I have recently interviewed by a professor in US after sending him my CV. A few days after the interview he mailed me and told me to do the formal application process and mention him as the professor I want to work with. Now, I want to thank him for considering me as a choice of his future PhD student. What should I write?
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)
As far as I know, the diamond symbol is given to the folks who  are the community elected moderators, for example,  are employees of the Stack Exchange, Inc., for example,   In those regards,  is neither a , nor is he a part of the  since March 1st, 2012. So my question is, other than the fact that he is the , is there any other reason why he still has the diamond symbol next to his name and whether he can still exercise his moderation abilities? :) Note: I do not have any problems with him having the Diamond Symbol. I just wanted to know the reason and whether he still has those privileges or not. In fact, I'd be very happy to know that he still has those privileges because, you know, he knows the site, the Best. :) Note: as of October 2017, . Gravatar links on "Filtered Questions" page are not HTTPS Finite $G$ with involutory automorphism $\alpha$ with no nontrivial fixed points. Proving properties of $\alpha$. The question at hand is:     Let G be a finite group and $\alpha$ an involutory automorphism of G, which doesn't fixate any element aside from the trivial one.    1) Prove that $ g \mapsto g^{-1}g^{\alpha} $ is an injection    2) Prove that $\alpha$ maps every element to its inverse    3) Prove that G is abelian    I think I've found 1).  I assume $ g_1^{-1}g_1^{\alpha} = g_2^{-1}g_2^{\alpha} $ and from this I get $ (g_2g_1^{-1})^\alpha = g_2g_1^{-1} $, so $g_2 = g_1$ (is this correct?)   For 2) I'm sort of stumped though, not sure how to start proving that, so any help please? What is the maximum value of the Process ID?  Also, is it possible to change a Process ID? Can not create SFTP user Debian 7 I have a linode and I access via ssh throw terminal. I need to create an sftp user which his default directory (and the only he can access) is /var/www/xxxxxx.com/public_html/directory  Now, I did it, but when I try to connect I get broken pipe or connection rejected by peer  What I did is this:  $ adduser --home /var/www/xxxxxx.com/public_html/directory/ username $ chown username:username /var/www/xxxxxx.com/public_html/directory/ $ chmod 755 /var/www/xxxxxx.com/public_html/directory/ $ nano /etc/ssh/sshd_config   In /etc/ssh/sshd_config I added the following lines  Match User username    ChrootDirectory /var/www/xxxxxx.com/public_html/directory/    AllowTCPForwarding no    X11Forwarding no    ForceCommand internal-sftp   What am I doing wrong?  EDIT: This is the actual error    EDIT2: this is the error in filezilla    EDIT 3: auth.log   Oct 15 17:47:11 (none) sshd[361]: fatal: bad ownership or modes for chroot directory "/var/www/xxxxxxxxxxxx.com/public_html/extras_html" Calculate the sum of the infinite series $\sum_{n=0}^{\infty} \frac{n}{4^n}$ A previous problem had us solving $\sum_{n=0}^{\infty} \frac{1}{4^n}$ which I calculated to be $\frac{4}{3}$ using a bit of mathematical manipulation.   Wonderful. Thank you for all the prompt responses.  Could anyone suggest an alternate technique that does not involve differentiation? Assume f is a bounded continuous function on $\mathbf{R}$ and $X$ is a random variable with distribution $F$.  Assume for all $x \in \mathbf{R}$ that  $$ f(x) = \int_\mathbf{R}f(x+y)F(dy) $$  Please help conclude that $f(x+s) = f(x)$ where $s$ is any value in the support of $F$.  The hints that I have come across are to use Martingale theory and consider $\{ X_n\}$ to be i.i.d. with distribution $F$ and make a martingale with some function of $S_n = \sum_{j=1}^nX_j$.    Thanks! Can't access my home directory "Encrypted private directory is not setup properly" Hi I'm trying to access my home directory on my laptop hard drive through a live usb. I cannot boot into the OS on the hard drive and the home and root directory is encrypted. I have the encryption key but when I try to run the tool to gain access it pops up for a second then disappears and when I run the command in Terminal it says "Encrypted private directory is not setup properly". What are my options on getting into the directory? I really need to get the data off my laptop. What type of differential equation is $f'(x) = f(x/2)$ and how do you solve it? I have the following different equation $$f'(x) = f(x/2)$$ with $f(0)=10$. What type of DE is this, and how would you solve it? It seems $f(x)$ is likely to be some relative of $e^x$, since $f'(x) = f(x)$, which is close, but I don't even know what that type of DE is called with that $f(x/2)$ feature, so I'm not having any luck searching for a tutorial. The best candidate I've found was a &quot;delay differential equation&quot;, but that seems more suited to $f(x-3)$ than $f(x/2)$. What exactly is an environment variable? I know that VARIABLE=value creates an environment variable, and export VARIABLE=value makes it available to processes created by the current shell. env shows the current environment variables, but where do they live? What comprises an environment variable (or an environment, for that matter)? How can one motivate the relativistic momentum? Motivating the non-relativistic momentum $$\mathbf{p} = m\mathbf{v}$$ is quite easy: it is meant to represent the quantity of motion of the particle, and since the mass is one measure of quantity of matter it should be proportional to mass (how much thing is moving) and should be proportional to velocity (how fast and to where it is moving). Now, in Special Relativity the momentum changes. The new quantity of motion becomes $$\mathbf{p} = \dfrac{m\mathbf{v}}{\sqrt{1-\dfrac{v^2}{c^2}}}$$ Or, using $\gamma$ the Lorentz factor $$\mathbf{p} = \gamma(v) m\mathbf{v}$$ where I write $\gamma(v)$ to indicate that the velocity is that of the particle relative to the frame in which the movement is being observed. The need for this new momentum is because the old one fails to be conserved and because using the old one in Newton's second law leads to a law which is not invariant under Lorentz transformations. So the need for a new momentum is perfectly well motivated. What I would like to know is how can one motivate that the correct choice for $\mathbf{p}$ is the $\gamma(v)m\mathbf{v}$. There are some arguments using the mass: considering a colision, requiring momentum to be conserved, transform the velocity and then find how mass should transform. Although this work, it doesn't seem natural, and it is derived in one particular example. On my book there's even something that Einstein wote saying that he didn't think it was a good idea to try transforming the mass from $m$ to $M = \gamma(v)m$, that it was better to simply keep $\gamma$ on the new momentum without trying to combine it with the mass. So I would like to know: without resorting to arguments based on transformation of the mass, how can one motivate the new form of momentum that works for special relativity? For fixed $z_i$s inside the unit disc, can we always choose $a_i$s such that $\left|\sum_{i=1}^n a_iz_i\right|<\sqrt3$? Let $z_1,z_2,\ldots,z_n$ be complex number such that $|z_i|&lt;1$ for all $i=1,2,\ldots,n$. Show that we can choose $a_i \in\{-1,1\}$, $i=1,2,\ldots,n$ such that $$\left|\sum_{i=1}^n a_iz_i\right|&lt;\sqrt3.$$ Chmod to allow read and write permissions for directory I have created directories in root. I am looking for the chmod command to allow all users read and write permissions to a specific directory. I have done chmod 775 for a file but I need this for a directory. This includes permissions on all files and sub directories. Plotting graphs using bash Name of mean absolute error analogue to Brier score? Yesterday's question  got me curious about probability scoring. The  $$\frac{1}{N}\sum\limits _{i=1}^{N}(\text{prediction}_i - \text{reference}_i)^2$$ is a mean squared error measure. Does the analogous mean absolute error performance measure $$\frac{1}{N}\sum\limits _{i=1}^{N}|\text{prediction}_i - \text{reference}_i|$$ have a name, too? I have been having a discussion regarding the Shape Water cantrip from the Elemental Evil Player's Companion. A friend and I are trying to come to an accurate view of how this spell actually functions.   Some example questions:   Must the targeted water be within a 5 foot cube area, or does it need to be of a volume not exceeding 125 cubic feet? If you shape water that is within a 5 foot cube, can the final shape you animate it to extend outside the cube? Can you cause the shaping to affect ice and snow, or only liquid water? Would you be able to carry a globe of water alongside you over distances?   Really, there are two parts:    What can be targeted by the spell? What are the limitations on the 'shape and animate' portion of the spell?   The answer I am looking for, if possible, would use the language of the spell, possibly with precedent from other game text, to clearly define the limitations of this cantrip. Why is there no overload of Interlocked.Add that accepts Doubles as parameters? How to reinstall many removed packages at once? I used sudo apt-get remove python command and accidently removed a bunch of packages that were required. I logged in via command line and installed ubuntu-desktop again but there are other packages that are missing, and I'm looking for a way to easily reinstall those removed packages. Since there's the log at software-center I wanted to ask what the easiest way might be to roll back changes or extract the removed packages list from the software center...  note: I typed sudo apt-get install .... .... ... ... for about two dozen of those removed programs in that list, but when I pressed enter it didn't install any of them because some package names couldn't be found.  The programs were removed at the same date. How to use figure inside a minipage? I'm trying to include an image, and keep it centered, and prevent from wrapping from the next page.  The following code works for that:  \begin{minipage}{\textwidth}     \begin{center}         Caption for image          \includegraphics[scale=0.5]{myimage.png}      \end{center} \end{minipage}   I'd like this image to be in a figure, with a caption.  The following doesn't compile:  \begin{minipage}{\textwidth}     \begin{figure}         \includegraphics[scale=0.5]{myimage.png}         \caption{Caption for image}         \label{fig:sample_figure}     \end{figure} \end{minipage}   I get the errors:  ! LaTeX Error: Not in outer par mode. ! Undefined control sequence.   How can I fix this? There are two directories shown by 'ls'.  Normally directories anywhere are blue on black background.  But the first one is blue on green and impossible to read.  Why is this?  How to make it blue on black, or at least something light on something dark?  This is on Ubuntu 12.04, using bash in Gnome Terminal.  In Konsole, the blue is slightly darker, and possible to read, though could be way better.