How to flip columns into rows in MySQL
transpose columns to rows
How do I set a default host for nginx? Let $A$ be a ring that is not a field and $M$, $N$ modules over $A$. What conditions on $M,N$ (and maybe also on $A$) guarantee that $\operatorname{Hom}_A(M,N)$ is finitely generated? Is it enough to assume $M,N$ finitely generated? Is "tri-quarterly" a real English word meaning 3 times a year? Is "tri-quarterly" a real English word meaning 3 times a year? Are there any other words that mean 3 times a year? I am trying to mimic our institute's PPt-template for presentation foils using the beamer-class. The corporate quidelines prescribe the use of Helvetica as the main font. However, package helvet does not provide a good mathematical font. Therefore I want to replace it with the math font from the cmbright package:  \documentclass{beamer}  \usepackage{lmodern} \usepackage[T1]{fontenc}  %main font Helevtica \renewcommand{\familydefault}{\sfdefault} \usepackage{helvet}  %prevent beamer from meddling with math fonts \usefonttheme{professionalfonts}  %following lines borrowed from cmbright.sty \DeclareSymbolFont      {operators} {OT1}{cmbr}{m}{n} \DeclareSymbolFont        {letters} {OML}{cmbrm}{m}{it} \SetSymbolFont      {letters}{bold} {OML}{cmbrm}{b}{it} \DeclareSymbolFont        {symbols} {OMS}{cmbrs}{m}{n} \DeclareMathAlphabet{\mathit} {OT1}{cmbr}{m}{sl} \DeclareMathAlphabet{\mathbf} {OT1}{cmbr}{bx}{n} \DeclareMathAlphabet{\mathtt} {OT1}{cmtl}{m}{n} \DeclareMathAlphabet{\mathbold}{OML}{cmbrm}{b}{it} \DeclareMathSymbol{\alpha}{\mathalpha}{letters}{11} \DeclareMathSymbol{\beta}{\mathalpha}{letters}{12} \DeclareMathSymbol{\gamma}{\mathalpha}{letters}{13} \DeclareMathSymbol{\delta}{\mathalpha}{letters}{14} \DeclareMathSymbol{\epsilon}{\mathalpha}{letters}{15} \DeclareMathSymbol{\zeta}{\mathalpha}{letters}{16} \DeclareMathSymbol{\eta}{\mathalpha}{letters}{17} \DeclareMathSymbol{\theta}{\mathalpha}{letters}{18} \DeclareMathSymbol{\iota}{\mathalpha}{letters}{19} \DeclareMathSymbol{\kappa}{\mathalpha}{letters}{20} \DeclareMathSymbol{\lambda}{\mathalpha}{letters}{21} \DeclareMathSymbol{\mu}{\mathalpha}{letters}{22} \DeclareMathSymbol{\nu}{\mathalpha}{letters}{23} \DeclareMathSymbol{\xi}{\mathalpha}{letters}{24} \DeclareMathSymbol{\pi}{\mathalpha}{letters}{25} \DeclareMathSymbol{\rho}{\mathalpha}{letters}{26} \DeclareMathSymbol{\sigma}{\mathalpha}{letters}{27} \DeclareMathSymbol{\tau}{\mathalpha}{letters}{28} \DeclareMathSymbol{\upsilon}{\mathalpha}{letters}{29} \DeclareMathSymbol{\phi}{\mathalpha}{letters}{30} \DeclareMathSymbol{\chi}{\mathalpha}{letters}{31} \DeclareMathSymbol{\psi}{\mathalpha}{letters}{32} \DeclareMathSymbol{\omega}{\mathalpha}{letters}{33} \DeclareMathSymbol{\varepsilon}{\mathalpha}{letters}{34} \DeclareMathSymbol{\vartheta}{\mathalpha}{letters}{35} \DeclareMathSymbol{\varpi}{\mathalpha}{letters}{36} \DeclareMathSymbol{\varrho}{\mathalpha}{letters}{37} \DeclareMathSymbol{\varsigma}{\mathalpha}{letters}{38} \DeclareMathSymbol{\varphi}{\mathalpha}{letters}{39} \let\upDelta\Delta \let\upOmega\Omega \let\upGamma\Gamma \let\upTheta\Theta \let\upLambda\Lambda \let\upXi\Xi \let\upPi\Pi \let\upSigma\Sigma \let\upUpsilon\Upsilon \let\upPhi\Phi \let\upPsi\Psi  %doesn't seem to have an effect %\DeclareMathSizes{12}{12.5}{10}{10}  \begin{document} \begin{frame}  Some Math E$E$ \end{frame} \end{document}   This works quite well, except that the math letters are somewhat smaller than the normal Helvetica text. Is there a way to scale the fontsize, say by 1.1, if the typesetter is in math mode? Fixing scrolling in nano running in tmux in mate-terminal The problem:   I open a terminal (in Linux Mint, so mate-terminal) zsh is the shell Then I run tmux Edit a file with nano Scroll up and down that file with the cursor Issue: When scrolling down in nano, only the bottom half of the terminal window gets refreshed Issue: When scrolling up in nano, only the top half of the terminal windo gets refreshed   The complete nano view of file does not get refreshed in my terminal window when scrolling. Any tips?  Edit: my .tmux.conf  It seems that this line specifically is the culprit (as commenting it out fixes the problem):  set -g default-terminal "xterm-256color"   I'm pretty sure I added that line because I have issues even running nano during an SSH session.  Here is the full file:  set-option -g default-shell /bin/zsh  # Make sure tmux knows we're using 256 colours, for # correct colourised output set -g default-terminal "xterm-256color"  # The following were marked as "unknown", so # I do know what I'm doing wrong. #set -g mode-mouse on #setw -g mouse-select-window on #setw -g mouse-select-pane on  # Attempting to stop "alert" sound upon startup # but none of these are working... set-option bell-on-alert off set-option bell-action none set-option visual-bell off Print floating point values without leading zero So I have a mac computer but i plugged in a windows keyboard in my mac. I am still trying to figure out how to paste commands into a command block. So how can I paste a command? Is my ESTA valid for a second trip? Short story with competitors complaining to government about a new very popular synthetic food Synthetic foods are all the rage, and while some are new and novel, many are attempts to recreate the taste and texture of a natural foods, with varying degrees of success. One company introduces a new synthetic food that becomes wildly popular. The competition analyzes it, and based on discovering what natural creature it is based on, they petition the government to ban it.      They discover that the product is synthetic human flesh, so consuming it is not technically cannibalism, but it is similar, as they explain to the panel of government officials. Use "does" in front of another verb in a question? What time does sound good to you?     What time sounds good to you?    Is there a difference? Compactness of  Multiplication Operator on $L^2$ Suppose we have an bounded linear operator A that operates from $L^2([a,b]) \mapsto L^2([a,b])$.  Now suppose that $A(f)(t) = tf(t)$.    Is A compact?  Edit: I know $A = A^*$ but I'm not really sure how to start on this.  It's not homework, just summer fun :D Prove that $\int f\ d\lambda = \int_{a}^{b} f(x)\ dx,$ for any $f \in \mathcal R[a,b].$ Theorem $:$ Let $f : [a,b] \longrightarrow \Bbb R$ be a Riemann integrable function. Then $f \in L_1[a,b]$ and $$\int f\ d\lambda = \int_{a}^{b} f(x)\ dx.$$  The proof given in my book is as follows $:$     At the fag end of the proof $f$ has been proved to be measurable which uses the completeness of the measure space $\left ([a,b], \mathcal L \cap [a,b], \lambda |_{[a,b]} \right ).$ Then it has been stated that $f \leq \Phi_n,$ $\forall$ $n$ and hence $f \in L_1[a,b]$ since $\Phi_n \in L_1[a,b]$ by the proposition $5.4.3 \ $(i) which states the following $:$  Let $f \in \Bbb L$ and $g \in L_1[a,b].$ If $|f(x)| \leq g(x)$ for a.e. $x(\mu).$ Then $f \in L_1[a,b].$  I don't know how to use this proposition to claim that $f \in L_1[a,b].$ Also I don't understand the way dominated convergence theorem used here. What I know about dominated convergence theorem is as follows $:$  Let $(X, \mathcal S, \mu)$ be a complete measure space. Let $g \in L_1(X)$ and $\{f_n \}_{n \geq 1}$ be a sequence in $\Bbb L$ such that $|f_n(x)| \leq g(x)$ a.e. $x(\mu).$ Let $f_n(x) \to f(x)$ as $n \to \infty$ a.e. $x (\mu).$ Then $f \in L_1(X)$ and $$\int f\ d\mu = \lim\limits_{n \to \infty} \int f_n\ d\mu.$$  From here how to conclude that $$\Psi_n\ \bigg\uparrow\ f \implies \int f\ d\lambda = \lim\limits_{n \to \infty} \int \Psi_n\ d\lambda.$$ Please help me in this regard. Thanks in advance. Number of ways to pair off $2n$ points such that no chords intersect For $n \geq 0$ evenly distribute $2n$ points on the circumference of a circle, and label these point cyclically with the numbers $1, 2 . . . , 2n$ Let $h_n$ be the number of ways in which these $2n$ points can be paired off as $n$ chords where no two chords intersect  I want to find a recursive formula for $h_n$.  First I find $h_1,h_2,h_3$ to see the recursive nature.    $h_1 = 1$ as their only one way to make one chord  $h_2 = 2$   Now $\require{enclose}      \enclose{horizontalstrike}{h_3=4}h_3=5$ ((1,4), (2,3), (5,6) case is missed in image)  I found a wikipedia link    and it is very close to my problem, But in this link you don't need to pair off $n$ chords.  But I can't get to come up with a recursive formula for my question.  If I would to guess I would say $h_n = 2 \times h_{n-1}$, And would this means that $h_4 = 8$ ?? How can I implement "cut outs" for lighting in OpenGL? So, I'm working with OpenGL (I'm not exactly sure of the version), and I want to do an old-style lighting setup by essentially drawing a black rectangle over the screen, and drawing white circles over the areas that should be lit. I already have the rectangle and the circles, but I can't figure out how to make it so that the white circles are transparent when applied to the black areas. Any ideas? I tried to use blending modes, but it still evades me...  EDIT: Here's the code that I'm using (Python).  view_buf = Buffer(GL_INT, 4) glGetIntegerv(GL_VIEWPORT, view_buf) view = view_buf.to_list() if hasattr(view_buf, "to_list") else view_buf.list  glDisable(GL_DEPTH_TEST)  glDisable(GL_LIGHTING)  glEnable(GL_BLEND)  if logic.lights['smooth']:     glEnable(GL_LINE_SMOOTH)  # # Make sure we're using smooth shading instead of flat # glShadeModel(GL_SMOOTH)  # Setup the matrices  glMatrixMode(GL_PROJECTION) glPushMatrix() glLoadIdentity() gluOrtho2D(0, view[2], 0, view[3]) glMatrixMode(GL_MODELVIEW) glPushMatrix() glLoadIdentity()  #glAlphaFunc(GL_GREATER, 0.5)  glColor4f(0.0, 0, 0, 0.75)  glBegin(GL_QUADS);                              # Draw Black screen glVertex2d(0.0, 0.0); glVertex2d(view[2], 0.0); glVertex2d(view[2], view[3]); glVertex2d(0.0, view[3]); glEnd()  glColor4f(1, 1, 1, 1)  degtorad = 3.14159/180.0   glBlendFunc(GL_ZERO, GL_SRC_ALPHA)  def DrawCircle(x, y, radius, fill = 1, step = 11):      glVertex2f(x, y)      if fill:         glBegin(GL_TRIANGLE_FAN)     else:         glBegin(GL_LINE_LOOP)      for a in range(0, 360, step):         angle = degtorad * a         glVertex2f(x + (sin(angle) * radius), y + (cos(angle) * radius))      glEnd()   #for layer in range(len(logic.lights['layers'])): #   size =  for light in logic.lights['points']:     DrawCircle(light[0][0] * view[2], (1 - light[0][1]) * view[3], light[1], step = light[2])     if logic.lights['smooth']:         DrawCircle(light[0][0] * view[2], (1 - light[0][1]) * view[3], light[1], 0, light[2])  # Reset the state glPopMatrix() glMatrixMode(GL_PROJECTION) glPopMatrix() Can command substitution be nested in variable substitution? Answers to a  mention that it is illegal for a US citizen to enter/leave their home country on a foreign passport. However this raises the following questions:   What is the maximum prescribed penalty for violating these rules? Are US immigration officials known for actually applying the penalty? E.g. the Cuba embargo banning visits to Cuba was almost never enforced, so it's possible this law is ignored as well. I recently read that:     What our current level of thermodynamics does tell us though is that if there is such a thing as a Big Crunch, the universe will look a lot different as it heads towards collapse than it did when expanding – the universe started in a state of low entropy and high order and will end in a state of high entropy and   low order.   But shouldn't the order be in a high state and hence entropy becomes a low state in the Big Crunch (assuming a closed universe)?  The reason I write this is because the gravitational forces in a closed universe are so strong they will cause gravitational collapse so the universe will shrink and go backwards, eventually through all the stages of the big bang and become a singularity once more.   It was my understanding that a singularity has a state of high order and low entropy. Have I got this the wrong way round?   If so; Can someone please explain why? How to create a graph with two Y axis with different values in Excel How do you make a scatter graph with 2 Y axis (one on the left and one on the right)? I have 2 scatter graphs that I want to combine. I need to have 2 lines, both lines have the same dependent variable but have their own independent variable. Click the link "graph" below to get an idea of what I'm looking for.  (I'm using google sheets but I can also find a computer with Excel if needed) Is it possible to overload the null-coalescing operator for a class in C#?    Say for example I want to return a default value if an instance is null and return the instance if it's not. The code would look like something like this:     return instance ?? new MyClass("Default");     But what if I would like to use the null-coalescing operator to also check if the MyClass.MyValue is set? I would really love to play wizard/warlock multiclass with low charisma (just 13 for mutliclass). The handbook says that I can use Pact Magic slots to cast wizard spells, but doesn't specify which ability I use for spellcasting.     Pact Magic.   If you have both the Spellcasting class feature and the Pact Magic class feature from the warlock class, you can use the spell slots you gain from the Pact Magic feature to cast spells you know or have prepared from classes with the Spellcasting class feature, and [vice versa].   When I cast wizard spells using Pact Magic slots (or warlock spells using wizard's "Spellcasting" slots) do I use spellcasting ability of the slot, or do I get to choose?