Under what circumstances would a University revoke a student's degree?
Can a university retract a degree for actions taken after the degree is awarded?
Plot $|z - i| + |z + i| = 16$ on the complex plane Cauchy-Product of non-absolutely convergent series While grading some basic coursework on analysis, I read an argument, that a Cauchy product of two series that converge but not absolutely can never converge i.e. if $\sum a_n$, $\sum b_n$ converge but not absolutely, the series $\sum c_n$ with $$c_n= \sum_{k=0}^n a_{n-k}b_k$$ diverges.  Although we didn't have any theorem in the course stating something like this, it made me wonder if it was true. How do airlines determine ticket prices? How to generate multiple maps where one highlighted attribute changes? I have a layer that contains counties within the state of Washington.    I need to build one map (jpg) for each county.  For that specific map all counties will show as light grey, but the specific county will be green, and the file name will be the county name. I am able to produce a standard length \sim with a tiny S above it, but I would like the \sim tilde to be longer (maybe one and half times as wide as a capital letter).  Any tips on how to change the width/length of \sim? Number of Pairs of Subsets Find the number of Pairs $(A,B)$ of subsets of $[n]$ such that $A ⊆ B$? I just need clarification in my thought process. My professor's wording at times can through me off. I just want to know if I am on the right track. We will have $3$ regions: 1.Outside $B$ 2.Inside $A$ 3. Inside $B$, Outside $A$ I believe the number of pairs is $3^n$ but I am not sure. Any help would be appreciated. I'm creating a model for a 3D game that will eventually be exported using a custom Python script. This model makes heavy use of UV textures.  However, the project now references a bunch of images that are not used by any objects in the project. Example:    I don't want the first two, or the red_bubble.png image. However, I have no idea how to remove them from the project. Selecting one of them reveals that there are "2 users of the data" although I am not using it anywhere.  How can I get rid of these excess images? Changing deleted partition back to NTFS without having to recover to another drive Recently, I accidentally deleted a partition off of my external hard disk. I had a copy of Minitool Power Data Recovery left over when the same drive had become RAW about a year ago. When I selected lost partition recovery, it immediately identified my deleted partition and allowed me to access and recover the files that were there.  My question is this. Is there any way to change the deleted partition back to NTFS without having to have a drive that you need to recover the files to and then move them back after formatting, as I don’t have any space left on either the computer or on my other external hard drive, so that I don’t need to buy a new one. The files on the disk were really important.  I am using Windows 7 Home Premium.  I appreciate any help in solving this crisis. Ubuntu Server 18.04 LVM out of space with improper default partitioning Show that if $a$ and $b$ are positive integers with $(a,b)=1$ then $(a^n, b^n) = 1$ for all positive integers n  Hi everyone, for the proof to the above question,  Can I assume that since $(a, b) = 1$, then in the prime-power factorization of a and b, they have no prime factor in common, when they are taken to the $nth$ power, they will still have no prime factors in common, and so $(a^n, b^n) = 1$ for all positive integers n.  I think I'm jumping to conclusions here again, if so, leave some tips on how to do the proof properly, thanks :)  And also, I do not know how to approach the reverse problem where if $(a^n, b^n) = 1 then (a, b) = 1$, any guidance will be much appreciated! Apparently,     the Fisher analysis aims at simultaneously maximising the   between-class separation, while minimising the within-class   dispersion. A useful measure of the discrimination power of a variable   is hence given by the diagonal quantity: $B_{ii}/W_{ii}$.     I understand that the size (p x p) of the Between (B) and Within-Class (W) matrices are given by the number of input variables, p. Given this, how can $B_{ii}/W_{ii}$ be a "useful measure of the discrimination power" of a single variable? At least two variables are required to construct the matrices B and W, so the respective traces would represent more than one variable.  Update: Am I right in thinking that $B_{ii}/W_{ii}$ is not a trace over a trace, where the sum is implied, but the matrix element $B_{ii}$ divided by $W_{ii}$? Currently that is the only way I can reconcile the expression with the concept. My WiFi adapter is not working at all, how to troubleshoot? What is the correct way to completely remove an application? I've searched the net for such information and found different command lines, like these ones:  sudo apt-get remove application sudo apt-get remove application*  sudo apt-get remove --purge application sudo apt-get remove --purge application*  sudo apt-get purge application sudo apt-get purge application*   So, what is the correct way? Is it necessary to use that "*"?  After that, I also found these commands:  sudo updatedb sudo locate application sudo rm -rf (file/folder name) I just bought a new MTB and am planning to change my previous MTB into a Road Bike.   How do I do it? What kind of parts do I need to change or add or remove?  I am not looking to for a full conversion into specialised road bike. But like the answers are suggesting, I am looking for a bridge between commuter or road bike. My majors concerns to be met are:   Should be fast enough to compete with road racers over short distance Should be light as a road  Should be as close as possible in as cheap as possible. A matrix inside a table Possible Duplicate:          I am trying to insert a matrix inside a table, and I am looking for a good way to do this. Usually when I write matrices in equations, I use array environment, so I naively defined an array inside tabular, and it sort of works. The only problem is that the matrix itself seems to take up a huge amount of space inside the cell. An example is   \begin{tabular}{|c|c|} \hline \textbf{EKF} &amp; \textbf{UKF}\\ \hline $Q = \left[ \begin{array}{cc} 0.1 &amp; 0 \\ 0 &amp; 0.1 \end{array}\right]$ &amp; $Q = left[ \begin{array}{cc} 0.01 &amp; 0 \\ 0 &amp; 0.01  \end{array}\right]$\\ \hline $R = 5 \times 10^{-3}$ &amp; $R = 5 \times 10^{-5}$ \\ \hline \end{tabular}   Is there any way to increase the spacing in the cell containing the matrix without that matrix taking up all the space? SQL query or method to list all sql services running This might be a simple one, but i searched a lot and unable to find one.  Is there a sql query or a way i can run on registered server to find the list of all sql related services running like, ssis , ssas, ssrs, sql, agent, broswer, etc...  Tried googling out and can find sys.dm_server_services dmv but it does not show all the services running Using jQuery, how do I change the elements html value? (div) Using a ajax request I want to change content of my div.  &lt;div id="d1"&gt;202&lt;/div&gt;   So I want to change the content to a different number.  $('d1').InnerText???   Also, say I wanted to increment the number, how could I do that? Do I have to convert to int? How old is Chewbacca? How old is Chewbacca, anyway? Do Wookiees get gray fur when they are old? Evaluating $\int\limits_0^{\pi} \frac{dx}{1+2\sin^2x}$ After making u substitution two times, I am getting indefinite integral as $$\int\limits\dfrac{dx}{1+2\sin^2x} = \dfrac{\arctan(\sqrt{3}\tan(x))}{\sqrt{3}}+ C$$  I am stuck at working the bounds because I am getting $0$ but the answer needs to be $\pi/\sqrt{3}$.  I think $\arctan(x)$ is defined in $-\pi/2 \lt x\lt\pi/2$ while making u substitution. However I don't see how to use this observation to my advantage. Can anybody help in getting the answer and understanding whats going on. Thanks ! How can I dynamically unload a javascript file?