The developer console is the most part rather useful however it does exhibit JS crashes; does anyone know where to report them to the team maintaining it?
I recently found a bug, which I mentioned on , as well as submitting a case, and after a few days fumbling around with the case, they closed it by saying that they only provide this type of support for Premier Support customers.  Is there a better channel for reporting bugs than by submitting a case, or is there something "special" we have to do? I realize this question is similar to , except that I've already gone the route of , as suggested by the answer there (i.e. submitting a case), to no avail.  How can I make sure that a bug like this can find its way to someone capable of at least confirming that the behavior was expected? This behavior isn't documented anywhere, and so I assume that it's a bug that needs to be addressed.
Deriving a QM expectation value for a square of momentum $\langle p^2 \rangle$ I already derived a QM expectation value for ordinary momentum which is: $$ \langle p \rangle=  \int\limits_{-\infty}^{\infty} \overline{\Psi}  \left(- i\hbar\frac{d}{dx}\right) \Psi \, d x $$ And I can read clearly that operator for momentum equals $\widehat{p}=- i\hbar\frac{d}{dx}$. Is there an easy way to derive an expectation value for $\langle p^2 \rangle$ and its QM operator $\widehat{p^2}$? Minimum of $\sqrt{\frac{a}{b+c}}+\sqrt{\frac{b}{c+a}}+\sqrt{\frac{c}{a+b}}$ What is the minimum of $$f(a,b,c):=\sqrt{\dfrac{a}{b+c}}+\sqrt{\dfrac{b}{c+a}}+\sqrt{\dfrac{c}{a+b}}$$ where $a,b,c$ are positive real numbers?  When $a=b=c$, we have $f(a,b,c)=\dfrac{3}{\sqrt{2}}\approx 2.12$  When $a=1,b=c\rightarrow\infty$, we have $f(a,b,c)\rightarrow 2$. So the minimum is at most $2$. Can anyone enter as a student at the Citadel ? Or must one be recommended by Lords or a powerful institution?   Aemon Targaryen was a son of a King, so the Citadel would let him access without questioning. Samwell Tarly was sent by Lord Commander Jon Snow, from the Night's Watch. , a novice of the Citadel. A common born but it is not known how he entered the Citadel. We can notice that he is not a good student, but has not been fired.    I don't remember how the other Maesters were recruited, if they are always relatives of Lords, Kings... Can any lowborn commoner just "knock the door", and enter the Citadel? Commutator Subgroup of Direct Product equals the Direct Product of the Commutator Subgroups I need to prove that $(G_{1}\times G_{2})^{\prime} = G_{1}^{\prime} \times G_{2}^{\prime}$, where $G^{\prime}$ denotes the commutator subgroup of $G$ - i.e., $G^{\prime}=[G,G]$, the subgroup generated by all commutators of elements of $G$.   Recall that the commutator of two elements $x$ and $y$ in a group $G$, denoted $[x,y]$ is defined to equal $x^{-1}y^{-1}xy$.  I have posted my proof as an answer below. Could somebody please take a look at it and let me know if it's okay? If not, please let me know what I need to do in order to fix it. Thank you. :)    Edit: I have been informed that my answer given below actually shows only equality of the set of commutators, and that $G^{\prime}$ consists of products of commutators. So, this question is no longer a proof check, but I am asking specifically how to fix what I have written below in order to make it actually answer the thing I set out to prove. I am having a bit of trouble understanding some of the hints given me thus far, and am going to need more detail in any answers given in order for them to be helpful. Where did Harry's parents get all of their money from? Session_ID_Remove Issue in API callouts in Salesforce Cannot change brightness setting using function buttons or using the brightness control bar on HP laptop Divisor function asymptotics Define $\tau_{r}(n) = \sum_{d_1...d_r = n}1$.   One exercise in a book on sieve theory asked for an elementary proof by induction of the fact that   $$\sum_{n\le x}\tau_r(n) = \frac{1}{(r - 1)!}x(\ln x)^{r - 1} + O\left(x(\ln x)^{r - 2}\right)$$  The base case $r = 2$ is easy with reversing the order of summation.  The only other progress that I made was the fact that $\sum_{n\le x}\tau_{r}(n) = \sum_{d\le x}\left\lfloor\frac{x}{d}\right\rfloor\tau_{r- 1}(d)$, but I don't know how to proceed. Find the default application for a certain extension Given xdg-open and an extension, is there a way to get the application which xdg-open is set to for that particular extension?  For example given xdg-open and .jpg the result is eog. I want to create a math problem-solution sheet. The coefficients a, b, c must be assigned on the fly at random so the generated pdf will show a numeric quadratic equation rather than a symbolic quadratic equation. Note a must not be zero.  \documentclass{article} \begin{document} \section{Problem} Let \(x_1\) and \(x_2\) be the roots of \(a x^2 +bx +c=0\). Find  \(x_1x_2\).  \section{Solution} \[ x_1x_2=\frac{c}{a} \] \end{document}   Please kindly make the solution get automatically simplified. For example: \frac{c}{a}=3 when a=2 and c=6.    Actually the real case is more complex than this one. Not only the equations must be generated at random, but also the associated graphic plots that I write in PSTricks.     I chose Paulo's answer because using Maxima as the computation engine is very very great idea. Other answers are also good and creative, especially Altermundus'. How do I analyze a .hprof file? Solving $a \sin\theta + b \cos\theta = c$ Could someone help me with the steps for solving the below equation $$a \sin\theta + b \cos\theta = c$$ I know that the solution is $$\theta = \tan^{-1} \frac{c}{^+_-\sqrt{a^2 + b^2 - c^2}} - \tan^{-1} \frac{a}{b} $$ I just can't figure out the right steps to arrive at this solution. Ubuntu 16.04 VIM without python support! Although Ubuntu 16.04 release notes mention that:  The default VIM package has been built against python3 instead of python2.  Yet after I installed vim with the following command:  sudo apt-get install vim   And checked:  vim --version   It showed:  -python -python3   Is it a bug? How do I get vim with Python support? How do I enable hardware virtualization technology (VT-x) for use in Virtualbox? I'm having trouble understanding Cantor's diagonal argument.  Specifically, I do not understand how it proves that something is "uncountable".  My understanding of the argument is that it takes the following form (modified slightly from the  article, assuming base 2, where the numbers must be from the set $ \lbrace 0,1 \rbrace $):  \begin{align} s_1 &amp;= (\mathbf{0},1,0,\dots)\\ s_2 &amp;= (1,\mathbf{1},0,\dots)\\ s_3 &amp;= (0,0,\mathbf{1},\dots)\\ \vdots &amp;= (s_n \text{ continues}) \end{align}  In this case, the diagonal number is the bold diagonal numbers $(0, 1, 1)$, which when "flipped" is $(1,0,0)$, neither of which is $s_1$, $s_2$, or $s_3$.  My question, or misunderstanding, is: When there exists the possibility that more $s_n$ exist, as is the case in the example above, how does this "prove" anything?  For example:  \begin{align} s_0 &amp;= (1,0,0,\mathbf{0},\dots)\ \ \textrm{ (...the wikipedia flipped diagonal)}\\ s_1 &amp;= (\mathbf{0},1,0,\dots)\\ s_2 &amp;= (1,\mathbf{1},0,\dots)\\ s_3 &amp;= (0,0,\mathbf{1},\dots)\\ s_4 &amp;= (0,1,1,\mathbf{1},\dots)\\ s_4 &amp;= (1,0,0,\mathbf{1},\dots)\ \ \textrm{ (...alternate, flipped } s_4\textrm{)}\\ s_5 &amp;= (1,0,0,0,\dots)\\ s_6 &amp;= (1,0,0,1,\dots)\\ \vdots &amp;= (s_n \text{ continues}) \end{align}  In other words, as long as there is a $\dots \text{ continues}$ at the end, the very next number could be the "impossible diagonal number", with the caveat that it's not strictly identical to the "impossible diagonal number" as the wikipedia article defines it:     For each $m$ and $n$ let $s_{n,m}$ be the $m^{th}$ element of the $n^{th}$ sequence on the list; so for each $n$,      $$s_n = (s_{n,1}, s_{n,2}, s_{n,3}, s_{n,4}, \dots).$$      ...snip...      Otherwise, it would be possible by the above process to construct a sequence $s_0$ which would both be in $T$ (because it is a sequence of 0s and 1s which is by the definition of $T$ in $T$) and at the same time not in $T$ (because we can deliberately construct it not to be in the list). $T$, containing all such sequences, must contain $s_0$, which is just such a sequence. But since $s_0$ does not appear anywhere on the list, $T$ cannot contain $s_0$.      Therefore $T$ cannot be placed in one-to-one correspondence with the natural numbers. In other words, it is uncountable.   I'm not sure this definition is correct, because if we assume that $m = (1, \dots)$, then this definition says that "$s_n$ is equal to itself"&mdadsh;there is no "diagonalization" in this particular description of the argument, nor does it incorporate the "flipping" part of the argument, never mind the fact that we have very clearly constructed just such an impossible $T$ list above.  An attempt to correct the "diagonalization" and "flipping" problem:  $$s_n = (\lnot s_{m,m}, \lnot s_{m,m}, \dots) \quad \text{where $m$ is the element index and} \quad\begin{equation}\lnot s_{m,m} = \begin{cases}0 &amp; \mathrm{if\ } s_{m,m} = 1\\1 &amp; \mathrm{if\ } s_{m,m} = 0\end{cases}\end{equation}$$  This definition doesn't quite work either, as we immediately run in to problems with just $s_1 = (0),$ which is impossible because by definition $s_1$ must be $ = (1)$ if $s_1 = (0)$, which would also be impossible because...   Or more generally, with the revised definition there is a contradiction whenever $n = m$, which would seem to invalidate the revised formulation of the argument / proof.  Nothing about this argument / proof makes any sense to me, nor why it only applies to real numbers and makes them "uncountable". As near as I can tell it would seem to apply equal well to natural numbers, which are "countable".  What am I missing? I have got hundreds images of products with clear white backgrounds. I would like to change the white background color to become transparent.   Is there a means of batch processing this particular process with Photoshop or any other applications? On mu Ubuntu 12.04 setups my tmux clipboard copy and paste commands are setup as follows:  set -g prefix M-a unbind C-b bind C-c run "tmux save-buffer - | xclip -i -sel clipboard" bind C-v run "tmux set-buffer \"$(xclip -o -sel clipboard)\"; tmux paste-buffer"   This worked great for the longest time up until a month or so ago, when I suspect some configuration change or package change was made that broke the above. In GNOME terminal, pasting still works fine with both prefix+ctrl-v and ctrl-shift-v.   However the xclip copy command no longer works no matter what I do, and I have tried removing the custom prefix binding above, using -select instead of -sel, not using clipboard etc. This is pretty much a show stopper for a GVim user like me, since I don't even have the GNOME terminal workaround of ctrl-shift-c with tmux taking over the shell. I go into copy mode, select text with space+movement, and when I execute prefix+ctrl-c absolutely nothing happens. Before this broke, tmux would display a confirmation message in the notification section at the bottom.  Does anybody have suggestions as far as how one might debug this? This is a pretty big productivity hit. I can probably use the , but it'd be great to know just what happened to xclip. $$\lim_{n\to \infty}\frac1{2n}\log\left({2n \choose n}\right)$$  Now, $\log(n!) = \Theta (n\log(n))$ so I think we could write,   $$\lim_{n\to\infty}\frac{1}{2n}\left(\log\left(2n!\right) - \log\left(n!^2\right)\right) = \frac{1}{2n}\left(\log\left(2n!\right) - 2\log\left(n!\right)\right) $$  $$\lim_{n\to\infty}\frac{1}{2n}\left(2n\log\left(2n\right) - 2n\log\left(n\right)\right) $$  $$\log\left(2n\right) - \log\left(n\right) = \log(2)$$  Is this legitimate? I feel this might be wrong since, the $\Theta$ notation conceals a constant factor. Showing that $e^z=z$ has infinitely many solutions One of our review problems for my complex analysis final is the following:     Show that $e^z=z$ has infinitely many solutions in $\mathbb{C}$.   I've seen a few solutions online, but none of them have used material that was covered in our introductory complex analysis course. Would anyone be able to provide a simple solution?  I'm trying to think of ways to invoke bounding in some way but I can't seem to come up with anything. How can I figure out why my washing machine is tripping the GFCI receptacle? I have a Kenmore 80 Series (Model No. 110.24872300) washing machine which up to this point has been working fine. Since it is near a sink, the outlet it is plugged into is a GFCI outlet. On the last load I came back after letting it run for some time to find that it had tripped the GFCI in the middle of the wash cycle - the washer was still full of soapy water. I reset the outlet and let it run again, only to come down the next morning and find it full of water still (it had tripped during the rinse cycle this time). I reset the outlet again and this time it finished the rest of the cycle.  My guess is that water is somehow getting onto the internal components of the washer and causing it to short - is there any way I can test this theory or fix the problem myself?