I'm having a hard time to figure out what is wrong with the follwoing MWE  \documentclass{article} \usepackage{amsmath} \begin{document} \begin{align*} \langle n,l',l_s',m',m_s'\vert H_{\rm SO}\vert n,l,l_s,m,m_s \rangle = \frac{1}{2m^2c^2 a_0^3n^3}\frac{\delta_{l'}^l}{l(2l+1)(l+1)} \left( &amp; \sqrt{l(l+1)-m(m+1)}\sqrt{3/4-m_s(m_s-1)}\delta_{m'}^{m+1}\delta_{m_s'}^{m_s-1}\\ &amp; \sqrt{l(l+1)-m(m-1)}\sqrt{3/4-m_s(m_s+1)}\delta_{m'}^{m-1}\delta_{m_s'}^{m_s+1}\\ &amp; (m+m_s)\delta_m^{m'}\delta_{m_s}^{m_s'} \right) \end{align*} \end{document}   It says that I forgot to close a bracket, but I fail to see where...
I have a very long equation that must be separated into two lines, and it has several pairs of nesting \left \right delimiters. Unfortunately, it seems that they need to be on the same line in order for them to work.  Also I'm using the align environment because I need the aligning functionality. Is there a way to have the size of delimiters automatically adjusted over multiple lines?
Is it possible to tell Google's Webmaster Tools that our site hosted on www. has moved to a sub folder, sub domain or a new domain with sub folder? Java is the key here. I need to be able to delete files but users expect to be able to "undelete" from the recycle bin.  As far as I can tell this isn't possible.  Anyone know otherwise? How to calculate Area Under the Curve (AUC), or the c-statistic, by hand Can anybody explain the necessity of the RC network shown in the figure. I found this in circuit for a logic power supply using Fly-Back converter? How does SQL Server handle logins when the user is a part of multiple groups with various privileges? I'm trying to wrap my head around how SQL Server decides to grant certain rights based on a users login privileges.  If a user is part of a group "READ ONLY" which has access to DB1, but they are also a part of a group "SysAdmin" which has full db owner rights to the same DB1, which rights are they given when they log in?  On a similar note. What if they are part of a group but also have a standalone account with other middle of the road privileges? Can the problem of unification of Quantum Mechanics and General Relativity be converted into a pure Mathematical problem? I mean to say, can you make someone understand the problem who only knows Mathematics, even if a Physics description is absent? I mean, describing the problem with unification using pure Mathematical formulation.  Can we make the problem seem as if it has nothing to do with the real world and describe it only as a problem of mathematics? Has anyone managed to get the Citrix receiver client (icaclient) working in Ubuntu? A compact Hausdorff space that is not metrizable Is there an example of a compact Hausdorff space that is not metrizable?  I was thinking maybe the space of continuous functions $f: X \rightarrow Y$ between topological spaces $X, Y$, might work, but I'm sure I'm missing some conditions. Suppose that $f(z)$ is analytic function in the disk $|z|\le R$ and $A(r)=\max_{|z|=r}Re(z)$ then prove that $r&lt;R$  $$\max_{|z|=r}\left|\frac{f^n(z)}{n!}\right|\le \frac{2^{n+2}R}{(R-r)^{n+1}}\{A(r)+|f(0)|\}$$  MY attempt   Using Cauchy generalized integral formula   $f^{(n)}(z_0)=\frac{n!}{2\pi i}\int _c\frac{f(z)dz}{(z-z_0)^{n+1}}$  then $\max_{|z|=r}\left|\frac{f^n(z)}{n!}\right|=\left|\max_{|z|=r} \frac{1}{2\pi i}\int _c\frac{f(z)dz}{(z-z_0)^{n+1}}\right|$  and i think we can solve by using Borel caratheodory theorem  Let $f(z)$ be holomorphic function on $|z|\le R$ and let $M(r)=\max_{|z|=r}|f(z)|$ and $A(r)=\max_{|z|=r}Re f(z)$ then  for $0&lt;r&lt;R$  $$ M(r)\le \frac{2r}{R-r}A(R)+\frac{R+r}{R-r}|f(0)|$$  from here how to processed ? How to install Windows 10 Home 19018 update? I'm using windows home edition, I have the latest update installed 1909.  I want to install docker for windows 10 home edition. It keeps saying  Docker Desktop requires Windows 10 Pro/Enterprise (15063+) or Windows 10 Home (19018+).  Should I join Windows insider? How long should I wait for that update to be released if I don't want to join windows insider? Is it possible to pagebreak aligned equations? The report I'm writting features a lot of long, multiple lines equations. To reduce visual polution I've been using an aligned environment nested inside equation. This way (unlike just using an align environment) I get only a single label for all the lines.  The problem is that so many long equations often need to be broken into two pages, otherwise I get lots of blank vertical space in the document. However the aligned environment does not allow the \displaybreak command.  Is there an alternative way to achieve a pagebreak inside an aligned equation?  Here's a sample ofthe equations I'm using  \begin{equation}     \begin{aligned}     ...\\     ...\\  %I need to pagebreak here     ...\\ \end{aligned}\end{equation} Pass C# ASP.NET array to Javascript array How to add a program as a startup application from a terminal? I am using Ubuntu 12.04 and I know the GUI way to maintain the startup program list but now I want to find out the way to add/remove startup applications using a command line interface (CLI). Why would you put Identity Increment other than 1 in SQL? If $E$ is a connected space, then so is $\overline{E}$. I have to prove that if $E$ is a connected space, then so is $\overline{E}$ (the closure of $E$) a connected space. I tried to prove the contrapositive. So suppose that $\overline{E}$ is not connected in a metric space $X$. This implies there are $A\subset X$ and $B\subset X$ such that $A\cap B=\emptyset$, $A\cap \overline{E}\neq \emptyset$, $B\cap \overline{E}\neq \emptyset$ and $\overline{E}\subset A\cup B$. I will try to prove that this $A$ and $B$ will also work for $E$. Suppose that $A\cap E=\emptyset$ and $B\cap E=\emptyset$, this implies that $A\cup B$ is a subset of the limit points of $E$, because $A\cap \overline{E}\neq \emptyset$ and $B\cap \overline{E}\neq \emptyset$. This contradicts the fact that $\overline{E}\subset A\cup B$, so we have to conclude that $A\cap E\neq \emptyset\neq B\cap E$. Since $E\subset\overline{E}\subset A\cup B$, we have that $E$ is also not connected.  My question is whether my proof is correct, because I have a little bit doubt. If it's not correct, what is the best I can do? Thanks in advance!   Edit1: The definition we use for a connected space $E$ in a metric space $X$ is that if $E$ is connected, then there are no open $A,B\subset X$ such that $A\cap B=\emptyset$, $A\cap E\neq \emptyset\neq B\cap E$ and $E\subset A\cup B$.  Edit2: $A$ and $B$ must be open. In the digital age of photography, we can see a range of digital camera sensors sizes in use, from 1/3.2" in small phones, up to Medium format sensors that are 53.4 x 40.0mm in size or more!  Why has no company endevoured to produce a sensor that can be considered to be large format (50mm X 80mm or larger)? Do such camera sensors exist in non-consumer products? test fails because of TestMethod do not support getContent call My below test fails because of Run Failures: TestRangehoodObjectionSheet.RangehoodObjectionSheetTest Methods defined as TestMethod do not support getContent call. I added the Blob thinking it might resolve but it doesn't work. What could be the problem here? Have I used the Blob correctly?  @isTest public with sharing class TestRangehoodObjectionSheet {      static testMethod void RangehoodObjectionSheetTest() {             String Build                = NBATRecords.getIdFromDeveloperName('Plan_Reviews__c','Building_Plan_Review');             Account a = new Account(Name = 'Test1' ,Type = 'Lead Acct',BillingState = 'CA',Industry = 'Business Services');             insert a;              Establishment_Record__c er = new Establishment_Record__c(Account__c=a.Id ,Project_Name__c = 'TestPreet',PremiseStreet__c='Manhattan ave',PremiseBorough__c='Manhattan',PremiseState__c='NY',PremisePostalCode__c='11102',Referral_Source__c='311',Data_Source__c='CAMIS',Phase__c='Initiate',Business_Status__c='Open' );             insert er;              Application__c ap = new Application__c(Establishment_Record__c=er.Id,Job_Number__c='222222222');             insert ap;              Plan_Reviews__c pr = new Plan_Reviews__c(Application__c =ap.Id ,DOB_Job_Number__c='222222222',RecordTypeId =Build,Objections__c='Pipe size not indicated');             insert pr;             PageReference pageRef = Page.RangehoodObjectionSheet;              Test.setCurrentPage(pageRef);               Blob content = Test.isRunningTest() ? Blob.valueOf('UNIT.TEST') : pageRef.getContent();              Plan_Reviews__c              p   = new Plan_Reviews__c(id=pr.Id);                ApexPages.StandardController sc  = new ApexPages.standardController(p);             System.assertNotEquals(sc,null);             RangehoodObjectionExtention    ext = new RangehoodObjectionExtention(sc);              ext.Savecopy();       } }   Actual class for the test:  public with sharing class RangehoodObjectionExtention { private final ApexPages.StandardController controller; private final Id                           planreviewID; public String imageURL{get;set;} public List&lt;String&gt; objlist {get;set;}  public string currentdate {get; set;}    public RangehoodObjectionExtention (ApexPages.StandardController stdController) {         controller   = stdController;         planreviewID = (Id)controller.getRecord().get('Id');         Date dt = Date.today();         currentdate = dt.format();         list&lt;Plan_Reviews__c&gt; prlist = [select FDNY_Objections__c from Plan_Reviews__c where id = :planreviewID limit 1];         string obj;         for(Plan_Reviews__c pr: prlist){            obj = pr.FDNY_Objections__c;             }         if(obj!=null){            list&lt;string&gt; objections = obj.split(';');             integer i =1;            objlist = new list&lt;string&gt;();            for(string o : objections){               objlist.add(i++ +'. '+o);            }         }         imageURL='/servlet/servlet.FileDownload?file=';         List&lt; document &gt; documentList=[select name from document where Name='RangehoodObjectionLogo'];         if(documentList.size()&gt;0)         {            imageURL=imageURL+documentList[0].id;         }       }          public PageReference Savecopy(){       PageReference p = Page.RangehoodObjectionSheet;       blob b = ApexPages.currentPage().getContentAsPDF ();       Attachment a = new Attachment();       a.body = b;       a.name = 'Rangehood Objection sheet Issued '+currentdate+'.pdf';       a.parentid = planreviewID;        insert a;        PageReference pref = new PageReference('/'+planreviewID);       return pref;    } } Is there a specific term for the association of certain verb(s) with certain nouns (as direct objects)? Or vice versa. Or perhaps a name for the pair itself?  For example:   hold an opinion make a complaint offer an apology   Also, where might I find a list of such pairs?    EDIT: I chose my title wording randomly. I have no idea whether 'cognate verb' is the correct term for these things. However, I've just found out that 'cognate objects' are a defined class in linguistics, so perhaps my choice of words was inappropriate. I'm going to leave the title as it is, anyway. What limits a motherboard from supporting more memory? My specific question is with the ASUS M3N78-VM motherboard that my home server uses. I currently have 4x2GB installed for a total of 8GB but I was hoping to upgrade to say 16GB (4x4GB). The official specifications of that motherboard says it only supports up to 8GB but it was released back when only 2GB sticks were available. What, if any, would prevent it from working with 4GB sticks now that 4GB sticks are available?  My general question is with motherboards in general... what would prevent a motherboard from working with bigger sticks if its all just the same type (DDR2 for example and same speeds) of memory? Different voltage characteristics of CMOS NAND gate for different connections Recently, I've played with a simple 2-input 1-output NAND gate realised in CMOS technology as shown in Fig. 1.     Fig. 1. CMOS NAND scheme.  I took some measurements of volteges U(output) vs. U(input). Using two independent voltage sources (constant high level Udd and Uin varying in 0-to-Udd range), I considered three different connection possibilities so to investigate all four input configurations. Those were:  a)  Input terminal A connected to Udd, input terminal B connected to Uin.  b)  Input terminal A connected to Uin, input terminal B connected to Udd.  c)  Both input terminals connected to Uin.  I've obtained following characteristics:    Fig. 2. CMOS NAND voltage characteristics with different connection methods.  As long as a difference between case c) and other cases I could have expected, I was surprised to see a) and b) differ as well. Could someone please explain to me why would changing voltages connection between A and B significantly changes threshold voltage of the gate? Is it a widely observed effect or have I just picked a defective NAND?