Characterizing the Homotopy of Path-Connected Space
(weak) homotopy equivalence
I'm trying to use Linq to return a list of ids given a list of objects where the id is a property. I'd like to be able to do this without looping through each object and pulling out the unique ids that I find.  I have a list of objects of type MyClass and one of the properties of this class is an ID.  public class MyClass {   public int ID { get; set; } }   What I want to do is write a Linq query to return me a list of those Ids  How do I do that given an IList&lt;MyClass&gt; such that it returns an IEnumerable&lt;int&gt; of the ids?  I'm sure it must be possible to do it in one or two lines using Linq rather than looping through each item in the MyClass list and adding the unique values into a list.  Any help in creating an elegant solution would be much appreciated! Using indefinite articles before adjectives: "Let's have a good breakfast" Let's have breakfast    Let's have a good breakfast      I've learned that indefinite articles aren't used before uncountable nouns, so why is a used before the adjective "good" here?    Is there an exception to the rules or is it wrong? Apply for Schengen visa in a third country Can a Kenyan citizen studying in Russia and temporarily visiting family in Kenya apply for a Schengen visa in Nairobi and not in Russia, where he has his residence? Landau's derivation of a free particle's kinetic energy- expansion of a function? I was reading a bit of Landau and Lifshitz's Mechanics the other day and ran into the following part, where the authors are about to derive the kinetic energy of a free particle. They use the fact that the Lagrangian of this particle must be the same (or at most, differ by the total time derivative of a function of co-ordinates and time) in different inertial frames.     We have $L'=L(v'^2)=L(v^2+2\mathbf{v}\cdot\boldsymbol{\epsilon}+\boldsymbol{\epsilon}^2)$. Expanding this expression in powers of $\boldsymbol{\epsilon}$ and neglecting terms above the first order, we obtain    $$L(v'^2)=L(v^2)+\frac{\partial L(v^2)}{\partial (v^2)}2\mathbf{v}\cdot\boldsymbol{\epsilon}.$$   I think I'm ok with all the physics in this section. What I don't get is just the part I quoted above (so maybe this post is better suited for the math site, but since this is book is so physics-y I thought I'd post it here). My math is pretty rusty, so I'm not really sure- how do the authors expand the function to arrive at the above expression? It reminds me a bit of a Taylor expansion, but not very much. What's the process used to arrive at it? Hydrostatic pressure - doesn't density vary with depth? Our class is learning about hydrostatic water pressure and we have been told that we can calculate the force of the liquid on an object at any depth using "the density x 9.8 x the depth". However, as the depth increases, wouldn't the density of the liquid increase because of the weight of the liquid above it compressing it? So should't there be something in the equation to account for the varying density? To me, "density x 9.8 x depth" seems like it is saying that the density will be constant... What do you call a person who "shuts down" ideas? Show that $\left(1+\dfrac{1}{n}\right)^n$ is monotonically increasing Get three highest values from the array Assume that $A$ is an $n\times n$  real matrix, i.e. $$A^T=-A.$$  Since $\det(A-\lambda I)=\det(A^T-\lambda I)$, $A$ and $A^T$ have the same eigenvalues. On the other hand, $A^T$ and $-A$ also have the same eigenvalues. Thus if $\lambda$ is an eigenvalue of $A$, so is $-\lambda$. If $n$ is odd, $\lambda = 0 $ is an eigenvalue.  A curious search in Google returns  the nonzero eigenvalues of $A$ are all pure imaginary and thus are of the form $iλ_1, −iλ_1, iλ_2, −iλ_2,$ … where each of the $λ_k$ are real.   Here is my question:     How can I prove the fact that "the nonzero eigenvalues of $A$ are all pure imaginary"? I've upgraded from 12.04 to 14.04 via command-line when my system froze, had to do REISUB and dpkg --configure -a to recover from crash after rebooting.  Now everything seems to work except automatically mounting external thumb drives and external hard disk drives. After plugging in said drives, they fail to show up on the left pane and remains unmounted. I can see the device if I run lsusb and fdisk though, so it's possibly to manually mount it but I'd rather resolve why it's not automatically mounting. I had this problem a week or two ago and I posted here but nothing from the suggested solutions seemed to work. I have managed to get some more details on it, in case anyone can help me, because this issue is causing me huge productivity problems and I really want it solved.  So I'm using Linux mint distribution, and I've installed Lyx via the software manager. Every time that I open a new document, I get an error claiming that some files are missing, and until they are installed, compiling the files or exporting them as pdfs is not possible. The file in question is called "extarticle.cls". Additionally, under Document->Settings->Document Class, every document class is marked as unavailable.  Here is the thing though.. this file is not missing... I have located it inside a folder associated with Lyx. It's definitely not missing.  I really need help with this one guys... It's been weeks since the problem came up and I really just want to be rid of it.. Why does this thing not work? Any help? Adding new ROLES and USERS through REST in GeoServer I use GeoServer stable version 2.14.1 and get error messages when trying to add new roles and users via REST. I suspect that the GeoServer REST documentation is buggy. When I call the REST interface of my GeoServer instance, I can see that the roles are accessible through the URI http://localhost:8080/geoserver/rest/security/roles. Users are under the URI http://localhost:8080/geoserver/rest/security/usergroup/users. I can query both resources via GET request, but adding new resources via POST or PUT will not work. A POST request to create new roles ends up with status code 405 (Method not allowed). After trying to create new users comes the status code 500 (Internal Server Error). For this, the GeoServer-REST documentation has been referencing the paths  /roles/roles/{role}  for new roles () or  /usergroup/users/  for new users () since several GeoServer versions. But when I use them, this always ends with Status code 404 (Not Found). How can I add new roles and users through REST in GeoServer? The workarround from @implssv in  does not work for me. How do I check if a given string is a legal/valid file name under Windows? I want to include a batch file rename functionality in my application. A user can type a destination filename pattern and (after replacing some wildcards in the pattern) I need to check if it's going to be a legal filename under Windows. I've tried to use regular expression like [a-zA-Z0-9_]+ but it doesn't include many national-specific characters from various languages (e.g. umlauts and so on). What is the best way to do such a check? I'm using Jabref to manage my Bibliography.  Sometimes, I put directly:     First Author et al.   when adding the article author's name in Jabref.  When compiling my .tex file, LaTeX doesn't recognize the et. al as more names. It takes it as a name/surname.  This is an example of a Bibliography entry in Jabref.  @ARTICLE{Wolf2003,     author = {Wolf, K.et al.},     title = {Compensation mechanism in tumor cell migration: mesenchymal–amoeboid     transition after blocking of pericellular proteolysis},     journal = {J. Cell Biol.},     year = {2003},     volume = {160},     pages = {267–277},    }   This is a .texMWE with the bib entry mentioned:  \documentclass[11pt]{book}   \usepackage{cite}   \bibliographystyle{unsrt} \begin{document}   Here is the bib entry mentioned\cite{Wolf2003}    \bibliography{bibfile}  \end{document}   Here's the output:   How can I solve this problem? Do we need a global test before post hoc tests? I'm currently an M. Phil student in Math and I failed a course last semester because I was not able to hand in a home work assignment (which was worth 40% of my grade) on time (I was 30 minutes late).   Apart from that I'd say I'm a fairly decent student, I got an upper second class honours bachelors degree, I have a B+ and A's for all my other courses in my current programme and I'm almost finished with my first paper to be published.   I've however been deeply worried about this failure as it would reflect poorly on my transcript if I were to apply to a Ph.D or another Master's programme.   Will my failing grade affect my chances of getting into a competitive programme or greatly lower my chances of getting a scholarship? Who else knew that Lord Voldemort was Tom Marvolo Riddle? We know that some people were aware of the fact that Lord Voldemort was Tom Marvolo Riddle prior to his return in Goblet of Fire; at the very least his close soon-to-be-Death-Eater &quot;friends&quot; and Albus Dumbledore:  “Very few people know that Lord Voldemort was once called Tom Riddle. I taught him myself, fifty years ago, at Hogwarts...&quot; ... underwent so many dangerous, magical transformations, that when he resurfaced as Lord Voldemort, he was barely recognizable. Hardly anyone connected Lord Voldemort with the clever, handsome boy who was once Head Boy here.” (Professor Dumbledore to Weasleys, Chamber of Secrets, CHAPTER EIGHTEEN, Dobby’s Reward)  and  “Voldemort,” said Riddle softly, “is my past, present, and future, Harry Potter…” He pulled Harry’s wand from his pocket and began to trace it through the air, writing three shimmering words: TOM MARVOLO RIDDLE Then he waved the wand once, and the letters of his name rearranged themselves: I AM LORD VOLDEMORT “You see?” he whispered. “It was a name I was already using at Hogwarts, to my most intimate friends only, of course. ...  (Tom's Diary manifestation in the Chamber of Secrets).  QUESTION: Who - based on canon (books/interviews/pottermore) - knew about the fact that Lord Voldemort was Tom Marvolo Riddle prior to Ginny being taken to the Chamber of Secrets? Obviously, Albus Dumbledore and Tom himself. Who else? How to make applications open on the correct monitor when using multiple monitors? I'm using Windows 8.1, which has much better multiple monitor support than Windows 7 (sort of). However when I'm in a full-screen app on one monitor, and I go to the Start menu on the other and open a desktop app, it opens on the opposite monitor because of it being on that one last time the app was used.  This suspends the full-screen app and switches to the desktop view on that monitor. I then have to drag the desktop app to the other monitor which I didn't have my mouse pointer near in the first place, then switch back to the full-screen app on that monitor by going to the upper-right corner.  This is so incredibly irritating, every time I plug in my laptop to my second monitor and try to use it, this happens. Not to mention whenever I have Netflix or any kind of video in the second monitor and it just randomly stops playing when I'm trying to work on the other screen.  Most likely there is going to have to be a third-party application to install to do this, right? I would really prefer if it was free, as this was less annoying in Windows 7 when the application would only open on top of the other that was on that monitor. This is one of the maybe two annoying things I don't like about Windows 8/8.1. Everything else is fantastic, to be honest. Simulating data to fit a mediation model How do I spell the possessive form of children? In the sentence below, are the usages of apostrophes correct?     In research about parent stereotypes, the correlation between parents’ beliefs about their early elementary age children’s’ mathematics abilities and the children’s actual abilities increased as children aged.