Test for No Correlation
Is it possible to prove a null hypothesis?
What is the correct way to use infinitive after the verb "help": with or without "to"? Social network login or not? I am developing a niche social networking iPhone app of my own.   I was wondering if it would be best to allow the user to connect to social networks such as Facebook and Twitter to login to my app (and of course an eMail/Password fallback) or just go with regular eMail and Password login.  Any thoughts would be appreciated! :) Concatenate multiple rows How to verify $H\otimes K \cong \bigoplus\limits_{i\in I}H$ Let $H,~K$ be the Hilbert space. if $\{v_{j}\}_{j\in J}\subset H$ and $\{w_{i}\}_{i\in I}\subset K$ are the orthonormal bases, then how to construct the isomorphic mapping: $H\otimes K \rightarrow \bigoplus\limits_{i\in I}H$. Here, the $H \otimes K$ is the tensor product of two Hilbert space. Is there a way to show Spotlight indexing status/progress in Yosemite? In previous versions of OS X, you could click the Spotlight icon in the menu bar to show the status of the Spotlight indexing, and it would show an estimate ("6 hours left"), along with a progress bar.  I've updated to Yosemite yesterday, and I noticed that Spotlight is not showing some expected results, i.e. files I know to be there, but it just doesn't find them if I type in their name and file type ("kind:excel vacation").  When I start typing in the Yosemite Spotlight window, it shows a small progress bar under the search box, but there's no estimate.    Is there another way to show the progress or an estimation on how long the indexing is going to take? I have this on the command line:    ln -sf $PWD/wine-   and then I hit Tab to complete the filename.  In earlier versions of Ubuntu, this worked just fine to complete the wine- filename (and as a side-effect $PWD would be expanded at that time).  But now it turns it in to  ln -sf \$PWD/wine-   which isn't what I meant at all and doesn't complete anything as the file does not literally start with $.  How do I get completion back to the less broken behaviour?  set tells me these are my current settings:  BASHOPTS=checkwinsize:cmdhist:expand_aliases:extquote:force_fignore:hostcomplete:interactive_comments:progcomp:promptvars:sourcepath SHELLOPTS=braceexpand:emacs:hashall:histexpand:history:interactive-comments:monitor I want to pose a question such as:  What is your name? Joe  How would I accomplish this using Console.WriteLine to also wait for the response on that same line instead of it being broken into:  What is your name? Joe Find coefficient of $x^{50}$ in $(\sum_{i=1}^{\infty}x^n)^3$ i have a simple sort of a database file which consists only of entries in the following format     variable=value   i want to create a simple vim syntax highlighting for it and set it for specific file extension  for instance, variable part could be light blue, and value part light red  i googled it and came across things such as $vimruntime\syntax\, syntax set=, syntax match, and hi keywords, but couldn't set it up myself eventually  so i want a very simple vim code snippet that would realize it by matching the left and right hand sides and coloring them separately Electric Potential produced by Hollow Sphere Let there be a hollow sphere (Throughout the question we will ignore the thickness of the sphere) which is positively uniformly charged,q of radius,  R. Suppose there to be a test positive charge, q' at point P which is r distance away from the hollow sphere(r>R, P is outside of hollow sphere).  Now I have an doubt on evaluating Electric Potential,V at point P.  Both source charge,q and test charge,q' are +ve, so source charge will repel the test charge which will make the charge, q' to go to infinity.I have to apply external force, F' to displace the charge, q' from infinity to point P against the equal but repulsive force, F.In short, F' is  displacing the q' from infinity to P.  So External Force, F' will do +ve work and Repulsive Force, F will do -ve work. This way the Electric Field,E produced by hollow sphere is Opposite to Displacement of test charge(i.e.,θ=180).  Now we know that E=k(q/(r^2))  [Please Notice that infinity is the lower limit of integration]  Also V=-∫r∞(E dr cosθ)=-∫r∞(E dr cos 180)=∫r∞(E dr)  At last I ended up to V=- k(q/r). I know that V=k(q/r).  I just want to know why I am having this shitty negative sign in my equation. what exactly is mathematical rigor? I am a programmer moving up to computer science and even in my past life as a mechanical engineer I used sufficient maths to get by but I have always wondered what exactly is this thing called rigor.  Please make me understand it. The  says that public class SomeObject {   public void SomeOperation()   {     lock(this)     {       //Access instance variables     }   } }  is &quot;a problem if the instance can be accessed publicly&quot;. I'm wondering why? Is it because the lock will be held longer than necessary? Or is there some more insidious reason? Integral $\int\frac{dy}{(y^2 + ay + b)^{3/2}}$ Need the indefinite integral with $a,b$ constants. This is not a homework question. Need it for a physics problem. Deriving curvature formula How do you derive the formula for unsigned curvature of a curve $\gamma (t) = (x(t), y(t)$ which is not necessarily parameterised by arc-length.   The formula given is $$|\kappa (t)| = \left|\frac{x'' y' - y'' x'}{((x')^2 + (y')^2)^{3/2}}\right|$$  All the definitions of curvature in my notes give it in terms for an arc-length parameterisation $T'(s) = \kappa(s) N(s)$. This is apparently meant to be 'easily derivable', am I missing something? From my understanding it's not prime because it's not greater than $0$. So my followup question is why did mathematicians exclude $-1$?  The definition of prime is having only two factors.   $-1 \cdot 1 = -1$ Self-deleted posts and the 3 vote / 60 day rule With regards to  post about  and the part about retaining reputation earned from deleted posts that have a score of 3 or better and were visible on the site for 60 days, does this also apply to self-deleted posts and will it continue to do so? I culled a few of my own answers over the weekend that were less than stellar, and my reputation dropped 1.8k, but the rep is back today after the changes were announced. I thought it would be useful to clarify that this also applies to self-deleted stuff. Do redirection operators always open file descriptors in parallel? Is there any "superlogarithm" or something to solve $x^x$? Is there any "superlogarithm" or something to solve an equation like this:  $$x^x = 10?$$ Multiple WHERE clause in Linq The usual example of unitary ring without the  property is the ring of column finite matrices, and in this case we have $R\simeq R^2$ as (left) $R$-modules. (See also .) In particular, we have $R^2\simeq R^3$.      I wonder if there is an example of unitary ring (without the IBN property) such that $R^2\simeq R^3$, but $R\not\simeq R^2$ (as $R$-modules).