In math mode, when I type   \dot{x}, \ddot{x}, \dddot{x}   the third expression doesn't look like the two previous ones. The three dots are widely spaced and higher above the symbol. Is there a way to have three dots above a symbol so that it looks more regular compare to one dot and two dots?
From , I have tried the using \hspace{0pt} and   \makeatletter \renewcommand{\dddot}[1]{%   {\mathop{\kern\z@#1}\limits^{\vbox to-1.4\ex@{\kern-\tw@\ex@    \hbox{\normalfont ...}\vss}}}} \renewcommand{\ddddot}[1]{%   {\mathop{\kern\z@#1}\limits^{\vbox to-1.4\ex@{\kern-\tw@\ex@    \hbox{\normalfont....}\vss}}}} \makeatother   after loading mathtools but the problem still persists.    \documentclass{article} \usepackage{mathtools} \begin{document} \[ \dot{\mathbf{r}}\times\ddot{\mathbf{r}}\times\dddot{\mathbf{r}} \] \end{document}   In the case the font scheme I am using has any affect as well, the fonts are:  \usepackage[utf8]{inputenx} \renewcommand{\rmdefault}{ppl}                  \linespread{1.05}                   \usepackage[scaled]{helvet} \usepackage{courier}               \usepackage{eulervm} \normalfont       \usepackage[T1]{fontenc}            \usepackage{textcomp}
Generating DLL assembly dynamically at run time Currently I have some code that is being generated dynamically.  In other words, a C# .cs file is created dynamically by the program, and the intention is to include this C# file in another project.  The challenge is that I would like to generate a .DLL file instead of generating a C# .cs file so that it could be referenced by any kind of .NET application (not only C#) and therefore be more useful. I have this setup:   The mesh is only the visible top side, with a mirror modifier for the bottom part. Now I want to unwrap it like in the picture. I want the inner circle (red) to go to the top of the UV map...  The problem is that no matter what automatic unwrapping I use, it never works as intended.  The closest I've gotten was by using "follow quads", but that skewed the UV map a lot:   I used the result from the second image and manually adjusted the vertices with a lot of scaling and "align auto", but its very far from perfect as you can see in the first image.  Here's what I want exactly:   The uv vertices should be distributed evenly (horizontally) The middle line (yellow) should be on a "natural" y height (so there's no stretching)   I hope it's clear what I want to achieve. I'm sure there must be some automatic way to perfectly align and distribute the UVs in this way.  By the way: If you look closely you can see that I already placed a uv seam (aligned with the green y axis in the screenshot) but that didn't really help. AWS S3, Paperclip missing required :bucket option I am trying to implement  using additive ElGamal.  I am trying to run the full protocol mentioned in Section 3.4 on the following inputs:   $p = 17$ (prime) $g = 6$ (generator) $x = 5$ (private key) $k = g^x \pmod p = 6^5 \pmod{17} = 7$ (public key)   Suppose the clients inputs are 1, 2. Then $P(x) = (x-1)(x-2) = x^2-3x+2$, and therefore the coeffiecients to encrypt are $(1, -3, 2)$. I chose $y = 10$ and so the encrypted values are:   $1$ becomes $(15,12)$ $-3$ becomes $(15, 1)$ $2$  becomes $(15, 4)$.   The Server Side Input Set $S=\{1\}$ and the random value $r0$ corresponding to $\{1\}$ is $r_0=2$.    With the above problem in context, I have some questions:   What does P 0,j refer to in Step 7. Can you please give an example? In Step 8, suddenly variable i is introduced along with j. What does i, j, refer to? In Step 8, ENC() function has a ; in between. How do we interpret ENC(a;b)? Reset Windows 10 from USB I have a Windows machine (laptop) that needs fixing. The current installation is really badly broken (e.g. the taskbar is unresponsive, but the Explorer windows work, booting takes literally half an hour) and when I try to access the settings app and click on the tile to access the reset settings it instantly crashes. The same happens in Safe Mode.  I have created a USB install medium using the tool offered by Windows on my own Windows desktop machine. I've ensured that both the laptop and the USB tool have the same version of Windows (Home, 64-bit, NL). When I want to reinstall Windows on the laptop with this stick I am asked to enter a serial number which I obviously don't have. I don't want to try and see if I can phone activate it, because if it fails the install is gone.  I need to reinstall this Windows machine from a USB stick. There are a few problems I can't find an immediate solution for on the .   If I use a tool such as  to extract the serial number, will this work? If the above does not work, how can I reinstall this Windows machine? Subadditive sequences and the limit $\sup_{n\to\infty} a_n / n$ Let $\{ a_n, n\geq 1\}$ be a sub-additive sequence, i.e. for any $m,p\geq 1$ $$ a_{m+p} \leq a_m + a_p. $$ .Prove that $$\lim_{n\to\infty} \frac{a_n}{n} = \inf_n \frac{a_n}{n}.$$ I guess the first step is to state $$a_{n} = a_{mp+q} \leq a_{mp} + a_q$$ but I'm not sure where to go from here.... NULL values inside NOT IN clause In this movie there are scientists who (spoilers ahead)       ...are creating a simulation. One scientist starts seeing odd looking characters but no one else sees them. He asks around and more and more characters are missing or don't know about the characters in the story he knows about.  He finds out that he is part of a simulation. He finds out that the characters only he remembers have been deleted. He also finds out that there are characters from his own simulation that have broken free of his simulation and are in his world.    Hints: I remember this being an older film (70's?); it might have been foreign film possibly with subtitles (not Hollywood); it might have been part of the Criterion collection; I'm pretty sure I streamed it from Hulu. Sorry, I can't remember more details. What's the fixed size of the suggested edit queue? Why is quadratic integer ring defined in that way? Quadratic integer ring $\mathcal{O}$ is defined by \begin{equation}    \mathcal{O}=\begin{cases}       \mathbb{Z}[\sqrt{D}] &amp; \text{if}\ D=2,3\ \pmod 4\\       \mathbb{Z}\left[\frac{1+\sqrt{D}}{2}\right]\  &amp; \text{if}\ D=1\pmod 4    \end{cases} \end{equation} where $D$ is square-free.   I understand $\mathbb{Z}\left[\frac{1+\sqrt{D}}{2}\right]$ is not closed under multiplication if $D=2,3\pmod 4$. But still, isn't it more natural to define $\mathcal{O}=\mathbb{Z}[\sqrt{D}]$ for all square-free $D$? (in that case, it really seems like 'quadratic integer') I wonder what is the motivation of this definition. I know this question is asked a lot, but the solutions I saw didn't work for me.  I only have one virtual host enabled, and I'm trying to enable access to a folder that's not under the document root  ServerAdmin webmaster@localhost DocumentRoot /var/www/html  Alias /movies /home/username/Videos/Movies  &lt;Directory /home/username/Videos/Movies/&gt;     Options Indexes FollowSymLinks     AllowOverride None     Require all granted &lt;/Directory&gt;   I set /etc/apache2/envvars as follows  export APACHE_RUN_USER=www-data export APACHE_RUN_GROUP=public   I made sure that /home/username/Videos/ and its sub folders are owned by username:public, set the permissions to 777 (after 775 didn't work) and made sure that user www-data belongs to group public.  Now, when I browse to http://localhost/movies I get  [Mon Apr 21 11:28:14.971844 2014] [core:error] [pid 1385:tid 140067725104896] (13)Permission denied: [client 127.0.0.1:46603] AH00035: access to /movies/ denied (filesystem path '/home/username/Videos') because search permissions are missing on a component of the path   But when I set /etc/apache2/envvars to run Apache under username (my own username) everything works fine. The problem is permission related, but I don't see how in my case; especially when I set the permissions to 777. Any ideas?  P.S. Ubuntu version is 14.04, Apache is 2.4.7 and I didn't edit other configuration files. Speed of light in a gravitational field? How do I solve the speed of light in gravitational field?  Should I just add gravitational acceleration in speed of light?  $$c'=c_0+g(r)t~?$$ String.Join vs. StringBuilder: which is faster? How do you change the size of figures drawn with Matplotlib? How do you change the size of figure drawn with Matplotlib? How to open the default webbrowser using java Speed $v$ of a wave on a tightrope Prove that for sufficiently large $x$, $(\log x)^p<x$ where $p$ is a positive integer. Is there any software to sync files-folders and software between two PCs? For example if I install program 'A' to my desktop I want to be installed to my laptop as well if I have synchronized these two. I want the same with my files and folders. If I change something to my desktop I want the changes to effect my laptop too(I exclude Ubuntu One as a solution).  Thanks for your time and patience! What does "official Ubuntu flavour" mean? What kind of support do they receive from Canonical or/and Ubuntu community? Who decides a distro should become official flavour? What privileges do "official flavours" have over unofficial derivatives of Ubuntu like Linux Mint, Elementary OS, Deepin OS,etc.? Would it be possible to generate the original data from a SHA-512 checksum? So, I have a file that is XY Exabytes big. I create a SHA-512 hash from it.    Are there any theoretical chances that I can retrieve the original data just from the sha512 hash?    Also, are there any better hashes then sha512?