Icons segment triangle
What is this triangle icon [Samsung Galaxy S9+]?
How to put a brace on the right, not left, to group cases? How can I get a brace on the right, not the left, to group cases, using cases? (I know actual cases look better with the brace on the left, but the items I need to group are not literally cases. They are a set of steps in an algorithm which I want to consider as an item.)  The following puts the brace on the left. All I need to do is to flip it to the right.  \begin{align} \begin{cases} a&amp;=bbb\\ c&amp;=ddddddd\\ e&amp;=ffffffffff \end{cases} \end{align}   Thanks for any help with this! Free vector graphic images, for commercial use Is there a free library of vector graphics for commercial use? Why does holding something up cost energy while no work is being done? If $p$ is congruent to $2 \pmod 3$, how can I prove that all $a$, $1 \le a \le p-1$ are cubic residues $\mod p$?  Here's what I've done:  $1^3$ congruent to $1 \pmod p$ thus, 1 is a cubic residue, Also $(p-1)^3=(p-1) \pmod p$ implies  $$(p-1)^3 - (p-1) = (p-1)[(p-1)^2 -1] = (p-1)(p^2 -2p) = p(p-1)(p-2) $$ implies $$p|(p-1)^3 -(p-1)$$ Thus  $p-1$ is a cubic residue $\mod p$. Now I don't know how to show for $1\lt a \lt p-1$ are all cubic residues when $p$ is congruent to $2\pmod 3$. Short story about a crew finding an ancient alien ship filled with tons of artifacts from their society Using different delimiters in sed commands and range addresses I typically have two needs:  Scenario A. Change a single PDF page.  In this case I have a PDF but not the original source file used to create the PDF. I don't want to try to recreate the document from scratch. I'd like to open the PDF and change a few things. A good example of this scenario: I was responsible for planning a big event at a campground site, I had a PDF of the site. I wanted to start with that document, highlight some parts, add some labels, remove some parts that weren't relevant.   or   Scenario B. Combine PDFs or extract page(s) from a PDF  This scenario usually arises because I want a single PDF deliverable that is made up of parts that are best created in different programs. In this case I have the source files for all the documents but they don't play well enough together to easily create a single PDF deliverable. For part of it, I may want to use Libre Office Writer. For another page I may want to use Gimp. Still another page I may use Libre Office Calc. I could use Writer as the master document and embed images or the Calc object into that, but for ultimate control, you can't beat separate PDF documents that are then combined.  What are the best tools / processes for editing PDFs in Ubuntu? Adding values to a C# array Why do rain waves form and what is their connection to the texture of the surface they're on? When it rains and water flows down an inclined street, ripples may form that are carried along with the current. Here's a picture with an example of what I'm talking about    I'd like to know what the fluid mechanical mechanism is for the formation of these waves. A quick google search reveals that they've been identified in some scientific literature as "rain waves" (if you have a jstor subscription you can see ) but I've only been able to find phenomenological descriptions of their properties without any details of the physics giving rise to them. In particular, I'm curious if people think that the surface on which the water is flowing must have a particular texture in order to give rise to the waves. How do I debug permissions? How do I debug permissions in Drupal 7?  I use core reporting, error logs, devel module error logs, backtrace and node access permission block but sometimes it is not enough. What else should I check to find out why certain fields, views or blocks are not showing to a user?  I also found there is a  for reporting on permissions called  but it is not available for Drupal 7.  I am using various permission related third-party modules:   - devel node access 7.x-1.x-dev   - fast permissions administration 7.x-2.0  - organic groups access control 7.x-1.x   - profile2 group access 7.x-1.x-dev   - ur-node access 7.x-1.x-dev How to expand the ext4 primary partition size in a VMware Player virtual disk? I have a VMware Player virtual machine setup, running Ubuntu 10.04 as the a guest OS.  The VM was created on a 20GB virtual drive, with a single partition for working space. Finally I got to the point where I need to expand the size of the virtual drive. Resizing the drive itself, adding some 10GB, was easy via the VMware Player menus. I now need to resize the main partition itself (I prefer this over creating a separate partition and mounting it).  According to GParted, I now have the following partitions:    My question is, how can I increase the size of the Filesystem partition to include the free 10GB?  From information I found online, it looks like one limitation is the fact that he swap partition is immediately adjacent to the filesystem, so my understanding is that first thing would be to move that partition to the end of the volume. How can this be done?  Also, some sources suggest that the system should be booted from a LiveCD, so the filesystem is not the boot partition, and thus make it easier to resize. As mentioned above, I run a VM, so I am not sure how to boot it from a LiveCD. Any ideas? Set of discontinuity of monotone function is countable The result I am trying to prove is the following:     Let $F:\Bbb R\to\Bbb R$ be increasing. Then the set of points, at which it is discontinuous, is countable.   I have been reading this form Folland's Real Analysis and he proves this by considering the sum $\sum_{|x|&lt;N}[F(x^+)-F(x^-)]$ which has to be finite by some sort of telescoping sum. Now, I am not sure how he defines this sum. I am assuming he does this by using nets (let me know if there is another way to look at this), but he doesn't introduce the concept of nets until the next chapter. So I was looking for some other ways to prove this result and I found the following result (from Stein-Shakarchi) which is quite similar but assumes $F$ to be bounded.      A bounded increasing function $F$ on $[a,b]$ has at most countably many discontinuities.   This is shown by using the density of rationals in $\Bbb R$, i.e. $\exists r_x\in\Bbb Q$ s. t. $F(x^-)&lt;r_x&lt;F(x^+)$ corresponding to each point of discontinuity $x$.   Now I feel like there shouldn't be a problem in doing the exact same thing for unbounded increasing function. Is this right? Secondly how does this proof relate to the first one? I feel like there isn't much of a difference between the two proofs. To be precise I think that the previous sum is well defined/finite because of this countability of discontinuous points. What do you think about this way of thinking?  Edit. Here is the Folland's proof in more detail:  Since $F$ is increasing, the intervals $(F(x^-),F(x^+))$ are disjoint for all $\forall x\in\Bbb R$. Moreover,  $\forall|x| &lt; N$ such intervals are contained in $(F(-N),F(N^+))$ and so  $$\sum_{|x|&lt;N}[F(x^+)-F(x^-)] \leqslant F(N) - F(-N) &lt; \infty. $$ Hence the set $\{ x \in (-N,N) : F(x^+) \neq F(x^-)\}$ is countable. The symmetric cryptosystem one-time pad (OTP) seems to be very beautiful since it is perfectly secret according to Shannon. Many books, however, point out the main drawback: one must create a secret key the same length as the plaintext. For this reason, the concept of perfect secrecy has these days been abandoned, and we prefer other cryptosystems.   Now, for example, suppose I want to encode my text message with the ASCII scheme, and moreover suppose that this plaintext is 10 gigabytes long, therefore (using an OTP) the key must be the same length, 10 gigabytes. I think, however, this is a ''sustainable price'' because I'm sure that the ciphertext can't be attacked.  Practically, I don't understand why having such long keys with an OTP is a big disadvantage if we reach "the dream"-- namely, perfect secrecy. Nowadays the storage of information is very easy, so what is the real problem? I can, for example, share the "long key" in person. Nesting HTML- anchor tags SD Card showing weird file names and files are lost I just plugged my SD Card to my PC after a long videography day, and I suddenly got this problem:    It is also not showing all the videos I took on my camera so what is the solution? How do the Flashes breathe utilizing their super speed? The air pressure would be extreme. Do they run in a pressurized bubble? Converting vector layer to raster using QGIS? In qgis in the raster menu there is an item "convert vector to raster".  This behaves strangely - I do not understand how it is supposed to work.  I can select a vector file, an attribute and an output raster. But, for some reason the output file is only accepted if it exists and even if I select an existing raster nothing seems to happen.  Also I do not understand how the program knows what kind of raster to create, what cell-size, projection etc.  How can I convert vector to raster? How do I make an Bootable Ubuntu USB containing the the latest version of Ubuntu?  For completeness, how would I be able to do this on Ubuntu, Windows, OS X or another Linux distro? How to add percent sign to NSString Photoshop using Marque Tool > Path > Circular But Not a perfect shape? Please consider this image below :   This is happened when I have a circular shape (marquee tool selection). THen after that I converted to Work Path (by right click of that selection). And I add 2.0 as its Tolerance Pixel.   After applying it. The shape become not perfect, could you see the difference? I make it with a black background so everyone could see it from the image no.2.  I realized this is a problem, because If i use that path for placing a text. the text wont follow the correct path as circular (selection), instead ... the shape a bit changed (i think it's ugly shape :: see the detail of the arrow).  How to solve this case ? I'm using Photoshop CS3.