Finding the Limiting Distribution of an order statistic
Consistency of an order statistic in exponential distribution
What measures does Cognito Forms take to ensure Privacy/ Security Level for Completed Forms/ User Data? Some forms may contain confidential information - even something basic like where a person lives.   What measures do Cognito Forms take to ensure that data stored within its site is secure? Where are the Unity desktop wallpapers located? Please see the picture below. Where are the Unity desktop wallpapers located? Let $G$ be a finite group and $F$ a field with $\mathrm{char}(F)=0$ or coprime to $|G|$. Let $V$ be a $FG$-module in a way that every $ FG$-homomorphism $ f : V \to V $ is given by $f(x)= \lambda x $. Then $V$ is irreducible.   I already managed to proof this by contradiction, using Maschke's Theorem. We can  write $V$ as $U\oplus W$ and get a $FG$-homomorphism $\pi:U\oplus W \to U\oplus W$, $\pi (u+w)=u$, then $\pi(u+w)=\lambda (u+w)=u $ then either $U$ or $W$ are trivial and thus $V$ is irreducible.  My question is if this statements still holds if the characterictic of $F$ divides the order of $G$, since I only used this fact in my proof to use Maschke's theorem. Idempotent linear operators are projections How to prevent mail from our website going into spam mail of users? I work for an educational services company based in India. We've around one million students enrolled as users. We're frequently facing the problem of our bulk mailers regarding upcoming exams, new product launches and promotions going into spam mail folders of the students. Is the problem in the headlines? Or where else? what can we do to reduce this number?   This is killing us, we cannot have an impossibly large precentage of mails not being opened..Please help. Cannot get grub menu to timeout (or go away) Why is it dangerous use a coiled extension cord Let $U\subset\mathbb R^3$ be an open set, and $f:U\to \mathbb R$ be a smooth function. Suppose that the level set $S=f^{-1}(\{0\})$ is non-empty, and that at each $p\in S,$ the gradient $\overrightarrow \nabla f(p)$ is not the zero vector. Then $S$ is a smooth two-dimensional surface in $U$, and $p\mapsto \overrightarrow \eta(p)=\frac{1}{||\overrightarrow \nabla f(p)||}\overrightarrow \nabla f(p)$ defines a smooth unit-length normal vector field along $S$. At each $x\in U,$ write $H(f)_{(x)}$ for the $3\times 3$ Hessian matrix specified by $$(H(f)_{(x)})_{ij}=\frac{\partial^2f}{\partial x_i\partial x_j}(x).$$   Show that, at each $p\in S$, the second fundamental form $II_p: T_p(s)\times T_p(s)\to \mathbb R$ is the symmetric bilinear map    $$II_p(\overrightarrow v,\overrightarrow w)=\frac{-1}{||\overrightarrow \nabla f(p)||}\overrightarrow v\cdot H(f)_{(p)}\overrightarrow w,$$for all $\overrightarrow v ,\overrightarrow w \in T_p(s)$.       (Here, we view the tagent space $T_p(S)$ as the two-dimensional subspace $(span\{ {\overrightarrow \eta(p)}\})^{\bot}$ of $\mathbb R^3$.      Edit: Actually my question is why the second fundamental form under the usual definition can be written in this way.      Definition: The quadratic form $II_p$, defined in $T_p(S)$ by $II_p(v)=-&lt;d  N_p(v),v&gt;$ is called the second fundamental form of $S$ at $p$, where $dN_p:T_p(S)\to T_p(S)$ is the differential of the Gauss map.   Hopefully, I express this problem explicitly. I was just wondering how to prove this statement.   I took a diffrential geometry class last semester, and when I organized my notes this morning, I found this statement, but there was no proof...  Looking forward to an understandable explaination. Thanks in advance.     Edit 2:Furthermore, show that, at each point $p\in S$, the expression   $$\phi_p(z)=det\pmatrix{-H(f)_{(p)}-zI_{3\times 3} &amp; \overrightarrow \nabla f(p)\\\ \pm \overrightarrow \nabla f(p)&amp; 0}$$   (the underlying matrix here is $4\times 4$) defines a second-degree polynomial whose roots $\lambda_1$ and $\lambda_2$ are $||\overrightarrow \nabla f(p)||k_1$ and $||\overrightarrow \nabla f(p)||k_2$, where $k_1$ and $k_2$ are the principal curvatures of $S$ at $p$.      Also, if a non-zero vector $\pmatrix {\overrightarrow v \\c}$ lies in the kernel of the $4\times 4$ matrix $$\pmatrix{-H(f)_{(p)}-\lambda_jI_{3\times 3} &amp; \overrightarrow \nabla f(p)\\\ \pm \overrightarrow \nabla f(p)&amp; 0},$$   then $\vec v$ is a non-zero element of $T_p(S)$ and lies in the "principal direction" corresponding to $K_j$. I've got a question about how to drive the car in Europe on Highways. In the US, I can overtake another car on either side, and I am fine.  In Europe I was told that I have to drive on the right side (Germany), and to overtake on the left side of the other driver.  Now I had following situation, and I did not know how to handle this properly: I was driving along on the right lane, the Autobahn was 3 lanes wide on my side, and was going around 110 km/h. Someone overtook me, but he stayed on the middle lane, and suddenly got slower. He wasn't really in front of me, so I could not change to the left lane, but I was told I may not overtake on the right side.  Would I have to brake in such a situation, or should I just ignore it, and overtake him again on the right side?  (I overtook him, and he was on the phone, so I guess that was why he got distracted and slowed down that much). Get total height of webView's content using Javascript I was loading an image resource with the following code and it works fine from my dev environment (netbeans) but threw an exception as soon as it ran from the desktop.  new ImageIcon(Images.class.getResource("images/highlighter24.gif"));   I traced it down to my file having different case than in the code.  Fine, my bad, but why the inconsistent behavior?  Gremlins?  Note: I'm running on windows before you ask. The first time I learnt LaTeX, I thought \newcommand properly fits for inline mode and \newenvironment for displayed mode.  Later I noticed it is not correct. So the question is   What is the rule of thumb when deciding whether we should use one over the other one? On all of the other SOFU sites a downvote means The question is unclear or not useful.  However, here on meta, a downvote has become a sign of I don't agree with the question, suggestion, feature request, bug, etc. being described in the question.   What does a downvote on Meta really mean? What other reasons do people downvote on Meta? Why is it okay for meta to redefine the meaning of the downvote?  The tooltips and instructions are all the same here on meta.   Note: I'm not saying I disagree with the practice, just curious. Union of uncountable cardinals I have to prove the following:  Let $\omega_1$ be the least uncountable cardinal and, for each $n \in \omega$ (here, $\omega$ is the set of natural numbers denoted as an ordinal/cardinal), $n\ge1$, let $\omega_{n+1}$ be the least cardinal that is greater than $\omega_n$. Show that $\bigcup_{n\in\omega}\omega_n$ is a cardinal.  I suppose the proof has something to do with transfinite induction/recursion, but I don't know exactly how I'm supposed to use it. Any thoughts? How are you dealing with the  in your machine learning models? Let's say you used to predict the number of sales each month. The virus affected your results last year and it will affect for at least a couple of months. So your model, I guess, is missing a lot. What are some approaches we can use to fix our models? Is "Michael here" correct? How to access namespace which is part of different project? How do I get the feature id after featureAdded signal (PyQGIS)? I'm trying to make an edit form in QGIS (Python code) ,and i want after feature drawing to get the id, and the feature to be selected. Do you have any ideas to do that?  Tried so far:  self.iface.activeLayer().featureAdded.connect(self.myfonction)  def myfonction(self):      for feat in self.iface.activeLayer().getFeatures():         self.iface.activeLayer().setSelectedFeatures([feat.id()]) Making separate Python installation that can call ArcPy? I see a lot of Q&amp;As asking how you can create a separate Python installation (e.g. the Anaconda or Python XY distribution) that can use arcpy, while not 'breaking' the original ArcGIS python installation.  I had this same problem, and I think I have found a 'universal' solution. So far we have done this on about 8 computers at work and it all works fine.   How to install a separate Python distribution that can use ArcGIS? How did Ron speak Parseltongue and re-enter the Chamber of Secrets? Although 'The Deathly Hallows' was overall an excellent conclusion to Harry Potter's saga, there were moments within the book that felt infuriatingly lazy, like Rowling was whipping the plot along regardless of the holes she tore in it. For me, the lowest point was when Ron gargles at the entrance of the Chamber of Secrets- and succeeds!- so he can get some Basilisk fangs to destroy a Horcrux (which are conveniently vulnerable to this venom).  This is, by itself, a shockingly slapdash deus ex machina, but even worse is how it is completely inconsistent with the guidelines Rowling herself set. First and foremost, Parseltongue is not just a language, but a magical ability that can only be learned through hereditary or magical means (Potter being the sole example of the latter). This is firmly established by the fact that even Dumbledore, the greatest wizard of all time and a polyglot, is completely unable to speak it despite understanding it perfectly.  Without linguistic knowledge nor inherent ability, the chances of making any kind of coherent sentence (let alone the right one!) would be incredibly slim even in the case of mundane languages; it would be like gibbering at a Filipino in the hope that what you said was fluent Tagalog and didn't insult their mother.  Other baffling issues somewhat related to my question are thus; even if Ron had somehow unlocked the gate, how did he make his way down? In the second novel, Lockheart's foolery demolished the main tunnel to the Chamber, making it impossible to access or leave; the fact that the teeth are still there also implies that the Chamber wasn't excavated and the rubble cleared in the interval. Granted, he could have tried Apparating, but then he wouldn't have needed to fake Parseltongue to begin with.