During big bang, everything expands same rate, homogenous, isotropic, nothing pulled towards each other. Did quantum randomness form stars, galaxies?
Was the singularity at Big Bang perfectly uniform and if so, why did the universe lose its uniformity?
Prove that a polynomial is irreducible or the field contains a $p$th root An exercise from Lang:  Let $k$ be a field. Let $n$ be a nonnegative integer. Consider the polynomial $x^{p^n}-a \in k[x]$. Assume that $\text{char}(k) = p &gt; 0$. Prove that either the polynomial $x^{p^n}-a$ is irreducible over the field $k$ or there exists a $b\in k$ such that $a = b^p$.  How to prove this statement? I am a little bit confused with this statement. How do I backup my Stackexchange favorites for offline use? Suppose $X$ is binomial $B(n,p)$. How can I find the probability that $X$ is even ?  I know $$P(X = k ) = \frac{ n!}{(n-k)!k!} p^k(1-p)^{n-k} $$  where $X=1,....,n$. Are they just asking to find $P(X = 2m )$ for some $m &gt; 0$ ? Ampere's circuital law for finite current carrying wire When I was studying about . Then there comes a question in my mind that "whether this law is applicable for finite current carrying wire or not" Taking the second derivative of a parametric curve Mac equivalent of Ctrl + Space to select an item on a list I want to select non-consecutive items on a list, without using a mouse/trackpad - there should be no clicks involved.  In Windows and Linux (at least Ubuntu) an item can be selected using Space/ button, which, in combination with arrows and Ctrl key allows me to select multiple items in any environment (file manager, IDE etc.) - e.g.  Enter a directory -> hold Ctrl -> down arrow twice -> press Space -> down arrow twice -> press Space.  Now I should have items 1, 3 and 5 selected. Is there a way to do the same thing in OS X?  PS. Sorry for such a verbose description, but so far every answer I encountered advices using Command + Click, and this is something I don't want to do. Image uploader shouldn't remove unused link references How many seconds count until bomb detonates in Counter Strike? In Counter-Strike, is there any count (in seconds/minutes) until the bomb explode when it's first set-up? And can the timing be modified? When writing large numbers, should a comma be inserted? I know that it is common to write the number 'ten thousand' as a numeral with a comma delimiting the 10 and the 000 like so: 10, 000  However, I have never seen a comma used for numbers less than 10,000, such as 8000 where, I assume using a comma would look like: 8,000.  Are there any rules relating to when a comma should be inserted into a numeral?  N.b. I live in the UK, so answers pertaining to UK English are preferred. Can you have multiple Dropbox accounts on one computer? Mapping building to only one grid which contains more than half of its area using QGIS? What issues should be considered when overriding equals and hashCode in Java? Writing C# debug output to .txt file Nodejs Nginx error: (13: Permission denied) while connecting to upstream I'm trying to run multiple Nodejs applications on Nginx server running on CentOS 7. I noticed that when I run a Nodejs app on some ports I get an 502 Bad Gateway error in the browser so I checked the error logs:  [notice] 12806#0: signal process started [crit] 12807#0: *13 connect() to 127.0.0.1:7777 failed (13: Permission denied) while connecting to upstream, client: **.**.99.58, server: myapp.com, request: "GET / HTTP/1.1", upstream: "http://127.0.0.1:7777/", host: "myapp.com" [crit] 12807#0: *13 connect() to [::1]:7777 failed (13: Permission denied) while connecting to upstream, client: **.**.99.58, server: myapp.com, request: "GET / HTTP/1.1", upstream: "http://[::1]:7777/", host: "myapp.com"   when I change the app to listen to 8008 for example everything is working fine. I checked permissions and if the process is running as root and everything seems ok. I played with the timeouts as well but no result. Can anyone help? 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. How to visualize a value resulted from math node,or just to know it. I tried the way of scaling this value to the scene size and then pick the color and get the value but I want more effective way to do this. Add a duplicate:0|1 search operator Format not available in tag wiki excerpt For example, :   Format like bold or italic are not available , so it leaves ugly text there:  **This tag is *extremely* ambiguous. Consider using other tags instead.**    Does this need to get fixed, or it's not supported and the tag-wiki needs to be format-free? Is "Logan" the last movie with Hugh Jackman as Wolverine? has played the role of Wolverine as a major character in various X-Men films since 2000 and contributed highly to the brand of the X-Men movie series. But is he playing the Wolverine character for the last time in Logan?  I am getting to know from my friends that  is the last movie in which he is playing Wolverine and they all say that this is his last contracted film.  Are these rumors true? Is there any official information that confirms that this is Hugh Jackman's last movie as Wolverine? How to return a part of an array in Ruby?