Some avatars (including my own) aren't loading anymore, and instead I get a transparent box. This occurs particularly after I refresh a page.  In my developer tools network tab, every request for an i.stack.imgur.com avatar seems to get a response of 301 (permanently moved) without content, which might explain why those avatars don't load up.  Related:
I just wrote a question before this one and had trouble uploading a screenshot. The drop your image dialog throws no warning or error, but after uploading it won't show.  I also noticed that other questions won't load their images. Could this be some issue with imgur or similar?  Example:     When opening the image in a separate tab, Chrome gives a "too many redirects" error:    This might be linked to
Delete Everything(the rest of the text) after a specific string Tikz won't plot the function properly I tried to plot the following function but it didn't work:  y = 300 + 1000/x + 2.5x.  This is the document, but instead of the plot it only shows the axis.  \documentclass{article}  \usepackage{pgfplots}% This uses tikz \pgfplotsset{compat=newest}% use newest version  \pgfmathdeclarefunction{Function}{1}{%   \pgfmathparse{300 + 1000/x + 2.5}% }  \tikzset{My Line Style/.style={smooth, thick, samples=400}}  \begin{document} \begin{tikzpicture} \begin{axis}[     xmin=0.0,     xmax=250,     ymin=0,     ymax=50,     axis x line=bottom,     axis y line=left,      xlabel= $y$,     ylabel=Cost,      xtick={250},     xticklabels={250},         restrict x to domain=0:250,     ]        \addplot+[My Line Style, color=black, samples at={1,2,3,4,...,249,250}] (\x,{Function(\x)});   \end{axis}  \end{tikzpicture} \end{document} \documentclass{article} Cancellation Law for Direct Sums - What is wrong with this argument? What component to use for audio signal switching? I'm looking to build a guitar pedal switcher based on a Raspberry Pi or Arduino (have not yet decided, but I have an unused Raspberry around and I lean towards that). Anyway, digital logic.  Now, I need to switch audio signal obviously and I need to do it quietly (both physical silence and electrical silence). Please note that the signal is line level throughout most of the build, except for the input which is much lower. I will probably have 2 or 3 loops before the preamp so those may not encounter line level signal.  From what I read and know, so far, mechanical relays are not really an option due to the clicking noise they make. I also read something about FETs, but that's a bit out of my league and I would appreciate any info on these.  PS: I will probably use different power rails for the digital and analog paths.  PS2: The whole thing will be mounted in a 1U rack enclosure, so please tell me if I should take into consideration any thermal issues. Recurrence relation for the determinant of a tridiagonal matrix Let  $$f_n := \begin{vmatrix} a_1 &amp; b_1 \\ c_1 &amp; a_2 &amp; b_2 \\ &amp; c_2 &amp; \ddots &amp; \ddots \\ &amp; &amp; \ddots &amp; \ddots &amp; b_{n-1} \\ &amp; &amp; &amp; c_{n-1} &amp; a_n \end{vmatrix}$$  Apparently, the determinant of the tridiagional matrix above is given by the recurrence relation   $$f_n = a_n f_{n-1} - c_{n-1} b_{n-1}f_{n-2}$$  with initial values $f_0 = 1$ and $f_{-1} = 0$ (according to Wikipedia). Can anyone please explain to me how they came to this recurrence relation?  I don't really understand how to derive it. So I watched the following .  In the clip, using what seems to be the recording from a standard bank camera, they zoom in at least 100, and see the image of the culprit in the reflection of the eye of the girl.  Now, I thought this was completely ridiculous, so much so that I thought it was actually really funny.    However, my friend argued that there are very good tricks for image enhancement, such as "super resolution" a procedure where multiple frames of a video to produce a much higher single resolution image.   He did think the show bends the truth quite a bit, but how much?  Honestly, I don't actually know anything about these things, so my question is:     How good is modern image resolution enhancement?  Also, how far off are the CSI television programs?    Thank you,  Remark: This is  on the Skeptics site.  I was told I might receive better answers here. Cannot get 2 raster files of same cell size to align ArcMap 10.2 Proving Binomial Identity without calculus How to establish the following identities without the help of calculus:  For positive integer $n, $ $$\sum_{1\le r\le n}\frac{(-1)^{r-1}\binom nr}r=\sum_{1\le r\le n}\frac1r $$  and  $$\sum_{0\le r\le n}\frac{(-1)^r\binom nr}{4r+1}=\frac{4^n\cdot  n!}{1\cdot5\cdot9\cdots(4n+1)}$$ What is the difference between [@] and [*] when referencing bash array values? says:  If the index number is @ or *, all members of an array are referenced.  When I do this: LIST=(1 2 3) for i in &quot;${LIST[@]}&quot;; do   echo &quot;example.$i&quot; done  it gives the desired result: example.1 example.2 example.3  But when I use ${LIST[*]}, I get example.1 2 3  instead. Why? Edit: when using printf, @ and * actually do give the same results. How to measure time taken by a function to execute Error: 'else' without 'if' Where can I find a reference to the format of the comment field (field 5) of the /etc/passwd file? In the /etc/passwd file on my system, the "comment" field, field 5, is inconsistent in its contents.  I thought that I could extract it to get the full name of the user.  fullname=`awk -F: '$1 == name {print $5}' name=$LOGNAME /etc/passwd`   However this returns with $fullname containing a name with 0, 3, or 4 commas following.  Exploring the man page (man 5 passwd) provides no details of this field other than describing it as "user name or comment field."  Perhaps there is additional information that is stored along with the user name? Syntax of bash alias definition I'm using Cygwin, and have installed all the developer packages as well as most if not all of the other packages. When I provide an alias for gcc, I get the error  -bash: alias: gcc: not found   What could I be doing wrong?  I am typing the following command into the terminal:  alias gcc "gcc -ansi -Wall -g -O0 -Wwrite-strings -Wshadow -pedantic-errors -fstack-protector-all"   FYI, this alias works on other systems. Meta Theory when studying Set Theory What exactly serves as the meta theory in the study of set theory (for example in Kunen's text). It seems to involve a certain amount of number theory and a certain concept of what it means to be finite.   Also: We usually use $\bigcup_{\alpha\in{ON}}R_{\alpha}$ as our set theortic universe $V$ (in the sense we believe that all sets we are interested in live there) where $R_{0}=\emptyset$, $R_{\alpha+1}= \mathcal{P}(R_{\alpha})$ and $R_{\alpha}=\bigcup_{\beta&lt;\alpha}R_{\beta}$ when $\alpha$ is a limit ordinal. The study of independence results then seem to be based on relatavizing notions with this $V$ as our set theoretic universe. It seems that it is implicitly assumed that the $\omega$ in $V$ has no non-standard elemements (in the sense that there is no $n&gt;a$ in $\omega$ where $a$ is obtained be repeatedly applying the successor operation to $0$.) Is this true and can it be formalized or is it something that is taken for granted?   e.g. If the above were true then $ZFC\vdash{\neg{Con(\ulcorner{ZFC}\urcorner)}}$ would imply that $ZFC$ is inconsistent since we may look at the $ZFC$ axioms $\phi_{1},...,\phi_{n}\vdash\neg{Con\ulcorner{ZFC}\urcorner}$, then look at a ctm these axioms (which exists by reflection and downward Lowenheim Skolem) and recover the proof of the contradiction. I'm just going to throw this out there, but Google indexes Stack Overflow really quickly For example, I  after using Google to try to find an answer. I then turned back to Google and did a search for  and it was already the first result! Similar searches also put my question on the first page, usually in the top 5!  This is insanity. Did I get lucky and post just before an indexing? Is the popularity of SO leading to Google indexing extremely frequently? Or is Jeff using some kind of crazy SEO? How to "flatten" a multi-dimensional array to simple one in PHP? It's probably beginner question but I'm going through documentation for longer time already and I can't find any solution. I thought I could use implode for each dimension and then put those strings back together with str_split to make new simple array. However I never know if the join pattern isn't also in values and so after doing str_split my original values could break.  Is there something like combine($array1, $array2) for arrays inside of multi-dimensional array? char!=(signed char), char!=(unsigned char) The code below compiles, but has different behavior for the char type than for the int types.  In particular     cout &lt;&lt; getIsTrue&lt; isX&lt;int8&gt;::ikIsX  &gt;() &lt;&lt; endl;    cout &lt;&lt; getIsTrue&lt; isX&lt;uint8&gt;::ikIsX  &gt;() &lt;&lt; endl;    cout &lt;&lt; getIsTrue&lt; isX&lt;char&gt;::ikIsX  &gt;() &lt;&lt; endl;   result in 3 instantiations of templates for three types: int8, uint8 and char. What gives?  The same is not true for ints: int and uint32 which result in the same template instantiation, and signed int another.  The reason seems to be that C++ sees char, signed char and unsigned char as three different types. Whereas int is the same as a signed int. Is this right or am I missing something?  #include &lt;iostream&gt;  using namespace std;  typedef   signed char       int8; typedef unsigned char      uint8; typedef   signed short      int16; typedef unsigned short     uint16; typedef   signed int        int32; typedef unsigned int       uint32; typedef   signed long long  int64; typedef unsigned long long uint64;  struct TrueType {}; struct FalseType {};  template &lt;typename T&gt; struct isX {    typedef typename T::ikIsX ikIsX; };   // This  int==int32 is ambiguous //template &lt;&gt;            struct isX&lt;int  &gt;    { typedef FalseType ikIsX; };  // Fails template &lt;&gt;            struct isX&lt;int32  &gt;  { typedef FalseType ikIsX; }; template &lt;&gt;            struct isX&lt;uint32 &gt;  { typedef FalseType ikIsX; };   // Whay isn't this ambiguous? char==int8 template &lt;&gt;            struct isX&lt;char  &gt;  { typedef FalseType ikIsX; }; template &lt;&gt;            struct isX&lt;int8  &gt;  { typedef FalseType ikIsX; }; template &lt;&gt;            struct isX&lt;uint8 &gt;  { typedef FalseType ikIsX; };   template &lt;typename T&gt; bool getIsTrue(); template &lt;&gt;           bool getIsTrue&lt;TrueType&gt;() { return true; } template &lt;&gt;           bool getIsTrue&lt;FalseType&gt;() { return false; }  int main(int, char **t ) {    cout &lt;&lt; sizeof(int8) &lt;&lt; endl;  // 1    cout &lt;&lt; sizeof(uint8) &lt;&lt; endl; // 1    cout &lt;&lt; sizeof(char) &lt;&lt; endl;  // 1     cout &lt;&lt; getIsTrue&lt; isX&lt;int8&gt;::ikIsX  &gt;() &lt;&lt; endl;    cout &lt;&lt; getIsTrue&lt; isX&lt;uint8&gt;::ikIsX  &gt;() &lt;&lt; endl;    cout &lt;&lt; getIsTrue&lt; isX&lt;char&gt;::ikIsX  &gt;() &lt;&lt; endl;     cout &lt;&lt; getIsTrue&lt; isX&lt;int32&gt;::ikIsX  &gt;() &lt;&lt; endl;    cout &lt;&lt; getIsTrue&lt; isX&lt;uint32&gt;::ikIsX  &gt;() &lt;&lt; endl;    cout &lt;&lt; getIsTrue&lt; isX&lt;int&gt;::ikIsX  &gt;() &lt;&lt; endl;  }   I'm using g++ 4.something The sum $\sum_{k=1}^nk(k!)$ can be easily calculated by noting $k(k!)=(k+1)!-k!$. Is there a way to calculate the sum nicely using a combinatorial argument. Is it possible to notice it is $(n+1)!-1$ combinatorially? Coordinate-Free Definition of Trace. $\DeclareMathOperator{\tr}{trace}$ I am reading the  on the trace operator. The section titled Coordinate-Free Definition defines the trace as follows.  Let $V$ be a finite dimensional vector space over a field $F$ and define a bilinear map $f:V\times V^*\to F$ as $f(v, \omega)=\omega(v)$ for all $(v, \omega)\in V\times V^*$. This maps induces a unique linear map $\tr:V\otimes V^*\to F$. Since $\text{End}(V)$ has a canonical isomorphism with $V\otimes V^*$, we have now a notion of trace of a linear operator on $V$.  The Question: The second paragraph of the section in the article says that  This also clarifies why $\tr(AB)=\tr(BA)$.  I can't see how $\tr(AB)=\tr(BA)$ follows from this definition at all. Can somebody give me a hint? Is there word for this, other than know-it-all? Just wondering, if there's a word for:  One who makes it appear as if they're an expert on a subject while there are also signals (subtly or blatantly noticeable) that this person doesn't know very much on the subject or at least as much as they're acting like they do on the subject; pretending to have much knowledge on a subject matter.  I found pedantic but I don't suppose it's the right word.