Prove that: $e^{-\frac{|t|}{2}}= \int_{\mathbb R} \frac{e^{ixt}}{1+x^2} dx.$
Cauchy distribution characteristic function
I have a DEM that I would like to smooth or generalize to remove topographic extremes (chop off peaks and fill-in valleys). Ideally, I would also like to have control over the radius or level of "blurriness". In the end, I will need a set of rasters that range from slightly blurry to really blurry. (Theoretically, the blurriest would be a constant raster of the arithmetic mean of all values).  Are there any tools or methods I can use (based on Esri, GDAL, GRASS)?   Do I need to home bake my own  routine?   Could I use a low-pass filter (e.g. ArcGIS's ), and if so, would I need to run it a bunch of times to get the effect of a large radius? How can I set the maximum amount of characters in a UITextField on the iPhone SDK when I load up a UIView? Georeferencing old map in QGIS? I have an old map over a part of Laos and wondering how do I georeference the map with the help of the Grid lines and other Longitude and Latitude information on the scanned map? I have searched for information on the internet and tried many times. My scanned map wont overly correctly on the base map. Any base map would be fine. As long as I can check the result.  Do I add X/East and Y/North values from the grid line crossings as marked and written in some parts of the map? How do I begin georeferencing this map? Do I have to add zeros after the two digits? For example if the Easting is 24 (its in KM right? Do I add like three/four zeros to convert it to meters?  I georeferenced the map with the option "From Map Canvas" in the georeferencer tool and I succeeded but I want to know the coordinate of a point on my old scanned map and write them as X/East and Y/North to georeference the map.   I hope I am not babbling and someone understands what I mean!  We can set the CRS to WGS84, EPSG:4326. Change the size/width of tabs in Notepad++ How can metagaming retries on poor skill checks be prevented? I'm sure every DM has had this happen: one PC is trying to find something cool on a dead monster's body. The player rolls poorly, and instead of accepting the paltry 2 copper pieces, the PC calls all the party members over to also try looting the corpse. Invariably, a different player rolls well, and everyone walks away satisfied that everything's been taken down to the poor dead monster's last holey sock.   Another example: One PC is trying to find some useful information in a library. There're no guards, no reason anyone would be bothered, and no time restraints to stress about. The player rolls poorly, so all the other PCs try, too.  I'd describe this as well-intentioned metagaming. The players are afraid of losing out on content, this despite multiple sessions of me making it clear that I don't structure my games to penalize gameplay that way.  These are situations that require a roll to determine the degree of success. (At least I think so; perhaps I'm wrong here?) Failure could set back the PCs a cool item or a bit of information that would have helped a little, but these minor failures aren't game-enders or anything. As a DM I can't see a reason to say "No" and disallow the practice, but it feels vaguely like cheating to let the players roll multiple times to get better results.  How do I prevent players ganging up on skill checks after they've seen someone roll poorly? Checking if two Poisson samples have the same mean OpenLayers 3 WMS GetFeatureInfo popup I have a map a at the link below:    I added one of my GeoServer WMS layers to the map, now I try to add the attributes window pop up on click. I found to examples on the OpenLayers 3 homepage, but I cannot put together a working code...      Is there any chance to have a working sample somewhere? Java GUI repaint() problem? I have a JFrame. This JFrame contains a JButton. I click the JButton and 10 JTextFields are created.  the problem: I cannot see them until "I force a repaint()" by resizing the window. Only then do I see the JTextFields created.  CODE:  JPanel points = new JPanel();  //Creating the JTextFields: for (int i=0; i&lt;10; i++) {     JTextField textField = new JTextField();     points.add(textField); }  repaint(); this.repaint(); super.repaint(); points.repaint();     THANK YOU - after the for loop, I just called points.validate() and it worked... How do I identify which features have NULL attributes in the attribute table of a shapefile?  When i try [field]= 'NULL' it selects the features with value = 0 (see picture) How do I iterate through each element in an n-dimensional matrix in MATLAB? ${!FOO} and zsh ${!FOO} performs a double substitution in bash, meaning it takes the (string) value of FOO and uses it as a variable name. zsh doesn’t support this feature.  Is there a way to make this work the same in bash and zsh?  Background:  I’ve got a list of environment variables, like  PATH MAIL EDITOR   and want to first print the variable names and afterwards their values.  This works in bash but not zsh:    for VAR in LIST do         echo $VAR         echo ${!VAR} done   It should be somehow possible “the old way” with eval, but I can’t get it to work:  for VAR in LIST do         echo $VAR         echo `eval \$$VAR` done   I’m never going to understand why I can’t simply do arbitrary deep substitutions like ${${VAR}} or even ${${${VAR}}} if need be, so an explanation for that would be nice, too. Is there way to replace value of symbolic link? Is there way to replace value of symbolic link?  For example I want to replace symbolic link like this:  first -&gt; /home/username/foo/very/long/directories/that/I/do/not/want/to/type/again    to   second -&gt; /home/username/bar/very/long/directories/that/I/do/not/want/to/type/again   I want to change only foo to bar.  Of course I can create a link again, but if it is possible to replace value of the link, it become easier. I'm having trouble opening jar files because there is no java runtime in open with listed. Even I have installed it via Software Center(i also try to reinstall it via synaptic and i do a --purge via terminal). How to connect two Dell P2415Q 4k displays to MacBook Pro 2016 What's the best way of connecting two Dell P2415Q 4k displays to the MacBook Pro 2016 with TouchBar and TouchID?  I have the monitors connected to an older MacBook Pro currently with two mini-DisplayPort cables. Can I somehow reuse those cables or do I need new ones?  Apple's support page  lets me know that:  "Note that although it uses a Mini DisplayPort connector, the Thunderbolt 3 (USB-C) to Thunderbolt 2 Adapter doesn't support connections to Mini DisplayPort displays."  So I guess reusing the cables is not the way to go? Incorrect plot using pgfplots (trigonometric functions like cos, sin and tan) I'm trying to plot a function with pgfplots for LaTeX. Unfortunately, pgfplots plots the function incorrectly.  Here is the LaTeX code I use:  \begin{figure}[H] \centering \begin{tikzpicture}     \begin{axis}[xlabel=Gameplays,ylabel=Rating]         \addplot+[gray,domain=1:30]         {0.5 + 0.5 * ((atan(x) * 2 / pi)^11.79)};     \end{axis} \end{tikzpicture} \caption{Omzetten van aantal gameplays tot impliciete rating} \label{fig:omzetten_impliciete_ratings} \end{figure}   Here is how the function should look like:     This is how it is plotted:    Does anyone know what I do wrong?  Thanks in advance! Prove inequality using Jensen's inequality I have a method that I would like to call.  However, I'm looking for a clean, simple way to kill it or force it to return if it is taking too long to execute.  I'm using Java.  to illustrate:  logger.info("sequentially executing all batches..."); for (TestExecutor executor : builder.getExecutors()) { logger.info("executing batch..."); executor.execute(); }   I figure the TestExecutor class should implement Callable and continue in that direction.  But all i want to be able to do is stop executor.execute() if it's taking too long.  Suggestions...?  EDIT  Many of the suggestions received assume that the method being executed that takes a long time contains some kind of loop and that a variable could periodically be checked. However, this is not the case.  So something that won't necessarily be clean and that will just stop the execution whereever it is is acceptable. I asked a  recently, looking for examples of an online tool. Per the , I answered my own question with a few examples that I had already found. I did this so that these examples would be included in the answers, along with the rest.  The question has received only down votes and insults saying that this shouldn't be done.   Should I not answer my own questions? When should comments be flagged/deleted on per-site metas? We all know , but that guidance is, naturally, geared toward main sites, where we want to keep things clean and focused.  Meta, on the other hand, is a site's "second place", with some different rules and conventions.  For example, questions on main sites can be closed as primarily-opinion-based, but meta is all about opinions.  There's a "discussion" tag and such questions collect many opinions.  Meta is different.  Occasionally I see comment flags on metas and I'm never sure what to do with them.  Setting aside things that are blatantly offensive or spam (that's a no-brainer), is there such a thing as "too chatty" or a comment discussion that should be moved to chat on meta?  I am very conservative in deleting things on per-site metas (except on  posts, which like main should stay focused).  Are there any guidelines specific to per-site metas?  I'm specifying per-site metas and not MSE because MSE seems to have conventions that fall somewhere between "main site" and "per-site meta".  If the answer is the same for all metas then great, but I don't want to assume it'll be the same. Finitely generated group which is not finitely presented Is there any easy group theoretical way of showing that the wreath product $G$ of two infinite cyclic groups is not finitely presented?  I was looking for a finitely presented group with a central subgroup isomorphic to the free group of countable rank and whose factor group is isomorphic to $G$; in this way assuming that $G$ is finitely presented we get a contradiction.   Any ideas?