Speed greater than light in circular motion
Rotate a long bar in space and get close to (or even beyond) the speed of light $c$
I noticed that, for each research project, there comes a point where I have to consult the literature, and find all the previous research related to the current project.  Unfortunately, I seem to be very inefficient in my approach. I spend a lot of time digging through papers that are really interesting, but only of tangential importance to my current work, just to find the few papers that actually do similar things. (The pile of "cool paper, read when time" just keeps growing.)  Hence, I'm wondering: What is the most time efficient way to get a thorough overview of the literature in a specific niche of a field?    While searching for an answer I came across these questions:   - This question is quite similar and I liked the approach. I debated with myself if this is a duplicate, but I think it is focused more on how to be sure the search was exhaustive, whereas I'm worried about time efficiency. (Also, I'm a bit curious if things have changed since 2012.)   - The answer provides tips on how to identify what literature generally is important in a field, but I am looking for the most cost effective (least time consuming) way to do it in an area, where I know the broad literature, but not the specifics. A book on quantum mechanics supported by the high-level mathematics I'm interested in quantum mechanics book that uses high level mathematics (not only the usual functional analysis and the theory of generalised functions but the theory of pseudodifferential operators etc, certainly the modern mathematics). If there isn't something similar please give me a reference to the book that is strictly supported by mathematics (given a set of mathematically descripted axioms author develops the theory using mathematics as a main tool). How to obtain inverse behavior for `tail` and `head`? Is there a way to head/tail a document and get the reverse output; because you don't know how many lines there are in a document?  I.e. I just want to get everything but the first 2 lines of foo.txt to append to another document. How can I resize NTFS partition in GParted? How do I get a Cron like scheduler in Python? How to find the mime type of a file in python? !! Do not use the future tense after unless   [✓]  I won't go unless you go   [✘] [I won't go] unless you will go. [✘]   Why not? Even if the above is prescriptive, what may be some reasons? In my separate question , I quote: unless = if not. If not can precede future tense; so why can't unless?  Footnote:  motivated this. Adding more than 15 digits in Excel Difference between 'such as' and 'like' This one never ceases to confuse me. When to use 'such as' and when to use 'like' while giving examples? Is there any clear rule?        Metros like Mumbai, Delhi and Karachi are unsafe after dark.    Metros such as Mumbai, Delhi and Karachi are unsafe after dark.       (Before anyone points out, Delhi and Karachi are unsafe round-the-clock, but it's just an example.) What happens if I am afflicted with a condition that worsens on a failed save and choose not to try to save? Do I:   Automatically suffer the effects of the failed save? Keep my current condition? Have no choice and must roll the save regardless?   This came up in a game earlier this afternoon when we decided to just stop saving against the effect that was causing us to fall unconscious. Draw somewhat random function I am trying to reconstruct this image here    I am not very happy with the code, as it uses hacking and adding white boxes and alike. My problem is now how do I draw the somewhat arbitary function in the figure? I tried to do a polynomial fit, but that did not work. I got dimensions to large, would a spline solution work better?    \documentclass{standalone}     \usepackage{tikz}     \usetikzlibrary{patterns}     \usepackage{pgfplots}     \pgfplotsset{compat=1.6}     \begin{document}     \begin{tikzpicture}      \begin{axis}[         xmin=-0.1,xmax=5,         xlabel={z},         ymin=0,ymax=4.5,     xtick={2.5,4},     xticklabels={$v_1$,$v_2$},     ytick={2.5,3.5},     yticklabels={$u_1$,$u_2$},     xlabel={$u$},       ylabel={$v$},     axis lines=middle]  \draw [fill=gray!40!white,thick,dashed] (axis cs:0,0) rectangle (axis cs:4,3.5); \draw [color=black,fill=white,thick,dashed] (axis cs:0,0) rectangle (axis cs:2.5,2); \draw [fill=black] (axis cs:0,0) rectangle (axis cs:0.01,4.45); \addplot+[black,thick,domain=0:5,no marks] {0}; % \node at (axis cs:2.5,0)    [anchor=south west] {$A$}; \node at (axis cs:4,0)      [anchor=south west] {$A'$}; \node at (axis cs:2.8,2.2)  [anchor=north]      {$B$}; \node at (axis cs:4.2,4)   [anchor=north]       {$B'$}; \node at (axis cs:0.25,2.5) [anchor=north]      {$C$}; \node at (axis cs:0.25,4)   [anchor=north]      {$C'$}; \node at (axis cs:0,0)     [anchor=south west]  {$O$}; % \end{axis} \end{tikzpicture} \end{document} Are there massless bosons at scales above electroweak scale? 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. I'm working with some code that widely uses the idiom of returning a pointer to a static local variable.  eg:  char* const GetString() {   static char sTest[5];   strcpy(sTest, "Test");   return sTest; }   Am I right in thinking that this is safe?  PS, I know that this would be a better way of doing the same thing:  char* const GetString() {   return "Test"; }   Edit: Apologies, the function signature should of course be:  const char* GetString(); Is it possible to sync files via rsync and let rsync only compare mtime informations?  Or is there another tool for this job?  That means that such a tool only copies src to destination if the src is newer than the destination. Comparable to GNU cp --update - but also over ssh ... Are the rationals a closed or open set in $\mathbb{R}$? Average length of the longest segment This post is related to a previous SE post  concerning average length of a smallest segment.  A rope of 1m is divided into three pieces by two random points. Find the average length of the largest segment. My answer is 11/18.  Here is how I do it:  Here we have two independent random variables $X,Y$, both uniform on $[0,1]$. Let  $A=\min (X,Y), B=\max (X,Y)$ and $C=\max (A, 1-B, B-A)$. First we want to find the probability density function $f_C(a)$ of $C$. Let $F_C(a)$ be the cumulative distribution function. Then $$ F_C(a) = P(C\le a)=P(A\le a, 1-B\le a, B-A\le a).$$  By rewriting this probability as area in the unit square, I get $$F_C(a)=\left\{\begin{array}{ll} (3a-1)^2 &amp; \frac{1}{3}\le a\le \frac{1}{2}\\ 1-3(1-a)^2 &amp; \frac{1}{2}\le a\le 1\end{array}\right.$$ from which it follows that  $$f_C(a)=\left\{\begin{array}{ll} 6(3a-1) &amp; \frac{1}{3}\le a\le \frac{1}{2}\\ 6(1-a) &amp; \frac{1}{2}\le a\le 1\end{array}\right.$$ Therefore the expected value of $C$ is $$\int_{1/3} ^{1/2}6a(3a-1) da+\int_{1/2} ^{1}6a(1-a) da= \frac{11}{18}.$$  My questions are:  (A) Is there a "clever" way to figure out this number 11/18?  (B) What is the answer if the rope is divided into $n&gt;3$ segments? Prove $f(S \cup T) = f(S) \cup f(T)$ $f(S \cup T) = f(S) \cup f(T)$  $f(S)$ encompasses all $x$ that is in $S$ $f(T)$ encompasses all $x$ that is in $T$  Thus the domain being the same, both the LHS and RHS map to the same $y$, since the function $f$ is the same for both.  Can you post the solution? Block any query in BIND I am travelling to Calgary from Delhi. I have an Air India flight from Delhi to Dubai then British Airways flight from Dubai to London and Air Canada flight from London to Calgary. My query is "Do I require a transit visa." Plz help as I am travelling in four days Continuous function on R which tends to infinity on open interval must have a minimum Suppose we have $f : \mathbb{R} \to \mathbb{R}$ continuous and $$\lim\limits_{x \to \pm \infty} f(x) = \infty.$$  Then must $f$ have a minimum on $\mathbb{R}$?  Intuitively it seems so, and it's easy to prove for some arbitrary closed interval in $\mathbb{R}$ with the Extreme Value Theorem, but how can we apply that to an open interval like $(-\infty, \infty)$?