"Everyone" or "everybody"
Is there a subtle difference between "somebody" and "someone", "anybody" and "anyone"?
In a conference on elliptic curves (an introduction to the subject), the speaker said that an elliptic curve (I.e. an equation of the form $y^2=x^3+ax+b $ where the RHS has distinct roots) is, in the complex space, a torus/Riemann surface of genus 1.  What is meant by that? Are we talking about a 2-dimensional manifold the 4D space? Upon trying to upgrade from 10.10 to 11.04 all seemed to go well until the restart. This error message is what comes up:  Kernel Panic - not syncing: VFS: Unable to mount root fs on unknown-block(0,0)   How do we fix that? Minimal Sufficient Statistic for location family In Casella &amp; Berger Statistical Inference,in exercise 6.8, we're asked to prove that, for any distribution belonging to the location family, the order statistics are minimal sufficient.  How does one prove this? I have no idea on how to tackle this exercise.  Any help would be appreciated. Continuity of $f(x)$ on $[a,b]$ implies continuity of $f(t) = \displaystyle \min_{a \leq x \leq t}f(x)$ at [a,b]. Writing a git post-receive hook to deal with a specific branch How to change the base of logarithmic-scale plots? ́╗┐' is not recognized as an internal or external command When executing certain files (mainly batch) using PsExec I get these weird ́╗┐' symbols before my command. My initial thought was, that I were using wrong encoding, but after checking, I realized that all my files were using UTF-8. Software for drawing geometry diagrams Seeking options for Spatial ETL (Extract, Transform, Load)? I am interested in the pros and cons of various spatial ETL (extract, transform, load) tools.  If you have used the items listed here (or add your own), I seek your opinions and experiences.  In particular I would like to see usability comparisons of:    (proprietary)  (proprietary, subset of FME features)  (open source)  (open source)  (I don't know that it is truly ETL, but more of a file translation toolset) Any additional lot listed   There is no need to give a review of ALL software mentioned.  If you are experienced with even one then that will be very beneficial in making a decision about which direction to go.  Example: I am looking to create a schema conversion function that will allow me to select the input layer, create a translation, and output to a new, pre-defined schema.  Optimally, after creating the translation script, I would like to have an interactive form where I can "map" fields in my input layer to the output layer (ie- The output layer will have a field called "Address", what is it called in the input layer?)  Some were mentioned in the Q&amp;A at   And here are a couple of related articles that I found. Trying to overwrite ... which is different from other instances of package I tried to upgrade Intel graphics in ubuntu 16.10 using the official installer. The last stage of unpacking libcairo2 produces an error (see figure).  When I do upgrade I get the same error also:   Preparing to unpack .../0-libcairo2_1.15.2-0intel1_amd64.deb ... Unpacking libcairo2:amd64 (1.15.2-0intel1) over (1.15.2-0intel1) ... dpkg: error processing archive /tmp/apt-dpkg-install-aYhdFd/0 libcairo2_1.15.2-0intel1_amd64.deb (--unpack): trying to overwrite shared '/usr/share/doc/libcairo2/changelog.Debian.gz', which is different from other instances of package libcairo2:amd64 Preparing to unpack .../1-libcairo2_1.15.2-0intel1_i386.deb ... Unpacking libcairo2:i386 (1.15.2-0intel1) over (1.15.2-0intel1) ... dpkg: error processing archive /tmp/apt-dpkg-install-aYhdFd/1-libcairo2_1.15.2-0intel1_i386.deb (--unpack): trying to overwrite shared '/usr/share/doc/libcairo2/changelog.Debian.gz', which is different from other instances of package libcairo2:i386 Errors were encountered while processing: /tmp/apt-dpkg-install-aYhdFd/0-libcairo2_1.15.2-0intel1_amd64.deb /tmp/apt-dpkg-install-aYhdFd/1-libcairo2_1.15.2-0intel1_i386.deb E: Sub-process /usr/bin/dpkg returned an error code (1)   It seems that there is a conflict in thelibcairo releases; if yes, how to resolve it ? moderncv: How to control the length of cvitems and cvlines? Stop iPhone alerting me when I'm in a phone call When I'm in a phone call, I still get alerts for emails and texts. The noise will play and, if the phone is on Speaker, it will vibrate -- often leading the person I'm talking to wonder what that weird noise was.  Surely there must be a way to silence the phone while you're talking on it. It's very distracting to have beepings going off right next to your ear! Background: I have the opportunity to pursue a Computer Science graduate degree at a well respected program (around top 20). I spoke with the professors at the university and I feel like I am a good fit with their research program. My ultimate pursuits are to complete a PhD in CS. I've done research as an undergraduate and it has only confirmed my notion that I want to pursue a research track career.  More background: I applied to jobs (in case I was rejected to all the programs I applied for) prior to hearing back from my respective graduate programs. I accepted a position for an industry job (this was to secure I wouldn't be both unemployed &amp; not in school).  Dilemma: Turns out my top graduate school is very interested in me, and I'm very interested in them. I would rather go to graduate school than work in industry forever. The industry job pays very well. I am split between A) working for a maximum of 1 year(It would only be 1 year, seriously I do not care about the money enough to work past a year) and B) going straight to graduate school.   My concerns are as follows, if I choose A):    Could I potentially defer my admissions? If I am not allowed to defer my admissions, would I have a good chance of re-applying and being accepted a year later? Would my potential advisers look down on me for deciding to work a year?   I already made my mind up it would be a 1 year gig if I decide A). I know some people say once you make money, you may not be able to readjust to the graduate salary pay. But I don't think that will apply to because I'm going to live very frugally with or without industry pay. The ability to undo reviews For $u:\mathbb{R}\times [0,1]$ with boundary conditions $u(0,x)=\cos (2\pi x)$ and $u(t,0)=u(t,1)$.   Solve $u_t=u_{xx}+u_x$.  I had this on an exam and tried to write $u$ as a product of two single variate functions and convert to an ode using the usual methods but things got messy and I couldn't finish. I also tried to write $u$ as a Fourier series in $x$ with coefficients $a_k(t)$ depending on $t$, but this also didn't seem to yield anything.  Is there a more clever way to approach this, possibly with Fourier series? I heard from a friend there may be a Fourier transform method since the equation was "homogeneous in momentum space."   Thanks! Value of $\lim_{n\to \infty}\frac{1^n+2^n+\cdots+(n-1)^n}{n^n}$ I remember that a couple of years ago a friend showed me and some other people the following expression:  $$\lim_{n\to \infty}\frac{1^n+2^n+\cdots+(n-1)^n}{n^n}.$$  As shown below, I can prove that this limit exists by the monotone convergence theorem. I also remember that my friend gave a very dubious "proof" that the value of the limit is $\frac{1}{e-1}$. I cannot remember the details of the proof, but I am fairly certain that it made the common error of treating $n$ as a variable in some places at some times and as a constant in other places at other times. Nevertheless, numerical analysis suggests that the value my friend gave was correct, even if his methods were flawed. My question is then:  What is the value of this limit and how do we prove it rigorously?  (Also, for bonus points, What might my friend's original proof have been and what exactly was his error, if any?)  I give my convergence proof below in two parts. In both parts, I define the sequence $a_n$ by $a_n=\frac{1^n+2^n+\cdots+(n-1)^n}{n^n}$ for all integers $n\ge 2$. First, I prove that $a_n$ is bounded above by $1$. Second, I prove that $a_n$ is increasing.   (1) The sequence $a_n$ satisfies $a_n&lt;1$ for all $n\ge 2$.  Note that $a_n&lt;1$ is equivalent to $1^n+2^n+\cdots+(n-1)^n&lt;n^n$. I prove this second statement by induction. Observe that $1^2=1&lt;4=2^2$. Now suppose that $1^n+2^n+\cdots+(n-1)^n&lt;n^n$ for some integer $n\ge 2$. Then  $$1^{n+1}+2^{n+1}+\cdots+(n-1)^{n+1}+n^{n+1}\le(n-1)(1^n+2^n+\cdots+(n-1)^n)+n^{n+1}&lt;(n-1)n^n+n^{n+1}&lt;(n+1)n^n+n^{n+1}\le n^{n+1}+(n+1)n^n+\binom{n+1}{2}n^{n-1}+\cdots+1=(n+1)^{n+1}.$$  (2) The sequence $a_n$ is increasing for all $n\ge 2$.  We must first prove the following preliminary proposition. (I'm not sure if "lemma" is appropriate for this.)  (2a) For all integers $n\ge 2$ and $2\le k\le n$, $\left(\frac{k-1}{k}\right)^n\le\left(\frac{k}{k+1}\right)^{n+1}$.  We observe that $k^2-1\le kn$, so upon division by $k(k^2-1)$, we get $\frac{1}{k}\le\frac{n}{k^2-1}$. By , we may find:  $$\frac{k+1}{k}\le 1+\frac{n}{k^2-1}\le\left(1+\frac{1}{k^2-1}\right)^n=\left(\frac{k^2}{k^2-1}\right)^n.$$  A little multiplication and we arrive at $\left(\frac{k-1}{k}\right)^n\le\left(\frac{k}{k+1}\right)^{n+1}$.  We may now first apply this to see that $\left(\frac{n-1}{n}\right)^n\le\left(\frac{n}{n+1}\right)^{n+1}$. Then we suppose that for some integer $2\le k\le n$, we have $\left(\frac{k}{n}\right)^n\le\left(\frac{k+1}{n+1}\right)^{n+1}$. Then:  $$\left(\frac{k-1}{n}\right)^n=\left(\frac{k}{n}\right)^n\left(\frac{k-1}{k}\right)^n\le\left(\frac{k+1}{n+1}\right)^{n+1}\left(\frac{k}{k+1}\right)^{n+1}=\left(\frac{k}{n+1}\right)^{n+1}.$$  By backwards (finite) induction from $n$, we have that $\left(\frac{k}{n}\right)^n\le\left(\frac{k+1}{n+1}\right)^{n+1}$ for all integers $1\le k\le n$, so:  $$a_n=\left(\frac{1}{n}\right)^n+\left(\frac{2}{n}\right)^n+\cdots+\left(\frac{n-1}{n}\right)^n\le\left(\frac{2}{n+1}\right)^{n+1}+\left(\frac{3}{n+1}\right)^{n+1}+\cdots+\left(\frac{n}{n+1}\right)^{n+1}&lt;\left(\frac{1}{n+1}\right)^{n+1}+\left(\frac{2}{n+1}\right)^{n+1}+\left(\frac{3}{n+1}\right)^{n+1}+\cdots+\left(\frac{n}{n+1}\right)^{n+1}=a_{n+1}.$$  (In fact, this proves that $a_n$ is strictly increasing.) By the monotone convergence theorem, $a_n$ converges.  I should note that I am not especially well-practiced in proving these sorts of inequalities, so I may have given a significantly more complicated proof than necessary. If this is the case, feel free to explain in a comment or in your answer. I'd love to get a better grip on these inequalities in addition to finding out what the limit is.  Thanks! Why does no line appear when using Interpolate Line in ArcMap? Suppose $f: \mathbb{R} \to \mathbb{R}$ is a continuous function which is 1-1, then does $f$ map Borel sets onto Borel sets? Adding arrows in curves How to handle UNABLE_LOCK_ROW errors when this is caused by a batch APEX job we are facing a serious issue. We have a batch APEX job running daily which makes updates on records fulfilling certain conditions. There is another job running parallel to this, in some cases updating or accessing to the same records than the batch job and hence, causing the error:     Update failed. First exception on row 400 with id XXX; first error:    UNABLE_TO_LOCK_ROW, unable to obtain exclusive access to this record or 200    records:   So, I had then read that in order to fix this kind of error you should use FOR_UPDATE in your select statement (records that have to be updated). The problem is, that you can not use FOR UPDATE for batch jobs. We tested this and effectively, we get the error:     System.QueryException: Locking is implied for each batch execution and   therefore FOR UPDATE should not be specified      It will however lock the records within each execution of execute. See   QueryLocator.getQuery()usage:      You cannot use the FOR UPDATE keywords with a getQueryLocator query to   lock  a set of records. The start method automatically locks the set   of records in  the batch.   Could you find a solution to this?. We would like to handle this in the code itself, because we don't have the permission to schedule the batch job for another time as the another job.