We have in and out degree of a directed graph G. if G does not includes loop (edge from one vertex to itself) and does not include multiple edge (from each vertex to another vertex at most one directed edge), we want to check for how many of the following we have a corresponding graph. the vertex number start from 1 to n and the degree sequence are sort by vertex numbers.  a) $d_{in}=(0,1,2,3), d_{out}=(2,2,1,1)$  b) $d_{in}=(2,2,1), d_{out}=(2,2,1)$  c) $d_{in}=(1,1,2,3,3), d_{out}=(2,2,3, 1,2)$  I want to find a nice way instead of drawing graph.  for (C):
We have in and out degree of a directed graph G. if G does not includes loop (edge from one vertex to itself) and does not include multiple edge (from each vertex to another vertex at most one directed edge), we want to check for how many of the following we have a corresponding graph. the vertex number start from 1 to n and the degree sequence are sort by vertex numbers.  a) $d_{in}=(0,1,2,3), d_{out}=(2,2,1,1)$  b) $d_{in}=(2,2,1), d_{out}=(2,2,1)$  c) $d_{in}=(1,1,2,3,3), d_{out}=(2,2,3, 1,2)$  I want to find a nice way instead of drawing graph.  for (C):
How do you return 1 value per row of the max of several columns:  TableName  [Number, Date1, Date2, Date3, Cost]   I need to return something like this:  [Number, Most_Recent_Date, Cost]   Query? OpenGL Texture Coordinates in Pixel Space Manipulating Partial Derivatives of Inverse Function In lectures we're told:  $$\dfrac {\partial y} {\partial x} = \dfrac 1 {\dfrac {\partial x} {\partial y}}$$  as long as the same variables are being held constant in each partial derivative.  The course is 'applied maths', i.e non-rigorous, so don't confuse me.  But anyway, if we have:  $$\xi = x - y \qquad \eta = x$$  Then $\dfrac {\partial x} {\partial \xi} = 0$ and $\dfrac {\partial \xi} {\partial x} = 1$.  The rule presumably fails because one of the partial derivatives is $0$.  But then isn't this rule useless? Since I cannot use it without checking that the partial derivative isn't in fact $0$, but then I've worked out the partial derivative manually anyway. Is a URI (specifically an HTTP URL) allowed to contain one or more space characters? If a URL must be encoded, is + just a commonly followed convention, or a legitimate alternative?    In particular, can someone point to an RFC that indicates that a URL with a space must be encoded?  Motivation for question: While beta-testing a web site, I noted that some URLs were constructed with spaces in them. Firefox seemed to do the right thing, which surprised me! But I wanted to be able to point the developers to an RFC so that they would feel the need to fix those URLs. How to format numbers as currency strings I would like to format a price in JavaScript. I'd like a function which takes a float as an argument and returns a string formatted like this: &quot;$ 2,500.00&quot;  What's the best way to do this? Why would someone use WHERE 1=1 AND &lt;conditions&gt; in a SQL clause (Either SQL obtained through concatenated strings, either view definition)  I've seen somewhere that this would be used to protect against SQL Injection, but it seems very weird.  If there is injection WHERE 1 = 1 AND injected OR 1=1 would have the same result as injected OR 1=1.  Later edit: What about the usage in a view definition?    Thank you for your answers.  Still, I don't understand why would someone use this construction for defining a view, or use it inside a stored procedure.  Take this for example:  CREATE VIEW vTest AS SELECT FROM Table WHERE 1=1 AND table.Field=Value How to make two people play at the same time? Tag score calculation wrong in Android App I see pictures online of everyone having all these Pokémon to catch being everywhere around them, but it seems like I can only ever see one or two. I live in a rural area, but even walking miles through the farmland, it's rare to find any Pokémon.  Why is this? How can I find more Pokémon? How to change sign text color in Minecraft? I have gone through every single website and video to try to make a sign with colored text, but nothing works. Can anyone help me to get a sign to say:  Place Block(dark blue and bold text)  I really want this for a map I am making and I need help. Using a new document class/template with LyX? I tried googling this elsewhere but I'm new to LaTeX and extremely confused about certain things. Basically I downloaded MikteX and I'm using the latest version of Lyx with it. Now all I basically know how to do is make pretty looking mathematics and add contents pages/titles/references/etc.  I'm looking to make a dissertation and my unviersity provides a template,  (available for download at that link).  So, what exactly do I need to do (and please be super specific as I am totally clueless to all the jargon I read).   Basically, I need to download ociamthesis.cls in the first line of that webpage. Does it matter where I save it? What exactly do I do next? I showed up here to write a perfectly normal rant about misaligned pixels, and there's a big fat checkbox cluttering up the "Ask" page:    WHAT THE EEEEK IS THIS NEW ABOMINATION? Formatting each part/section/subsection Are there some magic lines to be placed in the preamble that would, like in CSS,  specify how each generic section or subsection in the whole document should be formatted? "Questions like this" or "questions like these" Keyboard key stuck or not being recognized; how to fix Has anyone used PostgreSQL with PostGIS successfully?   I am a semi-experienced ArcGIS user and want to build out a database and connect it to ArcCatalog.   I've scoured the internet for resources but nobody has really given a good walkthrough. I have a code that prints a table with 2 rows. I want to keep format of it and change 2 rows into 3.   \documentclass[conference]{IEEEtran}  \usepackage{pgfplots} \usepackage{siunitx} \usepackage{multirow} \begin{document}  \begin{table}[h] \caption{Family data set results} \label{tbl::Fam} \centering \begin{tabular}{|l|l|c|c|c!{\vrule width 2pt}l|l|c|c|c|} %\noalign{\hrule height 2pt} \hline \textbf{Column}&amp;\textbf{Algorithm}&amp;\textbf{min}&amp;\textbf{max}&amp;\textbf{std}l&amp;\textbf{Column}&amp;\textbf{Algorithm}&amp;\textbf{min}&amp;\textbf{max}&amp;\textbf{std}\\\hline \multirow{2}{*}{age}&amp;Original&amp;9&amp;2.8&amp;100&amp;\multirow{2}{*}{employer\_type}&amp;Original&amp;13&amp;2&amp;10\\ \cline{2-5} \cline{7-10}&amp;PrivBayes&amp;2&amp;95&amp;96&amp;&amp;PrivBayes&amp;2&amp;100&amp;100\\\hline \multirow{2}{*}{education\_level}&amp;Original&amp;7&amp;2&amp;98&amp;\multirow{2}{*}{marital\_status}&amp;Original&amp;10&amp;2&amp;100\\ \cline{2-5} \cline{7-10}&amp;PrivBayes&amp;2&amp;6&amp;96&amp;&amp;PrivBayes&amp;2&amp;6&amp;100\\\hline \hline %\noalign{\hrule height 2pt} \end{tabular} \end{table}  \end{document}   In this picture, I have 2 algorithms {Original, PrivBayes}. I want to change 2 algorithms into 3 algorithms with keeping the format of table. Can you please help me to do it? Permutation module of $S_n$ Let $G=S_n$ and let $V$ be the permutation module of $G$ with basis $\{x_1,\ldots,x_n\}.$  Let $\lambda, \mu \in \mathbb{C}$ to allow one to define a $\mathbb{C}G$-homomorphism $\rho:V \to V$ by $$\rho(x_j):=\lambda x_j+\mu\sum_{i \neq j}x_i.$$  By using the above fact or otherwise, how can we prove that $V$ is the direct sum of two non-isomorphic irreducible $\mathbb{C}G$ -submodules?  I tried to prove this by construction. A familiar irreducible submodule in this case is the $1$-dimensional space $U:=\operatorname{span}\{x_1+\cdots+x_n\}$. I intend to find another $(n-1)$-dimensional submodule $W$  which makes $V=U\oplus W$ hold, but it's hard to do so. Is there a way to use the fact instead of a random construction? How can I draw a horizontal line spanning only some of the table cells? In a table, how can I draw a horizontal line that goes only through some of the cells? I mean a line like the one in the Foo and in the Bar area of this table:  +----+-----+ |Foo |1 |2 | |    |1 |2 | |    +--+--+ |    |1 |2 | |    |1 |2 | +----+-----+ |Bar |1 |2 | |    |1 |2 | |    +--+--+ |    |1 |2 | |    |1 |2 | +----+--+--+ When using the ssh or ftp commands from the Bash shell, does the server that I am connecting to learn of the domain name used? I understand that the domain name is locally translated into an IP address via DNS. In HTTP, after that happens, the server is told the original domain name as well in order to serve the correct page, or to present the correct TLS cert (SNI).  host serverfault.com GET /   Does a similar phenomenon happen when connecting to ssh or ftp?  I ask because I am  trying to ssh into a server (GoDaddy webhosting) which expects a domain name, but is not letting me in when I try to connect via user@IPaddress as the DNS is not yet moved to the GoDaddy IP address.