Find the start of a #region
How to jump to the region header from the endregion tag in c# visual studio 2012?
CSS :after not adding content to certain elements What are the differences between Iron Man and War Machine armours ?  In the movies, it seems that they are the same, except the War Machine armour features more heavy weapons. But if they are the same, why wouldn't Tony Stark use the War Machine armour?  Do they have different characteristics (like strength, resistance, flight time...)?  I am looking for answers from the movies and/or the comics. Is it common to review papers assigned to your supervisor? Is it common to supervisors to email their students papers to review (which were apparently assigned to the supervisor, and not to the student). The field is Computer Science, but I  would also like to hear from the other fields. I'm new to blender and trying to model the blade of my helicopter and can't figure out how to make an edge curved (for the red tip and selected edge). The object is a plane, with one loop cut. I attempted making a bevel Ctrl B, but nothing happens (A dotted line appears attached to the cursor, moving does nothing, left-clicking does nothing).  also I cant add a curve modifier, just says its disabled. What is the correct way to model this? Can I combine extension tubes and macro filters at once to give better macros? Let $R$ be an rng. (There may be no unity)  Then, does there always exist a ring(with unity) $A$ such that $R$ is a subrng of $A$? I know from the  that it is not possible to introduce direct abbreviations like \newcommand{\bal}{\begin{align}} % doesn't work \newcommand{\eal}{\end{align}}   % doesn't work  or \newcommand{\bal}{\align}    % doesn't work \newcommand{\eal}{\endalign} % doesn't work  What is puzzling me is that \newenvironment{foo}{\align}{\endalign}  does work, at least if one is well-behaved enough to diligently type \begin{foo}...\end{foo}, since \foo...\endfoo won't work either. I'd really appreciate some help to shed some light on what is going on behind the scenes :-) what is the total number of distinct arrangements of $n$ oranges and $n$ apples around a round table? I have no idea how to go about. How can I fade tabs in & out with the Twitter Bootstrap framework? I've seen videos of some folks having several armor sets (4 is the most I've seen so far) standing about on their settlement. I'm wondering if having too many would cause some sets to disappear. They're not like guns/items that you can safely store in settlement crates, the suits kind of just... stand around. (I know there's the extra step of taking out the fusion cores, so that NPC's don't use them.)  Is there a limit to the number of Power Armor sets you can keep? I have some data which looks like:  sampleA    ATGC    10   100 sampleA    ATGC    120  230 sampleA    ATGC    200  110   I want to print the min and max using the values in both column 3 and 4. So my output should look like:  sampleA   10  230   Thanks in advance Compute the integral $\int_{A} x^m y^n z^p (1-x-y-z)^q dx dy dz$ Under what assumptions can a semigroup $(S,*)$ be embedded into a group? Short story or novel from the 1970s or before about two warring alien tribes I'm level 16 which makes battling many Draugr Wrights hard. My defense is just way too low, and I don't have enough time or strong enough magic to take them out.   My one-handed skill is at 62 and my strongest weapon does 33+10 enchanted damage. Are there any ways to level up easily? Rotating hatch labels based on orientation changes in Data Driven Pages Strip maps? I've created a strip map for a linear feature and have it loaded as a data driven page.  I want to show stationing for the line.  The stationing displays properly on the first data driven page but on each subsequent page the stationing labels get messed up as the map orientation changes. I want the stationing labels perpendicular to the linear feature as shown in the first image.  The tick marks seem to rotate and stay perpendicular to the line but the labels won't.  How can I fix this? How to install League of Legends in Ubuntu Generalized RBF Kernels There is the notion of Generalized RBF Kernels, for example in "Towards Optimal Bag-of-Features for Object Categorization and Semantic Video Retrieval" from Jiang (1) or in formula (2.72) in  (2).  They define: Gen. RBF Kernel: $e^{-pd(x,y)}$, where (1) says d can be any distance function and (2) requires it to be a metric.  I now have been wondering for a long time: Is a function defined by $e^{-pd(x,y)}$ where d is a metric always a Mercer's Kernel? I think in (2) it sounds like it, but if it were true, not many people know of it, since they are still looking to prove that $e^{-EMD(x,y)}$ is a kernel, where EMD = Earth Mover's Distance, which is a metric.  If its not a Mercer's Kernel - do you know of any counter example? Number of possible marriage arrangements if Marriage Condition is satisfied Suppose I have a set of $n$ boys and each subset of $1\leqslant k \leqslant n$ boys knows at least $k$ girls then this means that the set of boys $B$ satisfies the marriage condition.  I am doing an exercise from a Graph Theory book and it says we can show by induction on $n$ that the number of possible marriage arrangements is $\geqslant t!$ if every individual boy knows at least $t \leqslant n$ girls or there are $\geqslant t!/(t-n)!$ possible marriages if each individual boy knows at least $t&gt;n$ girls.   I am struggling to see how the induction hypothesis can be implemented to prove the $n+1$ case. When you swap from the $n$ to $n+1$ case the conditions change and I can't see the link between them.  Would anyone be able to point me in the right direction? Fundamental Theorem of Algebra - an elementary complex analysis proof? We begin by assuming that a non-constant complex polynomial $$p(z)=a_n z^n+a_{n-1}z^{n-1}+...+a_1 z+a_0,$$ where $a_0 \neq 0$, doesn't vanish in $\mathbb{C}$. Therefore $1/p$ is also an analytical function everywhere. Note that $(p(z)-a_0)/z$ is a polynomial and therefore, due to Cauchy's theorem, the following integral must be zero.  $$\int_{S_r^1}\frac{(p(z)-a_0)/z}{p(z)}dz=\int_{S_r^1}\frac{a_nz^{n-1}+a_{n-1}z^{n-2}+...+a_1}{a_nz^n+a_{n-1}z^{n-1}+...+a_1 z+a_0}dz=0.$$  On the other hand  $$\int_{S_r^1}\frac{a_nz^{n-1}+a_{n-1}z^{n-2}+...+a_1}{a_nz^n+a_{n-1}z^{n-1}+...+a_1 z+a_0}dz$$  $$=\int_{0}^{2\pi}\frac{a_n(re^{i\theta})^{n-1}+a_{n-1}(re^{i\theta})^{n-2}+...+a_1}{a_n(re^{\theta})^n+a_{n-1}(re^{i\theta})^{n-1}+...+a_1 (re^{i\theta})+a_0}(ire^{i\theta})d\theta$$  $$=\int_{0}^{2\pi}i d\theta - \int_{0}^{2\pi}\frac{a_0 i}{a_n(re^{i\theta})^n+a_{n-1}(re^{i\theta})^{n-1}+...+a_1 (re^{i\theta})+a_0}d\theta$$ $$=2\pi i -\int_{0}^{2\pi}\frac{a_0i}{p(re^{i\theta})}d\theta.$$  Let $r \rightarrow \infty$ and the integral approaches value $2\pi i$ - a contradiction. Therefore $1/p$ can't be entire and $p$ must vanish somewhere in the complex plane.  EDIT: I have changed this post and deleted the idea that the integral $\int_{\partial D_r}\frac{(p(z)-a_0)/z}{p(z)}dz=0$ could be evaluated with the fundamental theorem of calculus. Now, as it stands, this proof is essentially the same as the one that Mr. José Carlos Santos points out in his comment.