I found it difficult to understand what behind the story of black hole, I have did some research but have no sense what it meant. This question is really base on my curiosity, I want to learn and understand the meaning behind the black hole! Thank you!
In  (ignoring Hawking radiation), why is a  black? Why nothing, not even light, can escape from inside a black hole? To make the question simpler, say, why is a  black hole black?
Grid System in LaTeX What do you call the process of combining two words to create a new one? How can I manually generate a random number from a given distribution, as for instance, 10 realisations from the standard normal distribution? Are old (>35) faculty candidates discriminated against all over the world? I think that in India research institutes will never take a faculty candidate who is over 35. Is it so all over the world?   I am asking this question from the point of view of if someone starts their PhD. at the age of 27 then its unlikely they will be faculty candidates till they are 40. Finding probability of other child also being a boy A man visits a couple who have two children.One of them, a boy, comes in to the room. Find the probability p that other is also a boy  a) 1/3 b) 2/3 c) 1/2 d) 3/4  Correct Ans: a) 1/3  However I am getting answer as 1/2.My solution is as follows.  The couple has two children, hence the sample space is as follows.  B- Boy G - Girl  BB BG GG ( BG and GB mean the same thing as Girl,Boy), but it is already known that one is boy.So the sample space reduces to  BB BG  So now p is 1/2  Is there some mistake is my approach ? I have a Schengen visa valid from 19/07/2016 to 10/08/2016. But the duration of stay is 7 days only.  I want to stay for 6 days more, for a total of 14 days. And my flight includes travel from a Schengen state to another. I will give this question a little context. Firstly, as I understand it, as soon as I "close the switch" on a circuit, electric current pretty quickly establishes a steady state where, at any given cross section along a wire, the average kinetic energy of that slice is both constant and equal anywhere along the wire. (Please correct me if I am misunderstanding).   If the average kinetic energy is constant anywhere throughout the wire in the circuit (which confuses me, as I would think that the electrons should all accelerate after exiting the resistor since they are no longer being impeded as much), that means that the average velocity is constant. So, in the example of a simple circuit with a battery of v Volts and a resistor of o Ohms, my question is the following:  Because a 'voltage drop' is known to occur across the resistor, what type energy is being "traded" to generate the heat that radiates from the resistor? I would think that the reflexive answer is "electrical energy"...hence the VOLTAGE drop (the sacrificed energy is clearly not kinetic, as the velocity is constant everywhere). However, I find this confusing. Does this mean that if I had a positive test charge, it would be easier for me to bring it to the beginning of the resistor as compared to bringing it to the end of the resister?     Further, if the correct answer IS "electrical energy", why exactly DOES electrical energy get "dissipated" as the electrons pass through the resistor? I always here the comment Oh! It's because all the electrons are running into densely packed crap which impedes their flow but that to me sounds like a reason for their KINETIC energy to be reduced. However, clearly that's not the case. So, ultimately, I guess the real question is:  **What goes on in the resistor that is literally removing electrical energy **. I am sure that this is a quantum mechanics question, but my quantum mechanics knowledge is not terribly strong. If I could get an answer that is devoid of crazy wave function equations, I would greatly appreciate it. Thanks! Is it acceptable to add a duplicate answer to several questions? Let $x$ and $y$ be nonzero elements of an integral domain $D$. Then $x$ and $y$ are associates if and only if $x = yd$ for some unit $d \in D$.    I am done proving the $\Leftarrow$ part. For $\Rightarrow$ what I did was: If $x$ and $y$ are associates then $x \mid y$ and $y \mid x$, so $x \mid y$ implies that $xs = y$ for some $s \in D$ and $y \mid x$ implies that $yt = x$ for some $t \in D$. That is, $yts=y$ which implies $ts=1$. Therefore $s$ is a unit and $t$ is a unit.    Am I on the right track? Can I say that the proof is complete? Just watched the 'How Big is the Universe?' TV program and it indicated that the universe is believed to be infinite in size. They used an approach involving measuring the internal angles of triangles. Or something like that anyway.  But hang on, the Universe has a known starting time and size followed by a finite time expanding at a finite speed. So surely, by definition, it cannot be infinite? I can accept it is honking big but by definition it cannot be infinite. Are they misleading me? Questions about a commutative ring with exactly three ideals Let $R$ be a commutative ring with identity. Assume that $R$ has exactly three distinct ideals: $\{0\},I, R.$      1) Show that if $a \in R-I$, then $a$ is a unit in $R$.      2) Let $a,b\ne0$ in $I$. Show that $ab=0$. How to handle calendar TimeZones using Java? I have a Timestamp value that comes from my application. The user can be in any given local TimeZone.  Since this date is used for a WebService that assumes the time given is always in GMT, I have a need to convert the user's parameter from say (EST) to (GMT). Here's the kicker: The user is oblivious to his TZ. He enters the creation date that he wants to send to the WS, so what I need is:  User enters: 5/1/2008 6:12 PM (EST)  The parameter to the WS needs to be: 5/1/2008 6:12 PM (GMT)  I know TimeStamps are always supposed to be in GMT by default, but when sending the parameter, even though I created my Calendar from the TS (which is supposed to be in GMT), the hours are always off unless the user is in GMT. What am I missing?  Timestamp issuedDate = (Timestamp) getACPValue(inputs_, "issuedDate"); Calendar issueDate = convertTimestampToJavaCalendar(issuedDate); ... private static java.util.Calendar convertTimestampToJavaCalendar(Timestamp ts_) {   java.util.Calendar cal = java.util.Calendar.getInstance(       GMT_TIMEZONE, EN_US_LOCALE);   cal.setTimeInMillis(ts_.getTime());   return cal; }   With the previous Code, this is what I get as a result (Short Format for easy reading):  [May 1, 2008 11:12 PM] Getting started with ArcObjects? What is the best route or place to get started with ArcObjects if one is not a developer and not aiming to become a developer?  I've been using gis professionally for a long time, almost two decades, arcinfo/arcgis for most of that; I'm pretty good. I'm learning software development, and even have a modestly successful small python application used in a public project; I'm not good! I don't want to become a full fledged software developer but I keep running into things I just can't do without programming (). In the arcgis world this puts me pretty squarely in the python camp, which is fine by me since I like python, however python does not have straightforward access to ArcObjects. (Python and ArcObjects , but it's an unsupported route. This question is about following a beaten path.)  I need to get started, but where?  to get started with the  but $1500/yr is definitely not in my budget, and sounds like using a sledge hammer to swat mosquitos. And which language .NET, Visual Basic, or Visual C++?    UPDATE: Thank you everyone for the wonderful answers. In light of them I realise  I unecessarily narrowed the scope of my question be pre-supposing "ArcObjects" is the direction I need to go in. A more open ended formulation is more along the lines of:     I keep running into problems I just   can't solve with arcgis and python   alone. What else can I learn/use to   solve problems like X? I've no   interest or intention of becoming a   software developer. I just need to do   a couple things which aren't exposed   to the arcgis python modules. It's so cool that the notification reminds you of the colour of badge you've earned. But I am a little puzzled by the symbols:      Is it feasible to use the symbol from the earned site? At the moment it uses the symbol from the site I happen to be on (as you can see by looking to the left of the dropdown in each case.) Is it true that an ideal is primary iff its radical is prime? I have installed Ubuntu on my D: partition using Wubi. Is there any way in which I can remove my Windows from C: drive and move my existing Ubuntu installation to C: drive and make it a regular install. Why would the command "ls *" generate an error about invalid options? There is a thread that talks about ls "*" not showing any files, but I actually wonder why the simple  ls *   command doesn't output anything in my terminal other than  ls: invalid option -- '|' Try 'ls --help' for more information.   while   ls   will list all the files in the current directories as    1                  ferol                      readme.txt  2                  fichier                    sarku  2018               GameShell                  Templates  22223333          '-|h4k3r|-'                 test  3                  hs_err_pid2301.log         test2  CA.txt             important.top.secret.txt   toto.text  CA.zip             JavaBlueJProject           tp1_inf1070  countryInfo.txt    liendur                   'tp1_inf1070_A19(2) (1)'  currency           liensymbolique             tp1_inf1070_A19.tar  curreny            LOL                        Videos  Desktop            Longueuil                 'VirtualBox VMs'  Documents          Music                      words  douffos            numbers                    Zip.zip  Downloads          Pictures  examples.desktop   Public   Any ideas as to why the globbing doesn't take effect here? I'm on Ubuntu, working in the terminal, I don't know if it makes a difference.  Thanks. How prove this $\prod_{1\le i<j\le n}\frac{a_{j}-a_{i}}{j-i}$ is integer let $a_{i},i=1,2,\cdots,n$ be postive integer ,show that $$1^{n-1}2^{n-2}\cdots (n-2)^2(n-1)|\prod_{1\le i&lt;j\le n}(a_{i}-a_{j})$$  I know this $\prod_{1\le i&lt;j\le n}(a_{i}-a_{j})$ is  Vandermonde  determinants,and I found $$1^{n-1}2^{n-2}\cdots (n-2)^2\cdot (n-1)=1!2!3!\cdots (n-1)!=\prod_{1\le i&lt;j\le n}(j-i)$$ we only prove $$\prod_{1\le i&lt;j\le n}\dfrac{a_{j}-a_{i}}{j-i}$$ is integer  maybe consider Vandermonde determinants ? But I can't prove this ASP.NET -> WCF concurrency problem lstlisting: how to set code color and frame color