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The origin of spin is some what a puzzle to me, everything spin from galaxies to planets to weather to electrons.  Where has all the angular momentum come from? Why is it so natural?  I was also thinking do photons spin? we always think of the wave as a standard 2d sin wave but could this rotate in 3d? What implications would this have?   And what about spacetime how does all the spinning effect?  This has always been avoided in all lectures and classes I ever went to. I am looking for a good source on group theory aimed at physicists. I'd prefer one with a good general introduction to group theory, not just focusing on Lie groups or crystal groups but one that covers "all" the basics, and then, in addition, talks about the specific subjects of group theory relevant to physicists, i.e. also some stuff on representations etc.  Is Wigner's text a good way to start? I guess it's a "classic", but I fear that its notation might be a bit outdated? What is the purpose of the Character Table in style files? What is the reason to insert the code below at the beginning of a style file? For example, the code below can be found on lipsum.sty.   %% \CharacterTable %%  {Upper-case    \A\B\C\D\E\F\G\H\I\J\K\L\M\N\O\P\Q\R\S\T\U\V\W\X\Y\Z %%   Lower-case    \a\b\c\d\e\f\g\h\i\j\k\l\m\n\o\p\q\r\s\t\u\v\w\x\y\z %%   Digits        \0\1\2\3\4\5\6\7\8\9 %%   Exclamation   \!     Double quote  \"     Hash (number) \# %%   Dollar        \$     Percent       \%     Ampersand     \&amp; %%   Acute accent  \'     Left paren    \(     Right paren   \) %%   Asterisk      \*     Plus          \+     Comma         \, %%   Minus         \-     Point         \.     Solidus       \/ %%   Colon         \:     Semicolon     \;     Less than     \&lt; %%   Equals        \=     Greater than  \&gt;     Question mark \? %%   Commercial at \@     Left bracket  \[     Backslash     \\ %%   Right bracket \]     Circumflex    \^     Underscore    \_ %%   Grave accent  \`     Left brace    \{     Vertical bar  \| %%   Right brace   \}     Tilde         \~} %%   What is it for? Google Mobile Friendly test shows "other error" for resource loads I get the error "Couldn't load 23 page resources" when doing the mobile friendly test at     However, the error message is (the rather unfriendly) "Other error."  When I visit the site in Chrome using Developer Tools and setting the device toolbar to "Responsive," it works fine with no errors, and when I go the Google Search Console and do Crawl->Fetch As Google, I get no errors. I am looking for a convenient way to set the background of tabular cells. I'd like to do two things:  (1) Set the background shaded in a color (2) Set the background hatched  I learned that the TikZ package provides means to do this but I am unable to come up with a solution that does not use matrices (such as here: ) but instead uses the tabular package.  Here's what I'd like to do:  \documentclass{article} \begin{document} \begin{tabular}{|l|l|l|} \hline   1 &amp; \setBGGray 2 &amp; 3 \\\hline   4 &amp; 5 &amp; 6 \\\hline   7 &amp; \setBGHatched 8 &amp; 9 \\\hline \end{tabular} \end{document}   The output should look like this:    Can someone please help me achieving this using tabular (or tabularx) and TikZ? Deleting 'garbage' nodes after polygon dissolve I work with QGIS 2.10.1 on Windows 7 (x64). I have dissolved polygons from an attribute value and the polygons geometries being not perfectly joined together, I get some 'garbage' nodes I need to delete. I have tried to edit the layer and using nodes tool, selecting and deleting the nodes, but it seems impossible to do (nodes are not deleted at all!). Any idea on how to process this kind of clean-up?  EDIT : you can  for testing. Symbol for “such that” (not in set) Module 'pdftexcmds' not found after update Yesterday I updated my distribution (tlmgr update --all) and now I cannot use TikZ with lualatex anymore.  Minimal working example:  \documentclass{article} \usepackage{tikz} \begin{document} a \end{document}   Compilation output:  &gt; lualatex a This is LuaTeX, Version 1.10.0 (TeX Live 2019)                                                                                                                                                                         restricted system commands enabled.                                                                                                                                                                                  (./a.tex                                                                                                                                                                                                              LaTeX2e &lt;2019-10-01&gt; patch level 3                                                                                                                                                                                     luaotfload | main : initialization completed in 0.098 seconds                                                                                                                                                         (/opt/texlive/2019/texmf-dist/tex/latex/base/article.cls                                                                                                                                                              Document Class: article 2019/10/25 v1.4k Standard LaTeX document class                                                                                                                                                (/opt/texlive/2019/texmf-dist/tex/latex/base/size10.clo))                                                                                                                                                             (/opt/texlive/2019/texmf-dist/tex/latex/pgf/frontendlayer/tikz.sty                                                                                                                                                    (/opt/texlive/2019/texmf-dist/tex/latex/pgf/basiclayer/pgf.sty                                                                                                                                                        (/opt/texlive/2019/texmf-dist/tex/latex/pgf/utilities/pgfrcs.sty              ...  (/opt/texlive/2019/texmf-dist/tex/generic/pgf/frontendlayer/tikz/tikz.code.tex (/opt/texlive/2019/texmf-dist/tex/generic/pgf/libraries/pgflibraryplothandlers. code.tex) (/opt/texlive/2019/texmf-dist/tex/generic/pgf/modules/pgfmodulematrix.code.tex)  (/opt/texlive/2019/texmf-dist/tex/generic/pgf/frontendlayer/tikz/libraries/tikz librarytopaths.code.tex))) No file a.aux. ABD: EveryShipout initializing macros (/opt/texlive/2019/texmf-dist/tex/context/base/mkii/supp-pdf.mkii [Loading MPS to PDF converter (version 2006.09.02).] ) (/opt/texlive/2019/texmf-dist/tex/latex/epstopdf-pkg/epstopdf-base.sty[\direc tlua]:1: module 'pdftexcmds' not found:         no field package.preload['pdftexcmds']         [kpse lua searcher] file not found: 'pdftexcmds'         [kpse C searcher] file not found: 'pdftexcmds' stack traceback:         [C]: in function 'require'         [\directlua]:1: in main chunk. l.165       \directlua{require("pdftexcmds")}  ?    It seems that a Lua package is missing.  Is this a bug? Am I missing a package? If I have multiple objects selected can I use scaling to make the objects closer together (without rescaling the objects)? How do I perform an IF...THEN in an SQL SELECT? How do I perform an IF...THEN in an SQL SELECT statement?  For example:  SELECT IF(Obsolete = 'N' OR InStock = 'Y' ? 1 : 0) AS Saleable, * FROM Product Who are the Steam Mascots? So with the Steam Summer Sale in full swing, I've finally taken notice of the Steam Mascots.  Judging by the latest background, the black one, at least, has a name: Cyl.  Do the other two have names as well? Are there only these three?   What's their story? Render not showing UV texture I have added a texture to a cube in the UV editor and it shows up fine in textured view  But when I render it there is no texture  What have I done wrong? Category-theoretic limit related to topological limit? Is there any connection between category-theoretic term 'limit' (=universal cone) over diagram, and topological term 'limit point' of a sequence, function, net...?  To be more precise, is there a category-theoretic setting of some non-trivial topological space such that these different concepts of term 'limit' somehow relate?  This question came to me after I saw (  ) a surprising fact that generalised metric spaces can be seen as categories enriched over preorder $([0,\infty],\leq)$. When water climbs up a piece of paper, where is the energy coming from? Take a glass of water and piece of toilet paper. If you keep the paper vertical, and touch the surface of the water with the tip of the paper, you can see the water being absorbed and climbing up the paper. This climbing up is intriguing me. Where is the energy coming from?  Supposedly, a lot of water molecules are moving up and gaining potential energy. This has to be balanced by something. I can think of a few possibilities, but I can't tell which one it is.   When the water molecules dilute into the paper, they are at a state of lower potential binding energy. Some molecular interaction (van der Waals?) is at lower energy when you have a water+paper solution, compared to a water-only solution. This compensates the gain in gravitational energy. The surface between the paper and the water is at lower pressure than the atmosphere. This causes the water to be pushed into the paper by the atmospheric pressure, up until the point that the column of water above the surface is heavy enough to counterbalance. The potential energy would be a result of work done by the atmosphere. Some water molecules climb up randomly and loose kinetic energy going up, and somehow get "stuck" up there. Something else? I have a sheet in which I first apply a filter to a certain column to show "Unique records only". Now I have a column which contains, for e.g., values like:  Applepie Applesauce Crabapple Banana Mango   What I need is the count of all visible cells containing the word "Apple". Note that this should exclude the hidden (filtered out) cells. Now I have found out a formula:  `=SUMPRODUCT(SUBTOTAL(3,OFFSET(Sheet1!A:A,ROW(Sheet1!A:A)-MIN(ROW(Sheet1!A:A)),,1))*(Sheet1!A:A="&lt;Text to search&gt;"))`   However the problem with this one is this formula searches for the entire text. NOT just a part of it. How do I modify this formula to return count of cells containing "Apple" i.e. for this example it should return 3 as the result. Is it possible to install an app and exclude some of its requested permissions? Occasionally I want to install an application which requires certain permissions that I feel it really shouldn't need. Can I install the app without giving it these permissions? For example, GPS location, , internet connection, etc.  Is it possible to change the permissions of an application once it is installed? Making an elastic waistband on clothing? How to see the full date on macOS Big Sur? Formula for calculating $\sum_{n=0}^{m}nr^n$ I want to know the general formula for $\sum_{n=0}^{m}nr^n$ for some constant r and how it is derived.  For example, when r = 2, the formula is given by: $\sum_{n=0}^{m}n2^n = 2(m2^m - 2^m +1)$ according to   Thanks! Where is the itoa function in Linux?