Why do we say "study window" not "study's window"?
In what cases I should skip 's in possessive case?
Why aren't these loops homotopic? Let $S^1 = \{z \in \mathbb{C} : |z| = 1\}$.  Take the loops $f,g : [0,1] \rightarrow S^1$, $f(t) = 1$, $g(t) = e^{2\pi it}$.  I know these represent different elements in $\pi_1(S^1, 1)$, but I don't see why $F(t,s) = e^{2\pi its}$ isn't a homotopy between $f$ and $g$. The PS4 is now released in the EU, but due to shipment shortages is not available for sale unless pre-ordered a long time ago. Luckily, it seems as though Dualshock 4 controllers are availble for sale in a number of shops already.  I've long decided to buy the PS4 as well as a second Dualshock 4 controller, so I've been considering buying the "second" controller now in order to replace my old Xbox 360 controller, whose D-Pad is useless and whose RB button no longer responds correctly. But before I buy the Dualshock 4 early, I wanted to know how well my PC will support it.  I already know that , but what exactly does work, and what doesn't?  Can I expect the same key-mapping on the PC as on a PS4?  Basically, can I replace my Xbox 360 controller with a Dualshock 4 and still play games like Batman Arkham Asylum/City/Origins as if I were using the old Xbox 360 controller? The whole multi-continent aspect of A Song of Ice and Fire seems to be getting out of hand. Do the other continents suffer those long winters?  Can the Others harm the other continents?  In The Lord of the Rings there were other realms than Middle-earth, but Middle-earth was still all of humanity and dwarf population and hobbits.  Sure there are stories like Romeo and Juliet where the only thing that matters is whether those 2 are going have a chance to love.  But in these fantasy / sci-fi stories there's usually danger of world domination by evil.  It's not usually just one continent is going to be a terrible (or impossible) place to live but other civilizations will flourish. How to check a particular directory is mounted on the Linux machine. For instance there is a folder named test, I want to check if it is mounted or not. $\mathcal N (A):=\mathcal P(A)\setminus\{\varnothing\}$ notation My only problem is making them line up three-across and have equal spacing. Apparently, spans can not have width and divs (and spans with display:block) don't appear horizontally next to each other. Suggestions?  &lt;div style='width:30%; text-align:center; float:left; clear:both;'&gt; Is what I have now. I get the point of having a minimum reputation to use the new chat feature. However, I was hoping my 2K reputation from Stack Overflow would be enough - but it looks like I need to acquire 20 rep here on Meta Stack Exchange.  So my question is - should this restriction be moved? Are getters and setters poor design? Contradictory advice seen Bibliography in Texmaker How to get Lookup ID from Search API with REST Java Code for calculating Leap Year How to properly restart unity? I keep on experiencing weird bugs. These usually start after a few hours of use. Sometimes the dash starts opening under every open window (becomes only visible on desktop, but I still can search and open anything with the enter key while it's not visible). Also, there are other minor annoyances, such as random places (especially maximized Chrome, tabs area) after navigating between programs with alt+tab can't be clicked with the mouse. Switching back and forth fixes this.  I cannot use  compiz --replace   since after that, all of the app indicator icons are gone (only teamviewer stays). Skype, network, languages, sound (also keyboard sound up/down stops working) and date are gone. Restarting unity-panel-service does not help.  Any thoughts on how to resolve these? Converting NumPy array into Python List structure? Suppose I am given a $2$x$2$ matrix $A=$ \begin{pmatrix} a &amp; b \\ c &amp; d \end{pmatrix}  And an initial vector $x_n$ = \begin{pmatrix} x_0 \\ y_0\end{pmatrix}.  Under repeated iteration $x_{n+1} = Ax_n$, we find that $x_{n+1}$ converges to a line in the direction of the $eigenvector$  of $A$ of the form $X$= $[u,mu]$ where $m$ is the slope of the line.  I know that this process somehow also involves the largest $eigenvalue, \lambda,$ of $A$, though I am unsure how it connects.  My question is: How does the largest eigenvalue connect to this repeated iteration, how do I find the slope of the line of convergence $m$, and what is meant by the "direction of the eigenvector"? What is the sign of the  done on the system and by the system?  My chemistry book says when work is done on the system, it is positive. When work is done by the system, it is negative.  My physics book says the opposite. It says that when work is done on the system, it is negative. When work is done by the system, it is positive.  Why do they differ? Using Nouns or Gerunds Could anyone explain when to use a noun or a gerund?  Are these sentences correct? What is the difference between usage of gerund and noun there?        I worked on the improvement of the article.   I worked on the article improving.   I worked on the improving of the article.                The investment idea was published.   Investing idea was published. Let $a$ and $b$ be two integers such that $\left(a,b\right) = 1$. Prove that $\left(a+b, ab\right) = 1$.   $(a,b)=1$ means $a$ and $b$ have no prime factors in common  $ab$ is simply the product of factors of $a$ and factors of $b$.  Let's say $k\mid a+b$ where $k$ is some factor of $a$.  Then $ka=a+b$ and $ka-a=b$ and $a(k-l)=b$.  So $a(k-l)=b, \  a\mid a(k-1)$ [$a$ divides the left hand side] therefore $a\mid b$ [the right hand side].  But $(a,b)=1$ so $a$ cannot divide $b$.  We have a similar argument for $b$.  So $a+b$ is not divisible by any factors of $ab$.  Therefore, $(a+b, ab)=1$.  Would this be correct? Am I missing anything? How to install and use Ubuntu from a USB flash drive on Windows 8? I am running 14.04 and have a HP Deskjet 2545 wireless printer which is supported by Ubuntu. I have run HpLIP, the latest version and installed the printer.  The printer is recognised by Ubuntu, printer and network, but LibreOffice do not see the printer. Only a Generic printer.  I don't know what to do anymore and would like to get some good advice How do I copy Word tables into Excel without splitting cells into multiple rows? I have data in a Word table that includes line and paragraph breaks. When I copy the data into Excel, it splits each line and paragraph I want into multiple cells. How do I copy the data to Excel and keep the breaks?