Why does C++ require breaks in switch statements?
Switch statement fall-through...should it be allowed?
If someone who is otherwise healthy decided to drink fairly heavily and consistently over a long period of time, what is the healthiest way to do so?  Example: Stay extra hydrated by drinking more water, take a multivitamin, get more sleep, etc.  Obviously the best solution would be to cease drinking, but IF that person is stubborn and won't quit - what's the best way to go about it? Why do liquids boil when their vapor pressure equals the ambient pressure? Given that the boiling point of a liquid is the temperature at which the vapor pressure is equal to the ambient (surrounding) pressure, what significance does a liquid's vapor pressure have in the formation of bubbles that happens at and above the boiling point?    The definition of boiling point seems to imply that the pressure inside of the bubbles must be at least as great as the liquid's vapor pressure in order to balance the outside pressure, but is there any particular reason why the pressure inside of the bubbles is related to the vapor pressure?    The vapor pressure seems to be a measurement describing the tendency of the molecules to escape from the surface of the liquid, but I don't see how that relates to bubble formation within the liquid.  This question has bothered me for a while, so any help would be much appreciated. Is it possible to play D&D 5e solo? Is it at all possible to run a solo game where you act as the DM/GM for yourself? I know there was a 4th edition adventure published in an old issue of one of the D&amp;D magazines but recently I read somewhere (Reddit I think) that the games Outbreak: Undead and Eclipse phase were good games to play solo.  Can anyone with experience with running a game of D&amp;D 5e for themselves explain how to do so? Sublime Command not working in SSH server on Ubuntu 14.04? A No-Nonsense Introduction to Quantum Field Theory I found Sean Carroll's "A No Nonsense Introduction to General Relativity" (about page .  pdf ), a 24-page overview of the topic, very helpful for beginning study.  It all got me over the hump of learning the meaning of various terms associated with GR, most of which I had heard before without understanding.  It also outlined the most important examples.  Is there a similar document for quantum field theory, which presents the main equations, briefly describes the main ideas, and summarizes the most important applications and results so that the reader can feel the lay of the land before studying in depth? Why is scale factor inversely proprotional to temperature? In all lectures, books and papers I have read about, the scale factor of the universe is inversely proportional to temperature  $$a \propto \frac{1}{T}$$  What is the reasoning behind this relation?  People did mention stretching of wavelength proportional to scale factor and wavelength being inversely proportional to temperature by Wein's law, but somehow this argument doesn't seem convincing to me. How did we initially come about to this relation? In how many ways can we choose k items from n distinct items put in a circle.   Then further extension of the question, if I want to find out the number of ways to choose k items from n distinct items in a circle such that no 2 are together.  Thanks In the Law of Reflection, the angle of incidence is equal to angle of reflection. Why is this true? This is clearly true experimentally, but how does one prove this true mathematically? In addition to whatever files I may choose to exclude, what files does the system exclude by rule or classification?    It might make sense not to backup Trash or Caches, but I'm looking for a way to tell what files are skipped "behind the scenes." Knowing if the system maintains an exclusion list or exclusion pattern would be very helpful in managing larger groups of macs. Let $f\colon X\to\overline{\mathbb{R}}_{\geq 0}$ be a measurable function. Show that     $$ \int f\, d\mu=\int\limits_0^{\infty}\mu(\left\{x\in X: f(x)&gt;t\right\})\, dt. $$     (The right integral is to be read as an Lebesgue-integral.)      Hello, my idea is to approximate $f$ by the functions $$ f_n:=2^{-n}\sum\limits_{k=1}^{\infty}\chi_{\left\{x\in X: f(x)&gt; k/2^n\right\}}. $$  With this approximation by simple functions I got $$ \int\limits_X f\, d\mu=\lim\limits_{n\to\infty}\int\limits_X f_n\, d\mu=\lim\limits_{n\to\infty}\sum\limits_{k=1}^{\infty}\frac{k}{2^n}\cdot\mu\left(\left\{x\in X: f_n(x)=k/2^n\right\}\right)\\=\lim\limits_{n\to\infty}\sum\limits_{k=1}^{\infty}\frac{k}{2^n}\cdot\mu\left(\left\{x\in X:f(x)&gt;k/2^n\right\}\right) $$  This is the point where I do not come along anymore... is that right to this point and if yes: How can I continue in order to get the desired right side?  With regards Background Video is shown in Rendered mode but not when szene is rendered i have a 3D Object and want to add a background image( if possible even a movie) to this 3D Object. I use Cycles to render and tried a plane with the  image as texture. When i go into render mode, it looks like this(picture with background) and when rendered, it has no background. The key also looks into  a different direction.  Should i even use Cycles for this or use motion tracking? i tried to use that but had several problems.     Rendered mode   When scene is rendered What is the name of a squircle with three, five, six or more corners? I know that the second shape is a squircle, but what are the other shapes called? Is there an actual name for them?    The shapes do not simply have rounded corners, but the sides have a "circularity". Here is a triangle with rounded corners next to the shape that I do not know the name of:    "Trircle", "Triarcle", and "Pentircle" do not seem to be used for them, at least Google's image search does not provide any results. Best way to select a subset of items in a long list One of our clients wants us to build a web application to share information about the magazines he publishes. Each edition of a magazine contains a variable amount of advertisers. These advertisers come from a central pool of advertisers. This pool contains (at the moment) about 150 advertisers. Each edition of a magazine contains a subset (about 70-80) of these advertisers.  Our client wants us to come up with a way for him to add 70-80 advertisers from this list of 150 to an edition of a magazine. It needs to be as fast as possible, as easy as possible and as intuitive as possible.  What would be an ideal solution here? I was thinking about something in the lines of the image below.   List of available advertisers. List of selected advertisers. Advertisers have a delete button. Textbox with auto-suggest for advertisers in the list on the left. &lt;Enter> removes the advertiser from the left list and adds it to the right one. Textbox gets cleared and remains focus.   My colleagues suggested drag-and-drop or just one list with a checkbox for each advertiser, but those approaches force the user to do a lot of searching and clicking. With my approach the user can just keep on typing.  Any other suggestions for this situation? Creating additional Virtual Host Ubuntu Server How long should it take to refresh a Developer Sandbox? I refreshed a Developer Sandbox, and almost 24 hours it is still "pending". Is this normal? Are there any actions I can take to speed up the process? When I created the Sandbox it took barely more than 10 minutes to create.  Thanks, Adrian Although we didn't do any changes, this new error appeared in the GSC Structured Data section:    I don't really get what it means. There are many fields for Schema.org, is homeLocation suddenly a required field? Does that make any sense? Finding critical points (extrema) directly without using eigenvalues If we have a function $f: \mathbb R^3\rightarrow \mathbb R$ of the form:  $$f(x)=(a_1x_1^2+a_2x_2^2+a_3x_3^2)e^{-x_1^2-x_2^2-x_3^2}$$  where $a_1&gt;a_2&gt;a_3&gt;0$.   We can find the critical points by:  $$\frac{\partial f}{\partial x_1} =2x_1e^{-x_1^2-x_2^2-x_3^2}(a_1-a_1x_1^2-a_2x_2^2-a_3x_3^2)=0$$  And solving symmetrically for $x_2$ and $x_3$. We get critical points: $(0,0,0) , (\pm 1,0,0) , (0,\pm 1, 0) , (0,0,\pm 1)$   We could determine the nature of them by looking at the eigenvalues of the Hessian, but is there a way to just analyse it directly? Obviously $(0,0,0)$ is a strict global minimum, but I can't quite see that the other points are. Any pointers/hints would be appreciated. I am currently reading Murphy's ML: A Probabilistic Perspective. In CH 3 he explains that a batch update of the posterior is equivalent to a sequential update of the posterior, and I am trying to understand this in the context of his example.  Suppose $D_a$ and $D_b$ are two data sets and $\theta$ is the parameter to our model. We are trying to update the posterior $P(\theta \mid D_a, D_b)$. In a sequential update, he states that, $$ (1) \ \ \ \ \ \ \ \  P(\theta \mid D_{a}, D_{b}) \propto P(D_b \mid \theta) P(\theta \mid D_a) $$ However, I am slightly confused as to how he got this mathematically. Conceptually, I understand that he is saying the posterior $P(\theta \mid D_a)$ is now a prior used to update the new posterior, which includes the new data $D_b$, and is multiplying this prior with the likelihood $P(D_b \mid \theta)$. Expanding the last statement out, I have, $$  P(D_b \mid \theta) P(\theta \mid D_a) = P(D_b \mid \theta) P(D_a \mid \theta) P(\theta) $$  but are we allowed to say $P(D_a \mid \theta) P(D_b \mid \theta) = P(D_a, D_b \mid \theta)$ in order to make the connection in (1)? Update: Now that it's 2016 I'd use PowerShell for this unless there's a really compelling backwards-compatible reason for it, particularly because of the regional settings issue with using date. See @npocmaka's     What's a Windows command line statement(s) I can use to get the current datetime in a format that I can put into a filename?  I want to have a .bat file that zips up a directory into an archive with the current date and time as part of the name, for example, Code_2008-10-14_2257.zip. Is there any easy way I can do this, independent of the regional settings of the machine?  I don't really mind about the date format, ideally it'd be yyyy-mm-dd, but anything simple is fine.  So far I've got this, which on my machine gives me Tue_10_14_2008_230050_91:  rem Get the datetime in a format that can go in a filename. set _my_datetime=%date%_%time% set _my_datetime=%_my_datetime: =_% set _my_datetime=%_my_datetime::=% set _my_datetime=%_my_datetime:/=_% set _my_datetime=%_my_datetime:.=_%  rem Now use the timestamp by in a new ZIP file name. "d:\Program Files\7-Zip\7z.exe" a -r Code_%_my_datetime%.zip Code   I can live with this, but it seems a bit clunky. Ideally it'd be briefer and have the format mentioned earlier.  I'm using Windows Server 2003 and Windows&nbsp;XP Professional. I don't want to install additional utilities to achieve this (although I realise there are some that will do nice date formatting). Defining the Product of Ideals Where does the &quot;naive definition&quot; of the product of two ideals $I$ and $J$, $IJ = \{ ij \mid i \in I, j \in J \}$ fall apart? (The product of two ideals $I$ and $J$ is defined to be $IJ := \sum_i a_ib_i$, where each $a_i$ is in $I$ and each $b_i$ is in $J$.)  Note: This is a question from a problem set I'm working on. I am not expecting a full solution for the answers, but I'd like some help knowing where to look. It seems to work fine in $\mathbb{Z}$ and $\mathbb{C}[x]$.