What is the English verb for completing the missing exam?
I'm looking for one word which describes what a student who missed classes needs to do
Say, we have a query like this:  select a.*,b.* from  a join b on a.col1=b.col1 and len(a.col1)=10   Assuming the above query uses a Hash Join and has a residual, the probe key will be col1 and the residual will be len(a.col1)=10.  But while going through another example, I could see both the probe and the residual to be the same column. Below is an elaboration on what I am trying to say:  Query:  select * from T1 join T2 on T1.a = T2.a    Execution plan, with probe and residual highlighted:         Test data:    create table T1 (a int, b int, x char(200)) create table T2 (a int, b int, x char(200))  set nocount on declare @i int set @i = 0 while @i &lt; 1000   begin       insert T1 values (@i * 2, @i * 5, @i)     set @i = @i + 1   end  declare @i int set @i = 0 while @i &lt; 10000   begin     insert T2 values (@i * 3, @i * 7, @i)     set @i = @i + 1   end   Question:    How can a probe and a residual be the same column? Why can't SQL Server use the probe column only? Why does it have to use the same column as a residual to filter rows again?  References for test data: Why are lamps and mesh lights not illuminating anything? I am interested in displaying some things (e.g.: title page) in full color on screen, while having the same object/page display in a black and white friendly form when printed.  According to , there is built-in functionality in the PDF specification for Screen-Only objects and Screen-And-Print objects.  There may also be a way to add a layer on top of the B&amp;W page that only displays the full color page on screen via the PDF 1.5 Optional Content Groups feature.  Similarly,  demonstrates the selective printing of text via ocg-p.  But it is not clear how I can use this package in the way that I need to.  My scenario is compounded by the fact that my color page text is white on a dark background.  MWE:  This code presents the way I am currently switching back and forth between color and b&amp;w.  I change the printincolor bool variable to make the change.  \documentclass[11pt]{article}  \usepackage[demo]{graphicx} \usepackage{etoolbox}  \providebool{printincolor} % Will set color title page and section headings \setbool{printincolor}{false}  % Setup color if needed \ifbool{printincolor}{% \usepackage[pagecolor=none]{pagecolor}% \definecolor{MyBlue}{HTML}{1b3667}% \usepackage{afterpage}}{}  \begin{document}  % Begin Title Page {  \thispagestyle{empty}   \ifbool{printincolor}{%   \pagecolor{MyBlue}%   \afterpage{\nopagecolor}}{}   \begin{center}   {\ifbool{printincolor}{\color{white}\sffamily}{\sffamily}%  Set text color white or leave [default] black   \ifbool{printincolor}{\includegraphics[width=1.5in]{logo-gold}}{\includegraphics{logo-blue}}% put logo gold or blue   \\ \vskip 1in   \begin{huge}         \textbf{Title}         \vskip 0.1ex\rule{0.5\textwidth}{0.8pt}\vskip 1ex         Subtitle         \\         \end{huge}   \vfill\vfill   \begin{large}    Authors:\\   John Doe and Jane Doe\\   \end{large}   }   \end{center} }  \end{document}   How can I layer (or otherwise display) two versions of the title page in a way that color displays on screen, but black and white is printed? Cu has an unpaired electron in 4s, but it is diamagnetic. I thought that it has to be paramagnetic. What am I missing? Change logo url link I'm trying to change the logo url of the site to "mywebsite.com/side2", but it is not working, can anyone tell me where is the error in the code below?  add_filter( 'login_headerurl', 'custom_loginlogo_url' ); function custom_loginlogo_url($url) {  return home_url( 'side2' ); } When does $120$ divide $n^5 - n$ Find n such that $n^5 - n$ is divisible by $120$. (*Here $n$ belongs to the natural number set)  Seems a trivial problem, but the answer mentioned in the text book seemed incomplete to me so I'm here just to ensure whether approach to this problem is correct or not.  So my approach is as follows: We know that $n^5 - n$ can be written as $n^5-n = n(n-1)(n+1)(n^2 + 1)$  Now since it's product of three consecutive natural numbers so it's divisible by $3! = 6$. Now using Fermat's Little theorem we can prove that $n^5= n \mod5$ hence $n^5 - n$ is divisible by $5$ as well. So $n^5 - n$ is divisible by $30$. Now to ensure their is another factor of $4$ in the term we need to ensure that $n^5 - n$ is divisible by $8$. I found that all odd natural numbers and multiples of $8$ makes $n^5 - n$ divisible by $8$, hence $n^5 - n$ is divisible by $120$. But in the text book they have only mentioned odd natural numbers as answer, which seemed incomplete to me.  Thanking everyone in advance:P Classifying whether a collection of objects is a set How to read a single character from the user? Is there a way of reading one single character from the user input? For instance, they press one key at the terminal and it is returned (sort of like getch()). I know there's a function in Windows for it, but I'd like something that is cross-platform. Search for a string and print everything before and after within a range I have this file:  sometext1{ string1 }  sometext2{ string2 string3 }  sometext3{ string4 string5 string6 }   I want to search this file for a specific string and print everything before this string up to the opening { and everything after this string up to the closing }. I tried to achieve this with sed but if I try to print everything in the range /{/,/string2/ for example sed prints this:  sometext1{ string1 }  sometext2{ string2 sometext3{ string4 string5 string6 }   If I search for the string "string2" I need the output to be:   sometext2{ string2 string3 }   Thanks. Extract date from a variable in a different format Let me explain you the problem   $ date +%c -d "$d" Tue 31 Dec 2013 01:13:06 PM CET $ date +'Today is %F' -d "$d" Today is 2013-12-31   This solution corresponds to current date.  But I have one variable which stores date other than current date  $Prev_date="Wed Dec 25 06:35:02 EST 2013"    I am looking for solution to read this date as 2013-12-25 and store it in a variable.  I have tried this:  a=`date --date=$Prev_date '+%y/%m/d'` echo $a   It's giving this error:  date: illegal option -- date=Wed usage: date [-u] mmddHHMM[[cc]yy][.SS] date [-u] [+format] date -a [-]sss[.fff] Raise bounty on question If just a single photon hit a single slit interferometer, what would happen? Would you just see a dot on the screen, or would there be a diffraction pattern? Furthermore, if you had a double slit interferometer but also had which-path information would there still be a diffraction pattern even though there is no interference? In the following sentence:     The city is populated by many people.   "many" can be replaced by something like "a great number of" (let us leave the perceived differences between the meanings of these two modifiers out of discussion):     The city is populated by a great number of people.   I understand that this replacement does not change the object "populating the city" from the original "people" to a "number", but rather shows the ability of expressions in the form "[numeral] of" to provide information about the quantity of nouns they modify.  Is this ability due to some special qualities of nouns such as "number", "quantity", "fraction", &amp;c., or is it just one usage of the preposition "of"? Can I pass a System.Net.MailMessage to a WCF service? I'd like to setup a WCF service to send emails. The System.Net.MailMessage doesn't seem to be serializable, and cannot be passed in a [DataContract]  The error I receive is      Type 'System.Net.Mail.MailAddress'   cannot be serialized. Consider marking   it with the DataContractAttribute   Any suggestions? Let $(X,\mathcal{M},\mu)$ be a measure space and $\{f\}$ be a sequence of functions on $X$, each of which is integrable over $X$. Show that $\{f_n\}$ is uniformly integrable if and only if for each $\varepsilon \gt 0$, there is a $\delta \gt 0$ such that for any natural number $n$ and measurable subset $E$ of $X$, if $\mu(E) \lt \delta$, $$ \left|\int_E f_n~d\mu\right| \lt \epsilon.$$     I think one direction $(\Rightarrow)$ is clear. Since $f_n$ being uniformly integrable imply that for every $\varepsilon\gt 0,~\exists \delta \gt 0$ such that for any $E\in \mathcal{M},~\mu(E)\lt \delta$, $\int_E |f_n|~d\mu$ for every natural $n$. But then   $$ \left|\int_E f_n~d\mu\right|\le \int_E|f_n|~d\mu \lt \varepsilon.$$    Any suggestions for the other direction?   Edit:  Following Davide's suggestions, I have   $$ \begin{align*} \int_E |f_n|~d\mu &amp; \le \int_{E\cap [f_n \ge 0]} f_n~d\mu + \int_{E\cap [f_n \lt 0]} (-f_n)~d\mu\\ &amp; = \left| \int_{E\cap [f_n \ge 0]} f_n~d\mu \right| + \left| \int_{E\cap [f_n \lt 0]}f_n~d\mu \right| \\ &amp; \lt \varepsilon + \varepsilon = 2\varepsilon. \end{align*} $$ What package should I use to typeset units? When can a noun be used attributively? Nouns can modify nouns: cat food, coffee cup, gold ring, laser surgery, flood insurance. It seems to me there are even cases where a noun sounds better than the corresponding adjective: sociology papers sounds a bit better than sociological papers.  Some noun-noun combinations don&rsquo;t work. You wouldn't say America gangsters or measurement spoons or greed crimes. If you spilled water on your keyboard you probably wouldn't call it a keyboard spill or even a water spill.  Are there rules that tell which combinations are acceptable? I'm trying to find a movie with an underground facility with people wearing white suits. The people have been affected such that they show no curiosity. There is one person that does and asks one of his co-workers where a tube leads to.      At the end there is an uprising where everyone gets to see the surface and sunlight.   What is the name of this movie? How align 2 adjacent divs horizontally WITHOUT float? Find $P(n+1)$ for a polynomial P Fix a nonnegative integer $n$. Let $P(x)$ be a polynomial of degree $n$ (over the real numbers) such that for all $k\in\left\{0,1,\ldots,n\right\}$, we have $P(k)=\dfrac{k}{k+1}$. Find $P(n+1)$.   My attempt:  I consider a new polynomial $Q(x)=(x+1)P(x)-x$. This $Q$ is a polynomial of degree $\leq n+1$ satisfying: $Q(k)=0\quad\forall k\in\{0,1,2,\ldots,n\}$. Therefore $Q(x)=\lambda x(x-1)\cdots(x-n)$ for a certain real $\lambda$. Hence, $Q(-1)=\lambda \cdot (-1)^{n+1}(n+1)!$, but also $Q(-1)=(-1+1)P(-1)+1=1$. Comparing these, we get $\lambda \cdot (-1)^{n+1} (n+1)! = 1$, thus $\lambda=\dfrac{(-1)^{n+1}}{(n+1)!}$. Since $Q(n+1)=\lambda(n+1)!$ then $Q(n+1)=(-1)^{n+1} $, and from $P(x) = \dfrac{Q(x)+x}{x+1}$ we deduce: $$P(n+1)=\dfrac{(-1)^{n+1}+n+1}{n+2}.$$ I doubted that the answer were $P(n+1)=\frac{n+1}{n+2}$ but the term $(-1)^{n+1}$ wasn’t expected. Is there any mistake here? Does someone have an alternative proof?