Change the "under review" date after revision
Change in "under review" date
How to limit execution time of a function call? There is a socket related function call in my code, that function is from another module thus out of my control, the problem is that it blocks for hours occasionally, which is totally unacceptable, How can I limit the function execution time from my code? I guess the solution must utilize another thread. Why do we assume $a+b=b+a$ in a Ring with 1. Also, is it true with Rings without 1? I was wondering why do some people use redundant axioms in definitions?  If you just expand $(a+1)(b+1)=(a+1)b+a+1=ab+b+a+1$ $(a+1)(b+1)=a(b+1)+b+1=ab+a+b+1$. Hence, $ab+a+b+1=ab+b+a+1$, then cancel ab and 1. Then, you get it's commutative for free.   Why do we then assume it?   Also, is it even stronger. If we drop the condition that 1 is in R, then can we still deduce a+b=b+a? As clearly the argument just done falls apart if you haven't got 1 in R. docky crashes from time to time for me. How can I make it restart automatically after it crashed? When is the graph of the divisor relation on $[n]$ planar? How can I control where smoke and fire are emitted from? Is there a general way to change the font of a particular symbol without switching packages?  For example, suppose I'm using Computer Modern for my entire document, but I want the "subset" operator to look as it does in mathabx.  How can I redefine it to appear in this way? How can I remove the first line of a text file using bash/sed script? What is the joint distribution of $Z=\min(X,Y)$ and $I_{Z=X}$? Assume that $X$ and $Y$ are independent random variables with $X \sim \exp(\lambda)$ and $Y \sim \exp(\mu)$. It is impossible to obtain direct observations of $X$ and $Y$. Instead, we observe the random variables $Z$ and $W$, where $Z = \min\{X,Y\}$ and $W =1$ if $Z=X$ and $W=0$ if $Z=Y$.  How to find the joint distribution of $Z$ and $W$? Find all entire functions $f(z)$ such that $|f(z)|=1$ for $|z|=1$  Hint: First show that $f(z)$ is a polynomial.  Clearly one can not use Cauchy Estimates to prove that $f(z)$ is a polynomial, the other way is to prove that $f(z)$ has a pole at infinity which I am not sure how to prove that, are there any other ways to prove that a given entire function is a polynomial ?  Thank you ! What does “would not have been possible had I remained” mean? What does this mean?      I am sure this would not have been possible had I remained a typical Anglophone North American.   I have never heard that before and I really find it strange.  I deduce that it means      I am sure this would not have been possible if I kept remaining Anglophone North American.   But I might be wrong in this. Runtime's exec() method is not redirecting the output Is there a rational number between any two irrationals? Suppose $i_1$ and $i_2$ are distinct irrational numbers with $i_1 &lt; i_2$.  Is it necessarily the case that there is a rational number $r$ in the interval $[i_1, i_2]$?  How would you construct such a rational number?  [I posted this only so that the useful answers at  could be merged here before that question was deleted.] Why are there two tensions on my free body diagram? Show that the sequence $a_{n+1}=a_{n}+\dfrac{a^2_{n}}{n^2}$ is upper bounded Let $\{a_{n}\}$ be defined with $a_{1}\in(0,1)$, and  $$a_{n+1}=a_{n}+\dfrac{a^2_{n}}{n^2}$$ for all $n\gt 0$.  Show that the sequence is  upper bounded.  My idea: since  $$a_{n+1}=a_{n}\left(1+\dfrac{a_{n}}{n^2}\right)$$ then $$\dfrac{1}{a_{n+1}}=\dfrac{1}{a_{n}}-\dfrac{1}{a_{n}+n^2}$$ then $$\dfrac{1}{a_{n}}-\dfrac{1}{a_{n+1}}=\dfrac{1}{a_{n}+n^2}$$ so $$\dfrac{1}{a_{1}}-\dfrac{1}{a_{n+1}}=\sum_{i=1}^{n}\dfrac{1}{a_{i}+i^2}$$ since $$a_{n+1}&gt;a_{n}\Longrightarrow \dfrac{1}{a_{i}+i^2}&lt;\dfrac{1}{a_{1}+i^2}$$ so $$\dfrac{1}{a_{n+1}}&gt;\dfrac{1}{a_{1}}-\left(\dfrac{1}{1+a_{1}}+\dfrac{1}{2^2+a_{1}}+\cdots+\dfrac{1}{a_{1}+n^2}\right)$$ But the RHS might be $\lt0$ for a sufficiently large starting value; for instance, with $a_{1}=\dfrac{99}{100}$ then $$\dfrac{1}{a_{1}}-\left(\dfrac{1}{1+a_{1}}+\dfrac{1}{2^2+a_{1}}+\cdots+\dfrac{1}{a_{1}+n^2}\right)&lt;0,n\to\infty$$  see:   so this method won't let me bound the series and I don't know what else to do. Landscape topography from grayscale image How do we perform transverse measurements in a two level system? In quantum mechanics any two level system can be mapped onto effective spin variables. If the system is defined by two energy levels, $|E_1\rangle$ and $|E_2\rangle$, the Hamiltonian is  $$ H = \left(\begin{array}{cc} E_1 &amp; 0 \\ 0 &amp; E_2 \end{array}\right) \, .$$  This can be recast as  $$ H = \frac{E_1+E_2}{2} 1\!\!1 + \frac{E_1-E_2}{2} \sigma_3\, .$$  $1\!\!1$ is the identity operator and $\sigma_3$ is the third pauli matrix. This is very nice because we can now apply our knowledge and intuition of spin dynamics to any two level system.  My question is the following: for a real spin I can measure expectation values of $\sigma_{1,2}$ by physically rotating my system and align its $x$ or $y$ axis with my measuring apparatus. How do I do this (in the lab!) with a pseudo-spin system? Imagine I am looking at a cold atom and I want to know if the system is in an symmetric or anti-symmetric superposition of $|E_1\rangle$ and $|E_2\rangle$, how do I do it? It's become clear that last night's (Tues Jan 8th 2019) patches to Windows 7 broke SMB2 networking in Lanman Server.  One or both of KB 4480970 and KB 4480960 results in any OS that uses SMB2 (such as Windows XP, some Windows 7, and same generation server OS' and Mac OS X machines (certainly 10.10, 10.11 not sure about others yet)) being unable to connect to Windows 7 Pro shares.  Client machines repeatedly prompt for login despite credentials being correct. Use of quotes in GNU grep regular expressions How can I verify a Google authentication access token?  I need to somehow query Google and ask: Is [given access token] valid for the [example@example.com] Google account?  Short version: It's clear how an access token supplied through the  can be used to then request data from a range of Google services. It is not clear how to check if a given access token is valid for a given Google account. I'd like to know how.  Long version: I'm developing an API that uses token-based authentication. A token will be returned upon provision of a valid username+password or upon provision of a third-party token from any one of N verifiable services.  One of the third-party services will be Google, allowing a user to authenticate against my service using their Google account. This will later be extended to include Yahoo accounts, trusted OpenID providers and so on.  Schematic example of Google-based access:    The 'API' entity is under my full control. The 'public interface' entity is any web- or desktop-based app. Some public interfaces are under my control, others will not be and others still I may never even know about.  Therefore I cannot trust the token supplied to the API in step 3. This will be supplied along with the corresponding Google account email address.  I need to somehow query Google and ask: Is this access token valid for example@example.com?  In this case, example@example.com is the Google account unique identifier - the email address someone uses to log in to their Google account. This cannot be assumed to be a Gmail address - someone can have a Google account without having a Gmail account.  The Google documentation clearly states how, with an access token, data can be retrieved from a number of Google services. Nothing seems to state how you can check if a given access token is valid in the first place.  Update The token is valid for N Google services. I can't try a token against a Google service as means of verifying it as I won't know which subset of all Google's services a given user actually uses.  Furthermore, I'll never be using the Google authentication access token to access any Google services, merely as a means of verifying a supposed Google user actually is who they say they are. If there is another way of doing this I'm happy to try. Why doesn't the Moon fall onto the Earth? For that matter, why doesn't anything rotating a larger body ever fall onto the larger body?