For Lie algebra $L$ with root $\alpha$, show that if $x \in L_{\alpha}$ then ad$x$ is nilpotent
Rootspaces are $\mathop{ad}$ nilpotent
Django - specify which model manager Django admin should use Does decrease in temperature affect mass $E=mc^2$? My understanding of Quantum physics and String Theory is very basic and I don't yet have a grasp on the maths, but in my research I have come up with a question.  Does a decrease in temperature also signify/create a decrease in mass?  I am quite willing to believe the concepts I think I am beginning to understand are totally misconceptions on my part.  But, as I see it mass is a product/mark of disruption to the Higgs field as a particle moves.  If these particles are ultimately composed of vibrating Strings, their mass is given by the rate at which they vibrate and how it interacts with the Higgs field.  I don't have any idea if, as the temperature (as we know it) approaches 0k, the string/quark/sparticle would change its state in any way or if the changing of the state of the String would change what type of particle it represents.  It seems I'm more full of questions than answers, but that's why I love these topics!  I know what I'm learning is new if the best and brightest are still working on the 'basics' to just make their systems work :). How many Valyrian steel swords are there at the beginning of GoT, and who owns them? Get the subdomain from a URL Getting the subdomain from a URL sounds easy at first.  http://www.domain.example   Scan for the first period then return whatever came after the "http://" ...  Then you remember  http://super.duper.domain.example   Oh. So then you think, okay, find the last period, go back a word and get everything before!   Then you remember  http://super.duper.domain.co.uk   And you're back to square one. Anyone have any great ideas besides storing a list of all TLDs? In the Avengers movie, was Thor going to kill Captain America during his woods battle with Iron Man? I was using , implemented in scikit-learn, for my research work. But I have no good understanding of this.   Can anyone please give a simple, good explanation of one class SVM? Can I have multiple primary keys in a single table? Can I have multiple primary keys in a single table? In class we've seen that $a$ (the weights) must satisfy $$X^T (y-Xa) =0$$  Here $X$ is a $(n\times d)$ matrix (so we have $n$ samples in $\mathbb R^d$)  let's denote the residuals $r = y-Xa$. In our class notes, it is written that     The normal equations require the residuals to be orthogonal to each of the columns of $X$.   Why?     Therefore, the solution of the linear regression is a projection of $y$ onto the subspace spanned by $v_1 , \ldots , v_d$ (the columns of $X$)   Can you please explain this? Can I disable full-disk encryption? I recently installed Ubuntu 12.10 and it requires a passphrase to boot up (I installed it with an encrypted file system).  Do I have to reinstall to change to a standard unencrypted file system? Why did a Dementor try to take Harry's soul in the train? In "Harry Potter and the Prisoner of Azkaban" - when Harry and his friends were travelling to Hogwarts by train, the train stopped in between and Dementors were searching for Sirius Black. Why did one of the Dementors try to take Harry's soul? Should I use Yes/No or Ok/Cancel on my message box? Semantically, the Yes/No buttons are roughly equivalent to the Ok/Cancel buttons, but in general what would you recommend to use? Should I always use Yes/No or always use Ok/Cancel? Or does it depend on the case? I am trying to prove the matrix norm equivalence for norms 1, 2, $\infty$ and Frobenius.  I have managed to solve find the constants for $||.||_{1}$ and  $||.||_{2}$ but I cannot see how to continue if I want to prove the following:  $||A||_{\infty} \leq \sqrt{n}||A||_{2}$   and the ones for Frobenius:  $||A||_{F} \leq \sqrt{n}||A||_{1}$  $||A||_{F} \leq \sqrt{n} ||A||_{2}$  Any help is appreciated. Thank you for your time Why does work depend on distance? Site hosted on EC2 / Amazon held hostage with private key I have a new client whose previous developer has left her high &amp; dry with her site on Amazon/EC2. He holds the private key to the instance, and though she has full access to the Amazon control panel (she's paying $300/mo for a site that has like 3 visitors per week) she doesn't have any way to get her content off and move to a new host.  I'm not familiar with AWS and am not sure how to help her. The site's group/file permissions are screwed up on the server so exporting the content/database via her WordPress control panel isn't working.  Any ideas on how to help her? Thanks! Do the *Result objects in Database have a common ancestor? I'm doing some polymorphic programming, and I decided that I wanted to be able to gracefully handle partial saves using SaveResult without blocking the user experience. The code looks roughly like this:  static void logDmlErrors(SObject[] src, SObject[] dest, SaveResult[] results, String message) {     // Transform results into Chatter error messages, send them to admins }   I then went about writing the utility methods that would use this function:  public static void insertRecords(SObject[] src, SObject[] dest, String message) {     logDmlErrors(src, dest, Database.insert(dest, false), message); }   Everything went well, until I came across the delete and undelete methods, which instead use DeleteResult and UndeleteResult. Both of those two classes contain the exact same methods as SaveResult, and yet don't appear to inherit from a common ancestor. This means that I can't just cast to a super-type to get to this information.  Thankfully, Summer 16 apparently introduced support for serializing (and deserializing) these classes as JSON, so I do have a fairly expensive (but accurate) workaround if I want proper polymorphic behavior, but I thought I'd throw it out there and see if someone has an alternative solution to this problem. Covering estate tax on US assets for non-resident alien I am a non-resident alien holding a brokerage account in the USA but residing outside the USA. My country does not have an estate tax treaty with the USA. So my estate is liable for a significant estate tax up to 40%. Is there any way to avoid or to cover this tax? I thought of buying term insurance for myself, but I am not sure whether US companies will sell term insurance to a non-resident. I want to buy insurance from a US company because I want the death benefit to be in USD. Can someone suggest as to what the best way to approach this issue is? Function always continuous in a Sobolev Space? Hy everybody got a quick question. I know that all function F in a Sobolev Space has a continuous representative called U such as U=F almost everywhere.  Lets take for example: The Sobolev space on ]-1,1[    the function F(x)=0 on x&lt;0 and F(x)=1 x>0  we can't find a continuous representative because it would be on a larger interval let say ]-eps ,eps[ so not in a Sobolev space the function F(x)=x on x&lt;0 and x>0 and F(0)=1 where we could find the representative U=x   My question is: if F isn't continuous is it sure that it isn't an element of a Sobolev Space? It was given was given as a necessary condition in my course.  Thanks for the help. Eclipse not working in 16.04 No Wifi-Adapter found on new Lenovo Yoga C930 with Ubuntu 18.10 Why is the ampere a base unit and not the coulomb? I always thought of current as the time derivative of charge, $\frac{dq}{dt}$. However, I found out recently that it is the ampere that is the base unit and not the coulomb. Why is this? It seems to me that charge can exist without current, but current cannot exist without charge. So the logical choice for a base unit would be the coulomb. Right?