How do I know what the symmetry group of a Lagrangian is?
Is there a systematic way to obtain all conserved quantities of a system?
Why can't you use the keyword 'this' in a static method in .Net? I'm trying to use the this keyword in a static method, but the compiler won't allow me to use it.  Why not? $A$ and $B$ are $n\times n$ matrices and $A+B=AB$. I have an interesting proof that this implies $A$ commutes with $B$, but the proof only works when $||B|| \lt 1$. I'm looking for a way to salvage the proof so that it works for all $B$.  $$A=AB-B$$ $$A=(A-I)B$$ by repeatedly substituting $A$ with $(A-I)B$ on the RHS, $$A= (A-I)B^N - \sum_{i=1} ^{N-1} B^i$$  Since the space of $n\times n$ matrices is Banach (hence complete) under the standard operator norm, the limit $\sum_{i=1}^{\infty}B^i$ is well defined given $||B|| \lt 1$. Hence, taking the limit as $N \rightarrow \infty$, $$A =  -\sum_{i=1}^{\infty}B^i$$  Now the LHS commutes with B, hence so does the RHS.    Is there some trick to extend the method to work with any $B$ where $||B|| \geq 1$? I know that the result is true due to another simple algebraic proof, but I'd like to see if this method can be salvaged. Use of var keyword in C# After discussion with colleagues regarding the use of the 'var' keyword in C# 3 I wondered what people's opinions were on the appropriate uses of type inference via var?  For example I rather lazily used var in questionable circumstances, e.g.:-  foreach(var item in someList) { // ... } // Type of 'item' not clear. var something = someObject.SomeProperty; // Type of 'something' not clear. var something = someMethod(); // Type of 'something' not clear.   More legitimate uses of var are as follows:-  var l = new List&lt;string&gt;(); // Obvious what l will be. var s = new SomeClass(); // Obvious what s will be.   Interestingly LINQ seems to be a bit of a grey area, e.g.:-  var results = from r in dataContext.SomeTable               select r; // Not *entirely clear* what results will be here.   It's clear what results will be in that it will be a type which implements IEnumerable, however it isn't entirely obvious in the same way a var declaring a new object is.  It's even worse when it comes to LINQ to objects, e.g.:-  var results = from item in someList               where item != 3               select item;   This is no better than the equivilent foreach(var item in someList) { // ... } equivilent.  There is a real concern about type safety here - for example if we were to place the results of that query into an overloaded method that accepted IEnumerable&lt;int&gt; and IEnumerable&lt;double&gt; the caller might inadvertently pass in the wrong type.  var does maintain strong typing but the question is really whether it's dangerous for the type to not be immediately apparent on definition, something which is magnified when overloads mean compiler errors might not be issued when you unintentionally pass the wrong type to a method. Error: j_id0:j_id1:j_id28:j_id30: Validation Error: Value is required Does being denied entry to a country affect future travel to other countries? I was denied entry to India due to a visa technicality. I was advised by organisation I was travelling with to get tourist visa when I actually needed miscellaneous visa. Will this affect future travel to other countries if I have been refused once by a country, or if I want to re-enter India? I've lost my portal home, and I am invincible. How can I leave the nether? php loop through json array Minimum requirements of Ubuntu 20.10 Does anyone know what are the minimum requirements to install Ubuntu 20.10? I have this struct:  struct Map {     public int Size;      public Map ( int size )     {         this.Size = size;     }      public override string ToString ( )     {         return String.Format ( "Size: {0}", this.Size );     } }   When using array, it works:  Map [ ] arr = new Map [ 4 ] {     new Map(10),     new Map(20),     new Map(30),     new Map(40)};  arr [ 2 ].Size = 0;   But when using List, it doesn't compile:  List&lt;Map&gt; list = new List&lt;Map&gt; ( ) {     new Map(10),     new Map(20),     new Map(30),     new Map(40)};  list [ 2 ].Size = 0;   Why? Rate limit suggested edits We need a hard rate limit on suggested edits, to limit the damage someone can do with blasting the review queue with minor edit suggestions.  Case in point:  peppered the site with a whopping 133 tag-only edit suggestions in 2 hours and 15 minutes. That's one edit every minute on average, but towards the end he was entering a new suggestion every 20 seconds. He only stopped because a  drew enough rejections to have him banned from entering more.  If there was a limit to the number of suggested edits you can enter in a time period we could have stopped this guy earlier. No &lt;2k user needs to edit hundreds of tags across that many questions in 2 hours time.  Considerations   There are cases where a retag drive or tag burninate justifies editing a larger number of posts, but I'd be fine if such tasks were limited to people with 2k+ reputation. A retag or burninate job requires a minimal engagement with the community to know when they are justified anyway. The suggested edit review process, by itself, was clearly not enough to stop this barrage. It cannot be seen as a rate limiting measure, at least not as a sufficiently efficient one.  The vast majority of the edits made in the above example were too minor, leaving spelling, grammar and formatting mistakes in the post untouched. The user was going too fast to pay attention to such details anyway. Yet this user has 98 approved edit suggestions, but all but 6 or 7 I'd have rejected as too minor, so the review process itself is broken.   What should be limited   The number of review votes reviewers have is already limited; I burned through 20 reviews in short order just reviewing the suggestions from just this one user. Certainly the number of unreviewed suggestions should be limited to let reviewers catch up with a user like this. I'd say having 20 outstanding suggested edits pending review is plenty. Suggested edits should be made with some consideration; we don't want minor edits, so if you are suggesting more than 20 in an hour (that's 1 every 3 minutes) you are not improving posts anymore, you are gaming the system to gain reputation. How to check that a cubic polynomial is irreducible? How to prove that $a \cdot b$ is not divisible by 5 for $\frac{1}{1} + \frac{1}{2} + ... + \frac{1}{99} + \frac{1}{100} = \frac{a}{b}$? How do I get started working with JSON in Apex? This is a canonical question and answer developed by the community to help address common questions. If you've been directed here, or your question has been closed as a duplicate, please look through the resources here and use them to shape more specific questions. To browse all canonical questions and answers, navigate to the  tag.  This question and answer is owned by the community! If you can improve it and make it more useful, you're welcome to edit it.  I have a specific JSON structure in mind. I need to either deserialize this structure that's coming in from a web service, or I need to serialize data into this structure to transmit it to another system. How should I get started on this project in Apex? PHP regex delimiter, what's the point? Is there console mode in Mac OS X? In unix/linux, any number of consecutive forwardslashes in a path is generally equivalent to a single forwardslash. eg.  $ cd /home/shum $ pwd /home/shum $ cd /home//shum $ pwd /home/shum $ cd /home///shum $ pwd /home/shum   Yet for some reason two forwardslashes at the beginning of an absolute path is treated specially. eg.  $ cd ////home $ pwd /home $ cd /// $ pwd / $ cd // $ pwd // $ cd home//shum $ pwd //home/shum   Any other number of consecutive forwardslashes anywhere else in a patch gets truncated, but two at the beginning will remain, even if you then navigate around the filesystem relative to it.  Why is this? Is there any difference between /... and //... ? I have a directory that I am trying to clean out that contains both files and subdirectories.  What I am trying to do is simple: move all the files into another directory, but leave all the sub-directories as they are.  I am thinking something like:  mv [*_but_no_dirs] ./other_directory   It seems like there should be a simple way to do this with wildcards * and regex...  Anyone have ideas? Is it considered normal to publish job offers inviting candidates to apply based on their gender and/or race in academia? I was browsing PhD position offers in Europe on different websites and I was quite surprised to find that several offers contained sentences such as     University of X value equality and diversity. We strongly encourage women and BAME applicants for this position.    where BAME stands for Black, Asian and Minority Ethnicities; or     The research group aims to increase the number of women in scientific positions. Female candidates are therefore encouraged to apply.   Is it considered normal in the academic environment to discriminate between  candidates according to their race and/or gender for "egalitarian" reasons?   How is the choice of a candidate based on their gender and/or race considered "egalitarian"? How can I stop the Devel module from generating blog/forum entries for Anonymous user? I'm using Devel's generate content feature to generate Blog/Forum entries for a site I'm working on and funny enough, I get to have a blog post by an anonymous user or forum topic by an anonymous user.  How can I stop Devel from doing this? I've only given Authenticated Users/ Administrators the permission to create a blog post or forum topic but still it generate for anonymous user. How can correct this? I'm using LyX and a custom class from  which is based on the  class.  I'm at another school and my advisor wants me to include titles of the readers on the signature page as well as a date line for each signator.  I've looked through some documentation on the thesis class and poked around in the .cls file in use but didn't come across anything obvious to change.  Perhaps this section would help though?  \newcommand*{\th@degreeyear}{\number\the\year} \newcommand*{\th@signature}[1]{ \begin{center}     \normalsize     \vspace*{16mm}  % works well?     \vrule width 80mm height 0.2mm\\     #1 \end{center} } \newcommand*{\th@dateline}{ \vspace*{9mm} \begin{flushright}     Date~{\vrule width 35mm height 0.2mm} \end{flushright}   How do I include this?