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Error "Settings to access printer 'printername' are not valid" when printing from Windows service How many inventions did Fred and George have? Fred and George Weasley are known for their trouble-making and general &quot;solemnly swearing they are up to no good&quot;. Their antics/adventures give something to smile about and show us not all wizards are as serious as Professor McGonagall and Hermione. This gives them a reputation of being less intelligent and indeed they only achieved three OWLs. However, we also see the twins have quite a brilliant side! Being able to open and successfully run a shop in Diagon Alley without having completed their Hogwarts education is no easy take (IMO, anyway). Their creations helped students get out of class, our heroes out of tight spot, and even stop our enemies execute an evil plot. Ginny may have said it best:  &quot;We’ve been hearing explosions out of their room for ages, but we never thought they were actually making things,&quot; said Ginny. &quot;We thought they just liked the noise.&quot; Harry Potter and the Goblet of Fire  Do we know how many things Fred and George invented? $|G|>2$ implies $G$ has non trivial automorphism Well, this is an exercise problem from Herstein which sounds difficult:   How does one prove that if $|G|&gt;2$, then $G$ has non-trivial automorphism?   The only thing I know which connects a group with its automorphism is the theorem, $$G/Z(G) \cong \mathcal{I}(G)$$ where $\mathcal{I}(G)$ denotes the Inner- Automorphism group of $G$. So for a group with $Z(G)=(e)$, we can conclude that it has a non-trivial automorphism, but what about groups with center? Defining scalable "white curly brackets" {| and |} (⦃ and ⦄) I would like to construct what Unicode calls "white curly brackets" that are in addition scalable. They look like ⦃ (≈{|) and ⦄ (≈|}) and have Unicode codepoints U+2983 and U+2984.  unicode-math has them as \lBrace and \rBrace, but (1) I don't presently use XeTeX or LuaTeX and (2) their design (shown in  on pages 3-4) is not to my liking: the brace part is too fat for my taste, and I would like the vertical bar to not leave any protrusions. I am trying to have them visually match the parentheses \llparenthesis, \rrparenthesis, \llbracket, and \rrbracket from stmaryrd.  Right now I am using a makeshift definition, which is sufficient for now, but the symbols don't scale (in general or with \left/\right). Here is sample code:  \documentclass{article} \usepackage{amsmath} \usepackage[only,llbracket,rrbracket,llparenthesis,rrparenthesis]{stmaryrd} % for comparison with 4 similar parenthesis symbols \usepackage{accsupp} % for ensuring the right Unicode codepoint upon pasting  \newcommand*{\llbrace}{%   \BeginAccSupp{method=hex,unicode,ActualText=2983}%     \textnormal{\usefont{OMS}{lmr}{m}{n}\char102}%     \mathchoice{\mkern-4.05mu}{\mkern-4.05mu}{\mkern-4.3mu}{\mkern-4.8mu}%     \textnormal{\usefont{OMS}{lmr}{m}{n}\char106}%   \EndAccSupp{}% } \newcommand*{\rrbrace}{%   \BeginAccSupp{method=hex,unicode,ActualText=2984}%     \textnormal{\usefont{OMS}{lmr}{m}{n}\char106}%     \mathchoice{\mkern-4.05mu}{\mkern-4.05mu}{\mkern-4.3mu}{\mkern-4.8mu}%     \textnormal{\usefont{OMS}{lmr}{m}{n}\char103}%   \EndAccSupp{}% }   \begin{document}  \noindent ok: \(\displaystyle\llbrace abc \rrbrace\) \(\textstyle\llbrace abc \rrbrace\) \(\scriptstyle\llbrace abc \rrbrace\) \(\scriptscriptstyle\llbrace abc \rrbrace\)  \noindent ok: \(\displaystyle \llbrace \frac{a}{b} \rrbrace\) \(\textstyle\llbrace \frac{a}{b} \rrbrace\) \(\scriptstyle\llbrace \frac{a}{b} \rrbrace\) \(\scriptscriptstyle\llbrace \frac{a}{b} \rrbrace\)  \noindent incorrectly scaled (\verb|\scriptsize|): {\scriptsize\(\llbrace abc \rrbrace\)} (large magnification required)  \noindent incorrectly scaled (\verb|\tiny|): {\tiny\(\llbrace abc \rrbrace\)}  \noindent \verb|\left| and \verb|\right| not possible before \verb|\llbrace| and \verb|\rrbrace|: \\ \indent \(\llbrace \left\llbracket\left\{\left[(a) \cdot bc^{2^3}\right]^4\right\}^5\right\rrbracket \rrbrace\) % Note: This is also not possible with \llparenthesis and \rrparenthesis from stmaryrd.  \noindent for comparison: \(\llparenthesis x \rrparenthesis, \llbracket x \rrbracket, \llbrace x \rrbrace; (x), [x], \{x\}\)  \end{document}   Lines 1 and 2 look just right with the present setup. Lines 3 and 4 demonstrate that my definitions don't scale. Lines 5a/b gives an example of where I would like to be able to use \left and \right. Line 6 juxtaposes different types of parentheses for visual comparison.  Is there an easy way to scale the glyphs I have constructed myself? Or is designing new glyphs the only way? While the vertical part of my glyphs doesn't leave any protrusions, the "brace part being too fat" part of my problem isn't being addressed by my code. With this in mind: I recognize that it might not be that easy to make the brace part of the glyph thinner (though if you can, more power to you), but I think that any solution that addresses the scaling problem for any manually constructed glyph cluster will be a valuable contribution to the community.    For a slightly different setup (original example code) with  \RequirePackage{fix-cm} \documentclass[12pt]{memoir} \usepackage{fixltx2e}[2006/09/13] \usepackage{amsmath} \usepackage{txfonts} \usepackage[only,llbracket,rrbracket,llparenthesis,rrparenthesis]{stmaryrd} \usepackage{accsupp}   in the preamble, one needs \mkern-5.7mu in the fourth argument to \mathchoice for "correct" scaling. To see what goes wrong in that case, it's best to include a line such as discontinuous small symbols in a footnote\footnote{\(\scriptscriptstyle\llbrace \frac{a}{b} \rrbrace\)}. This might help a potential answerer test things out. Metric is continuous function Let $X$ be a metric space , $d$ is the metric , show that $d$ is a continuous function from $X\times X$ to $R$.  I think the definition is all we need , but I just don't know where to start , can anyone help me. How to interpret the output of XGBoost importance? I ran a xgboost model. I don't exactly know how to interpret the output of xgb.importance.  What is the meaning of Gain, Cover, and Frequency and how do we interpret them?  Also, what does Split, RealCover, and RealCover% mean? I have some extra parameters   Are there any other parameters that can tell me more about feature importances?  From the R documentation, I have some understanding that Gain is something similar to Information gain and Frequency is number of times a feature is used across all the trees. I have no idea what Cover is.  I ran the example code given in the link (and also tried doing the same on the problem that I am working on), but the split definition given there did not match with the numbers that I calculated.  importance_matrix   Output:             Feature         Gain        Cover    Frequence   1:            xxx 2.276101e-01 0.0618490331 1.913283e-02   2:           xxxx 2.047495e-01 0.1337406946 1.373710e-01   3:           xxxx 1.239551e-01 0.1032614896 1.319798e-01   4:           xxxx 6.269780e-02 0.0431682707 1.098646e-01   5:          xxxxx 6.004842e-02 0.0305611830 1.709108e-02  214:     xxxxxxxxxx 4.599139e-06 0.0001551098 1.147052e-05 215:     xxxxxxxxxx 4.500927e-06 0.0001665320 1.147052e-05 216:   xxxxxxxxxxxx 3.899363e-06 0.0001536857 1.147052e-05 217: xxxxxxxxxxxxxx 3.619348e-06 0.0001808504 1.147052e-05 218:  xxxxxxxxxxxxx 3.429679e-06 0.0001792233 1.147052e-05 Read Value from URL in PHP Detect edits to add [SOLVED] or [RESOLVED] to the title and direct the user to add an answer Users often ask questions that they answer for themselves. Good for them. And good for us.  Symptom  The correct procedure seems to be:   Write new answer to own question  Wait two days Accept own answer   The incorrect, but fairly popular, procedure seems to be:   Edit the question to include the solution Put "[SOLVED] or [RESOLVED]" in the title   Proposed solution  Users should be warned when using the word "solved", delimited in any way, in a question title. This could be "[SOLVED]", "(solved)", or even "Solved - ". I imagine this:   The user tries to submit an edit that adds "solved" such that the word "solved is delimited. The user is brought to a warning page. If the only edit to the question was appending new lines (such as adding an "edit:" paragraph), that edit is copied into a text box The page mentioned in 1 is shown as follows:     $StackSite marks questions as answered when you accept an answer. You can accept an answer by clicking the green check mark next to that answer. There's no need to put "SOLVED" or "RESOLVED" in the title!      Are you answering your own question?      Create a proper answer to your question:         Move your edit to a new answer.   Write your answer.   If nobody writes a more correct or thorough answer after two days, come back and accept your answer.         By doing this, you remove your question from the Unanswered Questions list. You also allow other $StackSite users to vote your answer up. Thanks for helping out!      TEXT BOX WITH EDITS GOES HERE, FOLLOWED BY "POST YOUR ANSWER" BUTTON      Not answering your own question?      Sorry for slowing you down.      OVERVIEW OF EDIT, FOLLOWED BY "SAVE EDITS" BUTTON    Discussion  This would likely reduce the number of [RE]SOLVED questions that appear. However, it's unclear whether this should be a community moderation issue or a feature request issue. The increased engineering work required in building in the interstitial page is probably quite nontrivial, whereas this type of question makes up well under .  Note: Google also provides a . How can I add a "C" wire to my thermostat? So, the spiffy new wi-fi thermostats want power on the C wire from thermostat, but the old thermostat doesn't have a C wire at it.  What's the easiest way to add the C wire/24 volt to the thermostat location? Show that $E(X)=\int_{0}^{\infty}P(X\ge x)\,dx$ for non-negative random variable $X$ How to install Windows 10 Home 19018 update? I'm using windows home edition, I have the latest update installed 1909.  I want to install docker for windows 10 home edition. It keeps saying  Docker Desktop requires Windows 10 Pro/Enterprise (15063+) or Windows 10 Home (19018+).  Should I join Windows insider? How long should I wait for that update to be released if I don't want to join windows insider? How does Linux handle multiple consecutive path separators (/home////username///file)? How to compare a program's version in a shell script? Suppose I want to compare gcc version to see whether the system has the minimum version installed or not.  To check the gcc version, I executed the following  gcc --version | head -n1 | cut -d" " -f4   The output was  4.8.5   So, I wrote a simple if statement to check this version against some other value  if [ "$(gcc --version | head -n1 | cut -d" " -f4)" -lt 5.0.0 ]; then     echo "Less than 5.0.0" else     echo "Greater than 5.0.0" fi   But it throws an error:  [: integer expression expected: 4.8.5   I understood my mistake that I was using strings to compare and the -lt requires integer. So, is there any other way to compare the versions? Apple Macbook Dual Monitor MST Find all possible solutions of $$2^x + 3^y = z^2.$$    My approach.   First I substituted $x = 0$, and got the solution, then for $y = 0$. And for $x &gt;  0$ and $y &gt; 0$ , I just know the Pythagorean triple and got the solution as $(4,2,5)$ and $(4,2,-5)$. Please help me to solve it properly. Let $V$ be a representation with character $\chi$.  I would like to have a formula for the characters of the representations $\mathrm{Sym}^m[V]$ and $\wedge ^m[V]$ in terms of $\chi$.  Fulton and Harris presents such a formula for $m=2$, but not for general $m$.  Is there a "nice" such expression?  I found a paper by , but this doesn't seem to be what I'm looking for (it doesn't seem to give a general formula in terms of $\chi$).  In case the link does not work, here is the reference:  X. Zhou, P. Pulay. Characters for Symmetric and Antisymmetric Higher Powers of Representations: Application to  the  Number of Anharmonic Force Constants in Symmetrical Molecules. Journal of Computational Chemistry, Vol 10, Issue 7, (1989). I am new to TeX/LaTeX. How do I install TeX on Windows (7)? It seems that there are many different implementations, so which one is best for my OS? Maximum and minimum distance of two points Consider six distinct points in a plane. Let $m$ and $M$ denote respectively the minimum and the maximum distance between any pair of points.  Show that $M/m \geqslant \sqrt{3}$. I want to see you.   I look forward to seeing you.      How can one say "to" in the first sentence is an infinitive marker and in the second sentence a preposition when we are given just the following two sentences and are asked to fill in the blanks?        I want to ____(see/seeing) you.   I look forward to __(see/seeing) you. Use of Named Credentials seem to be tied to External Data Source