I was trying to execute a query on data.stackexchange.com, since I wasn't logged in I get  asked to solve the captcha (Which is fine).  However data.stackexchange.com  is failing to display the captcha for me and presents this error:
When I tried to run , I got the below screen:    The captcha is missing!  I tried in other browsers too.    Update:  From @Oded's comments, I changed to HTTP and it was working perfectly.  Out of curiosity I would like to know why the captcha isn't working when accessing Data Explorer over HTTPS.
Viewshed analysis plugin on QGIS keeps resulting in errors I've been trying to test the Viewshed analysis plugin on QGIS 2.10, but it keeps giving back error messages. I've tried to reduce the radius area and have also reprojected both my DEM and my point shapefile to UTM, in order to avoid a possible memory error mentioned in another question regarding this plugin (that the using of geographic coordinates might cause a memory error).  Still, I keep getting Python error messages when I try to run it. Does anyone know whats going on? Is this plugin "broken"? Sass .scss: Nesting and multiple classes? Conjectures that have been disproved with extremely large counterexamples? I just came back from my Number Theory course, and during the lecture there was mention of the Collatz Conjecture.  I'm sure that everyone here is familiar with it; it describes an operation on a natural number – $n/2$ if it is even, $3n+1$ if it is odd.  The conjecture states that if this operation is repeated, all numbers will eventually wind up at $1$ (or rather, in an infinite loop of $1-4-2-1-4-2-1$).  I fired up Python and ran a quick test on this for all numbers up to $5.76 \times 10^{18}$ (using the powers of cloud computing and dynamic programming magic).  Which is millions of millions of millions. And all of them eventually ended up at $1$.  Surely I am close to testing every natural number? How many natural numbers could there be?  Surely not much more than millions of millions of millions. (I kid.)  I explained this to my friend, who told me, "Why would numbers suddenly get different at a certain point?  Wouldn't they all be expected to behave the same?"  To which I said, "No, you are wrong!  In fact, I am sure there are many conjectures which have been disproved by counterexamples that are extremely large!"  And he said, "It is my conjecture that there are none! (and if any, they are rare)".  Please help me, smart math people.  Can you provide a counterexample to his conjecture?  Perhaps, more convincingly, several?  I've only managed to find one! (Polya's conjecture). One, out of the many thousands (I presume) of conjectures. It's also one that is hard to explain the finer points to the layman. Are there any more famous or accessible examples? If $A\simeq\prod A_i$ then $\sum e_i=1$ Given $A$ commutative ring with unity. If we have rings $A_1,\dots, A_n$such that $A\simeq A_1\times \dots \times A_n$ there are $e_1,\dots,e_n$ idempotent elements of $A$ such that $e_1+\dots+e_n = 1$ and $e_i e_j =0$ if $i\neq j$.  I'm not sure how general the proof should be written...  The isomorphic relation suggest that if $f$ defines the isomorphism then there is a $(a_1,\dots, a_n)\in \prod A_i$ such that $f(a_1,\dots,a_n)=1\in A$. Could it work thinking of the idemmpotent terms as $e_i=(0,\dots,0, a_i,0, \dots,0)?$ This should satisfy $e_i e_j =0$ if $i\neq j$. But I have two problems with it (1) I don't see why $e_i$ should idempotent as no assumptions in regard to the existence of idempotent elements in $A_i$ has been made. (2) The sum $\sum e_i=1$ has no reason to be true. How do you set the expiry date or a maximum age in the HTTP headers for static resources in IIS Prove if $n \in \mathbb N$, then $\frac{1}{2!}+\frac{2}{3!}+\frac{3}{4!}+\cdots+\frac{n}{\left(n+1\right)!} = 1-\frac{1}{\left(n+1\right)!}$   So I proved the base case where $n=1$ and got $\frac{1}{2}$  Then since $n=k$ implies $n=k+1$ I setup the problem like so:  $\frac{k}{(k+1)!}+\frac{(k+1)}{(k+2)!}=1-\frac{1}{(k+2)!}$  After trying to simplify it I got the following:  $\frac{k(k+2)!+(k+1)(k+1)!}{(k+1)!(k+2)!}=1-\frac{1}{(k+2)!}$  However, I'm having trouble simplifying it to match the RHS.  Hints? To Find Large Powers in C++ C# Lambda expressions: Why should I use them? I have quickly read over the  documentation.  This kind of example has helped me to understand better, though:   delegate int del(int i); del myDelegate = x =&gt; x * x; int j = myDelegate(5); //j = 25   Still, I don't understand why it's such an innovation. It's just a method that dies when the "method variable" ends, right? Why should I use this instead of a real method? I've just finished running my first session with only one player, and it felt pretty different from running a session for a group.  Could someone with more experience in this talk about what one should do differently in that situation?  I'm not referring to mechanics like encounter-building, but just how to handle the change to the social dynamics. Why do some badges appear white in color and others are dark? Is it possible to explicitly tell Stack Overflow the language of the code block you are including? Possible Duplicates:             Stack Overflow awesomely detects what language a code block is and syntax highlights it accordingly. But sometimes it fails. Is it possible to explicitly tell it what the language is?  php:  if ( force_ssl_admin() &amp;&amp; !is_ssl() ) {     if ( 0 === strpos($_SERVER['REQUEST_URI'], 'http') ) {         wp_redirect(preg_replace('|^http://|', 'https://', $_SERVER['REQUEST_URI']));         exit();     } else {         wp_redirect('https://' . $_SERVER['HTTP_HOST'] . $_SERVER['REQUEST_URI']);         exit();     } }   ruby:  def destroy   @payment = Payment.find(params[:id])   @payment.destroy    redirect_to :back end   yaml (FAIL)  foo: this is foo! bar: this is bar! id: 5 What is the fastest way to convert float to int on x86 What is the fastest way you know to convert a floating-point number to an int on an x86 CPU.  Preferrably in C or assembly (that can be in-lined in C) for any combination of the following:   32/64/80-bit float -> 32/64-bit integer   I'm looking for some technique that is faster than to just let the compiler do it. Complex number question on proving an inequality. If $|z_1|=1,|z_2|=1$, how can one prove $|1+z_1|+|1+z_2|+|1+z_1z_2|\ge2$ Let $p,q$ be primes, $p≠q$, then I have to show that $\mathbb{Q}(\sqrt{p},\sqrt[3]{q})= \mathbb{Q}(\sqrt{p}\cdot \sqrt[3]{q})$  So far I've tried a lot of things with minimal polynomials and bases, but I'm far from any argument that I find sufficient.  This is an example from my algebra course, first chapter about field extension. So far we know about basic definitions, minimal polynomials and their properties, algebraic elements and algebraic fields.  Could someone maybe give me a hint about how to proceed? Thanks a lot!!! Not getting edit's +2 rep after reaching 2k rep After reaching 2k rep , I'm not receiving  +2 rep per edit. Why? Find $F$-related vector fields on $M\times N$, where $F(x)=(x, f(x))$ I am reading Lee's book on Differential geometry. In Chapter 4, Lee has this exercise.  Let $M$, $N$ be smooth manifolds, and let $f:M\to N$ be a smooth map. Define $F : M\to M \times N$ by $F(x) = (x, f(x) )$. Show that for every smooth vector field $V$ of $M$ , there is a smooth vector field on $W$ on $M \times N$ that is $F$-related to $V$.  I can understand that we must have $W_{(x,f(x))}=V_x\oplus Df(x)V_p$ for all $x\in M.$ The set $\{(x,f(x)):x\in M\}$ is a closed set in $M\times N.$ Therefore, if we can show that for all $(p,f(p))\in M\times N$ there is a neighbourhood $U_p$ and a smooth vector field on $U_p$ extending $V_x\oplus Df(x)V_x$ we are done by partition of unity. But I cannot show that. Can someone help me out? I'm trying to recall the name of a book I read, probably published after 1990, where alien AI infects satellites and a barrier is established, isolating earth from space that maybe slows down time inside of it, relative to the passage of time outside.  Mars or the moon is also colonized in an attempt to flee the now real possibility that the sun will become a red giant and wipe out humanity in the not-too-distant future (as perceived on earth), but the colony gets one of the time barriers as well.  I think the name of the novel was short, "The _______" (one word).  The story focused more on the human cost and followed one particular family, one member of which was somehow also partially infected by the alien AI, but I don't remember as much about them. Why did sampling boost the performance of my model? I have an imbalanced dataset with 88 positive samples and 128575 negative samples. I was reluctant to over/undersample the data since it's a biological dataset and I didn't want to introduce synthetic data. I built a Random Forest Classifier with this original dataset. I got an F1 score of 0 for the positive class. Zero precision. Zero recall. I cross-checked the predictions and test data. The model predicts some positives none of which are actually positive. Worst performance.  So, I tried to oversample the positive class. I upsampled the positives to 1000 samples. To my surprise, the F1 score for this dataset was 0.97, for the positive class. Then I tried lesser samples. I was able to achieve an F1 score of 0.83 with 200 positive samples, which is just 2.25 times of the original positive samples.  I would like to know why this occurs. For 88 samples, F1 score is 0.00 (rounded off to two digits). For 200 samples it's 0.83. There is no data leakage. All the features are engineered. I used imbalanced-learn module for oversampling. Can someone explain why is this difference in performance? The question is based on the following exercise in real analysis:     Assume that $A,B\subset{\Bbb R}$ are both bounded and $x&gt;0$ for all $x\in A\cup B$. Show that $$ \sup(AB)=\sup A\sup B $$   where    $$ AB:=\{ab\in{\Bbb R}:a\in A, b\in B\}. $$   Since $0&lt;a\leq\sup A$ and $0&lt;b\leq\sup B$ for all $a\in A$ and $b\in B$, we have $$ ab\leq\sup A\sup B $$ for all $ab\in AB$ which implies that $\sup AB\leq\sup A\sup B$. I have trouble with another direction: $$ \sup AB\geq\sup A\sup B $$ I was trying to show that for every $\epsilon &gt;0$, $\sup AB-\epsilon \geq \sup A\sup B$. If one uses the definition of supremum, one has the estimates that for every $\epsilon&gt;0$, $$ \sup A-\epsilon\leq a, \quad \sup B-\epsilon\leq b $$ for some $a\in A,\ b\in B$. It follows that $$ \sup A\sup B\leq (a+\epsilon)(b+\epsilon)=ab+\epsilon(a+b)+\epsilon^2\leq \sup AB+\epsilon (a+b)+\epsilon^2 $$ which seems quite close to what I want. How can I go on? How to extract this format in xslt