Removing all E mails from a gmail (all mail) account
How do I delete all my mail from my Gmail account?
What is the significance of allowing nilpotents in scheme theory? Can a coin with an unknown bias be treated as fair? How to split numbers into columns with negative and positive values, without empty cells? This is from a problem seminar and I need help figuring out the solution.  Four bugs, $A,B,C,D$ are initially placed at the corners of a unit square. From a given initial moment, all four crawl simultaneously at one and the same speed $s&gt;0$, $A$ towards $B$, $B$ towards $C$, $C$ towards $D$, and $D$ towards $A$, with each heading at every instant along the line joining it with its target.  Find a system of differential equations describing the trajectory of $A$.  Do the bugs eventually all meet at the center of the square? If so, how long did it take?  My attempt so far: $\def\grad{\mathbf\nabla}$ $\newcommand{\norm}[1]{\left\Vert #1 \right\Vert}$ Call ${\vec x}_1,{\vec x}_2,{\vec x}_3,{\vec x}_4$  the positions in the plane of $A,B,C,D$ respectively. Then $$\grad {\vec x}_1 = \frac{{\vec x}_2-{\vec x}_1}{\norm{{\vec x}_2-{\vec x}_1}}s$$ $$\grad {\vec x}_2 = \frac{{\vec x}_3-{\vec x}_2}{\norm{{\vec x}_3-{\vec x}_2}}s$$  $$\grad {\vec x}_3 = \frac{{\vec x}_4-{\vec x}_3}{\norm{{\vec x}_4-{\vec x}_3}}s$$  $$\grad {\vec x}_4 = \frac{{\vec x}_1-{\vec x}_4}{\norm{{\vec x}_1-{\vec x}_4}}s$$  with ${\vec x}_1(0) = (0,0),\  {\vec x}_2(0) = (0,1),\ {\vec x}_3(0) = (1,1),\ {\vec x}_4(0) = (1,0)$.  I have noticed that the sum of the gradients is 0, but I don't know if that is helpful or not. Can someone help me figure this problem out? Help me understand Bayesian prior and posterior distributions In a group of students, there are 2 out of 18 that are left-handed. Find the posterior distribution of left-handed students in the population assuming uninformative prior. Summarize the results. According to the literature 5-20% of people are left-handed. Take this information into account in your prior and calculate new posterior.    I know the beta distribution should be used here. First, with $\alpha$ and $\beta$ values as 1? The equation I found in the material for posterior is   $$\pi(r \vert Y ) \propto r^{(Y +−1)} \times (1 − r)^{(N−Y +−1)} \\ $$  $Y=2$, $N=18$  Why is that $r$ in the equation? ($r$ denoting the proportion of left-handed people). It is unknown, so how can it be in this equation? To me it seems ridiculous to calculate $r$ given $Y$ and use that $r$ in the equation giving $r$. Well, with the sample $r=2/18$ the result was $0,0019$. The $f$ should I deduce from that?  The equation giving an expected value of $R$ given known $Y$ and $N$ worked better and gave me $0,15$ which sounds about right. The equation being $E(r | X, N, α, β) = (α + X)/(α + β + N)$ with value $1$ assigned to $α$ and $β$. What values should I give $α$ and $β$ to take into account prior information?  Some tips would be much appreciated. A general lecture on prior and posterior distributions wouldn't hurt either (I have vague understanding what they are but only vague) Also bear in mind I'm not very advanced statistician (actually I'm a political scientist by my main trade) so advanced mathematics will probably fly over my head. I have a Windows XP box (NTFS filesystem) on which I found a file named NUL. I have not been able to remove this file in any usual way. The file appears to be owned by Administrator in the SYSTEM group, unlike any other file in the same directory (the other files are owned by my user id).  How do I get rid of this file? Where did it come from? Numbering rows within groups in a data frame Index and length must refer to a location within the string My mom and I are having a dispute on much more easy versus much easier. For example, consider the sentence:     It's [much more easy]/[much easier] to do action X than action Y.   I say that much easier is correct and that much more easy is grammatically incorrect, while she says that both are okay. I understand that both are acceptable colloquially, but which is grammatically correct here? If you could explain why, that would be even better! How can I hide username and computer in terminal command prompt?   In Terminal it says  Last login: Mon Jan 13 00:00:14 on ttys000 Whatever:~ UserName$    Is it possible to show just the current folder and $ sign? Logic soundness and completeness I have to do a number of similar type questions, but I am having trouble grasping the general concepts around soundness and completeness. I have read up on the general definitions and think I understand them, but when asked to show something like the following I come up blank. Thanks for any ideas/help.   Show that the following propositional proof system, PCa, is sound but not complete.  PCa  Connectives (and constants) ∨, ∧, →, ↔, ¬, 0, 1  Axioms All tautologies of the form F→F  Rules of inference Hypothetical Syllogism Integral of $ 1 \, / \, (1 + a \, \cos(x) )$ How do I audit my reputation? If I am concerned that my reputation score is incorrect, how can I audit it, or get a report of a detailed breakdown of my reputation? How do I check where devices are mounted? What is the command that lets me see what and where devices are mounted?  I'm having trouble changing songs on my old iPod, and I have a feeling it's because of the mount point. Proving of Integral $\int_{0}^{\infty}\frac{e^{-bx}-e^{-ax}}{x}dx = \ln\left(\frac{a}{b}\right)$ Prove that      $$ \int_{0}^{\infty}\frac{e^{-bx}-e^{-ax}}{x}\,dx = \ln\left(\frac{a}{b}\right) $$   My Attempt:  Define the function $I(a,b)$ as  $$ I(a,b) = \int_{0}^{\infty}\frac{e^{-bx}-e^{-ax}}{x}\,dx $$  Differentiate both side with respect to $a$ to get  $$ \begin{align} \frac{dI(a,b)}{da} &amp;= \int_{0}^{\infty}\frac{0-e^{-ax}(-x)}{x}\,dx\\ &amp;= \int_{0}^{\infty}e^{-ax}\,dx\\ &amp;= -\frac{1}{a}(0-1)\\ &amp;= \frac{1}{a} \end{align} $$  How can I complete the proof from here? I have made a raster elevation map of Greenland, and have information of the region, cities and more as vectors. The information is not in the same place as my elevation map.  I have selected EPSG:5938 on the bottom right in QGIS and on my informations and elevation map I have set the CRS to the same like the picture    How do I get it all on the same position? Sequence of rationals with an irrational limit have denominators going to infinity This is a general question that was asked indirectly multiple times in here, but it lacks a single authoritative answer. It would be great to have a detailed answer to this for the reference.  , the proportion of correct classifications among all classifications, is very simple and very "intuitive" measure, yet it may be a . Why does our intuition misguide us here and are there any other problems with this measure? Why no ooVoo on ubuntu? For a login application, how would i go about checking the sha1 value of a password?