The Chicago Manual of Style (sec. 12.16) suggests medium space (a ¼ em) before and after   signs for binary operations (i.e., conjunctions); symbols of integration, summation, or union; and signs for binary relations (i.e., verbs)   except in exponents; also medium space after commas between "coordinate points" or between elements in a list; and "no space after a binary operation or relation sign when it is modifying a symbol (i.e., used as an adjective)".  I don't know whether LaTeX follows these guidelines, but anyway I would like to know the (generally accepted) "right" amount of space in the following situations (that is, do I need to add/remove space, and if so how much?)   after logarithm: \log x before factorial symbol: y! in an implicit multiplication: x y before and after "for all" symbol: x &gt; 0 \forall x between equations separated by a comma: x = 1, y = 2 between equations separated by text: x = 1 \text{ and } y = 2 after a comma separating elements of a set: \{0, 1\} after a comma separating arguments of a function: f(x, y)
In general, in most places, it is said that using TeX defaults is the best. However, TeX does provide things like \, and \quad etc. When one should use them? Both in general and in math mode in particular.
How do I view 'git diff' output with my preferred diff tool/ viewer? When I type git diff, I want to view the output with my visual diff tool of choice (SourceGear "diffmerge" on Windows). How do I configure git to do this? I'm trying to understand the UMP of the product functor as right adjoint to the diagonal functor but I'm having difficulties understanding the notation in Steve Awodey's . On page 210 he uses $(f_1, f_2)$, $\langle f_1, f_2 \rangle$ and $(f_1 \times f_2)$ all within one paragraph. What are those? How are these defined and how do they differ? What spell almost killed Hermione in The Order of the Phoenix? The spell was cast without words, simply a flick of the Death Eater's wand, and a 'streak of purple flame' that lanced across her chest. It was later mentioned that the spell was weakened because of the lack of a verbal component, but still 'did enough damage as it was'. She was in the infirmary healing from the damage for some time. What spell was this? Elementary central binomial coefficient estimates I'm trying to prove that the converse of Lagrange's theorem is true for finite abelian groups (i.e. "given an abelian group $G$ of order $m$, for all positive divisors $n$ of $m$, $G$ has a subgroup of order $n$"). This is an exercise from a book, and it is in the section on finite abelian groups, so I know I have to use the fundamental theorem of finite abelian groups. I have come up with a proof, but it seems a bit messy, and I'm not entirely sure if it's correct. It is given below.     Let the order of $G$ be $m$ = $p_1^{\alpha_1} \ldots p_k^{\alpha_k}$. It is known that $G$ is a direct product of $p$-groups, say:      $$G = G_1 \times \ldots \times G_k$$      where each $G_i$ is a $p_i$-group. By the fundamental theorem of finite abelian groups, each $G_i$ is isomorphic to a direct product of cyclic groups of the form      $$\mathbb{Z}_{{p_i}^{\beta_1}} \times \ldots \times \mathbb{Z}_{{p_i}^{\beta_l}},$$      where $\beta_1, \ldots, \beta_l$ are positive integers such that $\sum_{j=1}^l \beta_j = \alpha_i$. Now if $n$ divides $m$, then we must have      $$n = p_1^{\gamma_1} \ldots p_k^{\gamma_k}$$      for some $\gamma_1, \ldots, \gamma_k$ with $0 \leq \gamma_i \leq \alpha_i$.      Claim: Each $G_i$ has a subgroup of order $p_i^{\gamma_i}$      Proof: As above, we have that       $$ G_i \cong \mathbb{Z}_{{p_i}^{\beta_1}} \times \ldots \times \mathbb{Z}_{{p_i}^{\beta_l}} $$      where $\beta_1, \ldots, \beta_l$ are positive integers such that $\sum_{j=1}^l \beta_j = \alpha_i$.      Now since $0 \leq \gamma_i \leq \alpha_i$, we can find   $l$ numbers $\delta_1, \ldots , \delta_l$ such that $\gamma_i = \sum_{j=1}^l \delta_j$, and $0 \leq \delta_j \leq \beta_j$. (This choice of numbers is not necessarily unique).      Then $p_i^{\delta_j} | p_i^{\beta_j}$ for each $j = 1, \ldots , l$. Hence, for each factor $\mathbb{Z}_{{p_i}^{\beta_j}}$, there exists a subgroup of order $p_i^{\delta_j}$, namely $\mathbb{Z}_{{p_i}^{\delta_j}}$ (using the fact that the converse of Lagrange's theorem is true for finite cyclic groups). Taking the direct product of each of these subgroups, we get a new subgroup $G_i'$ of $G_i$:      $$G_i' \cong \mathbb{Z}_{{p_i}^{\delta_1}} \times \ldots \times \mathbb{Z}_{{p_i}^{\delta_l}}$$      The order of this subgroup is $p_i^{\delta_1} \times \ldots \times p_i^{\delta_l} = p_i^{\delta_1 + \ldots + \delta_l} = p_i^{\gamma_i} $. So we have found a subgroup of $G_i$ of order $p_i^{\gamma_i}$, as required.      So each factor $G_i$ in the product $G = G_1 \times \ldots \times G_k$ has a subgroup $G_i'$ of order $p_i^{\gamma_i}$.       Therefore, $G$ has a subgroup   $$G_1' \times G_2' \times \ldots \times G_k'$$       of order $p_1^{\gamma_i}...p_k^{\gamma_k} = n$, which completes the proof.   I have two questions about this: firstly, does this proof seem to work? Secondly, is there a way to make the proof more concise (e.g. a way to prove the statement without using all these indices)? Suppose f is a twice differentiable function with $f(0)=0$ and $f(1)=1$, $f'(0)=f'(1)=0$. Then show that $|f''(x)| > 4$ for some $x$ in $(0,1)$ Is there an old, rarely used word which means "an archaic word"? Using ArcPy to convert .txt to shapefile with coordinate system? I tried to define my coordinate system on creating the shapefile but when I zoom to layer I don't see my features and ArcGIS crashes. I know it's not in the coordinate system I defined for it but it shows the coordinate under properties but doesn't reflect when I zoom to layer. Here is my python code:  import arcpy  newfcName ="newfc.shp"   outpath = r"C:/FLOOD/IKEJA AND KOSOFE"  # Declaration arcpy.env.overwriteOutput=True  arcpy.env.workspace= outpath  # Create new Shapefile and add FIELDS newfc = arcpy.CreateFeatureclass_management(outpath, newfcName, "Point") # get the coordinate system by describing a feature class dsc = arcpy.Describe("newfc.shp" )  coord_sys = dsc.spatialReference  try:        # run the tool    arcpy.DefineProjection_management(newfcName , coord_sys)     # print messages when the tool runs successfully    print(arcpy.GetMessages(0))  except arcpy.ExecuteError:    print(arcpy.GetMessages(2))  except Exception as ex:    print(ex.args[0])  arcpy.AddField_management(newfc, "X", "STRING", field_length = 50) arcpy.AddField_management(newfc, "Y", "STRING", field_length = 50) arcpy.AddField_management(newfc, "Z", "STRING", field_length = 50) arcpy.AddField_management(newfc, "I", "FLOAT", field_length = 50)  # Reference Cursors cursor=arcpy.da.InsertCursor(newfc, ["X", "Y", "Z", "I"])  # Read File  a = open("C:/FLOOD/IKEJA AND KOSOFE/DEM/532722.txt","r")  inputF = a.readlines()  for line in inputF:     xCoordinate, yCoordinate, zValue, iValue = line.split(" ")      newRow = (str(xCoordinate), str(yCoordinate), str(zValue), float(iValue))      cursor.insertRow(newRow)  a.close() How can I stop mobs from despawning? I am using Spigot, some plugins, and I want to make like a zoo on a map, with mobs behind glass cubes. The problem is that when I load my map, every time some of the mobs just vanish, empty cages. I put eggs again, they spawn, I go to my other map in the multiverse (/mv tp my_other_map) and when I come back, empty cages again, always the same ones...   I've  read it's a question of distance of me (distance in cubes unit), if I'm too far away, the mobs will despawn... Is there a way for them to stay? Use Expect in a Bash script to provide a password to an SSH command How do I join a Windows Active Directory? We have a "mix-mode" Lab. and we want to migrate to Ubuntu, from Windows.  In this process, how do we add Ubuntu workstations to a Windows Domain / Active Directory ('AD') setup? In , it is established that Thieves' Cant is more of an encoding system built on top of a language than a language in its own right. According to the Basic Rules,  is:  ...a secret mix of dialect, jargon and code allows you to hide messages in seemingly normal conversation. Only another creature that knows thieves' cant understands such messages. It takes four times longer to convey such a message than it does to speak the same idea plainly. In addition, you understand a set of secret signs and symbols used to convey short, simple messages, such as whether an area is dangerous or the territory of a thieves' guild, whether loot is nearby, or whether the people in an area are easy marks or will provide a safe house for thieves on the run. (PBR, p. 27)  Can two creatures communicate using Thieves' Cant if they do not have a basic spoken language in common, or if they are speaking different basic languages? E.g. if one creature knows Orcish, Goblin, and Thieves' Cant, and another creature knows Elvish, Giant, Common, and Thieves' Cant, can they communicate with each other by embedding Thieves' Cant into their own languages? Hypothetically speaking, I can see how this could be possible in our own world, if we assume that Thieves' Cant depends on nuances of body language, emphasis, and tempo, e.g., one might say to a non-Spanish speaker:  Tenemos quEEEEEEE ir (wink) a la tieeeeenda de (shuffle left foot) armas para (twirl hair and giggle) comprar una espada (wink twice) para mi herMANO (wag right pinky and nod).  The literal message itself (&quot;We need to go to the weapon store to buy a sword for my brother.&quot;) would just be a carrier - the real message might be hidden within the gestures and the accented and extended syllables. Perhaps the drawn-out &quot;E&quot; vowel means &quot;robbery planned&quot;, the wink means &quot;bank&quot;, shuffling the left foot means &quot;be there at sunset&quot;, etc., and these are things that you wouldn't necessarily need to know Spanish to extract. Is this how Thieves' Cant actually works, or does it require actual comprehension of the literal message transmitted before the &quot;secret&quot; message can be extracted from it? Running the minimal example  \documentclass{article} \usepackage{filecontents} \begin{filecontents*}{\jobname.bib} @ARTICLE{example,   author  = {Other, Anthony Norman},   title   = {Some things I did},   year    = {2014},   journal = {J.~Irrep. Res.},   volume  = {1},   number  = {1},   pages   = {1-10} } \end{filecontents*} \usepackage[backend=biber]{biblatex} \addbibresource{\jobname.bib} \begin{document} Hello\cite{example}. \printbibliography \end{document}   I get the warning There were undefined references.  I have read  and know that I need to run:   LaTeX Biber LaTeX   However, my editor is only set up to run BibTeX. How do I go about setting up my editor/IDE to be able to run Biber, and how do I run the LaTeX/Biber/LaTeX cycle?  Answers (sorted alphabetically by editor name)                    Answer guidelines   Each answer should be for one editor. If the editor is cross-platform, if possible give a single answer with notes covering the minor platform variations. Please edit the question to include new answers in the 'link list' Each answer should be 'stand alone', i.e. don't say 'It's almost the same as editor Y but ...' for the editor part Instructions for 'build tools' such as arara or latexmk are welcome but should explain how to set up the editor in question as not all editors allow simple addition of arbitrary tools Algebraic Proof that $\sum\limits_{i=0}^n \binom{n}{i}=2^n$ A potentially dangerous Request.Form value was detected from the client Every time a user posts something containing &lt; or &gt; in a page in my web application, I get this exception thrown.  I don't want to go into the discussion about the smartness of throwing an exception or crashing an entire web application because somebody entered a character in a text box, but I am looking for an elegant way to handle this.  Trapping the exception and showing     An error has occurred please go back and re-type your entire form again, but this time please do not use &lt;   doesn't seem professional enough to me.  Disabling post validation (validateRequest="false") will definitely avoid this error, but it will leave the page vulnerable to a number of attacks.  Ideally: When a post back occurs containing HTML restricted characters, that posted value in the Form collection will be automatically HTML encoded. So the .Text property of my text-box will be something &amp; lt; html &amp; gt;  Is there a way I can do this from a handler? I'm trying to measure the execution time of a process that I call via the command line (i.e., I want to find out how long it takes to for the process to finish). Is there any command that I can add to the command calling the process that will achieve this? how to read xml file from url using php How to install Ubuntu on portable external Hard Drive? OS: Windows 7. I want install Linux Ubuntu on portable external Hard Drive USB 2.0. I read a variety of methods, but I'm confused by contradictory advices and methods. Actually, installing Ubuntu on anything other than clean PC looks much more complicated than installing Windows. I need to have Ubuntu package + Python 2.7 + C compiler installed. My external hard drive is partially filled, I need to keep all files.   Will Ubuntu run entirely on external hardrive, without writing anythinhg to Windows system folders and to registry?  Can anyone post detailed guide how install Ubuntu on external hard drive? Can I fine-tune my screen brightness? My laptop is Lenovo T400, and my OS is Ubuntu 10.10. I change the brightness of my screen by pressing the FN key and one of the two keys for increasing/decreasing brightness.  The brightness I feel comfortable is between two consecutive levels that are offered. So I wonder if it is possible to fine-tune the screen's brightness? I am trying to retrieve VersionData with a standard REST API call from a VisualForce Page a then upload it to a S3 bucket but end up with corrupted files. I believe this is an encoding problem on the client side as plain text or CSVs work like a charm. I can upload VersionData from Apex but there are heap and request size limitations so I need to send the data from the client.   This is the call and returned string, I tried changing mimeType and encoding on both sides (SF call and S3 upload) with no luck.   Any ideas how to properly process images or pdf files? Thanks a lot  THE PROBLEM IS NOW SOLVED  Files should not be treated as strings. I solved the problem by leaving jQuery's ajax as I did not succeed to request a response type. By switching to plain JS and making a GET call (XMLHttpRequest) with response type set to blob I received an Object, instead of a string. Base64 string can be then retreived using JS FileReader.