I'm halfway through my PhD and will be visiting another country for a conference. While I am there I would like to talk with some of the local researchers and hopefully visit their labs and discuss their research. I intend to email some of the researchers in my field in advance and ask if they would be happy to have a chat about their research and possibly visit their lab (briefly on the visit, more like a lab tour than anything else).   What is the best way to ask these PI's (via email) if I could meet with them while I am in town to visit their labs and discuss their research?
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)
Multiple solutions for a particle in an infinite potential well I am starting to learn about quantum mechanics and was wondering about the solutions to a question about a particle in an infinite potential well of length $L$.  The solutions are: $$\psi_n(x) = \sqrt{\frac{2}{L}}\sin\left(\frac{\pi n x}{L} \right)$$  And I was wondering what is the meaning of $n$. Isn't there supposed to be only one wave function? In that case, $\Psi = \sum_{n=1} ^\infty a_n \psi_n$, but what are the $a_n$? Or maybe it is probabilistic, and we don't know which $\psi_n$ the particle is currently in? I am trying to print a simple value for $AR1_p1 but the variable $i is not evaluating. for i in 1 2 3 4 do     AR1_p1=22     AR1_p2=23     AR1_p3=24     AR1_p3=25     echo $AR1_p$i done   It's like concatenating dynamically. Any suggestions on how to fix this?. This is a homework problem for my real analysis class. It is problem 13.1 from Mattuck's Introdution to Analysis. The question reads:       Suppose F(x) is continuous on some open interval I and c is a maximum point inside this interval. Is it true that f(x) must be increasing immediately to the left of c and decreasing immediately to the right of c? Proof or counterexample. (Note: A constant function is considered to be both increasing and decreasing.)      My friend and I have been attempting to find a counterexample. We figured a function that begins oscillating infinitely many times near c but converges to c would work. We're having difficulty constructing such a function out of elementary functions so we think we will have to define it in another way, piece-wise using receding intervals. I have no clue how this would look. Any advice would be greatly appreciated. Why do soap operas have the soap opera effect? The soap opera effect occurs when frame interpolation is used. For example, if a movie is shot at 24 frames per second and then shown on a TV screen which is capable of displaying 60 frames per second then it is possible to use a computer to do motion interpolation. In other words the computer can average (interpolate) two frames and create a synthetic third frame and stick it between the two real frames.  This interpolation makes the picture look unnatural and plastic, somewhat like soap operas look on TV, hence the name.  My understanding of why soap operas have the soap opera effect has something to do with the fact that many of them are shot using camcorders instead of film, but I am not completely sure.  Why do soap operas have the soap opera effect? Intersection Number of $B = Y^2 - X^3 + X$ and $F = (X^2 + Y^2)^3 - 4X^2Y^2$ using the fact $I(P,F \cap B) = ord_P^B(F) $. Let's say there is a user who has found a satisfactory answer to a common question asked on Stack Overflow (or other Stack Exchange website).  This answer may be a snippet of code, or an addon, or a framework, or something else.    Is it acceptable for this user to formulate an answer for one question, find every related question and then copy the exact answer to each of those questions?  And, if not, what should  users who finds themselves in this situation do? default constructor for int Flash drive .docx disappeared files I need to do create a file with a filename such as :&gt;?, is this possible somehow? Windows stops it. Calculating $\int_{- \infty}^{\infty} \frac{\sin x \,dx}{x+i} $ I'm having trouble calculating the integral  $$\int_{- \infty}^\infty \frac{\sin x}{x+i}\,dx $$  using residue calculus. I've previously encountered expressions of the form   $$\int_{- \infty}^\infty f(x) \sin x \,dx $$  where you would consider $f(z)e^{iz}$ on an appropriate contour (half circle), do away with the part of the contour that wasn't on the real axis by letting the radius go to infinity, then recover the imaginary part of the answer to get back the sine. However here, I can't replace the sine with $e^{iz}$ in my complex function because $$\operatorname{Im} \frac{e^{ix}}{x+i} \neq \frac{\sin x}{x+i}\cdots$$  How to remedy this? I'm not sure if substituting $\sin x = \frac{1}{2i}(e^{ix}-e^{-ix})$ and solving two integrals is how this problem is meant to be solved, although I'm 99% sure it would work Showing just color ramp in legend without values How does "virus been detected" on android pop up on chrome when visiting some sites? What is the cause of this chrome bug on android? The last site I went to was www.destructoid.com and all of a sudden it gets redirected to the following url. This happened previously awhile back, but I didn't document everything as I did today. I'm also on android chrome canary if that matters.   I took some screenshots before closing out of that tab. But my question is:   What chrome bug or malware is causing these random redirects? How can one detect if they have this vulnerability?   The url is: Calculating the optimal number of bins for severely skewed data What's the best way to draw UML class diagrams in LaTeX? How to align prices in columns when both 2 digit and 4 digit variations of a price exist? I am trying to display data similar to coinmarketcap with prices for coins, some above 1$ in which case they are rounded to 2 zeroes, some below 1$ in which case they have 4 digits following the decimal. I saw a bunch of posts here where people have suggested to use right alignment for numeric applications/prices  Approach 1 Decimal aligned   1. $13,700.05  2.      $0.0048   Approach 2 Right aligned   1. $13700.05  2.   $0.0048   Which of these approaches do you suggest? Thank you for your time The problem: The links at the bottom of the Stack&nbsp;Exchange newsletter link to a YouTube video instead of the right place on the website. I´m not sure if this is an oversight or a clever hack.  Screenshot: Flames with no gravity? I was watching  today, and noticed this: in some moment the space station changed orbit and the people inside experienced zero-gravity. At that moment, a candlestick passed floating in the air, with the candles burning ().   But in our environment the flames go upward because the hot air is less dense, and that effect should disappear when no gravity is present, am I right? How would a candle flame look then? iOS Launching Settings -> Restrictions URL Scheme Is there a design pattern for dropdown lists in iOS? Suppose $f$ is a continuous, strictly increasing function defined on a closed interval $[a,b]$ such that $f^{-1}$ is the inverse function of $f$. Prove that,   $$\int_{a}^bf(x)dx+\int_{f(a)}^{f(b)}f^{-1}(x)dx=bf(b)-af(a)$$   A high school student or a Calculus first year student will simply, possibly, apply change of variable technique, then integration by parts and he/she will arrive at the answer without giving much thought into the process. A smarter student would probably compare the integrals with areas and conclude that the equality is immediate.  However, I am an undergrad student of Analysis and I would want to solve the problem "carefully". That is, I wouldn't want to forget my definitions, and the conditions of each technique. For example, while applying change of variables technique, I cannot apply it blindly; I must be prudent enough to realize that the criterion to apply it includes continuous differentiability of a function. Simply with $f$ continuous, I cannot apply change of variables technique.  Is there any method to solve this problem rigorously? One may apply the techniques of integration (by parts, change of variables, etc.) only after proper justification.  The reason I am not adding any work of mine is simply that I could not proceed even one line since I am not given $f$ is differentiable. However, this seems to hold for non-differentiable functions also.  I would really want some help. Pictorial proofs and/or area arguments are invalid.