Bash variable number in ascending order
How do I iterate over a range of numbers defined by variables in Bash?
Solve $$\int \limits_{0}^{\infty} \frac{\cos(x)}{\cosh(x)} dx$$ without complex integration.  This integral can be very easily solved with contour integration, but how can you solve it without taking a tour in the complex plane? I've heard that you should use \[ ... \] for displayed equations instead of  $$ ... $$, but why is that?  I'd assumed that it's so that you can more easily tell which are starting and which are ending delimiters, but if I always use a syntax-highlighting text editor, I can see that easily based on the color of the symbols.  Is there any reason for this suggestion? How to set Command Block(s) to test for a particular time and output a message? I simply want one command block to test for the time of day or night (e.g. time = 18000) and output a message in the chat to everyone if that time returns true.  I was trying a simple set-up with two command blocks and a comparator in the middle, but I'm a beginner and am obviously missing the correct syntax (especially to test for a particular time of day, and if true, then trigger the say "message" block).  ETA: Kudos to @Ben for the Daylight Sensor/Redstone idea, but I'd really prefer a Command Block solution for the above, since my plan is to output several messages during the day and night cycle at very specific times in the world. Thanks. How do you express that your understanding of something is completely changed? When something blows your mind and changes your understanding of something that you've believed in for years, how do you express it (formally or informally)? Which homology groups of a closed orientable 6-manifold can be isomorphic to $\mathbb{Z}^3$? List all $i$ for which there is a closed orientable $6$-manifold $M$ with $H_i(M) =\mathbb{Z}\oplus\mathbb{Z}\oplus\mathbb{Z}$.   I am working on an old exam problem and this one stumped me. Progress so far:  I can take $Y=\mathbb{T}^3 \times \mathbb{S}^3$ and get the desired group for $i =1,5,2,4$ I think. But this construction I believe gives $H_3(Y)=\mathbb{Z}^2$. What to do in this case? With the ls command, is it possible to show only the files created after a specific date, hour...?  I'm asking it because I have a directory with thousand of files.  I want so see all files that were created since yesterday.   I use ls -ltr but I have to wait to see all files...  There is an equivalent of DIRECTORY/SINCE=date from OpenVMS ? Is it possible to create individual power settings for each hard drive? I have a number of different drives that I use for different purposes but I only use two of them frequently. I would like for the others to enter sleep mode when not in use, but never my main two.  Is there any way to edit power saving settings for individual drives? How can I create Light Streaks in Cycles? System Load Indicator only shows as a line unless hovered I installed the  GNOME extension on my Ubuntu 18.04, but for some reason, instead of showing a proper graph for CPU usage, it only shows a very thin line that seems to be a small portion of the actual graph. If I hover over it, the proper graph shows. How to make it show the whole graph all the time? Why hash the message before signing it with RSA? How to Expand , Resize "extended partition"? How can I expand/resize my extended partition (sda3) with unallocated free space to the left of it? I want this to be able to expand my / partition (sda5). Applying options to already loaded package Is there a way to apply some options to a package which is loaded in the cls file I am using? For instance, suppose that the cls file loads graphicx, and I want to apply the option demo to it from my tex file. Will higher temperatures damage a computer over time, even when not reaching max? How to select kernel for SVM? How to show that $\sum_{k=1}^n k(n+1-k)=\binom{n+2}3$? Here's the context       "Her heart leaping into her throat, she tiptoed into the salon. Such was her astonishment at seeing Mike chatting with her boss that she leaned against the wall, incapable of making another move."   Is this a phrase or what? Could it be used in other forms as well? Can a negative charge ionize air? Adding to this question, I have studied that positive charge ionizes air but never studied that negative charge ionize air. If possible, please explain how does it ionize air? Why do we care about eigenvalues of graphs?  Of course, any novel question in mathematics is interesting, but there is an entire discipline of mathematics devoted to studying these eigenvalues, so they must be important.  I always assumed that spectral graph theory extends graph theory by providing tools to prove things we couldn't otherwise, somewhat like how representation theory extends finite group theory.  But most results I see in spectral graph theory seem to concern eigenvalues  not as means to an end, but as objects of interest in their own right.  I also considered practical value as motivation, e.g. using a given set of eigenvalues to put bounds on essential properties of graphs, such as maximum vertex degree.  But I can't imagine a situation in which I would have access to a graph's eigenvalues before I would know much more elementary information like maximum vertex degree.  (EDIT: for example, dtldarek points out that $\lambda_2$ is related to diameter, but then why would we need $\lambda_2$ when we already have diameter?  Is this somehow conceptually beneficial?)     So, what is the meaning of graph spectra intuitively?  And for what practical purposes are they used?  Why is finding the eigenvalues of a graph's adjacency/Laplacian matrices more than just a novel problem? How can I get my graphics card to be recognized in System Info? I am new to Linux/Ubuntu. I installed Ubuntu 11.10 on my Lenovo IdeaPad y510.   System info says    Graphics: unknown.   Driver: unknown,   Experience: Standard.   What should I do to use all my laptop hardware components to work properly with Ubuntu? Screenshot: I have seen that the new  shows off H.265/HEVC playback, the successor of H.264. I wonder how I may get this support in Linux. Is there a need to install a codec specific for this format? How?