I am using Ubuntu 18.04.2 with GNOME. I am facing an issue of keyboard combinations blocking all other combinations that involve those keys. For example, in Firefox, ctrl+shift+p doesn't open private window like it should, but instead opens the print window, because I'm using ctrl+shift for something else.  This is not an isolated incident, it happens in other applications as well.  Is there a way to fix this?
I have Ubuntu 16.04 with GNOME shell. I set ctrl+shift for the "Modifiers-only switch to next source" option.   This shortcut conflicts with apps hot-keys. I can't use ctrl+shift+i to open devtools in Chrome, it just switches the layout. In VS code IDE if I press shortcuts with ctrl+shift (for example ctrl+shift+f), shortcuts work but always switch a keyboard layout. When I used Windows this problem didn't exist.  Can I set the ctrl+shift shortcut in such a way that it causes a switch action only after the keys are released and only if this 2 keys were pressed (without additional keys)?
Calculating the limit $\lim((n!)^{1/n})$ Find $\lim_{n\to\infty} ((n!)^{1/n})$. The question seemed rather simple at first, and then I realized I was not sure how to properly deal with this at all. My attempt: take the logarithm,  $$\lim_{n\to\infty} \ln((n!)^{1/n}) =  \lim_{n\to\infty} (1/n)\ln(n!) =  \lim_{n\to\infty} (\ln(n!)/n)$$ Applying L'hopital's rule:  $$\lim_{n\to\infty} [n! (-\gamma + \sum(1/k))]/n! = \lim_{n\to\infty} (-\gamma + \sum(1/k))=  \lim_{n\to\infty} (-(\lim(\sum(1/k) - \ln(n)) + \sum(1/k))  = \lim_{n\to\infty} (\ln(n) + \sum(1/k)-\sum(1/k)  = \lim_{n\to\infty} (\ln(n))$$ I proceeded to expand the $\ln(n)$ out into Maclaurin form $$\lim_{n\to\infty} (n + (n^2/2)+...) = \infty$$ Since I $\ln$'ed in the beginning, I proceeded to e the infinity  $$= e^\infty  = \infty$$  So am I write in how I approached this or am I just not on the right track? I know it diverges, I was just wanted to try my best to explicitly show it. Smooth structure of embedded submanifolds Here is a rather long quotation from "Introduction to smooth manifolds" by J. Lee.     Proposition 5.2 (Images of Embeddings as Submanifolds). Suppose $M$ is a   smooth manifold with or without boundary, $N$ is a smooth manifold, and   $F: N \to M$ is a smooth embedding. Let $S = F(N)$. With the subspace   topology, $S$ is a topological manifold, and it has a unique smooth   structure making it into an embedded submanifold of $M$ with the   property that $F$ is a diffeomorphism onto its image.      Proof. If we give $S$ the subspace topology that it inherits from $M$,   then the assumption that $F$ is an embedding means that $F$ can be   considered as a homeomorphism from $N$ onto $S$, and thus $S$ is a   topological manifold. We give S a smooth structure by taking the   smooth charts to be those of the form $(F(U), \phi \circ F^{-1})$, where $(U, \phi)$   is any smooth chart for $N$; smooth compatibility of these charts   follows immediately from the smooth compatibility of the   corresponding charts for $N$. With this smooth structure on $S$, the map   $F$ is a diffeomorphism onto its image (essentially by definition), and   this is obviously the only smooth structure with this property. ...   My question is about the bold sentence. He says that it is obvious, but it is not obvious to me. Why is the constructed smooth structure the only smooth structure that makes $F$ a diffeomorphism between $N$ and $S$? Objects not rotating with each other (Rubik's cube) How to get attention to a post on a child meta site If I want to draw people's attention to a post on a child meta site, how can I do that? I want to get people  over at Area 51 to see what they think of the idea, because it requires opinions from the community. However, posts on the discussion zone of Area 51 rarely get activity, so it seems like I'm out of luck, unless something is changed. And from the sounds of , it seems like this is a problem on all child metas.  That post is similar, but while it talks about increasing activity in general, I am talking about how to raise participation to an individual post; the equivalent of a bounty  I can't use bounties because reputation is the same.   Could there be another way of drawing attention to individual posts? File locked after sending it as attachment What is the word for the order of succession in which son assumes the throne after father? It can be any son-younger son after elder son after father. Also, what can be the term for only a single family in power? Please answer. Headers and font in KOMA-script I am setting up the layout for my bachelor thesis using scrbook as basis for a self-made documentclass with twosided print. I want a header containing the current part number and name on the outer side (left on even pages, right on odd pages), the current chapter number and name on the center of the head and the same for section on the inner side. I found this example in the KOMA-Script documentation:  \usepackage{scrlayer-scrpage} \pagestyle{scrheadings} \automark[chapter]{chapter} \automark*[section]{}   It puts the chapter on the outer side on even pages and the section on the outer side on odd pages. Sadly, I was not able to modify this to fit my needs because I do not really understand the way KOMA-Script works here. If a part starts but there is still no chapter in it, the place for the chapter shall remain empty (same for chapter and section). Can anyone help?  Furthermore, I would like to change all fonts that KOMA-Script changes (e.g. toc, section, chapter...) back to the default computer modern as I do not like the font KOMA-Script uses here. Is there a better way than changing all the fonts manually like this:  \addtokomafont{section}{\fontfamily{cmr}\selectfont} If $a^\phi = 1$ then the order of $a$ divides $\phi$ Why do the Localization of a Ring This question may be a bit vague, but neverthless, i would like to see an answer. Wikipedia tells me that:   In abstract algebra, localization is a systematic method of adding multiplicative inverses to a ring.   It is clear that for integral domains, we have the Field of Fractions, and we work on it. It's obvious that a Field has multiplicative inverses. Now if we consider any arbitrary ring $R$, by the definition of localization, it means that we are adding multiplicative inverses to $R$ thereby wanting $R$ to be a division ring or a field. My question, why is it so important to look at this concept of Localization. Or how would the theory look like if we never had the concept of Localization. Riemann integrabilty of an indicator function Consider the following function on $[0,1]$:   $$f(x)=\begin{cases}1&amp;x\in\{a_1,a_2,\dots,a_n\}\\0 &amp;\text{otherwise}\end{cases}$$   The $a_i$ are fixed and all in $[0,1]$. Determine whether $f$ is Riemintegrable or not.   By the Riemann&ndash;Lebesgue criterion $f$ is Riemann integrable. How to prove directly? What compiler warning level do you recommend for different C/C++ compilers?  gcc and g++ will let you get away with a lot on the default level.  I find the best warning level for me is '-Wall'.  And I always try to remove fix the code for the warnings it generates.  (Even the silly ones about using parenthesis for logical precedence rules or to say I really mean 'if (x = y)')  What are your favorite levels for the different compilers, such as Sun CC, aCC (HPUX ?), Visual Studio, intel?  Edit:  I just wanted to point out that I don't use "-Werror" (but I do understand it's utility) on gcc/g++ because, I use:   #warning "this is a note to myself"   in a few places in my code.  Do all the compilers understand the #warning macro? Let $A \in {M_n}$ is nonsingular and each eigenvalue of $A$ is either $+1$ or $-1$.Why $A$ is similar to ${A^{ - 1}}$? Div's class vs id When using divs when is it best to use a class vs id?   Is it best to use class, on say font variant or elements within the html? Then use id for the structure/containers?   This is something I've always been a little uncertain on, any help would  be great. How do I start a process from C#? Is there a maximum possible acceleration? What are Identity Columns? I was reviewing the  for PostgreSQL and I saw that Pg is likely going to get "identity columns" sometime soon.  I found some mention in  but nothing much  is_identity         yes_or_no         Applies to a feature not available in PostgreSQL identity_generation character_data    Applies to a feature not available in PostgreSQL identity_start      character_data    Applies to a feature not available in PostgreSQL identity_increment  character_data    Applies to a feature not available in PostgreSQL identity_maximum    character_data    Applies to a feature not available in PostgreSQL identity_minimum    character_data    Applies to a feature not available in PostgreSQL identity_cycle      yes_or_no         Applies to a feature not available in PostgreSQL    doesn't say much either     An identity column differs from a primary key in that its values are managed by the server and usually cannot be modified. In many cases an identity column is used as a primary key; however, this is not always the case.   But, I don't see anything else on them. How do identity columns work? Do they provide any new functionality or is this just a standard method to create sequences? Any breakdown of the new feature and how it works? Does quantum spin contribute to the angular momentum of a black hole? Does $\sum_{n=1}^{\infty} \sin(\pi(2+\sqrt{3})^n)$ converge? Converge absolutely? Per the title, does $\displaystyle\sum_{n=1}^{\infty} \sin(\pi(2+\sqrt{3})^n)$ converge? Converge absolutely?   I'm stuck on this question, not sure how to approach it.  Thank you! The Megahertz Myth became a promotional tactic due to differences between the PC's INTEL 8086 processor and Apple's Rockwell 6502 processor.  The 8086 ran at 4.77MHz while the 6502 ran at 1MHz.  However, instructions on the 6502 needed fewer cycles; so many fewer, in fact, that it ran faster than the 8086.  Why do some instructions need fewer cycles?  And why can't the instructions of the 6502, needing fewer cycles, be combined with a fast cycling processor of the 8086?  Wikipedia's article for instructions per cycle (IPC) says     Factors governing IPC   A given level of instructions per second can be achieved with a high IPC and a low clock speed...or from a low IPC and high clock speed.   Why can't you have both high instructions per cycle and high clock speed?  Maybe this has to do with what a clock cycle is?  Wikipedia mentions synchronization of circuits?  Not sure what that means.  Or maybe this has to do with how a pipeline works?  I'm not sure why instructions in a short pipeline are different from instructions in a long pipeline.  Any insight would be great!  Just trying to understand the architecture behind the myth.  Thanks!  References: C++ Program communicating with MySQL Database Does anyone know of a simple way for a C++ program to communicate directly with a MySQL database?  I have looked at MySQL++ and found it to be very confusing.  If anyone knows of a very simple way of doing this, please let me know.  Thanks  P.S. I am developing on a Windows machine.  PHP and MySQL web web application setup.  C++ setup to talk to the serial port.  Thus why I need a way for C++ to talk to the MySQL database directly.