Can a degree be revoked for minor misconduct?
Can a university revoke one's degree for his minor misconduct?
Helix in a helix I am trying to work out a "helix in a helix" mathematically.  Intuitively I think of this as a steel cable, which is made up of a number of smaller steel cables all bound together in spiral.  If I wanted to find the length of one of the individual cables, it would be bound in a spiral in the smaller cable and then those cables bound in a larger spiral cable.  I know that if I wanted to do a helix whose ends meet, I would use the parametrization $$((a+b\cos(\omega{t}))\cos{t},(a+b\cos(\omega{t})\sin{t},b\sin(\omega{t})),t=0..2\pi$$ I've been trying to map out in my head how to, instead of curling the helix, making the helix travel in the path of a helix.  I've achieved it partially with $$((a+b\cos(\omega{t}))\cos{t},(a+b\cos(\omega{t})\sin{t},t),t=0..\infty$$ But this doesn't keep the smaller helix in tact, and turns it into a sine wave helix.  I've also tried  $$((a+b\cos(\omega{t}))\cos{t},(a+b\cos(\omega{t})\sin{t},tb\sin(\omega{t})),t=0..2\pi$$ But this gives me sort of a nautilus shape where the helix curls into itself and increases in size and curls around into itself.  What am I missing?  EDIT:  Also, what if we wanted to do this again, like a 'helix in a helix in a ... in a helix'? What is a good introductory book on quantum mechanics? I'm really interested in quantum theory and would like to learn all that I can about it. I've followed a few tutorials and read a few books but none satisfied me completely. I'm looking for introductions for beginners which do not depend heavily on linear algebra or calculus, or which provide a soft introduction for the requisite mathematics as they go along.  What are good introductory guides to QM along these lines? Parsing an Int from a string in javascript In javascript, what is the best way to parse an INT from a string which starts with a letter (such as "test[123]")?  I need something that will work for the example below.  My JS:  $(document).ready(function() {      $(':input').change( function() {         id = parseInt($(this).attr("id"));  //fails for the data below         alert(id);     }); }   My generated HTML:  &lt;select id="attribute[123]"&gt; &lt;!-- various options --&gt; &lt;/select&gt; &lt;select id="attribute[456]"&gt; &lt;!-- various options --&gt; &lt;/select&gt;   Thank you! I am very new to LaTeX and I am writing my thesis. In a chapter, I want to show my codes, which are in Mathematica.   I use the listings package as follows:  \documentclass{article}   \usepackage{listings}   \begin{document}   \lstset{language=Mathematica}    \begin{lstlisting}   Do[i^j,{i,1,10},{j,1,10}]   \end{lstlisting}    \end{document}   However, the output is much different to what the code looks like in the Mathematica IDE (even if I use other languages in \lstset{language=&lt;name&gt;}):    I read some questions on the site but, in some of them, the font or color of the codes were not the same. Could you please help me to display something like the picture below in LaTeX?  If it is important, I am using the BiDi package. Find the summation of given expression: $\sum_{k=1}^n k^3\binom nk$ I am trying to solve the following question which is Ex3 from Arthur Engel, Problem Solving strategies. Here is the question: $\sum_{k=1}^n k^3 {n \choose k}$ and asks to find the sum. I am sincerely having a hard time trying to figure out how to solve it and get $n^2 (n+3)(2)^{n-3}$. I would really appreciate if someone could show the step-by-step process. Thank you! How to print all printable ASCII chars in CLI? Possible Duplicate:             Well, I remembered this after having Algebra II a year ago, is it possible that this is a valid proof that $1 = -1$?  $$ 1 = \sqrt{1} = \sqrt{-1\cdot-1} = \sqrt{-1} \cdot \sqrt{-1} = i \cdot i = i^2 = -1 $$  $$ \therefore 1 = -1 $$  So is this actually fully valid? Or can it be disproved? Why is the word 'number' abbreviated to 'No.' in UK English and '#' in American English? Why the disparity? And why use 'No.'? Is it from the French?  And the hash or pound sign seems a weird choice too, is there a history or any reason involved? Ever since I upgraded to 15.10, fdisk -l reports 16 ram disks (/dev/ram0 ... /dev/ram15). I'm a bit unsure what those are needed for. Is it safe to delete them? If not, how can I get rid of that fdisk output? How to hide title bar in Firefox 57 Quantum? I used to use an extension to hide/show the title bar in Firefox, but since Firefox 57 was released most of the extensions were disabled.  In Chrome I just uncheck the option "Use system title bar and borders" and it's done.  Are there any ways to do that? Find the sum $\frac{1}{2\cdot 3}+\frac{1}{3\cdot 4}+\dots+\frac{1}{99\cdot 100}$ Please help me calculate the following sum     $$\frac{1}{2\cdot 3}+\frac{1}{3\cdot 4}+\dots+\frac{1}{99\cdot 100}$$ Suppose the terms of the sequence of real numbers $\{a_n\}$ satisfy $|a_{n+1} - a_n| \le 2^{-n}$ for all $n$. Prove that $\{a_n\}$ is Cauchy.   My Work  So by the definition of a Cauchy sequence, for all $\varepsilon &gt; 0$ $\exists N$ so that for $n,m \ge N$ we have $|a_m - a_n| \le \varepsilon$. However, questions like  make me understand that the $2^{-n}$ condition is necessary for this to be a true statement.   So I am wondering how to appeal to the Cauchy definition for this proof. Do I prove that every convergent sequence is therefore Cauchy, and then try to prove convergence? Flowchart using Tikz I'm trying to create a fine flowchart that is a bit complicated. Therefore I need a block for a predefined process and a connector block as well as a data block. Can someone help me? In comment is what I'd like to see in my code to keep my code nicely arranged. The rest of the code is a simple example for the Tikz site.  \documentclass{article}  \usepackage[latin1]{inputenc} \usepackage{tikz} \usetikzlibrary{shapes,arrows} \begin{document} \pagestyle{empty}   % Define block styles \tikzstyle{decision} = [diamond, draw, fill=blue!20,      text width=4.5em, text badly centered, node distance=3cm, inner sep=0pt] \tikzstyle{block} = [rectangle, draw, fill=blue!20,      text width=5em, text centered, rounded corners, minimum height=4em] \tikzstyle{line} = [draw, -latex'] \tikzstyle{cloud} = [draw, ellipse,fill=red!20, node distance=3cm,     minimum height=2em]  %\tikzstyle{subroutine} = [draw,rectangle split, rectangle split         horizontal,rectangle split parts=3,minimum height=1cm]  %\tikzstyle{connector} = [draw,circle,...] %\tikzstyle{data} = [draw, trapezium, ...]  \begin{tikzpicture}[node distance = 2cm, auto]     % Place nodes     \node [block] (init) {initialize model};     \node [cloud, left of=init] (expert) {expert};     \node [cloud, right of=init] (system) {system};     \node [block, below of=init] (identify) {identify candidate models};     \node [block, below of=identify] (evaluate) {evaluate candidate models};     \node [block, left of=evaluate, node distance=3cm] (update) {update     model};     \node [decision, below of=evaluate] (decide) {is best candidate     better?};     \node [block, below of=decide, node distance=3cm] (stop) {stop};     % Draw edges     \path [line] (init) -- (identify);     \path [line] (identify) -- (evaluate);     \path [line] (evaluate) -- (decide);     \path [line] (decide) -| node [near start] {yes} (update);     \path [line] (update) |- (identify);     \path [line] (decide) -- node {no}(stop);     \path [line,dashed] (expert) -- (init);     \path [line,dashed] (system) -- (init);     \path [line,dashed] (system) |- (evaluate); \end{tikzpicture}   \end{document} Why does "unisex" mean both sexes? There are some places where men and women are segregated — for example public toilets and public swimming pool changing areas.  By this I mean, for example, that there are "Men's toilets" and "Ladies' toilets".  However, in some more cosmopolitan swimming baths, and other places, there are such things as unisex changing areas, or unisex toilets.  From my understanding uni- implies one, as in universe, unilateral or unicycle.  However when it comes to unisex, this means both sexes, so applies to two things.  How does uni- mean one in unisex? Does it mean one? I'm trying to model my face on Blender using  and it gives links to reference photos.  The thing is, as I mentioned above, I want to try and model my face.  So I've decided to take photos of my face. But it doesn't seem to be working well (not symmetrical enough and stuff), so how exactly should I take my reference photos so that it would work well when I try to model it with the Mirror modifier?  Note: I only have the 'webcam' on my Macbook Pro and the camera on my Hongmi phone and I don't want to spend money on a new camera. Anti-virus comparison for Mac OS X This is not a "I use OS X, do I need Anti-Virus?" question.    I am looking at comparison and user opinion of existing AV products. I know I can avoid most (if not all) threats by being careful on the sites I visit, and the emails I download. But I need an anti-virus, for a variety of reasons - mostly to prevent my Mac as a carrier for viruses. (Many friends' USB drives turn out to be infected).  I was looking for the "Best" of the anti virus software out there.  I am looking prominently at anti-virus. "Internet Security" and the like are not important, and would try to avoid them if it would save money or not make my mac slower.  By "Best" I mean the best combination of detect-rate (or whatever that is called) and performance.  I don't intend to run it always in the background. Maybe I would do a onetime scan of my system and hard drives, and then it would be mostly on a need basis, especially on USB drives/portable hard disks of friends. So primary objective: High Detect rate  I have used  and  (got this with one of those software bundles sometime before, not the latest version) and had problems with both. Both sometimes hog my CPU, and somehow "lock" my USB drives preventing me from Ejecting it (I had to force eject them or just pull them off from the port) (thought off late Norton seemed a little better)  Ok, thats a long one. But my question is simple: What anti-virus do you recommend for the Mac?  Thanks. I'm looking to find out if there's any easy way to calculate the number of ways to tile a $3 \times 2n$ rectangle with dominoes. I was able to do it with the two codependent recurrences  f(0) = g(0) = 1 f(n) = f(n-1) + 2g(n-1) g(n) = f(n) + g(n-1)   where $f(n)$ is the actual answer and $g(n)$ is a helper function that represents the number of ways to tile a $3 \times 2n$ rectangle with two extra squares on the end (the same as a $3 \times 2n+1$ rectangle missing one square).  By combining these and doing some algebra, I was able to reduce this to  f(n) = 4f(n-1) - f(n-2)   which shows up as sequence , confirming that this is the correct recurrence.  The number of ways to tile a $2 \times n$ rectangle is the Fibonacci numbers because every rectangle ends with either a verticle domino or two horizontal ones, which gives the exact recurrence that Fibonacci numbers do. My question is, is there a similar simple explanation for this recurrence for tiling a $3 \times 2n$ rectangle? One very convenient property of $\mathbb{R}$ as a ring is that there is an upper bound for the degree of irreducible polynomials in $\mathbb{R}[x]$, as      If $f\in\mathbb{R}[x]$ has degree larger than $2$, then $f$ is reducible.   However, the proof as I know depends highly on the fact that $\mathbb{C}$ is algebraically closed, and the very nice property: $z\in\mathbb{C}$ is in $\mathbb{R}$ if and only if $z=\bar{z}$.  This makes a generalization to other integral domains rather difficult. So the problem is      For what kind of integral domain $R$, we have a finite upper bound on the degree of irreducible elements in $R[x]$?   Some most familiar examples are ruled out: in $\mathbb{Z}[x]$, $\mathbb{Q}[x]$ and $\mathbb{F}_{p}[x]$, there is not such a bound. Unfortunately these exhaust all integral domains about which I have a working knowledge.  Another result might help is , which says if we can find a prime ideal $\mathfrak{p}$ in $R$ such that $\mathfrak{p}^2\neq\mathfrak{p}$, then by picking $a\in\mathfrak{p}^2\backslash\mathfrak{p}$ we have an irreducible $a+x^d$, where $d$ can be arbitrary, and hence the upper bound is not possible.  So we only need to focus on domains where $\mathfrak{p}^2=\mathfrak{p}$ for all prime ideals. This seems to be a quite strong restriction but I am not sure what to make of it.  Can someone give a hint?  Thanks! How to install the most common plugins? Is it possible to create an iron door which responds to levers on both sides