Tikz children of two sibling nodes overlap
Tikz, Tree without overlaps
I am looking for a JavaScript array insert method, in the style of:  arr.insert(index, item)   Preferably in jQuery, but any JavaScript implementation will do at this point. What do you call a person who does/thinks the opposite of the crowd for just that reason? Automorphism group of the quaternion group Let $Q_8$ be the quaternion group. How do we determine the automorphism group $Aut(Q_8)$ of $Q_8$ algebraically? I searched for this problem on internet. I found some geometric proofs that $Aut(Q_8)$ is isomorphic to the rotation group of a cube, hence it is isomorphic to the symmetric group $S_4$. I would like to know an algebraic proof that $Aut(Q_8)$ is isomorphic to $S_4$. Includegraphics maximum width With \includegraphics I can give the width of the resulting image (which would be scaled).   How can I give a maximum width of the image? That is, if the original is smaller than X, I'd like to keep the smaller image, if the image is larger than X, then the image width should be X.  Using pdflatex/graphicx. Creating a responsive menu system for a site with a lot of content I am currently creating a website which has a lot of content - text. For this I need a serious menu structure with 5-10 menu items per menu and at least 15 menu-blocks per main menu item.   Further it has to be accessible via mobile.   Till now I have used panels and added menus inside the panels. But mobile isn't to happy about that and the list-names in the menus overlap the content.   How would you go about solving this issue? I trust you experts here! :-) Difference between int[] array and int array[] I have recently been thinking about the difference between the two ways of defining an array:   int[] array int array[]   Is there a difference? Better than premium Is there something higher (better) than the word premium, or does it mean the best? Also, is there something in between premium and deluxe?  Graphically: Does any word fit here? > Premium > Does any word fit here? > Deluxe The Unix environment has some excellent tools for parsing text in various forms. However, of late, the data is not in the traditional (historical) formats (CSV, TSV, record-based or some other delimiter-based) it used to be before. Data these days is exchanged in structured formats like XML/JSON.  I know there are some good tools like sed, awk and Perl which can chew down nearly any form of data out there. However, to work with this sort of structured data, often one has to write a complete program, and, given the little time available to extract information, one has to sit down and figure out the whole logic of what one wants to query and put it down programmatically. Sometimes this is not OK – basically because the information extracted from those files acts as inputs for further work; also because of the time it takes to search for the appropriate solution and code it up. A command line tool is needed with sufficient switches to find, query and dump data.  I'm looking for tools that take a XML/JSON or other forms of structured data and dump it into other formats like csv, etc., so that from there one could use other commands to get any information out of it.  Are there any command line utilities you know of which do this kind of a job? Are there already awk/Perl scripts available to this? I caught an Eevee, which of its evolutions will it evolve into? So I just caught an Eevee. Now, I need 25 candies to evolve it. The fact is that in the GameBoy color versions, that Pokémon needed a stone to evolve instead of experience. Depending of the stone he was fed with (thunder, water or fire), he was evolving in a different Pokémon.   Is the stone feature also in Pokémon Go? If not, what decide the evolution of this Pokémon?   Bonus point : If it's possible, how can I get a stone? Was the significance of Arya's Braavosi coin ever explained? Jaqen H'ghar gives Arya the iron coin, she can apparently give it to any Braavosi and say Valar Morghulis and that gets her where she needs to go, but why?    Where do these coins come from and what do they indicate to a Braavosi? Seeking birth record for Jacob Schulthess from Wangen an der Aare in Switzerland? If we have a complex scalar $\phi$ we know that the gauge-invariant interaction with $A$ is given by $A^\mu J_\mu$, where $J$ is the Noether current of the $U(1)$ symmetry of the Lagrangian $$ J_\mu\sim \phi^\dagger\partial_\mu\phi-\phi\partial_\mu \phi^\dagger \tag{1} $$  If we have a real scalar instead, $J=0$ and the field doesn't couple to $A$: real particles aren't charged.  My question is: what if we took $$ J_\mu\sim \phi\partial_\mu\phi \tag{2} $$ to couple $\phi$ to $A$? The interaction is Lorentz invariant and renormalisable, but it is not gauge-invariant, which is probably a bad thing. At what point would this theory break down?  This is probably very naïve, but I think that the Feynman rules for this theory are straightforward. So I guess the theory makes sense at least perturbatively. The theory is probably flawed at a more fundamental level, but I cant't seem to find where (some kind of gauge anomaly perhaps?) I was going through the fundamental theorem in Number Theory where any non zero integer n can be represented as a product of distinct primes. A related problem with this theorem is to prove that for every such number, there exists a prime $p$ such that $p&lt; \sqrt n$. I was wondering if there is any mathematical proof that no prime $p$ exists for the number $n$ such that $p&gt; \sqrt n$. How to convert a column number (e.g. 127) into an Excel column (e.g. AA) How do you convert a numerical number to an Excel column name in C# without using automation getting the value directly from Excel.  Excel 2007 has a possible range of 1 to 16384, which is the number of columns that it supports. The resulting values should be in the form of excel column names, e.g. A, AA, AAA etc. Since humans are not large in mass, do we exert enough gravitational force for a small object to orbit around us? (Assuming that the only gravitational force acting on the object is from the human). Using Newton's law of gravity and using myself as the human mass, I exert a 10^-8 force on a 1 kg object .5 meter away, but I am not sure if even this small of a force will be acceptable. What is the baseline "force" between two objects for 1 to orbit another?  Edit: I am not sure if this is a SpaceExchange question. Let $a,b,c $ are non-negative real numbers, and $a+b+c=3$.  How to prove inequality $$ ab^2+bc^2+ca^2\le 4.\tag{*} $$    In other words, if $a,b,c$ are non-negative real numbers, then how to prove inequality $$ 27(ab^2+bc^2+ca^2)\le 4(a+b+c)^3.\tag {**} $$ $\color{gray}{\mbox{(Without using "universal" Lagrange multipliers method).}}$  Thanks! For some reason, when I try to run any programs (I am trying to run a rootkit hunter: rkhunter) as root on the command line with sudo like this:  sudo rkhunter   Then I get this message:  You must be the root user to run this program   and then I get these lines:  sudo: error in /etc/sudo.conf, line 0 while loading plugin 'sudoers_policy' sudo: /usr/lib/sudo/sudoers.so must only be writable by owner sudo: fatal error, unable to load plugins   I try typing in just sudo but that comes up with the same three errors as above. Also in /etc/ sudo.conf does not exist.  I cannot run any other programs as root through sudo. It was also strange because I could run as root a day ago. I would like it to work.  Just so you know, I am the only user of this computer, and the administrator, running Lubuntu 14.04.1. Inexact measurement and wavefunction collapse As is usually said, measurement of an observable $q$ leads to collapse of wavefunction to an eigenstate of the corresponding operator $\hat q$. That is, now the wavefunction in $q$ representation is $\psi(q)=\delta(q-q_0)$ where $q_0$ is result of measurement.  Now, in reality measurements are never exact, so the wavefunction should not have that sharp peak. Instead it should be broadened depending on precision of measurement. In this case, can we still introduce an operator, an eigenstate of which would the new wavefunction appear? Is it useful in any way? Or does the new wavefunction depend too much on the way it was measured so that each instrument would have its own operator? How would such opeartor look e.g. for a single-slit experiment? How can I edit/create new launcher items in Unity by hand? Open Attachment on Create of Child Record