Where to put alias commands for use in Windows 7
Command aliases in Command Prompt?
While working in a Java app, I recently needed to assemble a comma-delimited list of values to pass to another web service without knowing how many elements there would be in advance. The best I could come up with off the top of my head was something like this:  public String appendWithDelimiter( String original, String addition, String delimiter ) {     if ( original.equals( "" ) ) {         return addition;     } else {         return original + delimiter + addition;     } }  String parameterString = ""; if ( condition ) parameterString = appendWithDelimiter( parameterString, "elementName", "," ); if ( anotherCondition ) parameterString = appendWithDelimiter( parameterString, "anotherElementName", "," );   I realize this isn't particularly efficient, since there are strings being created all over the place, but I was going for clarity more than optimization.  In Ruby, I can do something like this instead, which feels much more elegant:  parameterArray = []; parameterArray &lt;&lt; "elementName" if condition; parameterArray &lt;&lt; "anotherElementName" if anotherCondition; parameterString = parameterArray.join(",");   But since Java lacks a join command, I couldn't figure out anything equivalent.  So, what's the best way to do this in Java? I"m studying normalization and have been reading through descriptions and examples online. One Concept that isn't clear to me is if the process can be automated at any point. I understand that a system can't tell you if you schema makes any real-world sense, but it seems likely to me that if you feed a program some arguments say, the functional dependencies, it would be able to do some steps for you.  Say you have a relationship R(A,B,C,D)  and you tell your program that A,B->C and A->D and that the primary key is (A,B)  Now if my understanding serves me correctly it should be possible for a program to identify that A->D violates 2NF because D depends on A and A is a subset of the primary key. That the proper decomposition would be R1(A,B,C) and R2(A,D).   The main book i'm learning from and my instructor indicate these normalization's are done all by hand. Is this correct or can some parts be automated? Every Artinian ring is isomorphic to a direct product of Artinian local rings Proposition. Let $R$ be commutative ring with $1_R$. We assume that $R$ is an Artinian ring and $M_1,\dots,M_n$ its maximal ideals. Then         $R/\mathrm{Jac}(R)\cong (R/M_1)\times \dotsb \times (R/M_n)$.   The ring $R$ is isomorphic to the direct product of a finite number of Artinian local rings.      Proof. 1. It's obvious that $M_i+M_j=R,\ \forall 1\leq i \neq j \leq n$. So, from Chinese Remainder Theorem, we have  $$R/\bigcap_{i=1}^{n}M_i = R/\mathrm{Jac}(R) \cong (R/M_1)\times \dotsb \times (R/M_n),$$ as we wanted.    Since $R$ is an Artinian ring, we have $\mathrm{Jac}(R)^m=\{0_R\}$, for some $m\in \Bbb Z^+$. But,  $$\{0_R\}\subseteq M_1^m\dotsb M_n^m=(M_1\dotsb M_n)^m\subseteq (\bigcap_{i=1}^{n}M_i=\mathrm{Jac}(R))^m=\{0_R\}.$$ So, if we apply CRT we will take  $$R\cong R/\{0_R\}\cong R/M_1^m\dotsb M_n^m\cong (R/M_1^m)\times \dots \times (R/M_n^m).$$   Questions.   1) Are these thoughts complete and correct?  2) Why $R/M_i^m$ are artinian local rings?  3) Could you please elaborate some examples as an application? Suppose f is a function such that $f'(x) = \frac{1}{x}$ for all $x &gt; 0$. Prove that if $f(1) = 0, then f(xy) = f(x) + f(y)$ for all $x,y &gt; 0$  As stated above, how do i go about doing this question?   Hi all, i would like to apologize if the question is missing context or other details.   This question was part of my calculus tutorial. I was on the topic of application of differentiation when this question was given to me.  Thus far i have learnt about intermediate value theorem, mean value theorem, rolle's theroem, Fermat's thereom.  As of this point in my learning, i have not touched upon integration. The only reason why i accepted the answer with integration in it was because i understood it.  Thus i believe i am suppose to use one the few theorems that i've stated to solve this question. But i have no idea where to start.  At first i differentiated the equation $f(xy)=f(x)+f(y)$ with respect to x  i believed the answer to be $f'(xy)\frac{dy}{dx}=f'(x)+f'(y)\frac{dy}{dx}$  which would be $\frac{1}{xy}\frac{1}{x}=\frac{1}{x}+\frac{1}{y}\frac{1}{x}$  At this point a few questions came to my mind  1) am i suppose to differentiate the eqn in the first place 2) what has $f(1)=0$ got to do with anything 3) what theorem am i suppose to use to solve this question  This was my thought process throughout the question and i hope someone would point out my mistakes. Thank you Determining if an arbitrary point lies inside a triangle defined by three points? Is there an algorithm available to determine if a point P lies inside a triangle ABC defined as three points A, B, and C? (The three line segments of the triangle can be determined as well as the centroid if they are needed.)  Grid space is defined as Screen Space, that is, 2D Cartesian with the Y-Axis flipped so "up" is negative y and the origin is the upper left corner. I'm aware there are been several similar questions, and some great answers with hints on how to prove this, for example  and .  But I've never really seen a detailed proof of the absolute convergence of the Riemann zeta function in the half-plane $\Re(s)&gt; 1$.  I hope there's interest on a detailed proof of this for reference. Here is my attempt. Please, fill in any detail that might be missing, or point out any mistake!  On $\Re(s)=\sigma&gt; 1$, we have  $$\sum_{n=1}^{\infty}\bigg|\frac{1}{n^s}\bigg|=\sum_{n=1}^{\infty}\frac{1}{n^\sigma}$$  and  $$\frac{1}{n^\sigma}\leq\frac{1}{n^{1+\epsilon}}$$  for any $\epsilon &gt;0$, so by the direct comparison test, if   $$\sum_{n=1}^{\infty}\frac{1}{n^{1+\epsilon}}$$  converges absolutely, then so do $\sum_{n=1}^{\infty}|1/n^s|$ and $\zeta(s)$.  By the integral test, the convergence of $\sum_{n=1}^{\infty}1/n^{1+\epsilon}$ is equivalente to the finitude of the integral  $$\int_1^\infty \frac{1}{n^{1+\epsilon}}=\bigg[-\frac{1}{\epsilon x^\epsilon}\bigg]=\frac{1}{\epsilon}$$  which holds for any $\epsilon &lt; \infty$.  Any correction or improvement is welcomed! Thanks in advance. How do I restrict my kids' computing time? Access to our computer (not only to the internet) needs to be restricted for the accounts of my kids (7, 8) until they are old enough to manage this by themselves. Until then we need to be able to define the following:   the hours of the day when computing is o.k. (e.g. 5 - 9 pm) the days of the week when computing is not o.k. (e.g. mondays to fridays) the amount of time allowed per day (e.g. 2 hours)   In 11.10 all of the following that used to do the job don't work any more:   : for > 11.10 no more available through the ppa. : command line alternative, but from 11.10 removed from the repositories. : Looks great but repeatedly crashes to force restarting X-server. So we can't use or recommed this program at the moment.   Are there any other alternatives? Do downvotes on Meta truly mean something different? It is often said that voting on Meta means something different than voting on regular sites. Upvotes mean "I agree", and downvotes mean "I disagree".  However, I submit that this is not the case. Downvoting of a question has one effect in particular: censorship.  Once a question reaches -8 votes, it disappears from the front page. It can still be found; it isn't deleted. But all it takes is a net 8 downvotes for a question to be more or less lost without a direct link.  You might say that a net 8 downvotes obviously means that the community doesn't agree or want that. Well... does it? Particularly on polarizing issues, a question can temporarily get -8 votes as different people come online and see it. Maybe certain people with a certain belief all see it at once and downvote it a lot.  The front page is how most people find stuff they want to talk about, vote on, or answer. Removal from the front page means that most people will not find it without being pointed directly to it. Once a question hits -8, it is unlikely to be upvoted again. Edits will be irrelevant, new answers won't matter. The question is basically exiled.  The problem is that, on polarized topics, fast mass downvoting can quash any idea that is not popular with the most active members. After all, the most active members are the ones who are most likely to be online and see it. If a bunch of MSO regulars see it and downvote it, it goes away. Someone who checks MSO maybe once a day is less likely to be able to catch the question before it is exiled. This gives undue power to members who are most active on MSO, simply because they have more free time to spend on MSO.  I think this is a significant problem for polarized topics. It becomes very difficult to adequately discuss something that a significant number of active members dislike, even if the community at large doesn't mind.  Consider . It currently stands at +9/-8. Initially, in the first few hours, the question was heavily downvoted and even closed. However, after a day, it was upvoted and reopened.  This shows that a question can initially have a negative response, but later get a positive one. And you can check; any edits I did to the question were relatively minor. The question posted as is was initially negative, but ultimately positive.   If that -8 happened to all come first, odds are good that the +9 and the reopen would never have happened. Those 9 people would never have had the chance to weigh in on the subject. And that's wrong.  It is wrong for someone's potential vote to not matter just because they don't visit MSO multiple times in a day. It is wrong for someone's potential vote to not matter just because they have a different sleep schedule from many of MSO's members.  The problem is one of timing. Heavy dislike from active members who quickly see the question and downvote it can kill a question before someone who might upvote it ever even sees it.  I suppose the best suggestion would be to either lower the -8 threshold (or remove it altogether) or keep it from kicking in until 1-2 days has passed. If the question isn't active, it'll already be off the front page. And if it is active, then enough people will have seen it to know if the threshold represents a real consensus or just the fast-acting few. Compiling a document with PGFplots processing only every x-th data point? How do I replace multiple spaces with a single space in C#? How can I replace multiple spaces in a string with only one space in C#?  Example:  1 2 3  4    5   would be:  1 2 3 4 5 I observe the following strange characters ^@ in syslog at the time when my machine freezes.  Then i have to hardboot my machine.  What could be wrong any ideas?  Oct 12 12:20:52 nanak-P570WM anacron[1074]: Normal exit (1 job run) ^@^@^@^@^@^@^@^@^@^@^@^@^@^@^@^@^@^@^@^@^@^@^@^@^@^@^@^@^@^@^@^@^@^@^@^@^@^@^@^@^@^@^@^@^@^@^@^@^@^@^@^@^@^@^@^@^@^@^@^@^@^@^@^@^@^@^@^@^@^@^@^@^@^@^@^@^@^@^@^@^@^@^@^@^@^@^@^@^@^@^@^@^@^@^@^@^@^@^@^@^@^@^@^@^@^@^@^@^@^@^@^@^@^@^@^@^@^@^@^@^@^@^@^@^@  Oct 12 12:24:28 nanak-P570WM kernel: imklog 5.8.11, log source = /proc/kmsg started. Oct 12 12:24:28 nanak-P570WM rsyslogd: [origin software="rsyslogd" swVersion="5.8.11" x-pid="543" x-info="http://www.rsyslog.com"] start Explaining Infinite Sets and The Fault in Our Stars In watching The Fault in Our Stars I could not help but cringe at a line that flew in the face of mathematics and subsequently ruined the movie for me:     "There are infinite numbers between 0 and 1. There's .1 and .12 and .112 and an infinite collection of others. Of course, there is a bigger infinite set of numbers between 0 and 2, or between 0 and a million. Some infinities are bigger than other infinities." - John Green   While walking out of the theater I tried to explain to my friends why there were, in fact, exactly the same amount of numbers between 0 and 1 as 0 and 2, but Cantor and bijective functions are not great learning tools to English majors.  Does anybody have an eloquent or elegant way to enumerate this phenomenon using an example accessible to those not familiar with advanced mathematics? Series as an integral (sophomore's dream) Trying to find vehicles which are free between 2 variable dates Why do some Debian packages have a "+deb7u2" suffix? I figured the "7u2" part stood for "Debian 7.2" (aka "wheezy"). But I'm wondering if anybody knows the official answer as to why some packages have it and others do not.  Example:   The only time "+deb7u2" is appended to the version is when the package gets put in the "stable" release. Does this mean that's a "tag" to indicate a checkin to stable from another repo? While reading a book, I came across the word I'd've, as in:     I'd've argued against it.   While it was obvious what it meant, it left me puzzled. Is I'd've a proper word? What sort of cheat sheets for a new DM lead to a better flowing 5e game of Dungeons and Dragons? The question is, what elements on a DM screen are essential? I'm new at playing and DMing, altough a lot of experience watching games, just got a group to play with now. Started with the starter set in 5E and the Lost Mine of Phandelver adventure, however I've noticed the game can come to a stop when checking the rules or how to do something, while getting the books and stuff like that. So I thought to make a DM screen with some cheat sheets, of the most usual things new players, and new DM's have doubts on, and how to make the game flow well without long rule-checking breaks. What are the essential things to have on that screen? So far this is what I found  but not sure if it has all I need or so much stuff that'll also make the game stop a lot while cheking it out. How to update libavcodec on ubuntu 14.04? On Ubuntu 14.04.5 I just upgraded firefox to version 50.0; now there is a message on some pages which reads:   libavcodec may be vulnerable or is not supported, and should be updated to play videos   So how can I update libavcodec?  A simple   sudo apt-get install libavcodec   gives the following output:  Reading package lists... Done Building dependency tree        Reading state information... Done E: Unable to locate package libavcodec   So maybe I don't have libavcodec installed in the first place? So why do I get this message...? Prove that $$\nabla_{\mathrm X} \mbox{tr} (\mathrm A \mathrm X^{-1} \mathrm B) = - \mathrm X^{-\top} \mathrm A^\top \mathrm B^\top \mathrm X^{-\top}$$   My proof is below. I am interested in other proofs.    My proof  Let   $$f (\mathrm X) := \mbox{tr} (\mathrm A \mathrm X^{-1} \mathrm B)$$  Hence,  $$\begin{array}{rl} f (\mathrm X + h \mathrm V) &amp;= \mbox{tr} (\mathrm A (\mathrm X + h \mathrm V)^{-1} \mathrm B)\\ &amp;= \mbox{tr} (\mathrm A (\mathrm X ( \mathrm I + h \mathrm X^{-1} \mathrm V))^{-1} \mathrm B)\\ &amp;= \mbox{tr} (\mathrm A ( \mathrm I + h \mathrm X^{-1} \mathrm V)^{-1} \mathrm X^{-1} \mathrm B)\\ &amp;= \mbox{tr} (\mathrm A ( \mathrm I - h \mathrm X^{-1} \mathrm V + O (h^2)) \mathrm X^{-1} \mathrm B)\\ &amp;= \mbox{tr} (\mathrm A \mathrm X^{-1} \mathrm B) - h \, \mbox{tr} ( \mathrm A \mathrm X^{-1} \mathrm V \mathrm X^{-1} \mathrm B) + O (h^2)\\ &amp;= f (\mathrm X) - h \, \mbox{tr} ( \mathrm X^{-1} \mathrm B \mathrm A \mathrm X^{-1} \mathrm V ) + O (h^2)\end{array}$$  Thus, the directional derivative of $f$ in the direction of $\mathrm V$ at $\mathrm X$ is  $$D_{\mathrm V} f (\mathrm X) = - \mbox{tr} ( \mathrm X^{-1} \mathrm B \mathrm A \mathrm X^{-1} \mathrm V ) = - \mbox{tr} ( (\mathrm X^{-\top} \mathrm A^\top \mathrm B^\top \mathrm X^{-\top})^\top \mathrm V ) = - \langle \mathrm X^{-\top} \mathrm A^\top \mathrm B^\top \mathrm X^{-\top}, \mathrm V \rangle$$  and, lastly,  $$\nabla_{\mathrm X} \mbox{tr} (\mathrm A \mathrm X^{-1} \mathrm B) = - \mathrm X^{-\top} \mathrm A^\top \mathrm B^\top \mathrm X^{-\top}$$ How much marmelade can I bring into the US? I want to bring homemade berry marmelade in little glass jars with me to the US from Europe as gifts for friends. I have found the following site on importing foods into the US  and would assume that marmelade falls under the condiments category, which should be admissible. However, I am wondering however if there is any limit to how much one is allowed to bring. Will there be any issues if, say, I bring 3 kilograms (6 lbs 10 oz)?   Also on related note, would they be suspiscious when they see many glass jars in my bag? Do I risk getting my bag searched or getting asked what the jars are? Is there anything I can do to avoid any such trouble?