SOQL query filter by value of another column
SOQL: Comparing two custom relationship fields in a nested query
I don't understand this. These identities are given in the online notes for MIT's 18.01 calculus class. It's related to taking the sum of two trig functions and transforming them into a single trig function. I can use the formulas to do this, but I am having trouble finding anything on the internet to use a proof for my understanding.  Thanks for any responses!  EDITED (added after the first answer):  Sorry, the identity goes like this:  $A\sin{k(x-c)}=a\sin{kx}+b\cos{kx}$ ,  with the relationships  $a=A\cos{kc}$ , $b=-A\sin{kc}$ , $A=\sqrt{a^2+b^2}$ , and $\tan{kc}=-b/a$ NOT IN vs NOT EXISTS How do I manage how many revisions snapd keeps of an application? Expected value of subset of variables in Bayesian setting Assume we have $N$ random variables $X_1, \ldots, X_N$ with known (posterior) distributions that are easy to sample from. For simplicity, assume that I am interested in the expected value of the ten largest of these random variables. There will be some uncertainty surrounding this expected value as there is uncertainty with respect to the rank of a given $X_i$ in case the distributions of $X_1, \ldots, X_N$ overlap. I want to use simulation based methods. My approach is to simulate $M$ samples from the distributions of $X_1, \ldots, X_N$, where in each iteration, I construct a binary indicator of length $N$ indicating whether random variable $i$ is within the set of the ten largest samples or not. Averaging over these $M$ draws gives me the probability that random variable $i$ is member of the top ten group. Denote this probability as $\pi_i$. Define a binary random variable that indicates membership in the top ten group as $S_i$. $S_i$ follows a Bernoulli distribution s.t. $S_i \sim Ber(\pi_i)$. In a second step, I draw $L$ samples from the distribution of $S_i$ and from the distributions of $X_1, \ldots, X_N$. Given a draw of $S_i$, I can select the top ten out of the samples of $X_1, \ldots, X_N$ in each iteration and average the respective samples within the top ten group. I save this average, so the result after $L$ iterations will be the distribution of the average outcome within the top ten group, taking into account all relevant sources of uncertainty. My questions are: Is this simulation approach valid in general? From a Bayesian perspective, is this simulation valid or do I need to treat additional quantities (e.g. $S_i$ or $\pi_i$) as random variables that need a prior? I have one Ethernet port that is wired directly to the router on another level.  However, I want to run a desktop and a server both off this one Ethernet port.  Can anyone tell me the difference between an Ethernet splitter and a switch?    Also, will either the splitter or switch slow down the connection as opposed to just one connection? So I was in the middle of making a ball-shaped smoke, but the volumetric effect didn't work following the basic shape. It remains cube in Eevee Blender 2.8; while in Cycle it works, but in Cycle it takes thousands of years for Render. Is it physically possible to build a long zoom (17-300 mm for example) at an aperture value of around 1.4 or 1.2? I'm curious if the physics allow a company to build such a lens of course with good IQ, minimal color aberration, maximum sharpness, and little to none lens vignetting or edge softness What is the best way(s) to fake function overloading in Javascript?   I know it is not possible to overload functions in Javascript as in other languages.  If I needed a function with two uses foo(x) and foo(x,y,z) which is the best / preferred way:   Using different names in the first place Using optional arguments like y = y || 'default' Using number of arguments Checking types of arguments Or how? I'm looking for a phrase that describes trying to fix problems caused by underlying issues, with the result of compounding the issue. I usually call this "targeting surface problems rather than root problems", but my terminology is verbose.  Example 1: A government bans buying and selling bananas in the state. Later, it passes a clause allowing citizens to purchase imported bananas.  Example 2: A divided highway is erected with two lanes going in each direction but, since it gets lots of traffic, the shoulders are widened into new lanes. This leaves no shoulder room.  What would be a more concise phrase? Position of "only" in “We 𝒐𝒏𝒍𝒚 have two possibilities” Is there any difference in meaning between the three following sentences?   We only have two possibilities. We have only two possibilities. We have two possibilities only.   I have already read  and I know that the position of only and the emphasis (written or oral) may change the meaning of some sentences, but I am not sure if it does here.  Note: It is clear that “only we have two possibilities” has a different meaning. My question is restricted to the sentences I’ve listed above. What does = +_ mean in JavaScript file /dev/* prints the description of a bunch of files as "block special (M/N)" and "character special (M/N)", where M and N are numbers. For example:  $ file /dev/null /dev/null: character special (1/3)   man file doesn't seem to document these, but refers vaguely to man stat, which seems to refer to these as major and minor device types. apropos 'device type' finds nothing. So what do these numbers mean? Is char *envp[] as a third argument to main() portable Let $\Gamma$ be a set of formulas and $\phi$ be a formula. Show that $\Gamma \cup \{\neg \phi\}$ is satisfiable if and only if $\Gamma\not \models \phi$.   This seemed pretty obvious but I wanted to see if my proof made sense:  Proof: $(\Rightarrow)$  To derive for a contradiction, suppose that: $\Gamma \models \phi$. That means for all truth assignments $v$, for $\gamma \in \Gamma$, if $v(\gamma) = T$, then $v(\phi) = T$.  But this contradicts our assumption that $\Gamma \cup \{\neg \phi \}$ is satisfiable by the fact that $v(\phi) = T$ cannot happen so: $\Gamma \not \models \phi$ .  $(\Leftarrow)$   So by the definition of $\Gamma \not \models \phi$, we have that there is some truth assignment $v$ which satisfies $\Gamma$ but does not satisfy $\phi$. So  that means $v(\phi) = F$ since $v(\phi) \not = T$ which implies that $v(\neg \phi) = T$ which means $v$ satisfies $\Gamma \cup \{\neg \phi\}$.    I feel like I'm missing something in the forward direction, but at the same time... It looks pretty trivial as well. Am I missing anything crucial?  Thank you! How to insert pipe symbol in (La)TeX? How to insert pipe symbol | in TeX (LaTeX)?  I have tried this sample with pdflatex tmp.tex  \documentclass{extarticle} \begin{document} \textpipe \end{document}   And it give undefined control sequence error  This is pdfTeX, Version 3.1415926-1.40.10 (TeX Live 2009/Debian) restricted \write18 enabled. entering extended mode (./tmp.tex LaTeX2e &lt;2009/09/24&gt; Babel &lt;v3.8l&gt; and hyphenation patterns for english, usenglishmax, dumylang, noh yphenation, loaded. (/usr/share/texmf-texlive/tex/latex/extsizes/extarticle.cls Document Class: extarticle 1996/10/08 v1.0 Non Standard LaTeX document class (/usr/share/texmf-texlive/tex/latex/base/size10.clo) (/usr/share/texmf-texlive/tex/latex/base/exscale.sty)) No file tmp.aux. ! Undefined control sequence. l.3 \textpipe How to pass an array of Uri between Activity using Bundle Limit of a Piecewise Function defined on Rationals and Irrationals How do I prove that in every commuting family there is a common eigenvector? I tried installing Office 2007 in Ubuntu with Wine but it was throwing an error after installing and also when I tried to open a PowerPoint document and save it. Has anybody gotten Office 2007 installed without any issues? Please help me. Extra }, or forgotten \right My MWE:  \documentclass{report}  \usepackage{amsmath}  \begin{document}  \begin{align} y &amp;= a \\ =&amp; -2c_1\bar{z}_1^2 + 2\bar{z}_1\bar{z}_2 + 2\bar{z}_2 \left ( -\bar{z}_1 -c_2z_2 - \frac{3\epsilon}{2}\bar{z}_2 -\sigma_{2,1}\cos(x_1)\Delta x_1 \notag \right. \\ \left. &amp;- \sigma_{2,2}\Delta x_2 -\sigma_{2,3} \Delta u +c_2 \chi_2 \vphantom{\frac{1}{1}} \right ) - 2\gamma \sigma_{2,1}^2\cos^2(x_1) \Delta x_1^2 - \gamma \sigma_{2,2}^2 \Delta x_2^2   - 2\gamma \sigma_{2,3}^2 \Delta u^2 \end{align}  \end{document}   The error I get:  Extra }, or forgotten \right.   The expected result: