Why do we say      Pauli exclusion principle   instead of     Pauli's exclusion principle   When we want to say that something belongs to somebody, we should use the "s" to form a genitive, i.e.  "this is Pauli's cat", not "this is Pauli cat".
Consider these two ways of coining a name: 1) Bolzano's theorem, Rolle's theorem 2) the Poincare conjecture, the Kantorovich theorem. What is the difference between these ways, why do people choose one over the other?  My guess is that the main difference is when you put 's at the end of a name, you strictly imply that the theorem/conjecture was written by this very person (Bolzano wrote Bolzano's theorem). But when it is "the [Name] theorem/conjecture," it doesn't mean that the person which name is used actually created this thing, maybe he just inspired it (Poincare might have only inspired the Poincare conjecture but did not propose it).  Sometimes there is only one way: ; you can not call it hairy ball's theorem.
I am looking for an easy way to create in Illustrator vintage style corners like on the picture provided.  I have some technical ideas, but they are time consuming, there should be an easier way I believe. I have B1/B2 Visa. Can I travel for Business trip to US with this Visa? Can someone confirm that its not possible to change the height of a dropdown that is shown when you click on a select box.   The size attribute of the select makes it look like a list, the height attribute in the CSS doesnt do much good either. Symmetrical twin paradox in a closed universe Take the following gedankenexperiment in which two astronauts meet each other again and again in a perfectly symmetrical setting - a hyperspherical (3-manifold) universe in which the 3 dimensions are curved into the 4. dimension so that they can travel without acceleration in straight opposite directions and yet meet each other time after time.  On the one hand this situation is perfectly symmetrical - even in terms of homotopy and winding number. On the other hand the Lorentz invariance should break down according to , so that one frame is preferred - but which one?  So the question is: Who will be older? And why?  And even if there is one prefered inertial frame - the frame of the other astronaut should be identical with respect to all relevant parameters so that both get older at the same rate. Which again seems to be a violation of SRT in which the other twin seems to be getting older faster/slower...  How should one find out what the preferred frame is when everything is symmetrical - even in terms of GRT?  And if we are back to a situation with a preferred frame: what is the difference to the classical Galilean transform? Don't we get all the problems back that seemed to be solved by RT - e.g. the speed limit of light, because if there was a preferred frame you should be allowed to classically add velocities and therefore also get speeds bigger than c ?!? (I know  is only a local theory but I don't understand why the global preferred frame should not 'override' the local one).  Could anyone please enlighten me (please in a not too technical way because otherwise I wouldn't understand!)  EDIT Because there are still things that are unclear to me I posted a follow-up question: Given $\frac{a}{c} + \frac{b}{d} = 1$ Prove that $$\lim_{(x,y)\rightarrow(0,0)} \frac{|x|^{a}|y|^{b}}{|x|^{c} + |y|^{d}}$$ does not exist.  So I have done the proof for strict inequalities. And the limit only exists when the fractions add up to an integer greater than $1$. I'm not sure how to approach this other than counter examples. What is the difference between dpkg and aptitude/apt-get? When installing a software via dpkg -i packageA.deb, will the dependencies required by packageA be downloaded and installed automatically? How is this different from using apt-get or aptitude? Increasing Letterspace for words in caps or small caps Some typographers say it's a good habit to increase the letterspace when writing words in caps or small caps. So my question is, how to do it with pdflatex and/or xelatex? And while we're at it, which words would you alter this way? Acronyms like USA, NATO, IBM, GNU, etc.? How about words like PCs, UdSSR, FreeBSD or TV-Station? I have a directory on my Windows 7 machine that has hundreds if not thousands of sub-directories.  Some of them have files, some do not.  I want to delete all the empty directories.  Looking at the del and rmdir DOS command, it does not look like you can recursively do this without deleting all the files.  Is there a way to do this from the command line? I'm having some difficulty with understanding why KVL (Kirchhoff voltage law) is valid when considering an AC circuit. I mean, the system is by definition not in steady state, right? That in turn means that the change in current causes a change in the magnetic field, which is manifested within the electric potential. I realize the potential is still defined and thus a line integral over a crossed curve of ALL of it's component should be zero.   However, what I often see (for, say, RLC circuits with an AC emf) is total disregard to the time varying components of the electric potential. Only the emf of the different components are considered and their sum is said to be zero. How can that be? What about the "second" part of the potentials? This is almost surely an Arzela-Ascoli question, since it comes from an old exam of which such problems are quite common. Unfortunately, I can't seem to get it though.  $\{ f_n \}$ is a sequence of functions $[0,1] \to \mathbb{R}$ satisfying $|f_n'(x)| \leq \frac{1 + |\ln (x)|}{\sqrt{x}}$ and $-10 \leq \int_0^1 f_n(x) dx \leq 10$ for every $n$. The question is to show the existence of a uniformly convergent subsequence.  In these kinds of situations, the bounds given usually turn into something nice  to force uniform boundedness. Maybe I could hope to establish equicontinuity using the integral somehow, but I'm not told that the $f_n$ are always positive, so the absolute values would probably screw things up anyway.  Is it an easy problem I'm missing or is this totally the wrong track? If so, what's the right track? What did Bill do to make Hanzo mad? During kill Bill, we learn that all the black mamba had to do to get Hanzo to build her a sword, was to mention Bill's name.  When black mamba meets Bill at the end, she tells him that all she did was mention his name. Bill responds with, "that'll do it!"  So what was it that Bill did to Hanzo to make him come out of retirement and make another weapon of death? How do I beat Uprising on Legendary difficulty? The achievement "Distinguished Service" requires that you beat Uprising on the regular gamemode on Legendary difficulty.  This means we can't pick our usual huge DPS heroes like Bastion and Orisa, and are stuck with Torbjorn, Reinhardt, Mercy, and Tracer.  The phases are as follows:   Hack all 3 terminals Defend the Payload until it's ready Escort the Payload until the gate Destroy all 4 Orisas.   So I ask this after having failed Uprising on Legendary dozens of times.   How do I beat Uprising on all 4 phases?   Specifically asking for the latter 3 phases.    Defending the payload is hard when it gets to the Bastions that drop in because Reinhardt's shield gets melted very quickly and Torbjorn has little to no DPS.  Tracer must be relied on but it seems there is no way to stop the perfect aim of Bastion as strafing around does nothing.  If and when we actually do manage to defend it, we're stuck on escorting, which is even harder thanks to the tank mode Bastions.  And finally, even if we do make it to the final fight, which has only happened once, the fight is so tough that even if we slowly inch ourselves closer to the end we run out of time.  The previous question I asked was different because Uprising (All Heroes) allows you to pick any 4 heroes to form your squad, but the original gamemode will not let you pick. Also, the achievement requires you to play the original mode -- Uprising (All Heroes) on Legendary does not reward players with the achievement. Positive series problem: $\sum\limits_{n\geq1}a_n=+\infty$ implies $\sum_{n\geq1}\frac{a_n}{1+a_n}=+\infty$ I've come across quite a few answers that request the asker to, for example: "send the user an email", after which the answerer will provide them with the code or other resources they're looking for.  A few examples:          Should we take action against these questions?  I feel like these answers aren't appropriate (see my answer below).  Update:  Perhaps there are some cases where this is acceptable. I've seen a few questions regarding a particular piece of commercial software where the author/developer of the software answers, telling the asker to contact either them or their organization's in-house support.  I'm on the fence about this case. If I came across a question here describing a similar problem I was having, it would be useful to me to have the support information and know that I could contact it for assistance.  I'm interested in others' opinions on this situation in particular. apache2 mod_rewrite redirect without http body Why is $R\cos{a} = mg$ in circular motion compared and not $R = mg\cos{a}$? Normally, if an object of mass $m$ is inclined to the horizontal at an angle $b$, we set the reaction force of the object on the inclined plane as $R = mg\cos{b}$ (if we resolve the force of gravity so the line of action coming out of the plane is perpendicular to it).  However in circular motion*. it's assumed that $R\cos{b} = mg$. In the example above, one would have to do this in order to arrive to the correct answer, instead of $R = mg\cos{b}$. Using $R = mg\cos{b}$ seems natural enough, as I am resolving vertically, however, both equations would produce two different values for $R$. Why is this?   To show what I mean: If we set the reaction force in this question as $mg\cos{a}$, then the centripetal force will be $mg\cos{b}\cos(\pi/2-b) = mg\cos{b}\sin{b} = \frac{1}{2}mg\sin(2b)$   Whereas If we use $R\cos{b} = mg$, $R = mg\sec{b}$ and the centripetal force will be $mg\sec{b}\sin{b} = mg\tan{b}$. This will end up with two different values for the radius of the circular motion, and hence two different final answers.  *In the circular motion questions I've seen in my mechanics module Why did my windshield freeze instantaneously? It was very cold outside, this morning, when I took the car that slept in the snow, with a simple cloth on the windshield. I entered the vehicle, drove a kilometer or so. The air inside was so cold I could see my breath (or maybe I forgot to brush my teeth). Warm air was blowing on the windshield from the inside and suddenly…  The glass in front of my became opaque, starting from the bottom (the place where the hot air was blowing) and freezing up, up, up until the whole screen was filled in about 5 seconds. It reminded my a little bit of how some baterias spread.  When I tried to remove the mist, I realised it was ice in the car. My windshield instant froze.  I know the theory behind supercooling: a very cold and still liquid can freeze when moved. I'm not sure what happened here, but there were some pretty big turns in the road before it froze. It really looked like the hot air froze the place and not the movement.  Any idea about what happened ? A word for "mercy killing" "Mercy killing" is an act of killing someone who is already dying and in terrible pain, in order to reduce his or her suffering.    Is there any single word for "mercy killing"? I am currently studying in class 10 and I am unable to do this problem. $$\tan 70 ° -\tan 20° -2 \tan 40° =4\tan 10°$$ Can anybody please help me.  Thanks! Proof of a formula involving Euler's totient function: $\varphi (mn) = \varphi (m) \varphi (n) \cdot \frac{d}{\varphi (d)}$