So I was wondering if there is a tool / similar to draw topological lines instead of straight lines on latex with points at their intersections? I was particularly looking to create this given image including the labels.
I'm trying, but something is wrong with my code in LaTeX: \begin{asy} pair dynkinMark(real x, real y, string s = &quot;&quot;, pen p = defaultpen, pair B = dir(45)) { if (s != &quot;&quot;) { dot(&quot;$&quot;+s+&quot;$&quot;, (x,y), B, p); }     else { dot((x,y), p); }     return (x,y); }  dynkinMark(0,1, &quot;1&quot;, dir(135)); dynkinMark(0,2, &quot;2&quot;, dir(135)); dynkinMark(0,3, &quot;3&quot;, dir(135)); dynkinMark(0,4, &quot;4&quot;, dir(135)); dynkinMark(7,1, &quot;1'&quot;); dynkinMark(7,2, &quot;2'&quot;); dynkinMark(7,3, &quot;3'&quot;); dynkinMark(7,4, &quot;4'&quot;); path p1 = (0,1)..(2,2.0)..(5,3.5)..(7,4); path p2 = (0,2)..(2,1.2)..(5,2.5)..(7,3); path p3 = (0,3)..(2,2.8)..(5,1.5)..(7,1); path p4 = (0,4)..(2,3.8)..(5,3.5)..(7,2); draw(p1, blue); draw(p2, heavycyan); draw(p3, mediumcyan); draw(p4, lightblue); dot(&quot;$12$&quot;, IP(p1, p2), dir(90), heavygreen); dot(&quot;$13$&quot;, IP(p1, p3), dir(90), heavygreen); dot(&quot;$23$&quot;, IP(p2, p3), dir(90), heavygreen); dot(&quot;$14$&quot;, IP(p1, p4), dir(90), heavygreen); dot(&quot;$24$&quot;, IP(p2, p4), dir(90), heavygreen); real y = 0.8; label(&quot;$s_1$&quot;, (IP(p1,p2).x, y), heavygreen); label(&quot;$s_2$&quot;, (IP(p1,p3).x, y), heavygreen); label(&quot;$s_1$&quot;, (IP(p2,p3).x, y), heavygreen); label(&quot;$s_3$&quot;, (IP(p1,p4).x, y), heavygreen); label(&quot;$s_2$&quot;, (IP(p2,p4).x, y), heavygreen); \end{asy}
How do I theme a webform? I just tried to access a folder like so:  \\somecomputeronmynetwork\somelocation$   When going to this location I'm prompted for a user name and password.  I put one in, and it let me in fine.  Now I need to remove that login, so I can try a different user name and password.  What's the easiest way to do this? I need to prove that the center of $A_n$ is trivial for $n \geq 4$.  $Z(A_3) = A_3$, since $A_3 = \mathbb{Z}/3\mathbb{Z}$ is commutative.  One idea is two use "counting" technique. First of, all we count cojugacy classes of even permutations in $S_n$. It's the classes correspodning to the types $[\lambda_1, ..., \lambda_r]$ where $n \equiv r \mod 2$  Now, the conjugacy class in $S_n$ correspoding to the type $[\lambda_1, ..., \lambda_r]$ splits into two equal-sized classes in $A_n$ if $\lambda_1, ..., \lambda_r$ are distinct odd numbers. If they aren't then it is preserved in $A_n$.  Then we can use "the counting formula"(  ) of elements in each "even" class of $S_n$ and divide one by $2$ if needed.  Still, I'm not sure if it can be done. Seems to be a lot of work there. Maybe there are other, he easier ways? Or, maybe, it is the way, in this case, I wouild appreciate any advices. $\forall$ At the beginning or at the end? I have a set of real numbers $x_1, x_2, \ldots, x_n$ and two functions $f:\mathbb{R} \rightarrow \mathbb{R}$ and $g:\mathbb{R} \rightarrow \mathbb{R}$.  What are the differences between the following statements?   $\forall v \in \{1, \ldots, n\} ~f(x_v) = 0 \vee g(x_v) = 0$ $f(x_v) = 0 \vee g(x_v) = 0 ~\forall v \in \{1, \ldots, n\} ~$ I've just updated to macOS 10.12 and when I try to execute srm in Terminal, it says -bash: srm: command not found.   Is srm removed? How to fix this? Why do Borg move so poorly (like 50s movie robots)? I recently installed an SSD and AFAIK Ubuntu makes a weekly FSTrim on SSD's that support it.  Is there a log file of this trims? Please give me feedback on my answer to this question. Question: For all $ n\geq1:\binom{2n}{0}+\binom{2n}{2}+\binom{2n}{4}+\cdots+\binom{2n}{2k}+\cdots+\binom{2n}{2n} $   is equal to $ \binom{2n}{1}+\binom{2n}{3}+\binom{2n}{5}+\cdots+\binom{2n}{2k+1}+\cdots+\binom{2n}{2n-1} $. Answer: False, since;  Let $a=1,  b=-1$  and $n=1$  ,$k=0$   , using Binomial expression.  $$(a+b)^n=  \sum   \binom{n}{k}  a^{k}b^{n-k}$$  Then $(1+-1)^{2(1)}=\binom{2}{0}1^{0}(-1)^{2-0}+\binom{2}{1}1^{1}(-1)^{2-1}+\binom{2}{2}1^{2}(-1)^{2-2}=\binom{2}{0}-\binom{2}{1}+\binom{2}{2}$  Thus :For all $n\geq1:  \binom{2n}{0}+\binom{2n}{2}+\binom{2n}{4}+\cdots+\binom{2n}{2k}+\cdots+\binom{2n}{2n}   \ne \binom{2n}{1}+\binom{2n}{3}+\binom{2n}{5}+\cdots+\binom{2n}{2k+1}+\cdots+\binom{2n}{2n-1}$  . Inno Setup: How to manipulate progress bar on Run section? I have a virtual instance of redhat running that I can ssh to from any host on the corporate network.  My ssh session was dropped while running some scripts that may or not have caused me to disconnect.  The who command locally still lists the dropped connection. Reconnecting with ssh starts a whole new session.  Is there a way to connect to the original session?  If not can I kill it?  I have root and physical access.  I was not using screen in the original session. Let $f$ be a continuous function. If $f$ is uniformly continuous then it maps cauhy sequence into cauchy sequence. Is the converse true? That is if $f$ maps cauchy into cauchy gives the uniform continuity of $f$. I think it's no. Can suggest a counter example How get the :hover css style of an anchor with jQuery? How can i get the :hover in css stylesheet on the fly with jquery?  stupid example:   a.foo {     color: red;     font-size: 11px; }  a.foo:hover {     color: blue;     font-size: 12px;  }   how to retrieve that color and font-size before that mouse will go over the anchor? How to change the voltage polarity in an inverting amplifier? I want to implement a simple circuit which can map -10V  +10V voltage range to 0V 5V voltage range. Thus I'm planning to use two op-Amps, one for the slope and the other for the offset. So basically I'm planning to use an inverting amplifier and a summing amplifier consecutively.  But Inverting amplifiers multiplies the input voltage with a minus sign. I need a positive slope. How can I overcome this?  Also Could you gibe me any ideas for a cheap op-Amp models for this purpose? 'undefined reference to symbol 'pthread_create@@GLIBC_2.2.5' while compiling bochs I'm trying to compile bochs with this command:  ./configure --with-x11 --with-wx --enable-ne2000 --enable-iodebug --enable-disasm --enable-debugger --enable-e1000 --enable-usb --enable-pci   it works, but then when I run make I got:  usr/bin/ld: gui/libgui.a(gtk_enh_dbg_osdep.o): undefined reference to symbol 'pthread_create@@GLIBC_2.2.5' /lib/x86_64-linux-gnu/libpthread.so.0: error adding symbols: DSO missing from command line   Any Help ? :/ I accidentally unset all the directories of $PATH while trying to add a new one in ~/.bashrc. I opened a new terminal window as I was editing and now $PATH is empty. I'm worried if I boot from another drive to find the $PATH I won't be able to boot into this drive again.  Basically, what is the default result of echo $PATH? Solve for $f(x)$ if $f(f(x))=6x-f(x)$ If $f: [0,\infty) \rightarrow [0,\infty)$ and   $f(f(x))=6x-f(x)$ $f(x)&gt;0$ $  \forall x \in (0,\infty) $   Find f(x) Why does C# disallow readonly local variables? I'm using wordpress multiste 3.3.1 I'm not gonna update it in the future. So I disabled all upgrade functions.  I want to remove the wordpress admin bar from both frontend as well as dashboard.  I can remove it from frontend using this code.  add_action( 'init', 'disable_admin_bar', 1 ); function disable_admin_bar() {     add_filter( 'show_admin_bar', '__return_false' ); }   But i couldn't find any solution to remove it from dashboard.   I don't want to use css solution to hide admin bar and I'm ready to edit the core files to remove it  Can anyone help me to remove it completely?. Thanks Haar measure on $SO(n)$ I am interested in describing the group of special orthogonal matrices $SO(n)$ by a set of parameters, in any dimension. 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