Replace string in a line, where the line is inputed by a variable
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Problem from Herstein on group theory What is the term for taking it out on someone even though you will be harmed by this too? When you are so mad at someone that you make a bad decision, even though you will be harmed by it as well, in order to harm that person; is there a good term for this?   For example burning $100 because he owns $20 of it. How to tell which row number is clicked in a table? How do you add a thin outline? I am new at this. I am extracting files a game. In the game they have thin black outlines, but they aren't part of a model. I am having trouble finding anything about this. What is the simplest way to do this?  Update: I think I am looking for something like freestyle. What is the simplest way to use this to create a thin black outline around a model? What's the incentive to flag duplicates? How far can you go with rm -rf / as root What happens if my ESTA expires on the day of arrival? I'm French and will travel the 14th of June to the US. My ESTA expires the 14th of  June 2013 and I'm wondering if my ESTA will be valid when I'll land in the US on the 14th of June 2013.  Does someone know anything about that? How are the degrees of freedom in the emmeans package calculated? - R Is WD-40 really bad to apply on bikes? I was told so but still see people doing that.   Also I saw WD-40 launching their new products of bike lubricant and degreaser. Did anybody try those? Unresolved external symbol on static class members Very simply put:  I have a class that consists mostly of static public members, so I can group similar functions together that still have to be called from other classes/functions.  Anyway, I have defined two static unsigned char variables in my class public scope, when I try to modify these values in the same class' constructor, I am getting an "unresolved external symbol" error at compilation.  class test  { public:     static unsigned char X;     static unsigned char Y;      ...      test(); };  test::test()  {     X = 1;     Y = 2; }   I'm new to C++ so go easy on me. Why can't I do this? Show that $d(z,a)=|\frac{z-a}{1-\overline{a}z}|$ is a metric on the unit disk For any $z, a$ in the open unit disk, we define$$d(z,a)=\left \vert \frac{z-a}{1-\overline{a}z} \right \vert$$  Show that $d$ is a metric on the open unit disk.     It is easy to show $d(z,a)=d(a,z)$ and $d(z,a)=0$ $\rm iff$ $z=a$. However, I am having trouble showing that it satisfies triangle inequality. Any help would be appreciated! Prove that there are no positive integers $x$ and $y$ such that $x^3 + y^3 = 10^3$. Prove that there are no positive integers $x$ and $y$ such that $x^3 + y^3 = 10^3$.   This is a homework question, and I understand that its part of Fermat's Last Theorem, but when I looked that up to try to figure out the homework, I realized that it is way further than what we've learned in class so far. We have to prove this, but the only way I can think to do it is by exhaustion, which would be extremely lengthy. Any little shove in the right direction would be appreciated. Thanks! How to calculate square root or cube root? I was reading Richard Feynman biography when I read that one time he was able to calculate the  cube root of large number in his brain by just using simple facts of everyday life. So my question is there a way to calculate square root or cube root by using just a pen a paper, I mean a systematic way not by trial and error. So this homework question is in the context of $\mathbb{R}$ only, and we are using Lebesgue measure.  The sum $A+B$ is defined to be $A+B=\{a+b|a\in A,b\in B\}$. The question is: If $m(A),m(B)&gt;0$, is it necessarily the case that $A+B$ contains an open interval?  This question is quite annoying, since it is quite difficult to calculate the sum even after you construct an example. However, it seems like no matter how I constructed a set of positive measure, there is a region that have a lot of point in it (yet this region is not necessarily dense). This suggest that when summed up, the holes should be covered up somehow and thus there would be an open interval, and so the answer is yes. Sorry for a rather vague idea, but I'm just not sure what to do with this problem. I have a feeling that somehow topology would have a way to capture precisely the idea above about a region with a lot of point.  (also, I think my middle school teacher mentioned this once, and I remembered the answer to be yes; but that is quite a while ago though)  Thank you. Any help will be appreciated.  EDIT2: So Camilo's answer is gone. I am looking at the convolution method right now. Because the convolution is continuous, if it is nonzero I am done. But then there is no guarantee that the convolution is nonzero even if $x\in A+B$. I still need help with this direction. Can someone give me some hints?  EDIT: Camilo's answer below essentially suggest the method of getting 2 open interval from regularity theorem, one cover a subset of A and one cover a subset of B such that the sum of the measure of these two subset is bigger than the measure of the larger interval. user99680's answer point to a wiki which show a method that essentially simply acquire an open set. After some thinking, I believe that these method simply can't be made to work. I constructed this example in the hope that it would convince you that it is the case:  Let $I_{0},I_{1},\ldots$ be disjoint open interval such that the distance between any 2 of them is nonzero and $m(I_{n})=9^{-n}$ and all of them are inside $[0,2]$. Let $J_{0},J_{1},\ldots$ be disjoint open interval such that the distance between any 2 of them is at least $3$ and $m(J_{3n})=m(J_{3n+1})=m(J_{3n+2})=\frac{m(I_{n})}{3}$. Let $O=\bigcup I_{n}$ and $H=\bigcup J_{n}$. Construct $A\subset O$ such that $m(A\bigcap I_{n})=\frac{3m(I_{n})}{4}$. Construct $B\subset H$ such that $m(B\bigcap J_{n})=\frac{3m(J_{n})}{4}$. Now if you apply Camilo's method, it is possible that your $I$ would be one of the $I_{n}$ above, and your $J$ is one of the $J_{m}$ above. No matter which $I_{n},J_{m}$ you have, the argument does not work. Rewrite $m=3q+r$ where $0\leq r\leq 2$. If $q&lt;n$ then $m(J_{m})&gt;m(I_{n})$ so the longer interval have length $\frac{m(I_{q})}{3}$; $m(A\bigcap I_{n})$ is at most $\frac{3m(I_{q+1})}{4}=\frac{m(I_{q})}{12}$ and $m(B\bigcap J_{m})=\frac{3m(J_{m})}{4}=\frac{m(I_{q})}{4}$. Thus $m(A\bigcap I_{n})+m(B\bigcap J_{m})$ is no larger than the larger interval. If $n\geq q$ then $m(I_{n})&gt;m(J_{m})$ so the larger interval is of length $m(I_{n})$; $m(A\bigcap I_{n})=\frac{3m(I_{n})}{4}$ and $m(B\bigcap J_{m})$ is at most $\frac{3m(J_{3n})}{4}=\frac{m(I_{n})}{4}$. Once again $m(A\bigcap I_{n})+m(B\bigcap J_{m})$ is no larger than the larger interval. Hence the Camilo's argument does not work. user99680's method does not work either, since you get $O$ and $H$ which is even bigger than any interval. exponentiation of cardinal number Jquery, changing background image with timer Lets say we have a dependent variable $Y$ with few categories and set of independent variables.    What are the advantages of multinomial logistic regression over set of binary logistic regressions (i.e. )? By set of binary logistic regression I mean that for each category $y_{i} \in Y$ we build separate binary logistic regression model with target=1 when $Y=y_{i}$ and 0 otherwise. How does Earth's interior dynamo work? I'm interested in getting a basic physical understanding of how Earth's magnetic field is generated. I understand that it's a "dynamo" type of effect, driven by convection currents in the molten outer core. These currents cause charges to move, and this generates the field.  However, what I can't find a good explanation of is why there is a separation of charges in the first place. Presumably, moving neutrally charged molten iron would have the same effect as moving any other neutrally charged thing, i.e. it wouldn't create a field.  And presumably, if the fluid wasn't moving then it would become neutral pretty quickly, since molten iron is a good electrical conductor.  So am I right in thinking that the charge separation is the result of positive feedback, in that an intial deviation from neutrality would generate a field, and this would (somehow) cause a greater separation of charges, resulting in a kind of self-maintaining charge separation?  Or is there another explanation?  In either case, does anyone know of a good resource that explains the basic principles in physical terms?  I know that the interior dynamo is a very complex phenomenon, but I'd like something that gives a good physical picture of how the electromagnetic and fluid dynamical phenomena interact, rather than diving straight into partial differential equations. I tried installing Office 2007 in Ubuntu with Wine but it was throwing an error after installing and also when I tried to open a PowerPoint document and save it. Has anybody gotten Office 2007 installed without any issues? Please help me. After swapping the positions of the hour and the minute hand, when will a clock still give a valid time? At 12 o'clock, the hour hand and minute hand of the clock can be swapped, and the clock still gives the same time, but at 6 o'clock, it can not be swapped. So in what cases when we swap the hour and the minute hand position does a clock still give a valid time?