Imagine we have a wave with a certain frequency. We can calculate the energy of this wave with the equation  $E=hf$, where $h$ is the Planck constant and $f$ the frequency  Now, we can create a second wave, with the same frequency but a phase of $\pi$, so when we add the two waves they cancel out.  However both waves have positive energy, so their energies should add up, giving twice the energy.  In reality, the waves might not perfectly cancel, giving a residual with the added energy of the two waves, but in a pure conceptual design, how can "nothing" have energy?  Or am I missing something?
What happens to the energy when waves perfectly cancel each other (destructive interference)? It appears that the energy "disappear" but the law of conservation of energy states that it can't be destructed. My guess is that the kinetic energy is transformed into potential energy. Or maybe it depends on the context of the waves where do the energy goes? Can someone elaborate on that or correct me if I'm wrong?
Graduate student in or of? In my cover letter I want to write that I am a graduate student in statistics. But I am not sure about the "in". So what is correct?     I am a graduate student in statistics.      I am a graduate student of statistics. When I look in sys.sql_logins, I see a column called is_policy_checked. Can I trust that my password policy has been checked for all of the logins where this column value is 1? gedit "cannot open display" , on remote computer , using ssh - Ubuntu 12.04 Possible Duplicate:          I am getting the following error message when using ssh to log into a remote machine:      gedit: cannot open display   I am using ssh in - Ubuntu 12.04. When I use the mobile app to vote for an answer that was awarded a bounty,  the bounty is no longer shown until I reload the answers. How OPTIONS are settled can be an eye opener and I hope I can get some answers The only reason why I put it here is to find out whether I am a victim or just ignorant of the way brokers deal with option positions that were exercised. Whether I am a victim or just ignorant depends on the answer that I posted here. The facts are: I had a 2 SHORT QS Option at 75 which was exercised against me on the 23 Dec 00.45 AM and I later exercised my 2 LONG QS Option at 70 on 23 Dec 9.31 AM. The broker charged me Borrow Fee for 24-27 Dec for $1102, which means instead of getting $1000 profit I turn this into a loss of $102 plus comm. My question:  Since both long and short options were exercised on the same day one at 45 mins on 23 Dec and the later at 9.31 am on the same day, how can there be a SHORT POSITION in the stocks since both are net-off in my account ?  The answer I got from my broker and this is the point that I want to clarify.  The response I got from IB was that the initial exercise at 45 mins on 23 Dec was actually on 22 Dec (not 23 as I alleged). They refused to show me how they got 22 Dec.  This is my explanation to my Broker in reply.  Even if the short call and long call was exercised on different dates 22 and 23 Dec respectively, IB can only charge me for the SHORT position for one day and not from 24-27 Dec by ignoring my long call position was not there.  Further Facts:  My Broker ignored my answer and insisted the dates are correct and therefore I was charged to borrow shares that was need to satisfy the short position on exercised. So I am lost as I do not know whether the broker is correct and they can do this by ignoring my long call position after exercised or there is something they had not tell me. That is the reason I came to this site soliciting answers from those who know more than I do or had experienced the same.  I hope I have explained this clearly now and why would I want to give an opinion when I am looking for an answer ? When needing to ask a professor about something important and potentially delicate, what is an appropriate way to phrase the question or write the email?  Examples include:   Requesting a recommendation letter Asking for exceptions to policy (e.g., ignoring a course prerequisite, rescheduling an exam) Asking if you can do research with them, join a group, get into a program Scheduling a meeting, exam, or defense Letting them know about a change of plans Letting them know about a life event affecting your work or studies (e.g., wedding, funeral, sickness, vacation) Extra Backslash Required in First Appended Newline in sed How do you normalize a zero vector Prove that $f(x)$ is irreducible iff its reciprocal polynomial $f^*(x)$ is irreducible. This is what I'm trying to prove:     Let $f(x)\in\mathbb{Q}[x]$ and $\deg(f(x))&gt;1$. Prove that $f(x)$ is irreducible in $\mathbb{Q}[x]$ iff its reciprocal polynomial $f^*(x)$ is irreducible in $\mathbb{Q}[x]$.    Note: The reciprocal polynomial $f^*(x)=x^nf(1/x) \in \mathbb{Q}[x]$, where $n=\deg f$.   So my thoughts are to prove the contrapositive, i.e. $f^*(x)$ is reducible iff $f(x)$ is reducible.   So to prove the ($\Rightarrow$) direction I assume that $f^*(x)=g(x)h(x)$, so I get that $g(x)h(x)=x^nf(1/x)$ which implies $f(1/x)=(1/x^n)g(x)h(x)$. I want to say this somehow makes $f(x)$ reducible but I am unable to proceed as $f(1/x)\notin \mathbb{Q}[x] $. I thought about substituting $y=1/x$, which gives $f(y)=y^ng(1/y)h(1/y)$, but I am unable to show that this is irreducible in $\mathbb{Q}[y]$. If I could, then it would be irreducible in $\mathbb{Q}[x]$ since $\mathbb{Q}[y]\cong \mathbb{Q}[x]$   Any suggestions or hints will be appreciated. Drop or change automatic migration-rejection based on non-existing tags I believe this feature creates more issues than it solves and thus would like to see it gone. (This is an out-growth of , which I repost here as it concerns several/all sites.)  The main reason why I think so is that there can be numerous reasons other than the subject being off-topic why some tag does not exist on some site, for one thing it could be a spelling, typesetting, or other formalistic reason. For example, for the two sites I know best MathOverflow and Mathematics hardly any of the most popular tags have a strictly matching tag on Mathematics but only because on MO there is the convention that certain tags are formatted in a specific way, which is not in place on Mathematics (for example nt.number-theory vs number-theory).  On top of that a user choosing the wrong site in the first place is likely not too well aware of the tags of the site they are posting too so that the question might be poorly tagged in the first place.         There is an additional detail I do not understand (it is obsolete if the actual request should be followed but in case it is not):   Even if on the source site a tag has a synonym and that synonym exists as a tag on the target site the migration is rejected. I do not understand the logic behind this at all. Possibly this is just an oversight.   I could also think of some other ways to improve the process while keeping the idea, but since I believe that it is best dropped I do not (yet) elaborate on this. Changing Login Logo After modifying the code in my functions.php file to display a different logo on my login page, I'm getting a blank square instead.  I've added a custom .png image (326x67) to my (child) theme's image folder, and the code I've added to functions.php is as follows:  function custom_loginlogo() {     echo '&lt;style type="text/css"&gt;     h1 a {background-image: url('.get_bloginfo('template_directory').'/images/login_logo.png) !important; }     &lt;/style&gt;'; } add_action('login_head', 'custom_loginlogo');   Could it be a permissions problem (like an .htaccess file blocking the image)? What would I prefer - an over-fitted model or a less accurate model? Let's say we have two models trained. And let's say we are looking for good accuracy.  The first has an accuracy of 100% on training set and 84% on test set. Clearly over-fitted. The second has an accuracy of 83% on training set and 83% on test set.   On the one hand, model #1 is over-fitted but on the other hand it still yields better performance on an unseen test set than the good general model in #2.   Which model would you choose to use in production? The First or the Second and why? I am relatively fresh to the DI party and am struggling to get my head around how exactly to use Dependency Injection. I understand that I can pass requirements as part of a service, but what about in my own class?  Say I have the below class where I want the language manager service to be injected:  class Foo implements ContainerInjectionInterface {    protected $languageManager;     public function __construct(LanguageManagerInterface $languageManager) {     $this-&gt;languageManager = $languageManager;   }    public static function create(ContainerInterface $container) {     return new static(       $container-&gt;get('language_manager')     );   } }   When I call new Foo() I am required to pass an instance of LanguageManagerInterface. That makes sense in terms of a normal constructor method, but that would require me to instantiate the class like the below:  $languageManager = \Drupal::service('language_manager'); $foo = new Foo($languageManager)   That just doesn't feel right to me.  Is there something I am missing, or would this class always have to be a service to take advantage of dependency injection? I've taken multivariate calculus and am wondering if I can see a specific function where the order of taking the partial derivative matters. I've been told that there are some exceptions where $ \dfrac{\partial ^2 f}{\partial x \partial y} \ne \dfrac{\partial ^2 f}{\partial y \partial x} $, so I'm curious to see what this looks like.  EDIT: And why would this true? How can i make my Java Swing GUI Components [Right To Left] for Arabic language from NetBeans Desktop Application? I have three partitions on my drive, arranged something like the following:   ___________ | 1 |  2 | 3| -------------   I wish to merge partitions 1 and 3.  Is there a way to do this, or do I have to manually "slide" partition 2 over to partition 3, and then merge the newly open space where partition 2 used to be?  Note: I do not have the space to copy partition 2 to partition 3 (2 is 200GB and 3 is 65GB). I am wondering how to recreate some kinds of effects (you can easily do in Photoshop) in Blender.  I want to create the gradient textures like ones pictured below, should I render objects and blur them in compositor? Or can I achieve it using only material nodes? Self-Contained Proof that $\sum\limits_{n=1}^{\infty} \frac1{n^p}$ Converges for $p > 1$ To prove the convergence of the p-series   $$\sum_{n=1}^{\infty} \frac1{n^p}$$  for $p &gt; 1$, one typically appeals to either the Integral Test or the Cauchy Condensation Test.  I am wondering if there is a self-contained proof that this series converges which does not rely on either test.    I suspect that any proof would have to use the ideas behind one of these two tests. 'pyrcc5' is not recognized as an internal or external command I installed QGIS 3.0 on Windows 10. I get this error everytime i run the pyrcc4 or pyrcc5 command:  'pyrcc4' is not recognized as an internal or external command  Even if I find a place with a pyrcc4.exe file or a place with apyrcc5.bat file and add the path to the environment variables I get the same error. In the previous installation of osgeo4w i had a pyqtdev folder or something similar appear I think it was on C/. Was there supposed to be such a folder, do I need to download pyqt separately? Looking for qt-at-spi for ubuntu 20.04