WHat's the exact bug fix kernel version?
What is Ubuntu's status on the Meltdown and Spectre vulnerabilities?
Add the ability to lock a question against edits Expectation of Exit Time of Brownian Motion from Interval I am trying to solve the following:  Let $W_t$ be a brownian motion and $a,b &gt;0.$  Define $\tau$ to be the exit time of $W_t$ from $[-a,b]$, that is $$\tau = \inf\{t \ge 0\ :\ W_{t}(\omega) \notin [-a,b]\}.$$  Show that $\tau$ is integrable and compute $\mathbb{E}(\tau)$.  I have seen this stated without proof multiple places that $\mathbb{E}(\tau)=ab.$  What is the logical argument that backs up this statement?  How are we guaranteed $\tau$ is integrable? In a batch file I need to extract a month, day, year from the date command.  So I used the following, which essentially parses the Date command to extract its sub strings into a variable:  set Day=%Date:~3,2% set Mth=%Date:~0,2% set Yr=%Date:~6,4%   This is all great, but if I deploy this batch file to a machine with a different regional/country settings, it fails because month, day and year are in different locations.   How can I extract month, day and year regardless of the date format? How fast would someone have to run to run over water? I was thinking about Flash, the superhero, or the little boy in the Incredibles.   There is  that doesn't answer a lot. Especially, I don't think surface tension would help a lot for a human to run over water, I think one would have to build on the inertial effect of the water.  There is one empirical approach based on figuring out the speed at which bare-footed water skiing is done, but I wasn't able to find a decent number. Still the difference may be that a hypothetical runner would have to propulse herself over the water, which may or may not make the thing more difficult.  Hence, I raise the question here. Help needed with definite integral for $\lim_{n\rightarrow \infty}\sum_{k=1}^{n} \frac{1}{n+k}$ What causes a force field to be "non-conservative?" Alternative methods to prove that $Z_m$ is a field under addition and multiplication $\bmod\ m$ iff $m$ is a prime I am looking for ways to prove that $\mathbb{Z}_m=\{0,1,2,\dots,m-1\}$ is a field under addition and multiplication $\bmod\ m$ iff $m$ is a prime.   I tried it this way: If $m$ is a prime $p$,it is obvious that most importantly, we need to prove that every non-zero element in $\mathbb{Z_p}$ has an inverse in $\mathbb{Z_p}$.We note that if $a,b\in \mathbb{Z_p}$, then $a\cdot b\in \mathbb{Z_p} \dots \boxed{*}$. Next, $a^p\equiv a \bmod p$ for prime $p$(the proof follows by induction on $a$).As  $\displaystyle 0\leq a\leq p-1$,$a\not =p$. Thus $$a^{p-1}\equiv 1 \bmod p$$ for prime $p$ which,together with $\boxed{*}$ guarantees the existence of an inverse in $\mathbb{Z_p}$.Proving the other properties is simple.  Conversely,if $\mathbb{Z_m}$ is a field,then every non-zero element of $\mathbb{Z_m}$ has an inverse.Note that inverse of an element is unique.For if $a\cdot b\equiv a\cdot c\equiv 1 \bmod m$,then $(a\cdot b)\cdot c\equiv c\equiv (a\cdot c)\cdot b\equiv b \bmod m$ i.e $m|(b-c)\implies b-c=0(0\leq a\leq m-1,a\in \mathbb{Z_m})$.So, inverses must be unique and every element is either an inverse of itself or has in inverse in the field.That allows us to conclude that $[(m-1)!]^2\equiv 1 \bmod m$ which can only mean that either  $(m-1)!\equiv 1 \bmod m$ or $(m-1)!\equiv -1 \bmod m$. If $m$ is not a prime, it has a prime factor, say $p$. $ 0\leq p\leq m-1\implies p|(m-1)!\implies p|1$or $-1$ which is absurd, a contradiction.Thus $m$ is prime.  I feel that this method is too involved and complicated. Can anyone please suggest some other method?(Some context: This is a problem from Finite Dimensional Vector Spaces by Paul Halmos. I am learning linear algebra for the first time.It seems some of the comments have been posted on the assumption that I know rings and fields; I don't. ) When conducting multiple regression, when should you center your predictor variables & when should you standardize them? In some literature, I have read that a regression with multiple explanatory variables, if in different units, needed to be standardized.  (Standardizing consists in subtracting the mean and dividing by the standard deviation.)  In which other cases do I need to standardize my data?  Are there cases in which I should only center my data (i.e., without dividing by standard deviation)? Reputation for comments? I have seen many good comments that really improve the quality of questions and answers, and I think they deserve a bit of reputation (maybe just 1 point) for a upvote. "A/An" preceding a parenthetical statement When a/an precedes a parenthetical aside (sometimes seen in informal/conversational writing), should the vowel rule depend on the first word in parentheses, or the next word in the "regular" flow of the sentence?     I need a (memorable) idiom (preceding an m word; use a)   or     I need an (memorable) idiom (preceding an i word; use an) Spaces in variable assignments in shell scripts Just a curiosity. I just saw a video where pi was being calculated by the series  $$1-(1/3)+(1/5)-(1/7)+...$$  My question is how can $\pi$ be irrational if we can calculate it using rational numbers? How can I stop Lollipop ignoring my wifi network? Android 5.0 has a new "feature": If a wifi network has no connection to the internet, it will remain connected to it but route traffic over mobile data instead. A small exclamation mark shows in the status bar over the wifi symbol.  Unfortunately, for some reason Android has decided that my home wifi does not have a good internet connection - which is not true, as I'm using it to access Stackexchange at the moment - and is, instead, trying to send everything over GPRS.  With mobile data disabled, things work over wifi just fine, despite the exclamation mark - so it isn't a problem with the wifi not working, per se.  Is there any way to override this "smart" feature? The only way I have found to make things work at the moment is to disable mobile data while I am in my house - which is not a practical long-term solution.   EDITING to add that I have now solved this problem by buying a new router! I was using something very old... But, I'll leave the question here for the benefit of anybody else with the same difficulty. I'm going to encrypt the characters Zhu, and decrypt them using RSA. I'm using the public key $\{e, n\}$ and private key $\{d, n\}$. The values of $e$, $d$ and $p$ I get from my textbook: $e = 17$, $d = 53$, $n = 77$.  It works fine when the number is smaller than 76, but in my example below, it doesn't work:  z = 90  h = 104  u = 107  e = 17 d = 53 n = 77  print z,h,u  c_z = z ** e % n c_h = h ** e % n c_u = u ** e % n  print c_z, c_h, c_u  p_z = c_z ** d % n p_h = c_h ** d % n p_u = c_u ** d % n  print p_z, p_h, p_u   The outputs are:  90 104 107 62 69 46 13 27 30     Do you have any idea what's going wrong? Confirming that my own question is a duplicate by voting to close should have immediate effect When hyperref is loaded I receive the following error:     TeX capacity exceeded, sorry [input stack size=5000].   However, when I remove hyperref package it compiles successfully. I traced it back and found that \maketitle causes the error but don't know how to fix it. Is there any way to use hyperref in my setup.   Code:       %!TEX TS-program = xelatex     \documentclass[journal,transmag,]{IEEEtran}      \usepackage[hyphens]{url}     \usepackage{hyperref}      \usepackage{xunicode}      \usepackage{fontspec}      \usepackage{polyglossia}     \setmainlanguage{english}     \setotherlanguage{arabic}     \newfontfamily\arabicfont[Script = Arabic]{Amiri} % Replace 'Simplified Arabic' with a font from your system       \begin{document}     \title{A Very Nice Title}      \author{\IEEEauthorblockN{             John Doe\IEEEauthorrefmark{1}}%,~\IEEEmembership{Member,~IEEE}         \IEEEauthorblockA{\IEEEauthorrefmark{1}My address}         % &lt;-this % stops an unwanted space         \thanks{Manuscript received mm dd, 20xx; revised mm dd, 20xx.               }     }      % The paper headers     \markboth{headers...}%     {Shell \MakeLowercase{\textit{et al.}}: Bare Demo of IEEEtran.cls for IEEE Transactions on Magnetics Journals}      \IEEEtitleabstractindextext{%         \begin{abstract}My Abstract.\end{abstract}          % Note that keywords are not normally used for peerreview papers.         \begin{IEEEkeywords}             Key 1, Key 2     \end{IEEEkeywords}}      \maketitle       \IEEEdisplaynontitleabstractindextext     % \IEEEdisplaynontitleabstractindextext has no effect when using     \IEEEpeerreviewmaketitle       \section{Introduction}     English Text      \begin{Arabic}      السَلَامُ عَلَيكُمْ     \end{Arabic}       \end{document} How to show that every Boolean ring is commutative? How to draw open-close interval in LaTeX I am using the following commands to have half-open interval in a real line:   \begin{tikzpicture}[scale=7] \draw[-&gt;, thick] (-0.1,0) -- (1.7,0); \foreach \x/\xtext in {0/8,0.2/$S_1$,0.4/$T_4$,0.6/$S_3$,0.8/$T_2$,1/$S_3$,1.2/14,1.4/$S_3$,1.6/16}     \draw[thick] (\x,0.5pt) -- (\x,-0.5pt) node[below] {\xtext}; \draw (0.2,0.5pt) node[above] {$c$}; \draw[[-), ultra thick, blue] (0.2,.01) -- (.4,0.01); \draw[(-, ultra thick, green] (0.6,.02) -- (1,0.02); \end{tikzpicture}   Now, I need to have an open-close interval, but I am not able to have that close interval at the end, using the following command:  \begin{tikzpicture}[scale=7] \draw[-&gt;, thick] (-0.1,0) -- (1.7,0); \foreach \x/\xtext in {0/8,0.2/$S_1$,0.4/$T_4$,0.6/$S_3$,0.8/$T_2$,1/$S_3$,1.2/14,1.4/$S_3$,1.6/16}     \draw[thick] (\x,0.5pt) -- (\x,-0.5pt) node[below] {\xtext}; \draw (0.2,0.5pt) node[above] {$c$}; \draw[(-], ultra thick, green] (0.6,.02) -- (1,0.02); \end{tikzpicture}   May I ask for anybody help? What do you call the process of combining two words to create a new one? For an existing set of line features, I would like to generate a perpendicular line, of say 1km, at the midpoint of each existing line feature in ArcGIS.  I imagine that The methodology would be to:   create a tangent line at the midpoint of each existing line feature calculate the angle of the tangent line based on the angle of the tangent line, calculate the location of the endpoint of the new line create the new line with the calculated endpoint of the new line and the existing midpoint of the old line   Let's assume that we are in a UTM projection and can use coordinates to calculate distance and direction.  How would I do this with ArcGIS tools or with ArcPy?