Why is $(x_i-\bar{x})^2$ in the formula for variance as opposed to $|x_i-\bar{x}|$?
Why is variance squared?
How can I calculate the number of work days between two dates in SQL Server?   Monday to Friday and it must be T-SQL. booting windows 10 spends too long Best way to clone an installation (copying to identical hardware) Kind-of like  but slightly different (I think), in that I have 6 identical Acer Aspire Revo R3610 machines. One is (almost) configured to my requirements - when I'm done preparing it I'd like to make the other 5 machines absolutely the same. I'm very new to Ubuntu, what's the most straightforward (easiest) way of doing this?  The machines are going to live on different networks if that might otherwise be a problem (eg with Windows you can clone disks but you then have to make registry changes afterwards if they're going to run on the same network etc). The hardware in all 6 machines is, I stress, the same!  How can I efficiently clone one source image on to these identical machines?  Please restrict one software/solution per answer How to see if certain representation of $SU(2)$ is symmetric/antisymmetric/mixed? I am looking at the tensor product of $n$ spin halfs (fundamental of $SU(2)$): \begin{equation} \left(\frac{1}{2}\right)^n = \frac{1}{2} \times \frac{1}{2} \times ... \times \frac{1}{2} = \frac{n}{2} + ... \end{equation} For example, for $n = 3$ \begin{equation} \frac{1}{2} \times \frac{1}{2} \times \frac{1}{2} = \frac{1}{2} \times \left(1 + 0\right) = \left(\frac{3}{2}\right)_1 + \left(\frac{1}{2}\right)_1 + \left( \frac{1}{2} \right)_0 \end{equation} where lower indexes on the right hand side specify from which tensor product representation came from. My question is how do I read off if a certain term on the right is a symmetric, antisymmetric or a mixed symmetry representation of $SU(2)$? I came up with two ways of approaching the problem.  First is Young Tableaux. As far as I understand rows of Young Tableaux correspond to symmetric indexes while columns to antisymmetric ones. So, for example, a diagram with just one row (like one that corresponds to the highest spin $\frac{3}{2}$ from the example - three boxes in a row) describes a totally symmetric representation. A diagram that has one column (maximum 2 boxes since we are dealing with $SU(2)$) describes totally antisymmetric representation. Everything that has both rows and columns is a mixed symmetry representation. Following this logic it looks like only the highest representation in the product can be totally symmetric, singlet is antisymmetric and everything in between has mixed symmetry. So, for the example \begin{equation} \left(\frac{3}{2}\right)_1: \text{symmetric rep}\\ \left(\frac{1}{2}\right)_{0,1}: \text{mixed symmetry reps}\\ \end{equation} Is this is a correct logic?  Another way to think about this is the following. Let's build representation the way we do in QM starting from the highest one, when all the spins are up. Then all components of the highest multiplet can be generated by applying lowering operators to the highest state. So, all the relative signs in the expressions are &quot;+&quot; and thus the highest representation is always symmetric as 1. also suggests. Then all the other representations must be constructed by writing down expressions orthogonal to components of the highest multiplet, so they will necessary get some &quot;-&quot; signs and as a result must be either antisymmetric or have mixed symmetry, but can not be totally symmetric.   Is this correct logic? Is it true that only the highest representation in the product can be symmetric and all the others have mixed symmetry or antisymmetric? In C++/CLI, what does the hat character ^ do? I was reading Ivor Horton's Beginning Visual C++ 2008 and many of its CLR examples have this definition for main:  int main(array&lt;System::String ^&gt; ^args)   I went back, page by page, to the beginning of the book to find the first such instance with an explanation what it really means, but couldn't find one.  Obviously it means the same as the standard int main(int argc, char *argv[]), but I'd like to know when and why that ^ is really used, and why it even exists (does it do something that pointers * and references &amp; cannot represent)? Cauchy principle value of $\int_{-\infty}^{\infty}\sin(x)/(x-a)dx$ Windows 10 stuck in install loop I was having a time getting my bootable USB 3, 32GB W10 install USB to be recognized. It recognized one time but I had to restart for something and it never came up again. I eventually removed all other boot up options to make it easier and faster to try again (no F12 needed).  Finally I gave up and tried another drive (16GB this time FWIW) and then it worked.  HOWEVER, it's stuck on a reboot loop now. I can choose to install, then to select the right disk, then it says it's loading file and then next thing I know it's saying do you want to install or upgrade. Why couldn't Bond have backup at the battle of Skyfall? I think I am missing a key plot point here.   Bond had to fake-kidnap M and bring her to Skyfall in order to lure Silva there for one last stand. Why did this have to be a secret from his colleagues at MI6? Why couldn't there have been other agents there to help defend the house and take down Silva?  Also, why did he have to have Q lay a fake trail to get Silva to follow him to Skyfall when he was actually going there, and he wanted Silva to follow him? A list of inconveniences between quantum mechanics and (general) relativity? It is well known that quantum mechanics and (general) relativity do not fit well. I am wondering whether it is possible to make a list of contradictions or problems between them?  E.g. relativity theory uses a space-time continuum, while quantum theory uses discrete states.  I am not merely looking for a solution or rebuttal of such opposites, more for a survey of the field out of interest. Convolution is uniformly continuous and bounded Suppose $f\in L^\infty(\mathbb{R})$ and $K\in L^1(\mathbb{R})$ with $\int_\mathbb{R}K(x)dx=1$. Show that the convolution $f\ast K$ is a uniformly continuous and bounded function.  The definition of the convolution is $(f\ast K)(x)=\int_\mathbb{R}f(x-y)K(y)dy$.   There is the inequality $\|f\ast K\|_\infty\leq\|f\|_\infty\|K\|_1$, which yields that $f\ast K$ is bounded. But what about uniform continuity? How do I configure swappiness? I got a situation where i need to invoke future method from batch class. And i know that it is not possible to do. But there might be some workarounds to achieve it, right? And i dont want to invoke future method using shedule apex as my requirement will hit governor limits of "Total number of schedule jobs exceed". So i tried in below ways, but still fighting with same issue.  My design is  Scenario 1 :   Schedule Apex ===> 2. BatchClass (Runs every hour) (Generates a map with "N" records for every batch context, and passes it to Future method in an apex class)  ===> 3. Future method ( then it will login to a salesforce account and generates an attachment and sends an email to a corresponding email address) .   Scenario 2 :  Since, It is not possible to invoke future method from batch, i tried implementing an apex class with a normal static method  invoking future method and in a batch class, for every context i.e., execute() method, it will invoke a normal method which in turn invokes future method, but still got the same error      FATAL ERROR: Future method cant be called from future or Batch   ie.,   global class BatchClass implements Database.batachable&lt;Sobject&gt; {    global Iterable&lt;ScheduledReport__c&gt; start(Database.BatchableContext BC)  {         query=[];        return query;  }  global void execute(Database.BatchableContext BC, List&lt;ScheduledReport__c&gt; scope) {      FutureClass.normalMethod(mapRecords);   }    global void finish(Database.BatchableContext BC){   }  }   Future Class:   global class FutureClass {  global static void normalMethod(Map&lt;&gt; mapR) {      futureMethod(mapR);  }  @future(callout=true)  global static void futureMethod(Map&lt;&gt; m) {      //some code;   }  }   Scenario 3 :  Instead of invoking future class method from batch i tried updating list of records and done checkbox value to true and i've implemented after update event trigger to get the all the records in which checkbox values are true and from trigger i tried invoking future method , still didnt work , i got an error      FATAL ERROR: Future method cant be called from future or Batch   Please help me out.   Thanks ! What are the advantages and limitations of dynamic type languages compared to static type languages?  See also:  (a far more argumentative thread...) Why does your reflection suddenly turn upside down while slowly walking away from a curved mirror? Many people should have realised, when looking into a concave curved mirror (or even a rather reflective spoon in that fact) at a close distance, you will see a slightly distorted reflection. But as you move further away, the image will suddenly become upside-down.  why is this? A map is continuous if and only if for every set, the image of closure is contained in the closure of image How do I mount a qcow2 disk image? Is Dishonored an open-world game? I was considering whether or not to buy Dishonored, and watching gameplay of it on Youtube, when a thought popped into my head: is Dishonored free-roam? Can you go anywhere you want, similarly to Fallout or The Elder Scrolls? Iterated self-composition of arbitrary function Does there exist some notation that represents the iterative composition of a single-input, single-output function with itself? As in, say, $f_5(x)=f(f(f(f(f(x)))))$.  In other words, going by the above (incorrect, I'm pretty sure) notation:  $f(x)=x+1$, $f_n(m)=m+n$  I'm looking for the correct way to express the notion of "$f_n(x)$" for any $f$. I saw a commercial on televison for preparing spaghetti without boiling the noodles, just place them in water for about on hour.  Can this be done? Last activity name still missing from migrated question