I was watching a video on Youtube which deduce Einstein's relation $E=mc^2$ and the process of deduction used the relation between , which is  $$m= \frac{m_0}{\sqrt{1-\frac{v^2}{c^2}}}.$$   So I look for a nice deduction of this relation.
I learned recently that when an object moves with a velocity comparable to the velocity of light the (relativistic) mass changes. How does this alteration take place?
I have georeferenced some images (ArcGIS -> Update Georeferencing) which creates a *.tfwx file with the new parameters for georeferencing.   I renamed it to *.tfw but QGIS is not able to read the georeferencing information.   Does anybody has any useful tips how to fix this? How to show that the nth power of a $n \times n$ nilpotent matrix equals to zero $A^n=0$ $A$ is a $n\times n$ matrix such that $ A^m = 0 $ for some positive integer $m$.   Show that $A^n = 0$.   My attempt: For $n &gt; m$, it's obvious since matrix multiplication is associative.  For $n &lt; m$, $A^n\times A^{m-n} = 0$; not sure what to do next. Also I know that $\det A = 0$. Non-Affine image transformations in .NET Are there any classes, methods in the .NET library, or any algorithms in general, to perform non- transformations? (i.e. transformations that involve more than just rotation, scale, translation and shear)  e.g.:      (source: )      Is there another term for s? has anybody been successful getting pandas to work with QGIS's Python installation, on Windows? I've used the OSGeo4W installer to install QGIS2.2, which comes with Python 2.7 and Numpy 1.5.1. Any reasonably new version of pandas requires Numpy 1.6.1 or newer. So that seems like my main problem. I've tried: - Building an older version of pandas (e.g. 0.7.3 and 0.4.1) using easy_install, but that gives me a very long list of errors, at least the last of which are related to distutils\msvc9compiler.py - Using binaries of old pandas versions, but they are all built for Numpy 1.6.1 - Upgrading Numpy, which also gives me an error message. In case anybody is interested, the message ends with "File “C:\OSGeo4W\apps\Python27\lib\distutils\msvc9compiler.py”, line 299, in query_vcvarsall” newline “raise ValueERror(str(list(result.keys())))” newline “ValueError: [u’path’]"  I'm wondering if anybody else has ever been successful in getting pandas to work with a QGIS install on Windows??  It would be so easy if QGIS would ship with, say, a version of Numpy that's less than three years old. Does anybody know if such an upgrade is in the works for upcoming QGIS versions? I have a live USB made with the standard Ubuntu disk image creator for 16.04 LTS. In the current state, I can boot to this disk, but it still requires the original USB to run properly at all times.  Attempting to pull the drive and use the system generates a large amount of I/O errors, further suggesting that the USB drive is actually needed for things not already loaded into RAM (For example, Firefox worked without the USB, but I used it once before already. apt, on the other hand, did not.)  Is there a way to copy the entire Ubuntu live disk to RAM, so I can remove the drive and free up a USB slot for other things? Why was Sam Wilson chosen for this, but not Bucky? At the end of the Avengers: Endgame movie,      old Steve Rogers passed down his mantle of Captain America   to Sam Wilson.  Why didn't he choose Bucky for this? Bucky seems more fit for the job as he is a super soldier. Shift numbers into a different range I was wondering how can I shift my data that fall between a range lets say [0, 125] to another range like [-128, 128].  Thanks for any help What's wrong with XKCD's Frequentists vs. Bayesians comic? makes fun of a frequentist statistician who derives an obviously wrong result.  However it seems to me that his reasoning is actually correct in the sense that it follows  the standard frequentist methodology.   So my question is "does he correctly apply the frequentist methodology?"    If no: what would be a correct frequentist inference in this scenario? How to integrate "prior knowledge" about the sun stability in the frequentist methodology? If yes: wtf? ;-) Character Limit in HTML During the movie, we learned that Ego tried to reproduce the Celestial gene by having a lot of children and then having them delivered to him. I am not sure if Yondu was contracted for all of them but he definitely delivered at least a few of them since he broke the ravager code and got banned for dealing in kids.  My question is: why did he stop with Peter? Was Peter the last one on the contract or did he keep on delivering some but just not Peter?  Also, why didn't Ego seek out Yondu to get his kid back?  I don't think this was touched on in the movie. This was slightly mentioned here () but that is not answering my question.  I think Yondu said it was because he could get to places where the Ravagers could not since he was a kid but that would have been true with all the others kids he abducted for Ego. Clearly this is an edge case and I probably shouldn't have even tried awarding the bounty to a deleted answer, but why is the bounty award button even available?  It's not a bug since someone added in the notification seen in the final image.  But that sure seems like a roundabout way to let the user know that they can't award a bounty to a deleted answer.  The second step is particularly strange since the system really ought to know that the warning is pointless: no bounty can be awarded.  My suggestion is to rip-off the  and let bounties be awarded without the warning.  Then remove the single click button from deleted answers. Delete files older than X days + I have found the command to delete files older than 5 days in a folder  find /path/to/files* -mtime +5 -exec rm {} \;   But how do I also do this for subdirectories in that folder? Polarization vectors of massive and massless particles Let $X$ be an arbitrary random variable  takes values in $\{0,1,2,...,10\}$. What are the minimum and  maximum values of variance of random variable $X$? Suppose, I want to refer multiple equations (1), (2), (3), (4), (5) and (7) so that they appear as (1-5, 7):  \documentclass[fleqn,preprint,10pt]{article} \usepackage{amsmath} \usepackage{amssymb} \usepackage{amsfonts} \begin{document} \begin{align} \label{1}\psi([e_1,e_2]) = \psi(e_2) = e_2 = (e_2,2e_3) = (-2e_3,e_2) = (\psi(e_1), \psi(e_2))\\ \label{2}\psi([e_1,e_3]) = \psi(2e_3) = 2e_1 = (e_1,2e_3) = (-2e_3,e_1) = (\psi(e_1),\psi(e_3))\\ \label{3}\psi([e_2,e_3]) = 0 = (e_2,e_1) = (\psi(e_2),\psi(e_3)),\\ \label{4}\left\{e_4, e_1\right\},\,\,\,\left\{e_4, e_2\right\},\,\,\,\left\{e_4, e_3\right\},\,\,\,\left\{e_4, e_1+\epsilon\,e_2\right\},\\ \label{5}\left\{e_1, e_2\right\},\,\,\,\left\{e_3, e_1\right\},\,\,\,\left\{e_3, e_2\right\},\\ \label{6}\left\{e_4, e_1\right\},\,\,\,\left\{e_4, e_2\right\},\,\,\,\left\{e_4, e_3\right\},\,\,\,\left\{e_4, e_1+\epsilon\,e_2\right\},\\ \label{7}\text{Nor}_{L_4\oplus L_3}\left(\{e_2\}\right)/\{e_2\}=\,\{e_1, e_3, e_4\} \end{align} \end{document} How to convert image of map into vector format? I am trying to prove a result, for which I have got one part, but I am not able to get the converse part.  Theorem. Let $R$ be a commutative ring with $1$. Then $f(X)=a_{0}+a_{1}X+a_{2}X^{2} + \cdots + a_{n}X^{n}$ is a unit in $R[X]$ if and only if $a_{0}$ is a unit in $R$ and $a_{1},a_{2},\dots,a_{n}$ are all nilpotent in $R$.  Proof. Suppose $f(X)=a_{0}+a_{1}X+\cdots +a_{n}X^{n}$ is such that $a_{0}$ is a unit in $R$ and $a_{1},a_{2}, \dots,a_{r}$ are all nilpotent in $R$. Since $R$ is commutative, we get that $a_{1}X,a_{2}X^{2},\cdots,a_{n}X^{n}$ are all nilpotent and hence also their sum is nilpotent. Let $z = \sum a_{i}X^{i}$ then $a_{0}^{-1}z$ is nilpotent and so $1+a_{0}^{-1}z$ is a unit. Thus $f(X)=a_{0}+z=a_{0} \cdot (1+a_{0}^{-1}z)$ is a unit since product of two units in $R[X]$ is a unit.   I have not been able to get the converse part and would like to see the proof for the converse part. Comma after introductory words, phrases, clauses: unacceptable, obligatory or optional? I am no native speaker and always confused about the comma in introductory phrases, in particular in prepositional phrases. Is there any hard rule when a comma must be set? If I make a google search for certain phrases, I often find both variants. Typical examples where I am not sure whether a comma must be set are:        First[ly][,] I must phone mother   In this case[,] we must...   For simple problems[,] the algorithm...   From Lemma 1.2[,] we obtain...   For a typical user[,] the algorithm...   In our theory[,] we...   A dark line on the horizon[,] the mountain range we were headed for seemed somehow not as threatening as when we had started out on the trip.   Avidly reading her novel[,] Jane did not notice that her stop was approaching.   To be sure[,] it is not easy to see a solution.   When you get to Rome[,] give me a ring. AlwaysOn AG: Current Host Server - Owner Node - Primary Instance Background image shows in front of 3D objects, not behind them. I've done a quick 3D track in blender and I'm trying to render my output, but the plate I used to track is showing up over my 3d objects.  I want to render the objects in the scene with an alpha channel and comp them over the plate I tracked. My renders however, are covered by the aforementioned plate.  Un-checking "Background Images" in the camera properties (only removes it from the viewport) isn't doing it for my render outputs.  Working on some production tests and am not really proficient with the software yet, my apologies in advance.