Should I publish as a master’s student?
When should I begin publishing?
Let $U$ be connected. A function $u \in H^1(U)$ is a weak solution   of Neumann's problem   \begin{equation} (*)\qquad\left\{ \begin{array}{rl} -\Delta = f &amp; \text{in } U \\ \frac{\partial u}{\partial \nu} = 0 &amp; \text{on } \partial U \end{array} \right. \end{equation}   if   $$ \int_U Du \cdot Dv \; dx = \int_Ufv \; dx $$   for all $v \in H^1(U)$. Let $f\in L^2(U)$. Prove $(*)$ has a weak solution   if and only if   $$ \int_U f \; dx =0. $$   For the only if part I set $v=1$. However I do not see where to start the if part. I was thinking of the Lax-Milgram theorem. That's where I'm now. How to upload a file of size 2GB from Apex? Is there any sobject that I can make use of? Self-references in object literals / initializers Why would parametric statistics ever be preferred over nonparametric? Log form of variables and descriptive measures Because of larger values of variables, I did a log- transformation in my dataset. Now I want to give a descriptive table regarding my variables like mean, max, min, median, skewness, kurtosis. Can I give standard measures like arithmetic mean or should I give geometric mean? In terms of skewness or kurtosis, do I need a transformation? We have in and out degree of a directed graph G. if G does not includes loop (edge from one vertex to itself) and does not include multiple edge (from each vertex to another vertex at most one directed edge), we want to check for how many of the following we have a corresponding graph. the vertex number start from 1 to n and the degree sequence are sort by vertex numbers.  a) $d_{in}=(0,1,2,3), d_{out}=(2,2,1,1)$  b) $d_{in}=(2,2,1), d_{out}=(2,2,1)$  c) $d_{in}=(1,1,2,3,3), d_{out}=(2,2,3, 1,2)$  I want to find a nice way instead of drawing graph.  for (C): Proving the Lorentz invariance of the Lorentz invariant phase space element I have been looking around for a satisfactory answer to prove that  $$\frac{d^3\vec{p}}{2E_{\vec{p}}}$$  where $E_{\vec{p}}=+\sqrt{(|\vec{p}|c)^2+(mc^2)^2}$, is Lorentz invariant. The standard answer seems to be that the above measure is equal to  $$d^4p \, \delta (p^2-m^2)\theta(p_0)$$  where $p^2=p_0^2-|\vec{p}|^2$, and $\theta(x)$ is the step function. I understand these two are equivalent, but I don't understand why the second has to be Lorentz invariant, in particular why the Dirac delta has to be Lorentz invariant. I have found a  (section 2.1) that proves that $\delta^{(4)}(p-p')$ is Lorentz invariant, but I can't find a way to extend their method successfully here. In fact, all I can seem to get tells me the above isn't Lorentz invariant, and that in fact it should transform to   $$\frac{d^3\vec{p}'}{2\gamma E_{\vec{p}'}}$$  which makes sense from $d^4p$ being Lorentz invaraint and $dp_0$ transforming proportional to $\gamma$, but it isn't what everyone else says. What's the problem here?    An alternative way to "derive" the factor of $1/\gamma$:  $$\delta (p^2-m^2)\theta(p_0)=\frac{1}{E_{\vec p}}\delta(p_0-E_{\vec{p}})$$  Now, as $dp_0$ transforms to $\gamma dp_0$, the $\delta(p_0-E_{\vec{p}})$ should transform to $\gamma^{-1}\delta(p_0-E_{\vec{p}})$, as can be shown with an analogous argument to the one shown in the . The $E_{\vec{p}}$ also transforms to $\gamma(E_{\vec{p}}-v p_x)$ for an $x$-boost, but this doesn't seem to solve it. This is my first time using a LaTeX editor.   I installed  allowing it to use the default directory on the C drive.  Software Versions   Windows: 7 Ultimate 64-bit  Texmaker 3.4.1 for Windows   I then did A Local guide for using Texmaker (There use to be a link to this but it is now dead)  Basically create a simple Hello World document and save it.  When I went to process the file   Tools -&gt; PDFLaTeX     I received    Error: Log file not found!   What I checked  I checked the configuration (Options -> configure Texmaker) and found no option for log files.  I checked for a log file under the C:\Program Files (x86)\Texmaker and found none.  I checked for a log path in the Windows registry using regedit and found none.  I checked the Texmaker issues and found  but it does not help.  Any ideas?  After reading answer  I installed MiKTeX as an administrator (didn't work as user) and chose the default options. After MiKTeX installed I was able to create a PDF file using Texmaker.   Also, correctly setting the PDF viewer options   Options -&gt; Configure Texmaker -&gt; Commands -&gt; PDF Viewer Built-in Viewer and Embed   I was able to preview the pdf in Texmaker   View -&gt; PDF Viewer   What I learned   is a LaTeX editor which generates a file containing LaTeX markup.     is a program that converts the LaTeX markup into an output format such as PDF. What is Thanos's motivation for his action? If I had a gauntlet with essentially unlimited power, and my goal was to help make sure life in the universe was able to prosper, then my first thought toward this goal probably would not be      to extinguish half of all life.   This doesn't directly help anyone, and it is, at best, a temporary solution, since      populations will eventually grow back.   Assuming that I am not, in fact, secretly in love with an avatar of death itself, why would I choose to      commit universal genocide   instead of directly solving the limited resource problem?  So, to be specific, my question is: In-universe, what is Thanos's motivation for attempting to do this instead of more reasonable alternatives? Can a parallel computer simulate a quantum computer? Is BQP inside NP? In Helgason, "Differential Geometry, Lie Groups and Symmetric Spaces"  we have the formula for the exterior derivative  $(p+1)d\omega(X_{1}, \ldots X_{p+1})=\Sigma_{i=1}^{p+1} (-1)^{i+1} X_{i} \cdot \omega(X_{1}, \ldots , \hat{X_{i}}, \ldots X_{p+1})+\Sigma_{i&lt;j} (-1)^{i+j}\omega([X_{i}, X_{j}], X_{1}, \ldots , \hat{X_{i}}, \ldots \hat{X_{j}}, \ldots , X_{p+1})$  but in other sources on-line they have the same formula without the factor of $p+1$ on the left-hand side.  Are there two different definitions of the exterior derivative, or is there an error in Helgason? self referential struct definition? I haven't been writing C for very long, and so I'm not sure about how I should go about doing these sorts of recursive things... I would like each cell to contain another cell, but I get an error along the lines of "field 'child' has incomplete type". What's up?  typedef struct Cell {   int isParent;   Cell child; } Cell; Why would a spinning space station create a centrifugal force on an astronaut rather than simply spinning around him/her? We often see films with spinning space station that create  by having the astronauts pulled outwards by centrifugal force.  I'd like to know if this would really happen, and if so, why is the following scenario not true:   Take an astronaut in open space. He doesn't move. Put a big open spinning cylinder around him - surely he still doesn't move. Close the cylinder. I still see no reason for him to be pulled outwards. Why is the Ideal Norm Multiplicative? How closely can a game legally resemble another? How do I uninstall Ubuntu Wubi? I am looking for a quick way to sleep without closing the lid, or using the mouse.  If it matters, I have Lion version OS and a MacBook Air. Zero probability and impossibility I read a comment under :     There are plenty of events that can occur that have zero probability.   This reminds me that I have seen similar saying before elsewhere, and have never been able to make sense out of it. So I was wondering    if zero probability and impossibility mean the same? if an event with zero probability doesn't mean that the event is impossible to occur, how probability theory represents/describes impossibility?   Thanks and regards! Decrease available inventory item on Cognito Form, removing it when zero I want to limit inventory quantities on a sales form, so that it can start at say 100 and count backwards as applicants submit orders and then shut down that particular option when it reaches 0.    Is this possible with Cognito? Suppose I have two tables that don't have many columns (3, for example). How can I position them side by side?