+1})(c+H^2),$
then $M$ is homeomorphic to a sphere.\\
$(ii)$ if $n=4,6,8$,  and $\frac{Ric^{[s]}_{\max}}{s}\leq(n-2+\frac{4}{n+2})(c+H^2)$, then $M$ is homeomorphic to a sphere.\\
Here $s$ is some integer in $[1, \frac{n+2}{2}]$.}\\\\
\textbf{Proof.} It follows from the assumption and the proof of Theorem 3.6 that  $H_{2}(M;Z)=H_{3}(M;Z)=0$ for $n=5$, and $$H_{q}(M;Z)=H_{n-q}(M;Z)=0$$ for $n=4$, $6$, $8$, where $q\in[2,\frac{n}{2}]$. Moreover, we have
\begin{eqnarray}
Ric_{\min}&\geq& R-(n-1)\frac{Ric^{[l]}_{\max}}{l}\nonumber\\
&>& n(n-2)(c+H^2)-(n-1)(n-2+\frac{4}{n+2})(c+H^2)\nonumber\\
&=&\frac{n(n-4)}{n+2}(c+H^2)\nonumber\\
&>&0.
\end{eqnarray}
Then a similar argument as in the proof of Theorem 3.2 shows that $$H_{1}(M;Z)=H_{n-1}(M;Z)=0,$$ and $M$ is simply connected. Therefore, $M$ is homeomorphic to a sphere. This proves Theorem 3.7.\qed\\\\
\textbf{Proof of Theorem 1.2.}  Choosing $s=1$, we get the conclusion from Theorems 3.6 and 3.7.\qed\\

Motivated by Theorem 1.1, Example 1.3, the convergence results of Brendle and Schoen for
Ricci flow \cite{Brendle, Brendle0, Brendle2}, and the differentiable sphere theorems for submanifolds with positive Ricci curvature proved in \cite{XG2, XT}, we propose the following conjecture.\\\\
\textbf{Conjecture 3.8.} \emph{Let $M$ be an $n(\geq 5)$-dimensional compact
submanifold in the space form $F^{n+p}(c)$ with $c+H^2>0$.
 If $n$ is odd, and  $$Ric_{M}>(n-2-\frac{2}{n-1})(c+H^2),$$ then
$M$ is diffeomorphic to $S^n$.}\\

To verify Conjecture 3.8,  we hope to prove the
following conjecture on the normalized Ricci flow.\\\\
\textbf{Conjecture 3.9.} \emph{Let $(M,g_0)$ be an
$n(\geq5)$-dimensional compact submanifold in an $(n+p)$-dimensional
space form $F^{n+p}(c)$ with $c+H^2>0$. If $n$ is odd, and the Ricci curvature of
$M$ satisfies
$$Ric_{M} >
(n-2-\frac{2}{n-1})(c+H^2),$$
then the normalized Ricci flow with initial metric
$g_0$
$$\frac{\partial}{\partial t}g(t) = -2Ric_{g(t)} +\frac{2}{n}
r_{g(t)}g(t),$$ exists for all time and converges to a constant
curvature metric as $t\rightarrow\infty$. Moreover, $M$ is
diffeomorphic to a spherical space form.}\\


The Deep Secrets Of The Earth puzzle is one of the more difficult puzzles in the game. It requires you to align two panels, each with five rings in them, in the correct order to unlock the path. The puzzle is found in the “Deep Secrets Of The Earth” mission and cannot be missed. Use the following steps to solve the puzzle. When you enter the room, there will be two panels. The panel on the left can be solved right away, but the one on the right side is missing a ring. To align the panel on the left, use Focus Device (R3) on the wall panel to the left to see the correct combination. The direction of the red lines will indicate the alignment of the ring. The rings need to be aligned in the following sequence from left to right: Left, Up, Left, Down, Right. Once the puzzle on the left is completed, the bunker door will open. Proceed upstairs to get an emitter. Then, go back downstairs and install it in the panel on the right side. After the panel is in place, use Focus Device to check the solution of the panel. However, the rings will have been turned around so their actual alignment is reversed. The ones facing up should be facing down and vice versa. The following is the correct combination to align this panel: Down, Left, Up, Right, Down. Once both panels are aligned, the puzzle will be completed.
A vegetable that does not require special care, but is liked by many. Zucchini is especially appreciated by nutritionists - it is low-calorie and very healthy. It was brought to our area from northern Mexico, where only seeds were used for food. It came to Europe at the beginning of the 16th century and was originally grown in botanical gardens.
Only in the 18th century, the Italians began to use its unripe fruits for food. Since then, he has slowly gained popularity. Today, zucchini is already used in food by many. But in order to enjoy this tasty and healthy vegetable, you need to grow it.
How to choose zucchini seeds for planting?
Zucchini is a plant of the pumpkin family. Its fruits are oblong in shape and in different shades - from almost black to pure white. Today, two varieties of this plant are known - these are ordinary zucchini and zucchini. They belong to the same species, but they are not quite similar to each other in physical properties. Zucchini have a greater number of female flowers and, due to this, an excellent yield.
They have a tender and juicy pulp, and the skin does not coarse for a long time, compared to ordinary varieties of zucchini. However, let's return to the choice of seeds for planting. There are many varieties of this healthy vegetable. You need to choose them depending on what kind of crop and when you plan to get it. It is optimal to have several bushes of different varieties, in which case you will be provided with zucchini from June to October. What to look for when choosing seeds? If you buy them from a store, then to the manufacturer. It is better to purchase seeds from those firms with whose products you are already familiar. Many people choose to grow vegetables for seeds. There are some nuances here.
There are many hybrids that are not suitable for seed production. Therefore, if you decide to get yours, then know that they can only be successful if it was not a hybrid plant. Zucchini seeds are very well stored and do not lose their germination up to 8 years. And even after the expiration date, they can ascend normally.
Gardener notes - Pumpkin: planting and care.
Read the features of growing tomatoes in greenhouses here.
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Planting - seeds or seedlings?
Zucchini is a rather thermophilic plant and does not withstand the slightest frost, so it is better to grow them in seedlings. This requires peat pots and specialized soil. But if you do not want to spend extra money, then you can prepare the soil yourself. You need to mix compost, peat and garden soil in equal proportions.
Then the prepared soil is moistened, and one grain is laid out in each of the pots, immersed in the soil to a depth of 2-3 cm. Growing seedlings requires a certain temperature regime - from 10 to 22 degrees and good illumination.
With a lack of light, the plants will stretch and turn out thinner. After the sprouts appear, if necessary, they are watered with water at room temperature. During the cultivation of seedlings, it must be fed. It is best to use Kemir's or Agricola's complex fertilizers designed for pumpkin crops for such purposes.
In this case, you do not have to measure the dose for each element and add them separately. In the early days, the plants must be treated with one of the growth stimulants. It will prevent the seedlings from stretching and make them strong and resistant to disease.
Zucchini prefer light nutritious soil and do not tolerate stagnant moisture. Therefore, clay soils are not suitable for them. Moreover, the preparation of the beds for planting must be carried out in the fall, removing the previous crops. It is dug up for the winter, and in the spring it is leveled with a rake, while adding compost and