Can we travel faster than the speed of light?
Is it possible for information to be transmitted faster than light by using a rigid pole?
Studying from Roman's Advanced Linear Algebra, I want to prove that $$U^* \otimes V^* \cong (U \otimes V)^* \cong \hom(U,V;\mathbb{F})$$ The author proves that $U^* \otimes V^* \cong (U \otimes V)^*$ by showing that there is an unique linear transformation   $$\theta:U^* \otimes V^* \to (U \otimes V)^*$$  defined by $\theta(f \otimes g)=f \odot g$ where $(f \odot g)(u \otimes v)=f(u)g(v)$  I want to prove that $U^* \otimes V^* \cong \hom(U,V;\mathbb{F})$. I tried to use the universal property by fixing $f \in U^*, g\in V^*$ and defining $S: U^*\times V^* \to \hom(U,V;\mathbb{F})$ as $S(f,g)=F_{f,g}$, where $F_{f,g}(u,v)=f(u)g(v)$, but I got stuck. How can I find unanswered questions with zero answers in some tag? I am wondering if there is a modifier or tool that will essentially undo a subsurf or subdivide command. Fiction novel or movie about sentient dinosaurs Provide two arguments to one option using getopts In below code when I give option r then getopts requires one arguments:  while getopts ":hr::l:" opt; do     case $opt in         r ) echo "Run Numbers - argument = $OPTARG " ;;         l ) echo "Latency range - argument = $OPTARG" ;;         h ) helptext             graceful_exit ;;         * ) usage             clean_up             exit 1     esac done   But I need to pass two arguments after -r option, instead of one. Is there an easy way to do this? I am going to Santa Monica for 4 weeks to polish my English in July and would like to volunteer at the Planetary Society located in Pasadena.  I am a Swiss citizen and have a biometric passport. However, I don't have any special visa, as there is no visa needed for the school I am attending and using the Visa Waiver Program, I am allowed to stay up to 90 days in the US.  Am I allowed to do volunteer work during my stay? Trace map from finite surjective morphism of normal irreducible varieties Why do we get the same differential equations from both principles? Surely there is a fundamental connection between them? When written out, the two seem to have nothing in common.   $$\sum _i ( \mathbf F _i - \dot{\mathbf p}_i) \cdot \delta \mathbf r _i = 0$$  $$S[q(t)] = \int ^{t_2} _{t_1} \mathcal L (q,\dot{q},t)dt$$  After playing with d'Alembert's principle  we find that we can rewrite the whole thing as $$\sum _i \left[ \frac{d}{dt} \left( \frac{\partial T}{\partial \dot{q}_i} \right) - \frac{\partial T}{\partial q_i}-Q_i\right] \delta q_i$$  This can further be rewritten under certain conditions so we get the exact form of the E-L equation.   It seems to me that both ways of arriving at the result are fundamentally different.   A function must obey the E-L equations in order to minimize the action over a path, but when we look at the virtual work, it appears that they come from the fact that (quoting Goldstein) "particles in the system will be in equilibrium under a force equal to the actual force plus a 'reversed effective force'."  I think I understand the principle of stationary action, I can see how it leads to the E-L equations, but d'Alembert's Principle seems so arbitrary, I can't see any motivation for it. Symbol Table from Apex Class In an earlier question  I asked in general about the symbol table for an Apex class.  Using the Tooling API wrapper from  I am able to get part way there. But am unGodly confused.  If I go to the developer console, query editor, check the "Use Tooling API" box and run this query:  Select Id, Name, symbolTable FROM ApexClass Where Name Like '%NewCaseListController%'   I get back an ID, Name and [object Object] for the symbol table, meaning there is a symbol table object there.   But if I try the same query in Apex code in the execute anonymous window I get the error:   System.CalloutException: Web service callout failed: Unable to parse callout response. Apex type not found for element location   If I do this in Apex I can get a result back, and according to the code for the class the result should be of type ToolingAPIWSDL.QueryResult. The QueryResult should contain a member consisting of a list of sObject_x records sObject_x[], unless I am mis-reading what that means.  ToolingAPIWSDL.QueryResult result = tooley.query('select Id, Name from ApexClass WHERE Name Like \'NewCaseListController\'');   I can take the result and apparently put the sObject_x object in it like this:  List&lt;ToolingAPIWSDL.sObject_x&gt; objList = new List&lt;ToolingAPIWSDL.sObject_x&gt;(); for(Integer i = 0; i&lt;result.records.size(); i++){     objList.add(result.records[i]); }   At least that does not throw an error and I can write:     System.debug('objList: ' + objList[0]);  And get a result, but how do I access the symbol table? Or more to the point, how can I get a list of methods and variables? I am assuming the symbolTable is the only way? How do I install the latest stable version of Thunderbird? Compress a directory using tar/gz over SSH to local computer? I'd like to essentially tar/gz a directory on a remote machine and save the file to my local computer without having to connect back into my local machine from the remote one. Is there a way to do this over SSH? The tar file doesn't need to be stored on the remote machine, only on the local machine. Is this possible? How can I restrict various roles with limit in creating nodes of a particular content type How can I restrict various roles with limit in creating nodes of a particular content type? I am totally stumped for what to do here, any help would be appreciated.   1) What happens if you apply the method of steepest descent to $f(x)=x_1^2+x_2^2+x_3^2$?  2)Lagrange multipliers method- Find the dimensions of the rectangular box open at the top of greatest internal volume, given the surface area of the five faces is $108 \, \mathbb{cm}^2$.  Thanks Is it true that the order of $ab$ is always equal to the order of $ba$? How do I prove that if $a$, $b$ are elements of group, then $o(ab) = o(ba)$?   For some reason I end up doing the proof for abelian(ness?), i.e., I assume that the order of $ab$ is $2$ and do the steps that lead me to conclude that $ab=ba$, so the orders must be the same. Is that the right way to do it? Note: I am very new to the more advanced side of electricity. I do not have a firm grasp on the exact mechanics.  Lets say I have an example circuit:  5V Power Supply -&gt; LED -&gt; Resistor -&gt; Ground  Now the LED is receiving 20ma and 5V. If I were to switch the LED and the resistor however, the LED should receive less voltage but the same current, so wouldn't it be dimmer? Or would it receive the same voltage?  I've looked at these two threads and their answer doesn't help. P-adic expansion construction My computer does not store the history of the entries entered in RUN (WIN+R).   Thus, how to enable Windows to store the history? I'm trying to solve the following equation:  $$x^3-y^3=xy+61$$  I got:  $$(x-y)(x^2+xy+y^2)=xy+61$$  But I can't go any further. I am looking for a solution in integers.  I need some hints to proceed, please! Want to install VirtualBox Guest Additions on CentOS 7 but get a header mismatch How to implement a single instance Java application? Sometime I see many application such as msn, windows media player etc that are single instance applications (when user executes while application is running a new application instance will not created).  In C#, I use Mutex class for this but I don't know how to do this in Java.