Labelling feynman diagrams in tikz-feynman package Consider the following piece of code using the tikz-feynman package.  \begin{center}     \begin{tikzpicture}[baseline={(current bounding box.center)}]     \begin{feynman}         \diagram [vertical'=a to b] {             {   [edges={draw=none}]                 a -- b [label=0:\(\mu_{3}\)]                 -- c [label=-180:\(\mu_{4}\)]                 -- d [label=-180:\(\mu_{1}\)]                 -- a [label=0:\(\mu_{2}\)],             },             {   [edges={photon}]                 a -- ap [particle=\(p_{2}\)],                 b -- bp [particle=\(p_{3}\)],                 d -- dp [particle=\(p_{1}\)],                 c -- cp [particle=\(p_{4}\)],             },         };         \diagram* {             (c) -- [fermion] (b)                 -- [fermion] (d)                 -- [fermion] (a)                 -- (c),         };     \end{feynman}     \end{tikzpicture}     %     \feynmandiagram[baseline={(current bounding box.center)}, vertical'=a to b,] {         {   [edges={fermion}]             a -- [edge label=\(k+p_{1}+p_{2}\)] b [label=0:\(\mu_{3}\)]             -- [edge label=\(k-p_{4}\)] c [label=-180:\(\mu_{4}\)]             -- [edge label=\(k\)] d [label=-180:\(\mu_{1}\)]             -- [edge label=\(k+p_{1}\)] a [label=0:\(\mu_{2}\)],         },         {   [edges={photon}]             a -- ap [particle=\(p_{2}\)],             b -- bp [particle=\(p_{3}\)],             d -- dp [particle=\(p_{1}\)],             c -- cp [particle=\(p_{4}\)],         },     };     %     \begin{tikzpicture}[baseline={(current bounding box.center)}]     \begin{feynman}         \diagram [vertical'=a to b] {             {   [edges={draw=none}]                 a -- b [label=0:\(\mu_{3}\)]                 -- c [label=-180:\(\mu_{4}\)]                 -- d [label=-180:\(\mu_{1}\)]                 -- a [label=0:\(\mu_{2}\)],             },             {   [edges={photon}]                 a -- ap [particle=\(p_{2}\)],                 b -- bp [particle=\(p_{3}\)],                 d -- dp [particle=\(p_{1}\)],                 c -- cp [particle=\(p_{4}\)],             },         };         \diagram* {             (a) -- [anti fermion] (b)                 -- [anti fermion] (d)                 -- [anti fermion] (c)                 -- (a),         };     \end{feynman} \end{tikzpicture} \end{center}               It gives me the following output:    I would like to add a caption to each of these diagrams with the words 'Figure I,' 'Figure II' and 'Figure III' respectively.  How do I do so?
Labelling figures in the tikz package Consider the following piece of code, which uses the tikz-feynman package:  \usepackage{tikz-feynman, contour} \tikzfeynmanset{compat=1.1.0}  \begin{document} \begin{center}     \begin{tikzpicture}[baseline={(current bounding box.center)}]     \begin{feynman}         \diagram [vertical'=a to b] {             {   [edges={draw=none}]                 a -- b [label=0:\(\mu_{3}\)]                 -- c [label=-180:\(\mu_{4}\)]                 -- d [label=-180:\(\mu_{1}\)]                 -- a [label=0:\(\mu_{2}\)],             },             {   [edges={photon}]                 a -- ap [particle=\(p_{2}\)],                 b -- bp [particle=\(p_{3}\)],                 d -- dp [particle=\(p_{1}\)],                 c -- cp [particle=\(p_{4}\)],             },         };         \diagram* {             (c) -- [fermion] (b)                 -- [fermion] (d)                 -- [fermion] (a)                 -- (c),         };     \end{feynman}     \end{tikzpicture}     %     \feynmandiagram[baseline={(current bounding box.center)}, vertical'=a to b,] {         {   [edges={fermion}]             a -- b [label=0:\(\mu_{3}\)]             -- c [label=-180:\(\mu_{4}\)]             -- d [label=-180:\(\mu_{1}\)]             -- a [label=0:\(\mu_{2}\)],         },         {   [edges={photon}]             a -- ap [particle=\(p_{2}\)],             b -- bp [particle=\(p_{3}\)],             d -- dp [particle=\(p_{1}\)],             c -- cp [particle=\(p_{4}\)],         },     };     %     \begin{tikzpicture}[baseline={(current bounding box.center)}]     \begin{feynman}         \diagram [vertical'=a to b] {             {   [edges={draw=none}]                 a -- b [label=0:\(\mu_{3}\)]                 -- c [label=-180:\(\mu_{4}\)]                 -- d [label=-180:\(\mu_{1}\)]                 -- a [label=0:\(\mu_{2}\)],             },             {   [edges={photon}]                 a -- ap [particle=\(p_{2}\)],                 b -- bp [particle=\(p_{3}\)],                 d -- dp [particle=\(p_{1}\)],                 c -- cp [particle=\(p_{4}\)],             },         };         \diagram* {             (a) -- [anti fermion] (b)                 -- [anti fermion] (d)                 -- [anti fermion] (c)                 -- (a),         };     \end{feynman}     \end{tikzpicture}     \end{center} \end{document}   This piece of code draws the following figure:    I would like to label each figure. I do not want a caption, but just a label beneath each diagram. The label should say Diagram I, Diagram II, Diagram III.  How do I implement this into my code?
Here the lower box dimension and the upper box dimension are exactly what Falconer talks about in his book "Fractal Geometry". I already know that the upper box dimension is finitely stable since $N_\delta(A\cup B)\le N_\delta (A)+N_\delta(B)$, where $N_\delta(A)$ is defined as usual, and Falconer gives an example to show the box dimension may not be countably stable. (We know that, however, the Hausdorff dimension is countably stable).  But now I want to find the example to show the lower box dimension may not even be finitely stable.It seems that we can use von Koch curve to illustrate this, but what is the explicit explanation for this? Since the lower box dimension is monotonic, we need to find set A and B and show that   $\underline{\dim}_B(A\cup B)&gt;\max\{\underline{\dim}_B(A),\underline{\dim}_B(B)\}$. I was wondering if it was possible to use any of the API's provided by SF to build an external (C#, Java) application to manage building changesets.   Building changesets is very tedious when trying to include 100's of items and I was hoping to streamline the process for our team by building an application I can load an excel file to with the required components and have it build the outbound changeset. Show that $A \setminus ( B \setminus C ) \equiv ( A \setminus B) \cup ( A \cap C )$ Show that  $A \setminus ( B \setminus C ) \equiv ( A \setminus B) \cup ( A \cap C )$  This is an exercise I was trying to do ( not homework ) and I got stuck as follows:  Working from $A \setminus ( B \setminus C )$:  $x \in A \wedge x \notin ( B \setminus C )$ $x \in A \wedge ((x \in B \wedge x \in C) \vee (x \notin B \wedge x \in C) \vee (x \notin B \wedge x \notin C) )$  At this point I'm not sure how to proceed.  Working from the other side $ ( A \setminus B) \cup ( A \cap C ) $:  $ x \in ( A \setminus B) \cup ( A \cap C ) $  $ x \in ( A \setminus B) \vee x \in ( A \cap C ) $  $ ( x \in A \wedge x \notin B ) \vee ( x \in A \wedge x \notin C ) $  $ x \in A \wedge (x \notin B \vee x \notin C ) $  $ x \in A \wedge x \notin ( B \cap C ) $  $ A \setminus ( B \cap C ) $  I could also use some formating tips like how display logical not and how to get the lines to display properly without blank lines inbetween. :-) Insert title of table of contents into toc I have a little bit of problem. I have to put the title of toc into toc. I've used the following code to do that and it works for me, kind of. The problem is in the title is aligned with the titles of the chapters and not with list of figures etc.  { \makeatletter \let\@oldstarttoc\@starttoc \renewcommand{\@starttoc}{%   \addcontentsline{toc}{chapter}{\protect\numberline{}\contentsname}% Add ToC to ToC   \@oldstarttoc } \tableofcontents \makeatother }   Here is the picture of my toc.    My idea is to use the same code for  Acknowledgements, Lists of... , Abbreviations etc. Is it ok to try that or there is an alternative? Can you cast a spell at a higher level, even if it doesn't have an "At higher levels" entry? My daughter is a US Citizen. We (parents)are also planning to permanently settle in US. We will go their as Permanent Resident,as per US Law. We have a house here in India worth Rs.2 Crores.  We want to sell it and take money with us. We have ordinary savings Bank account here in India.  My US Citizen Daughter is a Income Tax payer.  Now your advises are required as under:   What are the routes to take money from India to US and our tax liabilities Can I gift this whole amount to my US Citizen Daughter or what is the maximum limit of Gift amount.  What will be the tax liability on me and on my Daughter in case of Gift   Whether I have to show it in my Income Tax Return or in my Daughter's Tax Return. What US Income Tax Laws says. What will be the procedure to send money as Gift to my Daughter. Will the money will go directly from my Bank Act.to my Daughter's Bank Account. Will there will be wire transfer from bank to bank Can I send money through other money sender Certified Companies also.    Please advise. If there is something more on the subject to make me understand, please advise. Thanks, Are proofs by contradiction really logical? Let's say that I prove statement $A$ by showing that the negation of $A$ leads to a contradiction.   My question is this: How does one go from "so there's a contradiction if we don't have $A$" to concluding that "we have $A$"?  That, to me, seems the exact opposite of logical. It sounds like we say "so, I'll have a really big problem if this thing isn't true, so out of convenience, I am just going to act like it's true". How to prove this inequality $\left|x\sin{\frac{1}{x}}-y\sin{\frac{1}{y}}\right|<2\sqrt{|x-y|}$? For any real numbers $x,y\neq 0$,show that $$\left|x\sin{\dfrac{1}{x}}-y\sin{\dfrac{1}{y}}\right|&lt;2\sqrt{|x-y|}$$ I found this problem when I dealt with . But I can't prove it. Maybe the constant $2$ on the right hand side can be replaced by the better constant $\sqrt{2}$? Thank you. 2D and 3D vectors in Tikz I would like to draw some 2D and 3D vectors in Tikz with certain properties. The following primitive graph sums what I desire:   I just need the first quadrant of the Cartesian coordinate system for my representation.  I need the vector to be connected to the respective values on the distinct dimensions(not a projection, just orthogonal dashed lines).   The code segment below does what I want to achieve in 3D with two exceptions:  The projections on the xy plane and z dimension are given instead of connecting the head of the vector to the corresponding value in each dimension.  Numerical values are missing in dimensions.   Code: \documentclass[tikz]{standalone} \usepackage{tikz-3dplot} \begin{document}  \tdplotsetmaincoords{60}{120} \begin{tikzpicture}     [scale=3,     tdplot_main_coords,     axis/.style={-&gt;,blue,thick},     vector/.style={-stealth,red,very thick},     vector guide/.style={dashed,red,thick}]  %standard tikz coordinate definition using x, y, z coords \coordinate (O) at (0,0,0);  %tikz-3dplot coordinate definition using r, theta, phi coords \tdplotsetcoord{P}{.8}{55}{60}  %draw axes \draw[axis] (0,0,0) -- (1,0,0) node[anchor=north east]{$x$};     \draw[axis] (0,0,0) -- (0,1,0) node[anchor=north west]{$y$};     \draw[axis] (0,0,0) -- (0,0,1) node[anchor=south]{$z$};  %draw a vector from O to P \draw[vector] (O) -- (P);  %draw guide lines to components \draw[vector guide] (O) -- (Pxy); \draw[vector guide] (Pxy) -- (P); \end{tikzpicture} \end{document} How to close/open a view panel I can't find a way to close a view panel, in particular the horizontal at the bottom, is pretty useless to me at this moment. I want my Java code to be typeset in a monospaced font, so I am using the verbatim environment. LaTeX commands are highlighted in Eclipse, but as soon as I use the verbatim environment everything inside and the color of the environment itself becomes gray.  \begin{verbatim}   public class main {  public static void main (string[] args){      for(int i = 0; i &lt; arg.length; i ++){          System.out.println(args[i]);      }    }  };  \end{verbatim}   I'm using the verbatim and alltt packages.  Update 1.  MWE.  \documentclass[xcolor=dvipsnames]{beamer}  \mode&lt;presentation&gt; { \usetheme{CambridgeUS} \setbeamercovered{transparent} }  % Поддержка русского языка \RequirePackage[utf8]{inputenc} \RequirePackage[T2A]{fontenc} \RequirePackage[russian]{babel}  \RequirePackage{amsfonts}  \usepackage{algorithmic} \usepackage{mathptmx} \usepackage[scaled=.90]{helvet} \usepackage{courier} \usepackage{pst-node} \usepackage{pst-tree} \usepackage{auto-pst-pdf} \usepackage{color} \usepackage{colortbl} \usepackage{pstricks} \usepackage{verbatim} \usepackage{alltt} \usepackage{listings} \usepackage{animate} \usepackage{multimedia}  \title{Title}  \author{Name}  \institute{}  \date{\today}  \begin{document}  \begin{frame} \titlepage \end{frame}  \begin{frame} \frametitle{Outline} \tableofcontents \end{frame}  \section{Introduction}  \begin{frame}{Классификация по поколениям}  \begin{itemize}  \item Третьего поколения (высокоуровневые языки) - последовательность высокоуровневых конструкций (циклы, условные выражения, классы, интерфейсы, методы, процедуры, \ldots) \pause  \begin{exampleblock}{Пример}  \begin{centering}  Fortran, C, C++, C\#, Java, Lisp.  \begin{verbatim}  public class main { public statiс void main (string[] args){ for(int i = 0; i &lt; arg.length; i ++){ System.out.println(args[i]); } } };  \end{verbatim}  \end{centering}  \end{exampleblock}\pause  \item Четвертого поколения (для конкретного применения) - последовательность инструкций конкретной предметной области \pause  \begin{exampleblock}{Пример} SQL, Postscript, XML, Mathlab. \end{exampleblock} \pause  \end{itemize}  \end{frame}  \end{document} This is a  about Monitoring Software. 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Also, when a rebel ship wants to escape from a planet and there is a single star destroyer hovering in the atmosphere (or some more of them further up, like in the Empire Strikes Back) how come it's not a viable maneuver to fly low altitude for a couple of hundred kilometers horizontally (they would be out of the single-point blockade), then make a vertical dash upwards? How to fix soft 404 errors in GWT? In GWT I have been receiving soft 404 errors for some URLs of my online shopping website. Ichecked all those URLs and those pages are looking good and there is nothing wrong in that page. Then why I'm receiving that errors?  This is the notification that I received in my GWT:     Dear owner or webmaster,      While crawling your site, we have noticed an increase in the number of   transient soft 404 errors around 2013-06-30 16:00 UTC (London, Dublin,   Edinburgh). Your site may have experienced outages. These issues may   have been resolved. Intuition for multiple temporal dimensions It’s easy, relatively speaking, to develop an intuition for higher spatial dimensions, usually by induction on familiar lower-dimensional spaces. But I’m having difficulty envisioning a universe with multiple dimensions of time. Even if such a thing may not be real or possible, it seems like a good intellectual exercise. Can anyone offer an illustrative example? Is there something wrong with VertexConnectivity Is there a way to do the following using LINQ?  foreach (var c in collection) {     c.PropertyToSet = value; }   To clarify, I want to iterate through each object in a collection and then update a property on each object.  My use case is I have a bunch of comments on a blog post, and I want to iterate through each comment on a blog post and set the datetime on the blog post to be +10 hours. I could do it in SQL, but I want to keep it in the business layer. Difference between DispatchQueue.main.async and DispatchQueue.main.sync