Framed BarChart - Bars outside frame
Is it possible to induce Mathematica to chop off parts of Graphics objects that exist outside of a Frame?
Let $\{X_\alpha\}_{\alpha\in J}$ be a family of topological spaces and let $X=\prod_{\alpha\in J}X_\alpha$ be endowed with the product topology. Show that $X$ is path connected if and only if each $X_\alpha$ is path connected.  I know this is true if path coennected is changed by connection but I am very confused with this problem, I have tried to do the following:  $\Rightarrow $ let $x,y \in X_\alpha$ be then $(x_\alpha), (y_\alpha)\in \prod X_\alpha$ where $x_\alpha=x, y_\alpha=y$ and $x_\beta=0, y_\beta=0$ for any $\beta\neq\alpha$, and since P is path connected then there is continuous $f:[0,1]\rightarrow \prod X_\alpha$ such that $f(0)=(x_\alpha)$ and $f(1)=(y_\alpha)$, then if $\pi_\alpha:\prod X_\alpha \rightarrow X_\alpha$ is the projection, which is continuous, we have that $\pi_\alpha f:[0,1]\rightarrow X_\alpha$ is continuous and $\pi_\alpha (f(0))=x$ and $\pi_\alpha (f(1))=y$.  $\Leftarrow$ I do not know how to do this address, could someone help me please? Thank you very much. How can I obtain the command line arguments of another process?   Using static functions of the System.Diagnostics.Process class I can obtain a list of running processes, e.g. by name:  Process[] processList = Process.GetProcessesByName(processName);   However, there is no way to access the command line used to start this process. How would one do that? iOS App stuck in 'Loading...' I tried downloading Tumblr yesterday but it never completed. At the moment I have an App icon stuck at 'Loading...'.  I have tried restarting the iPhone (holding down both home and side buttons at the same time) and I have also tried shutting down the iPhone (holding the side button and swiping).  I have also tried deleting it as usual (holding the icon down and choosing delete but it doesn't go away).  Any ideas on what I can do to get rid of this icon? iOS 11-13 - unable to paste into comments In Delphi, is TDataSet thread safe? I'd like to be able to open a TDataSet asynchronously in its own thread so that the main VCL thread can continue until that's done, and then have the main VCL thread read from that TDataSet afterwards. I've done some experimenting and have gotten into some very weird situations, so I'm wondering if anyone has done this before.  I've seen some sample apps where a TDataSet is created in a separate thread, it's opened and then data is read from it, but that's all done in the separate thread. I'm wondering if it's safe to read from the TDataSet from the main VCL thread after the other thread opens the data source.  I'm doing Win32 programming in Delphi 7, using TmySQLQuery from  as my TDataSet descendant. After I installed Ubuntu 13.04, I can't mount my NTFS partition.  Error mounting /dev/sda5 at /media/mrxfly/xFLyDiskData: Command-line `mount -t "ntfs" -o "uhelper=udisks2,nodev,nosuid,uid=1000,gid=1000,dmask=0077,fmask=0177" "/dev/sda5" "/media/mrxfly/xFLyDiskData"' exited with non-zero exit status 14: The disk contains an unclean file system (0, 0). Metadata kept in Windows cache, refused to mount. Failed to mount '/dev/sda5': Operation not permitted The NTFS partition is in an unsafe state. Please resume and shutdown Windows fully (no hibernation or fast restarting), or mount the volume read-only with the 'ro' mount option. Why isn't sizeof for a struct equal to the sum of sizeof of each member? Why does the sizeof operator return a size larger for a structure than the total sizes of the structure's members? How to set a JavaScript breakpoint from code in Chrome? Preserving order with LINQ I use LINQ to Objects instructions on an ordered array.  Which operations shouldn't I do to be sure the order of the array is not changed? Under what conditions does loot despawn? Previously, someone posted his/her proof of "every neighborhood is open" . I am focusing on the same statement, but it seems that my approach is different from his/hers. Could someone comment on my own proof? Here we go:  Let $X$ be a metric space and $p\in X$. Fix $r&gt;0$. Define a neighborhood around $p$ as $N_r (p)=\{q\in X| d(p, q)&lt;r\}$. Now, take $w = \frac{r}{2}$. Then, $N_w (p)\subset N_r(p)$. In other words, every point of $N_r(p)$ is interior. Therefore, $N_r (p)$ is open. Since $r$ is arbitrary, this proves every neighborhood is open.  Update:  Under my definition of "neighborhood," can I prove in this way instead: For all $m\in N_r(p)$, take $w=\frac{r−d(m,p)}{2}$. Then, $N_w(m)\subset N_r(p)$.   Update2  From the hints given in comments, I solve it:  Assume $m\in N_r(p)$ and $q\in N_w(m)$. Take $w=r-d(m, p)$. Then, $d(p, q)\leq d(p, m) + d(m, q)&lt; d(p, m) + r-d(m,p) =r$.   Thanks to @JoséCarlosSantos and @fleablood ! How can I work with file uploads during a Webdriver test? This is a canonical question, intended to provide a comprehensive answer to many related questions  During the course of a Webdriver test, I want to upload files. However, this opens a native file picker, which Webdriver doesn't seem to support interacting with. How do I interact with it? How to convince airport security that I am not dangerous when having metallic parts in my body? I had an operation some time ago and now I have small screws in my shoulder which will not be removed anymore. When I decided to fly for vacation, I supposed that these will may bring me into trouble at the airport when going through the metal detector.  So I asked my doctor and at the hospital if there is any kind of "passport" or something similar which confirms the screws in my shoulder so that I do not get into many problems. Unfortunately, they told me such things do only exist if you get a new knee or something, not if you just have a few screws in your body.  When I flew from Vienna to Amsterdam and back, my fears were confirmed: The security staff inspected me very precise, and I had to explain them my story. Thank god I have some scars left so they believed me!  However this is not a permanent solution for the future. Is there any international "passport" which my doctor and hospital do not know about? If not, what else are my possibilities?  I am not that afraid when travelling within the EU, however I fear that this situation might get quite dangerous when I'm in other countries... I created a view to show Users. These users can create nodes of the "Questions" content type.  The view has to render a table to show how many (the total number) Questions the user has created. Something like:  User +++ Questions created John --- 10 Ted  --- 4 Alf  --- 19 How to clean an E: drive (new Recovery drive since Windows 10 1803) on HP laptop Finite choice without AC Can anyone explain how we choose one sock from each of finitely many pairs without the axiom of choice?  I mean : To choose one sock from each of infinitely many pairs of socks requires the Axiom of Choice, but for shoes the Axiom is not needed.  The idea is that the two socks in a pair are identical in appearance, and so we must make an arbitrary choice if we wish to choose one of them. For shoes, we can use an explicit algorithm -- e.g., "always choose the left shoe." Why does Russell's statement mention infinitely many pairs? Well, if we only have finitely many pairs of socks, then AC is not needed -- we can choose one member of each pair using the definition of "nonempty," and we can repeat an operation finitely many times using the rules of formal logic (not discussed here). Comments are useful. Many, many posts need some small amount of meta discussion, and comments fulfill this need.   Comments are also noisy and distracting. Occasionally, someone will post an insightful and informative comment that complements the post its attached to... But more often, they're tangential, quickly irrelevant and in the way: stale comments show up first, making newer comments less visible.  The guidance here for a long time has been that comments are transient, . And yet, some do hang around for months or years because .   So let's fix that.   I propose that all comments older than 7 days be hidden by default unless the comment has been up-voted in the past 30 days. Hidden comments should be indicated by a note below the post ("add / show 3 more comments") and made visible to anyone who cares to click it.   This doesn't destroy anything, but it would get it out of the way of most readers - and hopefully encourage folks to edit it into the actual answers as a result.  Note: I previously suggested this . Other  have been . However, I'm not suggesting that comments be automatically deleted, and they should be hidden based purely on the age / activity of the comment itself, not of the post to which they're attached. 1.  Why is the wave function complex? I've collected some layman explanations but they are incomplete and unsatisfactory. However in the book by Merzbacher in the initial few pages he provides an explanation that I need some help with: that the de Broglie wavelength and the wavelength of an elastic wave do not show similar properties under a Galilean transformation. He basically says that both are equivalent under a gauge transform and also, separately by Lorentz transforms. This, accompanied with the observation that $\psi$ is not observable, so there is no "reason for it being real". Can someone give me an intuitive prelude by what is a gauge transform and why does it give the same result as a Lorentz tranformation in a non-relativistic setting? And eventually how in this "grand scheme" the complex nature of the wave function becomes evident.. in a way that a dummy like me can understand.  2.   A wavefunction can be thought of as a scalar field (has a scalar value in every point ($r,t$) given by $\psi:\mathbb{R^3}\times \mathbb{R}\rightarrow \mathbb{C}$ and also as a ray in Hilbert space (a vector). How are these two perspectives the same (this is possibly something elementary that I am missing out, or getting confused by definitions and terminology, if that is the case I am desperate for help ;)   3.   One way I have thought about the above question is that the wave function can be equivalently written in $\psi:\mathbb{R^3}\times \mathbb{R}\rightarrow \mathbb{R}^2 $ i.e, Since a wave function is complex, the Schroedinger equation could in principle be written equivalently as coupled differential equations in two real functions which staisfy the Cauchy-Riemann conditions. ie, if $$\psi(x,t) = u(x,t) + i v(x,t)$$ and $u_x=v_t$ ; $u_t = -v_x$ and we get $$\hbar \partial_t u  = -\frac{\hbar^2}{2m} \partial_x^2v + V v$$ $$\hbar \partial_t v  = \frac{\hbar^2}{2m} \partial_x^2u - V u$$ (..in 1-D) If this is correct what are the interpretations of the $u,v$.. and why isn't it useful. (I am assuming that physical problems always have an analytic $\psi(r,t)$). How do you prove the  from statistical mechanics? To prove entropy will only increase with time? How to prove? Please guide. Or "Why is Ant-Man the last movie of Phase 2, rather than Avengers 2?"  The Marvel Cinematic Universe is the series of movies involving characters from Marvel comics and produced by Marvel Studio/Disney Studio. The series of movies is decomposed into phases, that are different steps in the studios' production plan.   Phase 1, entitled Avengers Assembled, is composed of all movies from Iron Man (2008) to The Avengers (2012). This phase relates the origins of each Avenger and how these mighty superheroes came to fight as a team.   The narrative purpose of Phase 2 is less clear to me. At first, I thought it was about Thanos' story arc but Thanos doesn't seem to appear in Ant-Man, the last movie of the Phase 2. Actually, Thanos will most likely be the main antagonist of Infinity War, which is a part of Phase 3.   Therefore, what story arc will be concluded at the end of Ant-Man? I believe it can be answered before the movie is released, as the purpose of Phase 1 was clear before the release of The Avengers. Marvel Studio may also have commented about the organization of the movies. In other words, what narrative elements unify the movie of Phase 2?