Combination: In n chooses r $\binom{n}{r}$, what if $r$ is larger than $n$?
$n$ choose $k$ where $n$ is less than $k$
Copy specific file type keeping the folder structure Does time freeze at Absolute Zero? Time has many definitions per se, but the basic idea being it's "the measurement of change" so as we know, all matter looses it's ability of changing with the loss of kinetic energy. and the where it becomes zero is the absolute zero (−273.15°C). so my question would be, will time stop/freeze at Absolute zero? and does time get slow while reaching there? What does this residuals versus fitted plot mean about my model? How to send data to a serial port and see any answer? On Linux, I want to send a command string (i.e. some data) to a serial port (containing control characters), and listen to the response (which also usually might contain control characters).   How can I do this as simplest as possible on Linux? An example is appreciated! If $a\neq 1$, find $(a+1)(a^2+1)(a^4+1)\ldots(a^{2^n}+1)$. If $a\neq 1$, find $$(a+1)(a^2+1)(a^4+1)\ldots(a^{2^n}+1)$$   Or i.e.     If $a\neq 1$, find $\prod_{i=0}^n(a^{2^i}+1)$.   It really does seem like $$(a+1)(a^2+1)(a^4+1)\ldots(a^{2^n}+1)=a^{2^n+2^{n-1}+\ldots+2+1}+a^{2^n+2^{n-1}+\ldots+2+1-1}+a^{2^n+2^{n-1}+\ldots+2+1-2}+\ldots+a^2+a+1$$  Or i.e. $$\prod_{i=0}^n(a^{2^i}+1)=\sum_{i=0}^{2^n+2^{n-1}+\ldots+2+1}a^i$$  Is there an interesting proof of this? I'd appreciate any help. $\mathbb Z^n/\langle (a,...,a) \rangle \cong \mathbb Z^{n-1} \oplus \mathbb Z/\langle a \rangle$ Is the reason why the time evolution operator is unitary based on purely physical arguments, i.e. that the physical processes that an isolated system undergoes shouldn't depend on any particular instant in time (homogeneity of time); thus two experimenters who conduct the same experiment starting from the same initial state, but at different times, should have the same probability amplitude for that state?! Or is there some mathematical argument as well?  Also, is the reason why the time evolution operator is linear implied by the superposition principle (as an arbitrary state can be expressed as a linear combination of basis states the operator should act linearly as otherwise the state as a whole would evolve differently to the superposition of states that it was initially represented by)?! How do I detach a process from Terminal, entirely? I use Tilda (drop-down terminal) on Ubuntu as my "command central" - pretty much the way others might use GNOME Do, Quicksilver or Launchy.  However, I'm struggling with how to completely detach a process (e.g. Firefox) from the terminal it's been launched from - i.e. prevent that such a (non-)child process   is terminated when closing the originating terminal  "pollutes" the originating terminal via STDOUT/STDERR   For example, in order to start Vim in a "proper" terminal window, I have tried a simple script like the following:  exec gnome-terminal -e "vim $@" &amp;&gt; /dev/null &amp;   However, that still causes pollution (also, passing a file name doesn't seem to work). Is it possible to find all classes or interfaces in a given package? (Quickly looking at e.g. , it would seem like no.) Multiple Image in Canvas ItemsControl How to set a font for math mode? I would like to have something like Segoe UI of something similar. Thank you  \documentclass{article} \usepackage{fontspec} \usepackage{firamath-otf} \begin{document} \begin{equation} x+y=45 \end{equation}  \end{document}   Error: Proof by induction on a rooted tree with even number of vertices Let $T = (V, E)$ be a rooted tree with an even number of vertices. Prove by induction that there exists a set of edges $S \subseteq E$ such that every $v \in V$ is incident with an odd number of edges in $S$.  I was wondering if my argument is sufficient to prove the statement above:  Base case: $|V|=2$, there is only 1 edge and both vertices are incident with 1 edge $-&gt;$ $S \subseteq E$.  Inductive step:  Let $|V|&gt;2$, implying that $T$ has at least 2 external vertices. Let us choose two arbitrary external vertices $w,u \in V$. Such vertices are only incident to 1 edge each, $e_w$ and $e_u$. We can say that $e_w,e_u \in S$.   By induction, there exists a set $S$ in $T'=T-\{w,u\}=(V',E')$ such that every $v \in V'$ is incident with an odd number of edges in $S$ because removing 2 vertices from a tree with an even number of vertices maintains the property $|V|=2n$. Measure the size of a PostgreSQL table row I have a PostgreSQL table. select * is very slow whereas select id is nice and quick. I think it may be that the size of the row is very large and it's taking a while to transport, or it may be some other factor. I need all of the fields (or nearly all of them), so selecting just a subset isn't a quick fix. Selecting the fields that I want is still slow. Here's my table schema minus the names: integer                  | not null default nextval('core_page_id_seq'::regclass) character varying(255)   | not null character varying(64)    | not null text                     | default '{}'::text character varying(255)   |  integer                  | not null default 0 text                     | default '{}'::text text                     |  timestamp with time zone |  integer                  |  timestamp with time zone |  integer                  |   The size of the text field may be any size. But still, no more than a few kilobytes in the worst case. Questions  Is there anything about this that screams 'crazy inefficient'? Is there a way to measure page size at the Postgres command-line to help me debug this? Distance Between Two Points in Matlab Find all integer solutions to Diophantine equation $x^3+y^3+z^3=w^3$ Compute all integer solutions to the equation  $$x^3+y^3+z^3=w^3$$ When to use ''[verb] that'' I would like to know when to say think(s) that, say(s) that and mean(s) that and when to omit that. Access personal views in a list with PowerShell I am trying to first access and then edit Personal Views for a SharePoint List using PowerShell. However only the public views are returned. In the example below the list called List1 has two views - 1 public and 1 personal created by a regular user account (contoso\user1).  I run the script below via an admin account (contoso\spadmin) -  $url= "http://portal.contoso.com/sites/TEST" $web = Get-SPWeb $url $list = $web.Lists["List1"] Write-Output "Count = $($list.views.count)" $list.views| % {Write-Output "Title = $($_.title)"}   Result -  Count = 1 Title = All Items   I tried the following as well but that did not return the personal views.   [Microsoft.SharePoint.SPSecurity]::RunWithElevatedPrivileges( {      $web = Get-SPWeb $url     $list = $web.Lists["List1"]     Write-Host "Count = $($list.views.count)"     $list.views| % {Write-Host "Title = $($_.title)"} } )    How do I access the personal views for a list with PowerShell? $_POST vs. $_SERVER['REQUEST_METHOD'] == 'POST' Some guy called one of my Snipplr submissions "crap" because I used if ($_SERVER['REQUEST_METHOD'] == 'POST') instead of if ($_POST)  Checking the request method seems more correct to me because that's what I really want to do. Is there some operational difference between the two or is this just a code clarity issue? Scala 2.10 + Json serialization and deserialization Difference between "while" and "whilst" Possible Duplicate:          In terms of construction of sentences, can the two words while and whilst be used interchangeably?