Simplify set-theoretic expressions
Define a mathematical set
startsWith() and endsWith() functions in PHP Outlier Detection on skewed Distributions Hi! I'm a beginner learner and I'd like to know how to snap these three objects. I'd like to snap the two cylinders with the different faces of the cube. The short one on the left and the highest cylinder on the top of the cube. I'd like to have the center of the cylinder aligned with the center of the cube (the base of the cylinder inscribed into the face of the cube)  I'm sorry for bad explanation I hope someone can help me  Thanks!   I add a screenshoot in which you can see what I have to do   Thanks again if someone can help me with this! How can I prove the formula for calculating successive entries in a given row of Pascal's triangle? I've found in Wikipedia the formula for calculating an individual row in Pascal's Triangle: $$v_c = v_{c-1}\left(\frac{r-c}{c}\right).$$ where $r = \mathrm{row}+1$, $c$ is the column starting from $0$ on left and $v_0 = 1$.  Now, I've tried to do by hand and it works,  but I don't understand how to find this magic formula when I don't have access to Wikipedia...:) Is it possible to run Microsoft Office 2010? I get the following error:     Strict warning: Only variables should be passed by reference in include() (line 18 of /home/sites/dev/theparce/sites/all/themes/parce/block--block--3.tpl.php).   This is the block code which is causing that error.  if ($user_gallery) {   print render(node_show($user_gallery));  // Line 18   print drupal_render ($user_gallery_edit);  } else {   print drupal_render($user_gallery_new); }   Why do I get that error, even if I get all printed as expected? How to use a file in a jar as javax.net.ssl.keystore? I'm trying to do something like   URL clientks = com.messaging.SubscriptionManager.class.getResource( "client.ks" ); String path = clientks.toURI().getPath(); System.setProperty( "javax.net.ssl.keyStore", path);   Where client.ks is a file stored in com/messaging in the jar file that I'm running.  The thing that reads the javax.net.ssl.keyStore is expecting a path to the client.ks file which is in the jar. I'd rather not extract the file and put in on the client's machine if possible. So is it possible to reference a file in a jar?  This doesn't work as getPath() returns null. Is there another way to do this? The sum is $$\sum_{n=1}^{\infty} \frac{n+2^n}{n+3^n}$$ Is this convergent or divergent? I tried to use the divergent test but the test fail because $a_n = (n+2^n)/(n+3^n) = 0 $ as $n$ goes to infinity. Could someone point me to the right direction?  Thanks In bibliography, how to print the page in my text where I cited certain paper? How to get, for instance,  [19] S. Roth and M. J. Black. Fields of experts: A framework for learning image priors. In IEEE Conf. on Computer Vision and Pattern Recognition, 2005. 1, 2, 7, 8  where the last numbers (1, 2, 7, 8) are the pages where I cited the paper in MY TEXT?  This would be like a reversed reference, or a index for bibliography. 3d transforms on SVG element How do I reinstall Unity? I tested out Unity 5, and of course, it broke things, so I tried downgrading by    sudo apt-get install ppa-purge sudo ppa-purge ppa:unity-team/staging   It removed Unity completely.    apt-get install unity   seemed to work, but the login screen now offers only Gnome.  How do I get back to Unity 4? Not sure if someone else has already raised this - I've got eleven notifications that I've received a Caucus badge on English Language Learners. Perhaps one notification for each community that I'm a member of?  I am a member of the community, and did visit the election. Also, the badge hasn't been awarded more that once (so I think it's just the notification that's at fault).  Note that this seems to happen for other badges, it has been reported for: Caucus, Nice Answer, Enthusiast. How to prove the midpoint of a chord is also the midpoint of the line segment defined by the points of intersection of other two chords with it? Bernhard Elsner, alias MathOMan, posted this exercise in plane Geometry,  on January $29$th, $2010.$  "Let $\mathcal{C}$ be a circle, $A,B$ two distinct points on $\mathcal{C}$ and $M$ be the midpoint of the chord $[AB]$. Take two other chords,$[PQ]$ and $[SR]$, that pass through $M$. Let $C$ (resp. $D$) be the intersection of $[AB]$ with $[PS]$ (resp. $[RQ]$). Prove that $M$ is the midpoint of the chord $[CD]$."    To prove it I've written the following (failed) argument, in the  of this post (translation of mine):    The figure is symmetric with respect to $M$: $\overline{AM}=\overline{MB}$, $\overline{PM}=\overline{MU}$, $\overline{RM}=\overline{MW}$, $\overline{QM}=\overline{MV}$, $\overline{QR}=\overline{VW}$, $\overline{SM}=\overline{MT}$. From $\dfrac{\overline{SC}}{\overline{DT}}=\dfrac{\overline{CM}}{\overline{MD}}=1$ follows that $\overline{CM}=\overline{MD}$.  Here is an extract of the author's reply (translation of mine):   "It is not clear that  $\overline{QM}=\overline{MV}$. Is the point $V$ on the line $(QM)$ defined by this equality or is $V$ defined as the intersection point of the lines $(QM)$ and $(WC)$? Why are both definitions to give the same point?  Let $C^{\prime }$ be the intersection of $(SP)$ and $(VW)$, and $D^{\prime }$ the intersection of $(TU)$ and $(QR)$. (...)  One still has to show that $C^{\prime }=C$ and $D^{\prime }=D$."   I have agreed with these objections.  Until now no proof has been posted. The author considers that the "proof is not quite simple".  Q. What is the theorem this exercise refers to? Or how does one prove it? Independence of disjoint events What is the $n$ times iterate of $f(x)=\frac{x}{\sqrt{1+x^2}}$? Removing phone number from iMessage I'd like to remove my phone number from my iMessage account, but still have my phone enabled to receive messages sent to my email address (also used on iPad, Mac). Is there a way of doing this? Understanding GeoTIFF tags? Firstly, how do you gain the score exactly? I know it shows in the bar on the side of the map, but I remember a match where I was lone-wolfing and still got a pretty high score in that bar. I suppose my other squad members were together, but do I also gain for their work?  Also, does the score reset when I start a new game? I mean, I play support with the Offensive perk and it took me a long game of conquest to just unlock lvl-3 extra grenade. In the next match, that 'nade is gone. Don't I keep it forever? I noticed a peculiar behavior of my Ubuntu 13.04 (although possibly it's also present in previous versions): when my system freezes completely (I do not ask for troubleshooting this) so that even X does not respond to Ctrl+Alt+FX keys, the CapsLock toggle diode on my keyboard blinks (with frequency of ~1Hz), although the system is completely unresponsive.   What is the cause of this phenomena? Is it caused by some internal kernel mechanisms? Is this specific to Ubuntu (is it caused some custom Ubuntu additional software)? Does it has anything to do with HAL? What is the purpose of it? Can I customize this behavior on Ubuntu? Can I stay overnight [15-hour layover] in Haneda airport without a Japan visa? I’m a Filipino citizen. My flight goes from Vancouver to Manila via Tokyo Haneda. I will arrive in Japan at 6pm then depart at 9am the next day. I'm not planning to go out of the airport during my layover, so I don't see a need to have a transit visa. However, I called the Consulate-General of Japan here in Canada, and they asked me to get a transit visa.  Then I called the Ministry of Foreign Affairs in Japan and asked them the same question.. at first, they told me I don’t need a visa as long as I stay inside the airport, but when I told them that the Consulate-General of Japan in Canada asked me to get a visa, they also asked me to get one.  I'm so confused. I would like to know your knowledge or experience regarding this.