span></span></span></span><span class=\"MJX_Assistive_MathML\" role=\"presentation\"><math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mstyle mathcolor=\"red\"><mi>t</mi><mi>e</mi><mi>x</mi><mi>t</mi></mstyle></math></span></span><script type=\"math/tex\" id=\"MathJax-Element-283\">\\color{red}{text}</script></span></td>\n</tr>\n<tr>\n<td style=\"text-align: center\">yellow</td>\n<td style=\"text-align: center\"><span class=\"math inline\"><span class=\"MathJax_Preview\" style=\"color: inherit;\"></span><span id=\"MathJax-Element-284-Frame\" class=\"mjx-chtml MathJax_CHTML\" tabindex=\"0\" style=\"font-size: 119%; position: relative;\" data-mathml=\"<math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;><mstyle mathcolor=&quot;yellow&quot;><mi>t</mi><mi>e</mi><mi>x</mi><mi>t</mi></mstyle></math>\" role=\"presentation\"><span id=\"MJXc-Node-5767\" class=\"mjx-math\" aria-hidden=\"true\"><span id=\"MJXc-Node-5768\" class=\"mjx-mrow\"><span id=\"MJXc-Node-5769\" class=\"mjx-mstyle\" style=\"color: yellow;\"><span id=\"MJXc-Node-5770\" class=\"mjx-mrow\"><span id=\"MJXc-Node-5771\" class=\"mjx-mi\"><span class=\"mjx-char MJXc-TeX-math-I\" style=\"padding-top: 0.391em; padding-bottom: 0.262em;\">t</span></span><span id=\"MJXc-Node-5772\" class=\"mjx-mi\"><span class=\"mjx-char MJXc-TeX-math-I\" style=\"padding-top: 0.197em; padding-bottom: 0.262em;\">e</span></span><span id=\"MJXc-Node-5773\" class=\"mjx-mi\"><span class=\"mjx-char MJXc-TeX-math-I\" style=\"padding-top: 0.197em; padding-bottom: 0.262em;\">x</span></span><span id=\"MJXc-Node-5774\" class=\"mjx-mi\"><span class=\"mjx-char MJXc-TeX-math-I\" style=\"padding-top: 0.391em; padding-bottom: 0.262em;\">t</span></span></span></span></span></span><span class=\"MJX_Assistive_MathML\" role=\"presentation\"><math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mstyle mathcolor=\"yellow\"><mi>t</mi><mi>e</mi><mi>x</mi><mi>t</mi></mstyle></math></span></span><script type=\"math/tex\" id=\"MathJax-Element-284\">\\color{yellow}{text}</script></span></td>\n<td style=\"text-align: center\">lime</td>\n<td style=\"text-align: center\"><span class=\"math inline\"><span class=\"MathJax_Preview\" style=\"color: inherit;\"></span><span id=\"MathJax-Element-285-Frame\" class=\"mjx-chtml MathJax_CHTML\" tabindex=\"0\" style=\"font-size: 119%; position: relative;\" data-mathml=\"<math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;><mstyle mathcolor=&quot;lime&quot;><mi>t</mi><mi>e</mi><mi>x</mi><mi>t</mi></mstyle></math>\" role=\"presentation\"><span id=\"MJXc-Node-5775\" class=\"mjx-math\" aria-hidden=\"true\"><span id=\"MJXc-Node-5776\" class=\"mjx-mrow\"><span id=\"MJXc-Node-5777\" class=\"mjx-mstyle\" style=\"color: lime;\"><span id=\"MJXc-Node-5778\" class=\"mjx-mrow\"><span id=\"MJXc-Node-5779\" class=\"mjx-mi\"><span class=\"mjx-char MJXc-TeX-math-I\" style=\"padding-top: 0.391em; padding-bottom: 0.262em;\">t</span></span><span id=\"MJXc-Node-5780\" class=\"mjx-mi\"><span class=\"mjx-char MJXc-TeX-math-I\" style=\"padding-top: 0.197em; padding-bottom: 0.262em;\">e</span></span><span id=\"MJXc-Node-5781\" class=\"mjx-mi\"><span class=\"mjx-char MJXc-TeX-math-I\" style=\"padding-top: 0.197em; padding-bottom: 0.262em;\">x</span></span><span id=\"MJXc-Node-5782\" class=\"mjx-mi\"><span class=\"mjx-char MJXc-TeX-math-I\" style=\"padding-top: 0.391em; padding-bottom: 0.262em;\">t</span></span></span></span></span></span><span class=\"MJX_Assistive_MathML\" role=\"presentation\"><math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mstyle mathcolor=\"lime\"><mi>t</mi><mi>e</mi><mi>x</mi><mi>t</mi></mstyle></math></span></span><script type=\"math/tex\" id=\"MathJax-Element-285\">\\color{lime}{text}</script></span></td>\n</tr>\n<tr>\n<td style=\"text-align: center\">olive</td>\n<td style=\"text-align: center\"><span class=\"math inline\"><span class=\"MathJax_Preview\" style=\"color: inherit;\"></span><span id=\"MathJax-Element-286-Frame\" class=\"mjx-chtml MathJax_CHTML\" tabindex=\"0\" style=\"font-size: 119%; position: relative;\" data-mathml=\"<math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;><mstyle mathcolor=&quot;olive&quot;><mi>t</mi><mi>e</mi><mi>x</mi><mi>t</mi></mstyle></math>\" role=\"presentation\"><span id=\"MJXc-Node-5783\" class=\"mjx-math\" aria-hidden=\"true\"><span id=\"MJXc-Node-5784\" class=\"mjx-mrow\"><span id=\"MJXc-Node-5785\" class=\"mjx-mstyle\" style=\"color: olive;\"><span id=\"MJXc-Node-5786\" class=\"mjx-mrow\"><span id=\"MJXc-Node-5787\" class=\"mjx-mi\"><span class=\"mjx-char MJXc-TeX-math-I\" style=\"padding-top: 0.391em; padding-bottom: 0.262em;\">t</span></span><span id=\"MJXc-Node-5788\" class=\"mjx-mi\"><span class=\"mjx-char MJXc-TeX-math-I\" style=\"padding-top: 0.197em; padding-bottom: 0.262em;\">e</span></span><span id=\"MJXc-Node-5789\" class=\"mjx-mi\"><span class=\"mjx-char MJXc-TeX-math-I\" style=\"padding-top: 0.197em; padding-bottom: 0.262em;\">x</span></span><span id=\"MJXc-Node-5790\" class=\"mjx-mi\"><span class=\"mjx-char MJXc-TeX-math-I\" style=\"padding-top: 0.391em; padding-bottom: 0.262em;\">t</span></span></span></span></span></span><span class=\"MJX_Assistive_MathML\" role=\"presentation\"><math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mstyle mathcolor=\"olive\"><mi>t</mi><mi>e</mi><mi>x</mi><mi>t</mi></mstyle></math></span></span><script type=\"math/tex\" id=\"MathJax-Element-286\">\\color{olive}{text}</script></span></td>\n<td style=\"text-align: center\">green</td>\n<td style=\"text-align: center\"><span class=\"math inline\"><span class=\"MathJax_Preview\" style=\"color: inherit;\"></span><span id=\"MathJax-Element-287-Frame\" class=\"mjx-chtml MathJax_CHTML\" tabindex=\"0\" style=\"font-size: 119%; position: relative;\" data-mathml=\"<math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;><mstyle mathcolor=&quot;green&quot;><mi>t</mi><mi>e</mi><mi>x</mi><mi>t</mi></mstyle></math>\" role=\"presentation\"><span id=\"MJXc-Node-5791\" class=\"mjx-math\" aria-hidden=\"true\"><span id=\"MJXc-Node-5792\" class=\"mjx-mrow\"><span id=\"MJXc-Node-5793\" class=\"mjx-mstyle\" style=\"color: green;\"><span id=\"MJXc-Node-5794\" class=\"mjx-mrow\"><span id=\"MJXc-Node-5795\" class=\"mjx-mi\"><span class=\"mjx-char MJXc-TeX-math-I\" style=\"padding-top: 0.391em; padding-bottom: 0.262em;\">t</span></span><span id=\"MJXc-Node-5796\" class=\"mjx-mi\"><span class=\"mjx-char MJXc-TeX-math-I\" style=\"padding-top: 0.197em; padding-bottom: 0.262em;\">e</span></span><span id=\"MJXc-Node-5797\" class=\"mjx-mi\"><span class=\"mjx-char MJXc-TeX-math-I\" style=\"padding-top: 0.197em; padding-bottom: 0.262em;\">x</span></span><span id=\"MJXc-Node-5798\" class=\"mjx-mi\"><span class=\"mjx-char MJXc-TeX-math-I\" style=\"padding-top: 0.391em; padding-bottom: 0.262em;\">t</span></span></span></span></span></span><span class=\"MJX_Assistive_MathML\" role=\"presentation\"><math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mstyle mathcolor=\"green\"><mi>t</mi><mi>e</mi><mi>x</mi><mi>t</mi></mstyle></math></span></span><script type=\"math/tex\" id=\"MathJax-Element-287\">\\color{green}{text}</script></span></td>\n</tr>\n<tr>\n<td style=\"text-align: center\">teal</td>\n<td style=\"text-align: center\"><span class=\"math inline\"><span class=\"MathJax_Preview\" style=\"color: inherit;\"></span><span id=\"MathJax-Element-288-Frame\" class=\"mjx-chtml MathJax_CHTML\" tabindex=\"0\" style=\"font-size: 119%; position: relative;\" data-mathml=\"<math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;><mstyle mathcolor=&quot;teal&quot;><mi>t</mi><mi>e</mi><mi>x</mi><mi>t</mi></mstyle></math>\" role=\"presentation\"><span id=\"MJXc-Node-5799\" class=\"mjx-math\" aria-hidden=\"true\"><span id=\"MJXc-Node-5800\" class=\"mjx-mrow\"><span id=\"MJXc-Node-5801\" class=\"mjx-mstyle\" style=\"color: teal;\"><span id=\"MJXc-Node-5802\" class=\"mjx-mrow\"><span id=\"MJXc-Node-5803\" class=\"mjx-mi\"><span class=\"mjx-char MJXc-TeX-math-I\" style=\"padding-top: 0.391em; padding-bottom: 0.262em;\">t</span></span><span id=\"MJXc-Node-5804\" class=\"mjx-mi\"><span class=\"mjx-char MJXc-TeX-math-I\" style=\"padding-top: 0.197em; padding-bottom: 0.262em;\">e</span></span><span id=\"MJXc-Node-5805\" class=\"mjx-mi\"><span class=\"mjx-char MJXc-TeX-math-I\" style=\"padding-top: 0.197em; padding-bottom: 0.262em;\">x</span></span><span id=\"MJXc-Node-5806\" class=\"mjx-mi\"><span class=\"mjx-char MJXc-TeX-math-I\" style=\"padding-top: 0.391em; padding-bottom: 0.262em;\">t</span></span></span></span></span></span><span class=\"MJX_Assistive_MathML\" role=\"presentation\"><math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mstyle mathcolor=\"teal\"><mi>t</mi><mi>e</mi><mi>x</mi><mi>t</mi></mstyle></math></span></span><script type=\"math/tex\" id=\"MathJax-Element-288\">\\color{teal}{text}</script></span></td>\n<td style=\"text-align: center\">auqa</td>\n<td style=\"text-align: center\"><span class=\"math inline\"><span class=\"MathJax_Preview\" style=\"color: inherit;\"></span><span id=\"MathJax-Element-289-Frame\" class=\"mjx-chtml MathJax_CHTML\" tabindex=\"0\" style=\"font-size: 119%; position: relative;\" data-mathml=\"<math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;><mstyle mathcolor=&quot;auqa&quot;><mi>t</mi><mi>e</mi><mi>x</mi><mi>t</mi></mstyle></math>\" role=\"presentation\"><span id=\"MJXc-Node-5807\" class=\"mjx-math\" aria-hidden=\"true\"><span id=\"MJXc-Node-5808\" class=\"mjx-mrow\"><span id=\"MJXc-Node-5809\" class=\"mjx-mstyle\"><span id=\"MJXc-Node-5810\" class=\"mjx-mrow\"><span id=\"MJXc-Node-5811\" class=\"mjx-mi\"><span class=\"mjx-char MJXc-TeX-math-I\" style=\"padding-top: 0.391em; padding-bottom: 0.262em;\">t</span></span><span id=\"MJXc-Node-5812\" class=\"mjx-mi\"><span class=\"mjx-char MJXc-TeX-math-I\" style=\"padding-top: 0.197em; padding-bottom: 0.262em;\">e</span></span><span id=\"MJXc-Node-5813\" class=\"mjx-mi\"><span class=\"mjx-char MJXc-TeX-math-I\" style=\"padding-top: 0.197em; padding-bottom: 0.262em;\">x</span></span><span id=\"MJXc-Node-5814\" class=\"mjx-mi\"><span class=\"mjx-char MJXc-TeX-math-I\" style=\"padding-top: 0.391em; padding-bottom: 0.262em;\">t</span></span></span></span></span></span><span class=\"MJX_Assistive_MathML\" role=\"presentation\"><math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mstyle mathcolor=\"auqa\"><mi>t</mi><mi>e</mi><mi>x</mi><mi>t</mi></mstyle></math></span></span><script type=\"math/tex\" id=\"MathJax-Element-289\">\\color{auqa}{text}</script></span></td>\n</tr>\n<tr>\n<td style=\"text-align: center\">blue</td>\n<td style=\"text-align: center\"><span class=\"math inline\"><span class=\"MathJax_Preview\" style=\"color: inherit;\"></span><span id=\"MathJax-Element-290-Frame\" class=\"mjx-chtml MathJax_CHTML\" tabindex=\"0\" style=\"font-size: 119%; position: relative;\" data-mathml=\"<math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;><mstyle mathcolor=&quot;blue&quot;><mi>t</mi><mi>e</mi><mi>x</mi><mi>t</mi></mstyle></math>\" role=\"presentation\"><span id=\"MJXc-Node-5815\" class=\"mjx-math\" aria-hidden=\"true\"><span id=\"MJXc-Node-5816\" class=\"mjx-mrow\"><span id=\"MJXc-Node-5817\" class=\"mjx-mstyle\" style=\"color: blue;\"><span id=\"MJXc-Node-5818\" class=\"mjx-mrow\"><span id=\"MJXc-Node-5819\" class=\"mjx-mi\"><span class=\"mjx-char MJXc-TeX-math-I\" style=\"padding-top: 0.391em; padding-bottom: 0.262em;\">t</span></span><span id=\"MJXc-Node-5820\" class=\"mjx-mi\"><span class=\"mjx-char MJXc-TeX-math-I\" style=\"padding-top: 0.197em; padding-bottom: 0.262em;\">e</span></span><span id=\"MJXc-Node-5821\" class=\"mjx-mi\"><span class=\"mjx-char MJXc-TeX-math-I\" style=\"padding-top: 0.197em; padding-bottom: 0.262em;\">x</span></span><span id=\"MJXc-Node-5822\" class=\"mjx-mi\"><span class=\"mjx-char MJXc-TeX-math-I\" style=\"padding-top: 0.391em; padding-bottom: 0.262em;\">t</span></span></span></span></span></span><span class=\"MJX_Assistive_MathML\" role=\"presentation\"><math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mstyle mathcolor=\"blue\"><mi>t</mi><mi>e</mi><mi>x</mi><mi>t</mi></mstyle></math></span></span><script type=\"math/tex\" id=\"MathJax-Element-290\">\\color{blue}{text}</script></span></td>\n<td style=\"text-align: center\">navy</td>\n<td style=\"text-align: center\"><span class=\"math inline\"><span class=\"MathJax_Preview\" style=\"color: inherit;\"></span><span id=\"MathJax-Element-291-Frame\" class=\"mjx-chtml MathJax_CHTML\" tabindex=\"0\" style=\"font-size: 119%; position: relative;\" data-mathml=\"<math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;><mstyle mathcolor=&quot;navy&quot;><mi>t</mi><mi>e</mi><mi>x</mi><mi>t</mi></mstyle></math>\" role=\"presentation\"><span id=\"MJXc-Node-5823\" class=\"mjx-math\" aria-hidden=\"true\"><span id=\"MJXc-Node-5824\" class=\"mjx-mrow\"><span id=\"MJXc-Node-5825\" class=\"mjx-mstyle\" style=\"color: navy;\"><span id=\"MJXc-Node-5826\" class=\"mjx-mrow\"><span id=\"MJXc-Node-5827\" class=\"mjx-mi\"><span class=\"mjx-char MJXc-TeX-math-I\" style=\"padding-top: 0.391em; padding-bottom: 0.262em;\">t</span></span><span id=\"MJXc-Node-5828\" class=\"mjx-mi\"><span class=\"mjx-char MJXc-TeX-math-I\" style=\"padding-top: 0.197em; padding-bottom: 0.262em;\">e</span></span><span id=\"MJXc-Node-5829\" class=\"mjx-mi\"><span class=\"mjx-char MJXc-TeX-math-I\" style=\"padding-top: 0.197em; padding-bottom: 0.262em;\">x</span></span><span id=\"MJXc-Node-5830\" class=\"mjx-mi\"><span class=\"mjx-char MJXc-TeX-math-I\" style=\"padding-top: 0.391em; padding-bottom: 0.262em;\">t</span></span></span></span></span></span><span class=\"MJX_Assistive_MathML\" role=\"presentation\"><math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mstyle mathcolor=\"navy\"><mi>t</mi><mi>e</mi><mi>x</mi><mi>t</mi></mstyle></math></span></span><script type=\"math/tex\" id=\"MathJax-Element-291\">\\color{navy}{text}</script></span></td>\n</tr>\n<tr>\n<td style=\"text-align: center\">purple</td>\n<td style=\"text-align: center\"><span class=\"math inline\"><span class=\"MathJax_Preview\" style=\"color: inherit;\"></span><span id=\"MathJax-Element-292-Frame\" class=\"mjx-chtml MathJax_CHTML\" tabindex=\"0\" style=\"font-size: 119%; position: relative;\" data-mathml=\"<math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;><mstyle mathcolor=&quot;purple&quot;><mi>t</mi><mi>e</mi><mi>x</mi><mi>t</mi></mstyle></math>\" role=\"presentation\"><span id=\"MJXc-Node-5831\" class=\"mjx-math\" aria-hidden=\"true\"><span id=\"MJXc-Node-5832\" class=\"mjx-mrow\"><span id=\"MJXc-Node-5833\" class=\"mjx-mstyle\" style=\"color: purple;\"><span id=\"MJXc-Node-5834\" class=\"mjx-mrow\"><span id=\"MJXc-Node-5835\" class=\"mjx-mi\"><span class=\"mjx-char MJXc-TeX-math-I\" style=\"padding-top: 0.391em; padding-bottom: 0.262em;\">t</span></span><span id=\"MJXc-Node-5836\" class=\"mjx-mi\"><span class=\"mjx-char MJXc-TeX-math-I\" style=\"padding-top: 0.197em; padding-bottom: 0.262em;\">e</span></span><span id=\"MJXc-Node-5837\" class=\"mjx-mi\"><span class=\"mjx-char MJXc-TeX-math-I\" style=\"padding-top: 0.197em; padding-bottom: 0.262em;\">x</span></span><span id=\"MJXc-Node-5838\" class=\"mjx-mi\"><span class=\"mjx-char MJXc-TeX-math-I\" style=\"padding-top: 0.391em; padding-bottom: 0.262em;\">t</span></span></span></span></span></span><span class=\"MJX_Assistive_MathML\" role=\"presentation\"><math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mstyle mathcolor=\"purple\"><mi>t</mi><mi>e</mi><mi>x</mi><mi>t</mi></mstyle></math></span></span><script type=\"math/tex\" id=\"MathJax-Element-292\">\\color{purple}{text}</script></span></td>\n<td style=\"text-align: center\">fuchsia</td>\n<td style=\"text-align: center\"><span class=\"math inline\"><span class=\"MathJax_Preview\" style=\"color: inherit;\"></span><span id=\"MathJax-Element-293-Frame\" class=\"mjx-chtml MathJax_CHTML\" tabindex=\"0\" style=\"font-size: 119%; position: relative;\" data-mathml=\"<math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;><mstyle mathcolor=&quot;fuchsia&quot;><mi>t</mi><mi>e</mi><mi>x</mi><mi>t</mi></mstyle></math>\" role=\"presentation\"><span id=\"MJXc-Node-5839\" class=\"mjx-math\" aria-hidden=\"true\"><span id=\"MJXc-Node-5840\" class=\"mjx-mrow\"><span id=\"MJXc-Node-5841\" class=\"mjx-mstyle\" style=\"color: fuchsia;\"><span id=\"MJXc-Node-5842\" class=\"mjx-mrow\"><span id=\"MJXc-Node-5843\" class=\"mjx-mi\"><span class=\"mjx-char MJXc-TeX-math-I\" style=\"padding-top: 0.391em; padding-bottom: 0.262em;\">t</span></span><span id=\"MJXc-Node-5844\" class=\"mjx-mi\"><span class=\"mjx-char MJXc-TeX-math-I\" style=\"padding-top: 0.197em; padding-bottom: 0.262em;\">e</span></span><span id=\"MJXc-Node-5845\" class=\"mjx-mi\"><span class=\"mjx-char MJXc-TeX-math-I\" style=\"padding-top: 0.197em; padding-bottom: 0.262em;\">x</span></span><span id=\"MJXc-Node-5846\" class=\"mjx-mi\"><span class=\"mjx-char MJXc-TeX-math-I\" style=\"padding-top: 0.391em; padding-bottom: 0.262em;\">t</span></span></span></span></span></span><span class=\"MJX_Assistive_MathML\" role=\"presentation\"><math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mstyle mathcolor=\"fuchsia\"><mi>t</mi><mi>e</mi><mi>x</mi><mi>t</mi></mstyle></math></span></span><script type=\"math/tex\" id=\"MathJax-Element-293\">\\color{fuchsia}{text}</script></span></td>\n</tr>\n</tbody>\n</table></div>", "| 输入   | 显示                   | 输入    | 显示                    |\n| -------- | ------------------------ | --------- | ------------------------- |\n| black  | $\\color{black}{text}$  | grey    | $\\color{grey}{text}$    |\n| silver | $\\color{silver}{text}$ | white   | $\\color{white}{text}$   |\n| maroon | $\\color{maroon}{text}$ | red     | $\\color{red}{text}$     |\n| yellow | $\\color{yellow}{text}$ | lime    | $\\color{lime}{text}$    |\n| olive  | $\\color{olive}{text}$  | green   | $\\color{green}{text}$   |\n| teal   | $\\color{teal}{text}$   | auqa    | $\\color{auqa}{text}$    |\n| blue   | $\\color{blue}{text}$   | navy    | $\\color{navy}{text}$    |\n| purple | $\\color{purple}{text}$ | fuchsia | $\\color{fuchsia}{text}$ |\n"},
	{"192", "<p><span class=\"MathJax_Preview\"></span><span class=\"mjx-chtml MJXc-display\"><span id=\"MathJax-Element-294-Frame\" class=\"mjx-chtml MathJax_CHTML\" tabindex=\"0\" data-mathml=\"<math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot; display=&quot;block&quot;><mtable columnalign=&quot;right right right right right right right right&quot; rowspacing=&quot;4pt&quot; columnspacing=&quot;1em&quot; rowlines=&quot;none none none&quot; columnlines=&quot;none none none none none none none&quot; frame=&quot;solid&quot;><mtr><mtd><mtext mathvariant=&quot;monospace&quot;>#000</mtext></mtd><mtd><mstyle mathcolor=&quot;#000&quot;><mi>t</mi><mi>e</mi><mi>x</mi><mi>t</mi></mstyle></mtd><mtd /><mtd /><mtd><mtext mathvariant=&quot;monospace&quot;>#00F</mtext></mtd><mtd><mstyle mathcolor=&quot;#00F&quot;><mi>t</mi><mi>e</mi><mi>x</mi><mi>t</mi></mstyle></mtd><mtd /><mtd /></mtr><mtr><mtd /><mtd /><mtd><mtext mathvariant=&quot;monospace&quot;>#0F0</mtext></mtd><mtd><mstyle mathcolor=&quot;#0F0&quot;><mi>t</mi><mi>e</mi><mi>x</mi><mi>t</mi></mstyle></mtd><mtd /><mtd /><mtd><mtext mathvariant=&quot;monospace&quot;>#0FF</mtext></mtd><mtd><mstyle mathcolor=&quot;#0FF&quot;><mi>t</mi><mi>e</mi><mi>x</mi><mi>t</mi></mstyle></mtd></mtr><mtr><mtd><mtext mathvariant=&quot;monospace&quot;>#F00</mtext></mtd><mtd><mstyle mathcolor=&quot;#F00&quot;><mi>t</mi><mi>e</mi><mi>x</mi><mi>t</mi></mstyle></mtd><mtd /><mtd /><mtd><mtext mathvariant=&quot;monospace&quot;>#F0F</mtext></mtd><mtd><mstyle mathcolor=&quot;#F0F&quot;><mi>t</mi><mi>e</mi><mi>x</mi><mi>t</mi></mstyle></mtd><mtd /><mtd /></mtr><mtr><mtd /><mtd /><mtd><mtext mathvariant=&quot;monospace&quot;>#FF0</mtext></mtd><mtd><mstyle mathcolor=&quot;#FF0&quot;><mi>t</mi><mi>e</mi><mi>x</mi><mi>t</mi></mstyle></mtd><mtd /><mtd /><mtd><mtext mathvariant=&quot;monospace&quot;>#FFF</mtext></mtd><mtd><mstyle mathcolor=&quot;#FFF&quot;><mi>t</mi><mi>e</mi><mi>x</mi><mi>t</mi></mstyle></mtd></mtr></mtable></math>\" role=\"presentation\"><span class=\"MJX_Assistive_MathML MJX_Assistive_MathML_Block\" role=\"presentation\"><math xmlns=\"http://www.w3.org/1998/Math/MathML\" display=\"block\"><mtable columnalign=\"right right right right right right right right\" rowspacing=\"4pt\" columnspacing=\"1em\" rowlines=\"none none none\" columnlines=\"none none none none none none none\"><mtr><mtd><mtext mathvariant=\"monospace\">#000</mtext></mtd><mtd><mstyle mathcolor=\"#000\"><mi>t</mi><mi>e</mi><mi>x</mi><mi>t</mi></mstyle></mtd><mtd></mtd><mtd></mtd><mtd><mtext mathvariant=\"monospace\">#00F</mtext></mtd><mtd><mstyle mathcolor=\"#00F\"><mi>t</mi><mi>e</mi><mi>x</mi><mi>t</mi></mstyle></mtd><mtd></mtd><mtd></mtd></mtr><mtr><mtd></mtd><mtd></mtd><mtd><mtext mathvariant=\"monospace\">#0F0</mtext></mtd><mtd><mstyle mathcolor=\"#0F0\"><mi>t</mi><mi>e</mi><mi>x</mi><mi>t</mi></mstyle></mtd><mtd></mtd><mtd></mtd><mtd><mtext mathvariant=\"monospace\">#0FF</mtext></mtd><mtd><mstyle mathcolor=\"#0FF\"><mi>t</mi><mi>e</mi><mi>x</mi><mi>t</mi></mstyle></mtd></mtr><mtr><mtd><mtext mathvariant=\"monospace\">#F00</mtext></mtd><mtd><mstyle mathcolor=\"#F00\"><mi>t</mi><mi>e</mi><mi>x</mi><mi>t</mi></mstyle></mtd><mtd></mtd><mtd></mtd><mtd><mtext mathvariant=\"monospace\">#F0F</mtext></mtd><mtd><mstyle mathcolor=\"#F0F\"><mi>t</mi><mi>e</mi><mi>x</mi><mi>t</mi></mstyle></mtd><mtd></mtd><mtd></mtd></mtr><mtr><mtd></mtd><mtd></mtd><mtd><mtext mathvariant=\"monospace\">#FF0</mtext></mtd><mtd><mstyle mathcolor=\"#FF0\"><mi>t</mi><mi>e</mi><mi>x</mi><mi>t</mi></mstyle></mtd><mtd></mtd><mtd></mtd><mtd><mtext mathvariant=\"monospace\">#FFF</mtext></mtd><mtd><mstyle mathcolor=\"#FFF\"><mi>t</mi><mi>e</mi><mi>x</mi><mi>t</mi></mstyle></mtd></mtr></mtable></math></span></span></span><script type=\"math/tex; mode=display\" id=\"MathJax-Element-294\">\\begin{array}{|rrrrrrrr|}\\hline\n\\verb+#000+ & \\color{#000}{text} & & &\n\\verb+#00F+ & \\color{#00F}{text} & & \\\\\n& & \\verb+#0F0+ & \\color{#0F0}{text} &\n& & \\verb+#0FF+ & \\color{#0FF}{text}\\\\\n\\verb+#F00+ & \\color{#F00}{text} & & &\n\\verb+#F0F+ & \\color{#F0F}{text} & & \\\\\n& & \\verb+#FF0+ & \\color{#FF0}{text} &\n& & \\verb+#FFF+ & \\color{#FFF}{text}\\\\\n\\hline\n\\end{array}\n    </script></p>", "$$\n\\begin{array}{|rrrrrrrr|}\\hline\n\\verb+#000+ & \\color{#000}{text} & & &\n\\verb+#00F+ & \\color{#00F}{text} & & \\\\\n& & \\verb+#0F0+ & \\color{#0F0}{text} &\n& & \\verb+#0FF+ & \\color{#0FF}{text}\\\\\n\\verb+#F00+ & \\color{#F00}{text} & & &\n\\verb+#F0F+ & \\color{#F0F}{text} & & \\\\\n& & \\verb+#FF0+ & \\color{#FF0}{text} &\n& & \\verb+#FFF+ & \\color{#FFF}{text}\\\\\n\\hline\n\\end{array}\n$$\n"},
	{"191", "<div class=\"math display\"><span class=\"MathJax_Preview\" style=\"color: inherit;\"></span><span class=\"mjx-chtml MJXc-display\" style=\"text-align: center;\"><span id=\"MathJax-Element-294-Frame\" class=\"mjx-chtml MathJax_CHTML\" tabindex=\"0\" style=\"font-size: 119%; text-align: center; position: relative;\" data-mathml=\"<math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot; display=&quot;block&quot;><mtable columnalign=&quot;right right right right right right right right&quot; rowspacing=&quot;4pt&quot; columnspacing=&quot;1em&quot; rowlines=&quot;none none none&quot; columnlines=&quot;none none none none none none none&quot; frame=&quot;solid&quot;><mtr><mtd><mtext mathvariant=&quot;monospace&quot;>#000</mtext></mtd><mtd><mstyle mathcolor=&quot;#000&quot;><mi>t</mi><mi>e</mi><mi>x</mi><mi>t</mi></mstyle></mtd><mtd /><mtd /><mtd><mtext mathvariant=&quot;monospace&quot;>#00F</mtext></mtd><mtd><mstyle mathcolor=&quot;#00F&quot;><mi>t</mi><mi>e</mi><mi>x</mi><mi>t</mi></mstyle></mtd><mtd /><mtd /></mtr><mtr><mtd /><mtd /><mtd><mtext mathvariant=&quot;monospace&quot;>#0F0</mtext></mtd><mtd><mstyle mathcolor=&quot;#0F0&quot;><mi>t</mi><mi>e</mi><mi>x</mi><mi>t</mi></mstyle></mtd><mtd /><mtd /><mtd><mtext mathvariant=&quot;monospace&quot;>#0FF</mtext></mtd><mtd><mstyle mathcolor=&quot;#0FF&quot;><mi>t</mi><mi>e</mi><mi>x</mi><mi>t</mi></mstyle></mtd></mtr><mtr><mtd><mtext mathvariant=&quot;monospace&quot;>#F00</mtext></mtd><mtd><mstyle mathcolor=&quot;#F00&quot;><mi>t</mi><mi>e</mi><mi>x</mi><mi>t</mi></mstyle></mtd><mtd /><mtd /><mtd><mtext mathvariant=&quot;monospace&quot;>#F0F</mtext></mtd><mtd><mstyle mathcolor=&quot;#F0F&quot;><mi>t</mi><mi>e</mi><mi>x</mi><mi>t</mi></mstyle></mtd><mtd /><mtd /></mtr><mtr><mtd /><mtd /><mtd><mtext mathvariant=&quot;monospace&quot;>#FF0</mtext></mtd><mtd><mstyle mathcolor=&quot;#FF0&quot;><mi>t</mi><mi>e</mi><mi>x</mi><mi>t</mi></mstyle></mtd><mtd /><mtd /><mtd><mtext mathvariant=&quot;monospace&quot;>#FFF</mtext></mtd><mtd><mstyle mathcolor=&quot;#FFF&quot;><mi>t</mi><mi>e</mi><mi>x</mi><mi>t</mi></mstyle></mtd></mtr></mtable></math>\" role=\"presentation\"><span id=\"MJXc-Node-5847\" class=\"mjx-math\" aria-hidden=\"true\"><span id=\"MJXc-Node-5848\" class=\"mjx-mrow\"><span id=\"MJXc-Node-5849\" class=\"mjx-mtable\" style=\"vertical-align: -2.624em;\"><span class=\"mjx-table\" style=\"border: 1.3px solid;\"><span id=\"MJXc-Node-5850\" class=\"mjx-mtr\" style=\"height: 1.421em;\"><span id=\"MJXc-Node-5851\" class=\"mjx-mtd\" style=\"padding: 0.221em 0.5em 0px 0.4em; text-align: right; width: 2.1em;\"><span id=\"MJXc-Node-5852\" class=\"mjx-mrow\" style=\"margin-top: -0.2em;\"><span id=\"MJXc-Node-5853\" class=\"mjx-mtext\"><span class=\"mjx-char MJXc-TeX-type-R\" style=\"padding-top: 0.423em; padding-bottom: 0.265em;\">#000</span></span><span class=\"mjx-strut\"></span></span></span><span id=\"MJXc-Node-5854\" class=\"mjx-mtd\" style=\"padding: 0.221em 0.5em 0px; text-align: right; width: 1.76em;\"><span id=\"MJXc-Node-5855\" class=\"mjx-mrow\" style=\"margin-top: -0.2em;\"><span id=\"MJXc-Node-5856\" class=\"mjx-mstyle\" style=\"color: rgb(0, 0, 0);\"><span id=\"MJXc-Node-5857\" class=\"mjx-mrow\"><span id=\"MJXc-Node-5858\" class=\"mjx-mi\"><span class=\"mjx-char MJXc-TeX-math-I\" style=\"padding-top: 0.423em; padding-bottom: 0.265em;\">t</span></span><span id=\"MJXc-Node-5859\" class=\"mjx-mi\"><span class=\"mjx-char MJXc-TeX-math-I\" style=\"padding-top: 0.213em; padding-bottom: 0.265em;\">e</span></span><span id=\"MJXc-Node-5860\" class=\"mjx-mi\"><span class=\"mjx-char MJXc-TeX-math-I\" style=\"padding-top: 0.213em; padding-bottom: 0.265em;\">x</span></span><span id=\"MJXc-Node-5861\" class=\"mjx-mi\"><span class=\"mjx-char MJXc-TeX-math-I\" style=\"padding-top: 0.423em; padding-bottom: 0.265em;\">t</span></span></span></span><span class=\"mjx-strut\"></span></span></span><span id=\"MJXc-Node-5862\" class=\"mjx-mtd\" style=\"padding: 0.221em 0.5em 0px; text-align: right; width: 2.1em;\"><span id=\"MJXc-Node-5863\" class=\"mjx-mrow\" style=\"margin-top: -0.2em;\"><span class=\"mjx-strut\"></span></span></span><span id=\"MJXc-Node-5864\" class=\"mjx-mtd\" style=\"padding: 0.221em 0.5em 0px; text-align: right; width: 1.76em;\"><span id=\"MJXc-Node-5865\" class=\"mjx-mrow\" style=\"margin-top: -0.2em;\"><span class=\"mjx-strut\"></span></span></span><span id=\"MJXc-Node-5866\" class=\"mjx-mtd\" style=\"padding: 0.221em 0.5em 0px; text-align: right; width: 2.1em;\"><span id=\"MJXc-Node-5867\" class=\"mjx-mrow\" style=\"margin-top: -0.2em;\"><span id=\"MJXc-Node-5868\" class=\"mjx-mtext\"><span class=\"mjx-char MJXc-TeX-type-R\" style=\"padding-top: 0.423em; padding-bottom: 0.265em;\">#00F</span></span><span class=\"mjx-strut\"></span></span></span><span id=\"MJXc-Node-5869\" class=\"mjx-mtd\" style=\"padding: 0.221em 0.5em 0px; text-align: right; width: 1.76em;\"><span id=\"MJXc-Node-5870\" class=\"mjx-mrow\" style=\"margin-top: -0.2em;\"><span id=\"MJXc-Node-5871\" class=\"mjx-mstyle\" style=\"color: rgb(0, 0, 255);\"><span id=\"MJXc-Node-5872\" class=\"mjx-mrow\"><span id=\"MJXc-Node-5873\" class=\"mjx-mi\"><span class=\"mjx-char MJXc-TeX-math-I\" style=\"padding-top: 0.423em; padding-bottom: 0.265em;\">t</span></span><span id=\"MJXc-Node-5874\" class=\"mjx-mi\"><span class=\"mjx-char MJXc-TeX-math-I\" style=\"padding-top: 0.213em; padding-bottom: 0.265em;\">e</span></span><span id=\"MJXc-Node-5875\" class=\"mjx-mi\"><span class=\"mjx-char MJXc-TeX-math-I\" style=\"padding-top: 0.213em; padding-bottom: 0.265em;\">x</span></span><span id=\"MJXc-Node-5876\" class=\"mjx-mi\"><span class=\"mjx-char MJXc-TeX-math-I\" style=\"padding-top: 0.423em; padding-bottom: 0.265em;\">t</span></span></span></span><span class=\"mjx-strut\"></span></span></span><span id=\"MJXc-Node-5877\" class=\"mjx-mtd\" style=\"padding: 0.221em 0.5em 0px; text-align: right; width: 2.1em;\"><span id=\"MJXc-Node-5878\" class=\"mjx-mrow\" style=\"margin-top: -0.2em;\"><span class=\"mjx-strut\"></span></span></span><span id=\"MJXc-Node-5879\" class=\"mjx-mtd\" style=\"padding: 0.221em 0.4em 0px 0.5em; text-align: right; width: 1.76em;\"><span id=\"MJXc-Node-5880\" class=\"mjx-mrow\" style=\"margin-top: -0.2em;\"><span class=\"mjx-strut\"></span></span></span></span><span id=\"MJXc-Node-5881\" class=\"mjx-mtr\" style=\"height: 1.4em;\"><span id=\"MJXc-Node-5882\" class=\"mjx-mtd\" style=\"padding: 0.2em 0.5em 0px 0.4em; text-align: right;\"><span id=\"MJXc-Node-5883\" class=\"mjx-mrow\" style=\"margin-top: -0.2em;\"><span class=\"mjx-strut\"></span></span></span><span id=\"MJXc-Node-5884\" class=\"mjx-mtd\" style=\"padding: 0.2em 0.5em 0px; text-align: right;\"><span id=\"MJXc-Node-5885\" class=\"mjx-mrow\" style=\"margin-top: -0.2em;\"><span class=\"mjx-strut\"></span></span></span><span id=\"MJXc-Node-5886\" class=\"mjx-mtd\" style=\"padding: 0.2em 0.5em 0px; text-align: right;\"><span id=\"MJXc-Node-5887\" class=\"mjx-mrow\" style=\"margin-top: -0.2em;\"><span id=\"MJXc-Node-5888\" class=\"mjx-mtext\"><span class=\"mjx-char MJXc-TeX-type-R\" style=\"padding-top: 0.423em; padding-bottom: 0.265em;\">#0F0</span></span><span class=\"mjx-strut\"></span></span></span><span id=\"MJXc-Node-5889\" class=\"mjx-mtd\" style=\"padding: 0.2em 0.5em 0px; text-align: right;\"><span id=\"MJXc-Node-5890\" class=\"mjx-mrow\" style=\"margin-top: -0.2em;\"><span id=\"MJXc-Node-5891\" class=\"mjx-mstyle\" style=\"color: rgb(0, 255, 0);\"><span id=\"MJXc-Node-5892\" class=\"mjx-mrow\"><span id=\"MJXc-Node-5893\" class=\"mjx-mi\"><span class=\"mjx-char MJXc-TeX-math-I\" style=\"padding-top: 0.423em; padding-bottom: 0.265em;\">t</span></span><span id=\"MJXc-Node-5894\" class=\"mjx-mi\"><span class=\"mjx-char MJXc-TeX-math-I\" style=\"padding-top: 0.213em; padding-bottom: 0.265em;\">e</span></span><span id=\"MJXc-Node-5895\" class=\"mjx-mi\"><span class=\"mjx-char MJXc-TeX-math-I\" style=\"padding-top: 0.213em; padding-bottom: 0.265em;\">x</span></span><span id=\"MJXc-Node-5896\" class=\"mjx-mi\"><span class=\"mjx-char MJXc-TeX-math-I\" style=\"padding-top: 0.423em; padding-bottom: 0.265em;\">t</span></span></span></span><span class=\"mjx-strut\"></span></span></span><span id=\"MJXc-Node-5897\" class=\"mjx-mtd\" style=\"padding: 0.2em 0.5em 0px; text-align: right;\"><span id=\"MJXc-Node-5898\" class=\"mjx-mrow\" style=\"margin-top: -0.2em;\"><span class=\"mjx-strut\"></span></span></span><span id=\"MJXc-Node-5899\" class=\"mjx-mtd\" style=\"padding: 0.2em 0.5em 0px; text-align: right;\"><span id=\"MJXc-Node-5900\" class=\"mjx-mrow\" style=\"margin-top: -0.2em;\"><span class=\"mjx-strut\"></span></span></span><span id=\"MJXc-Node-5901\" class=\"mjx-mtd\" style=\"padding: 0.2em 0.5em 0px; text-align: right;\"><span id=\"MJXc-Node-5902\" class=\"mjx-mrow\" style=\"margin-top: -0.2em;\"><span id=\"MJXc-Node-5903\" class=\"mjx-mtext\"><span class=\"mjx-char MJXc-TeX-type-R\" style=\"padding-top: 0.423em; padding-bottom: 0.265em;\">#0FF</span></span><span class=\"mjx-strut\"></span></span></span><span id=\"MJXc-Node-5904\" class=\"mjx-mtd\" style=\"padding: 0.2em 0.4em 0px 0.5em; text-align: right;\"><span id=\"MJXc-Node-5905\" class=\"mjx-mrow\" style=\"margin-top: -0.2em;\"><span id=\"MJXc-Node-5906\" class=\"mjx-mstyle\" style=\"color: rgb(0, 255, 255);\"><span id=\"MJXc-Node-5907\" class=\"mjx-mrow\"><span id=\"MJXc-Node-5908\" class=\"mjx-mi\"><span class=\"mjx-char MJXc-TeX-math-I\" style=\"padding-top: 0.423em; padding-bottom: 0.265em;\">t</span></span><span id=\"MJXc-Node-5909\" class=\"mjx-mi\"><span class=\"mjx-char MJXc-TeX-math-I\" style=\"padding-top: 0.213em; padding-bottom: 0.265em;\">e</span></span><span id=\"MJXc-Node-5910\" class=\"mjx-mi\"><span class=\"mjx-char MJXc-TeX-math-I\" style=\"padding-top: 0.213em; padding-bottom: 0.265em;\">x</span></span><span id=\"MJXc-Node-5911\" class=\"mjx-mi\"><span class=\"mjx-char MJXc-TeX-math-I\" style=\"padding-top: 0.423em; padding-bottom: 0.265em;\">t</span></span></span></span><span class=\"mjx-strut\"></span></span></span></span><span id=\"MJXc-Node-5912\" class=\"mjx-mtr\" style=\"height: 1.4em;\"><span id=\"MJXc-Node-5913\" class=\"mjx-mtd\" style=\"padding: 0.2em 0.5em 0px 0.4em; text-align: right;\"><span id=\"MJXc-Node-5914\" class=\"mjx-mrow\" style=\"margin-top: -0.2em;\"><span id=\"MJXc-Node-5915\" class=\"mjx-mtext\"><span class=\"mjx-char MJXc-TeX-type-R\" style=\"padding-top: 0.423em; padding-bottom: 0.265em;\">#F00</span></span><span class=\"mjx-strut\"></span></span></span><span id=\"MJXc-Node-5916\" class=\"mjx-mtd\" style=\"padding: 0.2em 0.5em 0px; text-align: right;\"><span id=\"MJXc-Node-5917\" class=\"mjx-mrow\" style=\"margin-top: -0.2em;\"><span id=\"MJXc-Node-5918\" class=\"mjx-mstyle\" style=\"color: rgb(255, 0, 0);\"><span id=\"MJXc-Node-5919\" class=\"mjx-mrow\"><span id=\"MJXc-Node-5920\" class=\"mjx-mi\"><span class=\"mjx-char MJXc-TeX-math-I\" style=\"padding-top: 0.423em; padding-bottom: 0.265em;\">t</span></span><span id=\"MJXc-Node-5921\" class=\"mjx-mi\"><span class=\"mjx-char MJXc-TeX-math-I\" style=\"padding-top: 0.213em; padding-bottom: 0.265em;\">e</span></span><span id=\"MJXc-Node-5922\" class=\"mjx-mi\"><span class=\"mjx-char MJXc-TeX-math-I\" style=\"padding-top: 0.213em; padding-bottom: 0.265em;\">x</span></span><span id=\"MJXc-Node-5923\" class=\"mjx-mi\"><span class=\"mjx-char MJXc-TeX-math-I\" style=\"padding-top: 0.423em; padding-bottom: 0.265em;\">t</span></span></span></span><span class=\"mjx-strut\"></span></span></span><span id=\"MJXc-Node-5924\" class=\"mjx-mtd\" style=\"padding: 0.2em 0.5em 0px; text-align: right;\"><span id=\"MJXc-Node-5925\" class=\"mjx-mrow\" style=\"margin-top: -0.2em;\"><span class=\"mjx-strut\"></span></span></span><span id=\"MJXc-Node-5926\" class=\"mjx-mtd\" style=\"padding: 0.2em 0.5em 0px; text-align: right;\"><span id=\"MJXc-Node-5927\" class=\"mjx-mrow\" style=\"margin-top: -0.2em;\"><span class=\"mjx-strut\"></span></span></span><span id=\"MJXc-Node-5928\" class=\"mjx-mtd\" style=\"padding: 0.2em 0.5em 0px; text-align: right;\"><span id=\"MJXc-Node-5929\" class=\"mjx-mrow\" style=\"margin-top: -0.2em;\"><span id=\"MJXc-Node-5930\" class=\"mjx-mtext\"><span class=\"mjx-char MJXc-TeX-type-R\" style=\"padding-top: 0.423em; padding-bottom: 0.265em;\">#F0F</span></span><span class=\"mjx-strut\"></span></span></span><span id=\"MJXc-Node-5931\" class=\"mjx-mtd\" style=\"padding: 0.2em 0.5em 0px; text-align: right;\"><span id=\"MJXc-Node-5932\" class=\"mjx-mrow\" style=\"margin-top: -0.2em;\"><span id=\"MJXc-Node-5933\" class=\"mjx-mstyle\" style=\"color: rgb(255, 0, 255);\"><span id=\"MJXc-Node-5934\" class=\"mjx-mrow\"><span id=\"MJXc-Node-5935\" class=\"mjx-mi\"><span class=\"mjx-char MJXc-TeX-math-I\" style=\"padding-top: 0.423em; padding-bottom: 0.265em;\">t</span></span><span id=\"MJXc-Node-5936\" class=\"mjx-mi\"><span class=\"mjx-char MJXc-TeX-math-I\" style=\"padding-top: 0.213em; padding-bottom: 0.265em;\">e</span></span><span id=\"MJXc-Node-5937\" class=\"mjx-mi\"><span class=\"mjx-char MJXc-TeX-math-I\" style=\"padding-top: 0.213em; padding-bottom: 0.265em;\">x</span></span><span id=\"MJXc-Node-5938\" class=\"mjx-mi\"><span class=\"mjx-char MJXc-TeX-math-I\" style=\"padding-top: 0.423em; padding-bottom: 0.265em;\">t</span></span></span></span><span class=\"mjx-strut\"></span></span></span><span id=\"MJXc-Node-5939\" class=\"mjx-mtd\" style=\"padding: 0.2em 0.5em 0px; text-align: right;\"><span id=\"MJXc-Node-5940\" class=\"mjx-mrow\" style=\"margin-top: -0.2em;\"><span class=\"mjx-strut\"></span></span></span><span id=\"MJXc-Node-5941\" class=\"mjx-mtd\" style=\"padding: 0.2em 0.4em 0px 0.5em; text-align: right;\"><span id=\"MJXc-Node-5942\" class=\"mjx-mrow\" style=\"margin-top: -0.2em;\"><span class=\"mjx-strut\"></span></span></span></span><span id=\"MJXc-Node-5943\" class=\"mjx-mtr\" style=\"height: 1.421em;\"><span id=\"MJXc-Node-5944\" class=\"mjx-mtd\" style=\"padding: 0.2em 0.5em 0px 0.4em; text-align: right;\"><span id=\"MJXc-Node-5945\" class=\"mjx-mrow\" style=\"margin-top: -0.2em;\"><span class=\"mjx-strut\"></span></span></span><span id=\"MJXc-Node-5946\" class=\"mjx-mtd\" style=\"padding: 0.2em 0.5em 0px; text-align: right;\"><span id=\"MJXc-Node-5947\" class=\"mjx-mrow\" style=\"margin-top: -0.2em;\"><span class=\"mjx-strut\"></span></span></span><span id=\"MJXc-Node-5948\" class=\"mjx-mtd\" style=\"padding: 0.2em 0.5em 0px; text-align: right;\"><span id=\"MJXc-Node-5949\" class=\"mjx-mrow\" style=\"margin-top: -0.2em;\"><span id=\"MJXc-Node-5950\" class=\"mjx-mtext\"><span class=\"mjx-char MJXc-TeX-type-R\" style=\"padding-top: 0.423em; padding-bottom: 0.265em;\">#FF0</span></span><span class=\"mjx-strut\"></span></span></span><span id=\"MJXc-Node-5951\" class=\"mjx-mtd\" style=\"padding: 0.2em 0.5em 0px; text-align: right;\"><span id=\"MJXc-Node-5952\" class=\"mjx-mrow\" style=\"margin-top: -0.2em;\"><span id=\"MJXc-Node-5953\" class=\"mjx-mstyle\" style=\"color: rgb(255, 255, 0);\"><span id=\"MJXc-Node-5954\" class=\"mjx-mrow\"><span id=\"MJXc-Node-5955\" class=\"mjx-mi\"><span class=\"mjx-char MJXc-TeX-math-I\" style=\"padding-top: 0.423em; padding-bottom: 0.265em;\">t</span></span><span id=\"MJXc-Node-5956\" class=\"mjx-mi\"><span class=\"mjx-char MJXc-TeX-math-I\" style=\"padding-top: 0.213em; padding-bottom: 0.265em;\">e</span></span><span id=\"MJXc-Node-5957\" class=\"mjx-mi\"><span class=\"mjx-char MJXc-TeX-math-I\" style=\"padding-top: 0.213em; padding-bottom: 0.265em;\">x</span></span><span id=\"MJXc-Node-5958\" class=\"mjx-mi\"><span class=\"mjx-char MJXc-TeX-math-I\" style=\"padding-top: 0.423em; padding-bottom: 0.265em;\">t</span></span></span></span><span class=\"mjx-strut\"></span></span></span><span id=\"MJXc-Node-5959\" class=\"mjx-mtd\" style=\"padding: 0.2em 0.5em 0px; text-align: right;\"><span id=\"MJXc-Node-5960\" class=\"mjx-mrow\" style=\"margin-top: -0.2em;\"><span class=\"mjx-strut\"></span></span></span><span id=\"MJXc-Node-5961\" class=\"mjx-mtd\" style=\"padding: 0.2em 0.5em 0px; text-align: right;\"><span id=\"MJXc-Node-5962\" class=\"mjx-mrow\" style=\"margin-top: -0.2em;\"><span class=\"mjx-strut\"></span></span></span><span id=\"MJXc-Node-5963\" class=\"mjx-mtd\" style=\"padding: 0.2em 0.5em 0px; text-align: right;\"><span id=\"MJXc-Node-5964\" class=\"mjx-mrow\" style=\"margin-top: -0.2em;\"><span id=\"MJXc-Node-5965\" class=\"mjx-mtext\"><span class=\"mjx-char MJXc-TeX-type-R\" style=\"padding-top: 0.423em; padding-bottom: 0.265em;\">#FFF</span></span><span class=\"mjx-strut\"></span></span></span><span id=\"MJXc-Node-5966\" class=\"mjx-mtd\" style=\"padding: 0.2em 0.4em 0px 0.5em; text-align: right;\"><span id=\"MJXc-Node-5967\" class=\"mjx-mrow\" style=\"margin-top: -0.2em;\"><span id=\"MJXc-Node-5968\" class=\"mjx-mstyle\" style=\"color: rgb(255, 255, 255);\"><span id=\"MJXc-Node-5969\" class=\"mjx-mrow\"><span id=\"MJXc-Node-5970\" class=\"mjx-mi\"><span class=\"mjx-char MJXc-TeX-math-I\" style=\"padding-top: 0.423em; padding-bottom: 0.265em;\">t</span></span><span id=\"MJXc-Node-5971\" class=\"mjx-mi\"><span class=\"mjx-char MJXc-TeX-math-I\" style=\"padding-top: 0.213em; padding-bottom: 0.265em;\">e</span></span><span id=\"MJXc-Node-5972\" class=\"mjx-mi\"><span class=\"mjx-char MJXc-TeX-math-I\" style=\"padding-top: 0.213em; padding-bottom: 0.265em;\">x</span></span><span id=\"MJXc-Node-5973\" class=\"mjx-mi\"><span class=\"mjx-char MJXc-TeX-math-I\" style=\"padding-top: 0.423em; padding-bottom: 0.265em;\">t</span></span></span></span><span class=\"mjx-strut\"></span></span></span></span></span></span></span></span><span class=\"MJX_Assistive_MathML MJX_Assistive_MathML_Block\" role=\"presentation\"><math xmlns=\"http://www.w3.org/1998/Math/MathML\" display=\"block\"><mtable columnalign=\"right right right right right right right right\" rowspacing=\"4pt\" columnspacing=\"1em\" rowlines=\"none none none\" columnlines=\"none none none none none none none\" frame=\"solid\"><mtr><mtd><mtext mathvariant=\"monospace\">#000</mtext></mtd><mtd><mstyle mathcolor=\"#000\"><mi>t</mi><mi>e</mi><mi>x</mi><mi>t</mi></mstyle></mtd><mtd></mtd><mtd></mtd><mtd><mtext mathvariant=\"monospace\">#00F</mtext></mtd><mtd><mstyle mathcolor=\"#00F\"><mi>t</mi><mi>e</mi><mi>x</mi><mi>t</mi></mstyle></mtd><mtd></mtd><mtd></mtd></mtr><mtr><mtd></mtd><mtd></mtd><mtd><mtext mathvariant=\"monospace\">#0F0</mtext></mtd><mtd><mstyle mathcolor=\"#0F0\"><mi>t</mi><mi>e</mi><mi>x</mi><mi>t</mi></mstyle></mtd><mtd></mtd><mtd></mtd><mtd><mtext mathvariant=\"monospace\">#0FF</mtext></mtd><mtd><mstyle mathcolor=\"#0FF\"><mi>t</mi><mi>e</mi><mi>x</mi><mi>t</mi></mstyle></mtd></mtr><mtr><mtd><mtext mathvariant=\"monospace\">#F00</mtext></mtd><mtd><mstyle mathcolor=\"#F00\"><mi>t</mi><mi>e</mi><mi>x</mi><mi>t</mi></mstyle></mtd><mtd></mtd><mtd></mtd><mtd><mtext mathvariant=\"monospace\">#F0F</mtext></mtd><mtd><mstyle mathcolor=\"#F0F\"><mi>t</mi><mi>e</mi><mi>x</mi><mi>t</mi></mstyle></mtd><mtd></mtd><mtd></mtd></mtr><mtr><mtd></mtd><mtd></mtd><mtd><mtext mathvariant=\"monospace\">#FF0</mtext></mtd><mtd><mstyle mathcolor=\"#FF0\"><mi>t</mi><mi>e</mi><mi>x</mi><mi>t</mi></mstyle></mtd><mtd></mtd><mtd></mtd><mtd><mtext mathvariant=\"monospace\">#FFF</mtext></mtd><mtd><mstyle mathcolor=\"#FFF\"><mi>t</mi><mi>e</mi><mi>x</mi><mi>t</mi></mstyle></mtd></mtr></mtable></math></span></span></span><script type=\"math/tex; mode=display\" id=\"MathJax-Element-294\">\\begin{array}{|rrrrrrrr|}\\hline\n\\verb+#000+ & \\color{#000}{text} & & &\n\\verb+#00F+ & \\color{#00F}{text} & & \\\\\n& & \\verb+#0F0+ & \\color{#0F0}{text} &\n& & \\verb+#0FF+ & \\color{#0FF}{text}\\\\\n\\verb+#F00+ & \\color{#F00}{text} & & &\n\\verb+#F0F+ & \\color{#F0F}{text} & & \\\\\n& & \\verb+#FF0+ & \\color{#FF0}{text} &\n& & \\verb+#FFF+ & \\color{#FFF}{text}\\\\\n\\hline\n\\end{array}\n</script></div>", "$$\n\\begin{array}{|rrrrrrrr|}\\hline\n\\verb+#000+ & \\color{#000}{text} & & &\n\\verb+#00F+ & \\color{#00F}{text} & & \\\\\n& & \\verb+#0F0+ & \\color{#0F0}{text} &\n& & \\verb+#0FF+ & \\color{#0FF}{text}\\\\\n\\verb+#F00+ & \\color{#F00}{text} & & &\n\\verb+#F0F+ & \\color{#F0F}{text} & & \\\\\n& & \\verb+#FF0+ & \\color{#FF0}{text} &\n& & \\verb+#FFF+ & \\color{#FFF}{text}\\\\\n\\hline\n\\end{array}\n$$\n"},
	{"190", "<div class=\"math display\"><span class=\"MathJax_Preview\" style=\"color: inherit;\"></span><span class=\"mjx-chtml MJXc-display\" style=\"text-align: center;\"><span id=\"MathJax-Element-151-Frame\" class=\"mjx-chtml MathJax_CHTML\" tabindex=\"0\" style=\"font-size: 119%; text-align: center; position: relative;\" data-mathml=\"<math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot; display=&quot;block&quot;><mtable columnalign=&quot;center center&quot; rowspacing=&quot;4pt&quot; columnspacing=&quot;1em&quot; rowlines=&quot;solid none&quot;><mtr><mtd><mrow class=&quot;MJX-TeXAtom-ORD&quot;><mi mathvariant=&quot;normal&quot;>B</mi><mi mathvariant=&quot;normal&quot;>a</mi><mi mathvariant=&quot;normal&quot;>d</mi></mrow></mtd><mtd><mrow class=&quot;MJX-TeXAtom-ORD&quot;><mi mathvariant=&quot;normal&quot;>B</mi><mi mathvariant=&quot;normal&quot;>e</mi><mi mathvariant=&quot;normal&quot;>t</mi><mi mathvariant=&quot;normal&quot;>t</mi><mi mathvariant=&quot;normal&quot;>e</mi><mi mathvariant=&quot;normal&quot;>r</mi></mrow></mtd></mtr><mtr><mtd /></mtr><mtr><mtd><msup><mi>e</mi><mrow class=&quot;MJX-TeXAtom-ORD&quot;><mi>i</mi><mfrac><mi>&amp;#x03C0;</mi><mn>2</mn></mfrac></mrow></msup><mspace width=&quot;1em&quot; /><msup><mi>e</mi><mrow class=&quot;MJX-TeXAtom-ORD&quot;><mfrac><mrow><mi>i</mi><mi>&amp;#x03C0;</mi></mrow><mn>2</mn></mfrac></mrow></msup></mtd><mtd><msup><mi>e</mi><mrow class=&quot;MJX-TeXAtom-ORD&quot;><mi>i</mi><mi>&amp;#x03C0;</mi><mrow class=&quot;MJX-TeXAtom-ORD&quot;><mo>/</mo></mrow><mn>2</mn></mrow></msup></mtd></mtr><mtr><mtd><msubsup><mo>&amp;#x222B;</mo><mrow class=&quot;MJX-TeXAtom-ORD&quot;><mo>&amp;#x2212;</mo><mfrac><mi>&amp;#x03C0;</mi><mn>2</mn></mfrac></mrow><mfrac><mi>&amp;#x03C0;</mi><mn>2</mn></mfrac></msubsup><mi>sin</mi><mo>&amp;#x2061;</mo><mi>x</mi><mspace width=&quot;thinmathspace&quot; /><mi>d</mi><mi>x</mi></mtd><mtd><msubsup><mo>&amp;#x222B;</mo><mrow class=&quot;MJX-TeXAtom-ORD&quot;><mo>&amp;#x2212;</mo><mi>&amp;#x03C0;</mi><mrow class=&quot;MJX-TeXAtom-ORD&quot;><mo>/</mo></mrow><mn>2</mn></mrow><mrow class=&quot;MJX-TeXAtom-ORD&quot;><mi>&amp;#x03C0;</mi><mrow class=&quot;MJX-TeXAtom-ORD&quot;><mo>/</mo></mrow><mn>2</mn></mrow></msubsup><mi>sin</mi><mo>&amp;#x2061;</mo><mi>x</mi><mspace width=&quot;thinmathspace&quot; /><mi>d</mi><mi>x</mi></mtd></mtr></mtable></math>\" role=\"presentation\"><span id=\"MJXc-Node-2915\" class=\"mjx-math\" aria-hidden=\"true\"><span id=\"MJXc-Node-2916\" class=\"mjx-mrow\"><span id=\"MJXc-Node-2917\" class=\"mjx-mtable\" style=\"vertical-align: -3.169em; padding: 0px 0.167em;\"><span class=\"mjx-table\"><span id=\"MJXc-Node-2918\" class=\"mjx-mtr\" style=\"height: 1.421em;\"><span id=\"MJXc-Node-2919\" class=\"mjx-mtd\" style=\"padding: 0.221em 0.5em 0px 0.4em; border-bottom: 1.3px solid; width: 5.009em;\"><span id=\"MJXc-Node-2920\" class=\"mjx-mrow\" style=\"margin-top: -0.2em;\"><span id=\"MJXc-Node-2921\" class=\"mjx-texatom\"><span id=\"MJXc-Node-2922\" class=\"mjx-mrow\"><span id=\"MJXc-Node-2923\" class=\"mjx-mi\"><span class=\"mjx-char MJXc-TeX-main-R\" style=\"padding-top: 0.423em; padding-bottom: 0.318em;\">B</span></span><span id=\"MJXc-Node-2924\" class=\"mjx-mi\"><span class=\"mjx-char MJXc-TeX-main-R\" style=\"padding-top: 0.16em; padding-bottom: 0.37em;\">a</span></span><span id=\"MJXc-Node-2925\" class=\"mjx-mi\"><span class=\"mjx-char MJXc-TeX-main-R\" style=\"padding-top: 0.423em; padding-bottom: 0.37em;\">d</span></span></span></span><span class=\"mjx-strut\"></span></span></span><span id=\"MJXc-Node-2926\" class=\"mjx-mtd\" style=\"padding: 0.221em 0.4em 0px 0.5em; border-bottom: 1.3px solid; width: 5.565em;\"><span id=\"MJXc-Node-2927\" class=\"mjx-mrow\" style=\"margin-top: -0.2em;\"><span id=\"MJXc-Node-2928\" class=\"mjx-texatom\"><span id=\"MJXc-Node-2929\" class=\"mjx-mrow\"><span id=\"MJXc-Node-2930\" class=\"mjx-mi\"><span class=\"mjx-char MJXc-TeX-main-R\" style=\"padding-top: 0.423em; padding-bottom: 0.318em;\">B</span></span><span id=\"MJXc-Node-2931\" class=\"mjx-mi\"><span class=\"mjx-char MJXc-TeX-main-R\" style=\"padding-top: 0.16em; padding-bottom: 0.37em;\">e</span></span><span id=\"MJXc-Node-2932\" class=\"mjx-mi\"><span class=\"mjx-char MJXc-TeX-main-R\" style=\"padding-top: 0.318em; padding-bottom: 0.37em;\">t</span></span><span id=\"MJXc-Node-2933\" class=\"mjx-mi\"><span class=\"mjx-char MJXc-TeX-main-R\" style=\"padding-top: 0.318em; padding-bottom: 0.37em;\">t</span></span><span id=\"MJXc-Node-2934\" class=\"mjx-mi\"><span class=\"mjx-char MJXc-TeX-main-R\" style=\"padding-top: 0.16em; padding-bottom: 0.37em;\">e</span></span><span id=\"MJXc-Node-2935\" class=\"mjx-mi\"><span class=\"mjx-char MJXc-TeX-main-R\" style=\"padding-top: 0.16em; padding-bottom: 0.318em;\">r</span></span></span></span><span class=\"mjx-strut\"></span></span></span></span><span id=\"MJXc-Node-2936\" class=\"mjx-mtr\" style=\"height: 1.4em;\"><span id=\"MJXc-Node-2937\" class=\"mjx-mtd\" style=\"padding: 0.2em 0.5em 0px 0.4em;\"><span id=\"MJXc-Node-2938\" class=\"mjx-mrow\" style=\"margin-top: -0.2em;\"><span class=\"mjx-strut\"></span></span></span><span class=\"mjx-mtd\" style=\"padding: 0.2em 0.4em 0px 0.5em;\"><span style=\"margin-top: -0.2em;\"></span></span></span><span id=\"MJXc-Node-2939\" class=\"mjx-mtr\" style=\"height: 1.689em;\"><span id=\"MJXc-Node-2940\" class=\"mjx-mtd\" style=\"padding: 0.2em 0.5em 0px 0.4em;\"><span id=\"MJXc-Node-2941\" class=\"mjx-mrow\"><span id=\"MJXc-Node-2942\" class=\"mjx-msubsup\"><span class=\"mjx-base\"><span id=\"MJXc-Node-2943\" class=\"mjx-mi\"><span class=\"mjx-char MJXc-TeX-math-I\" style=\"padding-top: 0.213em; padding-bottom: 0.265em;\">e</span></span></span><span class=\"mjx-sup\" style=\"font-size: 70.7%; vertical-align: 0.596em; padding-left: 0px; padding-right: 0.071em;\"><span id=\"MJXc-Node-2944\" class=\"mjx-texatom\" style=\"\"><span id=\"MJXc-Node-2945\" class=\"mjx-mrow\"><span id=\"MJXc-Node-2946\" class=\"mjx-mi\"><span class=\"mjx-char MJXc-TeX-math-I\" style=\"padding-top: 0.423em; padding-bottom: 0.265em;\">i</span></span><span id=\"MJXc-Node-2947\" class=\"mjx-mfrac\"><span class=\"mjx-box MJXc-stacked\" style=\"width: 0.547em; padding: 0px 0.12em;\"><span class=\"mjx-numerator\" style=\"font-size: 70.7%; width: 0.773em; top: -1.105em;\"><span id=\"MJXc-Node-2948\" class=\"mjx-mi\" style=\"\"><span class=\"mjx-char MJXc-TeX-math-I\" style=\"padding-top: 0.213em; padding-bottom: 0.265em; padding-right: 0.003em;\">π</span></span></span><span class=\"mjx-denominator\" style=\"font-size: 70.7%; width: 0.773em; bottom: -0.622em;\"><span id=\"MJXc-Node-2949\" class=\"mjx-mn\" style=\"\"><span class=\"mjx-char MJXc-TeX-main-R\" style=\"padding-top: 0.37em; padding-bottom: 0.318em;\">2</span></span></span><span class=\"mjx-line\" style=\"border-bottom: 1.1px solid; top: -0.292em; width: 0.547em;\"></span></span><span class=\"mjx-vsize\" style=\"height: 1.221em; vertical-align: -0.44em;\"></span></span></span></span></span></span><span id=\"MJXc-Node-2950\" class=\"mjx-mspace\" style=\"width: 1em; height: 0px;\"></span><span id=\"MJXc-Node-2951\" class=\"mjx-msubsup\"><span class=\"mjx-base\"><span id=\"MJXc-Node-2952\" class=\"mjx-mi\"><span class=\"mjx-char MJXc-TeX-math-I\" style=\"padding-top: 0.213em; padding-bottom: 0.265em;\">e</span></span></span><span class=\"mjx-sup\" style=\"font-size: 70.7%; vertical-align: 0.596em; padding-left: 0px; padding-right: 0.071em;\"><span id=\"MJXc-Node-2953\" class=\"mjx-texatom\" style=\"\"><span id=\"MJXc-Node-2954\" class=\"mjx-mrow\"><span id=\"MJXc-Node-2955\" class=\"mjx-mfrac\"><span class=\"mjx-box MJXc-stacked\" style=\"width: 0.791em; padding: 0px 0.12em;\"><span class=\"mjx-numerator\" style=\"font-size: 70.7%; width: 1.118em; top: -1.335em;\"><span id=\"MJXc-Node-2956\" class=\"mjx-mrow\" style=\"\"><span id=\"MJXc-Node-2957\" class=\"mjx-mi\"><span class=\"mjx-char MJXc-TeX-math-I\" style=\"padding-top: 0.423em; padding-bottom: 0.265em;\">i</span></span><span id=\"MJXc-Node-2958\" class=\"mjx-mi\"><span class=\"mjx-char MJXc-TeX-math-I\" style=\"padding-top: 0.213em; padding-bottom: 0.265em; padding-right: 0.003em;\">π</span></span></span></span><span class=\"mjx-denominator\" style=\"font-size: 70.7%; width: 1.118em; bottom: -0.622em;\"><span id=\"MJXc-Node-2959\" class=\"mjx-mn\" style=\"\"><span class=\"mjx-char MJXc-TeX-main-R\" style=\"padding-top: 0.37em; padding-bottom: 0.318em;\">2</span></span></span><span class=\"mjx-line\" style=\"border-bottom: 1.1px solid; top: -0.292em; width: 0.791em;\"></span></span><span class=\"mjx-vsize\" style=\"height: 1.383em; vertical-align: -0.44em;\"></span></span></span></span></span></span><span class=\"mjx-strut\"></span></span></span><span id=\"MJXc-Node-2960\" class=\"mjx-mtd\" style=\"padding: 0.2em 0.4em 0px 0.5em;\"><span id=\"MJXc-Node-2961\" class=\"mjx-mrow\" style=\"margin-top: 0.089em;\"><span id=\"MJXc-Node-2962\" class=\"mjx-msubsup\"><span class=\"mjx-base\"><span id=\"MJXc-Node-2963\" class=\"mjx-mi\"><span class=\"mjx-char MJXc-TeX-math-I\" style=\"padding-top: 0.213em; padding-bottom: 0.265em;\">e</span></span></span><span class=\"mjx-sup\" style=\"font-size: 70.7%; vertical-align: 0.513em; padding-left: 0px; padding-right: 0.071em;\"><span id=\"MJXc-Node-2964\" class=\"mjx-texatom\" style=\"\"><span id=\"MJXc-Node-2965\" class=\"mjx-mrow\"><span id=\"MJXc-Node-2966\" class=\"mjx-mi\"><span class=\"mjx-char MJXc-TeX-math-I\" style=\"padding-top: 0.423em; padding-bottom: 0.265em;\">i</span></span><span id=\"MJXc-Node-2967\" class=\"mjx-mi\"><span class=\"mjx-char MJXc-TeX-math-I\" style=\"padding-top: 0.213em; padding-bottom: 0.265em; padding-right: 0.003em;\">π</span></span><span id=\"MJXc-Node-2968\" class=\"mjx-texatom\"><span id=\"MJXc-Node-2969\" class=\"mjx-mrow\"><span id=\"MJXc-Node-2970\" class=\"mjx-mo\"><span class=\"mjx-char MJXc-TeX-main-R\" style=\"padding-top: 0.475em; padding-bottom: 0.58em;\">/</span></span></span></span><span id=\"MJXc-Node-2971\" class=\"mjx-mn\"><span class=\"mjx-char MJXc-TeX-main-R\" style=\"padding-top: 0.37em; padding-bottom: 0.318em;\">2</span></span></span></span></span></span><span class=\"mjx-strut\"></span></span></span></span><span id=\"MJXc-Node-2972\" class=\"mjx-mtr\" style=\"height: 2.328em;\"><span id=\"MJXc-Node-2973\" class=\"mjx-mtd\" style=\"padding: 0.2em 0.5em 0px 0.4em;\"><span id=\"MJXc-Node-2974\" class=\"mjx-mrow\"><span id=\"MJXc-Node-2975\" class=\"mjx-msubsup\"><span class=\"mjx-base\" style=\"margin-right: -0.138em;\"><span id=\"MJXc-Node-2976\" class=\"mjx-mo\" style=\"padding-right: 0.138em;\"><span class=\"mjx-char MJXc-TeX-size1-R\" style=\"padding-top: 0.58em; padding-bottom: 0.58em;\">∫</span></span></span><span class=\"mjx-stack\" style=\"vertical-align: -0.379em;\"><span class=\"mjx-sup\" style=\"font-size: 70.7%; padding-bottom: 0.255em; padding-left: 0.324em; padding-right: 0.071em;\"><span id=\"MJXc-Node-2983\" class=\"mjx-mfrac\" style=\"\"><span class=\"mjx-box MJXc-stacked\" style=\"width: 0.547em; padding: 0px 0.12em;\"><span class=\"mjx-numerator\" style=\"font-size: 70.7%; width: 0.773em; top: -1.105em;\"><span id=\"MJXc-Node-2984\" class=\"mjx-mi\" style=\"\"><span class=\"mjx-char MJXc-TeX-math-I\" style=\"padding-top: 0.213em; padding-bottom: 0.265em; padding-right: 0.003em;\">π</span></span></span><span class=\"mjx-denominator\" style=\"font-size: 70.7%; width: 0.773em; bottom: -0.622em;\"><span id=\"MJXc-Node-2985\" class=\"mjx-mn\" style=\"\"><span class=\"mjx-char MJXc-TeX-main-R\" style=\"padding-top: 0.37em; padding-bottom: 0.318em;\">2</span></span></span><span class=\"mjx-line\" style=\"border-bottom: 1.1px solid; top: -0.292em; width: 0.547em;\"></span></span><span class=\"mjx-vsize\" style=\"height: 1.221em; vertical-align: -0.44em;\"></span></span></span><span class=\"mjx-sub\" style=\"font-size: 70.7%; padding-right: 0.071em;\"><span id=\"MJXc-Node-2977\" class=\"mjx-texatom\" style=\"\"><span id=\"MJXc-Node-2978\" class=\"mjx-mrow\"><span id=\"MJXc-Node-2979\" class=\"mjx-mo\"><span class=\"mjx-char MJXc-TeX-main-R\" style=\"padding-top: 0.318em; padding-bottom: 0.423em;\">−</span></span><span id=\"MJXc-Node-2980\" class=\"mjx-mfrac\"><span class=\"mjx-box MJXc-stacked\" style=\"width: 0.547em; padding: 0px 0.12em;\"><span class=\"mjx-numerator\" style=\"font-size: 70.7%; width: 0.773em; top: -1.105em;\"><span id=\"MJXc-Node-2981\" class=\"mjx-mi\" style=\"\"><span class=\"mjx-char MJXc-TeX-math-I\" style=\"padding-top: 0.213em; padding-bottom: 0.265em; padding-right: 0.003em;\">π</span></span></span><span class=\"mjx-denominator\" style=\"font-size: 70.7%; width: 0.773em; bottom: -0.622em;\"><span id=\"MJXc-Node-2982\" class=\"mjx-mn\" style=\"\"><span class=\"mjx-char MJXc-TeX-main-R\" style=\"padding-top: 0.37em; padding-bottom: 0.318em;\">2</span></span></span><span class=\"mjx-line\" style=\"border-bottom: 1.1px solid; top: -0.292em; width: 0.547em;\"></span></span><span class=\"mjx-vsize\" style=\"height: 1.221em; vertical-align: -0.44em;\"></span></span></span></span></span></span></span><span id=\"MJXc-Node-2986\" class=\"mjx-mi MJXc-space1\"><span class=\"mjx-char MJXc-TeX-main-R\" style=\"padding-top: 0.37em; padding-bottom: 0.37em;\">sin</span></span><span id=\"MJXc-Node-2987\" class=\"mjx-mo\"><span class=\"mjx-char\"></span></span><span id=\"MJXc-Node-2988\" class=\"mjx-mi MJXc-space1\"><span class=\"mjx-char MJXc-TeX-math-I\" style=\"padding-top: 0.213em; padding-bottom: 0.265em;\">x</span></span><span id=\"MJXc-Node-2989\" class=\"mjx-mspace\" style=\"width: 0.167em; height: 0px;\"></span><span id=\"MJXc-Node-2990\" class=\"mjx-mi\"><span class=\"mjx-char MJXc-TeX-math-I\" style=\"padding-top: 0.475em; padding-bottom: 0.265em; padding-right: 0.003em;\">d</span></span><span id=\"MJXc-Node-2991\" class=\"mjx-mi\"><span class=\"mjx-char MJXc-TeX-math-I\" style=\"padding-top: 0.213em; padding-bottom: 0.265em;\">x</span></span><span class=\"mjx-strut\"></span></span></span><span id=\"MJXc-Node-2992\" class=\"mjx-mtd\" style=\"padding: 0.2em 0.4em 0px 0.5em;\"><span id=\"MJXc-Node-2993\" class=\"mjx-mrow\" style=\"margin-top: 0.111em;\"><span id=\"MJXc-Node-2994\" class=\"mjx-msubsup\"><span class=\"mjx-base\" style=\"margin-right: -0.138em;\"><span id=\"MJXc-Node-2995\" class=\"mjx-mo\" style=\"padding-right: 0.138em;\"><span class=\"mjx-char MJXc-TeX-size1-R\" style=\"padding-top: 0.58em; padding-bottom: 0.58em;\">∫</span></span></span><span class=\"mjx-stack\" style=\"vertical-align: -0.366em;\"><span class=\"mjx-sup\" style=\"font-size: 70.7%; padding-bottom: 0.256em; padding-left: 0.324em; padding-right: 0.071em;\"><span id=\"MJXc-Node-3004\" class=\"mjx-texatom\" style=\"\"><span id=\"MJXc-Node-3005\" class=\"mjx-mrow\"><span id=\"MJXc-Node-3006\" class=\"mjx-mi\"><span class=\"mjx-char MJXc-TeX-math-I\" style=\"padding-top: 0.213em; padding-bottom: 0.265em; padding-right: 0.003em;\">π</span></span><span id=\"MJXc-Node-3007\" class=\"mjx-texatom\"><span id=\"MJXc-Node-3008\" class=\"mjx-mrow\"><span id=\"MJXc-Node-3009\" class=\"mjx-mo\"><span class=\"mjx-char MJXc-TeX-main-R\" style=\"padding-top: 0.475em; padding-bottom: 0.58em;\">/</span></span></span></span><span id=\"MJXc-Node-3010\" class=\"mjx-mn\"><span class=\"mjx-char MJXc-TeX-main-R\" style=\"padding-top: 0.37em; padding-bottom: 0.318em;\">2</span></span></span></span></span><span class=\"mjx-sub\" style=\"font-size: 70.7%; padding-right: 0.071em;\"><span id=\"MJXc-Node-2996\" class=\"mjx-texatom\" style=\"\"><span id=\"MJXc-Node-2997\" class=\"mjx-mrow\"><span id=\"MJXc-Node-2998\" class=\"mjx-mo\"><span class=\"mjx-char MJXc-TeX-main-R\" style=\"padding-top: 0.318em; padding-bottom: 0.423em;\">−</span></span><span id=\"MJXc-Node-2999\" class=\"mjx-mi\"><span class=\"mjx-char MJXc-TeX-math-I\" style=\"padding-top: 0.213em; padding-bottom: 0.265em; padding-right: 0.003em;\">π</span></span><span id=\"MJXc-Node-3000\" class=\"mjx-texatom\"><span id=\"MJXc-Node-3001\" class=\"mjx-mrow\"><span id=\"MJXc-Node-3002\" class=\"mjx-mo\"><span class=\"mjx-char MJXc-TeX-main-R\" style=\"padding-top: 0.475em; padding-bottom: 0.58em;\">/</span></span></span></span><span id=\"MJXc-Node-3003\" class=\"mjx-mn\"><span class=\"mjx-char MJXc-TeX-main-R\" style=\"padding-top: 0.37em; padding-bottom: 0.318em;\">2</span></span></span></span></span></span></span><span id=\"MJXc-Node-3011\" class=\"mjx-mi MJXc-space1\"><span class=\"mjx-char MJXc-TeX-main-R\" style=\"padding-top: 0.37em; padding-bottom: 0.37em;\">sin</span></span><span id=\"MJXc-Node-3012\" class=\"mjx-mo\"><span class=\"mjx-char\"></span></span><span id=\"MJXc-Node-3013\" class=\"mjx-mi MJXc-space1\"><span class=\"mjx-char MJXc-TeX-math-I\" style=\"padding-top: 0.213em; padding-bottom: 0.265em;\">x</span></span><span id=\"MJXc-Node-3014\" class=\"mjx-mspace\" style=\"width: 0.167em; height: 0px;\"></span><span id=\"MJXc-Node-3015\" class=\"mjx-mi\"><span class=\"mjx-char MJXc-TeX-math-I\" style=\"padding-top: 0.475em; padding-bottom: 0.265em; padding-right: 0.003em;\">d</span></span><span id=\"MJXc-Node-3016\" class=\"mjx-mi\"><span class=\"mjx-char MJXc-TeX-math-I\" style=\"padding-top: 0.213em; padding-bottom: 0.265em;\">x</span></span><span class=\"mjx-strut\"></span></span></span></span></span></span></span></span><span class=\"MJX_Assistive_MathML MJX_Assistive_MathML_Block\" role=\"presentation\"><math xmlns=\"http://www.w3.org/1998/Math/MathML\" display=\"block\"><mtable columnalign=\"center center\" rowspacing=\"4pt\" columnspacing=\"1em\" rowlines=\"solid none\"><mtr><mtd><mrow class=\"MJX-TeXAtom-ORD\"><mi mathvariant=\"normal\">B</mi><mi mathvariant=\"normal\">a</mi><mi mathvariant=\"normal\">d</mi></mrow></mtd><mtd><mrow class=\"MJX-TeXAtom-ORD\"><mi mathvariant=\"normal\">B</mi><mi mathvariant=\"normal\">e</mi><mi mathvariant=\"normal\">t</mi><mi mathvariant=\"normal\">t</mi><mi mathvariant=\"normal\">e</mi><mi mathvariant=\"normal\">r</mi></mrow></mtd></mtr><mtr><mtd></mtd></mtr><mtr><mtd><msup><mi>e</mi><mrow class=\"MJX-TeXAtom-ORD\"><mi>i</mi><mfrac><mi>π</mi><mn>2</mn></mfrac></mrow></msup><mspace width=\"1em\"></mspace><msup><mi>e</mi><mrow class=\"MJX-TeXAtom-ORD\"><mfrac><mrow><mi>i</mi><mi>π</mi></mrow><mn>2</mn></mfrac></mrow></msup></mtd><mtd><msup><mi>e</mi><mrow class=\"MJX-TeXAtom-ORD\"><mi>i</mi><mi>π</mi><mrow class=\"MJX-TeXAtom-ORD\"><mo>/</mo></mrow><mn>2</mn></mrow></msup></mtd></mtr><mtr><mtd><msubsup><mo>∫</mo><mrow class=\"MJX-TeXAtom-ORD\"><mo>−</mo><mfrac><mi>π</mi><mn>2</mn></mfrac></mrow><mfrac><mi>π</mi><mn>2</mn></mfrac></msubsup><mi>sin</mi><mo>⁡</mo><mi>x</mi><mspace width=\"thinmathspace\"></mspace><mi>d</mi><mi>x</mi></mtd><mtd><msubsup><mo>∫</mo><mrow class=\"MJX-TeXAtom-ORD\"><mo>−</mo><mi>π</mi><mrow class=\"MJX-TeXAtom-ORD\"><mo>/</mo></mrow><mn>2</mn></mrow><mrow class=\"MJX-TeXAtom-ORD\"><mi>π</mi><mrow class=\"MJX-TeXAtom-ORD\"><mo>/</mo></mrow><mn>2</mn></mrow></msubsup><mi>sin</mi><mo>⁡</mo><mi>x</mi><mspace width=\"thinmathspace\"></mspace><mi>d</mi><mi>x</mi></mtd></mtr></mtable></math></span></span></span><script type=\"math/tex; mode=display\" id=\"MathJax-Element-151\">\\begin{array}{cc}\n\\mathrm{Bad} & \\mathrm{Better} \\\\\n\\hline \\\\\ne^{i\\frac{\\pi}2} \\quad e^{\\frac{i\\pi}2}& e^{i\\pi/2} \\\\\n\\int_{-\\frac\\pi2}^\\frac\\pi2 \\sin x\\,dx & \\int_{-\\pi/2}^{\\pi/2}\\sin x\\,dx \\\\\n\\end{array}\n</script></div>", "$$\n\\begin{array}{cc}\n\\mathrm{Bad} & \\mathrm{Better} \\\\\n\\hline \\\\\ne^{i\\frac{\\pi}2} \\quad e^{\\frac{i\\pi}2}& e^{i\\pi/2} \\\\\n\\int_{-\\frac\\pi2}^\\frac\\pi2 \\sin x\\,dx & \\int_{-\\pi/2}^{\\pi/2}\\sin x\\,dx \\\\\n\\end{array}\n$$\n"},
	{"189", "<div id=\"readability-page-1\" class=\"page\"><div _ngcontent-dpn-c180=\"\" class=\"document-content-html\"><app-document-text _ngcontent-dpn-c180=\"\" id=\"document-text\" _nghost-dpn-c173=\"\"><div _ngcontent-dpn-c173=\"\" id=\"mark\" class=\"idpContent\"><div _ngcontent-dpn-c173=\"\" class=\"markdown-body ng-star-inserted\">   <div>    <p>开发者可以通过本指导了解如何使用Native Image的接口。</p>    <div class=\"tiledSection\">     <h2 id=\"开发步骤\">开发步骤<i class=\"anchorIcon\" anchorid=\"开发步骤\" tips=\"复制节点链接\"></i></h2>          <p><strong>添加依赖</strong></p>     <p>在进行应用开发之前，开发者需要打开native工程的src/main/cpp/CMakeLists.txt，在target_link_libraries依赖中添加image的libace_napi.z.so、libpixelmap_ndk.z.so以及日志依赖libhilog_ndk.z.so。</p>     <pre class=\"txt prettyprint linenums hljs language-plaintext\" data-highlighted=\"yes\"><ol class=\"linenums\"><li>target_link_libraries(entry PUBLIC libace_napi.z.so libhilog_ndk.z.so libpixelmap_ndk.z.so)</li></ol></pre>     <p><strong>添加接口映射</strong></p>     <p>打开src/main/cpp/hello.cpp文件，在Init函数中添加接口映射如下：</p>     <pre class=\"prettyprint linenums hljs language-cpp\" data-highlighted=\"yes\"><ol class=\"linenums\"><li><span class=\"hljs-function\">EXTERN_C_START</span></li><li><span class=\"hljs-function\"><span class=\"hljs-type\">static</span> napi_value <span class=\"hljs-title\">Init</span><span class=\"hljs-params\">(napi_env env, napi_value exports)</span></span></li><li><span class=\"hljs-function\"></span>{</li><li>    napi_property_descriptor desc[] = {</li><li>        { <span class=\"hljs-string\">\"createPixelMapTest\"</span>, <span class=\"hljs-literal\">nullptr</span>, CreatePixelMapTest, <span class=\"hljs-literal\">nullptr</span>, <span class=\"hljs-literal\">nullptr</span>, <span class=\"hljs-literal\">nullptr</span>, napi_default, <span class=\"hljs-literal\">nullptr</span> },</li><li>        { <span class=\"hljs-string\">\"createAlphaPixelMap\"</span>, <span class=\"hljs-literal\">nullptr</span>, CreateAlphaPixelMap, <span class=\"hljs-literal\">nullptr</span>, <span class=\"hljs-literal\">nullptr</span>, <span class=\"hljs-literal\">nullptr</span>, napi_default, <span class=\"hljs-literal\">nullptr</span> },</li><li>        { <span class=\"hljs-string\">\"transform\"</span>, <span class=\"hljs-literal\">nullptr</span>, Transform, <span class=\"hljs-literal\">nullptr</span>, <span class=\"hljs-literal\">nullptr</span>, <span class=\"hljs-literal\">nullptr</span>, napi_default, <span class=\"hljs-literal\">nullptr</span> },</li><li>    };</li><li>\n</li><li>    <span class=\"hljs-built_in\">napi_define_properties</span>(env, exports, <span class=\"hljs-built_in\">sizeof</span>(desc) / <span class=\"hljs-built_in\">sizeof</span>(desc[<span class=\"hljs-number\">0</span>]), desc);</li><li>    <span class=\"hljs-keyword\">return</span> exports;</li><li>}</li><li>EXTERN_C_END</li></ol></pre>     <p><strong>Native接口调用</strong></p>     <p>具体接口说明请参考<a href=\"https://developer.huawei.com/consumer/cn/doc/harmonyos-references-V5/image-V5\" target=\"_blank\">API文档</a>。</p>     <p>在hello.cpp文件中获取JS的资源对象，并转为Native的资源对象，即可调用Native接口，调用方式示例代码如下：</p>     <p><strong>添加引用文件</strong></p>     <pre class=\"prettyprint linenums hljs language-cpp\" data-highlighted=\"yes\"><ol class=\"linenums\"><li><span class=\"hljs-meta\">#<span class=\"hljs-keyword\">include</span> <span class=\"hljs-string\">&lt;multimedia/image_framework/image_mdk_common.h&gt;</span></span></li><li><span class=\"hljs-meta\">#<span class=\"hljs-keyword\">include</span> <span class=\"hljs-string\">&lt;multimedia/image_framework/image_pixel_map_mdk.h&gt;</span></span></li><li><span class=\"hljs-meta\">#<span class=\"hljs-keyword\">include</span> <span class=\"hljs-string\">&lt;stdlib.h&gt;</span></span></li></ol></pre>     <ol>      <li><p>创建一个 <strong>PixelMap</strong> 对象。</p> <pre class=\"prettyprint linenums hljs language-cpp\" data-highlighted=\"yes\"><ol class=\"linenums\"><li><span class=\"hljs-function\">napi_value <span class=\"hljs-title\">CreatePixelMapTest</span><span class=\"hljs-params\">(napi_env env, napi_callback_info info)</span> </span>{</li><li>    napi_value udfVar = <span class=\"hljs-literal\">nullptr</span>;</li><li>    napi_value pixelMap = <span class=\"hljs-literal\">nullptr</span>;</li><li>\n</li><li>    <span class=\"hljs-keyword\">struct</span> <span class=\"hljs-title class_\">OhosPixelMapCreateOps</span> createOps;</li><li>    createOps.width = <span class=\"hljs-number\">4</span>;</li><li>    createOps.height = <span class=\"hljs-number\">6</span>;</li><li>    createOps.pixelFormat = <span class=\"hljs-number\">4</span>;</li><li>    createOps.alphaType = <span class=\"hljs-number\">0</span>;</li><li>    <span class=\"hljs-type\">size_t</span> bufferSize = createOps.width * createOps.height * <span class=\"hljs-number\">4</span>;</li><li>    <span class=\"hljs-type\">void</span> *buff = <span class=\"hljs-built_in\">malloc</span>(bufferSize);</li><li>    <span class=\"hljs-keyword\">if</span> (buff == <span class=\"hljs-literal\">nullptr</span>) {</li><li>        <span class=\"hljs-keyword\">return</span> udfVar;</li><li>    }</li><li>\n</li><li>    <span class=\"hljs-type\">char</span> *cc = (<span class=\"hljs-type\">char</span> *)buff;</li><li>    <span class=\"hljs-keyword\">for</span> (<span class=\"hljs-type\">int</span> i = <span class=\"hljs-number\">0</span>; i &lt; <span class=\"hljs-number\">96</span>; i++) {</li><li>        *(cc++) = (<span class=\"hljs-type\">char</span>)i;</li><li>    }</li><li>    <span class=\"hljs-type\">int32_t</span> res = <span class=\"hljs-built_in\">OH_PixelMap_CreatePixelMap</span>(env, createOps, (<span class=\"hljs-type\">uint8_t</span> *)buff, bufferSize, &amp;pixelMap);</li><li>    <span class=\"hljs-built_in\">free</span>(buff);</li><li>    <span class=\"hljs-keyword\">if</span> (res != IMAGE_RESULT_SUCCESS || pixelMap == <span class=\"hljs-literal\">nullptr</span>) {</li><li>        <span class=\"hljs-keyword\">return</span> udfVar;</li><li>    }</li><li>    <span class=\"hljs-keyword\">return</span> pixelMap;</li><li>}</li></ol></pre></li>      <li><p>根据Alpha通道的信息，来生成一个仅包含Alpha通道信息的 <strong>PixelMap</strong> 对象。</p> <pre class=\"prettyprint linenums hljs language-cpp\" data-highlighted=\"yes\"><ol class=\"linenums\"><li><span class=\"hljs-function\">napi_value <span class=\"hljs-title\">CreateAlphaPixelMap</span><span class=\"hljs-params\">(napi_env env, napi_callback_info info)</span> </span>{</li><li>    napi_value udfVar = <span class=\"hljs-literal\">nullptr</span>;</li><li>    napi_value thisVar = <span class=\"hljs-literal\">nullptr</span>;</li><li>    napi_value argValue[<span class=\"hljs-number\">1</span>] = {<span class=\"hljs-number\">0</span>};</li><li>    <span class=\"hljs-type\">size_t</span> argCount = <span class=\"hljs-number\">1</span>;</li><li>\n</li><li>    napi_value alphaPixelMap = <span class=\"hljs-literal\">nullptr</span>;</li><li>\n</li><li>    <span class=\"hljs-built_in\">napi_get_undefined</span>(env, &amp;udfVar);</li><li>\n</li><li>    <span class=\"hljs-keyword\">if</span> (<span class=\"hljs-built_in\">napi_get_cb_info</span>(env, info, &amp;argCount, argValue, &amp;thisVar, <span class=\"hljs-literal\">nullptr</span>) != napi_ok || argCount &lt; <span class=\"hljs-number\">1</span> ||</li><li>        argValue[<span class=\"hljs-number\">0</span>] == <span class=\"hljs-literal\">nullptr</span>) {</li><li>        <span class=\"hljs-keyword\">return</span> udfVar;</li><li>    }</li><li>    <span class=\"hljs-type\">int32_t</span> res = <span class=\"hljs-built_in\">OH_PixelMap_CreateAlphaPixelMap</span>(env, argValue[<span class=\"hljs-number\">0</span>], &amp;alphaPixelMap);</li><li>    <span class=\"hljs-keyword\">if</span> (res != IMAGE_RESULT_SUCCESS || alphaPixelMap == <span class=\"hljs-literal\">nullptr</span>) {</li><li>        <span class=\"hljs-keyword\">return</span> udfVar;</li><li>    }</li><li>    <span class=\"hljs-keyword\">return</span> alphaPixelMap;</li><li>}</li></ol></pre></li>      <li><p>对 <strong>PixelMap</strong> 数据进行处理。</p> <pre class=\"prettyprint linenums hljs language-cpp\" data-highlighted=\"yes\"><ol class=\"linenums\"><li><span class=\"hljs-function\">napi_value <span class=\"hljs-title\">Transform</span><span class=\"hljs-params\">(napi_env env, napi_callback_info info)</span> </span>{</li><li>    napi_value thisVar = <span class=\"hljs-literal\">nullptr</span>;</li><li>    napi_value argValue[<span class=\"hljs-number\">1</span>] = {<span class=\"hljs-number\">0</span>};</li><li>    <span class=\"hljs-type\">size_t</span> argCount = <span class=\"hljs-number\">1</span>;</li><li>\n</li><li>    <span class=\"hljs-keyword\">if</span> (<span class=\"hljs-built_in\">napi_get_cb_info</span>(env, info, &amp;argCount, argValue, &amp;thisVar, <span class=\"hljs-literal\">nullptr</span>) != napi_ok || argCount &lt; <span class=\"hljs-number\">1</span> ||</li><li>        argValue[<span class=\"hljs-number\">0</span>] == <span class=\"hljs-literal\">nullptr</span>) {</li><li>        <span class=\"hljs-keyword\">return</span> <span class=\"hljs-literal\">nullptr</span>;</li><li>    }</li><li>    napi_value result = <span class=\"hljs-literal\">nullptr</span>;</li><li>    <span class=\"hljs-built_in\">napi_get_undefined</span>(env, &amp;result);</li><li>    </li><li>    <span class=\"hljs-cmt\">// 初始化NativePixelMap对象。</span></li><li>    NativePixelMap *native = <span class=\"hljs-built_in\">OH_PixelMap_InitNativePixelMap</span>(env, argValue[<span class=\"hljs-number\">0</span>]);</li><li>    <span class=\"hljs-keyword\">if</span> (native == <span class=\"hljs-literal\">nullptr</span>) {</li><li>        <span class=\"hljs-keyword\">return</span> result;</li><li>    }</li><li>\n</li><li>    <span class=\"hljs-cmt\">// 获取图片信息。</span></li><li>    <span class=\"hljs-keyword\">struct</span> <span class=\"hljs-title class_\">OhosPixelMapInfos</span> pixelMapInfo;</li><li>    <span class=\"hljs-built_in\">OH_PixelMap_GetImageInfo</span>(native, &amp;pixelMapInfo);</li><li>\n</li><li>    <span class=\"hljs-cmt\">// 获取PixelMap对象每行字节数。</span></li><li>    <span class=\"hljs-type\">int32_t</span> rowBytes;</li><li>    <span class=\"hljs-built_in\">OH_PixelMap_GetBytesNumberPerRow</span>(native, &amp;rowBytes);</li><li>\n</li><li>    <span class=\"hljs-cmt\">// 获取PixelMap对象是否可编辑的状态。</span></li><li>    <span class=\"hljs-type\">int32_t</span> editable = <span class=\"hljs-number\">0</span>;</li><li>    <span class=\"hljs-built_in\">OH_PixelMap_GetIsEditable</span>(native, &amp;editable);</li><li>\n</li><li>    <span class=\"hljs-cmt\">// 获取PixelMap对象是否支持Alpha通道。</span></li><li>    <span class=\"hljs-type\">int32_t</span> supportAlpha = <span class=\"hljs-number\">0</span>;</li><li>    <span class=\"hljs-built_in\">OH_PixelMap_IsSupportAlpha</span>(native, &amp;supportAlpha);</li><li>\n</li><li>    <span class=\"hljs-cmt\">// 设置PixelMap对象的Alpha通道。</span></li><li>    <span class=\"hljs-type\">int32_t</span> alphaAble = <span class=\"hljs-number\">0</span>;</li><li>    <span class=\"hljs-built_in\">OH_PixelMap_SetAlphaAble</span>(native, alphaAble);</li><li>\n</li><li>    <span class=\"hljs-cmt\">// 获取PixelMap对象像素密度。</span></li><li>    <span class=\"hljs-type\">int32_t</span> densityG;</li><li>    <span class=\"hljs-built_in\">OH_PixelMap_GetDensity</span>(native, &amp;densityG);</li><li>\n</li><li>    <span class=\"hljs-cmt\">// 设置PixelMap对象像素密度。</span></li><li>    <span class=\"hljs-type\">int32_t</span> densityS = <span class=\"hljs-number\">100</span>;</li><li>    <span class=\"hljs-built_in\">OH_PixelMap_SetDensity</span>(native, densityS);</li><li>\n</li><li>    <span class=\"hljs-cmt\">// 设置PixelMap对象的透明度。</span></li><li>    <span class=\"hljs-type\">float</span> opacity = <span class=\"hljs-number\">0.5</span>;</li><li>    <span class=\"hljs-built_in\">OH_PixelMap_SetOpacity</span>(native, opacity);</li><li>\n</li><li>    <span class=\"hljs-cmt\">// 设置缩放比例。</span></li><li>    <span class=\"hljs-cmt\">// scaleX: 宽为原来的0.5。</span></li><li>    <span class=\"hljs-cmt\">// scaleY: 高为原来的0.5。</span></li><li>    <span class=\"hljs-type\">float</span> scaleX = <span class=\"hljs-number\">0.5</span>;</li><li>    <span class=\"hljs-type\">float</span> scaleY = <span class=\"hljs-number\">0.5</span>;</li><li>    <span class=\"hljs-built_in\">OH_PixelMap_Scale</span>(native, scaleX, scaleY);</li><li>\n</li><li>    <span class=\"hljs-cmt\">// 设置偏移。</span></li><li>    <span class=\"hljs-cmt\">// translateX: 向下偏移50。</span></li><li>    <span class=\"hljs-cmt\">// translateY: 向右偏移50。</span></li><li>    <span class=\"hljs-type\">float</span> translateX = <span class=\"hljs-number\">50</span>;</li><li>    <span class=\"hljs-type\">float</span> translateY = <span class=\"hljs-number\">50</span>;</li><li>    <span class=\"hljs-built_in\">OH_PixelMap_Translate</span>(native, translateX, translateY);</li><li>\n</li><li>    <span class=\"hljs-cmt\">// 设置顺时针旋转90度。</span></li><li>    <span class=\"hljs-type\">float</span> angle = <span class=\"hljs-number\">90</span>;</li><li>    <span class=\"hljs-built_in\">OH_PixelMap_Rotate</span>(native, angle);</li><li>\n</li><li>    <span class=\"hljs-cmt\">// 设置翻转</span></li><li>    <span class=\"hljs-cmt\">// flipX: 水平翻转，0为不翻转，1为翻转。</span></li><li>    <span class=\"hljs-cmt\">// flipY: 垂直翻转，0为不翻转，1为翻转。</span></li><li>    <span class=\"hljs-type\">int32_t</span> flipX = <span class=\"hljs-number\">0</span>;</li><li>    <span class=\"hljs-type\">int32_t</span> flipY = <span class=\"hljs-number\">1</span>;</li><li>    <span class=\"hljs-built_in\">OH_PixelMap_Flip</span>(native, flipX, flipY);</li><li>\n</li><li>    <span class=\"hljs-cmt\">// 设置裁剪区域。</span></li><li>    <span class=\"hljs-cmt\">// cropX: 裁剪起始点横坐标。</span></li><li>    <span class=\"hljs-cmt\">// cropY: 裁剪起始点纵坐标。</span></li><li>    <span class=\"hljs-cmt\">// cropH: 裁剪高度10，方向为从上往下（裁剪后的图片高度为10）。</span></li><li>    <span class=\"hljs-cmt\">// cropW: 裁剪宽度10，方向为从左到右（裁剪后的图片宽度为10）。</span></li><li>    <span class=\"hljs-type\">int32_t</span> cropX = <span class=\"hljs-number\">1</span>;</li><li>    <span class=\"hljs-type\">int32_t</span> cropY = <span class=\"hljs-number\">1</span>;</li><li>    <span class=\"hljs-type\">int32_t</span> cropW = <span class=\"hljs-number\">10</span>;</li><li>    <span class=\"hljs-type\">int32_t</span> cropH = <span class=\"hljs-number\">10</span>;</li><li>    <span class=\"hljs-built_in\">OH_PixelMap_Crop</span>(native, cropX, cropY, cropW, cropH);</li><li>\n</li><li>    <span class=\"hljs-cmt\">// 获取PixelMap对象数据的内存地址，并锁定该内存。</span></li><li>    <span class=\"hljs-type\">void</span> *pixelAddr = <span class=\"hljs-literal\">nullptr</span>;</li><li>    <span class=\"hljs-built_in\">OH_PixelMap_AccessPixels</span>(native, &amp;pixelAddr);</li><li>\n</li><li>    <span class=\"hljs-cmt\">// 释放PixelMap对象数据的内存锁。</span></li><li>    <span class=\"hljs-built_in\">OH_PixelMap_UnAccessPixels</span>(native);</li><li>\n</li><li>    <span class=\"hljs-keyword\">return</span> result;</li><li>}</li></ol></pre></li>     </ol>     <p><strong>JS侧调用</strong></p>     <ol>      <li><p>打开src\\main\\cpp\\types\\libentry\\index.d.ts（其中libentry根据工程名生成），导入如下引用文件:</p> <pre class=\"js prettyprint linenums hljs language-javascript\" data-highlighted=\"yes\"><ol class=\"linenums\"><li><span class=\"hljs-keyword\">import</span> { image } <span class=\"hljs-keyword\">from</span> <span class=\"hljs-string\">'@kit.ImageKit'</span>;</li><li>\n</li><li><span class=\"hljs-keyword\">export</span> <span class=\"hljs-keyword\">const</span> <span class=\"hljs-attr\">createPixelMapTest</span>: <span class=\"hljs-function\">() =&gt;</span> image.<span class=\"hljs-property\">PixelMap</span>;</li><li><span class=\"hljs-keyword\">export</span> <span class=\"hljs-keyword\">const</span> <span class=\"hljs-attr\">transform</span>: <span class=\"hljs-function\">(<span class=\"hljs-params\">a: image.PixelMap</span>) =&gt;</span> <span class=\"hljs-keyword\">void</span>;</li></ol></pre></li>      <li><p>打开src\\main\\ets\\pages\\index.ets, 导入\"libentry.so\"(根据工程名生成)，调用Native接口，传入JS的资源对象。示例如下:</p> <pre class=\"js prettyprint linenums hljs language-javascript\" data-highlighted=\"yes\"><ol class=\"linenums\"><li><span class=\"hljs-keyword\">import</span> testNapi <span class=\"hljs-keyword\">from</span> <span class=\"hljs-string\">'libentry.so'</span>;</li><li><span class=\"hljs-keyword\">import</span> { image } <span class=\"hljs-keyword\">from</span> <span class=\"hljs-string\">'@kit.ImageKit'</span>;</li><li>\n</li><li>@<span class=\"hljs-title class_\">Entry</span></li><li>@<span class=\"hljs-title class_\">Component</span></li><li>struct <span class=\"hljs-title class_\">Index</span> {</li><li>@<span class=\"hljs-title class_\">State</span> _pixelMap : image.<span class=\"hljs-property\">PixelMap</span> | <span class=\"hljs-literal\">undefined</span> = <span class=\"hljs-literal\">undefined</span>;</li><li>\n</li><li><span class=\"hljs-title function_\">build</span>(<span class=\"hljs-params\"></span>) {</li><li>    <span class=\"hljs-title class_\">Row</span>() {</li><li>        <span class=\"hljs-title class_\">Column</span>() {</li><li>            <span class=\"hljs-title class_\">Button</span>(<span class=\"hljs-string\">\"PixelMap\"</span>)</li><li>            .<span class=\"hljs-title function_\">width</span>(<span class=\"hljs-number\">100</span>)</li><li>            .<span class=\"hljs-title function_\">height</span>(<span class=\"hljs-number\">100</span>)</li><li>            .<span class=\"hljs-title function_\">onClick</span>(<span class=\"hljs-function\">() =&gt;</span> {</li><li>                <span class=\"hljs-variable language_\">console</span>.<span class=\"hljs-title function_\">log</span>(<span class=\"hljs-string\">\"com.example.native_ndk_api10 button click in\"</span>);</li><li>                <span class=\"hljs-variable language_\">this</span>.<span class=\"hljs-property\">_pixelMap</span> = testNapi.<span class=\"hljs-title function_\">createPixelMapTest</span>();</li><li>                testNapi.<span class=\"hljs-title function_\">transform</span>(<span class=\"hljs-variable language_\">this</span>.<span class=\"hljs-property\">_pixelMap</span>);</li><li>            })</li><li>            <span class=\"hljs-title class_\">Image</span>(<span class=\"hljs-variable language_\">this</span>.<span class=\"hljs-property\">_pixelMap</span>)</li><li>            .<span class=\"hljs-title function_\">width</span>(<span class=\"hljs-number\">500</span>)</li><li>            .<span class=\"hljs-title function_\">height</span>(<span class=\"hljs-number\">500</span>)</li><li>            .<span class=\"hljs-title function_\">objectFit</span>(<span class=\"hljs-title class_\">ImageFit</span>.<span class=\"hljs-property\">Cover</span>)</li><li>            .<span class=\"hljs-title function_\">border</span>({<span class=\"hljs-attr\">width</span>: <span class=\"hljs-number\">1</span>, <span class=\"hljs-attr\">color</span>: <span class=\"hljs-title class_\">Color</span>.<span class=\"hljs-property\">Blue</span>})</li><li>            }</li><li>            .<span class=\"hljs-title function_\">width</span>(<span class=\"hljs-string\">'100%'</span>)</li><li>        }</li><li>        .<span class=\"hljs-title function_\">height</span>(<span class=\"hljs-string\">'100%'</span>)</li><li>    }</li><li>}</li></ol></pre></li>     </ol>    </div>   </div>   </div><!----><!----></div><!----></app-document-text></div></div>", "开发者可以通过本指导了解如何使用 Native Image 的接口。\n\n## 开发步骤\n\n**添加依赖**\n\n在进行应用开发之前，开发者需要打开 native 工程的 src/main/cpp/CMakeLists.txt，在 target\\_link\\_libraries 依赖中添加 image 的 libace\\_napi.z.so、libpixelmap\\_ndk.z.so 以及日志依赖 libhilog\\_ndk.z.so。\n\n```plaintext\ntarget_link_libraries(entry PUBLIC libace_napi.z.so libhilog_ndk.z.so libpixelmap_ndk.z.so)\n```\n**添加接口映射**\n\n打开 src/main/cpp/hello.cpp 文件，在 Init 函数中添加接口映射如下：\n\n```cpp\nEXTERN_C_START\nstatic napi_value Init(napi_env env, napi_value exports)\n{\n    napi_property_descriptor desc[] = {\n        { \"createPixelMapTest\", nullptr, CreatePixelMapTest, nullptr, nullptr, nullptr, napi_default, nullptr },\n        { \"createAlphaPixelMap\", nullptr, CreateAlphaPixelMap, nullptr, nullptr, nullptr, napi_default, nullptr },\n        { \"transform\", nullptr, Transform, nullptr, nullptr, nullptr, napi_default, nullptr },\n    };\n    napi_define_properties(env, exports, sizeof(desc) / sizeof(desc[0]), desc);\n    return exports;\n}\nEXTERN_C_END\n```\n**Native 接口调用**\n\n具体接口说明请参考 [API 文档](https://developer.huawei.com/consumer/cn/doc/harmonyos-references-V5/image-V5)。\n\n在 hello.cpp 文件中获取 JS 的资源对象，并转为 Native 的资源对象，即可调用 Native 接口，调用方式示例代码如下：\n\n**添加引用文件**\n\n```cpp\n#include <multimedia/image_framework/image_mdk_common.h>\n#include <multimedia/image_framework/image_pixel_map_mdk.h>\n#include <stdlib.h>\n```\n1. 创建一个 **PixelMap** 对象。\n   ```cpp\n   napi_value CreatePixelMapTest(napi_env env, napi_callback_info info) {\n       napi_value udfVar = nullptr;\n       napi_value pixelMap = nullptr;\n       struct OhosPixelMapCreateOps createOps;\n       createOps.width = 4;\n       createOps.height = 6;\n       createOps.pixelFormat = 4;\n       createOps.alphaType = 0;\n       size_t bufferSize = createOps.width * createOps.height * 4;\n       void *buff = malloc(bufferSize);\n       if (buff == nullptr) {\n           return udfVar;\n       }\n       char *cc = (char *)buff;\n       for (int i = 0; i < 96; i++) {\n           *(cc++) = (char)i;\n       }\n       int32_t res = OH_PixelMap_CreatePixelMap(env, createOps, (uint8_t *)buff, bufferSize, &pixelMap);\n       free(buff);\n       if (res != IMAGE_RESULT_SUCCESS || pixelMap == nullptr) {\n           return udfVar;\n       }\n       return pixelMap;\n   }\n   ```\n2. 根据 Alpha 通道的信息，来生成一个仅包含 Alpha 通道信息的 **PixelMap** 对象。\n   ```cpp\n   napi_value CreateAlphaPixelMap(napi_env env, napi_callback_info info) {\n       napi_value udfVar = nullptr;\n       napi_value thisVar = nullptr;\n       napi_value argValue[1] = {0};\n       size_t argCount = 1;\n       napi_value alphaPixelMap = nullptr;\n       napi_get_undefined(env, &udfVar);\n       if (napi_get_cb_info(env, info, &argCount, argValue, &thisVar, nullptr) != napi_ok || argCount < 1 ||\n           argValue[0] == nullptr) {\n           return udfVar;\n       }\n       int32_t res = OH_PixelMap_CreateAlphaPixelMap(env, argValue[0], &alphaPixelMap);\n       if (res != IMAGE_RESULT_SUCCESS || alphaPixelMap == nullptr) {\n           return udfVar;\n       }\n       return alphaPixelMap;\n   }\n   ```\n3. 对 **PixelMap** 数据进行处理。\n   ```cpp\n   napi_value Transform(napi_env env, napi_callback_info info) {\n       napi_value thisVar = nullptr;\n       napi_value argValue[1] = {0};\n       size_t argCount = 1;\n       if (napi_get_cb_info(env, info, &argCount, argValue, &thisVar, nullptr) != napi_ok || argCount < 1 ||\n           argValue[0] == nullptr) {\n           return nullptr;\n       }\n       napi_value result = nullptr;\n       napi_get_undefined(env, &result);\n       // 初始化NativePixelMap对象。\n       NativePixelMap *native = OH_PixelMap_InitNativePixelMap(env, argValue[0]);\n       if (native == nullptr) {\n           return result;\n       }\n       // 获取图片信息。\n       struct OhosPixelMapInfos pixelMapInfo;\n       OH_PixelMap_GetImageInfo(native, &pixelMapInfo);\n       // 获取PixelMap对象每行字节数。\n       int32_t rowBytes;\n       OH_PixelMap_GetBytesNumberPerRow(native, &rowBytes);\n       // 获取PixelMap对象是否可编辑的状态。\n       int32_t editable = 0;\n       OH_PixelMap_GetIsEditable(native, &editable);\n       // 获取PixelMap对象是否支持Alpha通道。\n       int32_t supportAlpha = 0;\n       OH_PixelMap_IsSupportAlpha(native, &supportAlpha);\n       // 设置PixelMap对象的Alpha通道。\n       int32_t alphaAble = 0;\n       OH_PixelMap_SetAlphaAble(native, alphaAble);\n       // 获取PixelMap对象像素密度。\n       int32_t densityG;\n       OH_PixelMap_GetDensity(native, &densityG);\n       // 设置PixelMap对象像素密度。\n       int32_t densityS = 100;\n       OH_PixelMap_SetDensity(native, densityS);\n       // 设置PixelMap对象的透明度。\n       float opacity = 0.5;\n       OH_PixelMap_SetOpacity(native, opacity);\n       // 设置缩放比例。\n       // scaleX: 宽为原来的0.5。\n       // scaleY: 高为原来的0.5。\n       float scaleX = 0.5;\n       float scaleY = 0.5;\n       OH_PixelMap_Scale(native, scaleX, scaleY);\n       // 设置偏移。\n       // translateX: 向下偏移50。\n       // translateY: 向右偏移50。\n       float translateX = 50;\n       float translateY = 50;\n       OH_PixelMap_Translate(native, translateX, translateY);\n       // 设置顺时针旋转90度。\n       float angle = 90;\n       OH_PixelMap_Rotate(native, angle);\n       // 设置翻转\n       // flipX: 水平翻转，0为不翻转，1为翻转。\n       // flipY: 垂直翻转，0为不翻转，1为翻转。\n       int32_t flipX = 0;\n       int32_t flipY = 1;\n       OH_PixelMap_Flip(native, flipX, flipY);\n       // 设置裁剪区域。\n       // cropX: 裁剪起始点横坐标。\n       // cropY: 裁剪起始点纵坐标。\n       // cropH: 裁剪高度10，方向为从上往下（裁剪后的图片高度为10）。\n       // cropW: 裁剪宽度10，方向为从左到右（裁剪后的图片宽度为10）。\n       int32_t cropX = 1;\n       int32_t cropY = 1;\n       int32_t cropW = 10;\n       int32_t cropH = 10;\n       OH_PixelMap_Crop(native, cropX, cropY, cropW, cropH);\n       // 获取PixelMap对象数据的内存地址，并锁定该内存。\n       void *pixelAddr = nullptr;\n       OH_PixelMap_AccessPixels(native, &pixelAddr);\n       // 释放PixelMap对象数据的内存锁。\n       OH_PixelMap_UnAccessPixels(native);\n       return result;\n   }\n   ```\n\n**JS 侧调用**\n\n1. 打开 src\\\\main\\\\cpp\\\\types\\\\libentry\\\\index.d.ts（其中 libentry 根据工程名生成），导入如下引用文件:\n   ```javascript\n   import { image } from '@kit.ImageKit';\n   export const createPixelMapTest: () => image.PixelMap;\n   export const transform: (a: image.PixelMap) => void;\n   ```\n2. 打开 src\\\\main\\\\ets\\\\pages\\\\index.ets, 导入\"libentry.so\"(根据工程名生成)，调用 Native 接口，传入 JS 的资源对象。示例如下:\n   ```javascript\n   import testNapi from 'libentry.so';\n   import { image } from '@kit.ImageKit';\n   @Entry\n   @Component\n   struct Index {\n   @State _pixelMap : image.PixelMap | undefined = undefined;\n   build() {\n       Row() {\n           Column() {\n               Button(\"PixelMap\")\n               .width(100)\n               .height(100)\n               .onClick(() => {\n                   console.log(\"com.example.native_ndk_api10 button click in\");\n                   this._pixelMap = testNapi.createPixelMapTest();\n                   testNapi.transform(this._pixelMap);\n               })\n               Image(this._pixelMap)\n               .width(500)\n               .height(500)\n               .objectFit(ImageFit.Cover)\n               .border({width: 1, color: Color.Blue})\n               }\n               .width('100%')\n           }\n           .height('100%')\n       }\n   }\n   ```\n"},
	{"188", "<h1 id=\"43c05a2c-5f78-43c1-a48e-12813034c9bf\" class=\"\">特殊段落</h1><h2 id=\"a1347ee9-a6db-4790-8c15-b9244d37cc56\" class=\"\">1.代码</h2><pre id=\"ac4ab4a8-d2f8-48e4-90e6-9d4a986f93fc\" class=\"code\"><code class=\"language-bash\"># Bash 安装zsh\n    $ sudo apt install zsh\n    \n    # 配置ohmyzsh\n    $ sh -c \"$(curl -fsSL &lt;https://raw.github.com/robbyrussell/oh-my-zsh/master/tools/install.sh&gt;)\"\n    \n    # 配置ohmyzsh插件\n    # zsh-autosuggestions\n    $ git clone git://github.com/zsh-users/zsh-autosuggestions $ZSH_CUSTOM/plugins/zsh-autosuggestions\n    \n    // 启用插件\n    $ vim .zshrc\n    plugins=(git z zsh-autosuggestions zsh-syntax-highlighting)</code></pre><ul><li><summary>其他更多语言</summary><pre id=\"9f8fa36a-b592-4974-b4cc-29724d54c63a\" class=\"code\"><code class=\"language-bash\" style=\"white-space:pre-wrap;word-break:break-all\">ps -ef | grep java | awk '{print $2}' | xargs kill -9</code></pre><pre id=\"c0c14d9f-2167-422e-b266-4fdf168d5d8b\" class=\"code\"><code class=\"language-java\" style=\"white-space:pre-wrap;word-break:break-all\">@Test\n    public void test11() {\n    \n      long start = System.currentTimeMillis();\n      int a = 0;\n      for(int i=0;i&lt;1000000000;i++){\n          try {\n              a++;\n          }catch (Exception e){\n              e.printStackTrace();\n          }\n      }\n      long useTime = System.currentTimeMillis()-start;\n      System.out.println(\"useTime:\"+useTime);\n    }</code></pre><pre id=\"8473507e-5d42-45d4-a7e6-9dc522b744e1\" class=\"code\"><code class=\"language-python\">#!/usr/bin/python3\n    import json\n     \n    # Python 字典类型转换为 JSON 对象\n    data = {\n        'no' : 1,\n        'name' : 'hello',\n        'url' : 'http://tangly1024.com'\n    }\n     \n    json_str = json.dumps(data)\n    print (\"Python 原始数据：\", repr(data))\n    print (\"JSON 对象：\", json_str)</code></pre></li></ul><h2 id=\"5eaba42c-181d-4dad-8c21-1a87c1dd5fff\" class=\"\">2.公式</h2><ul><li style=\"list-style-type:disc\">数学公式<figure id=\"d67c5ed2-200c-4e30-a8ba-62378b6b1488\" class=\"equation\"><div class=\"equation-container\"><span class=\"katex-display\"><annotation encoding=\"application/x-tex\">f\\left(\\left[\\frac{1+\\{x, y\\}}{\\left(\\frac{x}{y}+\\frac{y}{x}\\right)(u+1)}+a\\right]^{3 / 2}\\right)\\tag{行标}</annotation></span></div></figure><figure id=\"2d9f9109-ff37-4185-84b9-ae5a9f8a50b6\" class=\"equation\"><div class=\"equation-container\"><span class=\"katex-display\"><annotation encoding=\"application/x-tex\">\\tau_{xy}=-\\tau_{yx}\\tau_{xz}=-\\tau_{zx}\\tau_{yz}=-\\tau{zy}</annotation></span></div></figure></li><li style=\"list-style-type:disc\">化学方程<p id=\"1b13a7ba-c335-4def-bc48-1ad61bc9f038\" class=\"\"><span data-token-index=\"0\" contenteditable=\"false\" class=\"notion-text-equation-token\" style=\"user-select:all;-webkit-user-select:all;-moz-user-select:all\"><span></span><span><annotation encoding=\"application/x-tex\">\\ce{2H2O-&gt;2H2 + O2}\n    </annotation></span><span></span></span></p></li></ul><ul><li><summary>其他更多公式</summary><figure id=\"dd0e5601-0322-464e-8f04-e108e2d9fea4\" class=\"equation\"><div class=\"equation-container\"><span class=\"katex-display\"><annotation encoding=\"application/x-tex\">\\begin{aligned}\n    AACD \\Rightarrow AAAD &amp;= \\frac 1 3\\\\ \n    AACD \\Rightarrow AACD &amp;= \\frac 1 3 + \\frac 1 6 = \\frac 1 2  \\\\ \n    AACD \\Rightarrow AACC &amp;= \\frac 1 6 \\end{aligned}</annotation></span></div></figure><figure id=\"0596cc73-c9f2-4f14-9e7e-6acfd84fd307\" class=\"equation\"><div class=\"equation-container\"><span class=\"katex-display\"><annotation encoding=\"application/x-tex\">\\begin{bmatrix}\n            c_{0}&amp;c_{n-1}&amp;c_{n-2}&amp;\\cdots &amp;c_{1}\\\\\n            c_{1}&amp;c_{0}&amp;c_{n-1} &amp;  \\cdots &amp;c_{2}\\\\\n            c_{2}&amp;c_{1}&amp;c_{0}&amp;\\cdots  &amp;c_3 \\\\\n            \\vdots &amp;\\vdots&amp; \\vdots&amp;\\ddots &amp;\\vdots \\\\\n            c_{n-1}&amp;c_{n-2}&amp;c_{n-3}&amp;\\dots &amp;c_{0}\n    \\end{bmatrix}</annotation></span></div></figure><figure id=\"e33bfe63-f618-463a-beda-eda0882fb89d\" class=\"equation\"><div class=\"equation-container\"><span class=\"katex-display\"><annotation encoding=\"application/x-tex\">\\begin{aligned} \\sin 2\\theta &amp; = 2\\sin \\theta \\cos \\theta \\\\ &amp; = \\cfrac{2 \\tan \\theta}{1+\\tan^2 \\theta} \\end{aligned}</annotation></span></div></figure><p id=\"2a9ce3d2-d667-402e-be83-a9986c1401f2\" class=\"\">\n    </p><figure id=\"1971da03-ef04-42f6-8a85-31b47dfc459b\" class=\"equation\"><div class=\"equation-container\"><span class=\"katex-display\"><annotation encoding=\"application/x-tex\">AACD\\Rightarrow \\left\\{\\begin{matrix}\n    第1次取值 &amp; 第2次取值 &amp; 概率 &amp; 最终状态\\\\\n    A &amp; C,D &amp;= \\frac 1 2 \\times \\frac 2 3= \\frac 1 3 &amp;\\Rightarrow AAAD \\\\ \n    A &amp; A &amp;= \\frac 1 2 \\times \\frac 1 3= \\frac 1 6 &amp;\\Rightarrow AACD \\\\ \n    C,D &amp; A &amp;= 2 \\times \\frac 1 4 \\times \\frac 2 3= \\frac 1 3 &amp;\\Rightarrow CCAD \\\\ \n    C,D &amp; C,D &amp;= 2 \\times \\frac 1 4 \\times \\frac 1 3= \\frac 1 6 &amp;\\Rightarrow CCAA\n    \\end{matrix}\\right.&nbsp;</annotation></span></div></figure></li></ul>", "# 特殊段落\n\n## 1.代码\n\n```bash\n# Bash 安装zsh\n    $ sudo apt install zsh\n    \n    # 配置ohmyzsh\n    $ sh -c \"$(curl -fsSL <https://raw.github.com/robbyrussell/oh-my-zsh/master/tools/install.sh>)\"\n    \n    # 配置ohmyzsh插件\n    # zsh-autosuggestions\n    $ git clone git://github.com/zsh-users/zsh-autosuggestions $ZSH_CUSTOM/plugins/zsh-autosuggestions\n    \n    // 启用插件\n    $ vim .zshrc\n    plugins=(git z zsh-autosuggestions zsh-syntax-highlighting)\n```\n\n* ```bash\n  ps -ef | grep java | awk '{print $2}' | xargs kill -9\n  ```\n\n  ```java\n  @Test\n      public void test11() {\n      \n        long start = System.currentTimeMillis();\n        int a = 0;\n        for(int i=0;i<1000000000;i++){\n            try {\n                a++;\n            }catch (Exception e){\n                e.printStackTrace();\n            }\n        }\n        long useTime = System.currentTimeMillis()-start;\n        System.out.println(\"useTime:\"+useTime);\n      }\n  ```\n\n  ```python\n  #!/usr/bin/python3\n      import json\n       \n      # Python 字典类型转换为 JSON 对象\n      data = {\n          'no' : 1,\n          'name' : 'hello',\n          'url' : 'http://tangly1024.com'\n      }\n       \n      json_str = json.dumps(data)\n      print (\"Python 原始数据：\", repr(data))\n      print (\"JSON 对象：\", json_str)\n  ```\n\n## 2.公式\n\n* 数学公式\n  $$\n  f\\left(\\left[\\frac{1+\\{x, y\\}}{\\left(\\frac{x}{y}+\\frac{y}{x}\\right)(u+1)}+a\\right]^{3 / 2}\\right)\\tag{行标}\n  $$\n\n\n  $$\n  \\tau_{xy}=-\\tau_{yx}\\tau_{xz}=-\\tau_{zx}\\tau_{yz}=-\\tau{zy}\n  $$\n\n* 化学方程\\\\ce{2H2O->2H2 + O2}\n* $$\n  \\begin{aligned}\n      AACD \\Rightarrow AAAD &= \\frac 1 3\\\\ \n      AACD \\Rightarrow AACD &= \\frac 1 3 + \\frac 1 6 = \\frac 1 2  \\\\ \n      AACD \\Rightarrow AACC &= \\frac 1 6 \\end{aligned}\n  $$\n\n\n  $$\n  \\begin{bmatrix}\n              c_{0}&c_{n-1}&c_{n-2}&\\cdots &c_{1}\\\\\n              c_{1}&c_{0}&c_{n-1} &  \\cdots &c_{2}\\\\\n              c_{2}&c_{1}&c_{0}&\\cdots  &c_3 \\\\\n              \\vdots &\\vdots& \\vdots&\\ddots &\\vdots \\\\\n              c_{n-1}&c_{n-2}&c_{n-3}&\\dots &c_{0}\n      \\end{bmatrix}\n  $$\n$$\n\\begin{aligned} \\sin 2\\theta & = 2\\sin \\theta \\cos \\theta \\\\ & = \\cfrac{2 \\tan \\theta}{1+\\tan^2 \\theta} \\end{aligned}\n$$\n\n$$\nAACD\\Rightarrow \\left\\{\\begin{matrix}\n    第1次取值 & 第2次取值 & 概率 & 最终状态\\\\\n    A & C,D &= \\frac 1 2 \\times \\frac 2 3= \\frac 1 3 &\\Rightarrow AAAD \\\\ \n    A & A &= \\frac 1 2 \\times \\frac 1 3= \\frac 1 6 &\\Rightarrow AACD \\\\ \n    C,D & A &= 2 \\times \\frac 1 4 \\times \\frac 2 3= \\frac 1 3 &\\Rightarrow CCAD \\\\ \n    C,D & C,D &= 2 \\times \\frac 1 4 \\times \\frac 1 3= \\frac 1 6 &\\Rightarrow CCAA\n    \\end{matrix}\\right.\n$$\n"},
	{"187", "$foo$", "\\$foo\\$\n"},
	{"186", "<span>$foo$</span>", "$foo$\n"},
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transform=\"translate(8749,0)\"><g transform=\"translate(342,0)\"><rect stroke=\"none\" width=\"796\" height=\"60\" x=\"0\" y=\"220\"></rect><g transform=\"translate(60,566)\"><use transform=\"scale(0.707)\" xlink:href=\"#MJMATHI-70\" x=\"0\" y=\"0\"></use><use transform=\"scale(0.5)\" xlink:href=\"#MJMAIN-32\" x=\"712\" y=\"-326\"></use></g><use transform=\"scale(0.707)\" xlink:href=\"#MJMAIN-32\" x=\"313\" y=\"-531\"></use></g></g><use xlink:href=\"#MJMAIN-29\" x=\"10009\" y=\"0\"></use><use xlink:href=\"#MJMAIN-3D\" x=\"10676\" y=\"0\"></use><g transform=\"translate(11732,0)\"><use xlink:href=\"#MJMATHI-73\" x=\"0\" y=\"0\"></use><use transform=\"scale(0.707)\" xlink:href=\"#MJMAIN-2032\" x=\"663\" y=\"445\"></use><use transform=\"scale(0.707)\" xlink:href=\"#MJMAIN-32\" x=\"663\" y=\"-435\"></use></g><use xlink:href=\"#MJMAIN-28\" x=\"12656\" y=\"0\"></use><use xlink:href=\"#MJMATHI-78\" x=\"13045\" y=\"0\"></use><use xlink:href=\"#MJMAIN-29\" x=\"13618\" y=\"0\"></use></g><g transform=\"translate(0,-6046)\"><use xlink:href=\"#MJMATHI-68\" x=\"0\" y=\"0\"></use><use transform=\"scale(0.707)\" xlink:href=\"#MJMAIN-31\" x=\"815\" y=\"-213\"></use><g transform=\"translate(1030,0)\"><use xlink:href=\"#MJMATHI-70\" x=\"0\" y=\"0\"></use><use transform=\"scale(0.707)\" xlink:href=\"#MJMAIN-32\" x=\"712\" y=\"-213\"></use></g></g></g></svg><span class=\"MJX_Assistive_MathML\" role=\"presentation\"><math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mtext>&nbsp;</mtext><mspace linebreak=\"newline\"></mspace><msub><mi>h</mi><mn>0</mn></msub><msub><mi>p</mi><mn>0</mn></msub><mo>=</mo><msubsup><mi>s</mi><mn>0</mn><mo>′</mo></msubsup><mo stretchy=\"false\">(</mo><mi>x</mi><mo stretchy=\"false\">)</mo><mspace linebreak=\"newline\"></mspace><mo stretchy=\"false\">(</mo><msub><mi>h</mi><mn>0</mn></msub><mo>+</mo><msub><mi>h</mi><mn>1</mn></msub><mo stretchy=\"false\">)</mo><mo stretchy=\"false\">(</mo><mfrac><msub><mi>p</mi><mn>0</mn></msub><mn>2</mn></mfrac><mo>+</mo><mfrac><msub><mi>p</mi><mn>1</mn></msub><mn>2</mn></mfrac><mo>+</mo><mfrac><msub><mi>p</mi><mn>2</mn></msub><mn>2</mn></mfrac><mo stretchy=\"false\">)</mo><mo>=</mo><msubsup><mi>s</mi><mn>1</mn><mo>′</mo></msubsup><mo stretchy=\"false\">(</mo><mi>x</mi><mo stretchy=\"false\">)</mo><mspace linebreak=\"newline\"></mspace><mo stretchy=\"false\">(</mo><msub><mi>h</mi><mn>0</mn></msub><mo>−</mo><msub><mi>h</mi><mn>1</mn></msub><mo stretchy=\"false\">)</mo><mo stretchy=\"false\">(</mo><mfrac><msub><mi>p</mi><mn>0</mn></msub><mn>2</mn></mfrac><mo>−</mo><mfrac><msub><mi>p</mi><mn>1</mn></msub><mn>2</mn></mfrac><mo>+</mo><mfrac><msub><mi>p</mi><mn>2</mn></msub><mn>2</mn></mfrac><mo stretchy=\"false\">)</mo><mo>=</mo><msubsup><mi>s</mi><mn>2</mn><mo>′</mo></msubsup><mo stretchy=\"false\">(</mo><mi>x</mi><mo stretchy=\"false\">)</mo><mspace linebreak=\"newline\"></mspace><msub><mi>h</mi><mn>1</mn></msub><msub><mi>p</mi><mn>2</mn></msub></math></span></span><script type=\"math/tex;mode=inline\" id=\"MathJax-Element-58\">\\ \\\\ h_0p_0=s'_0(x) \\\\ (h_0+h_1)(\\frac{p_0}{2}+\\frac{p_1}{2}+\\frac{p_2}{2})=s'_1(x)\\\\ (h_0-h_1)(\\frac{p_0}{2}-\\frac{p_1}{2}+\\frac{p_2}{2} )=s'_2(x) \\\\ h_1p_2</script><span class=\"tex2jax_ignore math-holder\">\\ \\\\ h_0p_0=s'_0(x) \\\\ (h_0+h_1)(\\frac{p_0}{2}+\\frac{p_1}{2}+\\frac{p_2}{2})=s'_1(x)\\\\ (h_0-h_1)(\\frac{p_0}{2}-\\frac{p_1}{2}+\\frac{p_2}{2} )=s'_2(x) \\\\ h_1p_2</span></span></span> </p>", "$$\n\\ \\\\ h_0p_0=s'_0(x) \\\\ (h_0+h_1)(\\frac{p_0}{2}+\\frac{p_1}{2}+\\frac{p_2}{2})=s'_1(x)\\\\ (h_0-h_1)(\\frac{p_0}{2}-\\frac{p_1}{2}+\\frac{p_2}{2} )=s'_2(x) \\\\ h_1p_2\n$$\n"},
	{"184", "<div class=\"highlight-container\" data-rel=\"C\"><div class=\"highlight-container\"><figure class=\"iseeu highlight c\"><table><tbody><tr><td class=\"gutter\"><pre><span class=\"line\">1</span><br><span class=\"line\">2</span><br><span class=\"line\">3</span><br><span class=\"line\">4</span><br><span class=\"line\">5</span><br><span class=\"line\">6</span><br><span class=\"line\">7</span><br><span class=\"line\">8</span><br></pre></td><td class=\"code\"><pre><span class=\"line\"><span class=\"comment\">// 如果alpha的值域是[0,1]，这里相当于将其拉伸为[0,255]</span></span><br><span class=\"line\"><span class=\"comment\">// 所以相当于是 Alpha = 1 - (1 - Alpha1) * ( 1 - Alpha2)乘以了两次255</span></span><br><span class=\"line\"><span class=\"comment\">// 当a1和a2都接近于0的时候，会导致计算得到的A值不为0，导致叠加不正常</span></span><br><span class=\"line\"><span class=\"type\">uint32_t</span> A = (<span class=\"number\">0xffff</span> - (<span class=\"number\">0xff</span> - a1) * (<span class=\"number\">0xff</span> - a2));</span><br><span class=\"line\"><span class=\"comment\">// 下面左边部分少左移8位，相当于乘以了255</span></span><br><span class=\"line\"><span class=\"type\">uint32_t</span> R = (((rgba1 &lt;&lt; <span class=\"number\">8</span> &amp; <span class=\"number\">0xff00</span>U) * a1 + (rgba2 &gt;&gt; <span class=\"number\">0</span>  &amp; <span class=\"number\">0xff</span>U) * a2 *(<span class=\"number\">0xff</span> - a1)) / A) &amp; <span class=\"number\">0xff</span>U;</span><br><span class=\"line\"><span class=\"type\">uint32_t</span> G = (((rgba1 &gt;&gt; <span class=\"number\">0</span> &amp; <span class=\"number\">0xff00</span>U) * a1 + (rgba2 &gt;&gt; <span class=\"number\">8</span>  &amp; <span class=\"number\">0xff</span>U) * a2 *(<span class=\"number\">0xff</span> - a1)) / A) &amp; <span class=\"number\">0xff</span>U;</span><br><span class=\"line\"><span class=\"type\">uint32_t</span> B = (((rgba1 &gt;&gt; <span class=\"number\">8</span> &amp; <span class=\"number\">0xff00</span>U) * a1 + (rgba2 &gt;&gt; <span class=\"number\">16</span> &amp; <span class=\"number\">0xff</span>U) * a2 *(<span class=\"number\">0xff</span> - a1)) / A) &amp; <span class=\"number\">0xff</span>U;</span><br></pre></td></tr></tbody></table></figure><div class=\"copy-button\"><i class=\"fa-regular fa-copy\"></i></div><div class=\"fold-button\"><i class=\"fa-solid fa-chevron-down\"></i></div></div></div>", "```c\n// 如果alpha的值域是[0,1]，这里相当于将其拉伸为[0,255]\n// 所以相当于是 Alpha = 1 - (1 - Alpha1) * ( 1 - Alpha2)乘以了两次255\n// 当a1和a2都接近于0的时候，会导致计算得到的A值不为0，导致叠加不正常\nuint32_t A = (0xffff - (0xff - a1) * (0xff - a2));\n// 下面左边部分少左移8位，相当于乘以了255\nuint32_t R = (((rgba1 << 8 & 0xff00U) * a1 + (rgba2 >> 0  & 0xffU) * a2 *(0xff - a1)) / A) & 0xffU;\nuint32_t G = (((rgba1 >> 0 & 0xff00U) * a1 + (rgba2 >> 8  & 0xffU) * a2 *(0xff - a1)) / A) & 0xffU;\nuint32_t B = (((rgba1 >> 8 & 0xff00U) * a1 + (rgba2 >> 16 & 0xffU) * a2 *(0xff - a1)) / A) & 0xffU;\n```\n"},
	{"183", "<pre data-index=\"0\" class=\"set-code-show\" name=\"code\"><code class=\"language-css hljs\"><ol class=\"hljs-ln\" style=\"width:100%\"><li><div class=\"hljs-ln-numbers\"><div class=\"hljs-ln-line hljs-ln-n\" data-line-number=\"1\"></div></div><div class=\"hljs-ln-code\"><div class=\"hljs-ln-line\"><span class=\"hljs-selector-tag\">html</span> {</div></div></li><li><div class=\"hljs-ln-numbers\"><div class=\"hljs-ln-line hljs-ln-n\" data-line-number=\"2\"></div></div><div class=\"hljs-ln-code\"><div class=\"hljs-ln-line\">  <span class=\"hljs-attribute\">overflow-y</span>: overlay;</div></div></li><li><div class=\"hljs-ln-numbers\"><div class=\"hljs-ln-line hljs-ln-n\" data-line-number=\"3\"></div></div><div class=\"hljs-ln-code\"><div class=\"hljs-ln-line\">}</div></div></li></ol></code><div class=\"hljs-button signin active\" data-title=\"登录复制\" data-report-click=\"{&quot;spm&quot;:&quot;1001.2101.3001.4334&quot;}\" onclick=\"hljs.signin(event)\"></div></pre>", "```css\nhtml {\n  overflow-y: overlay;\n}\n```\n"},
	{"182", "<p><markerow8 data-id=\"G2wN\" data-pkid=\"5272681\" class=\"wucaiclrx1\" style=\"color: rgb(0, 0, 0); background-color: rgba(244, 220, 97, 0.698);\">清晨的阳光透过淡薄的云层，纷纷扬扬地落在了</markerow8><strong><markerow8 data-id=\"G2wN\" data-pkid=\"5272681\" class=\"wucaiclrx1\" style=\"color: rgb(0, 0, 0); background-color: rgba(244, 220, 97, 0.698);\">幽静的林间小道</markerow8></strong><markerow8 data-id=\"G2wN\" data-pkid=\"5272681\" class=\"wucaiclrx1\" style=\"color: rgb(0, 0, 0); background-color: rgba(244, 220, 97, 0.698);\">上。树叶在微</markerow8><em><markerow8 data-id=\"G2wN\" data-pkid=\"5272681\" class=\"wucaiclrx1\" style=\"color: rgb(0, 0, 0); background-color: rgba(244, 220, 97, 0.698);\">风中轻轻摇曳，</markerow8></em> <markerow8 data-id=\"G2wN\" data-pkid=\"5272681\" class=\"wucaiclrx1\" style=\"color: rgb(0, 0, 0); background-color: rgba(244, 220, 97, 0.698);\">仿佛在跳着一场优雅的舞蹈。草丛中，晶莹的露珠闪烁着微光，宛如一颗颗细碎的宝石。鸟儿欢快地歌唱着，声音</markerow8><em><strong><markerow8 data-id=\"G2wN\" data-pkid=\"5272681\" class=\"wucaiclrx1\" style=\"color: rgb(0, 0, 0); background-color: rgba(244, 220, 97, 0.698);\">清脆悦耳，在这宁静而美丽的画面中增添了一</markerow8></strong></em><markerow8 data-id=\"G2wN\" data-pkid=\"5272681\" class=\"wucaiclrx1\" style=\"color: rgb(0, 0, 0); background-color: rgba(244, 220, 97, 0.698);\">抹灵动的气息。</markerow8></p>", "清晨的阳光透过淡薄的云层，纷纷扬扬地落在了**幽静的林间小道**上。树叶在微*风中轻轻摇曳，* 仿佛在跳着一场优雅的舞蹈。草丛中，晶莹的露珠闪烁着微光，宛如一颗颗细碎的宝石。鸟儿欢快地歌唱着，声音***清脆悦耳，在这宁静而美丽的画面中增添了一***抹灵动的气息。\n"},
	{"181", "<p><span class=\"vditor-reset__preview\"><img src=\"https://b3logfile.com/file/2024/08/image-tU91NvB.png?imageView2/2/interlace/1/format/webp\" alt=\"image.png\" style=\"background-image: none; background-color: transparent;\"><div class=\"fn__flex-inline\">\n<svg><use xlink:href=\"#iconPhotoActual\"></use></svg>\n<span class=\"fn__space5\"></span>496 x 344</div></span></p>", "![image.png](https://b3logfile.com/file/2024/08/image-tU91NvB.png?imageView2/2/interlace/1/format/webp)\n"},
	{"180", "<ul class=\"fa-ul\">\n  <li data-marker=\"*\"><span class=\"fa-li\"><i class=\"fas fa-square\"></i></span>\n    <p>foo</p>\n\n    <div class=\"language-c highlighter-rouge\"><div class=\"highlight\"><pre class=\"highlight\"><code><span class=\"cp\">#include</span> <span class=\"cpf\">&lt;stdio.h&gt;</span><span class=\"cp\">\n</span>\n<span class=\"kt\">int</span> <span class=\"nf\">main</span><span class=\"p\">(</span><span class=\"kt\">void</span><span class=\"p\">)</span>\n<span class=\"p\">{</span>\n    <span class=\"n\">string</span> <span class=\"n\">answer</span> <span class=\"o\">=</span> <span class=\"n\">get_string</span><span class=\"p\">(</span><span class=\"s\">\"What's your name? \"</span><span class=\"p\">);</span>\n    <span class=\"n\">printf</span><span class=\"p\">(</span><span class=\"s\">\"hello, %s</span><span class=\"se\">\\n</span><span class=\"s\">\"</span><span class=\"p\">,</span> <span class=\"n\">answer</span><span class=\"p\">);</span>\n<span class=\"p\">}</span>\n</code></pre></div>    </div>\n    <p>bar</p>\n  </li>\n</ul>", "* foo\n\n  ```c\n  #include <stdio.h>\n\n  int main(void)\n  {\n      string answer = get_string(\"What's your name? \");\n      printf(\"hello, %s\\n\", answer);\n  }\n  ```\n\n  bar\n"},
	{"179", "<ul>\n<li>foo\n<pre><div class=\"vditor-copy\"><textarea></textarea><span aria-label=\"复制\" onmouseover=\"this.setAttribute('aria-label', '复制')\" class=\"vditor-tooltipped vditor-tooltipped__w\" onclick=\"this.previousElementSibling.select();document.execCommand('copy');this.setAttribute('aria-label', '已复制')\"><svg><use xlink:href=\"#vditor-icon-copy\"></use></svg></span></div><code class=\"highlight-chroma hljs nginx\" style=\"max-height: 992px;\"><span class=\"highlight-line\"><span class=\"highlight-cl\"><span class=\"hljs-attribute\">bar</span>\n</span></span></code><span style=\"position: absolute\">&ZeroWidthSpace;</span></pre>\n</li>\n</ul>", "* foo\n  ```\n  bar\n  ```\n"},
	{"178", "<details open=\"\">\n\t\t\t\t<summary>Example Feature Code Implementation</summary>\n\t\t\t\t<pre><code class=\"language-fea\">feature aalt {\n  feature salt;\n  feature smcp;\n  feature swsh;\n  sub quoteleft by quoteleft.fr;\n  sub quoteright by quoteright.fr;\n} aalt;\n</code></pre>\n\t\t\t</details>", "* Example Feature Code Implementation\n  ```fea\n  feature aalt {\n    feature salt;\n    feature smcp;\n    feature swsh;\n    sub quoteleft by quoteleft.fr;\n    sub quoteright by quoteright.fr;\n  } aalt;\n  ```\n"},
	{"177", "<details open=\"\"><summary>foo1</summary>bar1</details><details open=\"\"><summary>foo2</summary>bar2</details>", "* foo1\n  bar1\n\n* foo2\n  bar2\n"},
	{"176", "<details open=\"\">\n<summary>Docker Deployment</summary>\n<div class=\"markdown-heading\" dir=\"auto\"><h4 tabindex=\"-1\" class=\"heading-element\" dir=\"auto\">Overview</h4><a id=\"user-content-overview\" class=\"anchor\" aria-label=\"Permalink: Overview\" href=\"#overview\"><svg class=\"octicon octicon-link\" viewBox=\"0 0 16 16\" version=\"1.1\" width=\"16\" height=\"16\" aria-hidden=\"true\"><path d=\"m7.775 3.275 1.25-1.25a3.5 3.5 0 1 1 4.95 4.95l-2.5 2.5a3.5 3.5 0 0 1-4.95 0 .751.751 0 0 1 .018-1.042.751.751 0 0 1 1.042-.018 1.998 1.998 0 0 0 2.83 0l2.5-2.5a2.002 2.002 0 0 0-2.83-2.83l-1.25 1.25a.751.751 0 0 1-1.042-.018.751.751 0 0 1-.018-1.042Zm-4.69 9.64a1.998 1.998 0 0 0 2.83 0l1.25-1.25a.751.751 0 0 1 1.042.018.751.751 0 0 1 .018 1.042l-1.25 1.25a3.5 3.5 0 1 1-4.95-4.95l2.5-2.5a3.5 3.5 0 0 1 4.95 0 .751.751 0 0 1-.018 1.042.751.751 0 0 1-1.042.018 1.998 1.998 0 0 0-2.83 0l-2.5 2.5a1.998 1.998 0 0 0 0 2.83Z\"></path></svg></a></div>\n<p dir=\"auto\">The easiest way to serve SiYuan on a server is to deploy it through Docker.</p>\n<ul dir=\"auto\">\n<li>Image name <code>b3log/siyuan</code></li>\n<li><a href=\"https://hub.docker.com/r/b3log/siyuan\" rel=\"nofollow\">Image URL</a></li>\n</ul>\n</details>", "* Docker Deployment\n  #### Overview\n\n  The easiest way to serve SiYuan on a server is to deploy it through Docker.\n  * Image name `b3log/siyuan`\n  * [Image URL](https://hub.docker.com/r/b3log/siyuan)\n"},
	{"175", "<p><span class=\"math math-inline\"><span class=\"katex\"><span class=\"katex-mathml\"><math xmlns=\"http://www.w3.org/1998/Math/MathML\"><semantics><mrow><mi>E</mi><mo>=</mo><mi>m</mi><msup><mi>c</mi><mn>2</mn></msup></mrow><annotation encoding=\"application/x-tex\">E = mc^2</annotation></semantics></math></span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6833em;\"></span><span class=\"mord mathnormal\" style=\"margin-right: 0.05764em;\">E</span><span class=\"mspace\" style=\"margin-right: 0.2778em;\"></span><span class=\"mrel\">=</span><span class=\"mspace\" style=\"margin-right: 0.2778em;\"></span></span><span class=\"base\"><span class=\"strut\" style=\"height: 0.8141em;\"></span><span class=\"mord mathnormal\">m</span><span class=\"mord\"><span class=\"mord mathnormal\">c</span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.8141em;\"><span style=\"top: -3.063em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"></span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">2</span></span></span></span></span></span></span></span></span></span></span></span></p>", "$E = mc^2$\n"},
	{"174", "<p><span class=\"katex ds-markdown-math\"><span class=\"katex-mathml\"><math xmlns=\"http://www.w3.org/1998/Math/MathML\"><semantics><mrow><mi>x</mi><mo>=</mo><mfrac><mrow><mo>−</mo><mi>b</mi><mo>±</mo><msqrt><mrow><msup><mi>b</mi><mn>2</mn></msup><mo>−</mo><mn>4</mn><mi>a</mi><mi>c</mi></mrow></msqrt></mrow><mrow><mn>2</mn><mi>a</mi></mrow></mfrac></mrow><annotation encoding=\"application/x-tex\">x = \\frac{-b \\pm \\sqrt{b^2 - 4ac}}{2a}</annotation></semantics></math></span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"strut\" style=\"height:0.4306em;\"></span><span class=\"mord mathnormal\">x</span><span class=\"mspace\" style=\"margin-right:0.2778em;\"></span><span class=\"mrel\">=</span><span class=\"mspace\" style=\"margin-right:0.2778em;\"></span></span><span class=\"base\"><span class=\"strut\" style=\"height:1.3845em;vertical-align:-0.345em;\"></span><span class=\"mord\"><span class=\"mopen nulldelimiter\"></span><span class=\"mfrac\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:1.0395em;\"><span style=\"top:-2.655em;\"><span class=\"pstrut\" style=\"height:3em;\"></span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\">2</span><span class=\"mord mathnormal mtight\">a</span></span></span></span><span style=\"top:-3.23em;\"><span class=\"pstrut\" style=\"height:3em;\"></span><span class=\"frac-line\" style=\"border-bottom-width:0.04em;\"></span></span><span style=\"top:-3.394em;\"><span class=\"pstrut\" style=\"height:3em;\"></span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\">−</span><span class=\"mord mathnormal mtight\">b</span><span class=\"mbin mtight\">±</span><span class=\"mord sqrt mtight\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.9221em;\"><span class=\"svg-align\" style=\"top:-3em;\"><span class=\"pstrut\" style=\"height:3em;\"></span><span class=\"mord mtight\" style=\"padding-left:0.833em;\"><span class=\"mord mtight\"><span class=\"mord mathnormal mtight\">b</span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.7463em;\"><span style=\"top:-2.786em;margin-right:0.0714em;\"><span class=\"pstrut\" style=\"height:2.5em;\"></span><span class=\"sizing reset-size3 size1 mtight\"><span class=\"mord mtight\">2</span></span></span></span></span></span></span></span><span class=\"mbin mtight\">−</span><span class=\"mord mtight\">4</span><span class=\"mord mathnormal mtight\">a</span><span class=\"mord mathnormal mtight\">c</span></span></span><span style=\"top:-2.8821em;\"><span class=\"pstrut\" style=\"height:3em;\"></span><span class=\"hide-tail mtight\" style=\"min-width:0.853em;height:1.08em;\"><svg xmlns=\"http://www.w3.org/2000/svg\" width=\"400em\" height=\"1.08em\" viewBox=\"0 0 400000 1080\" preserveAspectRatio=\"xMinYMin slice\"><path d=\"M95,702\nc-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5,-10,-9.5,-14\nc0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54\nc44.2,-33.3,65.8,-50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10\ns173,378,173,378c0.7,0,35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429\nc69,-144,104.5,-217.7,106.5,-221\nl0 -0\nc5.3,-9.3,12,-14,20,-14\nH400000v40H845.2724\ns-225.272,467,-225.272,467s-235,486,-235,486c-2.7,4.7,-9,7,-19,7\nc-6,0,-10,-1,-12,-3s-194,-422,-194,-422s-65,47,-65,47z\nM834 80h400000v40h-400000z\"></path></svg></span></span></span><span class=\"vlist-s\">&ZeroWidthSpace;</span></span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.1179em;\"><span></span></span></span></span></span></span></span></span></span><span class=\"vlist-s\">&ZeroWidthSpace;</span></span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.345em;\"><span></span></span></span></span></span><span class=\"mclose nulldelimiter\"></span></span></span></span></span></p>", "$$\nx = \\frac{-b \\pm \\sqrt{b^2 - 4ac}}{2a}\n$$\n"},
	{"173", "<p>对于二次方程 <span class=\"katex\"><span class=\"katex-mathml\"><math xmlns=\"http://www.w3.org/1998/Math/MathML\"><semantics><mrow><mi>a</mi><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mi>b</mi><mi>x</mi><mo>+</mo><mi>c</mi><mo>=</mo><mn>0</mn></mrow><annotation encoding=\"application/x-tex\">ax^2 + bx + c = 0</annotation></semantics></math></span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"strut\" style=\"height:0.8974em;vertical-align:-0.0833em;\"></span><span class=\"mord mathnormal\">a</span><span class=\"mord\"><span class=\"mord mathnormal\">x</span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height:0.8141em;\"><span style=\"top:-3.063em;margin-right:0.05em;\"><span class=\"pstrut\" style=\"height:2.7em;\"></span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">2</span></span></span></span></span></span></span></span><span class=\"mspace\" style=\"margin-right:0.2222em;\"></span><span class=\"mbin\">+</span><span class=\"mspace\" style=\"margin-right:0.2222em;\"></span></span><span class=\"base\"><span class=\"strut\" style=\"height:0.7778em;vertical-align:-0.0833em;\"></span><span class=\"mord mathnormal\">b</span><span class=\"mord mathnormal\">x</span><span class=\"mspace\" style=\"margin-right:0.2222em;\"></span><span class=\"mbin\">+</span><span class=\"mspace\" style=\"margin-right:0.2222em;\"></span></span><span class=\"base\"><span class=\"strut\" style=\"height:0.4306em;\"></span><span class=\"mord mathnormal\">c</span><span class=\"mspace\" style=\"margin-right:0.2778em;\"></span><span class=\"mrel\">=</span><span class=\"mspace\" style=\"margin-right:0.2778em;\"></span></span><span class=\"base\"><span class=\"strut\" style=\"height:0.6444em;\"></span><span class=\"mord\">0</span></span></span></span>，其解可以通过以下公式求得：</p>", "对于二次方程 $ax^2 + bx + c = 0$，其解可以通过以下公式求得：\n"},
	{"172", "<pre><section><pre><code><span><span>interface</span>&nbsp;<span>IUserAction</span>&nbsp;</span>{<p>&nbsp;&nbsp;&nbsp;&nbsp;<span><span>fun</span>&nbsp;<span>attack</span><span>()</span></span></p><p>&nbsp;&nbsp;&nbsp;&nbsp;<span><span>fun</span>&nbsp;<span>defense</span><span>()</span></span><br>}</p></code></pre></section></pre>", "```\ninterface IUserAction {\n\n    fun attack()\n\n    fun defense()\n}\n```\n"},
	{"171", "<pre style=\"text-align: left;\"><section style=\"font-size: 16px;color: rgb(62, 62, 62);line-height: 1.6;letter-spacing: 0px;font-family: &quot;Helvetica Neue&quot;, Helvetica, &quot;Hiragino Sans GB&quot;, &quot;Microsoft YaHei&quot;, Arial, sans-serif;\"><pre style=\"font-size: inherit;color: inherit;line-height: inherit;\"><code style=\"margin-right: 2px;margin-left: 2px;line-height: 15px;font-size: 11px;word-spacing: -3px;letter-spacing: 0px;font-family: Consolas, Inconsolata, Courier, monospace;border-radius: 0px;color: rgb(169, 183, 198);background: rgb(40, 43, 46);padding: 0.5em;overflow-wrap: normal !important;word-break: normal !important;overflow: auto !important;display: -webkit-box !important;\"><span style=\"font-size: inherit;color: inherit;line-height: inherit;overflow-wrap: inherit !important;word-break: inherit !important;\"><span style=\"line-height: inherit;color: rgb(248, 35, 117);overflow-wrap: inherit !important;word-break: inherit !important;\">interface</span>&nbsp;<span style=\"line-height: inherit;color: rgb(165, 218, 45);overflow-wrap: inherit !important;word-break: inherit !important;\">IUserAction</span>&nbsp;</span>{<br><br>&nbsp;&nbsp;&nbsp;&nbsp;<span style=\"font-size: inherit;line-height: inherit;color: rgb(248, 35, 117);overflow-wrap: inherit !important;word-break: inherit !important;\"><span style=\"line-height: inherit;overflow-wrap: inherit !important;word-break: inherit !important;\">fun</span>&nbsp;<span style=\"line-height: inherit;color: rgb(165, 218, 45);overflow-wrap: inherit !important;word-break: inherit !important;\">attack</span><span style=\"line-height: inherit;color: rgb(255, 152, 35);overflow-wrap: inherit !important;word-break: inherit !important;\">()</span></span><br><br>&nbsp;&nbsp;&nbsp;&nbsp;<span style=\"font-size: inherit;line-height: inherit;color: rgb(248, 35, 117);overflow-wrap: inherit !important;word-break: inherit !important;\"><span style=\"line-height: inherit;overflow-wrap: inherit !important;word-break: inherit !important;\">fun</span>&nbsp;<span style=\"line-height: inherit;color: rgb(165, 218, 45);overflow-wrap: inherit !important;word-break: inherit !important;\">defense</span><span style=\"line-height: inherit;color: rgb(255, 152, 35);overflow-wrap: inherit !important;word-break: inherit !important;\">()</span></span><br>}<br></code></pre></section><section style=\"margin-bottom: 24px;\"><br></section></pre>", "```\ninterface IUserAction {\n\n    fun attack()\n\n    fun defense()\n}\n\n```\n"},
	{"170", "<code>: ~ ! @ # $ % ^ &amp; * ( ) ` ; &lt; &gt; ? , [ ] { } ‘ “</code>", "``: ~ ! @ # $ % ^ & * ( ) ` ; < > ? , [ ] { } ‘ “``\n"},
	{"169", "<kbd class=\"string\">foo</kbd>", "<kbd>foo</kbd>\n"},
	{"168", "<section style=\"font-size: 16px;color: rgb(62, 62, 62);line-height: 1.6;letter-spacing: 0px;font-family: &quot;Helvetica Neue&quot;, Helvetica, &quot;Hiragino Sans GB&quot;, &quot;Microsoft YaHei&quot;, Arial, sans-serif;\"><pre style=\"font-size: inherit;color: inherit;line-height: inherit;\"><p style=\"font-size: 11px;word-spacing: -3px;letter-spacing: 0px;font-family: Consolas, Inconsolata, Courier, monospace;border-radius: 0px;color: rgb(169, 183, 198);background: rgb(40, 43, 46);padding: 0.5em;margin: 0px 8px;line-height: 1.75em;overflow-wrap: normal !important;word-break: normal !important;overflow: auto !important;display: -webkit-box !important;\"><span style=\"letter-spacing: 1px;\"><span style=\"font-size: inherit;line-height: inherit;color: rgb(204, 120, 50);overflow-wrap: inherit !important;word-break: inherit !important;\"><span style=\"line-height: inherit;overflow-wrap: inherit !important;word-break: inherit !important;\">fun</span>&nbsp;<span style=\"line-height: inherit;color: rgb(255, 198, 109);overflow-wrap: inherit !important;word-break: inherit !important;\">main</span><span style=\"line-height: inherit;color: rgb(104, 151, 187);overflow-wrap: inherit !important;word-break: inherit !important;\">()</span></span>:&nbsp;<span style=\"font-size: inherit;line-height: inherit;color: rgb(204, 120, 50);overflow-wrap: inherit !important;word-break: inherit !important;\">Unit</span>&nbsp;=&nbsp;runBlocking&nbsp;{<br>&nbsp;&nbsp;&nbsp;&nbsp;<span style=\"font-size: inherit;line-height: inherit;color: rgb(128, 128, 128);overflow-wrap: inherit !important;word-break: inherit !important;\">//&nbsp;创建3个Flow,生产数据</span><br>&nbsp;&nbsp;&nbsp;&nbsp;<span style=\"font-size: inherit;line-height: inherit;color: rgb(204, 120, 50);overflow-wrap: inherit !important;word-break: inherit !important;\">val</span>&nbsp;firstFlow&nbsp;=&nbsp;flowOf(<span style=\"font-size: inherit;line-height: inherit;color: rgb(104, 151, 187);overflow-wrap: inherit !important;word-break: inherit !important;\">1</span>,&nbsp;<span style=\"font-size: inherit;line-height: inherit;color: rgb(104, 151, 187);overflow-wrap: inherit !important;word-break: inherit !important;\">2</span>)<br>&nbsp;&nbsp;&nbsp;&nbsp;<span style=\"font-size: inherit;line-height: inherit;color: rgb(204, 120, 50);overflow-wrap: inherit !important;word-break: inherit !important;\">val</span>&nbsp;secondFlow&nbsp;=&nbsp;flow&nbsp;{<br>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;emit(<span style=\"font-size: inherit;line-height: inherit;color: rgb(104, 151, 187);overflow-wrap: inherit !important;word-break: inherit !important;\">3</span>)<br>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;emit(<span style=\"font-size: inherit;line-height: inherit;color: rgb(104, 151, 187);overflow-wrap: inherit !important;word-break: inherit !important;\">4</span>)<br>&nbsp;&nbsp;&nbsp;&nbsp;}<br>&nbsp;&nbsp;&nbsp;&nbsp;<span style=\"font-size: inherit;line-height: inherit;color: rgb(204, 120, 50);overflow-wrap: inherit !important;word-break: inherit !important;\">val</span>&nbsp;thirdFlow&nbsp;=&nbsp;listOf(<span style=\"font-size: inherit;line-height: inherit;color: rgb(104, 151, 187);overflow-wrap: inherit !important;word-break: inherit !important;\">5</span>,&nbsp;<span style=\"font-size: inherit;line-height: inherit;color: rgb(104, 151, 187);overflow-wrap: inherit !important;word-break: inherit !important;\">6</span>).asFlow()<br><br>&nbsp;&nbsp;&nbsp;&nbsp;<span style=\"font-size: inherit;line-height: inherit;color: rgb(128, 128, 128);overflow-wrap: inherit !important;word-break: inherit !important;\">//&nbsp;挨个收集,消费者</span><br>&nbsp;&nbsp;&nbsp;&nbsp;firstFlow.collect&nbsp;{<br>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;println(it)<br>&nbsp;&nbsp;&nbsp;&nbsp;}<br>&nbsp;&nbsp;&nbsp;&nbsp;secondFlow.collect&nbsp;{<br>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;println(it)<br>&nbsp;&nbsp;&nbsp;&nbsp;}<br>&nbsp;&nbsp;&nbsp;&nbsp;thirdFlow.collect&nbsp;{<br>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;println(it)<br>&nbsp;&nbsp;&nbsp;&nbsp;}<br>}<br></span></p></pre></section>", "```\nfun main(): Unit = runBlocking {\n    // 创建3个Flow,生产数据\n    val firstFlow = flowOf(1, 2)\n    val secondFlow = flow {\n        emit(3)\n        emit(4)\n    }\n    val thirdFlow = listOf(5, 6).asFlow()\n\n    // 挨个收集,消费者\n    firstFlow.collect {\n        println(it)\n    }\n    secondFlow.collect {\n        println(it)\n    }\n    thirdFlow.collect {\n        println(it)\n    }\n}\n```\n"},
	{"167", "<p style=\"text-align: left;\"><span style=\"cursor:pointer;\"><mjx-container jax=\"SVG\" display=\"true\" role=\"presentation\" tabindex=\"0\" ctxtmenu_counter=\"62\" data-formula=\"\\begin{aligned}\n    \\boldsymbol{m}\\times\\boldsymbol{n}\n    &amp;=\\begin{vmatrix}\\boldsymbol{i}&amp;1&amp;0\\\\\\boldsymbol{j}&amp;0&amp;1\\\\\\boldsymbol{k}&amp;f_x(x_0,y_0)&amp;f_y(x_0,y_0)\\end{vmatrix}\\\\\n    &amp;=\\begin{vmatrix}0&amp;1\\\\f_x(x_0,y_0)&amp;f_y(x_0,y_0)\\end{vmatrix}\\boldsymbol{i}-\\begin{vmatrix}1&amp;0\\\\f_x(x_0,y_0)&amp;f_y(x_0,y_0)\\end{vmatrix}\\boldsymbol{j}+\\begin{vmatrix}1&amp;0\\\\0&amp;1\\end{vmatrix}\\boldsymbol{k}\\\\\n    &amp;=-f_x(x_0,y_0)\\boldsymbol{i}-f_y(x_0,y_0)\\boldsymbol{j}+\\boldsymbol{k}=\\begin{pmatrix}-f_x(x_0,y_0)\\\\-f_y(x_0,y_0)\\\\1\\end{pmatrix}\n\\end{aligned}\" style=\"overflow-x: auto;outline: 0px;display: block;text-align: center;margin: 15px 0px;\"><svg xmlns=\"http://www.w3.org/2000/svg\" width=\"68.445ex\" height=\"24.287ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -5617.4 30252.9 10734.9\" aria-hidden=\"true\" style=\"height: auto;max-width: 300% !important;\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mtable\"><g data-mml-node=\"mtr\" transform=\"translate(0, 3445)\"><g data-mml-node=\"mtd\"><g data-mml-node=\"mi\"><path data-c=\"6D\" d=\"M24 296Q25 302 27 312T41 350T65 397T104 435T159 452Q203 452 234 435Q268 419 285 384L295 392Q305 401 317 410T349 429T389 445Q411 451 446 451Q560 451 592 383Q593 380 594 379L595 375L604 384Q675 452 762 452Q893 452 916 367Q918 356 918 334Q918 285 881 183T841 66Q838 43 849 43Q876 43 901 69T940 138Q945 156 949 159T969 162H975H986Q1006 162 1006 148Q1006 138 996 115T966 63T914 13T841 -8Q794 -8 758 16T721 82Q721 96 758 199T796 351Q796 401 753 401Q702 401 662 369T599 298Q597 294 567 172T533 40Q525 22 506 7T462 -8Q435 -8 422 8T409 39Q409 48 425 114T458 248T476 320Q478 330 478 348T474 377T462 393T449 399T433 400H428Q380 400 336 363Q301 332 281 298Q278 293 247 170T214 40Q206 22 187 7T143 -8T104 7T90 39Q90 47 108 124T146 274L164 347Q166 355 166 372Q166 401 149 401Q129 401 115 379T89 306Q84 288 80 285T55 282H44Q24 282 24 296Z\"></path></g><g data-mml-node=\"mo\" transform=\"translate(1254.2, 0)\"><path data-c=\"D7\" d=\"M630 29Q630 9 609 9Q604 9 587 25T493 118L389 222L284 117Q178 13 175 11Q171 9 168 9Q160 9 154 15T147 29Q147 36 161 51T255 146L359 250L255 354Q174 435 161 449T147 471Q147 480 153 485T168 490Q173 490 175 489Q178 487 284 383L389 278L493 382Q570 459 587 475T609 491Q630 491 630 471Q630 464 620 453T522 355L418 250L522 145Q606 61 618 48T630 29Z\"></path></g><g data-mml-node=\"mi\" transform=\"translate(2254.4, 0)\"><path data-c=\"6E\" d=\"M24 296Q25 302 27 312T41 350T65 397T104 435T159 452Q203 452 234 435Q268 419 285 384L293 391Q363 452 454 452Q575 446 597 367Q599 356 599 334Q599 285 562 183T522 66Q519 43 530 43Q557 43 582 69T621 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40T300 -303T89 -626Q78 -640 75 -642T61 -644H56Z\" transform=\"translate(0, -1028.5)\"></path><svg width=\"875\" height=\"427\" y=\"36.5\" x=\"0\" viewBox=\"0 96.4 875 427\"><path data-c=\"239F\" d=\"M579 -9Q578 -9 573 -9T554 -10T520 -10Q466 -10 463 -9Q460 -8 459 -5Q457 5 457 127V300Q457 602 458 605L462 609Q464 610 532 610Q548 610 558 610T573 610T578 609Q582 609 582 592T583 473V127Q583 -9 579 -9Z\" transform=\"scale(1, 1.033)\"></path></svg></g></g></g></g></g></g></g></svg></mjx-container></span><span style=\"color: black;font-family: &quot;PingFang SC&quot;;font-size: medium;letter-spacing: normal;text-align: start;\">知道了曲面</span><span style=\"font-family: &quot;PingFang SC&quot;;font-size: medium;letter-spacing: normal;text-align: start;color: rgb(136, 136, 136);\"></span><span style=\"color: black;font-family: &quot;PingFang SC&quot;;font-size: medium;letter-spacing: normal;text-align: start;cursor: pointer;visibility: visible;\">&nbsp;<mjx-container jax=\"SVG\" 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17Q309 13 296 6T270 -6Q250 -11 231 -11Q185 -11 150 11T104 82Q103 89 103 113Q103 170 138 262T173 379Q173 380 173 381Q173 390 173 393T169 400T158 404H154Q131 404 112 385T82 344T65 302T57 280Q55 278 41 278H27Q21 284 21 287Z\"></path></g><g transform=\"translate(4257,0)\"><path stroke-width=\"1\" d=\"M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z\"></path></g></g></svg>&nbsp;</mjx-container></span><span style=\"color: black;font-family: &quot;PingFang SC&quot;;font-size: medium;letter-spacing: normal;text-align: start;\">在</span><span style=\"font-family: &quot;PingFang SC&quot;;font-size: medium;letter-spacing: normal;text-align: start;color: rgb(136, 136, 136);\"></span><span style=\"color: black;font-family: &quot;PingFang SC&quot;;font-size: medium;letter-spacing: normal;text-align: start;cursor: pointer;visibility: visible;\">&nbsp;<mjx-container jax=\"SVG\" role=\"presentation\" tabindex=\"0\" ctxtmenu_counter=\"30\" data-formula=\"(x_0,y_0)\" style=\"visibility: visible;\"><svg xmlns:xlink=\"http://www.w3.org/1999/xlink\" width=\"7.421ex\" height=\"2.671ex\" viewBox=\"0 -835.3 3195 1149.8\" role=\"img\" focusable=\"false\" style=\"vertical-align: -0.73ex;font-size: 14px;\" xmlns=\"http://www.w3.org/2000/svg\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><path stroke-width=\"1\" d=\"M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z\"></path><g transform=\"translate(389,0)\"><path stroke-width=\"1\" d=\"M52 289Q59 331 106 386T222 442Q257 442 286 424T329 379Q371 442 430 442Q467 442 494 420T522 361Q522 332 508 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173 393T169 400T158 404H154Q131 404 112 385T82 344T65 302T57 280Q55 278 41 278H27Q21 284 21 287Z\"></path><g transform=\"translate(490,-150)\"><path stroke-width=\"1\" transform=\"scale(0.707)\" d=\"M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z\"></path></g></g><g transform=\"translate(2805,0)\"><path stroke-width=\"1\" d=\"M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z\"></path></g></g></svg>&nbsp;</mjx-container></span><span style=\"color: black;font-family: &quot;PingFang SC&quot;;font-size: medium;letter-spacing: normal;text-align: start;\">点的全微分的法向量</span><span style=\"font-family: &quot;PingFang SC&quot;;font-size: medium;letter-spacing: normal;text-align: start;color: rgb(136, 136, 136);\"></span><span style=\"color: black;font-family: &quot;PingFang SC&quot;;font-size: medium;letter-spacing: normal;text-align: start;cursor: pointer;visibility: visible;\">&nbsp;<mjx-container jax=\"SVG\" role=\"presentation\" tabindex=\"0\" ctxtmenu_counter=\"31\" data-formula=\"\\boldsymbol{m}\\times\\boldsymbol{n}\" style=\"visibility: visible;\"><svg xmlns:xlink=\"http://www.w3.org/1999/xlink\" width=\"6.896ex\" height=\"1.582ex\" viewBox=\"0 -574.9 2968.9 681.1\" role=\"img\" focusable=\"false\" style=\"vertical-align: -0.247ex;font-size: 14px;\" xmlns=\"http://www.w3.org/2000/svg\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><path stroke-width=\"1\" d=\"M24 296Q25 302 27 312T41 350T65 397T104 435T159 452Q203 452 234 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start;\">，又该全微分会过</span><span style=\"font-family: &quot;PingFang SC&quot;;font-size: medium;letter-spacing: normal;text-align: start;color: rgb(136, 136, 136);\"></span><span style=\"color: black;font-family: &quot;PingFang SC&quot;;font-size: medium;letter-spacing: normal;text-align: start;cursor: pointer;visibility: visible;\">&nbsp;<mjx-container jax=\"SVG\" role=\"presentation\" tabindex=\"0\" ctxtmenu_counter=\"32\" data-formula=\"\\mathrm{d}x\\mathrm{d}y\\mathrm{d}z\" style=\"visibility: visible;\"><svg xmlns:xlink=\"http://www.w3.org/1999/xlink\" width=\"7.451ex\" height=\"2.429ex\" viewBox=\"0 -783.2 3208 1045.7\" role=\"img\" focusable=\"false\" style=\"vertical-align: -0.609ex;font-size: 14px;\" xmlns=\"http://www.w3.org/2000/svg\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><path stroke-width=\"1\" d=\"M376 495Q376 511 376 535T377 568Q377 613 367 624T316 637H298V660Q298 683 300 683L310 684Q320 685 339 686T376 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360 197 356T174 346T162 335T155 324L153 320Q150 317 138 317Q117 317 117 325Q117 330 120 339Q133 378 163 406T229 440Q241 442 246 442Q271 442 291 425T329 392T367 375Q389 375 411 408T434 441Q435 442 449 442H462Q468 436 468 434Q468 430 463 420T449 399T432 377T418 358L411 349Q368 298 275 214T160 106L148 94L163 93Q185 93 227 82T290 71Q328 71 360 90T402 140Q406 149 409 151T424 153Q443 153 443 143Q443 138 442 134Q425 72 376 31T278 -11Q252 -11 232 6T193 40T155 57Q111 57 76 -3Q70 -11 59 -11H54H41Q35 -5 35 -2Q35 13 93 84Q132 129 225 214T340 322Q352 338 347 338Z\"></path></g></g></svg>&nbsp;</mjx-container></span><span style=\"color: black;font-family: &quot;PingFang SC&quot;;font-size: medium;letter-spacing: normal;text-align: start;\">坐标系的</span><span style=\"font-family: &quot;PingFang SC&quot;;font-size: medium;letter-spacing: normal;text-align: start;color: rgb(136, 136, 136);\"></span><span style=\"color: black;font-family: &quot;PingFang SC&quot;;font-size: medium;letter-spacing: normal;text-align: start;cursor: pointer;visibility: visible;\">&nbsp;<mjx-container jax=\"SVG\" role=\"presentation\" tabindex=\"0\" ctxtmenu_counter=\"33\" data-formula=\"(0,0,0)\" style=\"visibility: visible;\"><svg xmlns:xlink=\"http://www.w3.org/1999/xlink\" width=\"7.365ex\" height=\"2.671ex\" viewBox=\"0 -835.3 3170.8 1149.8\" role=\"img\" focusable=\"false\" style=\"vertical-align: -0.73ex;font-size: 14px;\" xmlns=\"http://www.w3.org/2000/svg\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><path stroke-width=\"1\" d=\"M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z\"></path><g transform=\"translate(389,0)\"><path stroke-width=\"1\" d=\"M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 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stroke-width=\"1\" d=\"M78 35T78 60T94 103T137 121Q165 121 187 96T210 8Q210 -27 201 -60T180 -117T154 -158T130 -185T117 -194Q113 -194 104 -185T95 -172Q95 -168 106 -156T131 -126T157 -76T173 -3V9L172 8Q170 7 167 6T161 3T152 1T140 0Q113 0 96 17Z\"></path></g><g transform=\"translate(2280,0)\"><path stroke-width=\"1\" d=\"M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z\"></path></g><g transform=\"translate(2781,0)\"><path stroke-width=\"1\" d=\"M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z\"></path></g></g></svg>&nbsp;</mjx-container></span><span style=\"color: black;font-family: &quot;PingFang SC&quot;;font-size: medium;letter-spacing: normal;text-align: start;\">点，所以根据平面的点法式方程，可得全微分</span><span style=\"font-family: &quot;PingFang SC&quot;;font-size: medium;letter-spacing: normal;text-align: start;color: rgb(136, 136, 136);\"></span><span style=\"color: black;font-family: &quot;PingFang SC&quot;;font-size: medium;letter-spacing: normal;text-align: start;cursor: pointer;visibility: visible;\">&nbsp;<mjx-container jax=\"SVG\" role=\"presentation\" tabindex=\"0\" ctxtmenu_counter=\"34\" data-formula=\"\\mathrm{d}z\" style=\"visibility: visible;\"><svg xmlns:xlink=\"http://www.w3.org/1999/xlink\" width=\"2.381ex\" height=\"2.066ex\" viewBox=\"0 -783.2 1025 889.4\" role=\"img\" focusable=\"false\" style=\"vertical-align: -0.247ex;font-size: 14px;\" xmlns=\"http://www.w3.org/2000/svg\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><path stroke-width=\"1\" d=\"M376 495Q376 511 376 535T377 568Q377 613 367 624T316 637H298V660Q298 683 300 683L310 684Q320 685 339 686T376 688Q393 689 413 690T443 693T454 694H457V390Q457 84 458 81Q461 61 472 55T517 46H535V0Q533 0 459 -5T380 -11H373V44L365 37Q307 -11 235 -11Q158 -11 96 50T34 215Q34 315 97 378T244 442Q319 442 376 393V495ZM373 342Q328 405 260 405Q211 405 173 369Q146 341 139 305T131 211Q131 155 138 120T173 59Q203 26 251 26Q322 26 373 103V342Z\"></path><g transform=\"translate(556,0)\"><path stroke-width=\"1\" d=\"M347 338Q337 338 294 349T231 360Q211 360 197 356T174 346T162 335T155 324L153 320Q150 317 138 317Q117 317 117 325Q117 330 120 339Q133 378 163 406T229 440Q241 442 246 442Q271 442 291 425T329 392T367 375Q389 375 411 408T434 441Q435 442 449 442H462Q468 436 468 434Q468 430 463 420T449 399T432 377T418 358L411 349Q368 298 275 214T160 106L148 94L163 93Q185 93 227 82T290 71Q328 71 360 90T402 140Q406 149 409 151T424 153Q443 153 443 143Q443 138 442 134Q425 72 376 31T278 -11Q252 -11 232 6T193 40T155 57Q111 57 76 -3Q70 -11 59 -11H54H41Q35 -5 35 -2Q35 13 93 84Q132 129 225 214T340 322Q352 338 347 338Z\"></path></g></g></svg>&nbsp;</mjx-container></span><span style=\"color: black;font-family: &quot;PingFang SC&quot;;font-size: medium;letter-spacing: normal;text-align: start;\">的方程为：</span></p>", "$$\n\\begin{aligned}\n    \\boldsymbol{m}\\times\\boldsymbol{n}\n    &=\\begin{vmatrix}\\boldsymbol{i}&1&0\\\\\\boldsymbol{j}&0&1\\\\\\boldsymbol{k}&f_x(x_0,y_0)&f_y(x_0,y_0)\\end{vmatrix}\\\\\n    &=\\begin{vmatrix}0&1\\\\f_x(x_0,y_0)&f_y(x_0,y_0)\\end{vmatrix}\\boldsymbol{i}-\\begin{vmatrix}1&0\\\\f_x(x_0,y_0)&f_y(x_0,y_0)\\end{vmatrix}\\boldsymbol{j}+\\begin{vmatrix}1&0\\\\0&1\\end{vmatrix}\\boldsymbol{k}\\\\\n    &=-f_x(x_0,y_0)\\boldsymbol{i}-f_y(x_0,y_0)\\boldsymbol{j}+\\boldsymbol{k}=\\begin{pmatrix}-f_x(x_0,y_0)\\\\-f_y(x_0,y_0)\\\\1\\end{pmatrix}\n\\end{aligned}\n$$\n\n知道了曲面 $z=f(x,y)$ 在 $(x_0,y_0)$ 点的全微分的法向量 $\\boldsymbol{m}\\times\\boldsymbol{n}$，又该全微分会过 $\\mathrm{d}x\\mathrm{d}y\\mathrm{d}z$ 坐标系的 $(0,0,0)$ 点，所以根据平面的点法式方程，可得全微分 $\\mathrm{d}z$ 的方程为：\n"},
	{"166", "<div class=\"title\">\n        <ucaptitle>中华人民共和国工业和信息化部 财政部 税务总局关于调整享受车船税优惠的节能 新能源汽车产品技术要求的公告</ucaptitle>\n      </div>", "## 中华人民共和国工业和信息化部 财政部 税务总局关于调整享受车船税优惠的节能 新能源汽车产品技术要求的公告\n"},
	{"165", "<figure data-size=\"normal\"><img src=\"https://pic4.zhimg.com/v2-5ccc82114197bd14865d212935a3fe8b_b.jpg\" data-size=\"normal\" data-rawwidth=\"1348\" data-rawheight=\"1026\" class=\"origin_image zh-lightbox-thumb\" width=\"1348\" data-original=\"https://pic4.zhimg.com/v2-5ccc82114197bd14865d212935a3fe8b_r.jpg\"><figcaption>图1 PS并行梯度下降过程</figcaption></figure>", "![](https://pic4.zhimg.com/v2-5ccc82114197bd14865d212935a3fe8b_r.jpg \"图1 PS并行梯度下降过程\"){: style=\"width: 1348px;\"}\n"},
	{"164", "<div class=\"content\" id=\"zoomcon\">\n<ucapcontent><p align=\"\" style=\"text-indent: 2em; text-align: justify; line-height: 2;\">为适应节能与新能源汽车产业发展和技术进步需要，促进节约能源，鼓励使用新能源，现就《财政部 税务总局 工业和信息化部 交通运输部关于节能 新能源车船享受车船税优惠政策的通知》（财税〔2018〕74号）中享受车船税优惠的节能、新能源汽车产品技术要求有关事项公告如下：</p>\n</ucapcontent>\n</div>", "为适应节能与新能源汽车产业发展和技术进步需要，促进节约能源，鼓励使用新能源，现就《财政部 税务总局 工业和信息化部 交通运输部关于节能 新能源车船享受车船税优惠政策的通知》（财税〔2018〕74 号）中享受车船税优惠的节能、新能源汽车产品技术要求有关事项公告如下：\n"},
	{"163", "<mjx-container jax=\"SVG\" role=\"presentation\" tabindex=\"0\" ctxtmenu_counter=\"6\" data-formula=\"(x_0,y_0)\" style=\"visibility: visible;\"><svg xmlns:xlink=\"http://www.w3.org/1999/xlink\" width=\"7.421ex\" height=\"2.671ex\" viewBox=\"0 -835.3 3195 1149.8\" role=\"img\" focusable=\"false\" style=\"vertical-align: -0.73ex; font-size: 14px; visibility: visible;\" xmlns=\"http://www.w3.org/2000/svg\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\" style=\"visibility: visible;\"><path stroke-width=\"1\" d=\"M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z\" style=\"visibility: visible;\"></path><g transform=\"translate(389,0)\" style=\"visibility: visible;\"><path stroke-width=\"1\" d=\"M52 289Q59 331 106 386T222 442Q257 442 286 424T329 379Q371 442 430 442Q467 442 494 420T522 361Q522 332 508 314T481 292T458 288Q439 288 427 299T415 328Q415 374 465 391Q454 404 425 404Q412 404 406 402Q368 386 350 336Q290 115 290 78Q290 50 306 38T341 26Q378 26 414 59T463 140Q466 150 469 151T485 153H489Q504 153 504 145Q504 144 502 134Q486 77 440 33T333 -11Q263 -11 227 52Q186 -10 133 -10H127Q78 -10 57 16T35 71Q35 103 54 123T99 143Q142 143 142 101Q142 81 130 66T107 46T94 41L91 40Q91 39 97 36T113 29T132 26Q168 26 194 71Q203 87 217 139T245 247T261 313Q266 340 266 352Q266 380 251 392T217 404Q177 404 142 372T93 290Q91 281 88 280T72 278H58Q52 284 52 289Z\" style=\"visibility: visible;\"></path><g transform=\"translate(572,-150)\" style=\"visibility: visible;\"><path stroke-width=\"1\" transform=\"scale(0.707)\" d=\"M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z\" style=\"visibility: visible;\"></path></g></g><g transform=\"translate(1415,0)\" style=\"visibility: visible;\"><path stroke-width=\"1\" d=\"M78 35T78 60T94 103T137 121Q165 121 187 96T210 8Q210 -27 201 -60T180 -117T154 -158T130 -185T117 -194Q113 -194 104 -185T95 -172Q95 -168 106 -156T131 -126T157 -76T173 -3V9L172 8Q170 7 167 6T161 3T152 1T140 0Q113 0 96 17Z\" style=\"visibility: visible;\"></path></g><g transform=\"translate(1861,0)\" style=\"visibility: visible;\"><path stroke-width=\"1\" d=\"M21 287Q21 301 36 335T84 406T158 442Q199 442 224 419T250 355Q248 336 247 334Q247 331 231 288T198 191T182 105Q182 62 196 45T238 27Q261 27 281 38T312 61T339 94Q339 95 344 114T358 173T377 247Q415 397 419 404Q432 431 462 431Q475 431 483 424T494 412T496 403Q496 390 447 193T391 -23Q363 -106 294 -155T156 -205Q111 -205 77 -183T43 -117Q43 -95 50 -80T69 -58T89 -48T106 -45Q150 -45 150 -87Q150 -107 138 -122T115 -142T102 -147L99 -148Q101 -153 118 -160T152 -167H160Q177 -167 186 -165Q219 -156 247 -127T290 -65T313 -9T321 21L315 17Q309 13 296 6T270 -6Q250 -11 231 -11Q185 -11 150 11T104 82Q103 89 103 113Q103 170 138 262T173 379Q173 380 173 381Q173 390 173 393T169 400T158 404H154Q131 404 112 385T82 344T65 302T57 280Q55 278 41 278H27Q21 284 21 287Z\" style=\"visibility: visible;\"></path><g transform=\"translate(490,-150)\" style=\"visibility: visible;\"><path stroke-width=\"1\" transform=\"scale(0.707)\" d=\"M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z\" style=\"visibility: visible;\"></path></g></g><g transform=\"translate(2805,0)\" style=\"visibility: visible;\"><path stroke-width=\"1\" d=\"M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z\" style=\"visibility: visible;\"></path></g></g></svg>&nbsp;</mjx-container>", "$$\n(x_0,y_0)\n$$\n"},
	{"162", "<figure data-size=\"normal\"><noscript><img src=\"https://pic2.zhimg.com/v2-75dc0f59d2630e85a79090c1c7cd7dd5_b.gif\" data-size=\"normal\" data-rawwidth=\"592\" data-rawheight=\"448\" data-thumbnail=\"https://pic2.zhimg.com/v2-75dc0f59d2630e85a79090c1c7cd7dd5_b.jpg\" class=\"origin_image zh-lightbox-thumb\" width=\"592\" data-original=\"https://pic2.zhimg.com/v2-75dc0f59d2630e85a79090c1c7cd7dd5_r.jpg\"/></noscript><div><div class=\"GifPlayer css-1isopsn\" data-size=\"normal\" data-za-detail-view-path-module=\"GifItem\"><img class=\"ztext-gif GifPlayer-gif2mp4Image\" width=\"592\" role=\"presentation\" src=\"https://pic2.zhimg.com/v2-75dc0f59d2630e85a79090c1c7cd7dd5_b.jpg\" data-thumbnail=\"https://pic2.zhimg.com/v2-75dc0f59d2630e85a79090c1c7cd7dd5_b.jpg\" data-size=\"normal\" alt=\"动图封面\" style=\"display: block;\"><video class=\"ztext-gif GifPlayer-gif2mp4 css-1xeqk96\" src=\"https://vdn6.vzuu.com/SD/acfbc2e8-236e-11eb-a7d2-3e2df5db3b6f.mp4?pkey=AAXyt-BzKx_ecDxDGOEtsGZ18YAiBUFu_6i-H-JQKevkuYIpsiXBtjkrOEHpIHq5jesfZ5lVrea8c4KHM-aH58MU&amp;c=avc.0.0&amp;f=mp4&amp;pu=078babd7&amp;bu=078babd7&amp;expiration=1719239939&amp;v=ks6\" data-thumbnail=\"https://pic2.zhimg.com/v2-75dc0f59d2630e85a79090c1c7cd7dd5_b.jpg\" poster=\"https://pic2.zhimg.com/v2-75dc0f59d2630e85a79090c1c7cd7dd5_b.jpg\" data-size=\"normal\" preload=\"metadata\" loop=\"\" playsinline=\"\"></video><div class=\"GifPlayer-icon css-d39tw7\"><svg width=\"50\" height=\"50\" viewBox=\"0 0 60 60\" xmlns=\"http://www.w3.org/2000/svg\"><g stroke=\"none\" stroke-width=\"1\" fill=\"none\" fill-rule=\"evenodd\"><ellipse fill=\"#000\" opacity=\"0.45\" cx=\"30\" cy=\"30\" rx=\"30\" ry=\"30\"></ellipse><ellipse stroke=\"#FFF\" stroke-width=\"2\" stroke-linecap=\"round\" stroke-linejoin=\"round\" opacity=\"0.5\" cx=\"30\" cy=\"30\" rx=\"26\" ry=\"26\"></ellipse></g><svg x=\"16\" y=\"18.5\"><g fill=\"#fff\"><path x=\"100\" y=\"100\" d=\"M12.8422852,12.9814453 L12.8422852,11.3994141 L7.63916016,11.3994141 L7.63916016,13.0517578 L10.9086914,13.0517578 L10.9086914,13.3242188 C10.8911133,15.2050781 9.46728516,16.4707031 7.39306641,16.4707031 C5.01123047,16.4707031 3.51708984,14.625 3.51708984,11.6367188 C3.51708984,8.70117188 5.00244141,6.84667969 7.34912109,6.84667969 C9.08056641,6.84667969 10.284668,7.68164062 10.7768555,9.2109375 L12.7543945,9.2109375 C12.3237305,6.64453125 10.2319336,5.00976562 7.34912109,5.00976562 C3.79833984,5.00976562 1.50439453,7.61132812 1.50439453,11.6542969 C1.50439453,15.75 3.77197266,18.3076172 7.36669922,18.3076172 C10.6889648,18.3076172 12.8422852,16.2246094 12.8422852,12.9814453 Z M17.5180664,18 L17.5180664,5.31738281 L15.5493164,5.31738281 L15.5493164,18 L17.5180664,18 Z M22.659668,18 L22.659668,12.7441406 L28.1088867,12.7441406 L28.1088867,11.0039062 L22.659668,11.0039062 L22.659668,7.11035156 L28.6098633,7.11035156 L28.6098633,5.31738281 L20.690918,5.31738281 L20.690918,18 L22.659668,18 Z\"></path></g></svg></svg></div></div></div><figcaption>异步更新动画示意图</figcaption></figure>", "![](https://pic2.zhimg.com/v2-75dc0f59d2630e85a79090c1c7cd7dd5_b.gif \"异步更新动画示意图\"){: style=\"width: 592px;\"}\n"},
	{"161", "<span style=\"letter-spacing: 1px;\"><span style=\"outline: 0px;background-color: rgb(255, 104, 39);font-size: 17px;color: rgb(255, 255, 255);\"><strong style=\"outline: 0px;\"><span style=\"background-color: rgb(255, 104, 39);font-size: 17px;outline: 0px;font-family: Optima-Regular, PingFangTC-light;\">&nbsp;1&nbsp;</span></strong></span><span style=\"outline: 0px;font-size: 17px;\"><strong style=\"outline: 0px;\"><span style=\"outline: 0px;font-family: Optima-Regular, PingFangTC-light;\">&nbsp;</span></strong></span><strong style=\"font-family: mp-quote, -apple-system-font, BlinkMacSystemFont, &quot;Helvetica Neue&quot;, &quot;PingFang SC&quot;, &quot;Hiragino Sans GB&quot;, &quot;Microsoft YaHei UI&quot;, &quot;Microsoft YaHei&quot;, Arial, sans-serif;font-size: 17px;letter-spacing: 1px;outline: 0px;\"><span style=\"outline: 0px;font-family: Optima-Regular, PingFangTC-light;\">小米科技理念</span></strong><strong style=\"font-family: mp-quote, -apple-system-font, BlinkMacSystemFont, &quot;Helvetica Neue&quot;, &quot;PingFang SC&quot;, &quot;Hiragino Sans GB&quot;, &quot;Microsoft YaHei UI&quot;, &quot;Microsoft YaHei&quot;, Arial, sans-serif;font-size: 17px;letter-spacing: 1px;outline: 0px;\"></strong></span>", "**\u200b 1 \u200b** **小米科技理念**\n"},
	{"160", "<p><strong><span>&nbsp; &nbsp; 并发和并行是即相似又有区别的两个概念</span>，并行是指两个或者多个事件在同一时刻发生；而并发是指两个或多个事件在同一时间间隔内发生。在多道程序环境下，并发性是指在一段时间内宏观上有多个程序在同时运行，但在单处理机系统中，每一时刻却仅能有一道程序执行，故微观上这些程序只能是分时地交替执行。倘若在计算机系统中有多个处理机，则这些可以并发执行的程序便可被分配到多个处理机上，实现并行执行，即利用每个处理机来处理一个可并发执行的程序，这样，多个程序便可以同时执行。</strong></p> \n<p><strong>&nbsp; 3.</strong><span><strong>串行、并行：</strong></span></p> ", "**\u200b    并发和并行是即相似又有区别的两个概念，并行是指两个或者多个事件在同一时刻发生；而并发是指两个或多个事件在同一时间间隔内发生。在多道程序环境下，并发性是指在一段时间内宏观上有多个程序在同时运行，但在单处理机系统中，每一时刻却仅能有一道程序执行，故微观上这些程序只能是分时地交替执行。倘若在计算机系统中有多个处理机，则这些可以并发执行的程序便可被分配到多个处理机上，实现并行执行，即利用每个处理机来处理一个可并发执行的程序，这样，多个程序便可以同时执行。**\n\n **\u200b\u200b  3.\u200b**\u200b**串行、并行：**\n"},
	{"159", "<table id=\"tablepress-74\" class=\"tablepress tablepress-id-74\">\n<thead>\n<tr class=\"row-1 odd\">\n<th colspan=\"2\" class=\"column-1\">\n<p style=\"text-align: center;\">&nbsp;<strong>以图搜图</strong> - <a href=\"https://www.runningcheese.cn/s13\" rel=\"noopener\" target=\"_blank\"><strong>详细</strong> <img decoding=\"async\" class=\"ico\" src=\"https://www.runningcheese.com/icons/open.svg\"></a></p>\n</th>\n</tr>\n</thead>\n<tbody class=\"row-hover\">\n<tr class=\"row-2 even\">\n<td class=\"column-1\"><img decoding=\"async\" class=\"ico\" src=\"https://www.runningcheese.com/icons/menu.svg\">&nbsp;<strong>通用搜索</strong></td>\n<td class=\"column-2\"><strong>简介</strong></td>\n</tr>\n<tr class=\"row-3 odd\">\n<td class=\"column-1\"><img decoding=\"async\" class=\"ico\" src=\"https://www.runningcheese.com/icons/web.svg\">&nbsp;<a href=\"https://images.google.com/\">Google Images</a></td>\n<td class=\"column-2\">国外第一，可能是最好用的。👍</td>\n</tr>\n</tbody>\n</table>", "|  **以图搜图**-[**详细** ![](https://www.runningcheese.com/icons/open.svg)](https://www.runningcheese.cn/s13) |                              |\n| --------------------------------------------------------------------------------------------------------------------- | ------------------------------ |\n| ![](https://www.runningcheese.com/icons/menu.svg) **通用搜索**                                                  | **简介**               |\n| ![](https://www.runningcheese.com/icons/web.svg) [Google Images](https://images.google.com/)                             | 国外第一，可能是最好用的。👍 |\n"},
	{"158", "<span style=\"outline: 0px;font-size: 17px;\"><strong style=\"outline: 0px;\"><span style=\"outline: 0px;font-family: Optima-Regular, PingFangTC-light;\">&nbsp;&nbsp;</span></strong><strong style=\"outline: 0px;\"><span style=\"font-size: 17px;outline: 0px;font-family: Optima-Regular, PingFangTC-light;\">梦想的起点</span></strong><strong style=\"outline: 0px;\"></strong></span>", "**\u200b  \u200b梦想的起点**\n"},
	{"157", "<figure data-size=\"normal\"><noscript><img src=\"https://picx.zhimg.com/50/v2-fa19ad5cf46134b3d568236bd95f8ee8_720w.jpg?source=2c26e567\" data-size=\"normal\" data-rawwidth=\"1113\" data-rawheight=\"731\" data-original-token=\"v2-fa19ad5cf46134b3d568236bd95f8ee8\" data-default-watermark-src=\"https://pic1.zhimg.com/50/v2-ce5892149198b4890c626cb5fce3fe74_720w.jpg?source=2c26e567\" class=\"origin_image zh-lightbox-thumb\" width=\"1113\" data-original=\"https://pica.zhimg.com/v2-fa19ad5cf46134b3d568236bd95f8ee8_r.jpg?source=2c26e567\"/></noscript><div><img src=\"https://picx.zhimg.com/80/v2-fa19ad5cf46134b3d568236bd95f8ee8_720w.webp?source=2c26e567\" data-size=\"normal\" data-rawwidth=\"1113\" data-rawheight=\"731\" data-original-token=\"v2-fa19ad5cf46134b3d568236bd95f8ee8\" data-default-watermark-src=\"https://pic1.zhimg.com/50/v2-ce5892149198b4890c626cb5fce3fe74_720w.jpg?source=2c26e567\" class=\"origin_image zh-lightbox-thumb lazy\" width=\"1113\" data-original=\"https://pica.zhimg.com/v2-fa19ad5cf46134b3d568236bd95f8ee8_r.jpg?source=2c26e567\" data-actualsrc=\"https://picx.zhimg.com/50/v2-fa19ad5cf46134b3d568236bd95f8ee8_720w.jpg?source=2c26e567\" height=\"731\" data-lazy-status=\"ok\"></div><figcaption>工具选型</figcaption></figure><p data-pid=\"yJnbdUed\">最后我选择是 Colube <i>( 20230907作者说即将改名为 Mefo ) </i>，这是一款类似 <span class=\"nolink\">Heptabase</span> 的<span><a class=\"RichContent-EntityWord css-b7erz1\" data-za-not-track-link=\"true\" data-paste-text=\"true\" href=\"https://www.zhihu.com/search?q=%E7%99%BD%E6%9D%BF%E7%AC%94%E8%AE%B0%E8%BD%AF%E4%BB%B6&amp;search_source=Entity&amp;hybrid_search_source=Entity&amp;hybrid_search_extra=%7B%22sourceType%22%3A%22answer%22%2C%22sourceId%22%3A3211660195%7D\" target=\"_blank\">白板笔记软件<svg width=\"10px\" height=\"10px\" viewBox=\"0 0 15 15\" class=\"css-1dvsrp\"><path d=\"M10.89 9.477l3.06 3.059a1 1 0 0 1-1.414 1.414l-3.06-3.06a6 6 0 1 1 1.414-1.414zM6 10a4 4 0 1 0 0-8 4 4 0 0 0 0 8z\" fill=\"currentColor\"></path></svg></a></span>，但相对而言有极大的价格优势，因此对我很有吸引力。</p>", "![](https://pica.zhimg.com/v2-fa19ad5cf46134b3d568236bd95f8ee8_r.jpg?source=2c26e567 \"工具选型\"){: style=\"width: 1113px;\"}\n\n最后我选择是 Colube \u200b*( 20230907 作者说即将改名为 Mefo ) \u200b*\u200b，这是一款类似 Heptabase 的[白板笔记软件](https://www.zhihu.com/search?q=%E7%99%BD%E6%9D%BF%E7%AC%94%E8%AE%B0%E8%BD%AF%E4%BB%B6&search_source=Entity&hybrid_search_source=Entity&hybrid_search_extra=%7B%22sourceType%22%3A%22answer%22%2C%22sourceId%22%3A3211660195%7D)，但相对而言有极大的价格优势，因此对我很有吸引力。\n"},
	{"156", "<p data-tool=\"mdnice编辑器\"><span><span role=\"presentation\" data-formula=\"w=[0, 1]\" data-formula-type=\"inline-equation\"></span></span>&nbsp;就是以向量的形式表示<span><span role=\"presentation\" data-formula=\"w_1=0, w_2=1\" data-formula-type=\"inline-equation\"></span></span>。现在，我们给这个神经元一个输入<span><span role=\"presentation\" data-formula=\"x=[2, 3]\" data-formula-type=\"inline-equation\"></span></span>。我们用点积来表示：</p>", "$w=[0, 1]$ 就是以向量的形式表示 $w_1=0, w_2=1$。现在，我们给这个神经元一个输入 $x=[2, 3]$。我们用点积来表示：\n"},
	{"155", "<span data-tool=\"mdnice编辑器\" style=\"cursor: pointer;\"><section role=\"presentation\" data-formula=\"y = f(w \\cdot x + b) = f(7) = 0.999\n\" data-formula-type=\"block-equation\" style=\"text-align: center;overflow: auto;\"><svg xmlns=\"http://www.w3.org/2000/svg\" role=\"img\" focusable=\"false\" viewBox=\"0 -750 13586.6 1000\" aria-hidden=\"true\" style=\"-webkit-overflow-scrolling: touch;font-size: 12px;margin: 0.1em;vertical-align: -0.566ex;width: 30.739ex;height: 2.262ex;max-width: 300% !important;\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mi\"><path data-c=\"79\" d=\"M21 287Q21 301 36 335T84 406T158 442Q199 442 224 419T250 355Q248 336 247 334Q247 331 231 288T198 191T182 105Q182 62 196 45T238 27Q261 27 281 38T312 61T339 94Q339 95 344 114T358 173T377 247Q415 397 419 404Q432 431 462 431Q475 431 483 424T494 412T496 403Q496 390 447 193T391 -23Q363 -106 294 -155T156 -205Q111 -205 77 -183T43 -117Q43 -95 50 -80T69 -58T89 -48T106 -45Q150 -45 150 -87Q150 -107 138 -122T115 -142T102 -147L99 -148Q101 -153 118 -160T152 -167H160Q177 -167 186 -165Q219 -156 247 -127T290 -65T313 -9T321 21L315 17Q309 13 296 6T270 -6Q250 -11 231 -11Q185 -11 150 11T104 82Q103 89 103 113Q103 170 138 262T173 379Q173 380 173 381Q173 390 173 393T169 400T158 404H154Q131 404 112 385T82 344T65 302T57 280Q55 278 41 278H27Q21 284 21 287Z\"></path></g><g data-mml-node=\"mo\" transform=\"translate(767.8, 0)\"><path data-c=\"3D\" d=\"M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z\"></path></g><g data-mml-node=\"mi\" transform=\"translate(1823.6, 0)\"><path data-c=\"66\" d=\"M118 -162Q120 -162 124 -164T135 -167T147 -168Q160 -168 171 -155T187 -126Q197 -99 221 27T267 267T289 382V385H242Q195 385 192 387Q188 390 188 397L195 425Q197 430 203 430T250 431Q298 431 298 432Q298 434 307 482T319 540Q356 705 465 705Q502 703 526 683T550 630Q550 594 529 578T487 561Q443 561 443 603Q443 622 454 636T478 657L487 662Q471 668 457 668Q445 668 434 658T419 630Q412 601 403 552T387 469T380 433Q380 431 435 431Q480 431 487 430T498 424Q499 420 496 407T491 391Q489 386 482 386T428 385H372L349 263Q301 15 282 -47Q255 -132 212 -173Q175 -205 139 -205Q107 -205 81 -186T55 -132Q55 -95 76 -78T118 -61Q162 -61 162 -103Q162 -122 151 -136T127 -157L118 -162Z\"></path></g><g data-mml-node=\"mo\" transform=\"translate(2373.6, 0)\"><path data-c=\"28\" d=\"M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z\"></path></g><g data-mml-node=\"mi\" transform=\"translate(2762.6, 0)\"><path data-c=\"77\" d=\"M580 385Q580 406 599 424T641 443Q659 443 674 425T690 368Q690 339 671 253Q656 197 644 161T609 80T554 12T482 -11Q438 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d=\"M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z\"></path></g><g data-mml-node=\"mn\" transform=\"translate(11308.6, 0)\"><path data-c=\"30\" d=\"M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z\"></path><path data-c=\"2E\" d=\"M78 60Q78 84 95 102T138 120Q162 120 180 104T199 61Q199 36 182 18T139 0T96 17T78 60Z\" transform=\"translate(500, 0)\"></path><path data-c=\"39\" d=\"M352 287Q304 211 232 211Q154 211 104 270T44 396Q42 412 42 436V444Q42 537 111 606Q171 666 243 666Q245 666 249 666T257 665H261Q273 665 286 663T323 651T370 619T413 560Q456 472 456 334Q456 194 396 97Q361 41 312 10T208 -22Q147 -22 108 7T68 93T121 149Q143 149 158 135T173 96Q173 78 164 65T148 49T135 44L131 43Q131 41 138 37T164 27T206 22H212Q272 22 313 86Q352 142 352 280V287ZM244 248Q292 248 321 297T351 430Q351 508 343 542Q341 552 337 562T323 588T293 615T246 625Q208 625 181 598Q160 576 154 546T147 441Q147 358 152 329T172 282Q197 248 244 248Z\" transform=\"translate(778, 0)\"></path><path data-c=\"39\" d=\"M352 287Q304 211 232 211Q154 211 104 270T44 396Q42 412 42 436V444Q42 537 111 606Q171 666 243 666Q245 666 249 666T257 665H261Q273 665 286 663T323 651T370 619T413 560Q456 472 456 334Q456 194 396 97Q361 41 312 10T208 -22Q147 -22 108 7T68 93T121 149Q143 149 158 135T173 96Q173 78 164 65T148 49T135 44L131 43Q131 41 138 37T164 27T206 22H212Q272 22 313 86Q352 142 352 280V287ZM244 248Q292 248 321 297T351 430Q351 508 343 542Q341 552 337 562T323 588T293 615T246 625Q208 625 181 598Q160 576 154 546T147 441Q147 358 152 329T172 282Q197 248 244 248Z\" transform=\"translate(1278, 0)\"></path><path data-c=\"39\" d=\"M352 287Q304 211 232 211Q154 211 104 270T44 396Q42 412 42 436V444Q42 537 111 606Q171 666 243 666Q245 666 249 666T257 665H261Q273 665 286 663T323 651T370 619T413 560Q456 472 456 334Q456 194 396 97Q361 41 312 10T208 -22Q147 -22 108 7T68 93T121 149Q143 149 158 135T173 96Q173 78 164 65T148 49T135 44L131 43Q131 41 138 37T164 27T206 22H212Q272 22 313 86Q352 142 352 280V287ZM244 248Q292 248 321 297T351 430Q351 508 343 542Q341 552 337 562T323 588T293 615T246 625Q208 625 181 598Q160 576 154 546T147 441Q147 358 152 329T172 282Q197 248 244 248Z\" transform=\"translate(1778, 0)\"></path></g></g></g></svg></section></span>", "$$\ny = f(w \\cdot x + b) = f(7) = 0.999\n$$\n"},
	{"154", "<p data-tool=\"mdnice编辑器\" style=\"padding-top: 8px;padding-bottom: 8px;margin-top: 15px;font-size: 15px;line-height: 28px;\"><span style=\"cursor: pointer;\"><span role=\"presentation\" data-formula=\"w=[0, 1]\" data-formula-type=\"inline-equation\" style=\"\"><svg xmlns=\"http://www.w3.org/2000/svg\" role=\"img\" focusable=\"false\" viewBox=\"0 -750 4050.2 1000\" aria-hidden=\"true\" style=\"font-size: 12px;vertical-align: -0.566ex;width: 9.163ex;height: 2.262ex;\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mi\"><path data-c=\"77\" d=\"M580 385Q580 406 599 424T641 443Q659 443 674 425T690 368Q690 339 671 253Q656 197 644 161T609 80T554 12T482 -11Q438 -11 404 5T355 48Q354 47 352 44Q311 -11 252 -11Q226 -11 202 -5T155 14T118 53T104 116Q104 170 138 262T173 379Q173 380 173 381Q173 390 173 393T169 400T158 404H154Q131 404 112 385T82 344T65 302T57 280Q55 278 41 278H27Q21 284 21 287Q21 293 29 315T52 366T96 418T161 441Q204 441 227 416T250 358Q250 340 217 250T184 111Q184 65 205 46T258 26Q301 26 334 87L339 96V119Q339 122 339 128T340 136T341 143T342 152T345 165T348 182T354 206T362 238T373 281Q402 395 406 404Q419 431 449 431Q468 431 475 421T483 402Q483 389 454 274T422 142Q420 131 420 107V100Q420 85 423 71T442 42T487 26Q558 26 600 148Q609 171 620 213T632 273Q632 306 619 325T593 357T580 385Z\"></path></g><g data-mml-node=\"mo\" transform=\"translate(993.8, 0)\"><path data-c=\"3D\" d=\"M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z\"></path></g><g data-mml-node=\"mo\" transform=\"translate(2049.6, 0)\"><path data-c=\"5B\" d=\"M118 -250V750H255V710H158V-210H255V-250H118Z\"></path></g><g data-mml-node=\"mn\" transform=\"translate(2327.6, 0)\"><path data-c=\"30\" d=\"M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z\"></path></g><g data-mml-node=\"mo\" transform=\"translate(2827.6, 0)\"><path data-c=\"2C\" d=\"M78 35T78 60T94 103T137 121Q165 121 187 96T210 8Q210 -27 201 -60T180 -117T154 -158T130 -185T117 -194Q113 -194 104 -185T95 -172Q95 -168 106 -156T131 -126T157 -76T173 -3V9L172 8Q170 7 167 6T161 3T152 1T140 0Q113 0 96 17Z\"></path></g><g data-mml-node=\"mn\" transform=\"translate(3272.2, 0)\"><path data-c=\"31\" d=\"M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z\"></path></g><g data-mml-node=\"mo\" transform=\"translate(3772.2, 0)\"><path data-c=\"5D\" d=\"M22 710V750H159V-250H22V-210H119V710H22Z\"></path></g></g></g></svg></span></span>&nbsp;就是以向量的形式表示<span style=\"cursor: pointer;\"><span role=\"presentation\" data-formula=\"w_1=0, w_2=1\" data-formula-type=\"inline-equation\" style=\"\"><svg xmlns=\"http://www.w3.org/2000/svg\" role=\"img\" focusable=\"false\" viewBox=\"0 -666 6350.9 860\" aria-hidden=\"true\" style=\"font-size: 12px;vertical-align: -0.439ex;width: 14.369ex;height: 1.946ex;\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"msub\"><g data-mml-node=\"mi\"><path data-c=\"77\" d=\"M580 385Q580 406 599 424T641 443Q659 443 674 425T690 368Q690 339 671 253Q656 197 644 161T609 80T554 12T482 -11Q438 -11 404 5T355 48Q354 47 352 44Q311 -11 252 -11Q226 -11 202 -5T155 14T118 53T104 116Q104 170 138 262T173 379Q173 380 173 381Q173 390 173 393T169 400T158 404H154Q131 404 112 385T82 344T65 302T57 280Q55 278 41 278H27Q21 284 21 287Q21 293 29 315T52 366T96 418T161 441Q204 441 227 416T250 358Q250 340 217 250T184 111Q184 65 205 46T258 26Q301 26 334 87L339 96V119Q339 122 339 128T340 136T341 143T342 152T345 165T348 182T354 206T362 238T373 281Q402 395 406 404Q419 431 449 431Q468 431 475 421T483 402Q483 389 454 274T422 142Q420 131 420 107V100Q420 85 423 71T442 42T487 26Q558 26 600 148Q609 171 620 213T632 273Q632 306 619 325T593 357T580 385Z\"></path></g><g data-mml-node=\"mn\" transform=\"translate(716, -150) scale(0.707)\"><path data-c=\"31\" d=\"M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z\"></path></g></g><g data-mml-node=\"mo\" transform=\"translate(1397.3, 0)\"><path data-c=\"3D\" d=\"M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z\"></path></g><g data-mml-node=\"mn\" transform=\"translate(2453.1, 0)\"><path data-c=\"30\" d=\"M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z\"></path></g><g data-mml-node=\"mo\" transform=\"translate(2953.1, 0)\"><path data-c=\"2C\" d=\"M78 35T78 60T94 103T137 121Q165 121 187 96T210 8Q210 -27 201 -60T180 -117T154 -158T130 -185T117 -194Q113 -194 104 -185T95 -172Q95 -168 106 -156T131 -126T157 -76T173 -3V9L172 8Q170 7 167 6T161 3T152 1T140 0Q113 0 96 17Z\"></path></g><g data-mml-node=\"msub\" transform=\"translate(3397.8, 0)\"><g data-mml-node=\"mi\"><path data-c=\"77\" d=\"M580 385Q580 406 599 424T641 443Q659 443 674 425T690 368Q690 339 671 253Q656 197 644 161T609 80T554 12T482 -11Q438 -11 404 5T355 48Q354 47 352 44Q311 -11 252 -11Q226 -11 202 -5T155 14T118 53T104 116Q104 170 138 262T173 379Q173 380 173 381Q173 390 173 393T169 400T158 404H154Q131 404 112 385T82 344T65 302T57 280Q55 278 41 278H27Q21 284 21 287Q21 293 29 315T52 366T96 418T161 441Q204 441 227 416T250 358Q250 340 217 250T184 111Q184 65 205 46T258 26Q301 26 334 87L339 96V119Q339 122 339 128T340 136T341 143T342 152T345 165T348 182T354 206T362 238T373 281Q402 395 406 404Q419 431 449 431Q468 431 475 421T483 402Q483 389 454 274T422 142Q420 131 420 107V100Q420 85 423 71T442 42T487 26Q558 26 600 148Q609 171 620 213T632 273Q632 306 619 325T593 357T580 385Z\"></path></g><g data-mml-node=\"mn\" transform=\"translate(716, -150) scale(0.707)\"><path data-c=\"32\" d=\"M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\"></path></g></g><g data-mml-node=\"mo\" transform=\"translate(4795.1, 0)\"><path data-c=\"3D\" d=\"M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z\"></path></g><g data-mml-node=\"mn\" transform=\"translate(5850.9, 0)\"><path data-c=\"31\" d=\"M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z\"></path></g></g></g></svg></span></span>。现在，我们给这个神经元一个输入<span style=\"cursor: pointer;\"><span role=\"presentation\" data-formula=\"x=[2, 3]\" data-formula-type=\"inline-equation\" style=\"\"><svg xmlns=\"http://www.w3.org/2000/svg\" role=\"img\" focusable=\"false\" viewBox=\"0 -750 3906.2 1000\" aria-hidden=\"true\" style=\"font-size: 12px;vertical-align: -0.566ex;width: 8.838ex;height: 2.262ex;\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g data-mml-node=\"math\"><g data-mml-node=\"mi\"><path data-c=\"78\" d=\"M52 289Q59 331 106 386T222 442Q257 442 286 424T329 379Q371 442 430 442Q467 442 494 420T522 361Q522 332 508 314T481 292T458 288Q439 288 427 299T415 328Q415 374 465 391Q454 404 425 404Q412 404 406 402Q368 386 350 336Q290 115 290 78Q290 50 306 38T341 26Q378 26 414 59T463 140Q466 150 469 151T485 153H489Q504 153 504 145Q504 144 502 134Q486 77 440 33T333 -11Q263 -11 227 52Q186 -10 133 -10H127Q78 -10 57 16T35 71Q35 103 54 123T99 143Q142 143 142 101Q142 81 130 66T107 46T94 41L91 40Q91 39 97 36T113 29T132 26Q168 26 194 71Q203 87 217 139T245 247T261 313Q266 340 266 352Q266 380 251 392T217 404Q177 404 142 372T93 290Q91 281 88 280T72 278H58Q52 284 52 289Z\"></path></g><g data-mml-node=\"mo\" transform=\"translate(849.8, 0)\"><path data-c=\"3D\" d=\"M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z\"></path></g><g data-mml-node=\"mo\" transform=\"translate(1905.6, 0)\"><path data-c=\"5B\" d=\"M118 -250V750H255V710H158V-210H255V-250H118Z\"></path></g><g data-mml-node=\"mn\" transform=\"translate(2183.6, 0)\"><path data-c=\"32\" d=\"M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\"></path></g><g data-mml-node=\"mo\" transform=\"translate(2683.6, 0)\"><path data-c=\"2C\" d=\"M78 35T78 60T94 103T137 121Q165 121 187 96T210 8Q210 -27 201 -60T180 -117T154 -158T130 -185T117 -194Q113 -194 104 -185T95 -172Q95 -168 106 -156T131 -126T157 -76T173 -3V9L172 8Q170 7 167 6T161 3T152 1T140 0Q113 0 96 17Z\"></path></g><g data-mml-node=\"mn\" transform=\"translate(3128.2, 0)\"><path data-c=\"33\" d=\"M127 463Q100 463 85 480T69 524Q69 579 117 622T233 665Q268 665 277 664Q351 652 390 611T430 522Q430 470 396 421T302 350L299 348Q299 347 308 345T337 336T375 315Q457 262 457 175Q457 96 395 37T238 -22Q158 -22 100 21T42 130Q42 158 60 175T105 193Q133 193 151 175T169 130Q169 119 166 110T159 94T148 82T136 74T126 70T118 67L114 66Q165 21 238 21Q293 21 321 74Q338 107 338 175V195Q338 290 274 322Q259 328 213 329L171 330L168 332Q166 335 166 348Q166 366 174 366Q202 366 232 371Q266 376 294 413T322 525V533Q322 590 287 612Q265 626 240 626Q208 626 181 615T143 592T132 580H135Q138 579 143 578T153 573T165 566T175 555T183 540T186 520Q186 498 172 481T127 463Z\"></path></g><g data-mml-node=\"mo\" transform=\"translate(3628.2, 0)\"><path data-c=\"5D\" d=\"M22 710V750H159V-250H22V-210H119V710H22Z\"></path></g></g></g></svg></span></span>。我们用点积来表示：</p>", "$w=[0, 1]$ 就是以向量的形式表示 $w_1=0, w_2=1$。现在，我们给这个神经元一个输入 $x=[2, 3]$。我们用点积来表示：\n"},
	{"153", "<p id=\"20240617111930-lwjmxuy\" updated=\"20240617111930\"><span data-type=\"inline-math\" data-subtype=\"math\" data-content=\"a^2 + b^2 = \\color{red}c^2\" contenteditable=\"false\" class=\"render-node\"></span></p>", "$a^2 + b^2 = \\color{red}c^2$\n"},
	{"152", "<p id=\"20240617111623-rcmt2rf\" updated=\"20240617111623\"><span data-type=\"tag\">标签</span></p>", "#标签#\n"},
	{"151", "<p id=\"20240617111532-emrgv5q\" updated=\"20240617111532\"><span data-type=\"sub\">下标</span></p>", "~下标~\n"},
	{"150", "<p id=\"20240617111424-wucju83\" updated=\"20240617111424\"><span data-type=\"sup\">上标</span></p>", "^上标^\n"},
	{"149", "<p id=\"20240617110224-td1ai09\" updated=\"20240617110224\"><span data-type=\"mark\">标记</span></p>", "==标记==\n"},
	{"148", "<p id=\"20240617105517-yxg1moc\" updated=\"20240617105517\"><span data-type=\"s\">删除线</span></p>", "~~删除线~~\n"},
	{"147", "<p id=\"20240617105507-ny4t730\" updated=\"20240617105507\"><span data-type=\"u\">下划线</span></p>", "<u>下划线</u>\n"},
	{"146", "<p id=\"20240617104538-j3kxs1l\" updated=\"20240617104538\"><span data-type=\"em\">倾斜</span></p>", "*倾斜*\n"},
	{"145", "<p id=\"20240617104535-6bq1ven\" updated=\"20240617104535\"><span data-type=\"strong\">加粗</span></p>", "**加粗**\n"},
	{"144", "<p id=\"20240617103533-7y9st36\" updated=\"20240617103533\"><span data-type=\"block-ref\" data-subtype=\"s\" data-id=\"20200812220555-lj3enxa\">块引用</span></p>", "((20200812220555-lj3enxa \"块引用\"))\n"},
	{"143", "<p id=\"20240617101755-hvpl0dk\" updated=\"20240617101755\">​<span data-type=\"kbd\">foo</span>​</p>", "\u200b<kbd>foo</kbd>\u200b\n"},
	{"142", "<div><div class=\"nx-rounded nx-pt-6\" id=\"headlessui-tabs-panel-:R38fd5cm:\" role=\"tabpanel\" aria-labelledby=\"headlessui-tabs-tab-:R2ofd5cm:\" tabindex=\"0\" data-headlessui-state=\"selected\"><div class=\"nextra-code-block nx-relative nx-mt-6 first:nx-mt-0\"><pre class=\"nx-bg-primary-700/5 nx-mb-4 nx-overflow-x-auto nx-rounded-xl nx-subpixel-antialiased dark:nx-bg-primary-300/10 nx-text-[.9em] contrast-more:nx-border contrast-more:nx-border-primary-900/20 contrast-more:nx-contrast-150 contrast-more:dark:nx-border-primary-100/40 nx-py-4\" data-language=\"python\" data-theme=\"default\"><code class=\"nx-border-black nx-border-opacity-[0.04] nx-bg-opacity-[0.03] nx-bg-black nx-break-words nx-rounded-md nx-border nx-py-0.5 nx-px-[.25em] nx-text-[.9em] dark:nx-border-white/10 dark:nx-bg-white/10 [counter-reset:line]\" dir=\"ltr\" data-line-numbers=\"\" data-language=\"python\" data-theme=\"default\" data-line-numbers-max-digits=\"2\"><span class=\"line\"><span style=\"color: var(--shiki-token-keyword);\">from</span><span style=\"color: var(--shiki-color-text);\"> openai </span><span style=\"color: var(--shiki-token-keyword);\">import</span><span style=\"color: var(--shiki-color-text);\"> OpenAI</span></span>\n<span class=\"line\"> </span>\n<span class=\"line\"><span style=\"color: var(--shiki-color-text);\">client </span><span style=\"color: var(--shiki-token-keyword);\">=</span><span style=\"color: var(--shiki-color-text);\"> </span><span style=\"color: var(--shiki-token-function);\">OpenAI</span><span style=\"color: var(--shiki-token-punctuation);\">(</span></span>\n<span class=\"line\"><span style=\"color: var(--shiki-token-punctuation);\">    api_key </span><span style=\"color: var(--shiki-token-keyword);\">=</span><span style=\"color: var(--shiki-token-punctuation);\"> </span><span style=\"color: var(--shiki-token-string-expression);\">\"$MOONSHOT_API_KEY\"</span><span style=\"color: var(--shiki-token-punctuation);\">,</span></span>\n<span class=\"line\"><span style=\"color: var(--shiki-token-punctuation);\">    base_url </span><span style=\"color: var(--shiki-token-keyword);\">=</span><span style=\"color: var(--shiki-token-punctuation);\"> </span><span style=\"color: var(--shiki-token-string-expression);\">\"https://api.moonshot.cn/v1\"</span><span style=\"color: var(--shiki-token-punctuation);\">,</span></span>\n<span class=\"line\"><span style=\"color: var(--shiki-token-punctuation);\">)</span></span>\n<span class=\"line\"> </span>\n<span class=\"line\"><span style=\"color: var(--shiki-color-text);\">completion </span><span style=\"color: var(--shiki-token-keyword);\">=</span><span style=\"color: var(--shiki-color-text);\"> client</span><span style=\"color: var(--shiki-token-punctuation);\">.</span><span style=\"color: var(--shiki-color-text);\">chat</span><span style=\"color: var(--shiki-token-punctuation);\">.</span><span style=\"color: var(--shiki-color-text);\">completions</span><span style=\"color: var(--shiki-token-punctuation);\">.</span><span style=\"color: var(--shiki-token-function);\">create</span><span style=\"color: var(--shiki-token-punctuation);\">(</span></span>\n<span class=\"line\"><span style=\"color: var(--shiki-token-punctuation);\">    model </span><span style=\"color: var(--shiki-token-keyword);\">=</span><span style=\"color: var(--shiki-token-punctuation);\"> </span><span style=\"color: var(--shiki-token-string-expression);\">\"moonshot-v1-8k\"</span><span style=\"color: var(--shiki-token-punctuation);\">,</span></span>\n<span class=\"line\"><span style=\"color: var(--shiki-token-punctuation);\">    messages </span><span style=\"color: var(--shiki-token-keyword);\">=</span><span style=\"color: var(--shiki-token-punctuation);\"> [</span></span>\n<span class=\"line\"><span style=\"color: var(--shiki-token-punctuation);\">        {</span><span style=\"color: var(--shiki-token-string-expression);\">\"role\"</span><span style=\"color: var(--shiki-token-punctuation);\">: </span><span style=\"color: var(--shiki-token-string-expression);\">\"system\"</span><span style=\"color: var(--shiki-token-punctuation);\">, </span><span style=\"color: var(--shiki-token-string-expression);\">\"content\"</span><span style=\"color: var(--shiki-token-punctuation);\">: </span><span style=\"color: var(--shiki-token-string-expression);\">\"你是 Kimi，由 Moonshot AI 提供的人工智能助手，你更擅长中文和英文的对话。你会为用户提供安全，有帮助，准确的回答。同时，你会拒绝一切涉及恐怖主义，种族歧视，黄色暴力等问题的回答。Moonshot AI 为专有名词，不可翻译成其他语言。\"</span><span style=\"color: var(--shiki-token-punctuation);\">},</span></span>\n<span class=\"line\"><span style=\"color: var(--shiki-token-punctuation);\">        {</span><span style=\"color: var(--shiki-token-string-expression);\">\"role\"</span><span style=\"color: var(--shiki-token-punctuation);\">: </span><span style=\"color: var(--shiki-token-string-expression);\">\"user\"</span><span style=\"color: var(--shiki-token-punctuation);\">, </span><span style=\"color: var(--shiki-token-string-expression);\">\"content\"</span><span style=\"color: var(--shiki-token-punctuation);\">: </span><span style=\"color: var(--shiki-token-string-expression);\">\"你好，我叫李雷，1+1等于多少？\"</span><span style=\"color: var(--shiki-token-punctuation);\">}</span></span>\n<span class=\"line\"><span style=\"color: var(--shiki-token-punctuation);\">    ],</span></span>\n<span class=\"line\"><span style=\"color: var(--shiki-token-punctuation);\">    temperature </span><span style=\"color: var(--shiki-token-keyword);\">=</span><span style=\"color: var(--shiki-token-punctuation);\"> </span><span style=\"color: var(--shiki-token-constant);\">0.3</span><span style=\"color: var(--shiki-token-punctuation);\">,</span></span>\n<span class=\"line\"><span style=\"color: var(--shiki-token-punctuation);\">)</span></span>\n<span class=\"line\"> </span>\n<span class=\"line\"><span style=\"color: var(--shiki-token-function);\">print</span><span style=\"color: var(--shiki-token-punctuation);\">(completion.choices[</span><span style=\"color: var(--shiki-token-constant);\">0</span><span style=\"color: var(--shiki-token-punctuation);\">].message.content)</span></span></code></pre><div class=\"nx-opacity-0 nx-transition [div:hover>&amp;]:nx-opacity-100 focus-within:nx-opacity-100 nx-flex nx-gap-1 nx-absolute nx-m-[11px] nx-right-0 nx-top-0\"><button class=\"nextra-button nx-transition-all active:nx-opacity-50 nx-bg-primary-700/5 nx-border nx-border-black/5 nx-text-gray-600 hover:nx-text-gray-900 nx-rounded-md nx-p-1.5 dark:nx-bg-primary-300/10 dark:nx-border-white/10 dark:nx-text-gray-400 dark:hover:nx-text-gray-50 md:nx-hidden\" title=\"Toggle word wrap\"><svg viewBox=\"0 0 24 24\" width=\"24\" height=\"24\" class=\"nx-pointer-events-none nx-h-4 nx-w-4\"><path fill=\"currentColor\" d=\"M4 19h6v-2H4v2zM20 5H4v2h16V5zm-3 6H4v2h13.25c1.1 0 2 .9 2 2s-.9 2-2 2H15v-2l-3 3l3 3v-2h2c2.21 0 4-1.79 4-4s-1.79-4-4-4z\"></path></svg></button><button class=\"nextra-button nx-transition-all active:nx-opacity-50 nx-bg-primary-700/5 nx-border nx-border-black/5 nx-text-gray-600 hover:nx-text-gray-900 nx-rounded-md nx-p-1.5 dark:nx-bg-primary-300/10 dark:nx-border-white/10 dark:nx-text-gray-400 dark:hover:nx-text-gray-50\" title=\"Copy code\" tabindex=\"0\"><svg width=\"24\" height=\"24\" viewBox=\"0 0 24 24\" fill=\"none\" xmlns=\"http://www.w3.org/2000/svg\" stroke=\"currentColor\" class=\"nextra-copy-icon nx-pointer-events-none nx-h-4 nx-w-4\"><rect x=\"9\" y=\"9\" width=\"13\" height=\"13\" rx=\"2\" stroke-width=\"2\" stroke-linecap=\"round\" stroke-linejoin=\"round\"></rect><path d=\"M5 15H4C2.89543 15 2 14.1046 2 13V4C2 2.89543 2.89543 2 4 2H13C14.1046 2 15 2.89543 15 4V5\" stroke-width=\"2\" stroke-linecap=\"round\" stroke-linejoin=\"round\"></path></svg></button></div></div></div><span aria-hidden=\"true\" id=\"headlessui-tabs-panel-:R58fd5cm:\" role=\"tabpanel\" aria-labelledby=\"headlessui-tabs-tab-:R4ofd5cm:\" tabindex=\"-1\" style=\"position: fixed; top: 1px; left: 1px; width: 1px; height: 0px; padding: 0px; margin: -1px; overflow: hidden; clip: rect(0px, 0px, 0px, 0px); white-space: nowrap; border-width: 0px;\"></span><span aria-hidden=\"true\" id=\"headlessui-tabs-panel-:R78fd5cm:\" role=\"tabpanel\" tabindex=\"-1\" style=\"position:fixed;top:1px;left:1px;width:1px;height:0;padding:0;margin:-1px;overflow:hidden;clip:rect(0, 0, 0, 0);white-space:nowrap;border-width:0\" aria-labelledby=\"headlessui-tabs-tab-:R6ofd5cm:\"></span></div>", "```python\nfrom openai import OpenAI\n \nclient = OpenAI(\n    api_key = \"$MOONSHOT_API_KEY\",\n    base_url = \"https://api.moonshot.cn/v1\",\n)\n \ncompletion = client.chat.completions.create(\n    model = \"moonshot-v1-8k\",\n    messages = [\n        {\"role\": \"system\", \"content\": \"你是 Kimi，由 Moonshot AI 提供的人工智能助手，你更擅长中文和英文的对话。你会为用户提供安全，有帮助，准确的回答。同时，你会拒绝一切涉及恐怖主义，种族歧视，黄色暴力等问题的回答。Moonshot AI 为专有名词，不可翻译成其他语言。\"},\n        {\"role\": \"user\", \"content\": \"你好，我叫李雷，1+1等于多少？\"}\n    ],\n    temperature = 0.3,\n)\n \nprint(completion.choices[0].message.content)\n```\n"},
	{"141", "<code>&amp;ZeroWidthSpace;</code>", "`&ZeroWidthSpace;`\n"},
	{"140", "<span class=\"texhtml\">{<i>f</i><sub><i>k</i></sub>}<sub><i>k</i> ∈ <b>N</b></sub></span>", "$$\n\\{f_{k}\\}_{k ∈ N}\n$$\n"},
	{"139", "<div id=\"readability-page-1\" class=\"page\">\n    <div class=\"tablet:max-xl:w-mid-content xl:w-content flex\" id=\"post-content\">\n        <div class=\" post-body text-gray-text xl:col-start-1 xl:order-4 order-4 text-lg\">\n            <p><img src=\"https://test.com/foo.png\"\n                    width=\"640\" height=\"366\" alt=\"bar\"></p>\n            <p>baz\n            </p>\n        </div>\n    </div>\n</div>", "![bar](https://test.com/foo.png){: style=\"width: 640px;\"}\n\nbaz\n"},
	{"138", "<code class=\"samp docutils literal notranslate\"><em><span class=\"pre\">package_name</span></em><span class=\"pre\">-</span><em><span class=\"pre\">version</span></em><span class=\"pre\">-</span><em><span class=\"pre\">python_tag</span></em><span class=\"pre\">-</span><em><span class=\"pre\">abi_tag</span></em><span class=\"pre\">-</span><em><span class=\"pre\">platform_tag</span></em><span class=\"pre\">.whl</span></code>", "`package_name-version-python_tag-abi_tag-platform_tag.whl`\n"},
	{"137", "<div><figure>foo<figcaption>bar</figcaption></figure><figure>foo1<figcaption>bar1</figcaption></figure><p>baz</p></div>", "foo\nbar\n\nfoo1\nbar1\n\nbaz\n"},
	{"136", "<figure>foo<figcaption>bar</figcaption></figure><p>baz</p>", "foo\nbar\n\nbaz\n"},
	{"135", "foo<span class=\"ztext-math\" data-eeimg=\"1\" data-tex=\"g_J(u,v)=\\omega(u,Jv)\\\\\"><span></span><span><span class=\"MathJax_Preview\" style=\"color: inherit;\"></span><span class=\"MathJax_SVG_Display\"><span class=\"MathJax_SVG\" id=\"MathJax-Element-32-Frame\" tabindex=\"0\" data-mathml=\"<math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot; display=&quot;block&quot;><msub><mi>g</mi><mi>J</mi></msub><mo stretchy=&quot;false&quot;>(</mo><mi>u</mi><mo>,</mo><mi>v</mi><mo stretchy=&quot;false&quot;>)</mo><mo>=</mo><mi>&amp;#x03C9;</mi><mo stretchy=&quot;false&quot;>(</mo><mi>u</mi><mo>,</mo><mi>J</mi><mi>v</mi><mo stretchy=&quot;false&quot;>)</mo><mspace linebreak=&quot;newline&quot; /></math>\" role=\"presentation\" style=\"font-size: 100%; display: inline-block; position: relative;\"><svg xmlns:xlink=\"http://www.w3.org/1999/xlink\" width=\"79.807ex\" height=\"4.99ex\" viewBox=\"0 -849.8 34361.2 2148.5\" role=\"img\" focusable=\"false\" aria-hidden=\"true\" style=\"vertical-align: -3.016ex; max-width: 68900px;\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><g transform=\"translate(13090,0)\"><use xlink:href=\"#MJMATHI-67\" x=\"0\" y=\"0\"></use><use transform=\"scale(0.707)\" xlink:href=\"#MJMATHI-4A\" x=\"675\" y=\"-213\"></use><use xlink:href=\"#MJMAIN-28\" x=\"1025\" y=\"0\"></use><use xlink:href=\"#MJMATHI-75\" x=\"1414\" y=\"0\"></use><use xlink:href=\"#MJMAIN-2C\" x=\"1987\" y=\"0\"></use><use xlink:href=\"#MJMATHI-76\" x=\"2432\" y=\"0\"></use><use xlink:href=\"#MJMAIN-29\" x=\"2918\" y=\"0\"></use><use xlink:href=\"#MJMAIN-3D\" x=\"3585\" y=\"0\"></use><use xlink:href=\"#MJMATHI-3C9\" x=\"4641\" y=\"0\"></use><use xlink:href=\"#MJMAIN-28\" x=\"5264\" y=\"0\"></use><use xlink:href=\"#MJMATHI-75\" x=\"5653\" y=\"0\"></use><use xlink:href=\"#MJMAIN-2C\" x=\"6226\" y=\"0\"></use><use xlink:href=\"#MJMATHI-4A\" x=\"6671\" y=\"0\"></use><use xlink:href=\"#MJMATHI-76\" x=\"7304\" y=\"0\"></use><use xlink:href=\"#MJMAIN-29\" x=\"7790\" y=\"0\"></use></g></g></svg><span class=\"MJX_Assistive_MathML MJX_Assistive_MathML_Block\" role=\"presentation\"><math xmlns=\"http://www.w3.org/1998/Math/MathML\" display=\"block\"><msub><mi>g</mi><mi>J</mi></msub><mo stretchy=\"false\">(</mo><mi>u</mi><mo>,</mo><mi>v</mi><mo stretchy=\"false\">)</mo><mo>=</mo><mi>ω</mi><mo stretchy=\"false\">(</mo><mi>u</mi><mo>,</mo><mi>J</mi><mi>v</mi><mo stretchy=\"false\">)</mo><mspace linebreak=\"newline\"></mspace></math></span></span></span><script type=\"math/tex;mode=display\" id=\"MathJax-Element-32\">g_J(u,v)=\\omega(u,Jv)\\\\</script><span class=\"tex2jax_ignore math-holder\">g_J(u,v)=\\omega(u,Jv)\\\\</span></span></span>bar", "foo\n$$\ng_J(u,v)=\\omega(u,Jv)\\\\\n$$\n\nbar\n"},
	{"134", "<p>In proving that (a) implies (b), I used Tao's suggestion to define the numbers <span class=\"math-container\"><span class=\"MathJax_Preview\" style=\"color: inherit;\"></span><span class=\"MathJax\" id=\"MathJax-Element-10-Frame\" tabindex=\"0\" data-mathml=\"<math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;><msub><mi>n</mi><mi>j</mi></msub></math>\" role=\"presentation\" style=\"position: relative;\"><nobr aria-hidden=\"true\"><span class=\"math\" id=\"MathJax-Span-94\" style=\"width: 1.084em; display: inline-block;\"><span style=\"display: inline-block; position: relative; width: 0.964em; height: 0px; font-size: 111%;\"><span style=\"position: absolute; clip: rect(1.565em, 1000.96em, 2.646em, -999.997em); top: -2.159em; left: 0em;\"><span class=\"mrow\" id=\"MathJax-Span-95\"><span class=\"msubsup\" id=\"MathJax-Span-96\"><span style=\"display: inline-block; position: relative; width: 0.964em; height: 0px;\"><span style=\"position: absolute; clip: rect(3.426em, 1000.6em, 4.207em, -999.997em); top: -4.021em; left: 0em;\"><span class=\"mi\" id=\"MathJax-Span-97\" style=\"font-family: MathJax_Math-italic;\">n</span><span style=\"display: inline-block; width: 0px; height: 4.027em;\"></span></span><span style=\"position: absolute; top: -3.901em; left: 0.604em;\"><span class=\"mi\" id=\"MathJax-Span-98\" style=\"font-size: 70.7%; font-family: MathJax_Math-italic;\">j</span><span style=\"display: inline-block; width: 0px; height: 4.027em;\"></span></span></span></span></span><span style=\"display: inline-block; width: 0px; height: 2.165em;\"></span></span></span><span style=\"display: inline-block; overflow: hidden; vertical-align: -0.397em; border-left: 0px solid; width: 0px; height: 0.937em;\"></span></span></nobr><span class=\"MJX_Assistive_MathML\" role=\"presentation\"><math xmlns=\"http://www.w3.org/1998/Math/MathML\"><msub><mi>n</mi><mi>j</mi></msub></math></span></span><script type=\"math/tex\" id=\"MathJax-Element-10\">n_j</script></span> for each natural number <span class=\"math-container\"><span class=\"MathJax_Preview\" style=\"color: inherit;\"></span><span class=\"MathJax\" id=\"MathJax-Element-11-Frame\" tabindex=\"0\" data-mathml=\"<math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;><mi>j</mi></math>\" role=\"presentation\" style=\"position: relative;\"><nobr aria-hidden=\"true\"><span class=\"math\" id=\"MathJax-Span-99\" style=\"width: 0.483em; display: inline-block;\"><span style=\"display: inline-block; position: relative; width: 0.423em; height: 0px; font-size: 111%;\"><span style=\"position: absolute; clip: rect(1.324em, 1000.42em, 2.526em, -999.997em); top: -2.159em; left: 0em;\"><span class=\"mrow\" id=\"MathJax-Span-100\"><span class=\"mi\" id=\"MathJax-Span-101\" style=\"font-family: MathJax_Math-italic;\">j</span></span><span style=\"display: inline-block; width: 0px; height: 2.165em;\"></span></span></span><span style=\"display: inline-block; overflow: hidden; vertical-align: -0.263em; border-left: 0px solid; width: 0px; height: 1.07em;\"></span></span></nobr><span class=\"MJX_Assistive_MathML\" role=\"presentation\"><math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mi>j</mi></math></span></span><script type=\"math/tex\" id=\"MathJax-Element-11\">j</script></span> by the formula:</p>", "In proving that (a) implies (b), I used Tao's suggestion to define the numbers $n_j$ for each natural number $j$ by the formula:\n"},
	{"133", "<p><span class=\"math-container\"><span class=\"MathJax_Preview\" style=\"color: inherit;\"></span><div class=\"MathJax_Display\" style=\"text-align: center;\"><span class=\"MathJax\" id=\"MathJax-Element-12-Frame\" tabindex=\"0\" style=\"text-align: center; position: relative;\" data-mathml=\"<math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot; display=&quot;block&quot;><msub><mi>n</mi><mi>j</mi></msub><mo>:=</mo><mo movablelimits=&quot;true&quot; form=&quot;prefix&quot;>min</mo><mrow><mo>{</mo><mi>n</mi><mo>&amp;gt;</mo><msub><mi>n</mi><mrow class=&quot;MJX-TeXAtom-ORD&quot;><mi>j</mi><mo>&amp;#x2212;</mo><mn>1</mn></mrow></msub><mo>:</mo><mrow class=&quot;MJX-TeXAtom-ORD&quot;><mo stretchy=&quot;false&quot;>|</mo></mrow><msub><mi>a</mi><mi>n</mi></msub><mo>&amp;#x2212;</mo><mi>L</mi><mrow class=&quot;MJX-TeXAtom-ORD&quot;><mo stretchy=&quot;false&quot;>|</mo></mrow><mo>&amp;#x2264;</mo><mfrac><mn>1</mn><mi>j</mi></mfrac><mo>}</mo></mrow></math>\" role=\"presentation\"><nobr aria-hidden=\"true\"><span class=\"math\" id=\"MathJax-Span-102\" style=\"width: 18.261em; display: inline-block;\"><span style=\"display: inline-block; position: relative; width: 16.459em; height: 0px; font-size: 111%;\"><span style=\"position: absolute; clip: rect(1.805em, 1016.34em, 4.568em, -999.997em); top: -3.42em; left: 0em;\"><span class=\"mrow\" id=\"MathJax-Span-103\"><span class=\"msubsup\" id=\"MathJax-Span-104\"><span style=\"display: inline-block; position: relative; width: 0.964em; height: 0px;\"><span style=\"position: absolute; clip: rect(3.426em, 1000.6em, 4.207em, -999.997em); top: -4.021em; left: 0em;\"><span class=\"mi\" id=\"MathJax-Span-105\" style=\"font-family: MathJax_Math-italic;\">n</span><span style=\"display: inline-block; width: 0px; height: 4.027em;\"></span></span><span style=\"position: absolute; top: -3.901em; left: 0.604em;\"><span class=\"mi\" id=\"MathJax-Span-106\" style=\"font-size: 70.7%; font-family: MathJax_Math-italic;\">j</span><span style=\"display: inline-block; width: 0px; height: 4.027em;\"></span></span></span></span><span class=\"mo\" id=\"MathJax-Span-107\" style=\"font-family: MathJax_Main; padding-left: 0.303em;\">:<span style=\"font-family: MathJax_Main;\">=</span></span><span class=\"mo\" id=\"MathJax-Span-108\" style=\"font-family: MathJax_Main; padding-left: 0.303em;\">min</span><span class=\"mrow\" id=\"MathJax-Span-109\" style=\"padding-left: 0.183em;\"><span class=\"mo\" id=\"MathJax-Span-110\" style=\"vertical-align: 0em;\"><span style=\"font-family: MathJax_Size3;\">{</span></span><span class=\"mi\" id=\"MathJax-Span-111\" style=\"font-family: MathJax_Math-italic;\">n</span><span class=\"mo\" id=\"MathJax-Span-112\" style=\"font-family: MathJax_Main; padding-left: 0.303em;\">&gt;</span><span class=\"msubsup\" id=\"MathJax-Span-113\" style=\"padding-left: 0.303em;\"><span style=\"display: inline-block; position: relative; width: 1.865em; height: 0px;\"><span style=\"position: absolute; clip: rect(3.426em, 1000.6em, 4.207em, -999.997em); top: -4.021em; left: 0em;\"><span class=\"mi\" id=\"MathJax-Span-114\" style=\"font-family: MathJax_Math-italic;\">n</span><span style=\"display: inline-block; width: 0px; height: 4.027em;\"></span></span><span style=\"position: absolute; top: -3.901em; left: 0.604em;\"><span class=\"texatom\" id=\"MathJax-Span-115\"><span class=\"mrow\" id=\"MathJax-Span-116\"><span class=\"mi\" id=\"MathJax-Span-117\" style=\"font-size: 70.7%; font-family: MathJax_Math-italic;\">j</span><span class=\"mo\" id=\"MathJax-Span-118\" style=\"font-size: 70.7%; font-family: MathJax_Main;\">−</span><span class=\"mn\" id=\"MathJax-Span-119\" style=\"font-size: 70.7%; font-family: MathJax_Main;\">1</span></span></span><span style=\"display: inline-block; width: 0px; height: 4.027em;\"></span></span></span></span><span class=\"mo\" id=\"MathJax-Span-120\" style=\"font-family: MathJax_Main; padding-left: 0.303em;\">:</span><span class=\"texatom\" id=\"MathJax-Span-121\" style=\"padding-left: 0.303em;\"><span class=\"mrow\" id=\"MathJax-Span-122\"><span class=\"mo\" id=\"MathJax-Span-123\" style=\"font-family: MathJax_Main;\">|</span></span></span><span class=\"msubsup\" id=\"MathJax-Span-124\"><span style=\"display: inline-block; position: relative; width: 1.024em; height: 0px;\"><span style=\"position: absolute; clip: rect(3.426em, 1000.48em, 4.207em, -999.997em); top: -4.021em; left: 0em;\"><span class=\"mi\" id=\"MathJax-Span-125\" style=\"font-family: MathJax_Math-italic;\">a</span><span style=\"display: inline-block; width: 0px; height: 4.027em;\"></span></span><span style=\"position: absolute; top: -3.901em; left: 0.544em;\"><span class=\"mi\" id=\"MathJax-Span-126\" style=\"font-size: 70.7%; font-family: MathJax_Math-italic;\">n</span><span style=\"display: inline-block; width: 0px; height: 4.027em;\"></span></span></span></span><span class=\"mo\" id=\"MathJax-Span-127\" style=\"font-family: MathJax_Main; padding-left: 0.243em;\">−</span><span class=\"mi\" id=\"MathJax-Span-128\" style=\"font-family: MathJax_Math-italic; padding-left: 0.243em;\">L</span><span class=\"texatom\" id=\"MathJax-Span-129\"><span class=\"mrow\" id=\"MathJax-Span-130\"><span class=\"mo\" id=\"MathJax-Span-131\" style=\"font-family: MathJax_Main;\">|</span></span></span><span class=\"mo\" id=\"MathJax-Span-132\" style=\"font-family: MathJax_Main; padding-left: 0.303em;\">≤</span><span class=\"mfrac\" id=\"MathJax-Span-133\" style=\"padding-left: 0.303em;\"><span style=\"display: inline-block; position: relative; width: 0.604em; height: 0px; margin-right: 0.123em; margin-left: 0.123em;\"><span style=\"position: absolute; clip: rect(3.186em, 1000.42em, 4.207em, -999.997em); top: -4.682em; left: 50%; margin-left: -0.237em;\"><span class=\"mn\" id=\"MathJax-Span-134\" style=\"font-family: MathJax_Main;\">1</span><span style=\"display: inline-block; width: 0px; height: 4.027em;\"></span></span><span style=\"position: absolute; clip: rect(3.186em, 1000.42em, 4.387em, -999.997em); top: -3.36em; left: 50%; margin-left: -0.177em;\"><span class=\"mi\" id=\"MathJax-Span-135\" style=\"font-family: MathJax_Math-italic;\">j</span><span style=\"display: inline-block; width: 0px; height: 4.027em;\"></span></span><span style=\"position: absolute; clip: rect(0.844em, 1000.6em, 1.264em, -999.997em); top: -1.318em; left: 0em;\"><span style=\"display: inline-block; overflow: hidden; vertical-align: 0em; border-top: 1.3px solid; width: 0.604em; height: 0px;\"></span><span style=\"display: inline-block; width: 0px; height: 1.084em;\"></span></span></span></span><span class=\"mo\" id=\"MathJax-Span-136\" style=\"vertical-align: 0em;\"><span style=\"font-family: MathJax_Size3;\">}</span></span></span></span><span style=\"display: inline-block; width: 0px; height: 3.426em;\"></span></span></span><span style=\"display: inline-block; overflow: hidden; vertical-align: -1.13em; border-left: 0px solid; width: 0px; height: 2.803em;\"></span></span></nobr><span class=\"MJX_Assistive_MathML MJX_Assistive_MathML_Block\" role=\"presentation\"><math xmlns=\"http://www.w3.org/1998/Math/MathML\" display=\"block\"><msub><mi>n</mi><mi>j</mi></msub><mo>:=</mo><mo movablelimits=\"true\" form=\"prefix\">min</mo><mrow><mo>{</mo><mi>n</mi><mo>&gt;</mo><msub><mi>n</mi><mrow class=\"MJX-TeXAtom-ORD\"><mi>j</mi><mo>−</mo><mn>1</mn></mrow></msub><mo>:</mo><mrow class=\"MJX-TeXAtom-ORD\"><mo stretchy=\"false\">|</mo></mrow><msub><mi>a</mi><mi>n</mi></msub><mo>−</mo><mi>L</mi><mrow class=\"MJX-TeXAtom-ORD\"><mo stretchy=\"false\">|</mo></mrow><mo>≤</mo><mfrac><mn>1</mn><mi>j</mi></mfrac><mo>}</mo></mrow></math></span></span></div><script type=\"math/tex; mode=display\" id=\"MathJax-Element-12\">\nn_j := \\min \\left\\{n > n_{j-1} : |a_n - L| \\leq \\frac{1}{j} \\right\\}\n</script></span></p>", "$$\nn_j := \\min \\left\\{n > n_{j-1} : |a_n - L| \\leq \\frac{1}{j} \\right\\}\n$$\n"},
	{"132", "<figure class=\"mw-halign-right\" typeof=\"mw:File/Thumb\"><a href=\"/wiki/File:Sphere_wrapped_round_itself.png\" class=\"mw-file-description\"><img src=\"//upload.wikimedia.org/wikipedia/commons/thumb/5/50/Sphere_wrapped_round_itself.png/200px-Sphere_wrapped_round_itself.png\" decoding=\"async\" width=\"200\" height=\"188\" class=\"mw-file-element\" srcset=\"//upload.wikimedia.org/wikipedia/commons/thumb/5/50/Sphere_wrapped_round_itself.png/300px-Sphere_wrapped_round_itself.png 1.5x, //upload.wikimedia.org/wikipedia/commons/5/50/Sphere_wrapped_round_itself.png 2x\" data-file-width=\"378\" data-file-height=\"356\"></a><figcaption>A degree two map of a <a href=\"/wiki/Sphere\" title=\"Sphere\">sphere</a> onto itself.</figcaption></figure>", "![](//upload.wikimedia.org/wikipedia/commons/5/50/Sphere_wrapped_round_itself.png){: style=\"width: 200px;\"}\nA degree two map of a [sphere](/wiki/Sphere \"Sphere\") onto itself.\n"},
	{"131", "<p>The <a href=\"/wiki/Elliptic_integral#Incomplete_elliptic_integral_of_the_first_kind\" title=\"Elliptic integral\">incomplete elliptic integral of the first kind</a> <span class=\"texhtml\">F</span> is \n</p>", "The [incomplete elliptic integral of the first kind](/wiki/Elliptic_integral#Incomplete_elliptic_integral_of_the_first_kind \"Elliptic integral\") $F$ is\n"},
	{"130", "<p>foo</p><dl><dd>bar</dd></dl><p>baz</p>", "foo\n\nbar\n\nbaz\n"},
	{"129", "<div id=\"mw-content-text\" class=\"mw-body-content\"><div class=\"mw-content-ltr mw-parser-output\" lang=\"zh-Hans-CN\" dir=\"ltr\"><figure class=\"mw-halign-right\" typeof=\"mw:File/Thumb\"><a href=\"/wiki/File:GaussianBeamWaist.svg\" class=\"mw-file-description\"><img src=\"//upload.wikimedia.org/wikipedia/commons/thumb/5/53/GaussianBeamWaist.svg/350px-GaussianBeamWaist.svg.png\" decoding=\"async\" width=\"350\" height=\"170\" class=\"mw-file-element\" srcset=\"//upload.wikimedia.org/wikipedia/commons/thumb/5/53/GaussianBeamWaist.svg/525px-GaussianBeamWaist.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/5/53/GaussianBeamWaist.svg/700px-GaussianBeamWaist.svg.png 2x\" data-file-width=\"416\" data-file-height=\"202\"></a><figcaption>高斯光束的宽度<span class=\"mwe-math-element\"><span class=\"mwe-math-mathml-inline mwe-math-mathml-a11y\" style=\"display: none;\"><math xmlns=\"http://www.w3.org/1998/Math/MathML\" alttext=\"{\\displaystyle w(z)}\">\n  <semantics>\n    <mrow class=\"MJX-TeXAtom-ORD\">\n      <mstyle displaystyle=\"true\" scriptlevel=\"0\">\n        <mi>w</mi>\n        <mo stretchy=\"false\">(</mo>\n        <mi>z</mi>\n        <mo stretchy=\"false\">)</mo>\n      </mstyle>\n    </mrow>\n    <annotation encoding=\"application/x-tex\">{\\displaystyle w(z)}</annotation>\n  </semantics>\n</math></span><img src=\"https://wikimedia.org/api/rest_v1/media/math/render/svg/13626102fd9be0d15ff137c157c1aed6caf339a0\" class=\"mwe-math-fallback-image-inline mw-invert\" aria-hidden=\"true\" style=\"vertical-align: -0.838ex; width:4.562ex; height:2.843ex;\" alt=\"{\\displaystyle w(z)}\"></span>是轴向距离<span class=\"mwe-math-element\"><span class=\"mwe-math-mathml-inline mwe-math-mathml-a11y\" style=\"display: none;\"><math xmlns=\"http://www.w3.org/1998/Math/MathML\" alttext=\"{\\displaystyle z}\">\n  <semantics>\n    <mrow class=\"MJX-TeXAtom-ORD\">\n      <mstyle displaystyle=\"true\" scriptlevel=\"0\">\n        <mi>z</mi>\n      </mstyle>\n    </mrow>\n    <annotation encoding=\"application/x-tex\">{\\displaystyle z}</annotation>\n  </semantics>\n</math></span><img src=\"https://wikimedia.org/api/rest_v1/media/math/render/svg/bf368e72c009decd9b6686ee84a375632e11de98\" class=\"mwe-math-fallback-image-inline mw-invert\" aria-hidden=\"true\" style=\"vertical-align: -0.338ex; width:1.088ex; height:1.676ex;\" alt=\"{\\displaystyle z}\"></span>、射束腰部 <span class=\"mwe-math-element\"><span class=\"mwe-math-mathml-inline mwe-math-mathml-a11y\" style=\"display: none;\"><math xmlns=\"http://www.w3.org/1998/Math/MathML\" alttext=\"{\\displaystyle w_{0}}\">\n  <semantics>\n    <mrow class=\"MJX-TeXAtom-ORD\">\n      <mstyle displaystyle=\"true\" scriptlevel=\"0\">\n        <msub>\n          <mi>w</mi>\n          <mrow class=\"MJX-TeXAtom-ORD\">\n            <mn>0</mn>\n          </mrow>\n        </msub>\n      </mstyle>\n    </mrow>\n    <annotation encoding=\"application/x-tex\">{\\displaystyle w_{0}}</annotation>\n  </semantics>\n</math></span><img src=\"https://wikimedia.org/api/rest_v1/media/math/render/svg/7aa052386ec49846179aa8bbe2b279b57a675e00\" class=\"mwe-math-fallback-image-inline mw-invert\" aria-hidden=\"true\" style=\"vertical-align: -0.671ex; width:2.718ex; height:2.009ex;\" alt=\"{\\displaystyle w_{0}}\"></span>、共焦参数<span class=\"mwe-math-element\"><span class=\"mwe-math-mathml-inline mwe-math-mathml-a11y\" style=\"display: none;\"><math xmlns=\"http://www.w3.org/1998/Math/MathML\" alttext=\"{\\displaystyle b}\">\n  <semantics>\n    <mrow class=\"MJX-TeXAtom-ORD\">\n      <mstyle displaystyle=\"true\" scriptlevel=\"0\">\n        <mi>b</mi>\n      </mstyle>\n    </mrow>\n    <annotation encoding=\"application/x-tex\">{\\displaystyle b}</annotation>\n  </semantics>\n</math></span><img src=\"https://wikimedia.org/api/rest_v1/media/math/render/svg/f11423fbb2e967f986e36804a8ae4271734917c3\" class=\"mwe-math-fallback-image-inline mw-invert\" aria-hidden=\"true\" style=\"vertical-align: -0.338ex; width:0.998ex; height:2.176ex;\" alt=\"{\\displaystyle b}\"></span>、瑞利距离<span class=\"mwe-math-element\"><span class=\"mwe-math-mathml-inline mwe-math-mathml-a11y\" style=\"display: none;\"><math xmlns=\"http://www.w3.org/1998/Math/MathML\" alttext=\"{\\displaystyle z_{\\mathrm {R} }}\">\n  <semantics>\n    <mrow class=\"MJX-TeXAtom-ORD\">\n      <mstyle displaystyle=\"true\" scriptlevel=\"0\">\n        <msub>\n          <mi>z</mi>\n          <mrow class=\"MJX-TeXAtom-ORD\">\n            <mrow class=\"MJX-TeXAtom-ORD\">\n              <mi mathvariant=\"normal\">R</mi>\n            </mrow>\n          </mrow>\n        </msub>\n      </mstyle>\n    </mrow>\n    <annotation encoding=\"application/x-tex\">{\\displaystyle z_{\\mathrm {R} }}</annotation>\n  </semantics>\n</math></span><img src=\"https://wikimedia.org/api/rest_v1/media/math/render/svg/5cc1f1605248e6a63ce87b19b4d725aa6a21c908\" class=\"mwe-math-fallback-image-inline mw-invert\" aria-hidden=\"true\" style=\"vertical-align: -0.671ex; width:2.523ex; height:2.009ex;\" alt=\"{\\displaystyle z_{\\mathrm {R} }}\"></span>及总角度分布<span class=\"mwe-math-element\"><span class=\"mwe-math-mathml-inline mwe-math-mathml-a11y\" style=\"display: none;\"><math xmlns=\"http://www.w3.org/1998/Math/MathML\" alttext=\"{\\displaystyle \\Theta }\">\n  <semantics>\n    <mrow class=\"MJX-TeXAtom-ORD\">\n      <mstyle displaystyle=\"true\" scriptlevel=\"0\">\n        <mi mathvariant=\"normal\">Θ<!-- Θ --></mi>\n      </mstyle>\n    </mrow>\n    <annotation encoding=\"application/x-tex\">{\\displaystyle \\Theta }</annotation>\n  </semantics>\n</math></span><img src=\"https://wikimedia.org/api/rest_v1/media/math/render/svg/bc927b19f46d005b4720db7a0f96cd5b6f1a0d9b\" class=\"mwe-math-fallback-image-inline mw-invert\" aria-hidden=\"true\" style=\"vertical-align: -0.338ex; width:1.808ex; height:2.176ex;\" alt=\"{\\displaystyle \\Theta }\"></span>的函数</figcaption></figure>\n<p>在<a href=\"/wiki/%E5%85%89%E5%AD%B8\" class=\"mw-redirect\" title=\"光学\">光学</a>及<a href=\"/wiki/%E9%9B%B7%E5%B0%84%E7%A7%91%E5%AD%B8\" title=\"激光科学\">激光科学</a>中，<b>瑞利距离</b>或<b>瑞利长度</b>（Rayleigh length）或<b>瑞利范围</b>（Rayleigh range）是指<a href=\"/wiki/%E5%85%89%E6%9D%9F\" title=\"光束\">光束</a>沿着其行进方向，从其<a href=\"/wiki/%E5%B0%84%E6%9D%9F%E8%85%B0%E9%83%A8\" class=\"mw-redirect\" title=\"射束腰部\">腰部</a>到其面积为腰部面积两倍的<a href=\"/wiki/%E6%88%AA%E9%9D%A2_(%E5%B9%BE%E4%BD%95)\" title=\"截面 (几何)\">截面</a>的距离<sup id=\"cite_ref-Siegman1986_1-0\" class=\"reference\"><a href=\"#cite_note-Siegman1986-1\" title=\"\">[1]</a></sup>，此时截面半径约为<span class=\"mwe-math-element\"><span class=\"mwe-math-mathml-inline mwe-math-mathml-a11y\" style=\"display: none;\"><math xmlns=\"http://www.w3.org/1998/Math/MathML\" alttext=\"{\\displaystyle {\\sqrt {2}}}\">\n  <semantics>\n    <mrow class=\"MJX-TeXAtom-ORD\">\n      <mstyle displaystyle=\"true\" scriptlevel=\"0\">\n        <mrow class=\"MJX-TeXAtom-ORD\">\n          <msqrt>\n            <mn>2</mn>\n          </msqrt>\n        </mrow>\n      </mstyle>\n    </mrow>\n    <annotation encoding=\"application/x-tex\">{\\displaystyle {\\sqrt {2}}}</annotation>\n  </semantics>\n</math></span><img src=\"https://wikimedia.org/api/rest_v1/media/math/render/svg/b4afc1e27d418021bf10898eb44a7f5f315735ff\" class=\"mwe-math-fallback-image-inline mw-invert\" aria-hidden=\"true\" style=\"vertical-align: -0.671ex; width:3.098ex; height:3.009ex;\" alt=\"{\\displaystyle {\\sqrt {2}}}\"></span> 倍的腰部半径。另一个相关的参数为<b>共焦参数</b>（confocal parameter）<i>b</i>，恰为瑞利距离的两倍<sup id=\"cite_ref-Damask_2-0\" class=\"reference\"><a href=\"#cite_note-Damask-2\">[2]</a></sup>。当用<a href=\"/wiki/%E9%AB%98%E6%96%AF%E5%85%89%E6%9D%9F\" title=\"高斯光束\">高斯光束</a>来做为光束模型时，瑞利距离是相当重要的参数。\n</p></div>\n</div>", "![](//upload.wikimedia.org/wikipedia/commons/5/53/GaussianBeamWaist.svg){: style=\"width: 350px;\"}\n高斯光束的宽度 ${\\displaystyle w(z)}$ 是轴向距离 ${\\displaystyle z}$、射束腰部 ${\\displaystyle w_{0}}$、共焦参数 ${\\displaystyle b}$、瑞利距离 ${\\displaystyle z_{\\mathrm {R} }}$ 及总角度分布 ${\\displaystyle \\Theta }$ 的函数\n\n在[光学](/wiki/%E5%85%89%E5%AD%B8 \"光学\")及[激光科学](/wiki/%E9%9B%B7%E5%B0%84%E7%A7%91%E5%AD%B8 \"激光科学\")中，**瑞利距离**或\u200b**瑞利长度**\u200b（Rayleigh length）或\u200b**瑞利范围**\u200b（Rayleigh range）是指[光束](/wiki/%E5%85%89%E6%9D%9F \"光束\")沿着其行进方向，从其[腰部](/wiki/%E5%B0%84%E6%9D%9F%E8%85%B0%E9%83%A8 \"射束腰部\")到其面积为腰部面积两倍的[截面](/wiki/%E6%88%AA%E9%9D%A2_(%E5%B9%BE%E4%BD%95) \"截面 (几何)\")的距离\u200b^[[1]](#cite_note-Siegman1986-1)^\u200b，此时截面半径约为 ${\\displaystyle {\\sqrt {2}}}$ 倍的腰部半径。另一个相关的参数为\u200b**共焦参数**\u200b（confocal parameter）\u200b*b*\u200b，恰为瑞利距离的两倍\u200b^[[2]](#cite_note-Damask-2)^\u200b。当用[高斯光束](/wiki/%E9%AB%98%E6%96%AF%E5%85%89%E6%9D%9F \"高斯光束\")来做为光束模型时，瑞利距离是相当重要的参数。\n"},
	{"128", "<figure class=\"code\"><div class=\"highlight\"><table><tbody><tr><td class=\"gutter\"><pre class=\"line-numbers\"><span class=\"line-number\">1</span>\n</pre></td><td class=\"code\"><pre><code class=\"\"><span class=\"line\">$ aria2c http://example.org/mylinux.iso</span></code></pre></td></tr></tbody></table></div></figure>", "```\n$ aria2c http://example.org/mylinux.iso\n```\n"},
	{"127", "<table id=\"tablepress-85\" class=\"tablepress tablepress-id-85\">\n<tbody class=\"row-hover\">\n<tr class=\"row-1 odd\">\n<td class=\"column-1\">参数</td>\n<td class=\"column-2\">作用</td>\n</tr>\n<tr class=\"row-2 even\">\n<td class=\"column-1\">listen=[YES|NO]</td>\n<td class=\"column-2\">是否以独立运行的方式监听服务</td>\n</tr>\n</tbody>\n</table>", "| 参数             | 作用                         |\n| ------------------ | ------------------------------ |\n| listen=[YES\\|NO] | 是否以独立运行的方式监听服务 |\n"},
	{"126", "<div class=\"mwe-math-element\"><div class=\"mwe-math-mathml-display mwe-math-mathml-a11y\" style=\"display: none;\"><math display=\"block\" xmlns=\"http://www.w3.org/1998/Math/MathML\" alttext=\"{\\displaystyle \\{x\\,\\mid \\,f(x)>t\\}\\in X\\quad \\forall t\\in \\mathbb {R} .}\">\n  <semantics>\n    <mrow class=\"MJX-TeXAtom-ORD\">\n      <mstyle displaystyle=\"true\" scriptlevel=\"0\">\n        <mo fence=\"false\" stretchy=\"false\">{</mo>\n        <mi>x</mi>\n        <mspace width=\"thinmathspace\"></mspace>\n        <mo>∣<!-- ∣ --></mo>\n        <mspace width=\"thinmathspace\"></mspace>\n        <mi>f</mi>\n        <mo stretchy=\"false\">(</mo>\n        <mi>x</mi>\n        <mo stretchy=\"false\">)</mo>\n        <mo>&gt;</mo>\n        <mi>t</mi>\n        <mo fence=\"false\" stretchy=\"false\">}</mo>\n        <mo>∈<!-- ∈ --></mo>\n        <mi>X</mi>\n        <mspace width=\"1em\"></mspace>\n        <mi mathvariant=\"normal\">∀<!-- ∀ --></mi>\n        <mi>t</mi>\n        <mo>∈<!-- ∈ --></mo>\n        <mrow class=\"MJX-TeXAtom-ORD\">\n          <mi mathvariant=\"double-struck\">R</mi>\n        </mrow>\n        <mo>.</mo>\n      </mstyle>\n    </mrow>\n    <annotation encoding=\"application/x-tex\">{\\displaystyle \\{x\\,\\mid \\,f(x)&gt;t\\}\\in X\\quad \\forall t\\in \\mathbb {R} .}</annotation>\n  </semantics>\n</math></div><img src=\"https://wikimedia.org/api/rest_v1/media/math/render/svg/f2121f534e667a154f49e6f5b9d2b5d10e08acd6\" class=\"mwe-math-fallback-image-display mw-invert skin-invert\" aria-hidden=\"true\" style=\"vertical-align: -0.838ex; width:29.163ex; height:2.843ex;\" alt=\"{\\displaystyle \\{x\\,\\mid \\,f(x)>t\\}\\in X\\quad \\forall t\\in \\mathbb {R} .}\"></div>", "$$\n{\\displaystyle \\{x\\,\\mid \\,f(x)>t\\}\\in X\\quad \\forall t\\in \\mathbb {R} .}\n$$\n"},
	{"125", "<p><span class=\"katex\"><span class=\"katex-mathml\"><math xmlns=\"http://www.w3.org/1998/Math/MathML\"><semantics><mrow><mo>∫</mo><mfrac><mrow><mi>d</mi><mi>x</mi></mrow><msqrt><mrow><mi>a</mi><mo>+</mo><mi>b</mi><msup><mi>x</mi><mn>2</mn></msup></mrow></msqrt></mfrac></mrow><annotation encoding=\"application/x-tex\">\\int \\frac{dx}{\\sqrt{a + bx^2}}</annotation></semantics></math></span></span></p>", "$$\n\\int \\frac{dx}{\\sqrt{a + bx^2}}\n$$\n"},
	{"124", "<strong>圆的面积</strong>：<span class=\"katex\"><span class=\"katex-mathml\"><math xmlns=\"http://www.w3.org/1998/Math/MathML\"><semantics><mrow><mi>A</mi><mo>=</mo><mi>π</mi><msup><mi>r</mi><mn>2</mn></msup></mrow><annotation encoding=\"application/x-tex\">A = \\pi r^2</annotation></semantics></math></span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"strut\"></span><span class=\"mord mathnormal\">A</span><span class=\"mspace\"></span><span class=\"mrel\">=</span><span class=\"mspace\"></span></span><span class=\"base\"><span class=\"strut\"></span><span class=\"mord mathnormal\">π</span><span class=\"mord\"><span class=\"mord mathnormal\">r</span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\"><span><span class=\"pstrut\"></span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">2</span></span></span></span></span></span></span></span></span></span></span>，其中 <span class=\"katex\"><span class=\"katex-mathml\"><math xmlns=\"http://www.w3.org/1998/Math/MathML\"><semantics><mrow><mi>r</mi></mrow><annotation encoding=\"application/x-tex\">r</annotation></semantics></math></span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"strut\"></span><span class=\"mord mathnormal\">r</span></span></span></span> 为圆的半径", "\u200b**圆的面积**\u200b：$A = \\pi r^2$，其中 $r$ 为圆的半径\n"},
	{"123", "<p><span class=\"katex\"><span class=\"katex-mathml\"><math xmlns=\"http://www.w3.org/1998/Math/MathML\"><semantics><mrow><mi>E</mi><mo>=</mo><mi>m</mi><msup><mi>c</mi><mn>2</mn></msup></mrow><annotation encoding=\"application/x-tex\">E = mc^2</annotation></semantics></math></span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.6833em;\"></span><span class=\"mord mathnormal\" style=\"margin-right: 0.05764em;\">E</span><span class=\"mspace\" style=\"margin-right: 0.2778em;\"></span><span class=\"mrel\">=</span><span class=\"mspace\" style=\"margin-right: 0.2778em;\"></span></span><span class=\"base\"><span class=\"strut\" style=\"height: 0.8141em;\"></span><span class=\"mord mathnormal\">m</span><span class=\"mord\"><span class=\"mord mathnormal\">c</span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.8141em;\"><span style=\"top: -3.063em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"></span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">2</span></span></span></span></span></span></span></span></span></span></span></p>", "$$\nE = mc^2\n$$\n"},
	{"122", "<span class=\"mwe-math-element\"><img src=\"https://wikimedia.org/api/rest_v1/media/math/render/svg/13626102fd9be0d15ff137c157c1aed6caf339a0\" class=\"mwe-math-fallback-image-inline mw-invert\" aria-hidden=\"true\" alt=\"{\\displaystyle w(z)}\"></span>", "$$\n{\\displaystyle w(z)}\n$$\n"},
	{"121", "<span class=\"mwe-math-element\"><span class=\"mwe-math-mathml-inline mwe-math-mathml-a11y\" style=\"display: none;\"><math xmlns=\"http://www.w3.org/1998/Math/MathML\" alttext=\"{\\displaystyle w_{0}\\geq 2\\lambda /\\pi }\">\n  <semantics>\n    <mrow class=\"MJX-TeXAtom-ORD\">\n      <mstyle displaystyle=\"true\" scriptlevel=\"0\">\n        <msub>\n          <mi>w</mi>\n          <mrow class=\"MJX-TeXAtom-ORD\">\n            <mn>0</mn>\n          </mrow>\n        </msub>\n        <mo>≥<!-- ≥ --></mo>\n        <mn>2</mn>\n        <mi>λ<!-- λ --></mi>\n        <mrow class=\"MJX-TeXAtom-ORD\">\n          <mo>/</mo>\n        </mrow>\n        <mi>π<!-- π --></mi>\n      </mstyle>\n    </mrow>\n    <annotation encoding=\"application/x-tex\">{\\displaystyle w_{0}\\geq 2\\lambda /\\pi }</annotation>\n  </semantics>\n</math></span><img src=\"https://wikimedia.org/api/rest_v1/media/math/render/svg/ea5cfd2c04b22b048f527356e22ef971e2c1b7df\" class=\"mwe-math-fallback-image-inline mw-invert\" aria-hidden=\"true\" style=\"vertical-align: -0.838ex; width:10.829ex; height:2.843ex;\" alt=\"{\\displaystyle w_{0}\\geq 2\\lambda /\\pi }\"></span>", "$$\n{\\displaystyle w_{0}\\geq 2\\lambda /\\pi }\n$$\n"},
	{"120", "<h1 id=\"firstHeading\" class=\"firstHeading mw-first-heading\" lang=\"zh-Hans-CN\" dir=\"ltr\"><span class=\"mw-page-title-main\">瑞利距离</span><span class=\"mw-editsection\"><span class=\"mw-editsection-bracket\">[</span><a href=\"https://zh.wikipedia.org/w/index.php?title=%E7%91%9E%E5%88%A9%E8%B7%9D%E7%A6%BB&amp;action=edit&amp;section=0&amp;summary=/*%20top%20*/%20\" title=\"编辑首段\"><span>编辑</span></a><span class=\"mw-editsection-bracket\">]</span></span></h1>", "# 瑞利距离\n"},
	{"119", "<div class=\"captioned-image-container\"><figure><a class=\"image-link is-viewable-img image2\" target=\"_blank\" href=\"https://substackcdn.com/image/fetch/f_auto,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2Fc7e8ccaf-d891-4b77-b044-3ed0ff28b187_1775x881.png\" data-component-name=\"Image2ToDOM\" rel=\"\"><div class=\"image2-inset\"><picture><source type=\"image/webp\" srcset=\"https://substackcdn.com/image/fetch/w_424,c_limit,f_webp,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2Fc7e8ccaf-d891-4b77-b044-3ed0ff28b187_1775x881.png 424w, https://substackcdn.com/image/fetch/w_848,c_limit,f_webp,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2Fc7e8ccaf-d891-4b77-b044-3ed0ff28b187_1775x881.png 848w, https://substackcdn.com/image/fetch/w_1272,c_limit,f_webp,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2Fc7e8ccaf-d891-4b77-b044-3ed0ff28b187_1775x881.png 1272w, https://substackcdn.com/image/fetch/w_1456,c_limit,f_webp,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2Fc7e8ccaf-d891-4b77-b044-3ed0ff28b187_1775x881.png 1456w\" sizes=\"100vw\"><img src=\"https://substackcdn.com/image/fetch/w_1456,c_limit,f_auto,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2Fc7e8ccaf-d891-4b77-b044-3ed0ff28b187_1775x881.png\" width=\"1456\" height=\"723\" data-attrs=\"{&quot;src&quot;:&quot;https://substack-post-media.s3.amazonaws.com/public/images/c7e8ccaf-d891-4b77-b044-3ed0ff28b187_1775x881.png&quot;,&quot;srcNoWatermark&quot;:null,&quot;fullscreen&quot;:null,&quot;imageSize&quot;:null,&quot;height&quot;:723,&quot;width&quot;:1456,&quot;resizeWidth&quot;:null,&quot;bytes&quot;:1310063,&quot;alt&quot;:null,&quot;title&quot;:null,&quot;type&quot;:&quot;image/png&quot;,&quot;href&quot;:null,&quot;belowTheFold&quot;:false,&quot;topImage&quot;:true,&quot;internalRedirect&quot;:null}\" class=\"sizing-normal\" alt=\"\" srcset=\"https://substackcdn.com/image/fetch/w_424,c_limit,f_auto,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2Fc7e8ccaf-d891-4b77-b044-3ed0ff28b187_1775x881.png 424w, https://substackcdn.com/image/fetch/w_848,c_limit,f_auto,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2Fc7e8ccaf-d891-4b77-b044-3ed0ff28b187_1775x881.png 848w, https://substackcdn.com/image/fetch/w_1272,c_limit,f_auto,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2Fc7e8ccaf-d891-4b77-b044-3ed0ff28b187_1775x881.png 1272w, https://substackcdn.com/image/fetch/w_1456,c_limit,f_auto,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2Fc7e8ccaf-d891-4b77-b044-3ed0ff28b187_1775x881.png 1456w\" sizes=\"100vw\" fetchpriority=\"high\"></picture><div class=\"image-link-expand\"><svg xmlns=\"http://www.w3.org/2000/svg\" width=\"20\" height=\"20\" viewBox=\"0 0 24 24\" fill=\"none\" stroke=\"currentColor\" stroke-width=\"2\" stroke-linecap=\"round\" stroke-linejoin=\"round\" class=\"lucide lucide-maximize2 \"><polyline points=\"15 3 21 3 21 9\"></polyline><polyline points=\"9 21 3 21 3 15\"></polyline><line x1=\"21\" x2=\"14\" y1=\"3\" y2=\"10\"></line><line x1=\"3\" x2=\"10\" y1=\"21\" y2=\"14\"></line></svg></div></div></a><figcaption class=\"image-caption\">Source: Nvidia, SemiAnalysis</figcaption></figure></div>", "[![](https://substackcdn.com/image/fetch/w_1456,c_limit,f_auto,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2Fc7e8ccaf-d891-4b77-b044-3ed0ff28b187_1775x881.png){: style=\"width: 1456px;\"}](https://substackcdn.com/image/fetch/f_auto,q_auto:good,fl_progressive:steep/https%3A%2F%2Fsubstack-post-media.s3.amazonaws.com%2Fpublic%2Fimages%2Fc7e8ccaf-d891-4b77-b044-3ed0ff28b187_1775x881.png)\nSource: Nvidia, SemiAnalysis\n"},
	{"118", "<p><span><strong data-brushtype=\"text\"><strong><span>foo</span></strong></strong></span></p>", "**foo**\n"},
	{"117", "<table border=\"0\" cellpadding=\"0\" cellspacing=\"0\" class=\"syntaxhighlighter  python\"><tbody><tr><td class=\"gutter\"><div class=\"line number1 index0 alt2\">1</div><div class=\"line number2 index1 alt1\">2</div><div class=\"line number3 index2 alt2\">3</div><div class=\"line number4 index3 alt1\">4</div><div class=\"line number5 index4 alt2\">5</div><div class=\"line number6 index5 alt1\">6</div><div class=\"line number7 index6 alt2\">7</div><div class=\"line number8 index7 alt1\">8</div><div class=\"line number9 index8 alt2\">9</div></td><td class=\"code\"><div class=\"container\"><div class=\"line number1 index0 alt2\"><code class=\"python keyword\">import</code> <code class=\"python plain\">os</code></div><div class=\"line number2 index1 alt1\">&nbsp;</div><div class=\"line number3 index2 alt2\"><code class=\"python plain\">res </code><code class=\"python keyword\">=</code> <code class=\"python plain\">os.popen(</code><code class=\"python string\">\"find ./ -name *.lua\"</code><code class=\"python plain\">).readlines()</code></div><div class=\"line number4 index3 alt1\">&nbsp;</div><div class=\"line number5 index4 alt2\"><code class=\"python keyword\">for</code> <code class=\"python plain\">i </code><code class=\"python keyword\">in</code> <code class=\"python functions\">range</code><code class=\"python plain\">(</code><code class=\"python value\">0</code><code class=\"python plain\">, </code><code class=\"python functions\">len</code><code class=\"python plain\">(res)) :</code></div><div class=\"line number6 index5 alt1\"><code class=\"python spaces\">&nbsp;&nbsp;&nbsp;&nbsp;</code><code class=\"python plain\">path </code><code class=\"python keyword\">=</code> <code class=\"python plain\">res[i].strip(</code><code class=\"python string\">\"\\n\"</code><code class=\"python plain\">)</code></div><div class=\"line number7 index6 alt2\"><code class=\"python spaces\">&nbsp;&nbsp;&nbsp;&nbsp;</code><code class=\"python plain\">cmd </code><code class=\"python keyword\">=</code> <code class=\"python string\">\"java -jar /home/winmt/unluac_miwifi/build/unluac.jar \"</code> <code class=\"python keyword\">+</code> <code class=\"python plain\">path </code><code class=\"python keyword\">+</code> <code class=\"python string\">\" &gt; \"</code> <code class=\"python keyword\">+</code> <code class=\"python plain\">path </code><code class=\"python keyword\">+</code> <code class=\"python string\">\".dis\"</code></div><div class=\"line number8 index7 alt1\"><code class=\"python spaces\">&nbsp;&nbsp;&nbsp;&nbsp;</code><code class=\"python functions\">print</code><code class=\"python plain\">(cmd)</code></div><div class=\"line number9 index8 alt2\"><code class=\"python spaces\">&nbsp;&nbsp;&nbsp;&nbsp;</code><code class=\"python plain\">os.system(cmd)</code></div></div></td></tr></tbody></table>", "```python\nimport os\n \nres = os.popen(\"find ./ -name *.lua\").readlines()\n \nfor i in range(0, len(res)) :\n    path = res[i].strip(\"\\n\")\n    cmd = \"java -jar /home/winmt/unluac_miwifi/build/unluac.jar \" + path + \" > \" + path + \".dis\"\n    print(cmd)\n    os.system(cmd)\n```\n"},
	{"116", "<p><span class=\"color-blue-03\"><strong><span class=\"font-size-16\">【Q</span></strong><strong><span class=\"font-size-16\">22</span></strong><strong><span class=\"font-size-16\">】</span></strong><strong><span class=\"font-size-16\">为什么</span></strong><strong><span class=\"font-size-16\">22</span></strong><strong><span class=\"font-size-16\">话</span></strong><strong><span class=\"font-size-16\">中助手说自己依然会存在于平行世界？&nbsp;&nbsp;&nbsp;&nbsp;</span></strong></span><strong><span class=\"font-size-16\">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;</span></strong></p>", "\u200b**【Q22**\u200b**】为什么**\u200b**22话**\u200b**中助手说自己依然会存在于平行世界？    \u200b**\n"},
	{"115", "<p><span class=\"font-size-16\">foo<span class=\"color-blue-03\"><strong>bar</strong></span>baz</span></p>", "foo**bar**baz\n"},
	{"114", "<h4 align=\"center\" tabindex=\"-1\" class=\"heading-element\" dir=\"auto\">\n  <a target=\"_blank\" rel=\"noopener noreferrer nofollow\" href=\"https://camo.githubusercontent.com/ea9748c960271146d31e98ffdfd905bc41b2f61f8b6db457ff418980d0f862a9/68747470733a2f2f696d672e736869656c64732e696f2f707970692f7374617475732f70796c6f61642d6e673f7374796c653d666c61742d737175617265\"><img alt=\"status\" src=\"https://camo.githubusercontent.com/ea9748c960271146d31e98ffdfd905bc41b2f61f8b6db457ff418980d0f862a9/68747470733a2f2f696d672e736869656c64732e696f2f707970692f7374617475732f70796c6f61642d6e673f7374796c653d666c61742d737175617265\" data-canonical-src=\"https://img.shields.io/pypi/status/pyload-ng?style=flat-square\" style=\"max-width: 100%;\"></a>\n  <a href=\"https://github.com/pyload/pyload/actions\">\n    <img alt=\"build\" src=\"https://camo.githubusercontent.com/a5f1eccdcc0f40c039ee0198897ee91f293a107c168eb3ff7998c7be096ed9e6/68747470733a2f2f696d672e736869656c64732e696f2f6769746875622f616374696f6e732f776f726b666c6f772f7374617475732f70796c6f61642f70796c6f61642f746573742e796d6c3f6576656e743d70757368267374796c653d666c61742d737175617265\" data-canonical-src=\"https://img.shields.io/github/actions/workflow/status/pyload/pyload/test.yml?event=push&amp;style=flat-square\" style=\"max-width: 100%;\">\n  </a>\n  <a href=\"https://www.codacy.com/gh/pyload/pyload\" rel=\"nofollow\">\n    <img alt=\"codacy\" src=\"https://camo.githubusercontent.com/745c50bf6126952288880983cb91fe07d2e3f1a18a4f076802bb4b4aaa4fe8d2/68747470733a2f2f696d672e736869656c64732e696f2f636f646163792f67726164652f31643034376637376330613634393665623730386531623363613833303036623f6c6162656c3d6772616465267374796c653d666c61742d737175617265\" 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[![status](https://camo.githubusercontent.com/ea9748c960271146d31e98ffdfd905bc41b2f61f8b6db457ff418980d0f862a9/68747470733a2f2f696d672e736869656c64732e696f2f707970692f7374617475732f70796c6f61642d6e673f7374796c653d666c61742d737175617265)](https://camo.githubusercontent.com/ea9748c960271146d31e98ffdfd905bc41b2f61f8b6db457ff418980d0f862a9/68747470733a2f2f696d672e736869656c64732e696f2f707970692f7374617475732f70796c6f61642d6e673f7374796c653d666c61742d737175617265)[![build](https://camo.githubusercontent.com/a5f1eccdcc0f40c039ee0198897ee91f293a107c168eb3ff7998c7be096ed9e6/68747470733a2f2f696d672e736869656c64732e696f2f6769746875622f616374696f6e732f776f726b666c6f772f7374617475732f70796c6f61642f70796c6f61642f746573742e796d6c3f6576656e743d70757368267374796c653d666c61742d737175617265)](https://github.com/pyload/pyload/actions)[![codacy](https://camo.githubusercontent.com/745c50bf6126952288880983cb91fe07d2e3f1a18a4f076802bb4b4aaa4fe8d2/68747470733a2f2f696d672e736869656c64732e696f2f636f646163792f67726164652f31643034376637376330613634393665623730386531623363613833303036623f6c6162656c3d6772616465267374796c653d666c61742d737175617265)](https://www.codacy.com/gh/pyload/pyload)[![python](https://camo.githubusercontent.com/40a8a08eda6b53498a0413597f05fa38dd41cced42c168d815b7462e7c392373/68747470733a2f2f696d672e736869656c64732e696f2f707970692f707976657273696f6e732f70796c6f61642d6e673f7374796c653d666c61742d737175617265)](https://camo.githubusercontent.com/40a8a08eda6b53498a0413597f05fa38dd41cced42c168d815b7462e7c392373/68747470733a2f2f696d672e736869656c64732e696f2f707970692f707976657273696f6e732f70796c6f61642d6e673f7374796c653d666c61742d737175617265)[![pypi](https://camo.githubusercontent.com/f7a24874e9efd6612e689237c95356779f086ee5a72c88280e1d3d4fd1a9d2d9/68747470733a2f2f696d672e736869656c64732e696f2f707970692f762f70796c6f61642d6e673f7374796c653d666c61742d737175617265)](https://pypi.python.org/pypi/pyload-ng)[![pyup](https://camo.githubusercontent.com/6e36a50dadd8380d410de01553600fb070677fa71790700f49f79b62b0456bdc/68747470733a2f2f707975702e696f2f7265706f732f6769746875622f70796c6f61642f70796c6f61642f736869656c642e737667)](https://pyup.io/repos/github/pyload/pyload)\n"},
	{"113", "<blockquote> \n <p>我们定义<span class=\"MathJax_Preview\" style=\"color: inherit; display: none;\"></span><span class=\"MathJax\" id=\"MathJax-Element-1-Frame\" tabindex=\"0\" style=\"position: relative;\" data-mathml=\"<math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;><mi>f</mi><mo stretchy=&quot;false&quot;>(</mo><mi>x</mi><mo stretchy=&quot;false&quot;>)</mo><mo>=</mo><munderover><mo>&amp;#x2211;</mo><mrow class=&quot;MJX-TeXAtom-ORD&quot;><mi>i</mi><mo>=</mo><mn>0</mn></mrow><mrow class=&quot;MJX-TeXAtom-ORD&quot;><mi>N</mi></mrow></munderover><msubsup><mo>&amp;#x222B;</mo><mrow class=&quot;MJX-TeXAtom-ORD&quot;><mi>a</mi></mrow><mrow class=&quot;MJX-TeXAtom-ORD&quot;><mi>b</mi></mrow></msubsup><mi>g</mi><mo stretchy=&quot;false&quot;>(</mo><mi>t</mi><mo>,</mo><mi>i</mi><mo stretchy=&quot;false&quot;>)</mo><mtext>&amp;#xA0;d</mtext><mi>t</mi></math>\" role=\"presentation\"><nobr aria-hidden=\"true\"><span class=\"math\" id=\"MathJax-Span-1\" style=\"width: 12.607em; display: inline-block;\"><span style=\"display: inline-block; position: relative; width: 10.471em; height: 0px; font-size: 120%;\"><span style=\"position: absolute; clip: rect(0.94em, 1010.42em, 2.659em, -999.997em); top: -2.133em; left: 0em;\"><span class=\"mrow\" id=\"MathJax-Span-2\"><span class=\"mi\" id=\"MathJax-Span-3\" style=\"font-family: MathJax_Math-italic;\">f<span style=\"display: inline-block; overflow: hidden; height: 1px; width: 0.055em;\"></span></span><span class=\"mo\" id=\"MathJax-Span-4\" style=\"font-family: MathJax_Main;\">(</span><span class=\"mi\" id=\"MathJax-Span-5\" style=\"font-family: MathJax_Math-italic;\">x</span><span class=\"mo\" id=\"MathJax-Span-6\" style=\"font-family: MathJax_Main;\">)</span><span class=\"mo\" id=\"MathJax-Span-7\" style=\"font-family: MathJax_Main; padding-left: 0.263em;\">=</span><span class=\"munderover\" id=\"MathJax-Span-8\" style=\"padding-left: 0.263em;\"><span style=\"display: inline-block; position: relative; width: 2.294em; height: 0px;\"><span style=\"position: absolute; clip: rect(3.128em, 1000.99em, 4.43em, -999.997em); top: -4.008em; left: 0em;\"><span class=\"mo\" id=\"MathJax-Span-9\" style=\"font-family: MathJax_Size1; vertical-align: 0em;\">∑</span><span style=\"display: inline-block; width: 0px; height: 4.013em;\"></span></span><span style=\"position: absolute; clip: rect(3.388em, 1000.68em, 4.169em, -999.997em); top: -4.477em; left: 1.044em;\"><span class=\"texatom\" id=\"MathJax-Span-10\"><span class=\"mrow\" id=\"MathJax-Span-11\"><span class=\"mi\" id=\"MathJax-Span-12\" style=\"font-size: 70.7%; font-family: MathJax_Math-italic;\">N<span style=\"display: inline-block; overflow: hidden; height: 1px; width: 0.055em;\"></span></span></span></span><span style=\"display: inline-block; width: 0px; height: 4.013em;\"></span></span><span style=\"position: absolute; clip: rect(3.388em, 1001.2em, 4.169em, -999.997em); top: -3.747em; left: 1.044em;\"><span class=\"texatom\" id=\"MathJax-Span-13\"><span class=\"mrow\" id=\"MathJax-Span-14\"><span class=\"mi\" id=\"MathJax-Span-15\" style=\"font-size: 70.7%; font-family: MathJax_Math-italic;\">i</span><span class=\"mo\" id=\"MathJax-Span-16\" style=\"font-size: 70.7%; font-family: MathJax_Main;\">=</span><span class=\"mn\" id=\"MathJax-Span-17\" style=\"font-size: 70.7%; font-family: MathJax_Main;\">0</span></span></span><span style=\"display: inline-block; width: 0px; height: 4.013em;\"></span></span></span></span><span class=\"msubsup\" id=\"MathJax-Span-18\" style=\"padding-left: 0.159em;\"><span style=\"display: inline-block; position: relative; width: 1.096em; height: 0px;\"><span style=\"position: absolute; clip: rect(3.076em, 1000.63em, 4.482em, -999.997em); top: -4.008em; left: 0em;\"><span class=\"mo\" id=\"MathJax-Span-19\" style=\"font-family: MathJax_Size1; vertical-align: 0em;\">∫<span style=\"display: inline-block; overflow: hidden; height: 1px; width: 0.159em;\"></span></span><span style=\"display: inline-block; width: 0px; height: 4.013em;\"></span></span><span style=\"position: absolute; clip: rect(3.388em, 1000.37em, 4.169em, -999.997em); top: -4.529em; left: 0.68em;\"><span class=\"texatom\" id=\"MathJax-Span-20\"><span class=\"mrow\" id=\"MathJax-Span-21\"><span class=\"mi\" id=\"MathJax-Span-22\" style=\"font-size: 70.7%; font-family: MathJax_Math-italic;\">b</span></span></span><span style=\"display: inline-block; width: 0px; height: 4.013em;\"></span></span><span style=\"position: absolute; clip: rect(3.544em, 1000.47em, 4.169em, -999.997em); top: -3.643em; left: 0.471em;\"><span class=\"texatom\" id=\"MathJax-Span-23\"><span class=\"mrow\" id=\"MathJax-Span-24\"><span class=\"mi\" id=\"MathJax-Span-25\" style=\"font-size: 70.7%; font-family: MathJax_Math-italic;\">a</span></span></span><span style=\"display: inline-block; width: 0px; height: 4.013em;\"></span></span></span></span><span class=\"mi\" id=\"MathJax-Span-26\" style=\"font-family: MathJax_Math-italic; padding-left: 0.159em;\">g<span style=\"display: inline-block; overflow: hidden; height: 1px; width: 0.003em;\"></span></span><span class=\"mo\" id=\"MathJax-Span-27\" style=\"font-family: MathJax_Main;\">(</span><span class=\"mi\" id=\"MathJax-Span-28\" style=\"font-family: MathJax_Math-italic;\">t</span><span class=\"mo\" id=\"MathJax-Span-29\" style=\"font-family: MathJax_Main;\">,</span><span class=\"mi\" id=\"MathJax-Span-30\" style=\"font-family: MathJax_Math-italic; padding-left: 0.159em;\">i</span><span class=\"mo\" id=\"MathJax-Span-31\" style=\"font-family: MathJax_Main;\">)</span><span class=\"mtext\" id=\"MathJax-Span-32\" style=\"font-family: MathJax_Main;\">&nbsp;d</span><span class=\"mi\" id=\"MathJax-Span-33\" style=\"font-family: MathJax_Math-italic;\">t</span></span><span style=\"display: inline-block; width: 0px; height: 2.138em;\"></span></span></span><span style=\"display: inline-block; overflow: hidden; vertical-align: -0.497em; border-left: 0px solid; width: 0px; height: 1.753em;\"></span></span></nobr><span class=\"MJX_Assistive_MathML\" role=\"presentation\"><math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mi>f</mi><mo stretchy=\"false\">(</mo><mi>x</mi><mo stretchy=\"false\">)</mo><mo>=</mo><munderover><mo>∑</mo><mrow class=\"MJX-TeXAtom-ORD\"><mi>i</mi><mo>=</mo><mn>0</mn></mrow><mrow class=\"MJX-TeXAtom-ORD\"><mi>N</mi></mrow></munderover><msubsup><mo>∫</mo><mrow class=\"MJX-TeXAtom-ORD\"><mi>a</mi></mrow><mrow class=\"MJX-TeXAtom-ORD\"><mi>b</mi></mrow></msubsup><mi>g</mi><mo stretchy=\"false\">(</mo><mi>t</mi><mo>,</mo><mi>i</mi><mo stretchy=\"false\">)</mo><mtext>&nbsp;d</mtext><mi>t</mi></math></span></span><script type=\"math/tex\" id=\"MathJax-Element-1\">f(x) = \\sum_{i=0}^{N}\\int_{a}^{b} g(t,i) \\text{ d}t</script>. (行内公式)</p> \n <p>或者定义<span class=\"MathJax_Preview\" style=\"color: inherit; display: none;\"></span><span class=\"MathJax\" id=\"MathJax-Element-2-Frame\" tabindex=\"0\" style=\"position: relative;\" data-mathml=\"<math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;><mi>f</mi><mo stretchy=&quot;false&quot;>(</mo><mi>x</mi><mo stretchy=&quot;false&quot;>)</mo></math>\" role=\"presentation\"><nobr aria-hidden=\"true\"><span class=\"math\" id=\"MathJax-Span-34\" style=\"width: 2.294em; display: inline-block;\"><span style=\"display: inline-block; position: relative; width: 1.878em; height: 0px; font-size: 120%;\"><span style=\"position: absolute; clip: rect(1.253em, 1001.77em, 2.555em, -999.997em); top: -2.133em; left: 0em;\"><span class=\"mrow\" id=\"MathJax-Span-35\"><span class=\"mi\" id=\"MathJax-Span-36\" style=\"font-family: MathJax_Math-italic;\">f<span style=\"display: inline-block; overflow: hidden; height: 1px; width: 0.055em;\"></span></span><span class=\"mo\" id=\"MathJax-Span-37\" style=\"font-family: MathJax_Main;\">(</span><span class=\"mi\" id=\"MathJax-Span-38\" style=\"font-family: MathJax_Math-italic;\">x</span><span class=\"mo\" id=\"MathJax-Span-39\" style=\"font-family: MathJax_Main;\">)</span></span><span style=\"display: inline-block; width: 0px; height: 2.138em;\"></span></span></span><span style=\"display: inline-block; overflow: hidden; vertical-align: -0.372em; border-left: 0px solid; width: 0px; height: 1.316em;\"></span></span></nobr><span class=\"MJX_Assistive_MathML\" role=\"presentation\"><math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mi>f</mi><mo stretchy=\"false\">(</mo><mi>x</mi><mo stretchy=\"false\">)</mo></math></span></span><script type=\"math/tex\" id=\"MathJax-Element-2\">f(x)</script>如下（行间公式）: <br> <span class=\"MathJax_Preview\"></span></p> \n <div class=\"MathJax_Display\"> \n   \n </div><span class=\"MathJax_Preview\" style=\"color: inherit; display: none;\"></span><div class=\"MathJax_Display\"><span class=\"MathJax MathJax_FullWidth\" id=\"MathJax-Element-3-Frame\" tabindex=\"0\" data-mathml=\"<math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot; display=&quot;block&quot;><mtable displaystyle=&quot;true&quot;><mlabeledtr><mtd id=&quot;mjx-eqn-1&quot;><mtext>(1)</mtext></mtd><mtd><mi>f</mi><mo stretchy=&quot;false&quot;>(</mo><mi>x</mi><mo stretchy=&quot;false&quot;>)</mo><mo>=</mo><munderover><mo>&amp;#x2211;</mo><mrow class=&quot;MJX-TeXAtom-ORD&quot;><mi>i</mi><mo>=</mo><mn>0</mn></mrow><mrow class=&quot;MJX-TeXAtom-ORD&quot;><mi>N</mi></mrow></munderover><msubsup><mo>&amp;#x222B;</mo><mrow class=&quot;MJX-TeXAtom-ORD&quot;><mi>a</mi></mrow><mrow class=&quot;MJX-TeXAtom-ORD&quot;><mi>b</mi></mrow></msubsup><mi>g</mi><mo stretchy=&quot;false&quot;>(</mo><mi>t</mi><mo>,</mo><mi>i</mi><mo stretchy=&quot;false&quot;>)</mo><mtext>&amp;#xA0;d</mtext><mi>t</mi></mtd></mlabeledtr></mtable></math>\" role=\"presentation\" style=\"position: relative;\"><nobr aria-hidden=\"true\"><span class=\"math\" id=\"MathJax-Span-40\" style=\"width: 100%; display: inline-block; min-width: 14.169em;\"><span style=\"display: inline-block; position: relative; width: 100%; height: 0px; font-size: 120%; min-width: 14.169em;\"><span style=\"position: absolute; clip: rect(2.138em, 1010em, 5.367em, -999.997em); top: -4.008em; left: 0em; width: 100%;\"><span class=\"mrow\" id=\"MathJax-Span-41\"><span class=\"mtable\" id=\"MathJax-Span-42\" style=\"min-width: 14.169em;\"><span style=\"display: inline-block; position: relative; width: 100%; height: 0px; min-width: 14.169em;\"><span style=\"display: inline-block; position: absolute; width: 10.003em; height: 0px; clip: rect(-1.872em, 1010em, 1.357em, -999.997em); top: 0em; left: 50%; margin-left: -4.997em;\"><span style=\"position: absolute; clip: rect(2.138em, 1010em, 5.367em, -999.997em); top: -4.008em; left: 0em;\"><span style=\"display: inline-block; position: relative; width: 10.003em; height: 0px;\"><span style=\"position: absolute; clip: rect(2.138em, 1010em, 5.367em, -999.997em); top: -4.008em; left: 50%; margin-left: -4.997em;\"><span class=\"mtd\" id=\"MathJax-Span-46\"><span class=\"mrow\" id=\"MathJax-Span-47\"><span class=\"mi\" id=\"MathJax-Span-48\" style=\"font-family: MathJax_Math-italic;\">f<span style=\"display: inline-block; overflow: hidden; height: 1px; width: 0.055em;\"></span></span><span class=\"mo\" id=\"MathJax-Span-49\" style=\"font-family: MathJax_Main;\">(</span><span class=\"mi\" id=\"MathJax-Span-50\" style=\"font-family: MathJax_Math-italic;\">x</span><span class=\"mo\" id=\"MathJax-Span-51\" style=\"font-family: MathJax_Main;\">)</span><span class=\"mo\" id=\"MathJax-Span-52\" style=\"font-family: MathJax_Main; padding-left: 0.263em;\">=</span><span class=\"munderover\" id=\"MathJax-Span-53\" style=\"padding-left: 0.263em;\"><span style=\"display: inline-block; position: relative; width: 1.461em; height: 0px;\"><span style=\"position: absolute; clip: rect(2.919em, 1001.41em, 4.638em, -999.997em); top: -4.008em; left: 0em;\"><span class=\"mo\" id=\"MathJax-Span-54\" style=\"font-family: MathJax_Size2; vertical-align: 0em;\">∑</span><span style=\"display: inline-block; width: 0px; height: 4.013em;\"></span></span><span style=\"position: absolute; clip: rect(3.388em, 1001.1em, 4.273em, -999.997em); top: -2.914em; left: 0.159em;\"><span class=\"texatom\" id=\"MathJax-Span-55\"><span class=\"mrow\" id=\"MathJax-Span-56\"><span class=\"mi\" id=\"MathJax-Span-57\" style=\"font-size: 70.7%; font-family: MathJax_Math-italic;\">i</span><span class=\"mo\" id=\"MathJax-Span-58\" style=\"font-size: 70.7%; font-family: MathJax_Main;\">=</span><span class=\"mn\" id=\"MathJax-Span-59\" style=\"font-size: 70.7%; font-family: MathJax_Main;\">0</span></span></span><span style=\"display: inline-block; width: 0px; height: 4.013em;\"></span></span><span style=\"position: absolute; clip: rect(3.284em, 1000.63em, 4.169em, -999.997em); top: -5.154em; left: 0.419em;\"><span class=\"texatom\" id=\"MathJax-Span-60\"><span class=\"mrow\" id=\"MathJax-Span-61\"><span class=\"mi\" id=\"MathJax-Span-62\" style=\"font-size: 70.7%; font-family: MathJax_Math-italic;\">N<span style=\"display: inline-block; overflow: hidden; height: 1px; width: 0.055em;\"></span></span></span></span><span style=\"display: inline-block; width: 0px; height: 4.013em;\"></span></span></span></span><span class=\"msubsup\" id=\"MathJax-Span-63\" style=\"padding-left: 0.159em;\"><span style=\"display: inline-block; position: relative; width: 1.513em; height: 0px;\"><span style=\"position: absolute; clip: rect(2.503em, 1000.94em, 5.055em, -999.997em); top: -4.008em; left: 0em;\"><span class=\"mo\" id=\"MathJax-Span-64\" style=\"font-family: MathJax_Size2; vertical-align: 0.003em;\">∫<span style=\"display: inline-block; overflow: hidden; height: 1px; width: 0.367em;\"></span></span><span style=\"display: inline-block; width: 0px; height: 4.013em;\"></span></span><span style=\"position: absolute; clip: rect(3.388em, 1000.37em, 4.169em, -999.997em); top: -5.102em; left: 1.096em;\"><span class=\"texatom\" id=\"MathJax-Span-65\"><span class=\"mrow\" id=\"MathJax-Span-66\"><span class=\"mi\" id=\"MathJax-Span-67\" style=\"font-size: 70.7%; font-family: MathJax_Math-italic;\">b</span></span></span><span style=\"display: inline-block; width: 0px; height: 4.013em;\"></span></span><span style=\"position: absolute; clip: rect(3.544em, 1000.47em, 4.169em, -999.997em); top: -3.122em; left: 0.576em;\"><span class=\"texatom\" id=\"MathJax-Span-68\"><span class=\"mrow\" id=\"MathJax-Span-69\"><span class=\"mi\" id=\"MathJax-Span-70\" style=\"font-size: 70.7%; font-family: MathJax_Math-italic;\">a</span></span></span><span style=\"display: inline-block; width: 0px; height: 4.013em;\"></span></span></span></span><span class=\"mi\" id=\"MathJax-Span-71\" style=\"font-family: MathJax_Math-italic; padding-left: 0.159em;\">g<span style=\"display: inline-block; overflow: hidden; height: 1px; width: 0.003em;\"></span></span><span class=\"mo\" id=\"MathJax-Span-72\" style=\"font-family: MathJax_Main;\">(</span><span class=\"mi\" id=\"MathJax-Span-73\" style=\"font-family: MathJax_Math-italic;\">t</span><span class=\"mo\" id=\"MathJax-Span-74\" style=\"font-family: MathJax_Main;\">,</span><span class=\"mi\" id=\"MathJax-Span-75\" style=\"font-family: MathJax_Math-italic; padding-left: 0.159em;\">i</span><span class=\"mo\" id=\"MathJax-Span-76\" style=\"font-family: MathJax_Main;\">)</span><span class=\"mtext\" id=\"MathJax-Span-77\" style=\"font-family: MathJax_Main;\">&nbsp;d</span><span class=\"mi\" id=\"MathJax-Span-78\" style=\"font-family: MathJax_Math-italic;\">t</span></span></span><span style=\"display: inline-block; width: 0px; height: 4.013em;\"></span></span></span><span style=\"display: inline-block; width: 0px; height: 4.013em;\"></span></span></span><span style=\"display: inline-block; position: absolute; width: 1.305em; height: 0px; clip: rect(-0.883em, 1001.2em, 0.419em, -999.997em); top: 0em; right: 0em; margin-right: 0em;\"><span style=\"position: absolute; clip: rect(3.128em, 1001.2em, 4.43em, -999.997em); top: -4.008em; right: 0em;\"><span class=\"mtd\" id=\"mjx-eqn-1\"><span class=\"mrow\" id=\"MathJax-Span-44\"><span class=\"mtext\" id=\"MathJax-Span-45\" style=\"font-family: MathJax_Main;\">(1)</span></span></span><span style=\"display: inline-block; width: 0px; height: 4.013em;\"></span></span></span></span></span></span><span style=\"display: inline-block; width: 0px; height: 4.013em;\"></span></span></span><span style=\"display: inline-block; overflow: hidden; vertical-align: -1.497em; border-left: 0px solid; width: 0px; height: 3.628em;\"></span></span></nobr><span class=\"MJX_Assistive_MathML MJX_Assistive_MathML_Block\" role=\"presentation\"><math xmlns=\"http://www.w3.org/1998/Math/MathML\" display=\"block\"><mtable displaystyle=\"true\"><mlabeledtr><mtd id=\"mjx-eqn-1\"><mtext>(1)</mtext></mtd><mtd><mi>f</mi><mo stretchy=\"false\">(</mo><mi>x</mi><mo stretchy=\"false\">)</mo><mo>=</mo><munderover><mo>∑</mo><mrow class=\"MJX-TeXAtom-ORD\"><mi>i</mi><mo>=</mo><mn>0</mn></mrow><mrow class=\"MJX-TeXAtom-ORD\"><mi>N</mi></mrow></munderover><msubsup><mo>∫</mo><mrow class=\"MJX-TeXAtom-ORD\"><mi>a</mi></mrow><mrow class=\"MJX-TeXAtom-ORD\"><mi>b</mi></mrow></msubsup><mi>g</mi><mo stretchy=\"false\">(</mo><mi>t</mi><mo>,</mo><mi>i</mi><mo stretchy=\"false\">)</mo><mtext>&nbsp;d</mtext><mi>t</mi></mtd></mlabeledtr></mtable></math></span></span></div><script type=\"math/tex; mode=display\" id=\"MathJax-Element-3\"> f(x) = \\sum_{i=0}^{N}\\int_{a}^{b} g(t,i) \\text{ d}t \\tag{1}</script> \n <p></p> \n</blockquote>", ">  我们定义 $f(x) = \\sum_{i=0}^{N}\\int_{a}^{b} g(t,i) \\text{ d}t$. (行内公式)\n>\n>  或者定义 $f(x)$ 如下（行间公式）: \n>  \n>\n>  \n> $$\n> f(x) = \\sum_{i=0}^{N}\\int_{a}^{b} g(t,i) \\text{ d}t \\tag{1}\n> $$\n"},
	{"112", "<p>对于第 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> \n     \n      \n       \n       \n         i \n        \n       \n      \n        i \n       \n      \n    </span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.65952em; vertical-align: 0em;\"></span><span class=\"mord mathit\">i</span></span></span></span></span> 个数（<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> \n     \n      \n       \n       \n         i \n        \n       \n         ≤ \n        \n       \n         k \n        \n       \n      \n        i≤k \n       \n      \n    </span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.79549em; vertical-align: -0.13597em;\"></span><span class=\"mord mathit\">i</span><span class=\"mspace\" style=\"margin-right: 0.277778em;\"></span><span class=\"mrel\">≤</span><span class=\"mspace\" style=\"margin-right: 0.277778em;\"></span></span><span class=\"base\"><span class=\"strut\" style=\"height: 0.69444em; vertical-align: 0em;\"></span><span class=\"mord mathit\" style=\"margin-right: 0.03148em;\">k</span></span></span></span></span>）。在 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> \n     \n      \n       \n       \n         k \n        \n       \n      \n        k \n       \n      \n    </span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.69444em; vertical-align: 0em;\"></span><span class=\"mord mathit\" style=\"margin-right: 0.03148em;\">k</span></span></span></span></span> 步之前，被选中的概率为 1。当走到第 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> \n     \n      \n       \n       \n         k \n        \n       \n         + \n        \n       \n         1 \n        \n       \n      \n        k+1 \n       \n      \n    </span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.77777em; vertical-align: -0.08333em;\"></span><span class=\"mord mathit\" style=\"margin-right: 0.03148em;\">k</span><span class=\"mspace\" style=\"margin-right: 0.222222em;\"></span><span class=\"mbin\">+</span><span class=\"mspace\" style=\"margin-right: 0.222222em;\"></span></span><span class=\"base\"><span class=\"strut\" style=\"height: 0.64444em; vertical-align: 0em;\"></span><span class=\"mord\">1</span></span></span></span></span> 步时，<strong>被 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> \n      \n       \n        \n        \n          k \n         \n        \n          + \n         \n        \n          1 \n         \n        \n       \n         k+1 \n        \n       \n     </span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.77777em; vertical-align: -0.08333em;\"></span><span class=\"mord mathit\" style=\"margin-right: 0.03148em;\">k</span><span class=\"mspace\" style=\"margin-right: 0.222222em;\"></span><span class=\"mbin\">+</span><span class=\"mspace\" style=\"margin-right: 0.222222em;\"></span></span><span class=\"base\"><span class=\"strut\" style=\"height: 0.64444em; vertical-align: 0em;\"></span><span class=\"mord\">1</span></span></span></span></span> 个元素替换的概率 = 第<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> \n      \n       \n        \n        \n          k \n         \n        \n          + \n         \n        \n          1 \n         \n        \n       \n         k+1 \n        \n       \n     </span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.77777em; vertical-align: -0.08333em;\"></span><span class=\"mord mathit\" style=\"margin-right: 0.03148em;\">k</span><span class=\"mspace\" style=\"margin-right: 0.222222em;\"></span><span class=\"mbin\">+</span><span class=\"mspace\" style=\"margin-right: 0.222222em;\"></span></span><span class=\"base\"><span class=\"strut\" style=\"height: 0.64444em; vertical-align: 0em;\"></span><span class=\"mord\">1</span></span></span></span></span> 个元素被选中的概率 * <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> \n      \n       \n        \n        \n          i \n         \n        \n       \n         i \n        \n       \n     </span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.65952em; vertical-align: 0em;\"></span><span class=\"mord mathit\">i</span></span></span></span></span> 被选中替换的概率</strong>，即为 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> \n     \n      \n       \n        \n        \n          k \n         \n         \n         \n           k \n          \n         \n           + \n          \n         \n           1 \n          \n         \n        \n       \n         × \n        \n        \n        \n          1 \n         \n        \n          k \n         \n        \n       \n         = \n        \n        \n        \n          1 \n         \n         \n         \n           k \n          \n         \n           + \n          \n         \n           1 \n          \n         \n        \n       \n      \n        \\frac{k}{k + 1} \\times \\frac{1}{k} = \\frac{1}{k + 1} \n       \n      \n    </span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1.28344em; vertical-align: -0.403331em;\"></span><span class=\"mord\"><span class=\"mopen nulldelimiter\"></span><span class=\"mfrac\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.880108em;\"><span class=\"\" style=\"top: -2.655em;\"><span class=\"pstrut\" style=\"height: 3em;\"></span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathit mtight\" style=\"margin-right: 0.03148em;\">k</span><span class=\"mbin mtight\">+</span><span class=\"mord mtight\">1</span></span></span></span><span class=\"\" style=\"top: -3.23em;\"><span class=\"pstrut\" style=\"height: 3em;\"></span><span class=\"frac-line\" style=\"border-bottom-width: 0.04em;\"></span></span><span class=\"\" style=\"top: -3.394em;\"><span class=\"pstrut\" style=\"height: 3em;\"></span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathit mtight\" style=\"margin-right: 0.03148em;\">k</span></span></span></span></span><span class=\"vlist-s\">&ZeroWidthSpace;</span></span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.403331em;\"><span class=\"\"></span></span></span></span></span><span class=\"mclose nulldelimiter\"></span></span><span class=\"mspace\" style=\"margin-right: 0.222222em;\"></span><span class=\"mbin\">×</span><span class=\"mspace\" style=\"margin-right: 0.222222em;\"></span></span><span class=\"base\"><span class=\"strut\" style=\"height: 1.19011em; vertical-align: -0.345em;\"></span><span class=\"mord\"><span class=\"mopen nulldelimiter\"></span><span class=\"mfrac\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.845108em;\"><span class=\"\" style=\"top: -2.655em;\"><span class=\"pstrut\" style=\"height: 3em;\"></span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathit mtight\" style=\"margin-right: 0.03148em;\">k</span></span></span></span><span class=\"\" style=\"top: -3.23em;\"><span class=\"pstrut\" style=\"height: 3em;\"></span><span class=\"frac-line\" style=\"border-bottom-width: 0.04em;\"></span></span><span class=\"\" style=\"top: -3.394em;\"><span class=\"pstrut\" style=\"height: 3em;\"></span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\">1</span></span></span></span></span><span class=\"vlist-s\">&ZeroWidthSpace;</span></span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.345em;\"><span class=\"\"></span></span></span></span></span><span class=\"mclose nulldelimiter\"></span></span><span class=\"mspace\" style=\"margin-right: 0.277778em;\"></span><span class=\"mrel\">=</span><span class=\"mspace\" style=\"margin-right: 0.277778em;\"></span></span><span class=\"base\"><span class=\"strut\" style=\"height: 1.24844em; vertical-align: -0.403331em;\"></span><span class=\"mord\"><span class=\"mopen nulldelimiter\"></span><span class=\"mfrac\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.845108em;\"><span class=\"\" style=\"top: -2.655em;\"><span class=\"pstrut\" style=\"height: 3em;\"></span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathit mtight\" style=\"margin-right: 0.03148em;\">k</span><span class=\"mbin mtight\">+</span><span class=\"mord mtight\">1</span></span></span></span><span class=\"\" style=\"top: -3.23em;\"><span class=\"pstrut\" style=\"height: 3em;\"></span><span class=\"frac-line\" style=\"border-bottom-width: 0.04em;\"></span></span><span class=\"\" style=\"top: -3.394em;\"><span class=\"pstrut\" style=\"height: 3em;\"></span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\">1</span></span></span></span></span><span class=\"vlist-s\">&ZeroWidthSpace;</span></span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.403331em;\"><span class=\"\"></span></span></span></span></span><span class=\"mclose nulldelimiter\"></span></span></span></span></span></span>。则不被第<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> \n     \n      \n       \n       \n         k \n        \n       \n         + \n        \n       \n         1 \n        \n       \n      \n        k+1 \n       \n      \n    </span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.77777em; vertical-align: -0.08333em;\"></span><span class=\"mord mathit\" style=\"margin-right: 0.03148em;\">k</span><span class=\"mspace\" style=\"margin-right: 0.222222em;\"></span><span class=\"mbin\">+</span><span class=\"mspace\" style=\"margin-right: 0.222222em;\"></span></span><span class=\"base\"><span class=\"strut\" style=\"height: 0.64444em; vertical-align: 0em;\"></span><span class=\"mord\">1</span></span></span></span></span>个元素替换的概率为<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> \n     \n      \n       \n       \n         1 \n        \n       \n         − \n        \n        \n        \n          1 \n         \n         \n         \n           k \n          \n         \n           + \n          \n         \n           1 \n          \n         \n        \n       \n         = \n        \n        \n        \n          k \n         \n         \n         \n           k \n          \n         \n           + \n          \n         \n           1 \n          \n         \n        \n       \n      \n        1 - \\frac{1}{k + 1} = \\frac{k}{k + 1} \n       \n      \n    </span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.72777em; vertical-align: -0.08333em;\"></span><span class=\"mord\">1</span><span class=\"mspace\" style=\"margin-right: 0.222222em;\"></span><span class=\"mbin\">−</span><span class=\"mspace\" style=\"margin-right: 0.222222em;\"></span></span><span class=\"base\"><span class=\"strut\" style=\"height: 1.24844em; vertical-align: -0.403331em;\"></span><span class=\"mord\"><span class=\"mopen nulldelimiter\"></span><span class=\"mfrac\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.845108em;\"><span class=\"\" style=\"top: -2.655em;\"><span class=\"pstrut\" style=\"height: 3em;\"></span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathit mtight\" style=\"margin-right: 0.03148em;\">k</span><span class=\"mbin mtight\">+</span><span class=\"mord mtight\">1</span></span></span></span><span class=\"\" style=\"top: -3.23em;\"><span class=\"pstrut\" style=\"height: 3em;\"></span><span class=\"frac-line\" style=\"border-bottom-width: 0.04em;\"></span></span><span class=\"\" style=\"top: -3.394em;\"><span class=\"pstrut\" style=\"height: 3em;\"></span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\">1</span></span></span></span></span><span class=\"vlist-s\">&ZeroWidthSpace;</span></span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.403331em;\"><span class=\"\"></span></span></span></span></span><span class=\"mclose nulldelimiter\"></span></span><span class=\"mspace\" style=\"margin-right: 0.277778em;\"></span><span class=\"mrel\">=</span><span class=\"mspace\" style=\"margin-right: 0.277778em;\"></span></span><span class=\"base\"><span class=\"strut\" style=\"height: 1.28344em; vertical-align: -0.403331em;\"></span><span class=\"mord\"><span class=\"mopen nulldelimiter\"></span><span class=\"mfrac\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.880108em;\"><span class=\"\" style=\"top: -2.655em;\"><span class=\"pstrut\" style=\"height: 3em;\"></span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathit mtight\" style=\"margin-right: 0.03148em;\">k</span><span class=\"mbin mtight\">+</span><span class=\"mord mtight\">1</span></span></span></span><span class=\"\" style=\"top: -3.23em;\"><span class=\"pstrut\" style=\"height: 3em;\"></span><span class=\"frac-line\" style=\"border-bottom-width: 0.04em;\"></span></span><span class=\"\" style=\"top: -3.394em;\"><span class=\"pstrut\" style=\"height: 3em;\"></span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathit mtight\" style=\"margin-right: 0.03148em;\">k</span></span></span></span></span><span class=\"vlist-s\">&ZeroWidthSpace;</span></span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.403331em;\"><span class=\"\"></span></span></span></span></span><span class=\"mclose nulldelimiter\"></span></span></span></span></span></span>。依次类推，不被 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> \n     \n      \n       \n       \n         k \n        \n       \n         + \n        \n       \n         2 \n        \n       \n      \n        k+2 \n       \n      \n    </span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.77777em; vertical-align: -0.08333em;\"></span><span class=\"mord mathit\" style=\"margin-right: 0.03148em;\">k</span><span class=\"mspace\" style=\"margin-right: 0.222222em;\"></span><span class=\"mbin\">+</span><span class=\"mspace\" style=\"margin-right: 0.222222em;\"></span></span><span class=\"base\"><span class=\"strut\" style=\"height: 0.64444em; vertical-align: 0em;\"></span><span class=\"mord\">2</span></span></span></span></span> 个元素替换的概率为 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> \n     \n      \n       \n       \n         1 \n        \n       \n         − \n        \n        \n        \n          k \n         \n         \n         \n           k \n          \n         \n           + \n          \n         \n           2 \n          \n         \n        \n       \n         × \n        \n        \n        \n          1 \n         \n        \n          k \n         \n        \n       \n         = \n        \n        \n         \n         \n           k \n          \n         \n           + \n          \n         \n           1 \n          \n         \n         \n         \n           k \n          \n         \n           + \n          \n         \n           2 \n          \n         \n        \n       \n      \n        1 - \\frac{k}{k + 2} \\times \\frac{1}{k} = \\frac{k + 1}{k + 2} \n       \n      \n    </span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.72777em; vertical-align: -0.08333em;\"></span><span class=\"mord\">1</span><span class=\"mspace\" style=\"margin-right: 0.222222em;\"></span><span class=\"mbin\">−</span><span class=\"mspace\" style=\"margin-right: 0.222222em;\"></span></span><span class=\"base\"><span class=\"strut\" style=\"height: 1.28344em; vertical-align: -0.403331em;\"></span><span class=\"mord\"><span class=\"mopen nulldelimiter\"></span><span class=\"mfrac\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.880108em;\"><span class=\"\" style=\"top: -2.655em;\"><span class=\"pstrut\" style=\"height: 3em;\"></span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathit mtight\" style=\"margin-right: 0.03148em;\">k</span><span class=\"mbin mtight\">+</span><span class=\"mord mtight\">2</span></span></span></span><span class=\"\" style=\"top: -3.23em;\"><span class=\"pstrut\" style=\"height: 3em;\"></span><span class=\"frac-line\" style=\"border-bottom-width: 0.04em;\"></span></span><span class=\"\" style=\"top: -3.394em;\"><span class=\"pstrut\" style=\"height: 3em;\"></span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathit mtight\" style=\"margin-right: 0.03148em;\">k</span></span></span></span></span><span class=\"vlist-s\">&ZeroWidthSpace;</span></span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.403331em;\"><span class=\"\"></span></span></span></span></span><span class=\"mclose nulldelimiter\"></span></span><span class=\"mspace\" style=\"margin-right: 0.222222em;\"></span><span class=\"mbin\">×</span><span class=\"mspace\" style=\"margin-right: 0.222222em;\"></span></span><span class=\"base\"><span class=\"strut\" style=\"height: 1.19011em; vertical-align: -0.345em;\"></span><span class=\"mord\"><span class=\"mopen nulldelimiter\"></span><span class=\"mfrac\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.845108em;\"><span class=\"\" style=\"top: -2.655em;\"><span class=\"pstrut\" style=\"height: 3em;\"></span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathit mtight\" style=\"margin-right: 0.03148em;\">k</span></span></span></span><span class=\"\" style=\"top: -3.23em;\"><span class=\"pstrut\" style=\"height: 3em;\"></span><span class=\"frac-line\" style=\"border-bottom-width: 0.04em;\"></span></span><span class=\"\" style=\"top: -3.394em;\"><span class=\"pstrut\" style=\"height: 3em;\"></span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mtight\">1</span></span></span></span></span><span class=\"vlist-s\">&ZeroWidthSpace;</span></span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.345em;\"><span class=\"\"></span></span></span></span></span><span class=\"mclose nulldelimiter\"></span></span><span class=\"mspace\" style=\"margin-right: 0.277778em;\"></span><span class=\"mrel\">=</span><span class=\"mspace\" style=\"margin-right: 0.277778em;\"></span></span><span class=\"base\"><span class=\"strut\" style=\"height: 1.28344em; vertical-align: -0.403331em;\"></span><span class=\"mord\"><span class=\"mopen nulldelimiter\"></span><span class=\"mfrac\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.880108em;\"><span class=\"\" style=\"top: -2.655em;\"><span class=\"pstrut\" style=\"height: 3em;\"></span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathit mtight\" style=\"margin-right: 0.03148em;\">k</span><span class=\"mbin mtight\">+</span><span class=\"mord mtight\">2</span></span></span></span><span class=\"\" style=\"top: -3.23em;\"><span class=\"pstrut\" style=\"height: 3em;\"></span><span class=\"frac-line\" style=\"border-bottom-width: 0.04em;\"></span></span><span class=\"\" style=\"top: -3.394em;\"><span class=\"pstrut\" style=\"height: 3em;\"></span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\"><span class=\"mord mathit mtight\" style=\"margin-right: 0.03148em;\">k</span><span class=\"mbin mtight\">+</span><span class=\"mord mtight\">1</span></span></span></span></span><span class=\"vlist-s\">&ZeroWidthSpace;</span></span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.403331em;\"><span class=\"\"></span></span></span></span></span><span class=\"mclose nulldelimiter\"></span></span></span></span></span></span>。则运行到第 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> \n     \n      \n       \n       \n         n \n        \n       \n      \n        n \n       \n      \n    </span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.43056em; vertical-align: 0em;\"></span><span class=\"mord mathit\">n</span></span></span></span></span> 步时，第 <span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> \n     \n      \n       \n       \n         i \n        \n       \n      \n        i \n       \n      \n    </span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.65952em; vertical-align: 0em;\"></span><span class=\"mord mathit\">i</span></span></span></span></span> 个数<strong>仍保留的概率 = 被选中的概率 * 不被替换的概率</strong>，即：<br> <span class=\"katex--display\"><span class=\"katex-display\"><span class=\"katex\"><span class=\"katex-mathml\"> \n      \n       \n        \n        \n          1 \n         \n        \n          × \n         \n         \n         \n           k \n          \n          \n          \n            k \n           \n          \n            + \n           \n          \n            1 \n           \n          \n         \n        \n          × \n         \n         \n          \n          \n            k \n           \n          \n            + \n           \n          \n            1 \n           \n          \n          \n          \n            k \n           \n          \n            + \n           \n          \n            2 \n           \n          \n         \n        \n          × \n         \n         \n          \n          \n            k \n           \n          \n            + \n           \n          \n            2 \n           \n          \n          \n          \n            k \n           \n          \n            + \n           \n          \n            3 \n           \n          \n         \n        \n          × \n         \n        \n          … \n         \n        \n          × \n         \n         \n          \n          \n            n \n           \n          \n            − \n           \n          \n            1 \n           \n          \n         \n           n \n          \n         \n        \n          = \n         \n         \n         \n           k \n          \n         \n           n \n          \n         \n        \n       \n         1 \\times \\frac{k}{k + 1} \\times \\frac{k + 1}{k + 2} \\times \\frac{k + 2}{k + 3} \\times … \\times \\frac{n - 1}{n} = \\frac{k}{n} \n        \n       \n     </span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.72777em; vertical-align: -0.08333em;\"></span><span class=\"mord\">1</span><span class=\"mspace\" style=\"margin-right: 0.222222em;\"></span><span class=\"mbin\">×</span><span class=\"mspace\" style=\"margin-right: 0.222222em;\"></span></span><span class=\"base\"><span class=\"strut\" style=\"height: 2.14077em; vertical-align: -0.76933em;\"></span><span class=\"mord\"><span class=\"mopen nulldelimiter\"></span><span class=\"mfrac\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 1.37144em;\"><span class=\"\" style=\"top: -2.314em;\"><span class=\"pstrut\" style=\"height: 3em;\"></span><span class=\"mord\"><span class=\"mord mathit\" style=\"margin-right: 0.03148em;\">k</span><span class=\"mspace\" style=\"margin-right: 0.222222em;\"></span><span class=\"mbin\">+</span><span class=\"mspace\" style=\"margin-right: 0.222222em;\"></span><span class=\"mord\">1</span></span></span><span class=\"\" style=\"top: -3.23em;\"><span class=\"pstrut\" style=\"height: 3em;\"></span><span class=\"frac-line\" style=\"border-bottom-width: 0.04em;\"></span></span><span class=\"\" style=\"top: -3.677em;\"><span class=\"pstrut\" style=\"height: 3em;\"></span><span class=\"mord\"><span class=\"mord mathit\" style=\"margin-right: 0.03148em;\">k</span></span></span></span><span class=\"vlist-s\">&ZeroWidthSpace;</span></span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.76933em;\"><span class=\"\"></span></span></span></span></span><span class=\"mclose nulldelimiter\"></span></span><span class=\"mspace\" style=\"margin-right: 0.222222em;\"></span><span class=\"mbin\">×</span><span class=\"mspace\" style=\"margin-right: 0.222222em;\"></span></span><span class=\"base\"><span class=\"strut\" style=\"height: 2.14077em; vertical-align: -0.76933em;\"></span><span class=\"mord\"><span class=\"mopen nulldelimiter\"></span><span class=\"mfrac\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 1.37144em;\"><span class=\"\" style=\"top: -2.314em;\"><span class=\"pstrut\" style=\"height: 3em;\"></span><span class=\"mord\"><span class=\"mord mathit\" style=\"margin-right: 0.03148em;\">k</span><span class=\"mspace\" style=\"margin-right: 0.222222em;\"></span><span class=\"mbin\">+</span><span class=\"mspace\" style=\"margin-right: 0.222222em;\"></span><span class=\"mord\">2</span></span></span><span class=\"\" style=\"top: -3.23em;\"><span class=\"pstrut\" style=\"height: 3em;\"></span><span class=\"frac-line\" style=\"border-bottom-width: 0.04em;\"></span></span><span class=\"\" style=\"top: -3.677em;\"><span class=\"pstrut\" style=\"height: 3em;\"></span><span class=\"mord\"><span class=\"mord mathit\" style=\"margin-right: 0.03148em;\">k</span><span class=\"mspace\" style=\"margin-right: 0.222222em;\"></span><span class=\"mbin\">+</span><span class=\"mspace\" style=\"margin-right: 0.222222em;\"></span><span class=\"mord\">1</span></span></span></span><span class=\"vlist-s\">&ZeroWidthSpace;</span></span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.76933em;\"><span class=\"\"></span></span></span></span></span><span class=\"mclose nulldelimiter\"></span></span><span class=\"mspace\" style=\"margin-right: 0.222222em;\"></span><span class=\"mbin\">×</span><span class=\"mspace\" style=\"margin-right: 0.222222em;\"></span></span><span class=\"base\"><span class=\"strut\" style=\"height: 2.14077em; vertical-align: -0.76933em;\"></span><span class=\"mord\"><span class=\"mopen nulldelimiter\"></span><span class=\"mfrac\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 1.37144em;\"><span class=\"\" style=\"top: -2.314em;\"><span class=\"pstrut\" style=\"height: 3em;\"></span><span class=\"mord\"><span class=\"mord mathit\" style=\"margin-right: 0.03148em;\">k</span><span class=\"mspace\" style=\"margin-right: 0.222222em;\"></span><span class=\"mbin\">+</span><span class=\"mspace\" style=\"margin-right: 0.222222em;\"></span><span class=\"mord\">3</span></span></span><span class=\"\" style=\"top: -3.23em;\"><span class=\"pstrut\" style=\"height: 3em;\"></span><span class=\"frac-line\" style=\"border-bottom-width: 0.04em;\"></span></span><span class=\"\" style=\"top: -3.677em;\"><span class=\"pstrut\" style=\"height: 3em;\"></span><span class=\"mord\"><span class=\"mord mathit\" style=\"margin-right: 0.03148em;\">k</span><span class=\"mspace\" style=\"margin-right: 0.222222em;\"></span><span class=\"mbin\">+</span><span class=\"mspace\" style=\"margin-right: 0.222222em;\"></span><span class=\"mord\">2</span></span></span></span><span class=\"vlist-s\">&ZeroWidthSpace;</span></span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.76933em;\"><span class=\"\"></span></span></span></span></span><span class=\"mclose nulldelimiter\"></span></span><span class=\"mspace\" style=\"margin-right: 0.222222em;\"></span><span class=\"mbin\">×</span><span class=\"mspace\" style=\"margin-right: 0.222222em;\"></span></span><span class=\"base\"><span class=\"strut\" style=\"height: 0.66666em; vertical-align: -0.08333em;\"></span><span class=\"minner\">…</span><span class=\"mspace\" style=\"margin-right: 0.222222em;\"></span><span class=\"mbin\">×</span><span class=\"mspace\" style=\"margin-right: 0.222222em;\"></span></span><span class=\"base\"><span class=\"strut\" style=\"height: 2.00744em; vertical-align: -0.686em;\"></span><span class=\"mord\"><span class=\"mopen nulldelimiter\"></span><span class=\"mfrac\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 1.32144em;\"><span class=\"\" style=\"top: -2.314em;\"><span class=\"pstrut\" style=\"height: 3em;\"></span><span class=\"mord\"><span class=\"mord mathit\">n</span></span></span><span class=\"\" style=\"top: -3.23em;\"><span class=\"pstrut\" style=\"height: 3em;\"></span><span class=\"frac-line\" style=\"border-bottom-width: 0.04em;\"></span></span><span class=\"\" style=\"top: -3.677em;\"><span class=\"pstrut\" style=\"height: 3em;\"></span><span class=\"mord\"><span class=\"mord mathit\">n</span><span class=\"mspace\" style=\"margin-right: 0.222222em;\"></span><span class=\"mbin\">−</span><span class=\"mspace\" style=\"margin-right: 0.222222em;\"></span><span class=\"mord\">1</span></span></span></span><span class=\"vlist-s\">&ZeroWidthSpace;</span></span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.686em;\"><span class=\"\"></span></span></span></span></span><span class=\"mclose nulldelimiter\"></span></span><span class=\"mspace\" style=\"margin-right: 0.277778em;\"></span><span class=\"mrel\">=</span><span class=\"mspace\" style=\"margin-right: 0.277778em;\"></span></span><span class=\"base\"><span class=\"strut\" style=\"height: 2.05744em; vertical-align: -0.686em;\"></span><span class=\"mord\"><span class=\"mopen nulldelimiter\"></span><span class=\"mfrac\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 1.37144em;\"><span class=\"\" style=\"top: -2.314em;\"><span class=\"pstrut\" style=\"height: 3em;\"></span><span class=\"mord\"><span class=\"mord mathit\">n</span></span></span><span class=\"\" style=\"top: -3.23em;\"><span class=\"pstrut\" style=\"height: 3em;\"></span><span class=\"frac-line\" style=\"border-bottom-width: 0.04em;\"></span></span><span class=\"\" style=\"top: -3.677em;\"><span class=\"pstrut\" style=\"height: 3em;\"></span><span class=\"mord\"><span class=\"mord mathit\" style=\"margin-right: 0.03148em;\">k</span></span></span></span><span class=\"vlist-s\">&ZeroWidthSpace;</span></span><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.686em;\"><span class=\"\"></span></span></span></span></span><span class=\"mclose nulldelimiter\"></span></span></span></span></span></span></span></p>", "对于第 $i$ 个数（$i≤k$）。在 $k$ 步之前，被选中的概率为 1。当走到第 $k+1$ 步时，\u200b**被 $k+1$ 个元素替换的概率 = 第 $k+1$ 个元素被选中的概率 \\* $i$ 被选中替换的概率**\u200b，即为 $\\frac{k}{k + 1} \\times \\frac{1}{k} = \\frac{1}{k + 1}$。则不被第 $k+1$ 个元素替换的概率为 $1 - \\frac{1}{k + 1} = \\frac{k}{k + 1}$。依次类推，不被 $k+2$ 个元素替换的概率为 $1 - \\frac{k}{k + 2} \\times \\frac{1}{k} = \\frac{k + 1}{k + 2}$。则运行到第 $n$ 步时，第 $i$ 个数\u200b**仍保留的概率 = 被选中的概率 \\* 不被替换的概率**\u200b，即：\n $1 \\times \\frac{k}{k + 1} \\times \\frac{k + 1}{k + 2} \\times \\frac{k + 2}{k + 3} \\times … \\times \\frac{n - 1}{n} = \\frac{k}{n}$\n"},
	{"111", "<blockquote> \n <p><span class=\"MathJax_Preview\"></span></p> \n <div class=\"MathJax_Display\"> \n   \n </div><span class=\"MathJax_Preview\" style=\"color: inherit; display: none;\"></span><div class=\"MathJax_Display\"><span class=\"MathJax MathJax_FullWidth\" id=\"MathJax-Element-760-Frame\" tabindex=\"0\" style=\"position: relative;\" data-mathml=\"<math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot; display=&quot;block&quot;><mtable displaystyle=&quot;true&quot;><mlabeledtr><mtd id=&quot;mjx-eqn-2&quot;><mtext>(2)</mtext></mtd><mtd><mi>&amp;#x0393;</mi><mo stretchy=&quot;false&quot;>(</mo><mi>x</mi><mo stretchy=&quot;false&quot;>)</mo><mo>=</mo><mfrac><mrow><msubsup><mo>&amp;#x222B;</mo><mrow class=&quot;MJX-TeXAtom-ORD&quot;><mi>&amp;#x03B1;</mi></mrow><mrow class=&quot;MJX-TeXAtom-ORD&quot;><mi>&amp;#x03B2;</mi></mrow></msubsup><mi>g</mi><mo stretchy=&quot;false&quot;>(</mo><mi>t</mi><mo stretchy=&quot;false&quot;>)</mo><mo stretchy=&quot;false&quot;>(</mo><mi>x</mi><mo>&amp;#x2212;</mo><mi>t</mi><msup><mo stretchy=&quot;false&quot;>)</mo><mn>2</mn></msup><mtext>&amp;#xA0;d</mtext><mi>t</mi></mrow><mrow><mi>&amp;#x03D5;</mi><mo stretchy=&quot;false&quot;>(</mo><mi>x</mi><mo stretchy=&quot;false&quot;>)</mo><munderover><mo>&amp;#x2211;</mo><mrow class=&quot;MJX-TeXAtom-ORD&quot;><mi>i</mi><mo>=</mo><mn>0</mn></mrow><mrow class=&quot;MJX-TeXAtom-ORD&quot;><mi>N</mi><mo>&amp;#x2212;</mo><mn>1</mn></mrow></munderover><msub><mi>&amp;#x03C9;</mi><mi>i</mi></msub></mrow></mfrac></mtd></mlabeledtr></mtable></math>\" role=\"presentation\"><nobr aria-hidden=\"true\"><span class=\"math\" id=\"MathJax-Span-154\" style=\"width: 100%; display: inline-block; min-width: 15.367em;\"><span style=\"display: inline-block; position: relative; width: 100%; height: 0px; font-size: 120%; min-width: 15.367em;\"><span style=\"position: absolute; clip: rect(2.138em, 1011.2em, 5.523em, -999.997em); top: -4.06em; left: 0em; width: 100%;\"><span class=\"mrow\" id=\"MathJax-Span-155\"><span class=\"mtable\" id=\"MathJax-Span-156\" style=\"min-width: 15.367em;\"><span style=\"display: inline-block; position: relative; width: 100%; height: 0px; min-width: 15.367em;\"><span style=\"display: inline-block; position: absolute; width: 11.201em; height: 0px; clip: rect(-1.924em, 1011.2em, 1.461em, -999.997em); top: 0em; left: 50%; margin-left: -5.622em;\"><span style=\"position: absolute; clip: rect(2.138em, 1011.2em, 5.523em, -999.997em); top: -4.06em; left: 0em;\"><span style=\"display: inline-block; position: relative; width: 11.201em; height: 0px;\"><span style=\"position: absolute; clip: rect(2.034em, 1011.2em, 5.471em, -999.997em); top: -4.008em; left: 50%; margin-left: -5.622em;\"><span class=\"mtd\" id=\"MathJax-Span-160\"><span class=\"mrow\" id=\"MathJax-Span-161\"><span class=\"mi\" id=\"MathJax-Span-162\" style=\"font-family: MathJax_Math-italic;\">Γ<span style=\"display: inline-block; overflow: hidden; height: 1px; width: 0.107em;\"></span></span><span class=\"mo\" id=\"MathJax-Span-163\" style=\"font-family: MathJax_Main;\">(</span><span class=\"mi\" id=\"MathJax-Span-164\" style=\"font-family: MathJax_Math-italic;\">x</span><span class=\"mo\" id=\"MathJax-Span-165\" style=\"font-family: MathJax_Main;\">)</span><span class=\"mo\" id=\"MathJax-Span-166\" style=\"font-family: MathJax_Main; padding-left: 0.263em;\">=</span><span class=\"mfrac\" id=\"MathJax-Span-167\" style=\"padding-left: 0.263em;\"><span style=\"display: inline-block; position: relative; width: 7.607em; height: 0px; margin-right: 0.107em; margin-left: 0.107em;\"><span style=\"position: absolute; clip: rect(2.815em, 1007.45em, 4.534em, -999.997em); top: -4.841em; left: 50%; margin-left: -3.747em;\"><span class=\"mrow\" id=\"MathJax-Span-168\"><span class=\"msubsup\" id=\"MathJax-Span-169\"><span style=\"display: inline-block; position: relative; width: 1.201em; height: 0px;\"><span style=\"position: absolute; clip: rect(3.076em, 1000.63em, 4.482em, -999.997em); top: -4.008em; left: 0em;\"><span class=\"mo\" id=\"MathJax-Span-170\" style=\"font-family: MathJax_Size1; vertical-align: 0em;\">∫<span style=\"display: inline-block; overflow: hidden; height: 1px; width: 0.159em;\"></span></span><span style=\"display: inline-block; width: 0px; height: 4.013em;\"></span></span><span style=\"position: absolute; clip: rect(3.336em, 1000.47em, 4.326em, -999.997em); top: -4.529em; left: 0.68em;\"><span class=\"texatom\" id=\"MathJax-Span-171\"><span class=\"mrow\" id=\"MathJax-Span-172\"><span class=\"mi\" id=\"MathJax-Span-173\" style=\"font-size: 70.7%; font-family: MathJax_Math-italic;\">β<span style=\"display: inline-block; overflow: hidden; height: 1px; width: 0.003em;\"></span></span></span></span><span style=\"display: inline-block; width: 0px; height: 4.013em;\"></span></span><span style=\"position: absolute; clip: rect(3.544em, 1000.52em, 4.169em, -999.997em); top: -3.643em; left: 0.471em;\"><span class=\"texatom\" id=\"MathJax-Span-174\"><span class=\"mrow\" id=\"MathJax-Span-175\"><span class=\"mi\" id=\"MathJax-Span-176\" style=\"font-size: 70.7%; font-family: MathJax_Math-italic;\">α</span></span></span><span style=\"display: inline-block; width: 0px; height: 4.013em;\"></span></span></span></span><span class=\"mi\" id=\"MathJax-Span-177\" style=\"font-family: MathJax_Math-italic; padding-left: 0.159em;\">g<span style=\"display: inline-block; overflow: hidden; height: 1px; width: 0.003em;\"></span></span><span class=\"mo\" id=\"MathJax-Span-178\" style=\"font-family: MathJax_Main;\">(</span><span class=\"mi\" id=\"MathJax-Span-179\" style=\"font-family: MathJax_Math-italic;\">t</span><span class=\"mo\" id=\"MathJax-Span-180\" style=\"font-family: MathJax_Main;\">)</span><span class=\"mo\" id=\"MathJax-Span-181\" style=\"font-family: MathJax_Main;\">(</span><span class=\"mi\" id=\"MathJax-Span-182\" style=\"font-family: MathJax_Math-italic;\">x</span><span class=\"mo\" id=\"MathJax-Span-183\" style=\"font-family: MathJax_Main; padding-left: 0.211em;\">−</span><span class=\"mi\" id=\"MathJax-Span-184\" style=\"font-family: MathJax_Math-italic; padding-left: 0.211em;\">t</span><span class=\"msubsup\" id=\"MathJax-Span-185\"><span style=\"display: inline-block; position: relative; width: 0.836em; height: 0px;\"><span style=\"position: absolute; clip: rect(3.128em, 1000.32em, 4.43em, -999.997em); top: -4.008em; left: 0em;\"><span class=\"mo\" id=\"MathJax-Span-186\" style=\"font-family: MathJax_Main;\">)</span><span style=\"display: inline-block; width: 0px; height: 4.013em;\"></span></span><span style=\"position: absolute; top: -4.372em; left: 0.367em;\"><span class=\"mn\" id=\"MathJax-Span-187\" style=\"font-size: 70.7%; font-family: MathJax_Main;\">2</span><span style=\"display: inline-block; width: 0px; height: 4.013em;\"></span></span></span></span><span class=\"mtext\" id=\"MathJax-Span-188\" style=\"font-family: MathJax_Main;\">&nbsp;d</span><span class=\"mi\" id=\"MathJax-Span-189\" style=\"font-family: MathJax_Math-italic;\">t</span></span><span style=\"display: inline-block; width: 0px; height: 4.013em;\"></span></span><span style=\"position: absolute; clip: rect(2.919em, 1005.89em, 4.482em, -999.997em); top: -3.07em; left: 50%; margin-left: -2.914em;\"><span class=\"mrow\" id=\"MathJax-Span-190\"><span class=\"mi\" id=\"MathJax-Span-191\" style=\"font-family: MathJax_Math-italic;\">ϕ</span><span class=\"mo\" id=\"MathJax-Span-192\" style=\"font-family: MathJax_Main;\">(</span><span class=\"mi\" id=\"MathJax-Span-193\" style=\"font-family: MathJax_Math-italic;\">x</span><span class=\"mo\" id=\"MathJax-Span-194\" style=\"font-family: MathJax_Main;\">)</span><span class=\"munderover\" id=\"MathJax-Span-195\" style=\"padding-left: 0.159em;\"><span style=\"display: inline-block; position: relative; width: 2.659em; height: 0px;\"><span style=\"position: absolute; clip: rect(3.128em, 1000.99em, 4.43em, -999.997em); top: -4.008em; left: 0em;\"><span class=\"mo\" id=\"MathJax-Span-196\" style=\"font-family: MathJax_Size1; vertical-align: 0em;\">∑</span><span style=\"display: inline-block; width: 0px; height: 4.013em;\"></span></span><span style=\"position: absolute; clip: rect(3.388em, 1001.62em, 4.221em, -999.997em); top: -4.477em; left: 1.044em;\"><span class=\"texatom\" id=\"MathJax-Span-197\"><span class=\"mrow\" id=\"MathJax-Span-198\"><span class=\"mi\" id=\"MathJax-Span-199\" style=\"font-size: 70.7%; font-family: MathJax_Math-italic;\">N<span style=\"display: inline-block; overflow: hidden; height: 1px; width: 0.055em;\"></span></span><span class=\"mo\" id=\"MathJax-Span-200\" style=\"font-size: 70.7%; font-family: MathJax_Main;\">−</span><span class=\"mn\" id=\"MathJax-Span-201\" style=\"font-size: 70.7%; font-family: MathJax_Main;\">1</span></span></span><span style=\"display: inline-block; width: 0px; height: 4.013em;\"></span></span><span style=\"position: absolute; clip: rect(3.388em, 1001.2em, 4.169em, -999.997em); top: -3.747em; left: 1.044em;\"><span class=\"texatom\" id=\"MathJax-Span-202\"><span class=\"mrow\" id=\"MathJax-Span-203\"><span class=\"mi\" id=\"MathJax-Span-204\" style=\"font-size: 70.7%; font-family: MathJax_Math-italic;\">i</span><span class=\"mo\" id=\"MathJax-Span-205\" style=\"font-size: 70.7%; font-family: MathJax_Main;\">=</span><span class=\"mn\" id=\"MathJax-Span-206\" style=\"font-size: 70.7%; font-family: MathJax_Main;\">0</span></span></span><span style=\"display: inline-block; width: 0px; height: 4.013em;\"></span></span></span></span><span class=\"msubsup\" id=\"MathJax-Span-207\" style=\"padding-left: 0.159em;\"><span style=\"display: inline-block; position: relative; width: 0.94em; height: 0px;\"><span style=\"position: absolute; clip: rect(3.388em, 1000.63em, 4.169em, -999.997em); top: -4.008em; left: 0em;\"><span class=\"mi\" id=\"MathJax-Span-208\" style=\"font-family: MathJax_Math-italic;\">ω</span><span style=\"display: inline-block; width: 0px; height: 4.013em;\"></span></span><span style=\"position: absolute; top: -3.852em; left: 0.628em;\"><span class=\"mi\" id=\"MathJax-Span-209\" style=\"font-size: 70.7%; font-family: MathJax_Math-italic;\">i</span><span style=\"display: inline-block; width: 0px; height: 4.013em;\"></span></span></span></span></span><span style=\"display: inline-block; width: 0px; height: 4.013em;\"></span></span><span style=\"position: absolute; clip: rect(0.836em, 1007.61em, 1.201em, -999.997em); top: -1.247em; left: 0em;\"><span style=\"display: inline-block; overflow: hidden; vertical-align: 0em; border-top: 1.3px solid; width: 7.607em; height: 0px;\"></span><span style=\"display: inline-block; width: 0px; height: 1.044em;\"></span></span></span></span></span></span><span style=\"display: inline-block; width: 0px; height: 4.065em;\"></span></span></span><span style=\"display: inline-block; width: 0px; height: 4.065em;\"></span></span></span><span style=\"display: inline-block; position: absolute; width: 1.305em; height: 0px; clip: rect(-0.831em, 1001.2em, 0.471em, -999.997em); top: 0em; right: 0em; margin-right: 0em;\"><span style=\"position: absolute; clip: rect(3.128em, 1001.2em, 4.43em, -999.997em); top: -3.956em; right: 0em;\"><span class=\"mtd\" id=\"mjx-eqn-2\"><span class=\"mrow\" id=\"MathJax-Span-158\"><span class=\"mtext\" id=\"MathJax-Span-159\" style=\"font-family: MathJax_Main;\">(2)</span></span></span><span style=\"display: inline-block; width: 0px; height: 4.013em;\"></span></span></span></span></span></span><span style=\"display: inline-block; width: 0px; height: 4.065em;\"></span></span></span><span style=\"display: inline-block; overflow: hidden; vertical-align: -1.622em; border-left: 0px solid; width: 0px; height: 3.816em;\"></span></span></nobr><span class=\"MJX_Assistive_MathML MJX_Assistive_MathML_Block\" role=\"presentation\"><math xmlns=\"http://www.w3.org/1998/Math/MathML\" display=\"block\"><mtable displaystyle=\"true\"><mlabeledtr><mtd id=\"mjx-eqn-2\"><mtext>(2)</mtext></mtd><mtd><mi>Γ</mi><mo stretchy=\"false\">(</mo><mi>x</mi><mo stretchy=\"false\">)</mo><mo>=</mo><mfrac><mrow><msubsup><mo>∫</mo><mrow class=\"MJX-TeXAtom-ORD\"><mi>α</mi></mrow><mrow class=\"MJX-TeXAtom-ORD\"><mi>β</mi></mrow></msubsup><mi>g</mi><mo stretchy=\"false\">(</mo><mi>t</mi><mo stretchy=\"false\">)</mo><mo stretchy=\"false\">(</mo><mi>x</mi><mo>−</mo><mi>t</mi><msup><mo stretchy=\"false\">)</mo><mn>2</mn></msup><mtext>&nbsp;d</mtext><mi>t</mi></mrow><mrow><mi>ϕ</mi><mo stretchy=\"false\">(</mo><mi>x</mi><mo stretchy=\"false\">)</mo><munderover><mo>∑</mo><mrow class=\"MJX-TeXAtom-ORD\"><mi>i</mi><mo>=</mo><mn>0</mn></mrow><mrow class=\"MJX-TeXAtom-ORD\"><mi>N</mi><mo>−</mo><mn>1</mn></mrow></munderover><msub><mi>ω</mi><mi>i</mi></msub></mrow></mfrac></mtd></mlabeledtr></mtable></math></span></span></div><script type=\"math/tex; mode=display\" id=\"MathJax-Element-760\">\n \\varGamma(x) = \\frac{\\int_{\\alpha}^{\\beta} g(t)(x-t)^2\\text{ d}t }{\\phi(x)\\sum_{i=0}^{N-1} \\omega_i} \\tag{2}\n </script> \n <p></p> \n</blockquote>", ">   \n> $$\n> \\varGamma(x) = \\frac{\\int_{\\alpha}^{\\beta} g(t)(x-t)^2\\text{ d}t }{\\phi(x)\\sum_{i=0}^{N-1} \\omega_i} \\tag{2}\n> $$\n"},
	{"110", "<p>假设一个随机变量<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> \n     \n      \n       \n       \n         X \n        \n       \n      \n        X \n       \n      \n    </span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.68333em; vertical-align: 0em;\"></span><span class=\"mord mathdefault\" style=\"margin-right: 0.07847em;\">X</span></span></span></span></span>，其一个表示定义为<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> \n     \n      \n       \n        \n        \n          X \n         \n        \n          ^ \n         \n        \n       \n         ( \n        \n       \n         X \n        \n       \n         ) \n        \n       \n      \n        \\hat{X}(X) \n       \n      \n    </span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 1.19677em; vertical-align: -0.25em;\"></span><span class=\"mord accent\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.94677em;\"><span class=\"\" style=\"top: -3em;\"><span class=\"pstrut\" style=\"height: 3em;\"></span><span class=\"mord\"><span class=\"mord mathdefault\" style=\"margin-right: 0.07847em;\">X</span></span></span><span class=\"\" style=\"top: -3.25233em;\"><span class=\"pstrut\" style=\"height: 3em;\"></span><span class=\"accent-body\" style=\"left: -0.16666em;\">^</span></span></span></span></span></span><span class=\"mopen\">(</span><span class=\"mord mathdefault\" style=\"margin-right: 0.07847em;\">X</span><span class=\"mclose\">)</span></span></span></span></span>，若我们使用<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> \n     \n      \n       \n       \n         R \n        \n       \n      \n        R \n       \n      \n    </span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.68333em; vertical-align: 0em;\"></span><span class=\"mord mathdefault\" style=\"margin-right: 0.00773em;\">R</span></span></span></span></span>个比特（bit）来表示<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> \n     \n      \n       \n       \n         X \n        \n       \n      \n        X \n       \n      \n    </span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.68333em; vertical-align: 0em;\"></span><span class=\"mord mathdefault\" style=\"margin-right: 0.07847em;\">X</span></span></span></span></span>，每个比特的数值为<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> \n     \n      \n       \n       \n         0 \n        \n       \n      \n        0 \n       \n      \n    </span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.64444em; vertical-align: 0em;\"></span><span class=\"mord\">0</span></span></span></span></span>或<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> \n     \n      \n       \n       \n         1 \n        \n       \n      \n        1 \n       \n      \n    </span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.64444em; vertical-align: 0em;\"></span><span class=\"mord\">1</span></span></span></span></span>，那么函数<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> \n     \n      \n       \n        \n        \n          X \n         \n        \n          ^ \n         \n        \n       \n      \n        \\hat{X} \n       \n      \n    </span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.94677em; vertical-align: 0em;\"></span><span class=\"mord accent\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.94677em;\"><span class=\"\" style=\"top: -3em;\"><span class=\"pstrut\" style=\"height: 3em;\"></span><span class=\"mord\"><span class=\"mord mathdefault\" style=\"margin-right: 0.07847em;\">X</span></span></span><span class=\"\" style=\"top: -3.25233em;\"><span class=\"pstrut\" style=\"height: 3em;\"></span><span class=\"accent-body\" style=\"left: -0.16666em;\">^</span></span></span></span></span></span></span></span></span></span>可以有<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> \n     \n      \n       \n        \n        \n          2 \n         \n        \n          R \n         \n        \n       \n      \n        2^R \n       \n      \n    </span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.841331em; vertical-align: 0em;\"></span><span class=\"mord\"><span class=\"mord\">2</span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.841331em;\"><span class=\"\" style=\"top: -3.063em; margin-right: 0.05em;\"><span class=\"pstrut\" style=\"height: 2.7em;\"></span><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathdefault mtight\" style=\"margin-right: 0.00773em;\">R</span></span></span></span></span></span></span></span></span></span></span></span>中不同取值，那么我们现在的问题是找到一个<span class=\"katex--inline\"><span class=\"katex\"><span class=\"katex-mathml\"> \n     \n      \n       \n        \n        \n          X \n         \n        \n          ^ \n         \n        \n       \n      \n        \\hat{X} \n       \n      \n    </span><span class=\"katex-html\"><span class=\"base\"><span class=\"strut\" style=\"height: 0.94677em; vertical-align: 0em;\"></span><span class=\"mord accent\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\" style=\"height: 0.94677em;\"><span class=\"\" style=\"top: -3em;\"><span class=\"pstrut\" style=\"height: 3em;\"></span><span class=\"mord\"><span class=\"mord mathdefault\" style=\"margin-right: 0.07847em;\">X</span></span></span><span class=\"\" style=\"top: -3.25233em;\"><span class=\"pstrut\" style=\"height: 3em;\"></span><span class=\"accent-body\" style=\"left: -0.16666em;\">^</span></span></span></span></span></span></span></span></span></span>的最优值集（称为再生点（reproduction points）或码点（code points）），而目的是通过最小化定义的一个失真度量得到。</p>", "假设一个随机变量 $X$，其一个表示定义为 $\\hat{X}(X)$，若我们使用 $R$ 个比特（bit）来表示 $X$，每个比特的数值为 $0$ 或 $1$，那么函数 $\\hat{X}$ 可以有 $2^R$ 中不同取值，那么我们现在的问题是找到一个 $\\hat{X}$ 的最优值集（称为再生点（reproduction points）或码点（code points）），而目的是通过最小化定义的一个失真度量得到。\n"},
	{"109", "<p data-pid=\"Ckt2x5Xz\"><span class=\"ztext-math\" data-eeimg=\"1\" data-tex=\"\\omega\"><span></span><span><span class=\"MathJax_Preview\" style=\"color: inherit;\"></span><span class=\"MathJax_SVG\" id=\"MathJax-Element-1-Frame\" tabindex=\"0\" style=\"font-size: 100%; display: inline-block; position: relative;\" data-mathml=\"<math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;><mi>&amp;#x03C9;</mi></math>\" role=\"presentation\"><svg xmlns:xlink=\"http://www.w3.org/1999/xlink\" width=\"1.446ex\" height=\"1.399ex\" viewBox=\"0 -500.7 622.5 602.5\" role=\"img\" focusable=\"false\" aria-hidden=\"true\" style=\"vertical-align: -0.236ex;\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><use xlink:href=\"#MJMATHI-3C9\" x=\"0\" y=\"0\"></use></g></svg><span class=\"MJX_Assistive_MathML\" role=\"presentation\"><math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mi>ω</mi></math></span></span><script type=\"math/tex;mode=inline\" id=\"MathJax-Element-1\">\\omega</script><span class=\"tex2jax_ignore math-holder\">\\omega</span></span></span> 表示 <span class=\"ztext-math\" data-eeimg=\"1\" data-tex=\"n\"><span></span><span><span class=\"MathJax_Preview\" style=\"color: inherit;\"></span><span class=\"MathJax_SVG\" id=\"MathJax-Element-5-Frame\" tabindex=\"0\" style=\"font-size: 100%; display: inline-block; position: relative;\" data-mathml=\"<math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;><mi>n</mi></math>\" role=\"presentation\"><svg xmlns:xlink=\"http://www.w3.org/1999/xlink\" width=\"1.395ex\" height=\"1.399ex\" viewBox=\"0 -500.7 600.5 602.5\" role=\"img\" focusable=\"false\" aria-hidden=\"true\" style=\"vertical-align: -0.236ex;\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><use xlink:href=\"#MJMATHI-6E\" x=\"0\" y=\"0\"></use></g></svg><span class=\"MJX_Assistive_MathML\" role=\"presentation\"><math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mi>n</mi></math></span></span><script type=\"math/tex;mode=inline\" id=\"MathJax-Element-5\">n</script><span class=\"tex2jax_ignore math-holder\">n</span></span></span> 次单位根 <span class=\"ztext-math\" data-eeimg=\"1\" data-tex=\"\\exp(2\\pi i/n)\"><span></span><span><span class=\"MathJax_Preview\" style=\"color: inherit;\"></span><span class=\"MathJax_SVG\" id=\"MathJax-Element-3-Frame\" tabindex=\"0\" style=\"font-size: 100%; display: inline-block; position: relative;\" data-mathml=\"<math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;><mi>exp</mi><mo>&amp;#x2061;</mo><mo stretchy=&quot;false&quot;>(</mo><mn>2</mn><mi>&amp;#x03C0;</mi><mi>i</mi><mrow class=&quot;MJX-TeXAtom-ORD&quot;><mo>/</mo></mrow><mi>n</mi><mo stretchy=&quot;false&quot;>)</mo></math>\" role=\"presentation\"><svg xmlns:xlink=\"http://www.w3.org/1999/xlink\" width=\"11.216ex\" height=\"2.789ex\" viewBox=\"0 -849.8 4829 1200.9\" role=\"img\" focusable=\"false\" aria-hidden=\"true\" style=\"vertical-align: -0.815ex;\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><use xlink:href=\"#MJMAIN-65\"></use><use xlink:href=\"#MJMAIN-78\" x=\"444\" y=\"0\"></use><use xlink:href=\"#MJMAIN-70\" x=\"973\" y=\"0\"></use><use xlink:href=\"#MJMAIN-28\" x=\"1529\" y=\"0\"></use><use xlink:href=\"#MJMAIN-32\" x=\"1919\" y=\"0\"></use><use xlink:href=\"#MJMATHI-3C0\" x=\"2419\" y=\"0\"></use><use xlink:href=\"#MJMATHI-69\" x=\"2993\" y=\"0\"></use><use xlink:href=\"#MJMAIN-2F\" x=\"3338\" y=\"0\"></use><use xlink:href=\"#MJMATHI-6E\" x=\"3839\" y=\"0\"></use><use xlink:href=\"#MJMAIN-29\" x=\"4439\" y=\"0\"></use></g></svg><span class=\"MJX_Assistive_MathML\" role=\"presentation\"><math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mi>exp</mi><mo>⁡</mo><mo stretchy=\"false\">(</mo><mn>2</mn><mi>π</mi><mi>i</mi><mrow class=\"MJX-TeXAtom-ORD\"><mo>/</mo></mrow><mi>n</mi><mo stretchy=\"false\">)</mo></math></span></span><script type=\"math/tex;mode=inline\" id=\"MathJax-Element-3\">\\exp(2\\pi i/n)</script><span class=\"tex2jax_ignore math-holder\">\\exp(2\\pi i/n)</span></span></span> , <span class=\"ztext-math\" data-eeimg=\"1\" data-tex=\"n \"><span></span><span><span class=\"MathJax_Preview\" style=\"color: inherit;\"></span><span class=\"MathJax_SVG\" id=\"MathJax-Element-2-Frame\" tabindex=\"0\" style=\"font-size: 100%; display: inline-block; position: relative;\" data-mathml=\"<math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;><mi>n</mi></math>\" role=\"presentation\"><svg xmlns:xlink=\"http://www.w3.org/1999/xlink\" width=\"1.395ex\" height=\"1.399ex\" viewBox=\"0 -500.7 600.5 602.5\" role=\"img\" focusable=\"false\" aria-hidden=\"true\" style=\"vertical-align: -0.236ex;\"><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"matrix(1 0 0 -1 0 0)\"><use xlink:href=\"#MJMATHI-6E\" x=\"0\" y=\"0\"></use></g></svg><span class=\"MJX_Assistive_MathML\" role=\"presentation\"><math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mi>n</mi></math></span></span><script type=\"math/tex;mode=inline\" id=\"MathJax-Element-2\">n </script><span class=\"tex2jax_ignore math-holder\">n </span></span></span> 取决于上下文.</p>", "$\\omega$ 表示 $n$ 次单位根 $\\exp(2\\pi i/n)$ , $n$ 取决于上下文.\n"},
	{"108", "<h3 class=\"notion-h notion-h2 notion-h-indent-0 notion-block-d8fdd235868745bc92378f9d0d2fa5ff\" data-id=\"d8fdd235868745bc92378f9d0d2fa5ff\"><span><div id=\"d8fdd235868745bc92378f9d0d2fa5ff\" class=\"notion-header-anchor\"></div><a class=\"notion-hash-link\" href=\"#d8fdd235868745bc92378f9d0d2fa5ff\" title=\"定义有效的笔记\"><svg viewBox=\"0 0 16 16\" width=\"16\" height=\"16\"><path fill-rule=\"evenodd\" d=\"M7.775 3.275a.75.75 0 001.06 1.06l1.25-1.25a2 2 0 112.83 2.83l-2.5 2.5a2 2 0 01-2.83 0 .75.75 0 00-1.06 1.06 3.5 3.5 0 004.95 0l2.5-2.5a3.5 3.5 0 00-4.95-4.95l-1.25 1.25zm-4.69 9.64a2 2 0 010-2.83l2.5-2.5a2 2 0 012.83 0 .75.75 0 001.06-1.06 3.5 3.5 0 00-4.95 0l-2.5 2.5a3.5 3.5 0 004.95 4.95l1.25-1.25a.75.75 0 00-1.06-1.06l-1.25 1.25a2 2 0 01-2.83 0z\"></path></svg></a><span class=\"notion-h-title\">定义有效的笔记</span></span></h3>", "### 定义有效的笔记\n"},
	{"107", "<p id=\"20240516161955-xaoakji\" updated=\"20240516161955\">​<span data-type=\"code\">bar</span></p>", "\u200b`bar`\n"},
	{"106", "<pre><div class=\"dark bg-gray-950 rounded-md border-[0.5px] border-token-border-medium\"><div class=\"flex items-center relative text-token-text-secondary bg-token-main-surface-secondary px-4 py-2 text-xs font-sans justify-between rounded-t-md\"><span>javascript</span><div class=\"flex items-center\"><span class=\"\" data-state=\"closed\"><button class=\"flex gap-1 items-center\"><svg xmlns=\"http://www.w3.org/2000/svg\" width=\"24\" height=\"24\" fill=\"none\" viewBox=\"0 0 24 24\" class=\"icon-sm\"><path fill=\"currentColor\" fill-rule=\"evenodd\" d=\"M7 5a3 3 0 0 1 3-3h9a3 3 0 0 1 3 3v9a3 3 0 0 1-3 3h-2v2a3 3 0 0 1-3 3H5a3 3 0 0 1-3-3v-9a3 3 0 0 1 3-3h2zm2 2h5a3 3 0 0 1 3 3v5h2a1 1 0 0 0 1-1V5a1 1 0 0 0-1-1h-9a1 1 0 0 0-1 1zM5 9a1 1 0 0 0-1 1v9a1 1 0 0 0 1 1h9a1 1 0 0 0 1-1v-9a1 1 0 0 0-1-1z\" clip-rule=\"evenodd\"></path></svg>复制代码</button></span></div></div><div class=\"overflow-y-auto p-4 text-left undefined\" dir=\"ltr\"><code class=\"!whitespace-pre hljs language-javascript\"><span class=\"hljs-keyword\">function</span> <span class=\"hljs-title function_\">bubbleSort</span>(<span class=\"hljs-params\">arr</span>) {\n    <span class=\"hljs-keyword\">const</span> len = arr.<span class=\"hljs-property\">length</span>;\n    <span class=\"hljs-keyword\">for</span> (<span class=\"hljs-keyword\">let</span> i = <span class=\"hljs-number\">0</span>; i &lt; len; i++) {\n        <span class=\"hljs-keyword\">for</span> (<span class=\"hljs-keyword\">let</span> j = <span class=\"hljs-number\">0</span>; j &lt; len - <span class=\"hljs-number\">1</span>; j++) {\n            <span class=\"hljs-keyword\">if</span> (arr[j] &gt; arr[j + <span class=\"hljs-number\">1</span>]) {\n                [arr[j], arr[j + <span class=\"hljs-number\">1</span>]] = [arr[j + <span class=\"hljs-number\">1</span>], arr[j]]; <span class=\"hljs-comment\">// ES6 解构赋值交换元素位置</span>\n            }\n        }\n    }\n    <span class=\"hljs-keyword\">return</span> arr;\n}\n\n<span class=\"hljs-keyword\">const</span> unsortedArray = [<span class=\"hljs-number\">64</span>, <span class=\"hljs-number\">34</span>, <span class=\"hljs-number\">25</span>, <span class=\"hljs-number\">12</span>, <span class=\"hljs-number\">22</span>, <span class=\"hljs-number\">11</span>, <span class=\"hljs-number\">90</span>];\n<span class=\"hljs-variable language_\">console</span>.<span class=\"hljs-title function_\">log</span>(<span class=\"hljs-string\">'Unsorted Array:'</span>, unsortedArray);\n<span class=\"hljs-keyword\">const</span> sortedArray = <span class=\"hljs-title function_\">bubbleSort</span>(unsortedArray);\n<span class=\"hljs-variable language_\">console</span>.<span class=\"hljs-title function_\">log</span>(<span class=\"hljs-string\">'Sorted Array:'</span>, sortedArray);\n</code></div></div></pre>", "```javascript\nfunction bubbleSort(arr) {\n    const len = arr.length;\n    for (let i = 0; i < len; i++) {\n        for (let j = 0; j < len - 1; j++) {\n            if (arr[j] > arr[j + 1]) {\n                [arr[j], arr[j + 1]] = [arr[j + 1], arr[j]]; // ES6 解构赋值交换元素位置\n            }\n        }\n    }\n    return arr;\n}\n\nconst unsortedArray = [64, 34, 25, 12, 22, 11, 90];\nconsole.log('Unsorted Array:', unsortedArray);\nconst sortedArray = bubbleSort(unsortedArray);\nconsole.log('Sorted Array:', sortedArray);\n```\n"},
	{"105", "<table class=\"docutils align-default\"><thead><tr class=\"row-odd\"><th class=\"head\"><p>优势</p></th></tr></thead><tbody><tr class=\"row-even\"><td><div class=\"line-block\"><div class=\"line\">- Python的内置标准库</div><div class=\"line\">- 执行速度较快</div><div class=\"line\">- 容错能力强</div></div></td></tr></tbody></table>", "| 优势                                            |\n| ------------------------------------------------- |\n| - Python 的内置标准库<br />- 执行速度较快<br />- 容错能力强 |\n"},
	{"104", "<table class=\"docutils align-default\">\n<thead>\n<tr class=\"row-odd\">\n\n<th class=\"head\"><p>优势</p></th>\n\n</tr>\n</thead>\n<tbody>\n<tr class=\"row-even\">\n\n<td><div class=\"line-block\">\n<div class=\"line\">- Python的内置标准库</div>\n<div class=\"line\">- 执行速度较快</div>\n<div class=\"line\">- 容错能力强</div>\n</div>\n</td>\n\n</tr>\n\n\n\n</tbody>\n</table>", "| 优势                                            |\n| ------------------------------------------------- |\n| - Python 的内置标准库<br />- 执行速度较快<br />- 容错能力强 |\n"},
	{"103", "<code class=\"docutils literal notranslate\"><span class=\"pre\">BeautifulSoup(markup,</span> <span class=\"pre\">\"lxml\")</span></code>", "`BeautifulSoup(markup, \"lxml\")`\n"},
	{"102", "<code><code class=\"idl\"><a data-link-type=\"idl\" href=\"#node\" id=\"ref-for-node③⑧\" aria-expanded=\"false\">Node</a></code> . <code class=\"idl\"><a data-link-type=\"idl\" href=\"#dom-node-element_node\" id=\"ref-for-dom-node-element_node①\">ELEMENT_NODE</a></code></code>", "[`Node`](#node) . [`ELEMENT_NODE`](#dom-node-element_node)\n"},
	{"101", "<p><code class=\"idl\"><a data-link-type=\"idl\" href=\"#dom-event-capturing_phase\" id=\"ref-for-dom-event-capturing_phase\" aria-expanded=\"false\">CAPTURING_PHASE</a></code> to <code class=\"idl\"><a data-link-type=\"idl\" href=\"#dom-event-bubbling_phase\" id=\"ref-for-dom-event-bubbling_phase\">BUBBLING_PHASE</a></code> </p>", "[`CAPTURING_PHASE`](#dom-event-capturing_phase) to [`BUBBLING_PHASE`](#dom-event-bubbling_phase)\n"},
	{"100", "<h3 class=\"heading settled\" data-level=\"2.2\" id=\"interface-event\"><span class=\"secno\">2.2. </span><span class=\"content\">Interface <code class=\"idl\"><a data-link-type=\"idl\" href=\"#event\" id=\"ref-for-event①\">Event</a></code></span><a class=\"self-link\" href=\"#interface-event\"></a></h3>", "### 2.2. Interface [`Event`](#event)\n"},
	{"99", "<div class=\"markdown-heading\"><h3 class=\"heading-element\"><code>subject:matches-attr(arg)</code></h3><a id=\"user-content-subjectmatches-attrarg\" class=\"anchor\" aria-label=\"Permalink: subject:matches-attr(arg)\" href=\"#subjectmatches-attrarg\"><svg class=\"octicon octicon-link\" viewBox=\"0 0 16 16\" version=\"1.1\" width=\"16\" height=\"16\" aria-hidden=\"true\"><path d=\"m7.775 3.275 1.25-1.25a3.5 3.5 0 1 1 4.95 4.95l-2.5 2.5a3.5 3.5 0 0 1-4.95 0 .751.751 0 0 1 .018-1.042.751.751 0 0 1 1.042-.018 1.998 1.998 0 0 0 2.83 0l2.5-2.5a2.002 2.002 0 0 0-2.83-2.83l-1.25 1.25a.751.751 0 0 1-1.042-.018.751.751 0 0 1-.018-1.042Zm-4.69 9.64a1.998 1.998 0 0 0 2.83 0l1.25-1.25a.751.751 0 0 1 1.042.018.751.751 0 0 1 .018 1.042l-1.25 1.25a3.5 3.5 0 1 1-4.95-4.95l2.5-2.5a3.5 3.5 0 0 1 4.95 0 .751.751 0 0 1-.018 1.042.751.751 0 0 1-1.042.018 1.998 1.998 0 0 0-2.83 0l-2.5 2.5a1.998 1.998 0 0 0 0 2.83Z\"></path></svg></a></div>", "### `subject:matches-attr(arg)`\n"},
	{"98", "<code class=\"notranslate\"><span>capture_stdout=True,</span><span>&nbsp;</span><span>stderr=subprocess.STDOUT</span></code>", "`capture_stdout=True, stderr=subprocess.STDOUT`\n"},
	{"97", "<pre class=\"prettyprint linenums prettyprinted\" style=\"\"><ol class=\"linenums\"><li class=\"L0\"><span class=\"pln\">sudo xattr </span><span class=\"pun\">-</span><span class=\"pln\">r </span><span class=\"pun\">-</span><span class=\"pln\">d com</span><span class=\"pun\">.</span><span class=\"pln\">apple</span><span class=\"pun\">.</span><span class=\"pln\">quarantine </span><span class=\"pun\">/</span><span class=\"typ\">Applications</span><span class=\"pun\">/</span><span class=\"pln\">host</span><span class=\"pun\">防验证工具.</span><span class=\"pln\">app</span></li></ol></pre>", "```\nsudo xattr -r -d com.apple.quarantine /Applications/host防验证工具.app\n```\n"},
	{"96", "<pre class=\"prettyprint linenums prettyprinted\" style=\"overflow: auto;\"><ol class=\"linenums\"><li class=\"L0\"><code class=\"go\"><span class=\"pln\">today </span><span class=\"pun\">:=</span><span class=\"pln\"> time</span><span class=\"pun\">.</span><span class=\"typ\">Date</span><span class=\"pun\">(</span><span class=\"lit\">2022</span><span class=\"pun\">,</span><span class=\"pln\"> </span><span class=\"lit\">10</span><span class=\"pun\">,</span><span class=\"pln\"> </span><span class=\"lit\">31</span><span class=\"pun\">,</span><span class=\"pln\"> </span><span class=\"lit\">0</span><span class=\"pun\">,</span><span class=\"pln\"> </span><span class=\"lit\">0</span><span class=\"pun\">,</span><span class=\"pln\"> </span><span class=\"lit\">0</span><span class=\"pun\">,</span><span class=\"pln\"> </span><span class=\"lit\">0</span><span class=\"pun\">,</span><span class=\"pln\"> time</span><span class=\"pun\">.</span><span class=\"typ\">Local</span><span class=\"pun\">)</span></code></li><li class=\"L1\"><code class=\"go\"><span class=\"pln\">nextDay </span><span class=\"pun\">:=</span><span class=\"pln\"> today</span><span class=\"pun\">.</span><span class=\"typ\">AddDate</span><span class=\"pun\">(</span><span class=\"lit\">0</span><span class=\"pun\">,</span><span class=\"pln\"> </span><span class=\"lit\">1</span><span class=\"pun\">,</span><span class=\"pln\"> </span><span class=\"lit\">0</span><span class=\"pun\">)</span></code></li><li class=\"L2\"><code class=\"go\"><span class=\"pln\">fmt</span><span class=\"pun\">.</span><span class=\"typ\">Println</span><span class=\"pun\">(</span><span class=\"pln\">nextDay</span><span class=\"pun\">.</span><span class=\"typ\">Format</span><span class=\"pun\">(</span><span class=\"str\">\"20060102\"</span><span class=\"pun\">))</span></code></li><li class=\"L3\"><code class=\"go\"></code></li><li class=\"L4\"><code class=\"go\"><span class=\"com\">// 输出：20221201</span></code></li></ol></pre>", "```go\ntoday := time.Date(2022, 10, 31, 0, 0, 0, 0, time.Local)\nnextDay := today.AddDate(0, 1, 0)\nfmt.Println(nextDay.Format(\"20060102\"))\n\n// 输出：20221201\n```\n"},
	{"95", "<p><a class=\"reference internal\" href=\"#module-ctypes\" title=\"ctypes: A foreign function library for Python.\"><code class=\"xref py py-mod docutils literal notranslate\"><span class=\"pre\">ctypes</span></code></a> 是 Python 的外部函数库。它提供了与 C 兼容的数据类型，并允许调用 DLL 或共享库中的函数。可使用该模块以纯 Python 形式对这些库进行封装。</p>", "[`ctypes`](#module-ctypes \"ctypes: A foreign function library for Python.\") 是 Python 的外部函数库。它提供了与 C 兼容的数据类型，并允许调用 DLL 或共享库中的函数。可使用该模块以纯 Python 形式对这些库进行封装。\n"},
	{"94", "<table>\n    <tbody>\n    <tr>\n        <td>\n            foo\n            bar\n            baz\n        </td>\n    </tr>\n    </tbody>\n</table>", "| foo bar baz |\n| ------------- |\n"},
	{"93", "<section style=\"margin: 8px 8px 16px;line-height: 1.75em;\"><strong><span style=\"font-size: 15px;letter-spacing: 1px;\">foo<br></span></strong></section>", "**foo**\n"},
	{"92", "<section style=\"margin: 8px 8px 16px;line-height: 1.75em;\"><strong><span style=\"font-size: 15px;letter-spacing: 1px;\">foo<br></span></strong></section>", "**foo**\n"},
	{"91", "<pre><div class=\"dark bg-gray-950 rounded-md border-[0.5px] border-token-border-medium\"><div class=\"flex items-center relative text-token-text-secondary bg-token-main-surface-secondary px-4 py-2 text-xs font-sans justify-between rounded-t-md\"><span>javascript</span><div class=\"flex items-center\"><span class=\"\" data-state=\"closed\"><button class=\"flex gap-1 items-center\"><svg width=\"24\" height=\"24\" viewBox=\"0 0 24 24\" fill=\"none\" xmlns=\"http://www.w3.org/2000/svg\" class=\"icon-sm\"><path fill-rule=\"evenodd\" clip-rule=\"evenodd\" d=\"M12 3.5C10.8954 3.5 10 4.39543 10 5.5H14C14 4.39543 13.1046 3.5 12 3.5ZM8.53513 3.5C9.22675 2.3044 10.5194 1.5 12 1.5C13.4806 1.5 14.7733 2.3044 15.4649 3.5H17.25C18.9069 3.5 20.25 4.84315 20.25 6.5V18.5C20.25 20.1569 19.1569 21.5 17.25 21.5H6.75C5.09315 21.5 3.75 20.1569 3.75 18.5V6.5C3.75 4.84315 5.09315 3.5 6.75 3.5H8.53513ZM8 5.5H6.75C6.19772 5.5 5.75 5.94772 5.75 6.5V18.5C5.75 19.0523 6.19772 19.5 6.75 19.5H17.25C18.0523 19.5 18.25 19.0523 18.25 18.5V6.5C18.25 5.94772 17.8023 5.5 17.25 5.5H16C16 6.60457 15.1046 7.5 14 7.5H10C8.89543 7.5 8 6.60457 8 5.5Z\" fill=\"currentColor\"></path></svg>Copy code</button></span></div></div><div class=\"p-4 overflow-y-auto\"><code class=\"!whitespace-pre hljs language-javascript\"><span class=\"hljs-variable language_\">console</span>.<span class=\"hljs-title function_\">log</span>(<span class=\"hljs-string\">\"Hello, World!\"</span>);\n</code></div></div></pre>", "```javascript\nconsole.log(\"Hello, World!\");\n```\n"},
	{"90", "<div class=\"highlight\"><div class=\"chroma open\"><div class=\"code-header language-go\"><span class=\"code-title\"><i class=\"arrow fas fa-chevron-right fa-fw\" aria-hidden=\"true\"></i></span><span class=\"ellipses\"><i class=\"fas fa-ellipsis-h fa-fw\" aria-hidden=\"true\"></i></span><span class=\"copy\" data-clipboard-text=\"import &quot;github.com/swaggo/gin-swagger&quot; // gin-swagger middleware\nimport &quot;github.com/swaggo/files&quot; // swagger embed files\n\" title=\"Copy to clipboard\"><i class=\"far fa-copy fa-fw\" aria-hidden=\"true\"></i></span></div><div class=\"table-wrapper\"><table><tbody><tr><td><pre tabindex=\"0\" class=\"chroma\"><code class=\"language-go\" data-lang=\"go\"><span class=\"line\"><span class=\"cl\"><span class=\"kn\">import</span> <span class=\"s\">\"github.com/swaggo/gin-swagger\"</span> <span class=\"c1\">// gin-swagger middleware\n</span></span></span><span class=\"line\"><span class=\"cl\"><span class=\"c1\"></span><span class=\"kn\">import</span> <span class=\"s\">\"github.com/swaggo/files\"</span> <span class=\"c1\">// swagger embed files\n</span></span></span></code></pre></td></tr></tbody></table></div></div></div>", "```go\nimport \"github.com/swaggo/gin-swagger\" // gin-swagger middleware\nimport \"github.com/swaggo/files\" // swagger embed files\n```\n"},
	{"89", "<pre class=\"Agda\"><a id=\"plfa_plfa-part1-Naturals-114\" class=\"Keyword\">module</a> <a id=\"plfa_plfa-part1-Naturals-121\" href=\"../Naturals/#\" class=\"Module\">plfa.part1.Naturals</a> <a id=\"plfa_plfa-part1-Naturals-141\" class=\"Keyword\">where</a>\n</pre>", "```Agda\nmodule plfa.part1.Naturals where\n```\n"},
	{"88", "<s>foo</s>", "~~foo~~\n"},
	{"87", "<h2 data-id=\"heading-4\">foo</h2><pre><div class=\"code-block-extension-header\"><div class=\"code-block-extension-headerLeft\"><div class=\"code-block-extension-foldBtn\"><svg xmlns=\"http://www.w3.org/2000/svg\" viewBox=\"0 0 24 24\"><path d=\"M16.924 9.617A1 1 0 0 0 16 9H8a1 1 0 0 0-.707 1.707l4 4a1 1 0 0 0 1.414 0l4-4a1 1 0 0 0 .217-1.09z\" data-name=\"Down\"></path></svg></div></div><div class=\"code-block-extension-headerRight\"><span class=\"code-block-extension-lang\">arduino</span><div class=\"code-block-extension-copyCodeBtn\">复制代码</div></div></div><code class=\"hljs language-arduino code-block-extension-codeShowNum\" lang=\"arduino\"><span class=\"code-block-extension-codeLine\" data-line-num=\"1\">bar</span>\n</code></pre><h2 data-id=\"heading-5\">baz</h2>", "## foo\n\n```arduino\nbar\n```\n\n## baz\n"},
	{"86", "<img src=\"a_1.png\" >", "![](a_1.png)\n"},
	{"85", "&lt;img src=\"a_1.png\" &gt;", "<img src=\"a\\_1.png\" >\n"},
	{"84", "<table cellspacing=\"0\">\n<colgroup>\n<col style=\"width:10%;\">\n<col style=\"width:15%;\">\n<col style=\"width:75%;\">\n    </colgroup>\n<thead>\n<tr>\n<th>符号</th>\n<th>意义</th>\n<th>说明</th>\n</tr>\n</thead><tbody>\n<tr>\n<td><code>\\n</code></td>\n<td>换行符</td>\n<td>表示文章的换行，这是一个不可见符号，在例子中，这个符号在 <code>_</code> 的位置。<p></p>\n<pre>aaa_<br>bbb</pre>\n<p>                你能够通过 <code>\\n</code> 找到换行符，但不能够插入换行符。要在替换结果中换行，需要用 <code>\\r</code>。\n            </p></td>\n</tr>\n\n</tbody>\n</table>", "| 符号     | 意义   | 说明                                                                                                                                                                      |\n| ---------- | -------- | --------------------------------------------------------------------------------------------------------------------------------------------------------------------------- |\n| `\\n` | 换行符 | 表示文章的换行，这是一个不可见符号，在例子中，这个符号在 `_` 的位置。<br />`aaa_`<br/>`bbb`<br />你能够通过 `\\n` 找到换行符，但不能够插入换行符。要在替换结果中换行，需要用 `\\r`。 |\n"},
	{"83", "<table cellspacing=\"0\">\n<colgroup>\n<col style=\"width:10%;\">\n<col style=\"width:15%;\">\n<col style=\"width:75%;\">\n    </colgroup>\n<thead>\n<tr>\n<th>符号</th>\n<th>意义</th>\n<th>说明</th>\n</tr>\n</thead><thead>\n</thead><tbody>\n<tr>\n<td><code>.</code></td>\n<td>任意一个字符</td>\n<td>最简单的元字符，匹配任意字符，但不包括换行符 <code>\\n</code>。</td>\n</tr>\n</tbody>\n</table>", "| 符号    | 意义         | 说明                                                   |\n| --------- | -------------- | -------------------------------------------------------- |\n| `.` | 任意一个字符 | 最简单的元字符，匹配任意字符，但不包括换行符 `\\n`。 |\n"},
	{"82", "<pre class=\"mb-4 mt-6 max-h-[650px] overflow-x-auto rounded border bg-[#1e1e1e]\"><pre style=\"color:#9CDCFE;background-color:#1E1E1E\" class=\"px-4 py-4 prism-code language-\"><div class=\"token-line\" style=\"color:#9CDCFE\"><span class=\"token plain\">foo</span></div><div class=\"token-line\" style=\"color:#9CDCFE\"><span class=\"token plain\">bar</span></div></pre></pre>", "```\nfoo\nbar\n```\n"},
	{"81", "<pre data-tool=\"mdnice编辑器\" style=\"margin-top: 10px;margin-bottom: 10px;color: rgb(0, 0, 0);text-align: left;border-radius: 5px;box-shadow: rgba(0, 0, 0, 0.55) 0px 2px 10px;\"><section style=\"padding: 15px 16px 16px;overflow-x: auto;color: rgb(171, 178, 191);display: -webkit-box;font-family: &quot;Operator Mono&quot;, Consolas, Monaco, Menlo, monospace;background-color: rgb(40, 44, 52);border-radius: 5px;margin-top: 0px;\"><span style=\"letter-spacing: normal;font-size: 12px;\">setbit key offset value  # 设置或者清空 key 的 value(字符串)在 offset 处的 bit 值<br>getbit key offset  # 返回 key 对应的 string 在 offset 处的 bit 值 <br>bitcount key [start end] # start end 范围内被设置为1的数量，不传递 start end 默认全范围<br></span></section></pre>", "```\nsetbit key offset value  # 设置或者清空 key 的 value(字符串)在 offset 处的 bit 值\ngetbit key offset  # 返回 key 对应的 string 在 offset 处的 bit 值 \nbitcount key [start end] # start end 范围内被设置为1的数量，不传递 start end 默认全范围\n```\n"},
	{"80", "<pre data-tool=\"mdnice编辑器\" style=\"margin-top: 10px;margin-bottom: 10px;color: rgb(0, 0, 0);text-align: left;border-radius: 5px;box-shadow: rgba(0, 0, 0, 0.55) 0px 2px 10px;\"><section style=\"padding: 15px 16px 16px;overflow-x: auto;color: rgb(171, 178, 191);display: -webkit-box;font-family: &quot;Operator Mono&quot;, Consolas, Monaco, Menlo, monospace;background-color: rgb(40, 44, 52);border-radius: 5px;margin-top: 0px;\"><span style=\"letter-spacing: normal;font-size: 12px;\">object encoding xxx  # xxx 为键名<br></span></section></pre>", "```\nobject encoding xxx  # xxx 为键名\n```\n"},
	{"79", "<p>foo <code class=\"docutils literal notranslate\"><span class=\"pre\">bar</span></code>) baz</p>", "foo `bar`) baz\n"},
	{"78", "foo $bar^2$ baz^3", "foo \\$bar^2\\$ baz^3\n"},
	{"77", "<p>在做拉丁字母间距设计的时候，比较好的方法是从 <code class=\"hljs language-undefined\">n</code> 和 <code class=\"hljs language-undefined\">o</code> 起步。一旦这两个字母的边距设置合理，剩下的就相对简单了。所以，我建议你键入一些类似 <code class=\"hljs language-undefined\">noononno</code> 的组合，然后开始摆弄它们的边距设置，直到你满意为止。你可以在灰色的信息面板（显示 &gt; 显示信息，Cmd-Shift-I）中检查任意字符形的边距和字宽设置：</p>\n<figure><div class=\"RatioContainer\">\n<picture class=\"js-only\"><source data-srcset=\"https://cdn2.glyphsapp.com/media/pages/learn/spacing/6e6a8e08ef-1624987024/spacing-1-320x-q80.webp 320w, https://cdn2.glyphsapp.com/media/pages/learn/spacing/6e6a8e08ef-1624987024/spacing-1-640x-q80.webp 640w, https://cdn2.glyphsapp.com/media/pages/learn/spacing/6e6a8e08ef-1624987024/spacing-1-1280x-q80.webp 1280w\" type=\"image/webp\" sizes=\"360px\" srcset=\"https://cdn2.glyphsapp.com/media/pages/learn/spacing/6e6a8e08ef-1624987024/spacing-1-320x-q80.webp 320w, https://cdn2.glyphsapp.com/media/pages/learn/spacing/6e6a8e08ef-1624987024/spacing-1-640x-q80.webp 640w, https://cdn2.glyphsapp.com/media/pages/learn/spacing/6e6a8e08ef-1624987024/spacing-1-1280x-q80.webp 1280w\"><source data-srcset=\"https://cdn2.glyphsapp.com/media/pages/learn/spacing/6e6a8e08ef-1624987024/spacing-1-320x-q80.png 320w, https://cdn2.glyphsapp.com/media/pages/learn/spacing/6e6a8e08ef-1624987024/spacing-1-640x-q80.png 640w, https://cdn2.glyphsapp.com/media/pages/learn/spacing/6e6a8e08ef-1624987024/spacing-1-1280x-q80.png 1280w\" type=\"image/png\" sizes=\"360px\" srcset=\"https://cdn2.glyphsapp.com/media/pages/learn/spacing/6e6a8e08ef-1624987024/spacing-1-320x-q80.png 320w, https://cdn2.glyphsapp.com/media/pages/learn/spacing/6e6a8e08ef-1624987024/spacing-1-640x-q80.png 640w, https://cdn2.glyphsapp.com/media/pages/learn/spacing/6e6a8e08ef-1624987024/spacing-1-1280x-q80.png 1280w\"><img alt=\"\" class=\"lazyautosizes lazyloaded\" data-sizes=\"auto\" data-srcset=\"https://cdn2.glyphsapp.com/media/pages/learn/spacing/6e6a8e08ef-1624987024/spacing-1-320x-q80.png 320w, https://cdn2.glyphsapp.com/media/pages/learn/spacing/6e6a8e08ef-1624987024/spacing-1-640x-q80.png 640w, https://cdn2.glyphsapp.com/media/pages/learn/spacing/6e6a8e08ef-1624987024/spacing-1-1280x-q80.png 1280w\" height=\"64\" width=\"360\" sizes=\"360px\" srcset=\"https://cdn2.glyphsapp.com/media/pages/learn/spacing/6e6a8e08ef-1624987024/spacing-1-320x-q80.png 320w, https://cdn2.glyphsapp.com/media/pages/learn/spacing/6e6a8e08ef-1624987024/spacing-1-640x-q80.png 640w, https://cdn2.glyphsapp.com/media/pages/learn/spacing/6e6a8e08ef-1624987024/spacing-1-1280x-q80.png 1280w\"></picture>\n</div></figure>", "在做拉丁字母间距设计的时候，比较好的方法是从 `n` 和 `o` 起步。一旦这两个字母的边距设置合理，剩下的就相对简单了。所以，我建议你键入一些类似 `noononno` 的组合，然后开始摆弄它们的边距设置，直到你满意为止。你可以在灰色的信息面板（显示 > 显示信息，Cmd-Shift-I）中检查任意字符形的边距和字宽设置：\n\n![](https://cdn2.glyphsapp.com/media/pages/learn/spacing/6e6a8e08ef-1624987024/spacing-1-1280x-q80.png){: style=\"width: 360px;\"}\n"},
	{"76", "<div>\n    <ul>\n        <li>foo</li>\n    </ul>\n    <h1>bar</h1>\n</div>", "* foo\n\n# bar\n"},
	{"75", "foo <mark>bar</mark> baz", "foo ==bar== baz\n"},
	{"74", "foo**bar**<strong>baz</strong>bazz", "foo\\*\\*bar\\*\\***baz**bazz\n"},
	{"73", "<p>foo</p>\n<ul>\n<li>bar</li>\n</ul>\n<p>baz</p>", "foo\n\n* bar\n\nbaz\n"},
	{"72", "<p>foo</p>\n\n<ul>\n<li>bar\n</ul>\n\n<p>baz</p>", "foo\n\n* bar\n\nbaz\n"},
	{"71", "<strong><sup>[1]</sup></strong>1", "**^[1]^**1\n"},
	{"70", "<code>foo</code><code>bar</code>", "`foo`\u200b`bar`\n"},
	{"69", "<em>foo</em><strong>bar</strong>", "*foo*\u200b**bar**\n"},
	{"68", "<strong>foo</strong><em>bar</em>", "**foo**\u200b*bar*\n"},
	{"67", "<em>foo</em><em>bar</em>", "*foo*\u200b*bar*\n"},
	{"66", "<strong>foo</strong><strong>bar</strong>", "**foo**\u200b**bar**\n"},
	{"65", "<a title=\"title\" href=\"url\"><strong>foo&nbsp;</strong></a>bar", "[**foo \u200b**](url \"title\")bar\n"},
	{"64", "<a title=\"title\" href=\"url\"><strong>foo</strong></a>", "[**foo**](url \"title\")\n"},
	{"63", "<strong><br></strong>", "\n"},
	{"62", "foo<strong><br>bar<br></strong>baz", "foo\n**bar**\nbaz\n"},
	{"61", "<p><a href=\"baz\"><img src=\"bar\" alt=\"foo\"></a></p>", "[![foo](bar)](baz)\n"},
	{"60", "<span style=\"color: rgb(0, 0, 0); font-family: 微软雅黑; font-size: 18px;\">foo <a name=\"4\"></a></span>", "foo\n"},
	{"59", "<pre data-index=\"2\"><code class=\"language-java hljs\"><ol class=\"hljs-ln\" style=\"width:100%\"><li><div class=\"hljs-ln-numbers\"><div class=\"hljs-ln-line hljs-ln-n\" data-line-number=\"1\"></div></div><div class=\"hljs-ln-code\"><div class=\"hljs-ln-line\"><span class=\"hljs-comment\"><span class=\"hljs-comment\">/**</span></span></div></div></li><li><div class=\"hljs-ln-numbers\"><div class=\"hljs-ln-line hljs-ln-n\" data-line-number=\"2\"></div></div><div class=\"hljs-ln-code\"><div class=\"hljs-ln-line\"><span class=\"hljs-comment\">&nbsp;* Create a new proxy according to the settings in this factory.</span></div></div></li><li><div class=\"hljs-ln-numbers\"><div class=\"hljs-ln-line hljs-ln-n\" data-line-number=\"3\"></div></div><div class=\"hljs-ln-code\"><div class=\"hljs-ln-line\"><span class=\"hljs-comment\">&nbsp;* &lt;p&gt;Can be called repeatedly. Effect will vary if we've added</span></div></div></li><li><div class=\"hljs-ln-numbers\"><div class=\"hljs-ln-line hljs-ln-n\" data-line-number=\"4\"></div></div><div class=\"hljs-ln-code\"><div class=\"hljs-ln-line\"><span class=\"hljs-comment\">&nbsp;* or removed interfaces. Can add and remove interceptors.</span></div></div></li><li><div class=\"hljs-ln-numbers\"><div class=\"hljs-ln-line hljs-ln-n\" data-line-number=\"5\"></div></div><div class=\"hljs-ln-code\"><div class=\"hljs-ln-line\"><span class=\"hljs-comment\">&nbsp;* &lt;p&gt;Uses the given class loader (if necessary for proxy creation).</span></div></div></li><li><div class=\"hljs-ln-numbers\"><div class=\"hljs-ln-line hljs-ln-n\" data-line-number=\"6\"></div></div><div class=\"hljs-ln-code\"><div class=\"hljs-ln-line\"><span class=\"hljs-comment\">&nbsp;* <span class=\"hljs-doctag\">@param</span> classLoader the class loader to create the proxy with</span></div></div></li><li><div class=\"hljs-ln-numbers\"><div class=\"hljs-ln-line hljs-ln-n\" data-line-number=\"7\"></div></div><div class=\"hljs-ln-code\"><div class=\"hljs-ln-line\"><span class=\"hljs-comment\">&nbsp;* (or {<span class=\"hljs-doctag\">@code</span> null} for the low-level proxy facility's default)</span></div></div></li><li><div class=\"hljs-ln-numbers\"><div class=\"hljs-ln-line hljs-ln-n\" data-line-number=\"8\"></div></div><div class=\"hljs-ln-code\"><div class=\"hljs-ln-line\"><span class=\"hljs-comment\">&nbsp;* <span class=\"hljs-doctag\">@return</span> the proxy object</span></div></div></li><li><div class=\"hljs-ln-numbers\"><div class=\"hljs-ln-line hljs-ln-n\" data-line-number=\"9\"></div></div><div class=\"hljs-ln-code\"><div class=\"hljs-ln-line\"><span class=\"hljs-comment\">&nbsp;*/</span></div></div></li><li><div class=\"hljs-ln-numbers\"><div class=\"hljs-ln-line hljs-ln-n\" data-line-number=\"10\"></div></div><div class=\"hljs-ln-code\"><div class=\"hljs-ln-line\"><span class=\"hljs-keyword\">public</span> Object <span class=\"hljs-title function_\">getProxy</span><span class=\"hljs-params\">(<span class=\"hljs-meta\">@Nullable</span> ClassLoader classLoader)</span> {</div></div></li><li><div class=\"hljs-ln-numbers\"><div class=\"hljs-ln-line hljs-ln-n\" data-line-number=\"11\"></div></div><div class=\"hljs-ln-code\"><div class=\"hljs-ln-line\">&nbsp;<span class=\"hljs-keyword\">return</span> createAopProxy().getProxy(classLoader);</div></div></li><li><div class=\"hljs-ln-numbers\"><div class=\"hljs-ln-line hljs-ln-n\" data-line-number=\"12\"></div></div><div class=\"hljs-ln-code\"><div class=\"hljs-ln-line\">}</div></div></li></ol></code><div class=\"hljs-button signin\" data-title=\"登录后复制\" data-report-click=\"{&quot;spm&quot;:&quot;1001.2101.3001.4334&quot;}\" onclick=\"hljs.signin(event)\"></div></pre>", "```java\n/**\n * Create a new proxy according to the settings in this factory.\n * <p>Can be called repeatedly. Effect will vary if we've added\n * or removed interfaces. Can add and remove interceptors.\n * <p>Uses the given class loader (if necessary for proxy creation).\n * @param classLoader the class loader to create the proxy with\n * (or {@code null} for the low-level proxy facility's default)\n * @return the proxy object\n */\npublic Object getProxy(@Nullable ClassLoader classLoader) {\n return createAopProxy().getProxy(classLoader);\n}\n```\n"},
	{"58", "<pre data-index=\"5\" class=\"prettyprint\"><code class=\"prism language-python has-numbering\" onclick=\"mdcp.signin(event)\" style=\"position: unset;\">a <span class=\"token operator\">=</span> torch<span class=\"token punctuation\">.</span>Tensor<span class=\"token punctuation\">(</span><span class=\"token punctuation\">[</span><span class=\"token number\">1</span><span class=\"token punctuation\">,</span> <span class=\"token number\">2</span><span class=\"token punctuation\">]</span><span class=\"token punctuation\">)</span>\n<span class=\"token keyword\">print</span><span class=\"token punctuation\">(</span>a<span class=\"token punctuation\">.</span><span class=\"token builtin\">type</span><span class=\"token punctuation\">(</span><span class=\"token punctuation\">)</span><span class=\"token punctuation\">)</span>\n<span class=\"token keyword\">print</span><span class=\"token punctuation\">(</span>a<span class=\"token punctuation\">)</span>\n<span class=\"token operator\">&gt;&gt;</span><span class=\"token operator\">&gt;</span>\ntorch<span class=\"token punctuation\">.</span>FloatTensor\ntensor<span class=\"token punctuation\">(</span><span class=\"token punctuation\">[</span><span class=\"token number\">1</span><span class=\"token punctuation\">.</span><span class=\"token punctuation\">,</span> <span class=\"token number\">2</span><span class=\"token punctuation\">.</span><span class=\"token punctuation\">]</span><span class=\"token punctuation\">)</span>\n<div class=\"hljs-button signin\" data-title=\"登录后复制\" data-report-click=\"{&quot;spm&quot;:&quot;1001.2101.3001.4334&quot;}\"></div></code><ul class=\"pre-numbering\" style=\"\"><li style=\"color: rgb(153, 153, 153);\">1</li><li style=\"color: rgb(153, 153, 153);\">2</li><li style=\"color: rgb(153, 153, 153);\">3</li><li style=\"color: rgb(153, 153, 153);\">4</li><li style=\"color: rgb(153, 153, 153);\">5</li><li style=\"color: rgb(153, 153, 153);\">6</li></ul></pre>", "```python\na = torch.Tensor([1, 2])\nprint(a.type())\nprint(a)\n>>>\ntorch.FloatTensor\ntensor([1., 2.])\n```\n"},
	{"57", "a<strong>  b: </strong>c", "a**\u200b  b: \u200b**c\n"},
	{"56", "<a href=\"https://b3log.org\">foo'bar</a>", "[foo'bar](https://b3log.org)\n"},
	{"55", "foo'bar", "foo'bar\n"},
	{"54", "<table border=\"0\" cellpadding=\"0\" cellspacing=\"0\" width=\"198\">\n <colgroup><col width=\"198\">\n </colgroup><tbody><tr height=\"45\">\n\n  <td height=\"45\" class=\"xl65\" width=\"198\">foobar\n  baz</td>\n\n </tr>\n</tbody></table>", "| foobar baz |\n| ------------ |\n"},
	{"53", "<figure data-size=\"normal\"><noscript><img src=\"https://foo.jpg\" data-caption=\"\" data-size=\"normal\" data-rawwidth=\"642\" data-rawheight=\"643\" class=\"origin_image zh-lightbox-thumb\" width=\"642\" data-original=\"https://foo.jpg\"/></noscript><img src=\"https://foo.jpg\" data-caption=\"\" data-size=\"normal\" data-rawwidth=\"642\" data-rawheight=\"643\" class=\"origin_image zh-lightbox-thumb lazy\" width=\"642\" data-original=\"https://foo.jpg\" data-actualsrc=\"https://foo.jpg\" data-lazy-status=\"ok\"></figure><h2 id=\"h_399935581_6\" data-into-catalog-status=\"\">bar</h2>", "![](https://foo.jpg){: style=\"width: 642px;\"}\n\n## bar\n"},
	{"52", "<p><span style=\"font-size:18px\">关键代码如下：</span></p> \n<p><span style=\"font-size:18px\"></span></p>\n<pre><code class=\"language-csharp hljs\"><ol class=\"hljs-ln\" style=\"width:930px\"><li><div class=\"hljs-ln-numbers\"><div class=\"hljs-ln-line hljs-ln-n\" data-line-number=\"1\"></div></div><div class=\"hljs-ln-code\"><div class=\"hljs-ln-line\">        <span class=\"hljs-function\"><span class=\"hljs-keyword\">public</span> <span class=\"hljs-keyword\">static</span> <span class=\"hljs-keyword\">string</span> <span class=\"hljs-title\">getFileHash</span>(<span class=\"hljs-params\"><span class=\"hljs-keyword\">string</span> filePath</span>)</span></div></div></li><li><div class=\"hljs-ln-numbers\"><div class=\"hljs-ln-line hljs-ln-n\" data-line-number=\"2\"></div></div><div class=\"hljs-ln-code\"><div class=\"hljs-ln-line\">        {           </div></div></li><li><div class=\"hljs-ln-numbers\"><div class=\"hljs-ln-line hljs-ln-n\" data-line-number=\"3\"></div></div><div class=\"hljs-ln-code\"><div class=\"hljs-ln-line\">            <span class=\"hljs-keyword\">try</span></div></div></li><li><div class=\"hljs-ln-numbers\"><div class=\"hljs-ln-line hljs-ln-n\" data-line-number=\"4\"></div></div><div class=\"hljs-ln-code\"><div class=\"hljs-ln-line\">            {</div></div></li><li><div class=\"hljs-ln-numbers\"><div class=\"hljs-ln-line hljs-ln-n\" data-line-number=\"5\"></div></div><div class=\"hljs-ln-code\"><div class=\"hljs-ln-line\">                FileStream fs = <span class=\"hljs-keyword\">new</span> FileStream(filePath, FileMode.Open);</div></div></li><li><div class=\"hljs-ln-numbers\"><div class=\"hljs-ln-line hljs-ln-n\" data-line-number=\"6\"></div></div><div class=\"hljs-ln-code\"><div class=\"hljs-ln-line\">                <span class=\"hljs-keyword\">int</span> len = (<span class=\"hljs-keyword\">int</span>)fs.Length;</div></div></li><li><div class=\"hljs-ln-numbers\"><div class=\"hljs-ln-line hljs-ln-n\" data-line-number=\"7\"></div></div><div class=\"hljs-ln-code\"><div class=\"hljs-ln-line\">                <span class=\"hljs-keyword\">byte</span>[] data = <span class=\"hljs-keyword\">new</span> <span class=\"hljs-keyword\">byte</span>[len];</div></div></li><li><div class=\"hljs-ln-numbers\"><div class=\"hljs-ln-line hljs-ln-n\" data-line-number=\"8\"></div></div><div class=\"hljs-ln-code\"><div class=\"hljs-ln-line\">                fs.Read(data, <span class=\"hljs-number\">0</span>, len);</div></div></li><li><div class=\"hljs-ln-numbers\"><div class=\"hljs-ln-line hljs-ln-n\" data-line-number=\"9\"></div></div><div class=\"hljs-ln-code\"><div class=\"hljs-ln-line\">                fs.Close();</div></div></li><li><div class=\"hljs-ln-numbers\"><div class=\"hljs-ln-line hljs-ln-n\" data-line-number=\"10\"></div></div><div class=\"hljs-ln-code\"><div class=\"hljs-ln-line\">                MD5 md5 = <span class=\"hljs-keyword\">new</span> MD5CryptoServiceProvider();</div></div></li><li><div class=\"hljs-ln-numbers\"><div class=\"hljs-ln-line hljs-ln-n\" data-line-number=\"11\"></div></div><div class=\"hljs-ln-code\"><div class=\"hljs-ln-line\">                <span class=\"hljs-keyword\">byte</span>[] result = md5.ComputeHash(data);</div></div></li><li><div class=\"hljs-ln-numbers\"><div class=\"hljs-ln-line hljs-ln-n\" data-line-number=\"12\"></div></div><div class=\"hljs-ln-code\"><div class=\"hljs-ln-line\">                <span class=\"hljs-keyword\">string</span> fileMD5 = <span class=\"hljs-string\">\"\"</span>;</div></div></li><li><div class=\"hljs-ln-numbers\"><div class=\"hljs-ln-line hljs-ln-n\" data-line-number=\"13\"></div></div><div class=\"hljs-ln-code\"><div class=\"hljs-ln-line\">                <span class=\"hljs-keyword\">foreach</span> (<span class=\"hljs-keyword\">byte</span> b <span class=\"hljs-keyword\">in</span> result)</div></div></li><li><div class=\"hljs-ln-numbers\"><div class=\"hljs-ln-line hljs-ln-n\" data-line-number=\"14\"></div></div><div class=\"hljs-ln-code\"><div class=\"hljs-ln-line\">                {</div></div></li><li><div class=\"hljs-ln-numbers\"><div class=\"hljs-ln-line hljs-ln-n\" data-line-number=\"15\"></div></div><div class=\"hljs-ln-code\"><div class=\"hljs-ln-line\">                    fileMD5 += Convert.ToString(b, <span class=\"hljs-number\">16</span>);</div></div></li><li><div class=\"hljs-ln-numbers\"><div class=\"hljs-ln-line hljs-ln-n\" data-line-number=\"16\"></div></div><div class=\"hljs-ln-code\"><div class=\"hljs-ln-line\">                }</div></div></li><li><div class=\"hljs-ln-numbers\"><div class=\"hljs-ln-line hljs-ln-n\" data-line-number=\"17\"></div></div><div class=\"hljs-ln-code\"><div class=\"hljs-ln-line\">                <span class=\"hljs-keyword\">return</span> fileMD5;   </div></div></li><li><div class=\"hljs-ln-numbers\"><div class=\"hljs-ln-line hljs-ln-n\" data-line-number=\"18\"></div></div><div class=\"hljs-ln-code\"><div class=\"hljs-ln-line\">            }</div></div></li><li><div class=\"hljs-ln-numbers\"><div class=\"hljs-ln-line hljs-ln-n\" data-line-number=\"19\"></div></div><div class=\"hljs-ln-code\"><div class=\"hljs-ln-line\">            <span class=\"hljs-keyword\">catch</span> (FileNotFoundException e)</div></div></li><li><div class=\"hljs-ln-numbers\"><div class=\"hljs-ln-line hljs-ln-n\" data-line-number=\"20\"></div></div><div class=\"hljs-ln-code\"><div class=\"hljs-ln-line\">            {</div></div></li><li><div class=\"hljs-ln-numbers\"><div class=\"hljs-ln-line hljs-ln-n\" data-line-number=\"21\"></div></div><div class=\"hljs-ln-code\"><div class=\"hljs-ln-line\">                Console.WriteLine(e.Message);</div></div></li><li><div class=\"hljs-ln-numbers\"><div class=\"hljs-ln-line hljs-ln-n\" data-line-number=\"22\"></div></div><div class=\"hljs-ln-code\"><div class=\"hljs-ln-line\">                <span class=\"hljs-keyword\">return</span> <span class=\"hljs-string\">\"\"</span>;</div></div></li><li><div class=\"hljs-ln-numbers\"><div class=\"hljs-ln-line hljs-ln-n\" data-line-number=\"23\"></div></div><div class=\"hljs-ln-code\"><div class=\"hljs-ln-line\">            }                                 </div></div></li><li><div class=\"hljs-ln-numbers\"><div class=\"hljs-ln-line hljs-ln-n\" data-line-number=\"24\"></div></div><div class=\"hljs-ln-code\"><div class=\"hljs-ln-line\">        }</div></div></li></ol></code><div class=\"hljs-button signin\" data-title=\"登录后复制\" data-report-click=\"{&quot;spm&quot;:&quot;1001.2101.3001.4334&quot;}\" onclick=\"hljs.signin(event)\"></div></pre>&nbsp; &nbsp; &nbsp; &nbsp; 调用的时候通过填写制定文件的完整目录，即可获得对应文件的MD5码：", "关键代码如下：\n\n \n```csharp\n        public static string getFileHash(string filePath)\n        {           \n            try\n            {\n                FileStream fs = new FileStream(filePath, FileMode.Open);\n                int len = (int)fs.Length;\n                byte[] data = new byte[len];\n                fs.Read(data, 0, len);\n                fs.Close();\n                MD5 md5 = new MD5CryptoServiceProvider();\n                byte[] result = md5.ComputeHash(data);\n                string fileMD5 = \"\";\n                foreach (byte b in result)\n                {\n                    fileMD5 += Convert.ToString(b, 16);\n                }\n                return fileMD5;   \n            }\n            catch (FileNotFoundException e)\n            {\n                Console.WriteLine(e.Message);\n                return \"\";\n            }                                 \n        }\n```\n\n        调用的时候通过填写制定文件的完整目录，即可获得对应文件的 MD5 码：\n"},
	{"51", "<div class=\"language-js line-numbers-mode\"><pre class=\"language-js\"><code><span class=\"token keyword\">const</span> count <span class=\"token operator\">=</span> <span class=\"token function\">ref</span><span class=\"token punctuation\">(</span><span class=\"token number\">0</span><span class=\"token punctuation\">)</span>\nconsole<span class=\"token punctuation\">.</span><span class=\"token function\">log</span><span class=\"token punctuation\">(</span>count<span class=\"token punctuation\">.</span>value<span class=\"token punctuation\">)</span> <span class=\"token comment\">// 0</span>\n\ncount<span class=\"token punctuation\">.</span>value<span class=\"token operator\">++</span>\nconsole<span class=\"token punctuation\">.</span><span class=\"token function\">log</span><span class=\"token punctuation\">(</span>count<span class=\"token punctuation\">.</span>value<span class=\"token punctuation\">)</span> <span class=\"token comment\">// 1</span>\n</code></pre> <div class=\"line-numbers-wrapper\"><span class=\"line-number\">1</span><br><span class=\"line-number\">2</span><br><span class=\"line-number\">3</span><br><span class=\"line-number\">4</span><br><span class=\"line-number\">5</span><br></div></div>", "```js\nconst count = ref(0)\nconsole.log(count.value) // 0\n\ncount.value++\nconsole.log(count.value) // 1\n```\n"},
	{"50", "<table border=\"0\" cellpadding=\"0\" cellspacing=\"0\" width=\"144\">  <colgroup><col width=\"72\" span=\"2\">  </colgroup><tbody><tr height=\"36\">    <td height=\"36\" class=\"xl65\" width=\"72\">1<br>     2</td>   <td class=\"xl65\" width=\"72\">3<br>     4</td>   </tr> </tbody></table>", "| 1<br/>2 | 3<br/>4 |\n| ----- | ----- |\n"},
	{"49", "<a href=\"https://b3log.org/siyuan\" data-ved=\"2ahUKEwiE1_PRiP3xAhXQtp4KHXw1AcMQFjAAegQIBhAD\" ping=\"/url?sa=t&amp;source=web&amp;rct=j&amp;url=https://b3log.org/siyuan&amp;ved=2ahUKEwiE1_PRiP3xAhXQtp4KHXw1AcMQFjAAegQIBhAD\"><h3 class=\"LC20lb DKV0Md\">思源笔记- 本地优先的个人知识管理系统，支持Markdown 排版 ...</h3></a>", "[思源笔记- 本地优先的个人知识管理系统，支持 Markdown 排版 ...](https://b3log.org/siyuan)\n"},
	{"48", "<figure data-size=\"normal\"><img src=\"foo.png\"></figure><h2>bar</h2>", "![](foo.png)\n\n## bar\n"},
	{"47", "<table border=\"0\" cellpadding=\"0\" cellspacing=\"0\" width=\"207\">\n <colgroup><col width=\"207\">\n </colgroup><tbody><tr height=\"126\">\n\n  <td height=\"126\" class=\"xl66\" width=\"207\">foo<font class=\"font7\">bar</font><font class=\"font6\">；<br>\n    baz</font></td>\n\n </tr>\n</tbody></table>", "| foobar； baz |\n| -------------- |\n"},
	{"46", "<table border=\"0\" cellpadding=\"0\" cellspacing=\"0\" width=\"207\">\n <colgroup><col width=\"207\">\n </colgroup><tbody><tr height=\"180\">\n\n  <td height=\"180\" class=\"xl66\" width=\"207\"><font class=\"font6\">foo<br>\n    </font><font class=\"font7\">bar</font></td>\n\n </tr>\n</tbody></table>", "| foo bar |\n| --------- |\n"},
	{"45", "<ul class=\"dictBing-Cdef\"><li class=\"dictBing-CdefItem\"><span class=\"dictBing-CdefItem_Pos\">adj.</span><span class=\"dictBing-CdefItem_Def\">完全正确；对极了</span></li><li class=\"dictBing-CdefItem\"></li></ul><br class=\"Apple-interchange-newline\">", "* adj.完全正确；对极了\n*\n"},
	{"44", "<table border=\"0\" cellpadding=\"0\" cellspacing=\"0\" width=\"72\">\n <colgroup><col width=\"72\">\n </colgroup><tbody><tr height=\"36\">\n\n  <td height=\"36\" class=\"xl65\" width=\"72\">foo<br>\n    bar</td>\n\n </tr>\n</tbody></table>", "| foo<br/>bar |\n| --------- |\n"},
	{"43", "<!--StartFragment-->foo<strong>bar.</strong><span>baz</span><!--EndFragment-->", "foo**\u200bbar.\u200b**baz\n"},
	{"42", "\n<!--StartFragment--><img class=\"rich_pages img_loading\" data-ratio=\"0.5625\" data-s=\"300,640\" data-src=\"https://foo\" data-type=\"jpeg\" data-w=\"1280\" data-backw=\"578\" data-backh=\"326\" _width=\"100%\" src=\"data:image/gif;base64,dataimge\" crossorigin=\"anonymous\" alt=\"图片\">", "![图片](https://foo)\n"},
	{"41", "<section class=\"code-snippet__fix code-snippet__js\"><pre class=\"code-snippet__js\" data-lang=\"makefile\"><code><span class=\"code-snippet_outer\">foo</span></code><code><span class=\"code-snippet_outer\">bar</span></code></pre></section>", "```\nfoo\nbar\n```\n"},
	{"40", "<!--StartFragment--><strong>foo.</strong><span>bar</span><!--EndFragment-->", "**​foo.​**bar\n"},
	{"39", "<!--StartFragment--><p><strong>Js版</strong></p><pre>&lt;script&gt;\n&nbsp;&nbsp;&nbsp;&nbsp; test = \"你好abc\"\n&nbsp;&nbsp;&nbsp;&nbsp; str = \"\"\n&nbsp;&nbsp;&nbsp;&nbsp; for( i=0;&nbsp;&nbsp;&nbsp; i&lt;test.length; i++ )\n&nbsp;&nbsp;&nbsp;&nbsp; {\n&nbsp;&nbsp;&nbsp;&nbsp;  temp = test.charCodeAt(i).toString(16);\n&nbsp;&nbsp;&nbsp;&nbsp;  str&nbsp;&nbsp;&nbsp; += \"\\\\u\"+ new Array(5-String(temp).length).join(\"0\") +temp;\n&nbsp;&nbsp;&nbsp;&nbsp; }\n&nbsp;&nbsp;&nbsp;&nbsp; document.write (str)\n&lt;/script&gt;</pre><br><!--EndFragment-->", "**Js 版**\n\n```\n<script>\n     test = \"你好abc\"\n     str = \"\"\n     for( i=0;    i<test.length; i++ )\n     {\n      temp = test.charCodeAt(i).toString(16);\n      str    += \"\\\\u\"+ new Array(5-String(temp).length).join(\"0\") +temp;\n     }\n     document.write (str)\n</script>\n```\n"},
	{"38", "<!--StartFragment--><table width=\"778\"><tbody><tr><td class=\"key\">ú</td><td>&amp;uacute;</td><td>&amp;#250;</td><td class=\"key\">û</td><td>&amp;ucirc;</td><td>&amp;#251;</td><td class=\"key\">ü</td><td>&amp;uuml;</td><td>&amp;#252;</td><td class=\"key\">ý</td><td>&amp;yacute;</td><td>&amp;#253;</td><td class=\"key\">þ</td><td>&amp;thorn;</td><td>&amp;#254;</td></tr><tr><td class=\"key\">ÿ</td><td>&amp;yuml;</td></tr></tbody></table><!--EndFragment-->\n", "| ú | &uacute; | &#250; | û | &ucirc; | &#251; | ü | &uuml; | &#252; | ý | &yacute; | &#253; | þ | &thorn; | &#254; |\n| ---- | ---------- | -------- | ---- | --------- | -------- | ---- | -------- | -------- | ---- | ---------- | -------- | ---- | --------- | -------- |\n| ÿ | &yuml;   |\n"},
	{"37", "<!--StartFragment--><table width=\"400\"><tbody><tr><th>显示</th><th>说明</th><th>实体名称</th><th>实体编号</th></tr><tr><td class=\"key\"></td><td>半方大的空白</td><td>&amp;ensp;</td><td>&amp;#8194;</td></tr><tr></tr><tr><td class=\"key\"></td><td>全方大的空白</td><td>&amp;emsp;</td><td>&amp;#8195;</td></tr><tr></tr><tr><td class=\"key\"></td><td>不断行的空白格</td><td>&amp;nbsp;</td><td>&amp;#160;</td></tr><tr><td class=\"key\">&lt;</td><td>小于</td><td>&amp;lt;</td><td>&amp;#60;</td></tr><tr><td class=\"key\">&gt;</td><td>大于</td><td>&amp;gt;</td><td>&amp;#62;</td></tr><tr><td class=\"key\">&amp;</td><td>&amp;符号</td><td>&amp;amp;</td><td>&amp;#38;</td></tr><tr><td class=\"key\">\"</td><td>双引号</td><td>&amp;quot;</td><td>&amp;#34;</td></tr><tr><td class=\"key\">©</td><td>版权</td><td>&amp;copy;</td><td>&amp;#169;</td></tr><tr><td class=\"key\">®</td><td>已注册商标</td><td>&amp;reg;</td><td>&amp;#174;</td></tr><tr><td class=\"key\">™</td><td>商标（美国）</td><td>™</td><td>&amp;#8482;</td></tr><tr></tr><tr><td class=\"key\">×</td><td>乘号</td><td>&amp;times;</td><td>&amp;#215;</td></tr><tr><td class=\"key\">÷</td><td>除号</td><td>&amp;divide;</td><td>&amp;#247;</td></tr></tbody></table><!--EndFragment-->\n", "| 显示 | 说明           | 实体名称 | 实体编号 |\n| ------ | ---------------- | ---------- | ---------- |\n|      | 半方大的空白   | &ensp;   | &#8194;  |\n|      | 全方大的空白   | &emsp;   | &#8195;  |\n|      | 不断行的空白格 | &nbsp;   | &#160;   |\n| <    | 小于           | &lt;     | &#60;    |\n| >    | 大于           | &gt;     | &#62;    |\n| &    | &符号          | &amp;    | &#38;    |\n| \"    | 双引号         | &quot;   | &#34;    |\n| ©   | 版权           | &copy;   | &#169;   |\n| ®   | 已注册商标     | &reg;    | &#174;   |\n| ™   | 商标（美国）   | ™       | &#8482;  |\n| ×   | 乘号           | &times;  | &#215;   |\n| ÷   | 除号           | &divide; | &#247;   |\n"},
	{"36", "<!--StartFragment--><h1><b><span>foo</span></b><b><span><o:p></o:p></span></b></h1><p class=\"MsoNormal\"><img width=\"554\" height=\"337\" src=\"file:///C:\\WINDOWS\\TEMP\\ksohtml15220\\wps4.jpg\"><span><o:p>&nbsp;</o:p></span></p><!--EndFragment-->", "# **foo**\n\n![](file:///C:\\WINDOWS\\TEMP\\ksohtml15220\\wps4.jpg){: style=\"width: 554px;\"}\n"},
	{"35", "<a href=\"bar\">&lt;foo&gt;</a>", "[<foo>](bar)\n"},
	{"34", "<div class=\"gatsby-highlight\" data-language=\"js\"><pre class=\"blog-code language-js\"><span class=\"token keyword\">const</span></pre></div>", "```js\nconst\n```\n"},
	{"33", "<table><tr><td><p>事件编号</p></td><td><p>事件类别(category)</p></td><td><p>事件操作(action)</p></td><td><p>事件标签(label)</p></td><td><p>事件值(value)</p></td></tr><tr><td><p>1</p></td><td><p>合作行业标签</p></td><td><p>点击</p></td><td><p>选择条件</p></td><td></td></tr><tr><td><p>2</p></td><td><p>营销目的标签</p></td><td><p>点击</p></td><td><p>选择条件</p></td><td></td></tr><tr><td><p>3</p></td><td><p>合作资源标签</p></td><td><p>点击</p></td><td><p>选择条件</p></td><td></td></tr><tr><td><p>4</p></td><td><p>合作平台标签</p></td><td><p>点击</p></td><td><p>选择条件</p></td><td></td></tr><tr><td><p>5</p></td><td><p>卡片</p></td><td><p>查看详情</p></td><td><p>案例名称</p></td><td></td></tr><tr><td><p>6</p></td><td><p>卡片</p></td><td><p>点赞</p></td><td><p>案例名称</p></td><td><p>点赞数</p></td></tr><tr><td><p>7</p></td><td><p>卡片</p></td><td><p>取消点赞</p></td><td><p>案例名称</p></td><td><p>点赞数</p></td></tr><tr><td><p>8</p></td><td><p>卡片</p></td><td><p>下载分享图</p></td><td><p>案例名称</p></td><td></td></tr></table>", "| 事件编号 | 事件类别(category) | 事件操作(action) | 事件标签(label) | 事件值(value) |\n| ---------- | -------------------- | ------------------ | ----------------- | --------------- |\n| 1        | 合作行业标签       | 点击             | 选择条件        |               |\n| 2        | 营销目的标签       | 点击             | 选择条件        |               |\n| 3        | 合作资源标签       | 点击             | 选择条件        |               |\n| 4        | 合作平台标签       | 点击             | 选择条件        |               |\n| 5        | 卡片               | 查看详情         | 案例名称        |               |\n| 6        | 卡片               | 点赞             | 案例名称        | 点赞数        |\n| 7        | 卡片               | 取消点赞         | 案例名称        | 点赞数        |\n| 8        | 卡片               | 下载分享图       | 案例名称        |               |\n"},
	{"32", "<ul>\n  <li>咖啡</li>\n  <li>茶\n    <ul>\n    <li>红茶</li>\n    <li>绿茶</li>\n    </ul>\n  </li>\n  <li>牛奶</li>\n</ul>", "* 咖啡\n* 茶\n  * 红茶\n  * 绿茶\n* 牛奶\n"},
	{"32", "<ul>\n<li>foo</li>\n<li>bar\n<ul>\n<li>baz</li>\n<li>baz</li>\n</ul>\n</li>\n<li>bar</li>\n</ul>", "* foo\n* bar\n  * baz\n  * baz\n* bar\n"},
	{"31", "<ul>\n<li>foo\n<ul>\n<li>bar</li>\n</ul>\n</li>\n</ul>", "* foo\n  * bar\n"},
	{"30", "<ul><li>foo</li><li>bar<ul><li>baz</li><li>baz</li></ul></li><li>bar</li></ul>", "* foo\n* bar\n  * baz\n  * baz\n* bar\n"},
	{"29", "<p>测试 <code>name</code> 属性。调用 <code>getValue</code> 时 <code>Method</code></p>", "测试 `name` 属性。调用 `getValue` 时 `Method`\n"},
	{"28", `<html>
	<body>
		<table>
			<tr>
	    	<th>Month</th>
	        <th>Savings</th>
			</tr>
			<tr>
	    	<td>January</td>
	        <td>$100</td>
			</tr>
			<tr>
	    	<td>February</td>
	        <td>$80</td>
			</tr>
		</table>
	</body>
	</html>`, "| Month    | Savings |\n| ---------- | --------- |\n| January  | \\$100   |\n| February | \\$80    |\n"},
	{"27", `<html>
	<body>
	  <table>
	          <thead>
	                  <tr>
	                          <th>Month</th>
	                          <th>Savings</th>
	                  </tr>
					</thead>
	          <tbody>
	                  <tr>
	                          <td>January</td>
	                          <td>$100</td>
	                  </tr>
	                  <tr>
	                          <td>February</td>
	                          <td>$80</td>
	                  </tr>
	          </tbody>
	  </table>
	</body>
	</html>`, "| Month    | Savings |\n| ---------- | --------- |\n| January  | \\$100   |\n| February | \\$80    |\n"},
	{"26", "<table class=\"markdown-reference\"><thead><tr><th>Type</th><th class=\"second-example\">Or</th><th>… to Get</th></tr></thead><tbody><tr><td class=\"preformatted\">*Italic*</td><td class=\"preformatted second-example\">_Italic_</td><td><em>Italic</em></td></tr><tr><td class=\"preformatted\">**Bold**</td><td class=\"preformatted second-example\">__Bold__</td><td><strong>Bold</strong></td></tr><tr><td class=\"preformatted\"># Heading 1</td><td class=\"preformatted second-example\">Heading 1<br>=========</td><td><h1 class=\"smaller-h1\">Heading 1</h1></td></tr><tr><td class=\"preformatted\">## Heading 2</td><td class=\"preformatted second-example\">Heading 2<br>---------</td><td><h2 class=\"smaller-h2\">Heading 2</h2></td></tr><tr><td class=\"preformatted\">[Link](http://a.com)</td><td class=\"preformatted second-example\">[Link][1]<br>⋮<br>[1]: http://b.org</td><td><a href=\"https://commonmark.org/\">Link</a></td></tr><tr><td class=\"preformatted\">![Image](http://url/a.png)</td><td class=\"preformatted second-example\">![Image][1]<br>⋮<br>[1]: http://url/b.jpg</td><td><img src=\"https://commonmark.org/help/images/favicon.png\" width=\"36\" height=\"36\" alt=\"Markdown\"></td></tr><tr><td class=\"preformatted\">&gt; Blockquote</td><td class=\"preformatted second-example\">&nbsp;</td><td><blockquote>Blockquote</blockquote></td></tr><tr><td class=\"preformatted\"><p>* List<br>* List<br>* List</p></td><td class=\"preformatted second-example\"><p>- List<br>- List<br>- List<br></p></td><td><ul><li>List</li><li>List</li><li>List</li></ul></td></tr></tbody></table>", "| Type                       | Or                                   | … to Get                                                                         |\n| ---------------------------- | -------------------------------------- | ----------------------------------------------------------------------------------- |\n| \\*Italic\\*                 | \\_Italic\\_                           | *Italic*                                                                        |\n| \\*\\*Bold\\*\\*               | \\_\\_Bold\\_\\_                         | **Bold**                                                                    |\n| # Heading 1                | Heading 1<br/>=========                  | # Heading 1                                                                      |\n| ## Heading 2               | Heading 2<br/>---------                  | ## Heading 2                                                                     |\n| [Link](http://a.com)       | [Link][1]<br/>⋮<br/>[1]: http://b.org       | [Link](https://commonmark.org/)                                                      |\n| ![Image](http://url/a.png) | ![Image][1]<br/>⋮<br/>[1]: http://url/b.jpg | ![Markdown](https://commonmark.org/help/images/favicon.png){: style=\"width: 36px;\"} |\n| > Blockquote               |                                      | > Blockquote                                                             |\n| \\* List<br/>\\* List<br/>\\* List    | - List<br/>- List<br/>- List                 | \\* List<br />\\* List<br />\\* List                                                 |\n"},
	{"25", "<table class=\"table table-bordered\"><thead class=\"thead-light\"><tr><th>Element</th><th>Markdown Syntax</th></tr></thead><tbody><tr><td><a href=\"https://www.markdownguide.org/extended-syntax/#tables\">Table</a></td><td><code>| Syntax | Description |<br>| ----------- | ----------- |<br>| Header | Title |<br>| Paragraph | Text |</code></td></tr><tr><td><a href=\"https://www.markdownguide.org/extended-syntax/#fenced-code-blocks\">Fenced Code Block</a></td><td><code>```<br>{<br>&nbsp;&nbsp;\"firstName\": \"John\",<br>&nbsp;&nbsp;\"lastName\": \"Smith\",<br>&nbsp;&nbsp;\"age\": 25<br>}<br>```</code></td></tr></tbody></table>", "| Element                                                                             | Markdown Syntax                                                                                                                                     |\n| ------------------------------------------------------------------------------------- | ----------------------------------------------------------------------------------------------------------------------------------------------------- |\n| [Table](https://www.markdownguide.org/extended-syntax/#tables)                         | `\\| Syntax \\| Description \\|\\| ----------- \\| ----------- \\|\\| Header \\| Title \\|\\| Paragraph \\| Text \\|`                                    |\n| [Fenced Code Block](https://www.markdownguide.org/extended-syntax/#fenced-code-blocks) | `` ```{\u00a0\u00a0&#34;firstName&#34;: &#34;John&#34;,\u00a0\u00a0&#34;lastName&#34;: &#34;Smith&#34;,\u00a0\u00a0&#34;age&#34;: 25}``` `` |\n"},
	{"24", "<table><thead><tr><th>Element</th><th>Markdown Syntax</th></tr></thead><tbody><tr><td>Table</td><td><code>| Syntax | Description |<br>| ----------- | ----------- |<br>| Header | Title |<br>| Paragraph | Text |</code></td></tr></tbody></table>", "| Element | Markdown Syntax                                                                                                  |\n| --------- | ------------------------------------------------------------------------------------------------------------------ |\n| Table   | `\\| Syntax \\| Description \\|\\| ----------- \\| ----------- \\|\\| Header \\| Title \\|\\| Paragraph \\| Text \\|` |\n"},
	{"23", "<h2 style=\"box-sizing: border-box; margin-top: 24px; margin-bottom: 16px; font-weight: 600; font-size: 1.5em; line-height: 1.25; padding-bottom: 0.3em; border-bottom: 1px solid rgb(234, 236, 239); color: rgb(36, 41, 46); font-family: -apple-system, BlinkMacSystemFont, &quot;Segoe UI&quot;, Helvetica, Arial, sans-serif, &quot;Apple Color Emoji&quot;, &quot;Segoe UI Emoji&quot;; font-style: normal; font-variant-ligatures: normal; font-variant-caps: normal; letter-spacing: normal; orphans: 2; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: 2; word-spacing: 0px; -webkit-text-stroke-width: 0px; background-color: rgb(255, 255, 255); text-decoration-style: initial; text-decoration-color: initial;\"><g-emoji class=\"g-emoji\" alias=\"m\" fallback-src=\"https://github.githubassets.com/images/icons/emoji/unicode/24c2.png\" style=\"box-sizing: border-box; font-family: &quot;Apple Color Emoji&quot;, &quot;Segoe UI&quot;, &quot;Segoe UI Emoji&quot;, &quot;Segoe UI Symbol&quot;; font-size: 1.2em; font-weight: 400; line-height: 20px; vertical-align: middle; font-style: normal !important;\">Ⓜ️</g-emoji><span> </span>Markdown User Guide</h2>", "## Ⓜ️ Markdown User Guide\n"},
	{"22", "<div class=\"highlight highlight-source-shell\"><pre>npm install vditor --save</pre></div>", "```shell\nnpm install vditor --save\n```\n"},
	{"21", "<h4><a id=\"user-content-id\" class=\"anchor\" aria-hidden=\"true\" href=\"https://github.com/Vanessa219/vditor/blob/master/README.md#id\"><svg class=\"octicon octicon-link\" viewBox=\"0 0 16 16\" version=\"1.1\" width=\"16\" height=\"16\" aria-hidden=\"true\"><path fill-rule=\"evenodd\" d=\"M4 9h1v1H4c-1.5 0-3-1.69-3-3.5S2.55 3 4 3h4c1.45 0 3 1.69 3 3.5 0 1.41-.91 2.72-2 3.25V8.59c.58-.45 1-1.27 1-2.09C10 5.22 8.98 4 8 4H4c-.98 0-2 1.22-2 2.5S3 9 4 9zm9-3h-1v1h1c1 0 2 1.22 2 2.5S13.98 12 13 12H9c-.98 0-2-1.22-2-2.5 0-.83.42-1.64 1-2.09V6.25c-1.09.53-2 1.84-2 3.25C6 11.31 7.55 13 9 13h4c1.45 0 3-1.69 3-3.5S14.5 6 13 6z\"></path></svg></a>id</h4>", "#### id\n"},
	{"20", "<h2 id=\"whats-markdown\">What’s Markdown?<a class=\"anchorjs-link \" aria-label=\"Anchor\" data-anchorjs-icon=\"\uE9CB\" href=\"https://www.markdownguide.org/getting-started/#whats-markdown\"></a></h2>", "## What’s Markdown?\n"},
	{"19", "<pre><span>`foo`</span></pre>", "```\n`foo`\n```\n"},
	{"18", "<del>foo</del>", "~~foo~~\n"},
	{"17", "<img src=\"bar.png\" alt=\"foo\">", "![foo](bar.png)\n"},
	{"16", "foo<br>bar", "foo\nbar\n"},
	{"15", "<em>foo</em>", "*foo*\n"},
	{"14", "<hr>", "---\n"},
	{"13", "<blockquote>foo</blockquote>", "> foo\n"},
	{"12", "<h1>foo</h1>", "# foo\n"},
	{"11", "<li>foo</li><li>bar</li>", "* foo\n* bar\n"},
	{"10", `<p data-block="0">foo'%'bar</p>`, "foo'%'bar\n"},
	{"9", `<code class="language-text">&gt;</code>`, "`>`\n"},
	{"8", `<div><a href="/bar">foo</a></div>`, "[foo](/bar)\n"},
	{"7", `<ul><li><p>Java</p><ul><li><p>Spring</p></li></ul></li></ul>`, "* Java\n  * Spring\n"},
	{"6", `<!--StartFragment--><p>这是一篇讲解如何正确使用<span>&nbsp;</span><strong>Markdown</strong><span>&nbsp;</span>的排版示例，学会这个很有必要，能让你的文章有更佳清晰的排版。</p><!--EndFragment-->`, "这是一篇讲解如何正确使用 **Markdown** 的排版示例，学会这个很有必要，能让你的文章有更佳清晰的排版。\n"},
	{"5", `<!--StartFragment--><ul><li><input checked="" disabled="" type="checkbox"><span>&nbsp;</span>发布 Solo</li></ul><!--EndFragment-->`, "* [X] 发布 Solo\n"},
	{"4", "<span>&nbsp;</span>发布 Solo", "发布 Solo\n"},
	{"3", "<pre><ul><li>foo</li></ul></pre>", "<pre><ul><li><p>foo</p></li></ul></pre>\n"},
	{"2", "<pre><span>//&#32;Lute&#32;-&#32;A&#32;structured&#32;markdown&#32;engine.<br></span><span>//&#32;Copyright&#32;(c)&#32;2019-present,&#32;b3log.org</span></pre>", "```\n// Lute - A structured markdown engine.\n// Copyright (c) 2019-present, b3log.org\n```\n"},
	{"1", "<meta charset='utf-8'><span>foo</span>", "foo\n"},
	{"0", "<html><body><!--StartFragment--><p>foo</p><!--EndFragment--></body></html>", "foo\n"},
}

func TestHTML2Md(t *testing.T) {
	luteEngine := lute.New()
	luteEngine.SetAutoSpace(true)
	luteEngine.SetSup(true)
	luteEngine.SetSub(true)
	luteEngine.SetMark(true)
	luteEngine.SetGFMStrikethrough(true)
	luteEngine.SetInlineAsterisk(true)
	luteEngine.SetInlineUnderscore(true)
	luteEngine.SetKramdownIAL(true)
	for _, test := range html2MdTests {
		md := luteEngine.HTML2Md(test.from)
		if test.to != md {
			t.Fatalf("test case [%s] failed\nexpected\n\t%q\ngot\n\t%q\noriginal html\n\t%q", test.name, test.to, md, test.from)
		}
	}
}

var html2MdDisableSyntaxTests = []parseTest{

	{"9", "<section style=\"-webkit-tap-highlight-color: transparent;margin-bottom: 8px;outline: 0px;letter-spacing: 0.578px;font-family: system-ui, -apple-system, BlinkMacSystemFont, &quot;Helvetica Neue&quot;, &quot;PingFang SC&quot;, &quot;Hiragino Sans GB&quot;, &quot;Microsoft YaHei UI&quot;, &quot;Microsoft YaHei&quot;, Arial, sans-serif;background-color: rgb(255, 255, 255);text-align: center;\"><span style=\"-webkit-tap-highlight-color: transparent;outline: 0px;font-size: 13px;\"><span style=\"-webkit-tap-highlight-color: transparent;outline: 0px;color: rgb(13, 52, 117);\"><em style=\"-webkit-tap-highlight-color: transparent;outline: 0px;\"><strong style=\"-webkit-tap-highlight-color: transparent;outline: 0px;\"><span style=\"-webkit-tap-highlight-color: transparent;outline: 0px;letter-spacing: 0.5px;text-decoration-style: solid;text-decoration-color: rgb(51, 51, 51);\">现在扫码<strong style=\"-webkit-tap-highlight-color: transparent;outline: 0px;font-size: 14px;\"><em style=\"-webkit-tap-highlight-color: transparent;outline: 0px;\">👇</em></strong></span></strong></em></span></span><span style=\"-webkit-tap-highlight-color: transparent;outline: 0px;font-size: 13px;\"><span style=\"-webkit-tap-highlight-color: transparent;outline: 0px;color: rgb(255, 0, 0);text-decoration: underline;\"><em style=\"-webkit-tap-highlight-color: transparent;outline: 0px;\"><strong style=\"-webkit-tap-highlight-color: transparent;outline: 0px;\"><span style=\"-webkit-tap-highlight-color: transparent;outline: 0px;letter-spacing: 0.5px;\">优先帮你解决卖房难题，</span></strong></em></span></span><span style=\"-webkit-tap-highlight-color: transparent;outline: 0px;font-size: 13px;\"><span style=\"-webkit-tap-highlight-color: transparent;outline: 0px;color: rgb(255, 0, 0);text-decoration: underline;\"><em style=\"-webkit-tap-highlight-color: transparent;outline: 0px;\"><strong style=\"-webkit-tap-highlight-color: transparent;outline: 0px;\"><span style=\"-webkit-tap-highlight-color: transparent;outline: 0px;letter-spacing: 0.5px;\">最后5个名额</span></strong></em></span></span><span style=\"-webkit-tap-highlight-color: transparent;outline: 0px;color: rgb(255, 0, 0);font-size: 13px;\"><em style=\"-webkit-tap-highlight-color: transparent;outline: 0px;\"><strong style=\"-webkit-tap-highlight-color: transparent;outline: 0px;\"><span style=\"-webkit-tap-highlight-color: transparent;outline: 0px;letter-spacing: 0.5px;\">！</span></strong></em></span></section>", "<em><strong>现在扫码<strong><em>👇</em></strong></strong></em><em><strong>优先帮你解决卖房难题，</strong></em><em><strong>最后 5 个名额</strong></em><em><strong>！</strong></em>\n"},
	{"8", "<span>这两个语素最开始</span><sup data-text=\"大概是春秋战国音吧。\" data-url=\"\" data-numero=\"1\" data-draft-node=\"inline\" data-draft-type=\"reference\" data-tooltip=\"大概是春秋战国音吧。\" data-tooltip-richtext=\"1\" data-tooltip-preset=\"white\" data-tooltip-classname=\"ztext-reference-tooltip\"><a id=\"ref_1_0\" href=\"https://www.zhihu.com/question/2127166482#ref_1\" data-reference-link=\"true\" aria-labelledby=\"ref_1\">[1]</a></sup><span>都很拟声</span>", "这两个语素最开始<sup>[[1]](https://www.zhihu.com/question/2127166482#ref_1)</sup>都很拟声\n"},
	{"7", "<strong><em>foo</em></strong> <em><strong>bar</strong></em>", "<strong><em>foo</em></strong> <em><strong>bar</strong></em>\n"},
	{"6", "<kbd>foo</kbd>", "<kbd>foo</kbd>\n"},
	{"5", "<mark>foo</mark>", "<mark>foo</mark>\n"},
	{"4", "<u>foo</u>", "<u>foo</u>\n"},
	{"3", "<s>foo</s> <del>bar</del> <strike>baz</strike>", "<s>foo</s> <s>bar</s> <s>baz</s>\n"},
	{"2", "foo<strong>bar</strong> <b>baz</b>", "foo<strong>bar</strong> <strong>baz</strong>\n"},
	{"1", "foo<em>bar</em> <i>baz</i>", "foo<em>bar</em> <em>baz</em>\n"},
	{"0", "foo<sup>bar</sup></span><sub>baz</sub>", "foo<sup>bar</sup><sub>baz</sub>\n"},
}

func TestHTML2MdDisableSyntax(t *testing.T) {
	luteEngine := lute.New()
	luteEngine.SetAutoSpace(true)
	luteEngine.SetSup(false)
	luteEngine.SetSub(false)
	luteEngine.SetMark(false)
	luteEngine.SetGFMStrikethrough(false)
	luteEngine.SetInlineAsterisk(false)
	luteEngine.SetInlineUnderscore(false)
	luteEngine.SetHTMLTag2TextMark(true)
	for _, test := range html2MdDisableSyntaxTests {
		md := luteEngine.HTML2Md(test.from)
		if test.to != md {
			t.Fatalf("test case [%s] failed\nexpected\n\t%q\ngot\n\t%q\noriginal html\n\t%q", test.name, test.to, md, test.from)
		}
	}
}
