Creating and linking chat rooms to questions Sometimes I'd like to discuss some ideas related to a question without including them in the comments. For (1) it gets too long and (2) often the discussion is quite specific and probably isn't relevant to others who come across the question.  Having the automatic "move to chat" feature when comments get too long is a great idea, but I think SO users should be able to pre-empt this and start a chat for a question, and maybe an answer too, manually.  For others who then come across this chat through another means than the question it'd be nice for them to know the context of the chat. I'd like to have an automatic explicit link between the chat and question created in such cases.
Should "move-to-chat" be provided on demand (as a button perhaps)? When comments get too chatty the move-to-chat feature asks if you'd like to move it out. But this often happens after the fact and thus doesn't prevent it.   I propose that:   Move-to-chat be provided as a button along side so that a user who knows their question or conversation may become drawn out may elect to preempt and take the conversation "off-line"
Physical Explanation for "Kolmogorov -5/3 spectrum" in Fluid Mechanics According to Kolmogorov, the energy spectrum function of a turbulent fluid is given as,  $E(k)=C\epsilon^{\frac{2}{3}}k^{\frac{-5}{3}}$  where $\epsilon$ is the energy flux and $k=\frac{2\pi}{r}$ where $r$ is the length scale.   The normal explanation I see in most physics texts and articles is that the -5/3 exponent is found purely through dimensional analysis. Obviously dimensional analysis is very useful, but often times there is a more physical explanation as well. Does anyone have any insights? Which form should be used for at­tribu­tive nouns like “stu­dent union”: sin­gu­lar or plu­ral, or pos­ses­sive sin­gu­lar or pos­ses­sive plu­ral? What are tag synonyms and merged tags? How do they work? Package in Java Do I end up richer paying down a mortgage or contributing to an IRA? I have $10,000 extra cash that I can either use to pay down my 5% mortgage, or contribute to my IRA.  I'm 30 years old.  I hope to pay off the mortgage in about 5 years.  I'm stymied, because:   Paying $10,000 into my mortgage earns me $500 a year (in interest savings) for the life of the mortgage -- hopefully 5 years. Paying $10,000 into my IRA earns me roughly a $3000 lowering of my tax bill now (plus CD ROI of about 1% at retirement time.)   So I can get $2500 ($500 a year over 5 years), after which I will have paid my mortgage off with other money; or I could get $3000 in cash right now plus a bit of extra money when I retire.  Even ignoring the future benefits of the IRA contribution, it feels like I should put the money into my IRA: it's an immediate 30% return on investment, as opposed to a 5% return for 5 years.  But if I always make that decision, I won't be paying off my mortgage early, and that $500 will stretch out over 30 years, costing me $15,000!  Which actually leaves me with more money in the end?  What basic principle of math am I missing?  Update:  The principle of math I was missing is that, assuming I'm taxed at the same rate when I retire as I am taxed now, I end up with exactly as much money as if I had invested the $10k and not received a $3k tax reduction.  (Of course, my income level and tax laws will have changed by then, but let's ignore that.)  So the question simplifies to, "Should I put $10k toward eliminating a 5% debt or toward a 1% investment?" in which case I should clearly put it toward the mortgage.  I was confused by the government incentive into thinking that retirement investment was a sweeter deal than it actually is.  This is probably their goal, and probably a noble one :) I'd like to extract the text from an HTML file using Python.  I want essentially the same output I would get if I copied the text from a browser and pasted it into notepad.    I'd like something more robust than using regular expressions that may fail on poorly formed HTML.  I've seen many people recommend Beautiful Soup, but I've had a few problems using it.  For one, it picked up unwanted text, such as JavaScript source.  Also, it did not interpret HTML entities.  For example, I would expect &amp;#39; in HTML source to be converted to an apostrophe in text, just as if I'd pasted the browser content into notepad.  Update html2text looks promising. It handles HTML entities correctly and ignores JavaScript.  However, it does not exactly produce plain text; it produces markdown that would then have to be turned into plain text. It comes with no examples or documentation, but the code looks clean.    Related questions: I have seen many camera review sites illustrate the effect of using different focal lengths on the same photograph using frames. There are also similar illustrations to compare different sensors (). I find this kind of visualization to be very useful in comparing the actual effect of the longer focal length\different sensor size. Of course the ability to do a wider focal length visualization would also be equally useful, but that's not possible.  Is there any ready-made software or plugin that enables this? If not, is there any simple technique to visualize the effect of longer focal lengths on an image (one would of course have to use the zoom information in the image EXIF data to accurately represent this)? All I can think of is to use some trigonometry to do the necessary calculations for the frame sizes for cropping. Does "corresponding author" carry an implied meaning? After reading the question , I got the impression that (at least in the writers' field) the "corresponding author" flag could carry an implied meaning, such as "did more work than the other authors", or "is a more senior author". Is it the case?  I am in mathematics, a field where we typically sort the authors alphabetically, and I've never given any importance to that role (apart from "this author is willing to answer a couple of extra e-mails, if needed"). How to add texture to fill colors in ggplot2 How to allow page break inside a float environment? I'm using new float enviroment to show some examples in my document. This  enviroment contains tcolorbox which provides a gray background. The main text in the enviroment is a mixture of plain text and code blocks (in lstlisting env). Each float should have it's own caption and label.  In style file:  \usepackage{newfloat} \DeclareFloatingEnvironment[name={Example}]{suppfigure}   In the main document:  \begin{suppfigure}[!h] \caption{Some code example}\label{suppfigure1} \begin{tcolorbox}[arc=0mm, left=1pt, right = 1pt, boxrule=0mm,colback = {shadow-gray}]   Text  \begin{lstlisting}  int i = 0;  \end{lstlisting}  Some more text  \begin{lstlisting}  String.Format("{0,10:0.0}", -123.4567);   \end{lstlisting}  \end{tcolorbox}  \end{suppfigure}   How can I allow page break inside the suppfigure to extend my example to multiple pages? Is there a max array length limit in C++? Is there a max length for an array in C++?  Is it a C++ limit or does it depend on my machine? Is it tweakable? Does it depend on the type the array is made of?  Can I break that limit somehow or do I have to search for a better way of storing information? And what should be the simplest way?  What I have to do is storing long long int on an array, I'm working in a Linux environment. My question is: what do I have to do if I need to store an array of N long long integers with N > 10 digits?  I need this because I'm writing some cryptographic algorithm (as for example the p-Pollard) for school, and hit this wall of integers and length of arrays representation. Baire: Show that $f\colon \mathbb{R}\to\mathbb{R}$ is a polynomial in an open bounded set Let $f\colon\mathbb{R}\to\mathbb{R}$ be an infinitely differentiable function, and suppose that for each $x\in\mathbb{R},$ $\exists\  n=n(x)\in\mathbb{N}$ such that $f^{(n)}(x)=0$. For each fixed $n\in\mathbb{N}$, consider the sets $F_n=\{x\in\mathbb{R} : f^{(n)}(x)=0\}$ and let $I=[a,b]$ a finite closed interval.  Show that $$I=\bigcup_{n=0}^\infty(I\cap F_n).$$ Show that there is a non empty open set $A\subset I$ where $f$ is a polynomial.   My attempt:  If $x\in I$ then by hypotesis there is $n$ such that $f^{(n)}(x)=0$ then $x\in F_n$ so then $\bigcup F_n\supset I$ then $$I=I\cap\bigcup_{n=0}^\infty F_n=\bigcup_{n=0}^\infty(I\cap F_n).$$  Let $$B_k=\bigcap_{n=k}^\infty F_n.$$ I want to show that $I\cap B_k$ has non-empty interior for some $k\in\mathbb{N}$. Then there is $A\subset B_k$ and by Taylor's Theorem $f$ will be a polynomial. But I didn't know how to prove this. I tried using the following bigger set: $$B=I\cap\bigcup_{k=0}^\infty B_k=I\cap\bigcup_{k=0}^\infty \bigcap_{n=k}^\infty F_n.$$ I think that it suffices to show that $B^o\neq\emptyset$ maybe using the Baire's Theorem proving that $B$ is a not meagre set.   More general Problem  Let $f$ be an infinitely differentiable function on $[0,1]$ and suppose that for each $x \in [0,1]$ there is an integer $n \in \mathbb{N}$ such that $f^{(n)}(x)=0$. Then does $f$ coincide on $[0,1]$ with some polynomial? If yes then how. I thought of using Weierstrass approximation theorem, but couldn't succeed. Answer: The proof is by contradiction. Assume $f$ is not a polynomial. Consider the following closed sets: $$ S_n = \{x: f^{(n)}(x) = 0\} $$ and $$ X = \{x: \forall (a,b)\ni x: f\restriction_{(a,b)}\text{ is not a polynomial} \}. $$ It is clear that $X$ is a non-empty closed set without isolated points. Applying Baire category theorem to the covering $\{X\cap S_n\}$ of $X$ we get that there exists an interval $(a,b)$ such that $(a,b)\cap X$ is non-empty and $$ (a,b)\cap X\subset S_n $$ for some $n$. Since every $x\in (a,b)\cap X$ is an accumulation point we also have that $x\in S_m$ for all $m\ge n$ and $x\in (a,b)\cap X$. Now consider any maximal interval $(c,e)\subset ((a,b)-X)$. Recall that $f$ is a polynomial of some degree $d$ on $(c,e)$. Therefore $f^{(d)}=\mathrm{const}\neq 0$ on $[c,e]$. Hence $d&lt; n$. (Since either $c$ or $e$ is in $X$.) So we get that $f^{(n)}=0$ on $(a,b)$ which is in contradiction with $(a,b)\cap X$ being non-empty. Center figure that is wider than \textwidth I have a figure that is wider than the \textwidth of my document. (I don't want to change the \textwidth.) As a result, the leftmost part of the figure is flush with the left margin, while the rightmost part spills into the right margin too much. I'd like to center the figure, so that it will exceed the \textwidth equally on both sides. I have Blender 2.79 on my Windows 7 system.    I want to install 2.8, but I'm completing some courses which use 2.79.  If I install 2.8, will it automatically replace 2.79?  Will they interfere with one another?  Thanks. How many switches can be stacked/interconnected? how to disable system apps without root? How to disable system apps without root?  My phone model is vivo x5 max+ and android 4.4.4  I have tried Debloater but it failed to connect (I am sure I've allowed USB debugging). Spontaneous electroweak symmetry breaking (i.e. $SU(2)\times U(1)\to U(1)_{em}$ ) is at scale about 100 Gev. So, for , gauge bosons $Z$ &amp; $W$ have masses about 100 GeV. But before this spontaneous symmetry breaking ( i.e. Energy > 100 GeV) the symmetry $SU(2)\times U(1)$ is not broken, and therefore gauge bosons are massless.  The same thing happens when we go around energy about $10^{16}$ GeV, where we have the Grand Unification between electroweak and strong interactions, in some bigger group ($SU(5)$, $SO(10)$ or others). So theoretically we should find gauge bosons $X$ and $Y$ with masses about $10^{16}$ GeV after GUT symmetry breaks into the Standard Model gauge group $SU(3)\times SU(2)\times U(1)$, and we should find massless X and Y bosons at bigger energies (where GUT isn't broken).  So this is what happened in the early universe: when temperature decreased, spontaneous symmetry breaking happened and firstly $X$ &amp; $Y$ gauge bosons obtained mass and finally $Z$ &amp; $W$ bosons obtained mass.   Now, I ask: have I understood this correctly? In other words, if we make experiments at energy above the electroweak scale (100 GeV) we are where $SU(2)\times U(1)$ isn't broken and then we should (experimentally) find $SU(2)$ and $U(1)$ massless gauge bosons, i.e. $W^1$, $W^2$, $W^3$ and $B$ with zero mass? But this is strange, because if I remember well in LHC we have just make experiments at energy about 1 TeV, but we haven't discovered any massless gauge bosons. Difference between 'struct' and 'typedef struct' in C++? Need to give permissions to /tmp/cache and /tmp/templates_c but can't find them Please use UK pre-uni methods only (at least at first). Thank you.