In my site I have two different roles for users named recruiter and candidate. when they register their account they can choose their role (recruiter or candidate). And when they login my site I will check user is recruiter or candidate. after this check I will show them a different page (recruiter page and candidate page).  How to proceed with this?
By default after a new user signs up, a redirect to the home page happens.  But in such case I want to redirect such user to another page like node/35.  In this node/35 I then want to display some content.
Value too great for base (error token is "09") Homotopy equivalence of universal cover As part of am exam question (Q21F ), I'm trying to prove that if $X$ and $Y$ are path-connected, locally path-connected spaces with universal covers $\widetilde{X}$ and $\widetilde{Y}$, respectively, then if $X \simeq Y$ then $\widetilde{X} \simeq \widetilde{Y}$.  My attempt might be correct, but it seems too complicated and amongst the jumble I may have made some incorrect assumptions. So what I'm looking for is (a) verification or correction; and (b) ideas as to how I could simplify my argument.    My argument:  Let $p:\widetilde{X} \to X$ and $q:\widetilde{Y} \to Y$ be the covering maps, and let $X \overset{f}{\underset{g}{\leftrightarrows}} Y$ be a homotopy equivalence.  Fix a point $\widetilde{x} \in \widetilde{X}$, let $x=p(x) \in X$ and $y=f(x) \in Y$, and fix $\widetilde{y} \in q^{-1}(\{y\}) \subseteq \widetilde{Y}$. Also let $x' = g(y) \in X$ and fix $\widetilde{x'} \in p^{-1}(\{x'\}) \subseteq \widetilde{X}$.  Define a map $\widetilde{f} : \widetilde{X} \to \widetilde{Y}$ as follows. For $\widetilde{z} \in \widetilde{X}$ let $\widetilde{u}:[0,1] \to \widetilde{X}$ be a path from $\widetilde{x}$ to $\widetilde{z}$. Let $z=p(z)$ so that $u=p\widetilde{u}$ is a path in $X$ from $x$ to $z$. Let $v=fu$, so that $v$ is a path in $Y$ from $y$ to $f(z)$. Lift $v$ to a path $\widetilde{v}$ in $\widetilde{Y}$ with $\widetilde{v}(0) = \widetilde{y}$. Define $\widetilde{f}(\widetilde{z}) = \widetilde{v}(1)$.  Notice that $q\widetilde{v}=v$ so that $q\widetilde{f} = fp$.  Define $\widetilde{g}:Y \to X$ analogously: For $\widetilde{z} \in \widetilde{Y}$ let $\widetilde{a}:[0,1] \to \widetilde{Y}$ be a path from $\widetilde{y}$ to $\widetilde{z}$. Let $z=q(z)$ so that $a=q\widetilde{a}$ is a path in $Y$ from $y$ to $z$. Let $b=fa$, so that $b$ is a path in $X$ from $x'$ to $g(z)$. Lift $b$ to a path $\widetilde{b}$ in $\widetilde{X}$ with $\widetilde{b}(0) = \widetilde{x'}$. Define $\widetilde{g}(\widetilde{z}) = \widetilde{b}(1)$.  Likewise, notice that $p\widetilde{g}=gq$.  Claim: $\widetilde{X} \overset{\widetilde{f}}{\underset{\widetilde{g}}{\leftrightarrows}} \widetilde{Y}$ is a homotopy equivalence.  We have $p\widetilde{g}\widetilde{f} = gq\widetilde{f}=gfp \simeq p$ and $q\widetilde{f}\widetilde{g} = fp\widetilde{g} = fgq \simeq q$.  This shows that $\widetilde{g}\widetilde{f}$ and $\widetilde{f}\widetilde{g}$ are covering translations (deck transformations) and are therefore homotopic to the respective identity maps. So we have a homotopy equivalence.    Any comments would be appreciated. What are some good books for learning general relativity? Fastest way to determine if an integer's square root is an integer I'm looking for the fastest way to determine if a long value is a perfect square (i.e. its square root is another integer):    I've done it the easy way, by using the built-in  function, but I'm wondering if there is a way to do it faster by restricting yourself to integer-only domain. Maintaining a lookup table is impractical (since there are about 231.5 integers whose square is less than 263).   Here is the very simple and straightforward way I'm doing it now:  public final static boolean isPerfectSquare(long n) {   if (n &lt; 0)     return false;    long tst = (long)(Math.sqrt(n) + 0.5);   return tst*tst == n; }   Note: I'm using this function in many  problems.  So no one else will ever have to maintain this code.  And this kind of micro-optimization could actually make a difference, since part of the challenge is to do every algorithm in less than a minute, and this function will need to be called millions of times in some problems.    I've tried the different solutions to the problem:   After exhaustive testing, I found that adding 0.5 to the result of Math.sqrt() is not necessary, at least not on my machine. The  was faster, but it gave incorrect results for n >= 410881.  However, as suggested by , we can use the FISR hack for n &lt; 410881. Newton's method was a good bit slower than Math.sqrt().  This is probably because Math.sqrt() uses something similar to Newton's Method, but implemented in the hardware so it's much faster than in Java.  Also, Newton's Method still required use of doubles. A modified Newton's method, which used a few tricks so that only integer math was involved, required some hacks to avoid overflow (I want this function to work with all positive 64-bit signed integers), and it was still slower than Math.sqrt(). Binary chop was even slower.  This makes sense because the binary chop will on average require 16 passes to find the square root of a 64-bit number. According to John's tests, using or statements is faster in C++ than using a switch, but in Java and C# there appears to be no difference between or and switch. I also tried making a lookup table (as a private static array of 64 boolean values).  Then instead of either switch or or statement, I would just say if(lookup[(int)(n&amp;0x3F)]) { test } else return false;.  To my surprise, this was (just slightly) slower. This is because . I've started using the dashicon fonts in my theme options page for WP 3.8+ users. To take care of users on &lt; 3.8, I've added the dashicon fonts to my theme folder and also an entry at the top of my custom admin stylesheet:  @font-face {     font-family: 'dashicons';     src: url('fonts/dashicons.eot'); }  @font-face {         font-family: 'dashicons';         src: url(data:application/x-font-woff;charset=utf-8;base64,xxx) format('woff'),         url('fonts/dashicons.ttf') format('truetype'),         url('fonts/dashicons.svg#dashicons') format('svg');     font-weight: normal;     font-style: normal; }   (I've left out the base64 encode for brevity)  This works great, however, I'm getting a bit of strange behavior with the fonts. When I leave the admin open in a tab and go away for a bit, then come back, every once in a while, the webfonts have turned to squares, as if the font is missing.  This does not happen every time. It appears to be somewhat random.  In those cases, simply doing a mouseover the page usually returns the webfonts to their proper symbols.  The screenshots below show the issue. The first screenshot is what I see when the problem occurs. The second screenshot is what I'm expecting to see when things go well.   Notice in the first shot, how the wordpress labels themselves have gone to a default serif font. Spacial curvature and expanding space If we take the analogy that in an empty space the space is just a flat sheet then if there is a single planet or a star then the flat sheet will curve below the planet leaving a curvature shaped like a hemisphere below the object, my question is, Does this curvature change as space expands? How do you correctly say large numbers I saw a post on  which links to a video where a person . Is he saying a large portion of the numbers wrong? Back in high school my algebra teacher was extremely picky.  If we were going to say the number 135, we would say one hundred thirty-five.  If a person said one hundred and thirty-five my teacher would interpret that to mean 100.35.  Was my algebra teacher wrong, or did Jon just waste over 80 hours counting to 100,000 incorrectly. I tried searching the web, but searching for ‘numbers and’  doesn’t work very well.  Can you point me to a reference or style guide that describes how to properly say large numbers? Difference of the \dots* I came to wonder, what is the difference between the following?  \dotsc \dotso   As well as between:  \dotsb \dotsi \dotsm What is the plural form of "Software"? Computing dominant area in polygon using ArcGIS Desktop? Right at the beginning of the game, Meowth comes into your room and attempts to wake you up. At this point, I assume I have to press some button to get out of bed, but the D-Pad or A button doesn't do anything, nor any of the other buttons. How do I get out of bed to start the game? How do I turn on workspaces? (Why do I only have one workspace?) My machine can't play encrypted DVDs on a fresh install.  How do I add this capability?  Another useful bit of information would be what programs are best for playing DVDs, once I'm able to do so.  See the .  Will I be able to play DVD movies from ? series of young adult science fiction books from early 1980s about last of a race of martial experts that sees the destruction of his home planet I remember that the main character is trying to find the group that destroyed his home planet while he was on a mission. His planet was very difficult to live on and the people became expert in martial arts and were the best soldiers in the galaxy. They were mercenaries and often helped against tyrants. There was a very memorable section in at least one book about an initiation task that the main character had to do in that he had to survive in their wilderness for days. He was at some point surrounded in a old building by thousands of poisonous worm/snake creatures that he managed to survive until rescued by the leaders. Why is $1$ not a prime number? Why is $1$ not considered a prime number?  Or, why is the definition of prime numbers given for integers greater than $1$? Why does the following code does'nt work when i am using PDFLaTeX or just LaTeX ? I tried it in different editors as well.  This is the code   $\{f^'_n\}$   Surprisingly it works on Math.SE site There are 8 crew members, The leading member wants that only a crew of 5 people or more could open a safe he bought, To each member he gave equal amount of keys, and locked the safe with several locks.  What's the minimal number of locks he should put:   at least 5 crew members would be required to open the safe? Any team of 5 crew members could open the safe, but none of the 4 team crew members.   1,2 stands individually of course. Best solution to protect PHP code without encryption First of all, I'm not looking for miracle... I know how PHP works and that there's not really way to hide my code from the clients without using encryption. But that comes with the cost of an extension to be installed on the running server.  I'm looking for something different though... I'm not looking to encrypt my code or even obfuscate it. There are many PHP scripts without encrypted/obfuscated code but they are commercial applications. For instance, vBulletin and/or IP.Board forum applications.  I just want to know what approach do these guys use for their applications...  I'm also open to any other suggestions.  Please note that I'm a single person and not working for a company. My product is also very specific, it won't sell that much. I just want you guys to know that I can't afford to consult a legal professional either to sue someone or prepare a commercial license. I'm just looking for a simple way to protect my simple product, if it's indeed possible, somehow... So I'm pretty sure there's at least 2, one for both X &amp; Y.   Much like other iterations of the other Pokemon games, are there other Legendaries? How many legendaries, and what are their names? Simple newbie help page about avoiding "Thanks"