Is it possible to remap the Super (Windows Start) button to open All Applications instead of the Activities Overview?  I installed Tweaks to do a few other things but haven't seen anything about mapping the Super Key directly and was wondering how it is possible in GNOME and if there was a UI I'm overlooking or if I should be looking for a terminal command?
In Ubuntu 18.04.1, I would like to use my left Super-key only to simply open the Show Applications menu (aka Dash) like a left click on the dock-icon (with the 9 dots) does and preferably close it again without showing me any open programs.   I can open it with Super + A and even close it again with Super R, but Super L appears to do nothing at all.   In Xfce, something similar was possible by adding a custom keyboard shortcut for Super L and setting the command to xfce4-popup-whiskermenu, which would open and close a menu with favourite applications. Unfortunately, I don't know the command that opens and closes the Show Applications menu.   Is there any way to add such a shortcut in the new Gnome Shell?
Spectral radii and norms of similar elements in a C*-algebra: $\|bab^{-1}\|<1$ if $b=(\sum_{n=0}^\infty (a^*)^n a^n)^{1/2}$ Let $A$ be a unital $C^*$-algebra and $a\in A$ such that $r(a) &lt; 1$. Define b  = $(\sum_{n=0}^\infty (a^*)^n a^n)^{1/2}$. We can prove that $b\geq e$ and that $b$ is invertible. I want to show $\| b a b^{-1} \| &lt; 1$.   From the definition of $b$ we see that $a^* b^2 a = b^2-e$ and we know $r(bab^{-1}) = r(a) &lt;1$.   So it suffices to prove $r(b a b^{-1}) = \| b a b^{-1} \|$. It can follow from the fact $c = ba b^{-1}$ is a normal element... I don't know how to prove it (I have tried to compare $c^* c$ and $c c^*$...).    Context: The question appears in Murphy's book, page 74.   I have managed to prove the first part. The second part of the question is to prove $$r(a)= \inf_{c\in Inv(A)}\{\|cac^{-1} \| \}$$ It's easy to see $$r(a) \leq \inf_{c\in Inv(A)}\{\|cac^{-1} \| \}$$ But I can't prove $$r(a) \geq \inf_{c\in Inv(A)}\{\|cac^{-1} \| \}$$ If we have had $r(a) = \|b a b^{-1} \|$ then it was obvious... But this is not true, so how we can prove this inequality? I have no idea how prove that $$\{(z_0,\ldots,z_n)\in\mathbb{C}^{n+1} \quad| \quad z_0^d+z_1^2\ldots+z_n^2=0, \quad |z_0|^2+|z_1|^2\ldots+|z_n|^2=2\}$$ is a $(2n-1)$-compact manifold.  How give the charts. For $n=1$ and $d=2$ not distinguish which 1- manifdold is? A curious integral The following integral has been on my mind for a while $$\int_0^\infty \frac{\sin(x)}{e^x-1}\,\mathrm d x \tag{$\dagger$}$$    Let us indicate the integrand as $f(x)=\frac{\sin(x)}{e^x-1}$. The following are a couple of observations.   The integrand can be extended by continuity in $0$ since $$\lim_{x\to 0}f(x)=\lim_{x\to 0}\frac{\frac{\sin(x)}{x}}{\frac{e^x-1}{x}}=1$$ This is the original reason I started playing around with this integral. Mathematica yields the result $$\int_0^\infty \frac{\sin(x)}{e^x-1}\,\mathrm d x=\frac{\pi}{2}\textrm{Coth}(\pi)-\frac 12 \approx 1.076674047$$ which, following numerical evidence, seems correct. Complex analysis may be useful here, since the integrand is a holomorphic function on $\mathbb C$. I tried writing $\sin(z)=\frac{e^{iz}-e^{-iz}}{2i}$, but I was not able to find an appropriate integration contour to solve the problem. The $-1$ in the denominator breaks the simmetry of the expression. This made most of my substitutions useless.   Can this integral be evaluated correctly, preferrably through complex analytic methods? Why is the potential energy equal to the negative integral of a force? Why is the potential energy equals to the negative integral of a force? I am really confused with this negative sign. For example, why there is a negative sign in the gravitational potential energy and what does it mean?   I read that the negative sign means you do the same force but in the opposite direction.  Doesn't that mean the object shouldn't move? Workaround for Android 4.4 not being able to write to SD cards? How do you disable anonymous login? Current situation: I'm required to cite "normative" documents (read: standards and manuals) separately from articles and books etc. Using biblatex and biber with the numeric style I'm doing that by issuing multiple printbibliography commands like so:  \usepackage[style=numeric,backend=biber,bibencoding=utf8]{biblatex} %... lots of stuff \printbibliography[type=standard,title=Standards \&amp; Manuals] \vskip\baselineskip \printbibliography[type=manual,heading=none] \printbibliography[nottype=standard,nottype=manual]   which gives a heading Standards &amp; Manuals, prints a list of manuals, leaves a bit of space then the list of standards and finally, under a new heading Bibliography gives books and articles etc. Thus far everything is fine, enter:  The Problem: I'm using the shorthand field in my database for the standards and manuals which works perfect as far as output within the text is concerned and sets the shorthand as the label in the bibliography and prints the details to the right of it - problem is: my shorthands are considerably longer than the labels generated by the numeric style, but even though they're in three different \printbibliography commands, everything gets indented to the maximum width of the label, making the part for books and articles look quite ridiculous.  The following shows the problem with only two separate \printbibliography (and an obviously exaggeratedly long shorthand):   Now  what I would obviously want is for each of the \printbibliography commands to only use the indentation actually necessary to accommodate the largest label appearing within, i.e. rendering the Manuals section as above, but the Bibliography section like follows:   Can anyone help me to achieve this? Or give me some pointer where to look?  The above was produced with the following MWE on an up-to-date TeXLive 2014:  \documentclass[10pt,british]{scrbook}  \usepackage{babel} \usepackage[T1]{fontenc} \usepackage[utf8]{inputenc} \usepackage{lmodern}  \usepackage{filecontents} \begin{filecontents*}{\jobname.bib} @manual{HowTo,     title = {How to Make the World Go Round},     shorthand = {HowToMakeTheWorlGoRound},     publisher = {The Publisher},     year = {2000} }  @article{Article,     author = {Author, A. and Buthor, B.},     journal = {Journal Title},     pages = {113--126},     title = {The Article},     volume = {65},     year = {1900} } \end{filecontents*}  \usepackage[style=numeric,backend=biber,bibencoding=utf8]{biblatex} \addbibresource{\jobname.bib}  \usepackage[hidelinks]{hyperref}  \begin{document} \let\cleardoublepage\relax \chapter{The Document} Nothing to see here, but we refer to the \parencite{HowTo} based on a principle discovered by \textcite{Article}.  \printbibliography[type=manual,title=Manuals] \printbibliography[nottype=manual] \end{document} What should I do if I have two libraries that provide functions with equivalent names? Textbook on the Geometry of Special Relativity I am looking for a textbook that treats the subject of Special Relativity from a geometric point of view, i.e. a textbook that introduces the theory right from the start in terms of 4-vectors and Minkowski tensors, instead of the more traditional "beginners" approach. Would anyone have a recommendation for such a textbook ?  I already have decent knowledge of the physics and maths of both SR and GR ( including vector and tensor calculus ), but would like to take a step back and expand and broaden my intuition of the geometry underlying SR, as described by 4-vectors and tensors. What I do not need is another "and here is the formula for time dilation..." type of text, of which there are thousands out there, but something much more geometric and in-depth.  Thanks in advance. Over time I realized a very annoying property of the Stack Overflow reputation system: Easy answers to popular question are rewarded with a lot more reputation points than actually great answers. In case anybody actually needs examples for this, here are two examples from :   gained me 420 rep, I invested 2 minutes writing it, and it only was a wild guess.   took me about an hour for the research and the math and gained me 40 rep.  Now I know that you are bound to get more rep for answers that are useful to more people, and I'd say that's fine. But the current situation is quite extreme: 30% of my reputation is from 5 of my 330 answers, and they are definitely far from being my best ones.  A final example that is not from my profile, but more extreme: Do you really think  is worth 40000 reputation?  My proposition to improve that situation would be to make the reputation gain from a single answer non-linear, maybe even have it capped at a certain point. I'm not sure on how that non-linear function should look exactly, and would leave good proposals for that to users with more experience than me. Inequality involving sides of a triangle How can one show that for triangles of sides $a,b,c$ that   $$\frac{a}{b+c}+\frac{b}{c+a}+\frac{c}{a+b} &lt; 2$$  My proof is long winded, which is why I am posting the problem here.   Step 1: let $a=x+y$, $b=y+z$, $c=x+z$, and let $x+y+z=1$ to get   $\frac{1-x}{1+x}+\frac{1-y}{1+y}+\frac{1-z}{1+z}&lt;2$  Step 2: consider the function $f(x)=\frac{1-x}{1+x}$, and note that it is convex on the interval (0,1), so the minimum of   $\frac{1-x}{1+x}+\frac{1-y}{1+y}+\frac{1-z}{1+z}$  is reached when the function takes the extreme points. i.e. $x=y=0, z=1$.    But going back to the fact that this is a triangle, we note that $x=y=0 \implies a=0$ which is not possible, so the inequality is strict. How can I obtain an 'unbalanced' grid of ggplots? I want to copy/modify/delete a Minecraft world. Where can I find my saves folder? Every time I read the tips for installing an SDK, IDE, some extension and so on, it says, that I should unpack them in /opt folder. Why do I need to do that?   When I was installing Ubuntu, I read that I should set only 10-20 GiB for the / file system and remaining space set for /home. So should I extend the space for root folder, or leave all stuff at /home? Is there any difference? How to switch between Ubuntu and Windows 7 without a reboot I have installed windows 7 and then Ubuntu 11.04. Now I want to know how I can switch from Ubuntu to Windows 7 and from Windows 7 to Ubuntu without restarting the computer. Man creates miniature population on different time-scale; uses them to invent the 'absolute protection' dome How can I make Devanagari fonts render properly in Ubuntu 16.04? Devanagari fonts appear broken like this:     It should appear this way    I have the same problem in browsers and office applications.  Is there any way to fix it? Adding hyperlinks to pop-up data in qgis2web? Does anyone know if it is possible to add hyperlinks to image fields etc. in the pop-up windows of Qgis2web?  I've had a look in the layers javascript file, but the image source path isn't rendered using html, so I can't simply append &lt;a href" to it.  The image is coming in via the usual method of having a field that contains the path of the image file.  I'd like to achieve linking of the image, like in the example below. Alternatively, I could just populate the 'more info' field with the URL, but if I did that I'd like to avoid just doing it by having a field that contains the entire URL, as some may be quite long (these will only be internal links). Which is correct?     Everyone were convinced that he would go to the game.   Everyone was convinced that he would go to the game.   I think it's "was", because "everyone" is singular, but I just wanted to check. Surface integral of a scalar over a unit cube. Evaluate the following integral $$\iint_S (x+y+z) \, dS$$  where $S$ is the surface of the cube $[0,1] \times [0,1] \times [0,1]$  Honestly, I don't know what to do. All I know is that you have to evaluate the integral for each of the 6 surfaces of the cube. The normals for them I can do and the equations of the planes, but other than that I couldn't do much.  Can someone break it down for me, please?  PS: No divergence theorem yet for me.