Abrupt changes in direction and loss of energy
velocity of an object after leaving a ramp
Where are the review queue counters? The review queue counters have disappeared:        Where are they?  When I did screenshot the Close Votes queue was not empty, if someone think so. Phase Potentials Looking to get a explanation of the following solution.   $x'=sinx$ I understand that you must integrate $sinx$ and then take the negative of it making it $v(x)=cos(x) + c = cos(x)$ with $c=0$. However I am having problems understanding the equilibrium points.   The equilibrium points of this system are,  $$x^*=kz$$ $x*=kz$ k is even, this is unstable $x^*=kz$ k is odd, are stable  Why is it unstable when even and stable when even? Test if there are files matching a pattern in order to execute a script I am trying to write an if statement to test whether there are any files matching a certain pattern. If there is a text file in a directory it should run a given script.  My code currently:  if [ -f /*.txt ]; then ./script fi   Please give some ideas; I only want to run the script if there is a .txt in the directory. Dual Channel RAM vs. Quad Channel RAM I just bought a motherboard that says it supports Dual-Channel RAM. The RAM I'm looking at says it's a "Quad-Channel Kit" . Will it work with my motherboard?  EDIT: Thanks all for the replies. Here is some more info:    Here is the RAM I'm looking at:    It all looks compatible to me, I just was curious about the four channel thing. I'm having difficulty solving an exercise in my course.  The question is:      Prove that $n!\geq 2^n$.   We have to do this by induction. I started like this:   The lowest natural number where the assumption is correct is $4$ as: $4! \geq 2^4 \iff 24 \ge 16$. The assumption is: $n! \ge 2^n$.   Now proof for $(n+1)$ which brings me to: $(n+1)! \ge 2^{(n+1)}$  I think I can rewrite it somehow like this:  $$ {(n+1)} \times {n!}  \stackrel{\text{(definition of factorial)}}{\ge} 2^n \times 2 $$  $$ (n+1) \times 2^n \ge 2^n \times 2 $$  Then I think I can eliminate the $2^n$ and have something like this: $n+1 \ge 2$, or $n \ge 1$.  But I think I'm wrong here some where and was hoping somebody has some advice on this. How can I prove the above assumption?  Any help would be appreciated, kind regards. How do I get a file extension in PHP? My wife and I didn't know we're pregnant and in a weekend fun with friends we smoked a bit of weed - we don't usually smoke weed or cigarettes.  This is not something we're regulary doing as I said, but how bad to the fetus can it be ? How to prove $|a^k|=n/\gcd(n,k)$ whenever $|a|=n$? Any complete group (that is, with trivial center and outer automorphism group) is isomorphic to its automorphism group. The inverse is not true, as the dihedral group of order 8 is isomorphic to its automorphism group but isn't complete.  Problem 15.29 in the Kourovka Notebook asks to find another exemple of a p-group, but I was wondering, is any other exemple known? Is there any other finite (or even infinite) group (not necessarily a p-group) which is isomorphic to its automorphism group but isn't complete? What are the differences between a HashMap and a Hashtable in Java? What are the differences between a  and a  in Java?  Which is more efficient for non-threaded applications? Command for taking a screenshot to a new file Desperate to locate and re-read exceptional book/series, but cannot remember the title. The high concept: The U.S. has just sent the first successful expedition to Mars, and it has just landed. As the astronauts make their initial exploration outside their ship, a tear in the fabric of space opens up right in front of them, and they look through to the insides of a laboratory (at a California university?) and two students who just figured out how to create arbitrary portals between two points in the Universe. The rest of the novel/series is a consequence of this breakthrough. But I can't remember the author and title(s). Surely someone reading this forum will remember it well! TIA.  (Reposted .) What statistical test can I use to compare two ratios from two independent samples. The ratios are after to before results. I need to compare the after/before ratios for two independent models and show whether they are have significant difference or not. Please help! examples:         Gift (German) = poison   poisson (French) = fish   embarazada (Spanish) = pregnant   sauce (Spanish) = willow   triviale (Italian) = vulgar   parentes (Portuguese) = relatives   slim (Dutch) = smart Since there is no word "shallowen", is there a good antonym of "deepen"? The meaning of "deepen" that I am referring to here is "to cause to become deeper." It doesn't necessarily refer to digging a hole. For example, a temporary deformation in a soft surface:     Putting the anvil on the mattress deepens the depression in it, but removing the anvil ______ it.   I would also be happy with an antonym of the intransitive version "to become deeper." Is it possible to take an image from the clipboard and output it to a file (using X)?  I can do this with text easily:  $ xclip -selection c -o &gt; file.text   But when I try the above with an image nothing is written.    The reason I want to do this is I don't have an image editor installed, and it got me thinking whether I could do this without installing one. No internet after upgrade to 17.10 No field properly between $\mathbb Q$ and $E$ iff $G(K/\mathbb Q) \cong A_4$ or $S_4$ Pgfplots with custom axis markers Assume you have a trigonometric function, say for simplicity sin(x). When plotting the function, how can one place the x-axis markers on 0, pi/2, pi, 3pi/2, 2pi, instead of the default numeric values that pgfplots uses? Determining the structure of the quotient ring $\mathbb{Z}[x]/(x^2+3,p)$