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The Monty Hall problem What are the various physical mechanisms for energy transfer to the photon during blackbody emission? By conservation of energy, the solid is left in a lower energy state following emission of a photon.  Clearly absorption and emission balance at thermal equilibrium, however, thermodynamic equilibrium is a statement of the mean behaviour of the system, not a statement that the internal energy is constant on arbitrarily short timescales.  The energy has to come from somewhere during emission, and go somewhere during absorption.  Energy in a solid can be stored as kinetic and potential energy of electrons and nuclei, either individually or in collective modes such as phonons and plasmons.  In thermal equilibrium energy will be stored more or less in various forms depending on the temperature and material.  However, even if most of the thermal energy in a particular solid at temperature $T$ is stored in the form of phonons, it could be that phonons primarily interact with light indirectly via electrons, e.g. a phonon excites an electron in a phonon-electron interaction, which can interact with light via the EM field.  Given that light is an EM field, it makes sense to me that it is emitted and absorbed by charged particles.  The electron-photon interaction is probably dominant for visible and ultraviolet light, given that metals are opaque, while semiconductors and insulators are transparent to (visible and UV) light with energy lower than their bandgap. However, once you get into energies in the IR and below, or X-rays and above, other mechanisms apparently take over.  For example, on the high-energy end of the spectrum I've heard that gamma rays can interact directly with nuclear degrees of freedom, which is reasonable considering that gamma rays are emitted during a lot of nuclear reactions.  A review of  might give clues to important light-matter interactions over a broad range of wavelengths.  Whether all of the these processes are involved in blackbody emission is a somewhat different question.  What physical processes mediate energy transfer during blackbody emission, and in which energy ranges are the various processes dominant? PDF of product of variables Could anyone please indicate a general strategy (if there is any) to get the PDF (or CDF) of the  product of two random variables, each having known distributions and limits?   My particular need is the following: Let $w :=u \cdot v$. The PDF of $u$ is $$\frac{1}{\pi u}\frac{1}{\sqrt{u^2-0.25}},$$ for $z&gt;0.5$ and the PDF of $v$ is $$\exp\left(-\frac{v}{v_0}\right),$$ for $v_1&lt;v&lt;v_2$. What's the PDF of $w$? Find Java classes implementing an interface Some time ago, I came across a piece of code, that used some piece of standard Java functionality to locate the classes that implemented a given interface. I know the functions were hidden in some non-logical place, but they could be used for other classes as the package name implied. Back then I did not need it, so I forgot about it, but now I do, and I can't seem to find the functions again. Where can these functions be found?  Edit: I'm not looking for any IDE functions or anything, but rather something that can be executed within the Java application. How can I obtain the limit of the series     $$\sum_{n=1}^{\infty} \frac{2^{[\sqrt{n}]}+2^{-[\sqrt{n}]}}{2^n}$$   Where $[\ \ ]$ is . I've seen this Kuratowski definition for ordered pairs, but can't fathom why it implies an order to $x$ and $y$  $(x,y):=\{\{x\}, \{x,y\}\}$  As I understand sets, $\{\{x\}, \{x,y\}\}$ is also $\{\{x,y\}, \{x\}\}$. Only when I think about the Axiom of Union does $\{\{x\}, \{x,y\}\}$ "collapse down" to $S = \{x, y\}$, but that doesn't give me much either. All I can see is some as yet hidden message in the set saying "I am the set $\{x,y\}$ and my order of $x$ first is indicated by having $\{x\}$ along for the ride." What are the prerequisites to encounter the legendaries in ORAS? There are a lot of legendaries available in ORAS, however a lot of them will only show up/be available if certain prerequisites are met.  I know Groudon/Kyogre are available through the Story, and      Rayquaza &amp; Deoxys   through the postgame Delta episode, but what about the other available legendaries? What do I need to do to catch them? Convergence of sequence given by $x_1=1$ and $x_{n+1}=x_n+\sqrt{x_n^2+1}$ Be $(x_n)_n\ge 1 $  such that $x_1=1$ and $x_{n+1}=x_n+\sqrt{x_n^2+1}$ for every $n\ge 1$. Prove that the sequence $y_n=(2^n/x_n)_n \ge 1$ is convergent and find it s limit.  Being positive and decreasing, $y_n$ is clearly convergent. But finding it's limit really put me intro trouble. Any help?  Thank you! Parse JSON in JavaScript? Bash copy all files that don't match the given extensions When I import pictures from my camera in Shotwell, it also imports the video clips. This is somewhat annoying, as I would like to store my videos in another folder. I've tried to write a bash command to do this, but have not had success.  I need a command that meets the following requirements:   Locate all files in a directory structure that do not have an extension of .jpg, .png, .gif, or .xcf (case insensitive). Move all of these files into a target directory, regardless of whether the file names or directory paths contain spaces or special characters.   Any help would be appreciated!  EDIT: I'm using the default shell in Ubuntu, meaning that some commands are aliased, etc.  EDIT 2: I've attempted this myself (not the copy part, just the listing of files part). I turned on extglob and ran the following command:  $ ls -R /path | awk '   /:$/&amp;&amp;f{s=$0;f=0}   /:$/&amp;&amp;!f{sub(/:$/,"");s=$0;f=1;next}   NF&amp;&amp;f{ print s"/"$0 }'   This lists everything. I tried using grep on the end of it, but haven't the foggiest idea of how to get it to not match a pattern I give it. The extglob switch didn't help much with grep, even though it does help with other commands. Automatically use specific language in Notepad++ for files with no extension FileZilla: How to copy files from one directory to another on the same server? I want to copy files from one directory to another on the same server using FileZilla. Please guide me how can it be done? What's the difference between a shunt resistor and a four-terminal resistor? I want to know if the four-terminal resistor and the shunt resistor are the same.   Is there another use for the four-terminal resistor except measuring current? Difference between phrase and idiom What is the difference between a phrase and an idiom? Probability of student passing an exam There're $25$ tests, each with $2$ questions. There're total of $50$ different questions (the questions do not repeat). The student knows the answer of $44$ questions. To pass the exam, the student needs to correctly answer both questions on the first test he drew, or answer $1$ question from the test he drew first, and $1$ question from the test he drew second. (meaning he draws twice if he answers a question incorrectly on his first try)  What is the probability that the student will pass the exam?  I have never faced a problem like this one so any help is appreciated. I was thinking about approaching it "manually" with some applied combinatorics but I feel like there's a much easier way that I am not familiar with. We know that for a position variable $x$ and momentum $p$, the uncertainties of the two quantities are bounded by  $$\Delta x \Delta p \gtrsim \hbar$$  Now, this is usually first explained with $x$ being a simple linearly measured position and $p$ being linear momentum.  But it should apply to any good coordinate and its conjugate momentum.  It should, for instance, apply to angle $\phi$ about the $z$ axis, and angular momentum $L_z$:  $$\Delta \phi \Delta L_z \gtrsim \hbar$$  The thing is, $\Delta \phi$ can never be greater than $2\pi$.  I mean, you have to have some value of $\phi$ and $\phi$ only runs from 0 to $2\pi$.  Therefore  $$\Delta L_z \gtrsim \hbar/\Delta \phi \geq \hbar/2\pi$$  But, uh-oh!  This means it is impossible for $\Delta L_z$ to be zero, and we should never be able to have angular momentum states with definite $L_z$ values.  Of course, it doesn't mean that.  But I have never figured out how this is not in contradiction with the Schroedinger eqn. calculations that give us states with definite values of $L_z$.  Can anyone help me out?  One answer I anticipate is that $\phi$ is sort of "abstract" in that if you chose your origin at some other point you will get completely different values of $\phi$ and $L_z$, and ipso facto, usual considerations don't apply.  I don't think this will work, though.  Consider a "quantum bead" sliding around on a rigid circular ring and you get the exact same problem with no ambiguity in $\phi$ or $L_z$.  (Well, there will be some limited ambiguity in $\phi$, but still, there won't be in $L_z$.) Restart my graphics card without rebooting? In vanilla Gmail, clicking on a conversation alters the fragment ID in the URL, allowing you to link back to that conversation.  (It opens in its own Gmail interface.)  I am using the preview pane, which is great, except that the URL no longer updates when viewing specific emails, so there appears to be no way to get the link to the currently-viewed conversation.  (The 'open in new window' button doesn't help, since it pulls its contents in on the client side; it isn't a standalone link.)  The only solution I've found is to turn off the preview pane, find the message again in the list, open it, grab the link, go back to the message list, and turn preview pane back on.  That's fairly onerous for something I do often though (to clip Gmail conversations to Evernote, where my GTD setup lives). The output from the following script \documentclass{article} \usepackage{tikz} \usepackage{graphicx} \begin{document} \begin{tikzpicture}   \node(title)[text width = 0.25\textwidth, text height = 3 cm, draw]{title};   \end{tikzpicture} \end{document}  is  How can I vertically align the text in the node? Specifying the text depth as in \node(title)[text width = 0.25\textwidth, text height = 1cm, text depth = 1 cm, draw]{     title line 1\\     title line 2\\     title line 3};  Does not result in the text being vertically centred. Do sets, whose power sets have the same cardinality, have the same cardinality?