What is pressure?
What exactly is "pressure", and what's its relation to force?
How can I animate an object fading out? I used the Import Images as Planes addon to import an image. It works fine but how do I change the transparency? I want to animate the plane so that it fades in and out. Here is my current node setup: As the title suggests, I'd like to prove that the sum $$ \sum_{n=2}^\infty (\ln n)^{- \ln n} $$ is finite.  The root and ratio test both fail here, but  suggests that there is a comparison that can be used to show convergence.  The only thought I have is that it may help to write the terms as $e^{-\ln(n)\ln(\ln(n))}$, but this has not led me to any particular insight.  Any ideas are appreciated. Sometimes I see a comma after the proper name:     Hello Mr. Black,      In order to give you....   But my native language is not English and I think that the comma in this phrase should be placed before the proper name:      Hello, Mr. Black.      In order to give you....   What is the correct punctuation in English? I have 24 reputation points, but SO chat is still giving me the message "you must have 20 reputation...." Why can't I join the chat? How do I connect the initial highway to my six-lane road? Prove that if $a+b+c$ divides $abc$, then $a+b+c$ must be composite. I have seen another post for this same question but it never got an answer. Since I am fairly new, I can't comment on other's posts, therefore I am creating a new one. The question states:  If a, b, and c are positive integers, prove that if $(a + b + c) | (a*b*c)$, then $a+b+c$ is composite.  I do not really know how to approach this.  The link to the post with the same question is: Unable to log in to Stack Exchange Too much whitespace in "Thanks for the feedback" While attempting to downvote something on a site I don't have an account on, I see this message, which has too much whitespace:    The same thing happens with upvotes (and プラス票が):    (I think it's safe to say that this is a network-wide bug, since I took these all on different sites.)  However, it looks more reasonable when you are not logged into the network at all (e.g. in private browsing):    An earlier version of this issue was reported at , but the difference is that there is no newsletter UI on the right anymore. (The extra space could have been justified before given the height of the newsletter; now it's definitely a bug.)  Also, is newsletter supposed to be gone? Effect Of Frequency on Photocurrent The situation is this.. I am performing a photoelectric effect experiment - just the usual - evacuated glass tube containing two metal electrodes connected to an external source of DC voltage (say an alkaline cell) and ammeter in series. I shine a light on one of the electrodes - the frequency is more than enough to cause eject photoelectrons, and the voltage of the cell opposes the electrons which are trying to get to the other electrode. The question is this - what happens to the current on increasing the intensity of light while keeping no. of photons falling on the electrode constant (in other words increasing the frequency)?   Does the current remain the same because the no. of photons falling on the electrode is constant and so no. of electrons being ejected is constant? Or does it increase because the electrons have more kinetic energy, ie, they are moving faster towards the other electrode so that the $t$ (time) term in $I$ = $q$/$t$ is less ($q$ remains constant because no. of electrons being ejected is still the same)?   This question appeared in one of my tests and the answer key says that the current remains constant but think that case 2 is correct and current would increase, which is why I asked this question.  Thanks. Determinant of a block lower triangular matrix I'm trying to prove the following: Let $A$ be a  $k\times k$ matrix, let $D$ have size $n\times n$, and $C$ have size $n\times k$. Then,  $$\det\left(\begin{array}{cc} A&amp;0\\ C&amp;D \end{array}\right) = \det(A)\det(D).$$  Can I just say that $AD - 0C = AD$, and I'm done? MySQL is giving weird result My recollection is very sketchy but this is what I remember....   Film was possibly black and white I saw it as a child in the late '80s early '90s but it's older It was subtitled and in Russian or similar language It involved some astronauts  travelling in space with possibly time travel The astronauts (mostly men) encounter a planet/civilization of only women The women no longer need men to breed and are so become superior and possibly want to eliminate all men    That's all I have to go on, sorry. Who made the decision for Gandalf's promotion from 'grey' to 'white'? In the first book of the LoTR, after his fight with the Balrog of Moria, Gandalf the Grey changed to .   My question is, who made the decision to 'promote' him from grey to white? Was it ? Or was it the ? Or was it the ? Accessing Reduce from DSolve When I apply to a PhD program, may I ask a postdoc who closely supervised me to write a recommendation letter? My supervisor also has written one for me, but I believe the postdoc can comment on my research skills in a more detailed and precise way. Does a postdoc have enough authority to convince admission committee? shade plane with a color function color(x,y) Remove space before punctuation I need to remove locally spaces arround (especially before) punctuation signs. This spaces are added by french polyglossia.  \documentclass{article} \usepackage{fontspec} \usepackage{polyglossia} \setmainlanguage{french}  \newcommand{\nospace}[1]{\texttt{#1}}  \begin{document} \nospace{a:b} \end{document}     Thanks for help. PDE separation of variables Hi could someone guide me this problem  It says ,  $ u_t - u_{xx}-2 u_x=0  $  Use the method of separation of variables to find all possible solutions.   Could someone help me out for this problem. I'm beginner at PDE. I would be much appreciated if you able to show some partial work so that I can understand.  Thanks in advance for taking my consideration After installing Adobe PDF reader, it opens files with the .PDF file extension. Ones' default web browser opens .html files and notepad opens .txt files, etc.  Where exactly in the registry are these filetype - program associations stored in the registry?   In other words, how does Windows know with which software/program it must open a certain file(type)? Testing pointers for validity (C/C++) Is there any way to determine (programatically, of course) if a given pointer is "valid"? Checking for NULL is easy, but what about things like 0x00001234? When trying to dereference this kind of pointer an exception/crash occurs.  A cross-platform method is preferred, but platform-specific (for Windows and Linux) is also ok.  Update for clarification: The problem is not with stale/freed/uninitialized pointers; instead, I'm implementing an API that takes pointers from the caller (like a pointer to a string, a file handle, etc.). The caller can send (in purpose or by mistake) an invalid value as the pointer. How do I prevent a crash?