&lt;?php   $pattern = "/http:\\/\\/(([A-Za-z0-9.\-])*)/";   $text = "http://www.google.com";   $text = preg_replace($pattern,"&lt;a href=\"\\0\"&gt;\\0&lt;/a&gt;",$text);   echo $text;  ?&gt;   The code above gets the URL from a string variable and adds an HTML tag           for a link. So "http://www.google.com" becomes "&lt;a href="http://www.google.com"&gt;http://www.google.com&lt;/a&gt;".  My question is how "\0" is something like placeholder for the value of the parameter "$text" in the "preg_repace" function, after it means NULL or 0x0?
I am trying to grab the capital letters of a couple of words and wrap them in span tags. I am using  for extract and wrapping purposes, but it's not outputting anything.  preg_replace("/[A-Z]/", "&lt;span class=\"initial\"&gt;$1&lt;/span&gt;", $str)
From :     Importantly, the DDH assumption does not hold in the multiplicative group $\mathbb {Z} _{p}^{*}$, where $p$ is prime. This is because given $g^{a}$ and $g^{b}$, one can efficiently compute the Legendre symbol of $g^{ab}$, giving a successful method to distinguish $g^{ab}$ from a random group element.   The only way I can think of to distinguish $g^c$ from $g^{ab}$ is:    If $\left(\frac{g}{p}\right)=-1$, then $\left(\frac{g^{ab}}{p}\right) = 1$ if and only if $a$ or $b$ is even (which is $3/4$ of the times). So if $\left(\frac{g^c}{p}\right) =-1$, probably $g^c\neq g^{ab}$. Nothing is certain.   How'd do you compute $\left(\frac{g^{ab}}{p}\right)$ given $g^a$ and $g^b$? Why is this true: The only orthogonal projection that is also unitary from $\Bbb C^n$ to $\Bbb C^n$ is the identity Can anyone explain me please how to see this statement: the only orthogonal projection that is also unitary from $\Bbb C^n$ to $\Bbb C^n$ is the Identity.  how can I prove formally that? or how can I see that only the Identity satisfy it? String.Join vs. StringBuilder: which is faster? I'm trying to prove whether or not the Laurent polynomials $\mathbb{Z}[x, x^{-1}]$ with coefficients in $\mathbb{Z}$ form a principal ideal domain.    I know that $\mathbb{F}[x, x^{-1}]$ is a PID when $\mathbb{F}$ is a field, but clearly $\mathbb{Z}$ is not a field so I cannot appeal to this result. And my intuitions are not serving me very well at the moment. Can anyone provide a hint or direction to take? I am trying to define an alternative \item command that would allow me to use a different color for some of the items. My code has the following form:  \documentclass{article} \usepackage{color}  \definecolor{gray}{rgb}{0.7,0.7,0.7} \newcommand{\grayitem}[1]{{\color{gray} \item #1}}  \begin{document}  \begin{enumerate} \item First item. \grayitem Second item. \item Third item. \end{enumerate}  \end{document}   I was hoping that  \grayitem Second item.   would produce the same result as  {\color{gray} \item Second item.}   but for some reason, these are not equivalent. They produce the following results, respectively:  &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;  &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;   Why are these two lines of code not equivalent? What am I doing wrong and how can I change the definition of \grayitem to produce the second result?  I have also tried removing a pair of braces, like this  \newcommand{\grayitem}[1]{\color{gray} \item #1}   but then the third item becomes gray as well.  The solution should also work for multi-paragraph items. Bjarne Stroustrup once mentioned in one of his bigthink interviews that one of the greatest problems most programmers have is not finding or using the right libraries.  On stackoverflow and programmers, I've observed a trend towards questions like "I want to do this, is there a [library | programming language] for that", or "I have these {n} [library | language] candidates for my project; which one would yield me the least amount of headache given these requirements".   Since questions like these aren't exactly programming questions in the sense of "this code should do this, but it does this, why?", they are often (though not always) being closed as "not constructive" because they do not have a definite answer (which is true, and according to the FAQ they would be off-topic on both stackoverflow and programmers).  Nonetheless, I think library questions are valid, and that it is helpful for any programmer to receive independent input from experienced programmers (at least it helps me a lot every time I browse through one of those closed questions, which I found through google). Does anyone agree that posting library choice questions should be explicitly allowed on either stackoverflow or programmers? I don't know if this is a famous problem but my professor assigned this for a research project and I am hitting a dead end( I don't know what to do next).   Note: In $\phi(n)$ ; $n=rows=columns$ and this function throws out total combination of matrices that satisfies the following rule:  Rule for this square binary matrix:  Every Row and Column has two 1's.  So,    $$\phi(2)=1$$ \begin{bmatrix}    1 1 \\    1 1 \\ \end{bmatrix} $$\phi(3)=6$$  I can't write out all the possible matrices for $n=3$ but this is one of them (btw i did this by hand): \begin{bmatrix}    0 1 1 \\    1 0 1 \\ 1 1 0 \\ \end{bmatrix}   According to a program made by my friend, he told me:   $$\phi(4)=90$$ $$\phi(5)=2040$$ Most of the time, it should be really easy to determine who is my ally and who is not. The people who try to kill me are most likely my foes, whereas the people who entered the dungeon with me are probably my allies.   But sometimes it’s not that simple. What if one of my party members got replaced by an evil doppelganger, who plans to kill me in the near future? What if one of my allies infiltrated the court of the evil king and I accidentally have to fight her, while she is (unbeknownst to me) under the effect of a  spell? What if a character fell in love with the BBEG and just wants to save him from himself, while the BBEG hates the character and actively tries to murder him?  Most spells and abilities that affect others specify the targets as “creatures” or “willing creatures”. Some explicitly affect allies only. That’s why I want to know, how to determine who’s allied with whom. Do I have to think that someone is my ally for someone to count as my ally? Does someone else have to believe to be my ally in order to count? Do both of us have to agree on being allies? Is there an objective observer who determines who’s allied? Can Person A be the ally of Person B, while Person B is not the ally of Person A?  There are many examples for spells/abilities that care about allies, among others:   the Exalted Champion feature from the  (SCAG, p. 132-133), that grants allies within 30 feet advantage on Wisdom saving throws. the Inspiring Surge feature from the  (SCAG, p. 128), that allows one or two allies within 60 feet to make a melee weapon attack as a reaction.   With features like this, you could accidentally affect someone who’s not actually your ally. You could fail to affect someone who is actually your ally, but you don’t know it (yet). Or you could affect someone who doesn’t want to be affected (because they don’t want to be allied with you). This all depends on the interpretation of the word “ally”. I’m not sure if "ally" is a defined game term (but I don’t think so), or if I have to rely on the dictionary definition. That’s why I want to ask:  How do I determine who’s allied with whom? Using tikzcd in newcommand (for inline arrows) I’m using tikz-cd for diagrams, and have a medium-sized diagram that I want to re-use several times.  However, when I try using a definition like:  \newcommand{\myarrow}{$\begin{tikzcd} A \ar{r} &amp; B \end{tikzcd}$   I get an error:  ERROR: Package pgfbasematrix Error: Single ampersand used with wrong catcode.   Is it possible to put a tikz-cd diagram into a defined command somehow? I have a problem. I have several large equations within the text. And when LaTeX does not manage to put the equation on the same page and moves it to the next one, he spreads the paragraphs of the text in the first page. How could I prevent this? I know about \pagebreak and \newpage, but I do not want to force the \newpage, as the text may move (if I add something later or so on) and the pagebreaks may not be valid. I would like to make LaTeX not to spread the paragraphs over a page automatically. Is it possible?  I tried to make an example:  \documentclass[a4paper,12pt,twoside]{book} \usepackage{amsmath} \begin{document}  LaLaLa\\\  LaLaLa\\\  LaLaLa\\\  LaLaLa\\\  \begin{eqnarray} 123&amp;+&amp;123 \\\ 123&amp;+&amp;123 \nonumber\\\ 123&amp;+&amp;123 \nonumber\\\ 123&amp;+&amp;123 \nonumber\\\ 123&amp;+&amp;123 \nonumber\\\ \end{eqnarray}  LaLaLa\\\  LaLaLa\\\  \begin{eqnarray} 123&amp;+&amp;123 \\\ 123&amp;+&amp;123 \nonumber\\\ 123&amp;+&amp;123 \nonumber\\\ 123&amp;+&amp;123 \nonumber\\\ 123&amp;+&amp;123 \nonumber\\\ 123&amp;+&amp;123 \nonumber\\\ 123&amp;+&amp;123 \nonumber\\\ 123&amp;+&amp;123 \nonumber\\\ 123&amp;+&amp;123 \nonumber\\\ 123&amp;+&amp;123 \nonumber\\\ 123&amp;+&amp;123 \nonumber\\\ 123&amp;+&amp;123 \nonumber\\\ 123&amp;+&amp;123 \nonumber\\\ 123&amp;+&amp;123 \nonumber\\\ 123&amp;+&amp;123 \nonumber\\\ \end{eqnarray}  \end{document} $\sum_{n=-\infty}^{\infty}\frac{1}{(u +n)^2}=\frac{\pi^2}{(\sin \pi u)^2}$ I've already see a  by Marko Riedel which I list it follows:     The standard way to treat these sums is to integrate   $$ f(z) = \frac{1}{(z+\alpha)^2} \pi \cot(\pi z)$$   along a contour consisting of a circle of radius $R$ and with $R$ going to infinity and hence being larger than $\alpha$, where the circle does not pass through the poles on the real axis.   Now along the semicircle in the upper half plane we have   $$|f(z)| \le \frac{1}{(R-|\alpha|)^2}\pi \left|\frac{e^{i\pi R\exp(i\theta)} + e^{-i\pi R\exp(i\theta)}} {e^{i\pi R\exp(i\theta)} - e^{-i\pi R\exp(i\theta)}}\right|= \frac{1}{(R-|\alpha|)^2} \pi  \left|\frac{e^{2i\pi R\exp(i\theta)}+1}{e^{2i\pi R\exp(i\theta)}-1}\right| &lt; \frac{1}{(R-|\alpha|)^2} \pi   \frac{1+e^{-2\pi R\sin(\theta)}e^{2i\pi R\cos(\theta)}} {1-e^{-2\pi R\sin(\theta)}e^{2i\pi R\cos(\theta)}}$$   This last term is clearly $O(1/R^2)$ as $R$ goes to infinity as the quotient of the two exponentials goes to one since $\exp(-R)$ vanishes and there is no singularity when $\theta = 0$ or $\theta = \pi$ as $R\cos\theta = \pm R$, which is not an integer by the assumption that the circle avoids the poles and hence cannot be one.     My question: It is clear that for each $z=Re^{i \theta}$ , $f(z)=O(1/R^2)$ ，but can this guarantee that the last term on RHS is uniform bounded ? Since $\theta$ varies on a compact interval $[0, \pi]$ , I want to show that for each $ \theta \in [0, \pi]$ , and a fixed positive number $M \gt 1 $ there exist an open ball contains $\theta$ and a fixed $R_{\theta}\gt 0$ , for every $R \ge R_{\theta}$ and $x \in $ the open ball $$\frac{1+e^{-2\pi R\sin(x)}e^{2i\pi R\cos(x)}} {1-e^{-2\pi R\sin(x)}e^{2i\pi R\cos(x)}} \le M$$  For $\theta \neq 0,\pi$ , it is easy to find the desired $R_{\theta}$ and the open ball , but if $\theta = 0$ or $ \theta = \pi$ , for every open ball containing $\theta$ , it behave erratically near $\theta$ , I have no idea how to deal with this . (mód 1) is not copied correctly Please consider the following MWE:  \documentclass{article} \usepackage[spanish]{babel} \selectlanguage{spanish} \usepackage[utf8]{inputenc} \usepackage[T1]{fontenc}  \begin{document} Works: áéà  Does not work: \(\pmod1\) \end{document}   The áéà text is copied correctly, but if I try to copy (mód 1) it says: (m´od 1).  Does anyone know why this happens? How is it solved?  Thanks! This is a question in Ahlfors in the section on the argument principle: How many roots of the equation $f(z)=z^4+8z^3+3z^2+8z+3=0$ lie in the right half plane?  He gives a hint that we should "sketch the image of the imaginary axis and apply the argument principle to a large half disk."  Since $f$ is an entire function, I think I understand that the argument principle tells us that for any closed curve $\gamma$ in $\mathbb{C}$, the winding number of $f(\gamma)$ around 0 is equal to the number of zeros of $f$ contained inside $\gamma$.  How would you go about actually applying the hint though? I am having trouble figuring out what the image of a large half disk under $f$ would look like. Possible Duplicate:             In the itemize environment, how do I use the ampersand symbol &amp; without LaTeX trying to use it as a command? Sole survivor of attack on mining vessel, abandoned by his employer, has ability to teleport There's a story my grandpa use to tell me when I was younger, about the sole survivor of of an attack on a mining vessel in space. The man lives in space for months/years, ignored by the company he worked for and never rescued. Then when he thinks he is being rescued, it's actually another set of raiders who attack him and kidnap him.  He then wakes up in captivity in some sort of prison inside of an asteroid, and has a word tattooed on his forehead. My grandpa called him Ronin (that's what the tattoo on his forehead said) but I don't know what the character's real name is. Anyways, he learns that he has the ability to teleport after having a brush with death and decides to make his way back to Earth so that he can exact revenge on the mining company who abandoned him and left him floating to die.  Does anyone know what this story or book may be? My grandpa told it to me when I was little, he said that he got it from a book he use to love reading when he was younger. I'm assuming the book is very old (possibly pre 1940's as he was born in the 20s). I can't ask him as he is no longer alive. I'm also unsure as to whether or not all the details in the story he told me, are the same as in the original. What tool do you use to monitor your servers? For a more comprehensive list of monitoring tools and their features, check out .   As the question states, what are the most commonly used tools used for this task and what are their strengths and weaknesses? Embed LaTeX math equations into Microsoft Word Let's say I have a (comparatively) lovely-looking document in LaTeX, full of lovingly typeset, (relatively) complex equations. Now, let's say some barbarians come along one day and decide that the document has to be put into Microsoft Word (2007). ...after the usual mourning period associated with such events, let's say I value my job (more specifically, the bread it provides) enough to get all the text and tables formatted and references organised into the Word document. –...related questions  and – Now I'm looking at the equations with fear and dread. One option of course is to just lift screenshots from the original document, but this is painstaking if I need to refer to parts of the equation in the text. Also, I might need to edit equations on the fly. Anyone know of a free application which allows embedding LaTeX math into MS Word? I've looked at  and  which do roughly what I want... they build LaTeX images from source and embed them into the Word document, allowing to edit the source later... but both are commerical. ...any help in these troubling times will be greatly appreciated. EDIT: Just a note that  offers a 30-day free trial and is working out really nicely... but still, it's not free. Might be a good solution for those with short-term needs, or money. Determine the size of a C++ array programmatically? This question was inspired by a similar question:   My question is a little different:  Is there any way to determine the size of a C++ array programmatically?  And if not, why?  Every function I've seen that takes an array also requires an integer parameter to give it the size.  But as the linked question pointed out, delete[] must know the size of the memory to be deallocated.  Consider this C++ code:  int* arr = new int[256]; printf("Size of arr: %d\n", sizeof(arr));   This prints "Size of arr: 4", which is just the size of the pointer.  It would be nice to have some function which prints 256, but I don't think one exists in C++.  (Again, part of the question is why it doesn't exist.)  Clarification: I know that if I declared the array on the stack instead of the heap (i.e. "int arr[256];") that the sizeof operator would return 1024 (array length * sizeof(int)). Why are there humans in the Star Wars Universe? Delaunay triangulation to generate abstract networks and nodes Is it possible to use Delaunay triangulation to generate an image like the below from a raster or vector of an object (in this case, a human heart)? What software and techniques would be required to make something like this? My intention is to make and use something like this in Inkscape without having to draw all the nodes/lines/effects manually.