How do I enforce set-like uniqueness between multiple columns?
sql unique constraint on a 2 columns combination
I wasn't aware of a difference, but a coworker says there is, although he can't back it up. What's the difference if any? Prove that $T$ has a cyclic vector iff its minimal and characteristic polynomials are the same Do opposite categories always exist? Use of "Or", inclusive or exclusive? My wife and I are playing a game where you roll dice and move so many spaces in a grid "vertically or horizontally".   In the use of English it is very common to say, this or the other when it comes to making a choice  (exclusive or). Now I know that "or" can also be inclusive, for example "she couldn't read or write", or can be clearly used as an xor "you either come or not" making the statement true for only one of the options but not both.   My issue is where it is not clear whether it is an inclusive/exclusive or, the best example being our game.   I argue that you can move in either direction (inclusive) and the normal use of this conjunction in English should be inclusive unless specified otherwise.   Is this right? How to cite sources written in a different language than English? Assume one wants to cite a paper written in a different language than the article citing said paper (e.g., ones own article is written in English, but the source is French).   How to properly handle citation in such a case?  Do I cite the original (French) title or a translated title? If I use a translated title, people might have a hard time to find the source; if the original (French) title is cited, people might have a hard time understanding it. Formula for determinant of block matrix with commuting blocks On , I saw the following formula  $$\det\begin{bmatrix}A &amp; B\\ C &amp; D\end{bmatrix} = \det(AD-BC)$$  if $C$ and $D$ commute. Is this always true?   Or is there a good counter example for each $2 \times 2$ block matrices? Asks a question; never responds to answers/comments What do we call someone who asks a question and never responds to answers/comments?    Think of it more as "a pattern of behavior" (somebody who has asked many questions and never responded). I had unresponsive in mind, but that doesn't say that they asked in the first place. Delete all data for a kind in Google App Engine I would like to wipe out all data for a specific kind in Google App Engine. What is the best way to do this? I wrote a delete script (hack), but since there is so much data is timeout's out after a few hundred records. Cleft sentences Let's assume that John gave me a cat. I can rephrase the fact with:     What John did was to give me a cat   What John did was give me a cat   What John did was, he gave me a cat   But can I say the following phrase?  What John did was gave me a cat How to convert image file data in a byte array to a Bitmap? What happens to matter in a standard model with zero Higgs VEV? Suppose you reset the parameters of the standard model so that the Higgs field average value is zero in the vacuum, what would happen to standard matter?  If the fundamental fermions go from a finite to a zero rest mass, I'm pretty sure that the electrons would fly away from nuclei at the speed of light, leaving positively charged nuclei trying to get away from each other.  Looking at the solution for the Hydrogen atom, I don't see how it would be possible to have atoms with zero rest mass electrons.  What happens to protons and neutrons?  Since only a very small part of the mass of protons and neutrons is the rest mass of the quarks, and since they're flying around in there at relativistic speeds already, and since the nuclear force is so much stronger than the electrical force with an incredible aversion to naked color, would protons and neutrons remain bound assemblages of quarks and virtual gluons?  Would they get a little larger?  A little less massive?  What would happen to nuclei?  Would they stay together?  If the protons and neutrons hold together and their properties change only some, then I might expect the same of nuclei.  Different stable isotopes, different sizes, and different masses, but I would expect there would still be nuclei.  Also the W and Z particles go to zero rest mass.  What does that do to the electroweak interactions?  Does that affect normal stable matter (outside of nuclear decay modes)?  Is the weak force no longer weak?  What happens to the forces overall? Compiling PHP 5.1.6 with PDO MySQL Cu has an unpaired electron in 4s, but it is diamagnetic. I thought that it has to be paramagnetic. What am I missing? How to avoid pagenumering with text in scrlttr2 Have a Letter in scrlttr2. I cannot avoid/exclude the text before the page number 'Seite' (see print-screen). The  recommends to add \pagenumbering{arabic}. But for my document, it has no effect.    %--------------------------------------------------------------------------- \documentclass%% %---------------------------------------------------------------------------   [fontsize=12pt,%%          Schriftgroesse %--------------------------------------------------------------------------- % Satzspiegel    paper=a4,%%               Papierformat    enlargefirstpage=on,%%    Erste Seite anders    pagenumber=footcenter,%%   Seitenzahl oben mittig %--------------------------------------------------------------------------- % Layout    headsepline=on,%%         Linie unter der Seitenzahl    parskip=half,%%           Abstand zwischen Absaetzen %--------------------------------------------------------------------------- % Formatierung    draft=on%%                Entwurfsmodus ]{scrlttr2} %--------------------------------------------------------------------------- \usepackage{german} \usepackage[T1]{fontenc} \usepackage[utf8]{inputenc}  %--------------------------------------------------------------------------- \begin{document} %--------------------------------------------------------------------------- % Briefstil und Position des Briefkopfs \LoadLetterOption{DIN} %% oder: DINmtext, SN, SNleft, KOMAold. \makeatletter \pagenumbering{arabic}  %--------------------------------------------------------------------------- % Seitenstil \pagestyle{plain}%% keine Header in der Kopfzeile %--------------------------------------------------------------------------- \begin{letter}{Herr\\                 Mustermann\\                Straße 1\\                12345 Stadt} %--------------------------------------------------------------------------- \setkomavar{subject}{Beispielschreiben} %--------------------------------------------------------------------------- \opening{Liebe Herr Mustermann,}  here is some Text.  \pagebreak  here is some Text. %--------------------------------------------------------------------------- \end{letter} %--------------------------------------------------------------------------- \end{document} %--------------------------------------------------------------------------- Variance of Wilcoxon Rank-Sum Test (no ties) $\newcommand{\E}[1]{\mathbb{E}\left[#1\right]} \newcommand{\r}[1]{r\left(#1\right)} \newcommand{\P}[1]{\mathbb{P}\left(#1\right)} \newcommand{\Var}[1]{\text{Var}\left[#1\right]}$  Given two sets of data $X$ with $m$ points and $Y$ with $n$ points, unioned (keeping duplicates) to create a data set $Z = \{Z_i\}$ with $m + n = N$ data points, the Wilcoxon Rank-Sum Test Statistic is given by \begin{equation*} T = \sum\limits_{i=1}^{N}r(Z_i)\cdot \mathbb{I}(Z_i \in X)\text{,} \end{equation*} where $\mathbb{I}(Z_i \in X)$ is $1$ if $Z_i \in X$, $0$ otherwise. ($r(\cdot)$ denotes the rank of the data point.)  Suppose there are no ties. Then  \begin{align*} \E{T} = \sum\limits_{i=1}^{N}\r{Z_i}\cdot \E{\mathbb{I}(Z_i \in X)} &amp;= \sum\limits_{i=1}^{N}\r{Z_i}\cdot\P{Z_i \in X} \\ &amp;= \dfrac{m}{N}\sum\limits_{i=1}^{N}\r{Z_i} \\ &amp;= \dfrac{mN(N+1)}{2N} \\ &amp;= \dfrac{m(N+1)}{2}\text{.} \end{align*} This comes out to what it says in the book Nonparametric Statistical Inference, 5th ed., by Gibbons and Chakraborti.  Now for $\Var{T}$: \begin{align*} \Var{T} &amp;= \Var{\sum\limits_{i=1}^{N}\r{Z_i}\mathbb{I}(Z_i \in X)}\\ &amp;= \sum\limits_{i=1}^{N}\left[\r{Z_i}\right]^2\Var{\mathbb{I}(Z_i \in X)} \\ &amp;= \sum\limits_{i=1}^{N}\left[\r{Z_i}\right]^2\P{Z_i \in X}\left[1-\P{Z_i \in X}\right]\\ &amp;= \left(\dfrac{m}{N}\right)\left(1-\dfrac{m}{N}\right)\sum\limits_{i=1}^{N}\left[\r{Z_i}\right]^2 \\ &amp;= \left(\dfrac{m}{N}\right)\left(1-\dfrac{m}{N}\right)\left[\dfrac{N(N+1)(2N+1)}{6}\right] \\ &amp;= \left(\dfrac{m}{N}\right)\left(\dfrac{N-m}{N}\right)\left[\dfrac{N(N+1)(2N+1)}{6}\right] \\ &amp;= \left(\dfrac{m}{N}\right)\left(\dfrac{n}{N}\right)\left[\dfrac{N(N+1)(2N+1)}{6}\right] \\ &amp;= \dfrac{2N+1}{N}\left[\dfrac{mn(N+1)}{6}\right] \end{align*} The answer should be $\dfrac{mn(N+1)}{12}$. What did I do wrong? Dropdownlist control with s for asp.net (webforms)? Can anyone recommend a dropdownlist control for asp.net (3.5) that can render option groups? Thanks Why is usable RAM less than total RAM? My girlfriend bought a laptop last week. It's a core 2 duo with 4 GB  We installed vista 64bit, and one of the first things we did was right click on "My computer" to see gthe properties. Immediately we noticed something strange about her RAM, the line said: Installed memory (RAM): 4,00 GB (3,68 GB usable)  I told her not to worry, thinking it must be something about the laptop hardware (considering her vista installation came from the same DVD as mine, and I never noticed anything like that on my 4 GB desktop). One hour ago, it got worse. We looked at Properties again, and it now says: Installed memory (RAM): 4,00 GB (2,98 GB usable)  What does that mean? Are those 1,02 GB missing or being used by the system?  EDIT: There is a possibility that the sytem information is wrong. I just noticed that it reports an intel T6500 processor, when it's actually a T6400.  How can I find out how much RAM is really available to the system?  EDIT2: Checking the resource monitors, it says 1003 MB are reserved for the hardware. Is that good or bad? Thanks What is the physical significance of the imaginary part when plane waves are represented as $e^{i(kx-\omega t)}$? I've read that plane wave equations can be represented in various forms, like sine or cosine curves, etc. What is the part of the imaginary unit $i$ when plane waves are represented in the form $$f(x) = Ae^{i (kx - \omega t)},$$ using complex exponentials? Is it true that for each set $M$ a given injective function $f: M \rightarrow M$ is surjective, too?  Can someone explain why it is true or not and give an example? What is wrong with my mob spawner?