Essentially I want to plot a function with singularities like   $\frac{1}{(x-0.5)^2+(y-0.5)^2}\cdot \frac{1}{(x+0.5)^2+(y+0.5)^2}$    at a higher sampling rate.  I tried to avoid the singularities by capping with some value ($20$):  \begin{tikzpicture} \begin{axis}[view={55}{45}] \addplot3[surf, colormap/jet, samples=50, domain=-1:1] {min(1/((x-0.5)^2+(y-0.5)^2)* 1/((x+0.5)^2+(y+0.5)^2),20)}; \end{axis} \end{tikzpicture}   Which yields    But that really does not stop TikZ/pfgplots from having to evaluate the function near its singularities, so it gets quite slow at compiling. So here is my question:  Is there a better/faster way to plot functions that contain singularities? Or do i have to precompute the data and give it to TikZ/pfgplots manually?
I want to plot the function 1/(x²+y²), but since it tends to infinity in (0,0), I get a horrible plot:  \documentclass{article} \usepackage{tikz} \usepackage{pgfplots} \begin{document} \begin{tikzpicture}   \begin{axis}[grid=both]     \addplot3 [surf] {1 / (x^2 + y^2)};   \end{axis} \end{tikzpicture} \end{document}     By restricting the domain of z, I get anyway a not so nice plot:  \documentclass{article} \usepackage{tikz} \usepackage{pgfplots} \begin{document} \begin{tikzpicture}   \begin{axis}[grid=both,restrict z to domain=0:1]     \addplot3 [surf] {1 / (x^2 + y^2)};   \end{axis} \end{tikzpicture} \end{document}     I would like to get something smooth, which finish in a circle (the circle of the intersection of this function with the plane z=1 for example).  Something like this would be great:
Has 'Ubuntu Software' been renamed to 'Snap Store'? I am currently studying  answer on the Moore-Penrose pseudoinverse and the Euclidean norm by the user &quot;Etienne dM&quot;. The first point of their answer proceeds as follows:  Let $x$ be $A^+y$.  Let me begin by the second point. For all $z$, we have: \begin{align} \lVert Az-b \rVert_2^2 &amp;= \lVert Ax-b \rVert_2^2 + \lVert A(z-x) \rVert_2^2 + 2 (z-x)^TA^T(Ax-b)\\ &amp; \geq  \lVert Ax-b \rVert_2^2 + 2 (z-x)^TA^T(Ax-b) \end{align} Moreover, because $(AA^+)^T = AA^+$, $$ A^T(Ax-b) = ((AA^+)A)^Tb - A^Tb = 0$$ Thus, we prove that for all $z$, $\rVert Az-b \lVert_2^2 \geq\rVert Ax-b \lVert_2^2$, that is to say $A^+b$ is as close as possible to $y$ in term of the Euclidian norm $\lVert Ax-b\rVert_2$.   I realise that $x = A^+ y$, but I don't understand how any of this implies that &quot;$A^+ b$ is as close as possible to $y$ in terms of the Euclidean norm $\lVert Ax-b\rVert_2$&quot;. I would greatly appreciate it if people would please take the time to explain this to me. If I was... If I were...   When is it correct to use "If I was" vs. "If I were" in standard English? Override a method at instance level It was nice to discover the option for a room owner to add any user to a room, even if their rep is too low.     ...so I notified the user in question, and as instructed on the next screen, I had them got to chat.stackoverflow.com so that I'd be able to add them.    ...but when they did their part, and I did my part, I got the message:    Obviously both frustrated, the user's next logical question was:  "So I just have ask a couple questions and get someone to upvote them, right?"    Needless to say, we don't want to encourage new users to post questions for the sole purpose of bypassing a frustrating, misdocumented rule.  I realize this will likely quickly get closed since it has at least one  - which hasn't been touched in 5½ years.  However it would be nice if the issue was revisited:  Ideally, it would be cool if RO's did have the option of deciding who had access to the room they "own", but short of that, is it possible to remove the 6 "misleading" words from that page? Prove linear combinations of logarithms of primes over $\mathbb{Q}$ is independent Suppose we have a set of primes $p_1,\dots,p_t$. Prove that  $\log p_1,\dots,\log p_t$ is linear independent over $\mathbb{Q}$. Now, this implies $ \sum_{j=1}^{t}x_j\log(p_j)=0 \iff x_1=\dots=x_t=0$.  I think I have to use that fact that every $q\in\mathbb{Q}$ can be written as $\prod_{\mathcal{P}}$, where $n_p$ is a unique sequence ($n_2$,$n_3$,$\dots$) with domain $\mathbb{Z}$. Here, $\mathcal{P}$ denotes the set of all integers.  Now how can I use this to prove the linear independency? This question led to a new package:      I'm giving my students an old exam and barely remembered to change the date at the top. A colleague and I joked about how long we could reuse the same exam, and it made me wonder if I could use LaTeX to create an exam that looked like it was written in 1963 on a typewriter.  Here's what I'd like to see:   Typewriter font even in math mode. (Several ways to accomplish this; is there a "best" way?) Slight inconsistencies in the printing of each letter. I attempt this below adapting code taken from . Each word has a random vertical shift, though I'd like to see it reduced to each letter having its own vertical shift. Other typewriter-like irregularities would be great. It would be great if math-mode delimeters \left(, \right}, etc., can be created in a piece-meal fashion as they did in days of old. Fraction bars, tops of square-root symbols -- any horizontal line, really -- is made up of a series of en-dashes that don't quite match up.   Here is what I've come up with so far:  \documentclass[10pt]{article}% This is a document class providing more font size options \usepackage{graphicx} \usepackage{ifthen} \usepackage[textwidth=7.5in,textheight=9.5in]{geometry} \pagestyle{empty}  % thanks to Bruno Le Floch: https://tex.stackexchange.com/q/9331/4012 % and in his comments to https://tex.stackexchange.com/a/29458/4012 \usepackage[first=-1,last=1]{lcg}% you can play around with these values \makeatletter \newcommand{\globalrand}{\rand\global\cr@nd\cr@nd} \makeatother  \newcommand{\randomvshift}[1]{\globalrand\raisebox{\value{rand}pt}{#1}}  %%% thanks to Martin Scharrer: https://tex.stackexchange.com/q/11598/4012 \makeatletter \def\typewriter#1{%     \@typewriter#1 \@empty } \def\@typewriter#1 #2{%    \randomvshift{#1}\space    \ifx #2\@empty\else     \expandafter\@typewriter    \fi    #2% } \makeatother \begin{document}\tt  \typewriter{Math 101 Fall 1963}  \begin{enumerate} \item   \typewriter{$\frac{\texttt{d}}{\texttt{dx}}\texttt{(x)}^2$}  \item \typewriter{State the Fundamental Theorem of Calculus.}  \end{enumerate}  \end{document} Understanding of the theorem that all norms are equivalent in finite dimensional vector spaces The following is a well-known result in functional analysis:     If the vector space $X$ is finite dimensional, all norms are equivalent.     Here is the standard proof in one textbook. First, pick a norm for $X$, say  $$\|x\|_1=\sum_{i=1}^n|\alpha_i|$$ where $x=\sum_{i=1}^n\alpha_ix_i$, and $(x_i)_{i=1}^n$ is a basis for $X$. Then show that every norm for $X$ is equivalent to $\|\cdot\|_1$, i.e.,  $$c\|x\|\leq\|x\|_1\leq C\|x\|.$$ For the first inequality, one can easily get $c$ by triangle inequality for the norm. For the second inequality, instead of constructing $C$, the  is applied to construct a contradiction.   The strategies for proving these two inequalities are so different. Here is my question,      Can one prove this theorem without Bolzano-Weierstrass theorem?   UPDATE:     Is the converse of the theorem true? In other words, if all norms for a vector space $X$ are equivalent, then can one conclude that $X$ is of finite dimension? How do exchanges match limit orders? Small caps font warning in beamer using biblatex Consider the following MWE  \documentclass{beamer} \usepackage{silence} \WarningFilter{biblatex}{Patching footnotes failed}  \usepackage{lmodern} \usepackage[T1]{fontenc}  \usepackage[style=authoryear-comp,backend=biber]{biblatex} \addbibresource{biblatex-examples.bib}  \begin{document} \begin{frame}   \fullcite{sarfraz} \end{frame} \end{document}   This generates the warning:  LaTeX Font Warning: Font shape `T1/lmss/m/sc' in size &lt;10.95&gt; not available (Font)              Font shape `T1/lmr/m/sc' tried instead on input line 28.   Is there a way to avoid the warning without using the silence package? Postgres JDBC connection in Eclipse Help I'm trying to get a postgres jdbc connection working in eclipse. It would be nice to use the Data Source Explorer, but for now I'm just trying to get a basic connection. What I have done so far is download the postgres JDBC connector. I then tried two different things. First, Preferences-> Data Management, I tried to add the postgres connector. Second, I added the jar to my project and tried to load the driver using Class.forName("org.postgresql.Driver"); but neither worked. Does anyone have any ideas?  Thanks,    Charlie What is the difference between re.search and re.match? How to delete a non-empty directory in Terminal? How do I delete the following directory?  I typed:  rmdir lampp   This error comes up:  rmdir: failed to remove `lampp': Directory not empty   Is there a command to delete all the files in the directory and delete the directory folder? I want to give a client access to my server, but I want to limit those users to their home directories. I will bind-mount in any files I want them to be able to see.  I've created a user called bob and added him to a new group called sftponly. They have a home directory at /home/bob. I've changed their shell to /bin/false to stop SSH logins. Here is their /etc/passwd line:  bob:x:1001:1002::/home/bob:/bin/false   I've also changed the /etc/ssh/sshd_config to include the following:  Match Group sftponly         ChrootDirectory /home/%u         ForceCommand internal-sftp         AllowTcpForwarding no   When I try to log in as them, here's what I see   $ sftp bob@server bob@server's password:  Write failed: Broken pipe Couldn't read packet: Connection reset by peer   If I comment out the ChrootDirectory line I can SFTP in but then they have free rein over the server. I have found that ChrootDirectory /home works, but it still gives them access to any home directory. I have explicitly tried ChrootDirectory /home/bob but that doesn't work either.  What am I doing wrong? How can I limit bob to /home/bob/?  ----EDIT-----  Okay so I just had a look at /var/log/auth.log and saw this:  May  9 14:45:48 nj sshd[5074]: pam_unix(sshd:session): session opened for user bob by (uid=0) May  9 14:45:48 nj sshd[5091]: fatal: bad ownership or modes for chroot directory component "/home/bob/" May  9 14:45:48 nj sshd[5074]: pam_unix(sshd:session): session closed for user bob   I'm not entirely sure what's going on there,  but it suggests something is wrong with the user directory. Here is the ls -h /home output:  drwxr-xr-x 26 oli      oli      4096 2012-01-19 17:19 oli drwxr-xr-x  3 bob      bob      4096 2012-05-09 14:11 bob Can I use Google Maps as a layer in ArcMap?  Is it possible? How to tenderize large squid? My whole life I've been buying small squid (maybe 4-6" long bodies without the head and tentacles), which are very mildly chewy and tender.  All it takes is sautee them in a little OO and they are good to eat, IOW, no additional tenderizing is needed.  Yesterday I got some large squid, about 1 lb each before cleaning, probably 10"+ long without the head, probably 5-6 times as much meat as the little ones I usually get.  I remember trying to cook that before and they came out very tough and with a bit of unpleasant odor.  Is there a way to marinate and tenderize large squid and to somehow neutralize the odor? Show that $\sum_{n = 1}^{+\infty} \frac{n}{2^n} = 2$ Let $b_n$ decrease monotonically to zero, prove $\sum b_nz^n$ converges for $|z|\leq 1$ and $z\neq 1$ Uninformative error message when using AUCTeX Mapping of zero vector under a linear transformation Let $T$ be a linear transformation from a vector space $V$ to $W$ that are defined over a field $\mathbb F$.   Now, $T(\mathbf0)=\mathbf0$.   Which implies the zero vector in $V$ can't move or be transformed to a new vector in $W$. Why is it so?   Does it also have a geometrical significance?