Is it possible to make a line style in tikz, similar to dotted or dashed, such that instead the decoration is a series of footsteps, as in the figure below? The footsteps do not need to be as complicated, but they should be recognizable as such.
I was wondering if someone knows if there is a foot/feet symbol available in any of latex packages that I could use in my text? I would appreciate any hint.  I do really mean a foot/feet icon as in the picture below.
I am working on a web application where I want the content to fill the height of the entire screen.  The page has a header, which contains a logo, and account information. This could be an arbitrary height. I want the content div to fill the rest of the page to the bottom.  I have a header div and a content div. At the moment I am using a table for the layout like so:  CSS and HTML    #page {     height: 100%; width: 100% }  #tdcontent {     height: 100%; }  #content {     overflow: auto; /* or overflow: hidden; */ } &lt;table id="page"&gt;     &lt;tr&gt;         &lt;td id="tdheader"&gt;             &lt;div id="header"&gt;...&lt;/div&gt;         &lt;/td&gt;     &lt;/tr&gt;     &lt;tr&gt;         &lt;td id="tdcontent"&gt;             &lt;div id="content"&gt;...&lt;/div&gt;         &lt;/td&gt;     &lt;/tr&gt; &lt;/table&gt;     The entire height of the page is filled, and no scrolling is required.  For anything inside the content div, setting top: 0; will put it right underneath the header. Sometimes the content will be a real table, with its height set to 100%. Putting header inside content will not allow this to work.  Is there a way to achieve the same effect without using the table?  Update:  Elements inside the content div will have heights set to percentages as well. So something at 100% inside the div will fill it to the bottom. As will two elements at 50%.  Update 2:  For instance, if the header takes up 20% of the screen's height, a table specified at 50% inside #content would take up 40% of the screen space. So far, wrapping the entire thing in a table is the only thing that works. Real numbers equipped with the metric $ d (x,y) = | \arctan(x) - \arctan(y)| $ is an incomplete metric space I have to show that the real numbers equipped with the metric $ d (x,y) = | \arctan(x) - \arctan(y)| $ is an incomplete metric space.  Certainly, I have to search for a Cauchy sequence of real numbers with respect to given metric that must not be convergent. But I am unable to figure out that.  Can anybody help me with this.   Thanks for helping me. "None is" or "none are" How would you do a "not in" query with LINQ? I have two collections which have property Email in both collections. I need to get a list of the items in the first list where Email does not exist in the second list. With SQL I would just use "not in", but I do not know the equivalent in LINQ. How is that done?  So far I have a join, like...  var matches = from item1 in list1 join item2 in list2 on item1.Email equals item2.Email select new { Email = list1.Email };   But I cannot join since I need the difference and the join would fail. I need some way of using Contains or Exists I believe. I just have not found an example to do that yet. For a distribution function $F(x)$ and constant $a$, integral of $F(x + a) - F(x)$ is $a$. For any distribution function and any $a \geq 0$, $\int_{-\infty}^{\infty} (F(x+a)-F(x))dx = a$.   In this case, "distribution function" means a right continuous function F with $F(-\infty) = 0$, $F(\infty)= 1$.   This problem comes after a section in the book on mathematical expectation, so I suspect I should use some property of expectation to prove it. Expectation appears to be something that applies to random variables, so I think I should be somehow transforming the problem into something in terms of expectations of random variables, but I'm not sure how. I know that given a distribution function, I can get a probability measure, but I'm not sure how to go from there to a random variable and actually get a relation between the expectation of the random variable and this integral. I'm sure whether this is the right way to go about this problem, but if it is, I'm missing a connection somewhere. I was putting the following in /etc/sysctl.conf in Ubuntu 16.04 and ipv6 was disabled.  net.ipv6.conf.all.disable_ipv6 = 1 net.ipv6.conf.default.disable_ipv6 = 1 net.ipv6.conf.lo.disable_ipv6 = 1   In Ubuntu 18.04 I have to add the following to grub.  GRUB_CMDLINE_LINUX_DEFAULT="ipv6.disable=1"   Just wanted to have confirmation whether this is the new way in Ubuntu 18.04 to disable IPv6. How to split a long regular expression into multiple lines in JavaScript? Determining bounds for the sum $\sum\limits_{n=1}^\infty \frac{1}{2^n - 3^n }$ Fraleigh(7ed) Theorem33.12. Let $p$ be a prime and let $n\in\mathbb{Z}^+$. If $E$ and $E&#39;$ are fields of order $p^n$, then $E \simeq E&#39;$.   Proof in the text: Both $E$ and $E&#39;$ have $\mathbb{Z}_p$ as prime field, up to isomorphism. By Corollary 33.6(A finite extension $E$ of a finite field $F$ is a simple extension of $F$), $E$ is a simple extension of $\mathbb{Z}_p$ of degree $n$, so there exists an irreducible polynomial $f(x)$ of degree $n$ in $\mathbb{Z}_p[x]$ such that $E\simeq \mathbb{Z}_p[x]/ \langle f(x) \rangle$. Because the elements of $E$ are zeros of $x^{p^n}-x$, *we see that $f(x)$ is a factor of $x^{p^n}-x$ in $\mathbb{Z}_p[x]$*. Because $E&#39;$ also consists of zeros of  $x^{p^n}-x$, we see that $E&#39;$ also contains zeros of irreducible $f(x)$ in $\mathbb{Z}_p[x]$. Thus, because $E&#39;$ also contains exactly $p^n$ elements, $E&#39;$ is also isomorphic to $E\simeq \mathbb{Z}_p[x]/\langle f(x) \rangle$.  I don't know why $f(x)$ divides $x^{p^n}-x$. $E$ has a zero $\alpha$ of $f(x)$, but it doesn't need to have all the zeros of $f(x)$. So $f(x)=(x-\alpha)g(x)$ in $E[x]$ and $g(x)$ need not be splitted into linear factors. How can $f(x)$ divide $x^{p^n}-x$? I'm porting a module that currently works with Blocks/BlockForms to Paragraphs/NodeForms. I'm inserting an embedded form inside a Paragraph inside a Node Edit page using a hook_field_widget_entity_reference_paragraphs_form_alter. The general structure where the form gets inserted is: $form['field']['widget'][0]['settings'][form here]  After this the form displays as expected on the node edit page. The inserted form goes through a number of #process steps. The element in question is a select form that when the button underneath it is pressed, is supposed to retrieve some data via a custom submit handler and place it on the page with ajax:  The array for this element looks like this:  You can see the custom submit handler that is supposed to fire when 'Select Segment Set' is pressed After debugging, I've found that the entire NodeForm appears to be submitted to the backend, and the only handler that is found is from some other field that uses ajax. In short 'updateSegmentSet' is never discovered as a submit handler. When I debug the original module based on block/blockforms, I do see the correct submit handler being discovered. Now in the latter case, of course a blockForm is submitted to the back end with the correct plugin. Given that this is basically a form within a form within a form, is there something special I have to do to get the custom submit handler to run? I've read a few things online e.g. the 'settings' key and '#tree' = true. EDIT The Ajax property looks like this:       '#ajax' =&gt; [         'callback' =&gt; [$this, 'updateSegmentSetAjax'],         'wrapper' =&gt; $wrapper_id,       ],    public function updateSegmentSetAjax(array &amp;$form, FormStateInterface $form_state) {     $button = $form_state-&gt;getTriggeringElement();     // Go one level up in the form, to the widgets container.     return NestedArray::getValue($form, array_slice($button['#array_parents'], 0, -2));   }  As best I can tell, this is never called either. Let $L$ and $R$ be $n \times n$ matrices. I am trying to solve the following minimization problem  $$ L^{k+1} := \arg \min_{L} \lambda \|L\|_{\ast} + \frac{1}{2\mu}\|L-R^{k}\|_{F}^{2} $$ $$ \mbox{s.t.}\ L \succeq 0 $$  where $\|\cdot\|_{\ast}$ and $\|\cdot\|_{F}$ denote the nuclear and Frobenius norms, respectively. Also, $k$ expresses the $k$th iteration when solving an optimization problem successively.  I don't know how to solve this problem. Would you tell me the way? What is $\int_0^1\frac{x^7-1}{\log(x)}\mathrm dx$? Induction proof: n lines in a plane Assume that there are $n$ infinitely long straight lines lying on a plane in such a way that no two lines are parallel, and no three lines intersect at a single point. Prove that these lines divide the plane into $\frac{n^2+n+2}{2}$ regions. (Hint: Any two non-parallel straight lines on a plane must intersect at exactly one point.)  Can someone tell me where to start here? I know to prove the base where $n=0$, but don't know how to proceed.  Any help is greatly appreciated! I am currently trying to develop my modeling skills, and following a tutorial found on YouTube. The tutorial teaches how to create an anvil. At 19:10 or so into the video, a subdivision surface modifier is used to create a smooth, soft look.  However, when I do the same, mine looks very sharp and generally bad.  Any ideas why? I will include the blend file below, I appreciate your time and suggestions.    This is his when he subdivides, which is very different from mine when I do the same at the same settings. (I cannot post more pictures because I am new, but if you check the blend file I attached, you should be able to see the difference.   This is what it looks like when I subsurf without the base face. How do I download torrents? I suspected that installing xfce4 cause some issues in Ubuntu so I removed them using apt-get remove xfce4 xfce4-goodeis.  But when I ran 'dpkg -l' I still can see some libraries and packages for xfce4:  $ dpkg -l | grep -i xfce rc  libexo-1-0:amd64                              0.10.2-2                                 amd64        Library with extensions for Xfce rc  libgarcon-1-0                                 0.2.1-1                                  amd64        freedesktop.org compliant menu implementation for Xfce rc  libxfce4ui-1-0                                4.11.0-0ubuntu1~ppa0.13.10.1             amd64        widget library for Xfce - Gtk+2 variant rc  libxfce4ui-common                             4.11.0-0ubuntu1~ppa0.13.10.1             all          common files for libxfce4ui rc  libxfce4util6                                 4.10.1-1                                 amd64        Utility functions library for Xfce4 rc  libxfcegui4-4                                 4.10.0-2                                 amd64        Basic GUI C functions for Xfce4 rc  libxfconf-0-2                                 4.10.0-2                                 amd64        Client library for Xfce4 configure interface rc  mousepad                                      0.3.0-2                                  amd64        simple Xfce oriented text editor rc  thunar                                        1.6.3-1ubuntu1                           amd64        File Manager for Xfce rc  xfce4-appfinder                               4.10.1-1                                 amd64        Application finder for the Xfce4 Desktop Environment rc  xfce4-clipman                                 2:1.2.3-2ubuntu1                         amd64        clipboard history utility rc  xfce4-mixer                                   1:4.10.0-1ubuntu2                        amd64        Xfce mixer application rc  xfce4-notes                                   1.7.7-3ubuntu2                           amd64        Notes application for the Xfce4 desktop rc  xfce4-panel                                   4.10.1-1ubuntu1                          amd64        panel for Xfce4 desktop environment rc  xfce4-power-manager                           1.2.0-2ubuntu1                           amd64        power manager for Xfce desktop rc  xfce4-session                                 4.10.1-1ubuntu1                          amd64        Xfce4 Session Manager rc  xfce4-settings                                4.11.1-0ubuntu1~ppa0.13.10.1             amd64        graphical application for managing Xfce settings rc  xfce4-terminal                                0.6.2-3ubuntu1.1                         amd64        Xfce terminal emulator rc  xfce4-volumed                                 0.2.0-0ubuntu1                           amd64        volume keys daemon rc  xfdesktop4                                    4.11.2-0ubuntu1~ppa0.13.10.1             amd64        xfce desktop background, icons and root menu manager rc  xfwm4                                         4.11.1-0ubuntu1~ppa0.13.10.1             amd64        window manager of the Xfce project   I copy-pasted all these packages\libraries to form an apt-get remove command to remove all of these dependencies, and the command ran normally, but running dpkg -l | grep -i xfce showed these dependencies again !  Why are these dependencies still installed ? I want to start an Xorg server (which should only feature a minimal xterm terminal emulator from a newly created &quot;pristine&quot; tty). I have thought this to be as simple as issuing a xinit or maybe a startx however both have failed me. Therefore the question: How to manually run/init/start a Xorg server on a different VT/TTY? here the Longer background story to the question at hand: This is the backgroud and what I have tried already: Looking at man openvt I was able to run a shell on a newly created tty (or vt, cannot tell precisly the different vt&lt;&gt;tty) like this:  $&gt; sudo openvt -s /bin/bash  the -s of causes the direct switch to that new tty/vt on that new tty I wanted to manually start a Xorg server which according to man xinit should start with a minimal xterm application. On the new shell on the switched to tty I (created via openvt) I hence issues this command:  $&gt; su -c 'xinit xterm -display :4 -- :4' - mahr &amp;&gt;/tmp/output  and I receive this output $&gt; cat /tmp/output X.Org X Server 1.19.6 Release Date: 2017-12-20 X Protocol Version 11, Revision 0 Build Operating System: Linux 4.4.0-148-generic x86_64 Ubuntu Current Operating System: Linux scitech 4.15.0-70-generic #79-Ubuntu SMP Tue Nov 12 10:36:11 UTC 2019 x86_64 Kernel command line: BOOT_IMAGE=/vmlinuz-4.15.0-70-generic root=/dev/mapper/ubuntu--vg-root ro Build Date: 03 June 2019  08:10:35AM xorg-server 2:1.19.6-1ubuntu4.3 (For technical support please see http://www.ubuntu.com/support)  Current version of pixman: 0.34.0     Before reporting problems, check http://wiki.x.org     to make sure that you have the latest version. Markers: (--) probed, (**) from config file, (==) default setting,     (++) from command line, (!!) notice, (II) informational,     (WW) warning, (EE) error, (NI) not implemented, (??) unknown. (==) Log file: &quot;/home/mahr/.local/share/xorg/Xorg.4.log&quot;, Time: Thu Nov 28 10:57:53 2019 (==) Using system config directory &quot;/usr/share/X11/xorg.conf.d&quot; (EE)  Fatal server error: (EE) parse_vt_settings: Cannot open /dev/tty0 (Permission denied) (EE)  (EE)  Please consult the The X.Org Foundation support       at http://wiki.x.org  for help.  (EE) Please also check the log file at &quot;/home/mahr/.local/share/xorg/Xorg.4.log&quot; for additional information. (EE)  (EE) Server terminated with error (1). Closing log file.  Session terminated, terminating shell...xinit: giving up xinit: unable to connect to X server: Connection refused xinit: unexpected signal 2  ...terminated. Omission of "the" in "elected him president" and "made captain" Creating a Snapshot of a Windows 7 System Is there a way to create a snapshot of a Windows 7 system?  My goal is to be able to save the current state of my Windows 7 OS, on external storage, and be able to restore it on the same hardware in the future. Much like a snapshot on a virtual machine.   One solution would be to install two hard drives in RAID 1, then take one of them out an store it. Is there an easier solution? How can I visualize boxes? This question led to a new package:      Some of you may know the Web Developer Toolbar for Firefox that can outline the block level elements of a page like this:  Is there a way to do something similar with TeX boxes for a complete document?