I am a current chemical engineering student with a 2.8 GPA and two years research experience and one paper in the works of being published. Is being admitted into a chemical engineering or bio-engineering masters program an unattainable goal?
When applying to a PhD program in the US, how does the admissions process work? If an applicant is weak in a particular area, is it possible to offset that by being strong in a different area?  Note that this question originated from this . Please feel free to edit the question to improve it.
How does Java Garbage Collection work with Circular References? How to encrypt folders (not in Home)? Function in Table I was hoping someone could give an overview as to how the Lie groups $SO(3)$ and $SU(2)$ and their representations can be applied to describe particle physics?  The application of Lie groups and their representations is an enormous field, with vast implications for physics with respect to such things as unification, but I what specifically made these groups of physical importance and why there study is useful.  I have just started studying these two groups in particular, but from a mathematical perspective, I'd very much appreciate understanding some sort of physical motivation. Rendering fire animations with transparent background I'm creating a simple fireball sprite for my game and I want to render a fire animation.  I would like to get the upper images with transparent background, but when is set the transparency on under Render -> Film one of my frames will look like lower pictures.  You can see the difference of these two images. What can I use to typeset MATLAB code in my document? This question led to a new package:      Does anybody have a quick and easy way to typeset some relatively long MATLAB code in the appendix? I looked up a few methods, and the mcode package emerged as a possibility, but it seems to be unmaintained...  I have a ton of equations in my code, so I'd prefer a solution that avoids having to use $ to denote equations.  Also, if possible, if there's a way to keep all of MATLAB's "natural" coding colors (e.g. green for comments), that would be great...  Any idea? What did Ken Thompson mean when he said, "I'd spell creat with an 'e'."? What is Ken referring to? Is there a "creat" command? How would you cut a shape out of an object using another object? Coming from SketchUp one of the tools I miss most is the circle draw tool which lets you draw a circle on any face and then you could extrude it in/out. The only tool that I know of that comes close to this is the knife tool but this would be very impractical to cut out with the knife  Example:    Is there any tool in blender that can match this function? also how could you do this with squares? The difference between GPU and CPU I know what a CPU is(I think). It's the thing who's speed is measured in GigaHertz(these days).  However, you hear a lot about a GPU, and letting the GPU take over, not letting the CPU but the GPU do it, GPU-based rendering, etc...  What is this GPU anyway? How can I access it and use it to my advantage? What am I missing out on here? What does “the lowest common denominator” mean in the context other than math? In the  (May 31) article under the title, “Stephen Hawking angers Trump supporters with baffling array of long words,” Andy Borowitz wrote;     “Speaking to a television interviewer in London, the theoretical   physicist, Hawking called Trump “a demagogue who seems to appeal to   the lowest common denominator. --- “For a so-called genius, this was an   epic fail,” Trump’s campaign manager, Corey Lewandowski, said. “If   Professor Hawking wants to do some damage, maybe he should try talking   in English next time.”        Later in the day, Hawking attempted to clarify his remark about the presumptive Republican Presidential nominee, telling a reporter, “Trump bad man. Real bad man.”   From the context of Professor Hawking’s remark, I take “the lowest common denominator” as referring to the  “social segment of low educated, unsophisticated people,” but I’m not sure.   I thought  "common denominator" is a simple mathematic term. What does it mean in the context of the above quote?  Mr. Trump’s campaign manager says Professor Hawking should try to talk in English. Is this a farfetched way of using “common denominator” from math to politics?   Did Professor Hawking misuse "the common denominator"? Or does Mr. Trump's campaign manager not understand the meaning of "common denominator", which some call an "everyday-use" English phrase?  P.S.  I found the following definition of 'common denominator' in Oxford Advanced Learners English Dictionary;   2) an idea, attitude or experience that is shared by all the members of group - see also Lowest common denominator.  Readers English Japanese Dictionary at hand, published by Kenkyu-sha, a foreign language, especially English language dictionary specialist publisher in Japan, and rated as the most reliable English Japanese dictionary totally dropped the reference to this paticular meaning.  It was a learning. I told to myself that I should have made more homework on English-to-English dictonaries beforehand. Reduce Spacing In $$ In math, one often needs to put a letter inside the symbols &lt;&gt;, e.g. to denote a cyclic group &lt;x&gt; generated by some element x. However, plain text displays the symbols &lt; and &gt; as an upside down exclamation point and an upside down question mark, respectively, while math type displays a large space like so:  &lt; x &gt;    Is there some way to reduce this spacing? When I place a multipage pdf file into InDesign CC, the pages go outside of my document settings, making this function useless.  What do I have to do to make the placed  pdf pages go within my document settings, which in this case is 11 in. Length X 8.5 in. width, .5 in. margins on all sides, with two columns per page. I would greatly appreciate an answer to this, Thank you. How to find and return a duplicate value in array I was trying to suggest a retag of  on Seasoned Advice, but the system won't let me; I get the familiar message     Edits must be at least 6 characters; is there something else to improve in this post?   In general, that's not true for retagging; if you don't change the question body at all, it should work. I suspect the logic checking the edit is thrown off guard because of the title warning:     The question you're asking appears subjective and is likely to be closed       I found , but I cannot find any evidence (in SEDE) for invisible characters being present in the question's source. Also, that's supposed to be . Show group of order $4n + 2$ has a subgroup of index 2. Let $n$ be a positive integer. Show that any group of order $4n + 2$ has a subgroup of index 2. (Hint: Use left regular representation and Cauchy's Theorem to get an odd permutation.)  I can easily observe that $\vert G \vert = 2(2n + 1)$ so $2 \mid \vert G \vert$ and 2 is prime. We have satisfied the hypothesis of Cauchy's Theorem so we can say $G$ contains an element of order 2.  This is where I am stuck  I am confused about how the left regular representation relates to the group. So my understanding at this point is that every group is isomorphic to a subgroup of some symmetric group. My question: is the left regular representation $\varphi : G \to S_G$ an isomorphism? where $G \cong S_G$ or is $S_G$ the same thing as $S_{\vert G \vert}$ and $\varphi$ is only an injection? I'm using Dummit and Foote for definitions.  I saw an argument online that said that since we have an element of order 2, there is a $\sigma \in S_G$ of order 2, but it is a product of $2n + 1$ disjoint 2-cycles. I don't understand how they could claim this and tried working it out on my own but didn't get there. -- They then went on to use the parity mapping $\varepsilon : S_G \to \{\pm1\}$ and since we have an odd permutation $\sigma$, we have $[S_G:\text{ker }\varepsilon] = 2$. I understood their computation but not how that directly shows that $G$ has a subgroup of order 2? unless $G \cong S_G$ because of how left regular representation is defined. (but again, I'm not understanding that concept very well yet.)  So, to be clear about my questions:   What is meant by left regular representation, is it an isomorphism or just an injection? and how would it be used here. If it is an isomorphism, the argument online starts to make more sense, but how can they say that since $\sigma$ is even, it is made up of $2n + 1$ disjoint transpositions? If you have a full, proof, I'd appreciate it, but good hints are just as good!   Thanks you! In Visual Studio, I can cycle through my clipboard history by pressing CTRL+SHIFT+V rather than CTRL+V. I believe it's called a clipboard ring. But that feature doesn't seem to exist outside of Visual Studio, at least not with the same key combination. Is there a key stroke combination built in to windows to do the same, i.e. be able to cycle through your clipboard history while pasting? When using the ssh or ftp commands from the Bash shell, does the server that I am connecting to learn of the domain name used? I understand that the domain name is locally translated into an IP address via DNS. In HTTP, after that happens, the server is told the original domain name as well in order to serve the correct page, or to present the correct TLS cert (SNI).  host serverfault.com GET /   Does a similar phenomenon happen when connecting to ssh or ftp?  I ask because I am  trying to ssh into a server (GoDaddy webhosting) which expects a domain name, but is not letting me in when I try to connect via user@IPaddress as the DNS is not yet moved to the GoDaddy IP address. show that $\sum_{i=0}^l \dfrac{{l\choose i}}{{n\choose k + i}} = \dfrac{n+1}{(n-l+1) {n-l\choose k}}$ Show that $\displaystyle\sum_{i=0}^l \dfrac{{l\choose i}}{{n\choose k + i}} = \dfrac{n+1}{(n-l+1) {n-l\choose k}}$ for all $k,l, n\geq 0$ with $k+l \leq n.$  The $k+l\leq n$ part doesn't seem that important. The claim clearly holds for $n=0,$ and in that case $k$ and $l$ must both be zero. I think the claim can be shown by induction, but I'm not sure how to do so; I'm not sure how to use the inductive hypothesis to prove the inductive step. The sum on the LHS is not always an integer, so finding a combinatorial argument doesn't seem very feasible. For $n = 1,$ we can have $(k,l) = (0,0), (1,0), (0,1),$ and in each case the sum holds. Perhaps multiplying both sides by a number (idk ${n-l\choose k}$) might be useful? Create WiFi hotspot on ubuntu Although many questions have already been asked regarding WiFi hotspot, I didn't get any of the solutions working for me.  I connect to the Internet using a 3G Dongle of Huawei 3772 (Vodafone). The connection type is Mobile Broadband connection. I have to share this Internet connection with my other devices like mobile phones and laptops.  How can I create a WiFi hotspot connection for this connection.  I am using Ubuntu 12.04 LTS.  I would like to note that I have already tried some help links from Ubuntu but, they are so confusing that I could not understand them. Exercise $7$, page 51 from Hungerford's book Algebra.     Show that $N=\{(1),(12)(34), (13)(24),(14)(23)\}$ is a normal subgroup   of $S_{4}$ contained in $A_{4}$ such that $S_{4}/N\cong S_{3}$ and   $A_{4}/N\cong \mathbb{Z}_{3}$.   I solved the question after many calculations. I would like to know if is possible to define an epimorphism $\varphi$ from $S_{4}$ to $S_{3}$ such that $N=\ker(\varphi)$.  Thanks for your kindly help.