Is it possible to get a PhD position in the USA without applying to a PhD program?
Can a professor influence the graduate admissions committee if he or she is interested in a particular student?
What did Dumbledore say his scar on his left knee was? In Philosopher's Stone, we hear Dumbledore replying to McGonagall's query as to whether he could do something about the scar baby Harry has on his forehead:     “Even if I could, I wouldn’t. Scars can come in handy. I have one   myself above my left knee that is a perfect map of the London Underground." - Chapter 1, The Boy Who Lived.   Now, I have no idea what that last sentence means.  It could be because English is not my native tongue. Is it some kind of a joke, or does it really mean something? All group homomorphism from $ \mathbb{Z} _m $ to $ \mathbb{Z}_n $  How could I find every group homomorphism? In a Silverlight application I'm trying to find out when a property on a usercontrol has changed. I'm interested in one particular DependencyProperty, but unfortunately the control itself doesn't implement INotifyPropertyChanged.  Is there any other way of determining if the value has changed? How to change the numbering of \part, \chapter, \section, ... to alphabetical, Roman numbers, etc How do I tell a script to wait for a process to start accepting requests on a port? I need a command that will wait for a process to start accepting requests on a specific port.    Is there something in linux that does that?  while (checkAlive -host localhost -port 13000 == false)   do some waiting  ... When I slam my hand onto my keyboard, only a maximum of 6 keys will be registered, I've tested this for the past few minutes and was unable to get more than 6. Is this the same on all keyboards? If not, what would be the distinguishing factor, If yes: why 6 specifically?  For clarification: I do not have a usecase for this, I am simply curious In , I used quotes to demark specific terms, but after I posted the question, I wondered if I'm doing it right.  Usually, when quoting something a person says, the quotation mark goes after the comma or period, like so:     "This is my opinion," she said.   However, I sometimes use quotes not to represent something said by anyone, but instead for delineating a set term or phrase to make it clear that those words go together and none of them should be mistaken for a part of the rest of the sentence. Like this:     Should I say "stand up", "standup", or "stand-up"?   This looks weird to me:     Should I say "stand up," "standup," or "stand-up"?   ... but maybe I'm wrong about the rules.  Is it correct to use quotes in this way? And if so, are the quotes positioned correctly relative to the other punctuation marks?  Are there other alternatives for delineating terms without the use of quotes? What's the easiest way to unrar a file? I just realized I can't unrar .rar files on my Ubuntu machine!  What's the easiest way to accomplish this fundamental task? If possible I'd love something like 7Zip that I can just right Click, and extract and have the program worry about how to do it regardless if it's a .zip, a .rar or a .foo compressed file. Fastest way to remove non-numeric characters from a VARCHAR in SQL Server I'm writing an import utility that is using phone numbers as a unique key within the import.  I need to check that the phone number does not already exist in my DB. The problem is that   phone numbers in the DB could have things like dashes and parenthesis and possibly other things. I wrote a function to remove these things, the problem is that it is slow and with thousands of records in my DB and thousands of records to import at once, this process can be unacceptably slow. I've already made the phone number column an index.  I tried using the script from this post:   But that didn't speed it up any.  Is there a faster way to remove non-numeric characters? Something that can perform well when 10,000 to 100,000 records have to be compared.  Whatever is done needs to perform fast.  Update Given what people responded with, I think I'm going to have to clean the fields before I run the import utility.   To answer the question of what I'm writing the import utility in, it is a C# app. I'm comparing BIGINT to BIGINT now, with no need to alter DB data and I'm still taking a performance hit with a very small set of data (about 2000 records).   Could comparing BIGINT to BIGINT be slowing things down?  I've optimized the code side of my app as much as I can (removed regexes, removed unneccessary DB calls). Although I can't isolate SQL as the source of the problem anymore, I still feel like it is. An investigator wishes to produce a combined analysis of several datasets.  In some datasets there are paired observations for treatment A and B.  In others there are unpaired A and/or B data.  I am looking for a reference for an adaptation of the t-test, or for a likelihood ratio test, for such partially paired data.  I am willing to (for now) to assume normality with equal variance and that the population means for A are the same for each study (and likewise for B). I would like to know if there is any man page documenting the construction of the most basic script commands like if/then/else, while, for each, and all the relative switches, like -eq, -e, -ge, and so on. Irreducible polynomial in field extension I have this problem      Let $L/K$ be a finite field extension and $|L:K|=m$. Let $f(x)$ be an irreducible polynomial of degree $n$ in $K[x]$ and $\gcd(m,n)=1$. Prove that $f$ is irreducible over $L$.   I'm just a beginner so I'm really confused with the $\gcd(m,n)=1$, I don't know how to use it. So help me with this problem. Thank you Unicode input retrieved via PrimeFaces input components become corrupted Prove there are k consecutive non-squarefree integers So, I've got a question for class that asks me to prove the existence of arbitrarily long runs of consecutive integers where $\mu(n)$ is zero.   I've started the proof, but I need a bit of help midway through.  Assume there exists a run of length n, which we currently assume is the longest possible chain.  If we induct on n, we can assume there is a run of the form $m_1p_1^2, m_2p_2^2, ..., m_np_n^2$ (where each of the $p_i$ are prime).  If I add $M =  lcm(m_1p_1^2, m_2p_2^2, ..., m_np_n^2)$ to each number, I get another run of length n.  So here's where the issue starts. When I talked to my advisor about it, he referenced a theorem where there exists a prime $p$ congruent to $1\ mod\ M$.  I am unfamiliar with this theorem, so I'm not sure how to use this information. Any chance I can get some help? Or else is there a simpler way to go about this problem? biblatex, biber, is it possible to \printbibliography between two years? With biblatex and Biber, is it possible to print all the bibliography (\printbibliography) from (let's say) 2003 to 2008 in one section? And then in another section print all the bibliography from 2009 to 2016? A problem of Schwarz-Pick theorem in complex analysis Set $f \in H(B(0,1)),f(B(0,1)) \subset B(0,1)$，prove that $$|f(z)-\frac{f(0)(1-|z|^2)}{1-|f(0)|^2||z|^2}| \le \frac{|z|(1-|f(0)|^2)}{1-|z|^2|f(0)|^2}$$  I think this problem is supposed to be proved by Schwarz-Pick theorem, I tried hard but failed to build a function to prove it. I even doubted that this problem is wrong, so I want to whether this problem can be proved or be falsified, and how.  Any help would be appreciated. Stack Exchange API too many requests from this IP address I am using the Stack Exchange API to get Stack&nbsp;Overflow data, but I am getting "too many request from this ip" after making only five requests. I got JSON content like this:  {u'error_id': 502, u'error_message': u'too many requests from this IP, more requests available in 68492 seconds', u'error_name': u'throttle_violation'}   I made the following requests to Stack&nbsp;Exchange without an access token:   "" ---> 2 times called this API "" --> 3 times called this API and on the 4th call I got an exception How to handle a native OS (Ubuntu) file upload window in selenium webdriver with python? This is my first time here but I have already posted this question on SO. I keep getting solutions for Windows + Java and not for Linux or python for that matter.  I am using Selenium and Python to automate a file upload application for the past many hours but nothing helpful!   The HTML DOM structure for this file upload is an input tag with its type attribute value = 'file'. I know I can make use of the send_keys.   The problem is I am not supposed to use send_keys() (as per the question I am trying to solve). The assumption is there are other ways of doing it.  Can anyone suggest me alternative ways to upload the file? I do get solutions for windows but not for Linux(Ubuntu). I know there are applications/tools to automate GUI components like AutoIt but there is nothing for Linux close to AutoIt.  I can say I have done my homework to find a solution. Only after not finding anything useful, I am asking this question, please help! Prove that $f'(0)$ exists and $f'(0) = b/(a - 1)$ Problem:   If $f(x)$ is continous at $x=0$, and $\lim\limits_{x\to 0} \dfrac{f(ax)-f(x)}{x}=b$, $a, b$ are constants and $|a|&gt;1$, prove that $f'(0)$ exists and $f'(0)=\dfrac{b}{a-1}$.   This approach is definitely wrong:    \begin{align} b&amp;=\lim_{x\to 0} \frac{f(ax)-f(x)}{x}\\ &amp;=\lim_{x\to 0} \frac{f(ax)-f(0)-(f(x)-f(0))}{x}\\ &amp;=af'(0)-f'(0)\\ &amp;=(a-1)f'(0) \end{align}  I will show you a case why this approach is wrong:     \[f(x)= \begin{cases} 1,&amp;x\neq0\\ 0,&amp;x=0 \end{cases}\]   $\lim_{x\to0}\dfrac{f(3x)-f(x)}{x}=\lim_{x\to0} \dfrac{1-1}{x}=0$   but $\lim_{x\to0}\dfrac{f(3x)}{x}=\infty$,$\lim_{x\to0}\dfrac{f(x)}{x}=\infty$   Does anyone know how to prove it? Thanks in advance! Is it possible to change the Environment of a parent process in Python? In Linux When I invoke python from the shell it replicates its environment, and starts the python process. Therefore if I do something like the following:  import os os.environ["FOO"] = "A_Value"   When the python process returns, FOO, assuming it was undefined originally, will still be undefined. Is there a way for the python process (or any child process) to modify the environment of its parent process?  I know you typically solve this problem using something like  source script_name.sh   But this conflicts with other requirements I have.