English isn't my native language. I need some help. I look for a word to name a sound.  This sound you can hear when you bend your finger in opposite site. This sound you can hear in your knees when you are doing squats.  I am trying to say something like this: "I hear in my wrist (here name of this sound) when I am doing something"
When I wake up and do stretching I hear some sounds from my joints. What do you call this crunching sound from bone joints?
MLE for Poisson-binomial distribution I am looking for the maximum likelihood estimator (MLE) for the .  I understand the derivation of the MLE for a  and a , but I am unable to derive the MLE equation for the Poisson-binomial distribution. $f(x,y)=4x^3y^2$ Dealing with Directional Derivatives and Vectors Let $f(x,y)=4x^3y^2$  How do I find the directional derivative of $f$ at $(2,1)$ in the direction of the vector $3i-4j$? What would be a unit vector in the direction in which $f$ decreases most rapidly from the point $(2,1)$? And, what is the rate of change of $f$ in the direction given in the second question?  My Work (What I have done so far):  For the first question: $\nabla f(x,y)=12x^2y^2$i$+8x^3y$j$\nabla f(2,1)=48$i$+64$j$u=(3/5)$i$-(4/5)$j $\therefore D_u f=\nabla f\bullet u=0$  I'm not entirely sure if this is right? Can someone please verify?  For the second question: $u=(3/5)$i$-(4/5)$j $\therefore -||\nabla f(2,1)||=$? How do I find this? And am I doing this right?  I have no idea what to do for the third question. What is the difference between \mathbin vs. \mathrel? These seem to be very similar as they both separate two operands. When would one be used over the other? Is there any difference in the math spacing surrounding them?  How would the spacing in these relate to to the spacing produced by \mathop? Is it possible to export the equations from Mathematica to MATLAB? No sound and flash videos play super fast after daily update I just updated my 11.10 Ubuntu from the regular auto updater. After I restarted my laptop I have no sound and the videos in YouTube (and other websites) play super fast.  Not sure if it has something to do with the case, but since last night I get hd0 out of disk error before the grub screen and on the login screen I have some delay before I can type my password. In the console I see errors like these: status: {DRDY err}.  I could say the errors have something to do with the sound problem and the flash player, but if this happened when I got the hd0 error, not now after the regular daily update.  Here is the update history log from /var/log/apt/history.log   Start-Date: 2012-04-03  10:04:39  Commandline: aptdaemon role='role-commit-packages' sender=':1.71' Upgrade: python-aptdaemon.gtkwidgets:amd64 (0.43+bzr697-0ubuntu1, 0.43+bzr697-0ubuntu1.2),  libvlc5:amd64 (2.0.1+git20120329+r134-0~r35~oneiric1, 2.0.1+git20120402+r146-0~r36~oneiric1),  python-aptdaemon:amd64 (0.43+bzr697-0ubuntu1, 0.43+bzr697-0ubuntu1.2),  vlc-nox:amd64 (2.0.1+git20120329+r134-0~r35~oneiric1, 2.0.1+git20120402+r146-0~r36~oneiric1),  vlc-plugin-notify:amd64 (2.0.1+git20120329+r134-0~r35~oneiric1, 2.0.1+git20120402+r146-0~r36~oneiric1),  aptdaemon:amd64 (0.43+bzr697-0ubuntu1, 0.43+bzr697-0ubuntu1.2),  python-aptdaemon-gtk:amd64 (0.43+bzr697-0ubuntu1, 0.43+bzr697-0ubuntu1.2),  vlc:amd64 (2.0.1+git20120329+r134-0~r35~oneiric1, 2.0.1+git20120402+r146-0~r36~oneiric1),  aptdaemon-data:amd64 (0.43+bzr697-0ubuntu1, 0.43+bzr697-0ubuntu1.2),  vlc-data:amd64 (2.0.1+git20120329+r134-0~r35~oneiric1, 2.0.1+git20120402+r146-0~r36~oneiric1),   python-aptdaemon.gtk3widgets:amd64, 0.43+bzr697-0ubuntu1,0.43+bzr697-0ubuntu1.2),  libvlccore5:amd64 (2.0.1+git20120329+r134-0~r35~oneiric1, 2.0.1+git20120402+r146-0~r36~oneiric1),  vlc-plugin-pulse:amd64 (2.0.1+git20120329+r134-0~r35~oneiric1, 2.0.1+git20120402+r146-0~r36~oneiric1) End-Date: 2012-04-03  10:05:15 Getting arguments underneath \min in an align environment There are so called "point releases" for LTS versions of Ubuntu. 10.04.3 for instance.  What are those "point releases" releases? Why are so many different types of objects white, yet appear gray when they are wet? There are many things with different textures that appear white – salt, beer foam, paper, shaving cream, snow, talcum powder, white paint, etc. The most common answer is all of the frequencies must be reflected in order for us to perceive white, which I already know. There must be more underlining details why such a huge variety of things are white. Furthermore, if you wet paper, snow or talcum powder, they appear off-white or gray. Why is this? Event handler not working on dynamic content Windows License stored in UEFI/BIOS Since Windows 10 (or earlier?). It has become standard to store the license product key in the UEFI/BIOS.  I am in the market for buying a new (custom build, individual parts) PC with a new Windows 10 License.  However I was wondering (and can't find clear information on this subject). What the differences between the licenses are when it comes to OEM and Retail.  If in the far future I were to sell this PC:   Would the license (whether OEM or Retail), be stored in the UEFI/BIOS, where it could be used by the new owner? If so, can I remove the license key from the UEFI/BIOS?   I want to know this because I don't want to buy Windows 10 every single time I buy a new PC (since no new versions of Windows will be created, only updates). At the moment, in major part because they are two separate post objects in the system, the excerpt and the body of a tag wiki count as two separate posts with regards to suggested edits in the queue. Mechanically, this is sane, but when it comes to handling the actual queue, it can be confusing. A body edit might consist of little more than a bed of links, which looks bad. But then an excerpt is shown that includes the rest of the data, and since excerpts can be included on the actual wiki page, it makes a lot more sense when they're taken in the same space.  And this is how they are composed, too. The actual edit interface for working on tag wikis has both the excerpt and the body on the same page. In a sense, the excerpt behaves a lot like the "title" of the wiki, if we make a parallel to normal post edits.  Thus, my suggestion (which is to say a suggestion that I repossessed from Robert Cartaino) is that when suggested edits are reviewed for tag wikis, that they be presented in a single unit, treating the excerpt the same as how a title is treated in a question edit. This way, relevant information that is crossed between the two isn't lost because they are reviewed separately. I am flying from the US to Edinburgh, UK. My layover is at Heathrow. Will I need to go through customs and check bags again at Heathrow before I take the next flight? JMustache attribution is incorrectly listed as Butterknife Compactness of a Sphere This fact is mentioned liberally in literature along with subsequent mention of Heine-Borel and I am trying to get my head around it. What would be a formal proof of this if we take for example, a unit sphere in $\mathbb R^3 $?  In addition, how could it be shown, non-trivially of course, that this sphere is not homeomorphic with $\mathbb R^2 $? As I understand this involves finding a bijective function with continuous inverse? Given, $\{x_n\}$ and $\{y_n\}$ are two real valued sequences such that $\lim_{n\to\infty} (x_{n}^{3}-y_{n}^{3})=0 $ Then is it always true that $\lim_{n\to\infty} (x_n-y_n) =0 $ ? I tried by splitting $ (x_{n}^{3}-y_{n}^{3}) $, but that didn't help as $\lim_{n\to \infty} (x_{n}^{2}+x_{n}y_{n}+y_{n}^{2}) $ can be $0$ or non zero or doesn't exist. Arrays in Java and how they are stored in memory I'm working on the following problem set.  Let $\mathcal{H}$ be a Hilbert space and $A$ and $B$ orthogonal subspaces of $\mathcal{H}$.  Prove or disprove:  1) $A \oplus B$ is closed, then $A$ and $B$ are closed.  2) $A$ and $B$ are closed, then $A \oplus B$ is closed.  I could prove 1) and if my proof is correct, it even holds if $\mathcal{H}$ is just an inner product space.  Unfortunately, I can't manage to prove 2). Since $\mathcal{H}$ is by assumption a Hilbert space and I didn't use that fact to prove 1), I should probably use it here.  It means that $A$ and $B$ are also complete. Given some convergent sequence in $A \oplus B$, I want to show that the limit is also in  $A \oplus B$. Here I'm stuck. I want to use the completeness of $A$ and $B$, but I don't see how to obtain suitable Cauchy sequences.  Can anyone drop me a hint? Or is my approach all wrong? How can I use a variable in the replacement side of the Perl substitution operator? I would like to do the following: $find = &quot;start (.*) end&quot;; $replace = &quot;foo \1 bar&quot;;  $var = &quot;start middle end&quot;; $var =~ s/$find/$replace/;  I would expect $var to contain &quot;foo middle bar&quot;, but it does not work. Neither does: $replace = 'foo \1 bar';  Somehow I am missing something regarding the escaping. How would I identify what's causing my Mac to permanently hang on shutdown? Whenever I try to shutdown or reboot my Mac (Macbook Pro 15" Retina late 2013, OS X 10.11.3) it closes all programs like normal and then it goes into that black screen with the progress bar. When it gets to about halfway it permanently hangs and won't ever finish rebooting. I looked at the log viewer and couldn't find anything in particular. Is there a way to monitor a shutdown more closely and find out what's causing it to get stuck? Sending Email via gmail smtp server in JAVA