How to replace svg tags from a string in Javascript
How do you use a variable in a regular expression?
a year on: what does it mean? PLease, dear native English speakers, help me to understand the meaning of the expression "a year on" within the context "The reality is that, a year on, a true 4K standard is still very much a work in progress..." Thank you a lot! How can you quickly get the complete path to a file for use in terminal? Adding vertical space at the start of a page I'd like to, first thing before writing anything on a page, add some vertical space.  Minimal (non)working example:  \documentclass{article} \begin{document}  \vspace{250px} I want to be further down on the page :(  \vspace{250px} Haha! Sucker :D \end{document}     How can I get the first \vspace to work, just like the second one? What games save to the Steam Cloud? How to create a Customized Ubuntu Server ISO? I'm currently working on the following problem for my computer theory class. It goes as follows:     Let $A$ and $B$ be regular expressions. Show then that $A^*B$ is the solution   of $X = AX + B$   Am I supposed to let $X = A^*B$? If so then   $A^*B = A(A^*B) + B$  I can understand that  $A(A^*B)$ could be reduced to $A^*B$ but what happens with the "${}+ B$" part of the expression? I've read up on Kleene algebra and found an axiom that seems relevant in which      $b + ax ≤ x → a^∗b ≤ x$   but I'm not actually sure if it applies. deploying and retrieving Address settings (State & Country picklists) Clarifications about Gstreamer I'm a bit confused about what Gstreamer does.   Does it come installed by default with Ubuntu ?  If so which version  is the default for 14.04?  Does it provide hardware accelerated video playback (decoding) ?   If so does it work with VA-API and VDPAU or is it an alternative to those?    Thanks for your help How to exclude files from Visual Studio compile? I'm in the process of refactoring a project.  I've got an entire subfolder which is known to be broken.  Is there any declarative way to exclude that folder from the compile temporarily while I test the refactoring thus far?  I realize I could delete the folder, but I'd like to do this through configuration if possible. Sakurai QM section 5.8 If anyone is familiar with Sakurai's book, specifically section 5.8 on energy shift and decay width, I am stuck and could use some help. I can't see how he derives 5.8.9 (in the revised edition). He starts with (3) (given below), and derives (1) and (2). The equation is as follows:$$(1){\space}{\space}\space{\space}\space{\space}{\dot c_i\over c_i}\approx{{-i\over \hbar}V_{ii}+{\left(-i \over \hbar\right)}^2{{{\left|V_{ii}\right|}^2}\over \eta}+\left({-i\over \hbar}\right) {\sum_{m\not=i}}{{{\left|V_{mi}\right|}^2}\over {(E_i-E_m+i\hbar\eta)}} \over 1-{i \over \hbar}{V_{ii} \over \eta}} $$ $$(2)\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\approx{-i\over \hbar}V_{ii}+\left({-i\over \hbar}\right) {\sum_{m\not=i}}{{{\left|V_{mi}\right|}^2}\over {(E_i-E_m+i\hbar\eta)}}$$ where $$(3)\,\,\,\,\,\,\,\,\,c_i(t)=\lim_{\eta\to 0}\left({1-{i\over \hbar\eta}V_{ii}}{e^{{\eta}t}}+{{\left({-i\over \hbar}\right)}^2}{{\left|V_{ii}\right|}^2}{e^{2{\eta}t}\over 2{\eta}^2}+\left({-i\over \hbar}\right){\sum_{m\not=i}{{{{\left|V_{mi}\right|}^2}}\over 2\eta(E_i-E_m+i{\hbar}\eta}}\right)$$First of all, he discards all kinds of terms in the denominator of the first expression, and I can't see how he justifies this, because as ${\eta}\to0$, every term in the expression for $c_i(t)$ blows up (besides the 1 of course). Then he seems to multiply top and bottom by the complex conjugate of the denominator in (1), arriving at (2). He seems to discard a term from the denominator here, which is of second order in V, and says the equation is formally correct up to second order. This doesn't make sense to me! Also, soon after, he has this strange expression with $$\lim_{x\to 0} {1\over(x+iε)}=Pr.(1/x)-iπδ(x)$$ What is this Pr symbol? Any help would be much appreciated! Prevent parameter expansion in shell script I often have to do a recursive search in files. Tired of typing the whole "find/grep" combination all the time, I just created a script with the following line:  find . -name $1 -exec grep $2 {} + 2&gt;/dev/null   The idea is that I should be able to run it as, for example:  myfind '*' hello   The problem is, when '*' gets passed into the script, the script is expanding it to each file in the directory.  I tried putting a quote around $1:   find . -name '$1' -exec grep $2 {} + 2&gt;/dev/null   However, this turns $1 into a literal string.  Would appreciate your help in finding the right syntax. Must be something simple that I am missing. Why is the last digit of $n^5$ equal to the last digit of $n$? I was wondering why the last digit of $n^5$ is that of $n$? What's the proof and logic behind the statement? I have no idea where to start. Can someone please provide a simple proof or some general ideas about how I can figure out the proof myself? Thanks. How to prove that $\lim_{n\rightarrow \infty}\frac {n^{2}}{2^{n}}=0$ & $\lim_{n\rightarrow \infty}\frac {n^{2}}{n!}=0$? How can I launch a GameObject at a target if I am given everything except for its launch angle? I am trying to launch an object at a target, given its position, its target position, the launch speed, and the gravity.  I am following this formula from :  $$ \theta = arctan \bigg( \frac{v^2 \pm \sqrt{v^4-g(gx^2 + 2yv^2)}}{gx} \bigg) $$  I have simplified the code to the best of my ability, but I still cannot consistently hit the target.  I am only considering the taller trajectory, of the two available from the +- choice in the formula.  Does anyone know what I am doing wrong?  using UnityEngine;  public class Launcher : MonoBehaviour {     public float speed = 10.0f;      void Start()     {         Launch(GameObject.Find("Target").transform);     }      public void Launch(Transform target)     {         float angle = GetAngle(transform.position, target.position, speed, -Physics2D.gravity.y);         var forceToAdd = new Vector2(Mathf.Cos(angle), Mathf.Sin(angle)) * speed;         GetComponent&lt;Rigidbody2D&gt;().AddForce(forceToAdd, ForceMode2D.Impulse);     }      private float GetAngle(Vector2 origin, Vector2 destination, float speed, float gravity)     {         float angle = 0.0f;          //Labeling variables to match formula         float x = Mathf.Abs(destination.x - origin.x);         float y = Mathf.Abs(destination.y - origin.y);         float v = speed;         float g = gravity;          //Formula seen above         float valueToBeSquareRooted = Mathf.Pow(v, 4) - g * (g * Mathf.Pow(x, 2) + 2 * y * Mathf.Pow(v, 2));         if (valueToBeSquareRooted &gt;= 0)         {             angle = Mathf.Atan((Mathf.Pow(v, 2) + Mathf.Sqrt(valueToBeSquareRooted)) / g * x);         }         else         {             //Destination is out of range         }          return angle;     } } Was it just coincidence that Tahir Mahmood went on stage? $K \subset \mathbb{R}^n$ is compact iff it is closed and bounded I want to prove $\Leftarrow$.  I just need one more step, now. If I find a compact set that contains K, then it will finish the proof. Rudin take a k-cell to do that, but before it he proves that every k-cell is compact, and I think I can take a more simple compact to do this step. I has thinked in the closed ball, but don't know how to prove that it is compact. Can anyone help me to find this set, if it really exists? Thanks. Distribution of $Z_n=n \log\left(\frac{\max\left(X_{(n)},Y_{(n)}\right)}{\min\left(X_{(n)},Y_{(n)}\right)}\right)$ The random variables $X_1,X_2,...X_n,Y_1,Y_2,...Y_n $ are independent and $U(0,a)$-distributed. Determine the distribution of $$Z_n=n\cdot \log\left(\frac{\max\left(X_{(n)},Y_{(n)}\right)}{\min\left(X_{(n)},Y_{(n)}\right)}\right)$$ where $X_{(n)},Y_{(n)}$ denotes $n$th order variable.  This problem is giving me a headache. The answer is that $Z_n$ is $\text{Exp}(1)$-distributed. But i can't derive that conclusion. I'd like to show you my derivation, but its so long and contains so many integrals and fractions that it would take a while to write it here. But basically my approach was to derive the distribution of $M=\max(X_{(n)},Y_{(n)})$ and $L=\min(X_{(n)},Y_{(n)})$. I get the following cdf's: $F_M=(F_X\cdot F_Y)^n=(F_X)^{2n}$ and $F_L=1-(1-(F_X)^n)\cdot (1-(F_Y)^n)=1-(1-(F_X)^n)^2$ ,  correct? $F_X $ stands for the cdf of $X_i$  Then i define the random variable $T=\frac{M}{L}$ and compute its cdf to finally be able to derive the distribution of $Z_n=n\cdot \log(T)$. But thats where i think everything goes wrong. Any help appreciated, thanks. Should it be /about_us or /about-us?  From usability point of view, I personally think /about-us is much better for end-user yet Google and most other websites (and javascript frameworks) use underscore naming pattern. Is it just matter of style? Are there any compatibility issues with dashes? Automatically hide old comments Comments are useful. Many, many posts need some small amount of meta discussion, and comments fulfill this need.   Comments are also noisy and distracting. Occasionally, someone will post an insightful and informative comment that complements the post its attached to... But more often, they're tangential, quickly irrelevant and in the way: stale comments show up first, making newer comments less visible.  The guidance here for a long time has been that comments are transient, . And yet, some do hang around for months or years because .   So let's fix that.   I propose that all comments older than 7 days be hidden by default unless the comment has been up-voted in the past 30 days. Hidden comments should be indicated by a note below the post ("add / show 3 more comments") and made visible to anyone who cares to click it.   This doesn't destroy anything, but it would get it out of the way of most readers - and hopefully encourage folks to edit it into the actual answers as a result.  Note: I previously suggested this . Other  have been . However, I'm not suggesting that comments be automatically deleted, and they should be hidden based purely on the age / activity of the comment itself, not of the post to which they're attached. I have two $2\times 2$ matrices, $A$ and $B$, with the same determinant. I want to know if they are similar or not.  I solved this by using a matrix called $S$: $$\left(\begin{array}{cc} a&amp; b\\ c&amp; d \end{array}\right)$$ and its inverse in terms of $a$, $b$, $c$, and $d$, then showing that there was no solution to $A = SBS^{-1}$. That worked fine, but what will I do if I have $3\times 3$ or $9\times 9$ matrices? I can't possibly make system that complex and solve it.  How can I know if any two matrices represent the "same" linear transformation with different bases?  That is, how can I find $S$ that change of basis matrix?  I tried making $A$ and $B$ into linear transformations... but without the bases for the linear transformations I had no way of comparing them.  (I have read that similar matrices will have the same eigenvalues... and the same "trace" --but my class has not studied these yet. Also, it may be the case that some matrices with the same trace and eigenvalues are not similar so this will not solve my problem.)  I have one idea. Maybe if I look at the reduced col. and row echelon forms that will tell me something about the basis for the linear transformation? I'm not really certain how this would work though? Please help.