What is the difference between these two sentences:     Tom was hiding in the barn.      Tom was hiding in a barn.
I can’t for the life of me figure out where to use a and where to use the — and where there is no article at all. Is there a simple rule of thumb to memorize?   The standard rule you always hear:     “If a person knows which item you are talking about then use "the"   . . . doesn’t clear things up for me, as I have no idea whether or not they know.
If the sum of $n$ cubes is zero, then the sum must be no larger than $\frac n3$. Map not loading when using getLegend and showing error for getView() I was able to run my application on using Legend earlier but now I want to update my Legend when scrolling on the map. So I tried to used this code  . And I got the gist of how he is able to do that but when I am trying the same I keeping getting the error var graphicUrl = wmsSource.getLegendUrl(currentResolution);  I think this is mainly due to the wmsSource not declare. But I tried to initialize  seems wmsSource in TileWMS but does not seems to work. var getExtent = function () {     return map.getView().calculateExtent(); } var getProjectionCode = function () {     return map.getView().getProjection().getCode(); }  var updateLegend = function() {     var currentResolution = map.getView().getResolution();     var graphicUrl = wmsSource.getLegendUrl(currentResolution);        const crs = `&amp;CRS=${getProjectionCode()}`;     const bbox = `&amp;BBOX=${getExtent().join(',')}`;     const height = getHeight(getExtent());     const width = getWidth(getExtent());     const heightAndWidth = `&amp;srcwidth=${height}&amp;srcheight=${width}` ;     const legenOptions = &quot;&amp;legend_options=countMatched:true;fontAntiAliasing:true;hideEmptyRules:true;forceLabels:on&quot; ;        var img = document.getElementById('legend');     img.src = `${graphicUrl}${crs}${bbox}${heightAndWidth}${legenOptions}`; }; //Updated Legend End   //View var myview = new ol.View({     center : [8717490.201868,2788422.791843],     zoom : 4 })  var firstSel = document.getElementById(&quot;City&quot;); var secSel = document.getElementById(&quot;Sector&quot;);  //var LayerArray = [baseLayer, firstLayer]  //Map var map = new ol.Map({       target : 'mymap',       view: myview,       layers: [         new ol.layer.Tile({             source : new ol.source.OSM({                 attributions: 'Surveyor Allpication'             })         }),         new ol.layer.Tile({             source : new ol.source.TileWMS({                url: 'http://localhost:8089/geoserver/India/wms',                params: {'LAYERS': 'India:India', 'TILED': true,'TRANSPARENT':true},                ratio: 1,                serverType: 'geoserver',                transition: 0,             })         })       ] }) updateLegend();   This here is my JS &lt;div class=&quot;innerMap&quot;&gt;     &lt;div class=&quot;map&quot; id=&quot;mymap&quot;&gt;&lt;/div&gt;         Legend:     &lt;div&gt;&lt;img id=&quot;legend&quot;/&gt;&lt;/div&gt;     &lt;!--    &lt;div&gt;&lt;img src=&quot;http://localhost:8089/geoserver/wms?REQUEST=GetLegendGraphic&amp;VERSION=1.0.0&amp;FORMAT=image/png&amp;WIDTH=20&amp;HEIGHT=20&amp;LAYER=India%3AIndia&amp;RULE=Agra&quot; /&gt;%Name&lt;/div&gt; --&gt; &lt;!--    &lt;div&gt;&lt;img src=&quot;http://localhost:8089/geoserver/India/wms?SERVICE=WMS&amp;VERSION=1.1.1&amp;REQUEST=GetLegendGraphic&amp;FORMAT=image/png&amp;WIDTH=20&amp;HEIGHT=20&amp;LAYER=India%3AIndia&amp;SRS=EPSG%3A4326&amp;STYLES=&amp;SRCWIDTH=742&amp;SRCHEIGHT=768&amp;BBOX=75.4541015625%2C14.21630859375%2C91.7578125%2C31.09130859375&amp;LEGEND_OPTIONS=countMatched:true;fontAntiAliasing:true;hideEmptyRules:true&quot; /&gt; &lt;/div&gt;  --&gt;     &lt;/div&gt;  This is my HTML. How do I make this work? Continuous weighted random distribution, biased toward one end I am currently contributing to a particle system for our game and developing some emitter shapes.  My uniform random distribution along a line or along a rectangular area works fine - no problem.  But now I would like to have something like a 1 dimensional gradient in this distribution. This would mean for example lower values are more common than higher values.  I don't know what would be appropriate mathematical terms for this problem, so my search skills are rather useless with this one. I need something that is computationally simple, as the particle system needs to be efficient. The performance impact of using instanceof in Java What are 'closures' in .NET? What is a closure? Do we have them in .NET?  If they do exist in .NET, could you please provide a code snippet (preferably in C#) explaining it? Where do I find the power cells to restore the bunker door in “Ancient armory”? I am trying to find the power cells to access the amor. Yet the placement is unmarked and I thought I would eventually stumble over them clearing the cauldrons.  Yet after clearing three cauldrons (RHO, XI, and Sigma) I still only have the one from the very beginning.  Where do I find all the power cells? Is there a "smallest" divergent sum? How to cleanly launch a GUI app via the Terminal? Some GUI apps launch cleanly via the Terminal command line, but some don't, and they cause the Terminal to wait for the app to terminate. Even then, some don't "release" the command line.  The mysterious ampersand &amp; suffix seems to cause the terminal to put the process into the background (but I'm not sure what happens there).  Is there a way to launch an app via the Terminal so that there is no "hang on" effect, just like launching something via Alt+F2?  I'd like to have the command line available again immediately, without something still in the background and printing in the terminal. Bash is not finding a program even though it's on my path I have a program on my path.  The program runs when executed with a full path specified.  But the program cannot be found when I run it with just its name.    Essentially, I want to understand how the below output is possible, and how to fix it so that my program can actually be found without a full path specified:  root:/usr/local/bin# ./siege **************************************************** siege: could not open /usr/local/bin/etc/siegerc run 'siege.config' to generate a new .siegerc file **************************************************** root:/usr/local/bin# echo $PATH /usr/local/sbin:/usr/local/bin:/usr/sbin:/usr/bin:/sbin:/bin:/usr/games root:/usr/local/bin# siege bash: /usr/bin/siege: No such file or directory root:/usr/local/bin# wtf!?!?   I'm on Ubuntu 12.04 using bash.  Also please note the warning output from siege is not relevant for the purposes of this question, as I am only interested in whether or not the program can be found and invoked. I have 100 files with 57,816 rows each.I want to do an outer join of these files by merging on basis of the common column.  I am using R programming for this but this is very slow.  fileList &lt;- list.files(, pattern=".txt") pm_list=lapply(fileList, read.table) merged_pm=merge_all(pm_list, by = "gene_short_name")   Is there any quick way to do this in bash? The other method that I can use is SQL but I have to create 100 tables first and then load them up before join,which is not very efficient way to do.  The number of rows are equal in each file, thats why I want to merge  based on common column and can't use cbind from R as the constants in the common column are a bit up and down in different files and not present at same location in each file.Below are two sample files.I want to join based on 'gene_short_name'  gene_short_name FPKM56  MT-TF   0.90 MT-TV   0 MT-RNR1 310.015 MT-TL1  0 MT-TM   0   File 2 is below:  gene_short_name FPKM53  MT-TF   0 MT-TV   0.344 MT-TM   0.10 MT-TL1  0 MT-RNR1 0 MT-ND2  158.332 List all columns for a specified table On per-site metas, users are given a rank based on meta participation, and this ranking is seen on the default tab of the users page on each per-site meta. How is this participation numerically calculated to give a ranking? Is it by votes? Something else? Are community wiki posts included in this? Divisibility Proof with Induction - Stuck on Induction Step I'm working on a problem that's given me the run around for about a weekend. The statement:  For all $m$ greater than or equal to $2$ and for all $n$ greater than or equal to $0$, $m - 1$ divides $m^n - 1$.  Using induction over $n$, the base step comes easy since $m^n - 1$ is $0$ when $n = 0$.  My induction hypothesis is letting $k \geq 0$ and assuming that $m - 1$ divides $m^k - 1$. In order to show that $m - 1$ divides $m^{k+1} - 1$, I obviously need to use the induction hypothesis. However, no matter where I try to use the fact that $m^k - 1 = (m-1)a$ for some $a$ in the integers, the expression $m^{k+1} - 1$ always becomes more difficult to get to $m^{k+1} - 1$ being equal to $(m-1)b$ for some $b$ in the integers.   In other words, I can't figure out any actually helpful way to apply the induction hypothesis with the goal of proving the next step.  Any help would be appreciated! Simulating the Windows key on an old keyboard Downloading all my questions with the answerer names I am writing several papers in which I use answers which I received in various StackExchange websites. Naturally I would like to acknowlege and thank the SE members that gave the useful answers. But there are many such answers, and each answer is relevant to a different paper.   So, I would like to download all the questions that I asked in the various SE websites, including the answerer names, to an Excel worksheet in which I can organize the questions by subject.  Is this possible? What is the integral of 1/x? What is the integral of $\frac{1}{x}$? Do you get $\ln(x)$ or $\ln|x|$? In general, does integrating $f'(x)/f(x)$ give $\ln(f(x))$ or $\ln|f(x)|$? Also, what is the derivative of $|f(x)|$? Is it $f'(x)$ or $|f'(x)|$? Does $\sum\limits_{k=1}^n 1 / k ^ 2$ converge when $n\rightarrow\infty$? I can prove this sum has a constant upper bound like this: $$\sum_{k=1}^n \frac1{k ^ 2} \lt 1 + \sum_{k=2}^n \frac 1  {k (k - 1)} = 2 - \frac 1 n \lt 2$$ And computer calculation shows that sum seems to converge to 1.6449.  But I still want to know:  Does this sum converge? Is there a name of this sum (or the series $\frac{1}{k^2} $)? "Writ large", "Writ small", and others I have seen this used with other words besides "large" and "small".  What other words can be used? Can this structure be used more generally with other adjectives? Why Java needs Serializable interface? Are dark energy and zero-point energy the same thing? According to Quantum Mechanics is it possible that the famous  and  are the same thing that drives the accelerated expansion of the universe or maybe related to each other?