I would like to draw the following picture. I have tried my best but nothing work. My document class memoir. thanks.
I feel intimidated in learning TikZ. I was wondering if there are some nice materials (or just your replies) at different level:   for providing big picture, which is important to beginners to not lose direction during learning. for comprehensive reference.   Examples are important, but only examples are not always clear for understanding the big picture and organization.
Does any one know the exact expression of the integral,  $$E_n(s)=\int_0^\infty \frac{r^{n-1}}{(1+r^2)^{\frac{s}{2}}}\,dr~~~~s&gt;n, n\in \mathbb{N}$$ or more generally, $$E_a(s)=\int_0^\infty \frac{r^{a-1}}{(1+r^2)^{\frac{s}{2}}}\,dr~~~~s&gt;a, a\in \mathbb{R}$$ For the special case $s=n, n+2$ I find out by induction that $$ E_{n-1}(n)=\frac{\omega_{n-1}}{2\omega_{n-2}}~~\text{and}~~E_{n-1}(n+2)=\frac{\omega_{n-1}}{2n\omega_{n-2}}. $$ where $\omega_{n-1} = \frac{\pi^{\frac{n}{2}}}{\Gamma(\frac{n}{2})}$ is the  surface measure of the n-dimensional sphere of $\mathbb{R}^n$. Further result is welcome Sublime Text 3 System Package Location? Add different materials to different parts of a mesh? Uncountable $\sigma$-algebra I'm stuck on the following problem (Source: Real Analysis for Graduate Students; Exercise 2.6; ):     Suppose $\mathcal A$ is a $\sigma$-algebra with the property that whenever $A \in \mathcal A$, there exists $B, C \in \mathcal A$ with $B \cap C = \emptyset$, $B \cup C = A$, and neither $B$ nor $C$ is empty. Prove that $\mathcal A$ is uncountable.   I think there is the added assumption that this is only true for $A \in \mathcal A$ having at least two elements, so it doesn't hold for singletons and the emptyset?  I tried to show this by way of contradiction and say that $\mathcal A = \{A_k\}$ is countable, but I didn't see how this could get me to a contradiction.  The other approach I tried was to look at $X = B_1 \cup C_1$ where $B_1 \cap C_1 = \emptyset$, then look at $B_1 = B_2 \cup C_2$ where $B_2 \cap C_2 = \emptyset$ and so on. If I look at the $C_k$'s they are pairwise disjoint and I either have a finite number of them or an infinite number of them in which case I've created a countable sequence of pairwise disjoint nonempty elements of $\mathcal A$. This path looked promising, but I couldn't see what to do next. Any ideas?  As a secondary question: I think this result is supposed to be used to show that if $\mathcal A$ is a $\sigma$-algebra with infinitely many elements, then it's uncountable, but I wasn't able to show that the property mentioned above (the one I'm trying to show) was satisfied in this case. How can I require a generic parameter to be an enum that implements an interface? Laptop randomly waking up = Hibernate / Low Battery? What does the size of the font translate to exactly? I have a 40 pixel font that I'm trying to translate into custom images. I'm trying to match the size of the image exactly, but I'm having some problems getting exactly the right size. Basically, what it comes down to is this. When a font says it is X pixels, what does this physically mean? that looks an interesting book; they look good guys That looks an interesting book. ()   ‘Look’ can take an NP for its complement by OALD. Now what I’m wondering about is if a person/people could be a subject in the structure, for instance, “They look good guys.” If we can’t, does it have to be “They look like good guys”? Canonical question: One has a Windows 10 installed with display language A, but uses keyboard layout B. What does one need to do, to stop Windows from automatically adding an unwanted keyboard layout from language A to one's system?  My example: I have a Windows 10 in English and I'm using a Slovenian keyboard layout. And this is working just fine, until I run a certain program that Windows ever so intelligently thinks needs an US keyboard layout. Windows adds this unwanted layout automatically, switches to it and doesn't remove it afterwards. The new layout isn't even listed in installed layouts. The only way to remove it after it appears, is to manually add it as a keyboard layout and remove it.  It seems that's a common problem for many people but after many hours of googling, I just couldn't find a good solution for it... It would be perfectly fine with me if I could just completely remove the US keyboard layout from my system, but if I do that, the keyboard stops working in some programs altogether.  Programs that I or other people have this problem with: ICQ, some versions of Microsoft Office (lol), games based on Source engine, some versions of UltraVNC, Adobe CC Suite, and the list goes on. How are the AES S-Boxes calculated? How to find the magnetic field due to a revolving electron of hydrogen atom in first orbit Additional needed documents for UK trip if someone will shoulder all expenses Someone (a relative) from the UK (already a naturalized British Citizen) will be financing my trip, as well as taking care of my accommodation. What are the documents I need to submit aside from bank statements? Does the sponsor need to fill-out the Sponsorship Undertaking Form? ()  something to consider from my question: -my relative is a naturalized citizen in the UK. Is proof of naturalization needed? Can you enter UK later than intended date of travel on the visa application? Conditionally enabling systemd files through Debian packaging I've created a  package which installs a service.  On our embedded devices, I want this package to automatically enable the service.  On our developer workstations, I want the developers to systemctl start foo manually (it's a heavy service, and so it just consumes resources if run all of the time on a desktop environment).  How can I go about prompting the user for their decision during the apt-get step? Is that the best solution?  Note, I've created the package using dh_make and debhelper and enabled it with:  %:     dh $@ --with=systemd  override_dh_systemd_enable:     dh_systemd_enable --name=foo foo.service Using a Sprite image with input "Scaled $L^p$ norm" and geometric mean Retrieving Current Location and Zip using Geolocation Button How to resolve "Failed to download repository information"? Whenever I try to install anything with the Ubuntu Software Center, the following error appears.     Failed to download repository information      Check your Internet connection.      E:Unable to parse package file /var/lib/apt/lists/partial/archive.ubuntu.com_ubuntu_dists_precise_multiverse_i18n_Index (1) Repeatedly rolling a six sided die four times and summing the highest three results gives you a distribution with what mean and standard deviation?  I've only taken AP statistics, but I would like to learn how to do this. Is it possible to make LaTeX mark overfull boxes in the output, for example by drawing red rectangles in the PDF where the boxes overflow? The purpose -- to more easily "see" where the problems are in the output.