Dropped out of maths PhD - options for later on?
Is it a good idea to take a break from studying a mathematics PhD and revisit academia at a later stage?
Object selection box in addon In my addon panel, how can I have an object selection box?  And what data type would I use to store the the selected object?  It should look like this: I searched for links__system_main_menu, but just find usages of this theme. Where is it defined? dimension of a subspace spanned by two subspaces If $M$ and $ N$ be the subspaces of a vector space $V$ then prove that  $(\dim M) + (\dim N) = (\dim M+N) + (\dim M \cap N)$. I accidentally rsynced .thunderbird to user@host instead of to user@host:/home/user.  Where is .thunderbird now?  Is there a good way to search for the folder? Let $f$ be an entire function and $L$ a line in $\mathbb{C}$ such that $f(\mathbb{C})\cap L=\emptyset$. Show that $f$ is constant function.  If $f$ is not constant  then $f(\mathbb{C})$ is dense set in $\mathbb{C}$, but how can I use that line does not intersect the image set? My internal storage capacity is running low,  what can I do? Currently, my internal storage is running low on space.    What can I do besides moving applications to the external memory, as to free up more space, but preserve my current applications and avoid uninstalling?  (Some of them won't be moved) After reading an article about Ubuntu's netflix support I decided to try running netflix through chromium but I got this error code: M7063-1913 I assumed that it was a problem with html5 but in the playback preferences it doesn't give me the option to use it. Do Squibs have to be pure-blood? If a Muggle was born of a wizard/witch and a Muggle, is that person a Squib, or is that reserved to people born from pure-blood families?    (Related: ) I am just looking for some clarification on this exercise:  Let $A = \{a,b,c,d\}$. Give an example of a relation $R$ on $A^2$ which is reflexive, symmetric, and not transitive.  I understand that if I was only dealing with $A$ and and not $A^2$ I could give an answer similar to:  $R = \{(a,a),(a,b),(a,d),(b,a),(b,b),(c,c),(d,a),(d,d)\}$  Here $R$ is reflexive, symmetric, and not transitive.  What is confusing me is the fact that we have $A^2$. I am not sure what I am missing here. I am looking through my book to see if I can figure this out, but if someone could help shed some light on this it would be appreciated.  Thanks,  Tony What exactly do the colors in htop status bars mean? How to lazy load images in ListView in Android I was given this question by a friend and after working tirelessly on it I have not come up with anything substantial. I was hoping someone in the community could provide a pointer or possibly a solution. The person who gave me the question says he has the answer to it, but I am more curious about the working.  Here is the question:     Three points $(B, C, D)$ lie on parabola  $y = x^2$ and a fourth point $A$ is placed such that $ABCD$ forms a square. Find the minimal area of $ABCD$.   So far my working out has involved a collection of distance/mid-point formula's and I haven't even reached the point where I differentiate to minimize the area.  Any pointers would be welcome.   Edit  Apparently the correct answer is $\sqrt{2}$ units squared. De Rham Cohomology of the tangent bundle of a manifold I would like to compute the de Rham cohomology of the tangent bundle $TM$ of a manifold $M$. It seems to me that we can just homotopy each fibre to a point, and that this would give a homotopy equivalence between $TM$ and $M$. Since de Rham cohomology is a homotopy invariant, this would imply that $H^*_{\text{dR}}(TM) \cong H^*_{\text{dR}}(M)$.     Is it always true that the tangent bundle of a manifold is homotopic to the manifold itself by the homotopy of each fibre with a point? According to  and my own understanding, the tilde expands to the home directory:  $ echo ~ /home/braiam   Now, whenever I want the shell expansion to work, i. e. using variable names such $FOO, and do not break due unexpected characters, such spaces, etc. one should use double quotes ":  $ FOO="some string with spaces" $ BAR="echo $FOO" $ echo $BAR echo some string with spaces   Why doesn't this expansion works with the tilde?  $ echo ~/some/path /home/braiam/some/path $ echo "~/some/path" ~/some/path As a 8th grader I am still a newbie at science and I have problems understanding the forces that I can not imagine and one of these "forces" is the moment.  We are told that,  $$\text{moment}= Nm$$ but how can a certain force (i.e. $N$) be applied when there is $m$? How does it depend on the length of the considered object?  And how can 1 moment be defined on the basis of that representation?  And what would be the effect if the moment value is increased by the newton part as opposed to the effect when the value is increased by the length part.  Or is the result the same in both cases? 35km commute possible? Currently, on every other day I commute to work which is a distance of 18km each way. I enjoy this ride but next year I may be moving to a place which will be about 35km from work. Questions:  1) Would it still be reasonable to commute this kind of distance each way once I have moved?  2) Google maps estimates that this distance would take 2 hours to complete. Would it be possible (depending on the bike and fitness) to do this distance in about an hour? I have a scenario. (Windows Forms, C#, .NET)   There is a main form which hosts some user control. The user control does some heavy data operation, such that if I directly call the UserControl_Load method the UI become nonresponsive for the duration for load method execution. To overcome this I load data on different thread (trying to change existing code as little as I can)   I used a background worker thread which will be loading the data and when done will notify the application that it has done its work.   Now came a real problem. All the UI (main form and its child usercontrols) was created on the primary main thread. In the LOAD method of the usercontrol I'm fetching data based on the values of some control (like textbox) on userControl.    The pseudocode would look like this:  CODE 1  UserContrl1_LoadDataMethod() {     if (textbox1.text == "MyName") // This gives exception     {         //Load data corresponding to "MyName".         //Populate a globale variable List&lt;string&gt; which will be binded to grid at some later stage.     } }   The Exception it gave was     Cross-thread operation not valid: Control accessed from a thread other than the thread it was created on.   To know more about this I did some googling and a suggestion came up like using the following code  CODE 2  UserContrl1_LoadDataMethod() {     if (InvokeRequired) // Line #1     {         this.Invoke(new MethodInvoker(UserContrl1_LoadDataMethod));         return;     }      if (textbox1.text == "MyName") // Now it wont give an exception     {     //Load data correspondin to "MyName"         //Populate a globale variable List&lt;string&gt; which will be binded to grid at some later stage     } }   BUT BUT BUT... it seems I'm back to square one. The Application again  become nonresponsive. It seems to be due to the execution of line #1 if condition. The loading task is again done by the parent thread and not the third that I spawned.  I don't know whether I perceived this right or wrong. I'm new to threading.  How do I resolve this and also what is the effect of execution of Line#1 if block?  The situation is this: I want to load data into a global variable based on the value of a control. I don't want to change the value of a control from the child thread. I'm not going to do it ever from a child thread.   So only accessing the value so that the corresponding data can be fetched from the database. This question was asked in an entrance test for an undergraduate mathematics program today, held all over India.   Question: $f$ is a differentiable function in $[0,1]$ such that $f(f(x))=x$ and $f(0)=1$.  Find the value of $\int_{0}^{1} (x-f(x))^{2016} dx$.  I tried to solve it by substituting $f(f(x))$ in place of $x$, but could not proceed much further. Any hints or solutions will be appreciated. onConfigurationChanged not getting called For sets $A,B$, let $|A|\leq^*|B|$ say that there exists an onto map $f:B\rightarrow A$ or $A=\emptyset$.   My question is, is $$\forall A,B(|A|\leq^*|B|\longrightarrow |A|\leq|B|)$$ equivalent to the axiom of choice?  Thanks