Lagrangian symmetry condition
Symmetry condition for continuous coordinate transformations
What is the difference between user and service account? Deriving Chinese Remainder Theorem from gcd Bezout identity We want to find the solution $x$ to the congruence system  $$\begin{align} x &amp;\equiv r_1 \!\!\!\pmod{\!m_1}\\ x &amp;\equiv r_2 \!\!\!\pmod{\!m_2}\end{align},\ \ {\rm where}\ \  \gcd(m_1, m_2) = 1$$  These can be rewritten as  $$\begin{align} x &amp;= r_1 + m_1 j\\ x &amp;= r_2 - m_2k\end{align}$$  for unknown integers $j, k$. So we set those two equations as equal and rearrange them to  $$m_1j + m_2k = r_2 - r_1$$  Now assume we perform $\text{egcd}(m_1, m_2)$, which gives us the solution to  $$m_1u + m_2v = \gcd(m_1, m_2)$$  Let the integer $\,h\,$ make $\,h \gcd(m_1, m_2) = r_2 - r_1$.  Then $\qquad hm_1u + hm_2v = h\gcd(m_1, m_2) =  r_2 - r_1 = m_1j + m_2k$  At this point I am lost because I don't think we can just assume  $hm_1u = m_1j$ and extract $j = hu$.   How do I get the values of $j$ or $k$ so I can get the value of $x$? 100 apples are/is considered as a large number of apples Limit of a function with powers (L'Hopital doesnt work) I have a little problem with limit of this function:  $\lim_{x \to \infty} x^2(2017^{\frac{1}{x}} - 2017^{\frac{1}{x+1}})$  I have tried de L'Hopital rule twice, but it doesn't work. Now I have no idea how to do it. If I traceroute to my server via a bunch of different methods, the external ip seems to not work. However the server is online and accessible by this ip.  Localhost:  michaelxu@michaelxu-server:~$ traceroute 127.0.0.1 traceroute to 127.0.0.1 (127.0.0.1), 30 hops max, 60 byte packets  1  localhost.localdomain (127.0.0.1)  0.120 ms  0.069 ms  0.064 ms   Internal Ip:  michaelxu@michaelxu-server:~$ traceroute 192.168.1.3 traceroute to 192.168.1.3 (192.168.1.3), 30 hops max, 60 byte packets  1  michaelxu-server (192.168.1.3)  0.122 ms  0.065 ms  0.067 ms   External IP:   michaelxu@michaelxu-server:~$ traceroute 24.24.174.153 traceroute to 24.24.174.153 (24.24.174.153), 30 hops max, 60 byte packets  1  * * *  2  * * *  3  * * *  4  * * *  5  * * *  6  * * *  7  * * *  8  * * *  9  * * * 10  * * * 11  * *^C michaelxu@michaelxu-server:~$   ...it contines all the way to 30 ... the same thing happens if I traceroute it through the dns server  It also occurs if i do it from another online service:     Tracing route to cpe-24-24-174-153.socal.res.rr.com [24.24.174.153]...  hop rtt rtt rtt     ip address  fully qualified domain name 1   1   1   1       70.84.211.97    61.d3.5446.static.theplanet.com 2   0   0   0       70.87.254.5 po101.dsr02.dllstx5.networklayer.com 3   0   0   1       70.85.127.109   po52.dsr02.dllstx3.networklayer.com 4   0   0   0       173.192.18.230  ae17.bbr02.eq01.dal03.networklayer.com 5   0   0   0       66.109.9.97 ae-11-0.pr0.dfw10.tbone.rr.com 6   41  40  39      66.109.6.208    ae-6-0.cr0.dfw10.tbone.rr.com 7   39  39  40      66.109.6.0  ae-3-0.cr0.lax30.tbone.rr.com 8   37  39  39      66.109.6.65  9   42  40  39      72.129.9.3  agg1.lamrcadq-ccr02.socal.rr.com 10  36  36  35      72.129.10.73     11  53  60  49      24.24.209.18    ge17-0-spsdca1-ars1.socal.rr.com 12  *   *   *            13  *   *   *            14  *   *   *            15  *   *   *          What do the * * * mean? Is there any way to "fix this" How to Query all opportunities ids from account I write a sample query to fetch account Ids from cases of a particular record type.Then i wrote another sample query parent to child relationship to fetch opportunity ids from accounts.  My sample code  List&lt;Case&gt; c=new List&lt;Case&gt;(); c=[Select Id,accountId from case where RecordTypeId = '01290000000sF3L']; List&lt;Id&gt; accountIds= new List&lt;Id&gt;(); List&lt;Account&gt; accounts=new List&lt;Account&gt;(); List&lt;Opportunity&gt; opps=new List&lt;Opportunity&gt;(); for(Case cl:c)  { accountIds.add(cl.accountId); } accounts=[Select Id,name,(select Id,name from opportunities) from account        where Id in:accountIds]; System.debug('Data in accounts '+accounts);   But my issue is how to get opportunity id from above Soql accounts means how to add those opportunity id's to the list.  for(Account ao:accounts) { //How to fetch Opportunity ids from above account list. } Cant find the solution when sorting an array in JavaScript Mathematical expression to form a vector from diagonal elements I would like to know is there any way to express mathematically (using matrices multiplication, addition, etc.) a vector which is formed from the diagonal elements of a matrix. For example, I have a matrix called $\mathbf{M}$ and I want to create a vector  $\mathbf{v}$ such that $\mathbf{v}= \text{diagonal elements of } \mathbf{M} $  Any matrix algebra or operation do that ? Thank you. How does an arcane focus work with an Eldritch Knight? My PC is an Eldritch Knight. I was wondering what is an Arcane Focus? Do I need to have it in my hand? If I get the War Caster Feat does my arcane focus become obsolete? Counting inversions in an array I'm designing an algorithm to do the following: Given array A[1... n], for every i &lt; j, find all inversion pairs such that A[i] &gt; A[j]. I'm using merge sort and copying array A to array B and then comparing the two arrays, but I'm having a difficult time seeing how I can use this to find the number of inversions. Any hints or help would be greatly appreciated. Is there an overall view of your cities? Run a program without administrative privileges in Windows 7 My account in Windows 7 is an administrator account. When I open the Run box (WinKey + R), I am warned, "This task will be created with administrative privileges."    Is there any way to run programs as myself, but without administrative privileges when logged in as an administrator? Hiding some slides in student handouts in Beamer I am preparing lecture slides for a class. I would like to hide some of the slides from the students. As an example, I would like to be able to compile students.pdf which has only student slides 1 and 2 (i.e., "teacher slide" is hidden); but teacher.pdf which has all three slides.  \documentclass{beamer}  \begin{document}  \begin{frame}{Student slide 1} blah blah blah \end{frame}  \begin{frame}{Teacher slide} secret stuff not to be shared with students \end{frame}  \begin{frame}{Student slide 2} blah blah blah \end{frame}  \end{document}   How would I do this in beamer? In a regular document, e.g., article, I would use the comment environment.  I feel that the approach in  is overkill for my needs. Can anybody please help me to prove this:  Let $p$ be greater than or equal to $1$. Show that for the space $\ell_p=\{(u_n):\sum_{n=1}^\infty |u_n|^p&lt;\infty\}$ of all $p$-summable sequences (with norm $||u||_p=\sqrt[p]{\sum_{n=1}^\infty |u_n|^p}\ )$, there is an inner product $&lt;\_\,|\,\_&gt; $ s.t. $||u||^2=&lt;u\,|\,u&gt;$ if and only if $p=2$. What does "65" mean? Possible Duplicate:          I tried to color only a cell of my table but I don't know how do it. I found the method to color an entire row.How could I color only a cell of my table of a precise color? Review Audit failed when "late answer" answer is a duplicate I just got a review audit where the "late answer" was a duplicate of the accepted answer, but flagging it on that basis failed the review. That seems like a bug to me.  Question here:   I found that by clicking the question to view the entire Q&amp;A, and noticed that the copy was from a generic "user12345" account (probably with 1 rep as well) and the original from a real-looking account. Viewing the whole Q&amp;A is often useful when reviewing, especially late answers (which are often repeats of earlier points, disagreements with those, or random addendums better submitted as edits). I looked at the duplicate and thought "weird, rep harvesting maybe?" so I clicked "needs moderator attention" and wrote "copy and paste of accepted answer". FAIL!  I think that this review type can't ever work, because to avoid the problem I found you'd need to make up whole new "late answers" which by definition the review bot can't know anything useful about. Either that or to pass you'd just need to take any action at all, including upvoting the original of the duplicated answer. Which I didn't do, BTW, because I had no idea or opinion about the question or answer.  (this is not a duplicate of "What are review tests", it predates that and focuses on a particular defect within the process. See the comments below). Newer "mainline" versions of the kernel are available from the , e.g. 3.4 and 3.5, while Ubuntu 12.04 is on 3.2.   What are the mainline kernels? Are they better than my existing kernel? What are the pros and cons of upgrading to a mainline kernel? Will I easily be able to go back? ZIP Code (US Postal Code) validation I thought people would be working on little code projects together, but I don't see them, so here's an easy one:  Code that validates a valid US Zip Code. I know there are ZIP code databases out there, but there are still uses, like web pages, quick validation, and also the fact that zip codes keep getting issued, so you might want to use weak validation.  I wrote a little bit about zip codes in a side project on my wiki/blog:    There is also a new, weird type of zip code.     I can do the javascript code, but it would be interesting to see how many languages we can get here. How to get the IPV4 address for an interface from /proc Is there a clean, simple way to get an IP address for a network interface from /proc, similar to the way I can get the MAC address for a network interface? Ideally I would just type cat /proc/&lt;foo&gt;/{interface_name} and get the IPv4 address.  I'd rather not run anything other than cat.