In my \lstset I have:  \lstset{ language=Java,                    % the language of the code basicstyle=\sffamily\large,        % the size of the fonts that are used for the code %numbers=left,                      % where to put the line-numbers %numberstyle=\footnotesize,         % the size of the fonts that are used for the line-numbers %stepnumber=1,                      % the step between two line-numbers. If it's 1, each line                                      % will be numbered %numbersep=10pt,                      % how far the line-numbers are from the code %backgroundcolor=\color{white},      % choose the background color. You must add \usepackage{color} showspaces=false,                   % show spaces adding particular underscores showstringspaces=false,           % underline spaces within strings showtabs=false,                   % show tabs within strings adding particular underscores frame=single,                      % adds a frame around the code tabsize=2,                        % sets default tabsize to 2 spaces captionpos=t,                     % sets the caption-position to bottom breaklines=true,                  % sets automatic line breaking breakatwhitespace=false,           % sets if automatic breaks should only happen at whitespace %title=\lstname,                   % show the filename of files included with \lstinputlisting; caption=grail.sablecc,             % also try caption instead of title escapeinside={\%*}{*)},            % if you want to add a comment within your code morekeywords={*,...}               % if you want to add more keywords to the set }      taken from a wikibook. The problem is that when the source code is really long and requires 2 or more pages, I would like that the frame would close on every page instead of having the bottom of the listing open. Is that possibile?
When I use the listings package with frame in my code the frame "breaks" when the page ends and it is open in the end of the page. I want the frame to be complete with four sides and continue in the next page again with all four frame sides complete. How can I do this? Why does the frame "breaks"?
What does functools.wraps do? How would you go about proving that $$\gcd \left(\frac{a}{\gcd (a,b)},\frac{b}{\gcd (a,b)}\right)=1$$  for any two integers $a$ and $b$?  Intuitively it is true because when you divide $a$ and $b$ by $\gcd(a,b)$ you cancel out any common factors between them resulting in them becoming coprime. However, how would you prove this rigorously and mathematically? Finding out NSArray/NSMutableArray changes' indices SQL Server 2008 R2 SP1  My company uses the Great Plains (GP) financial system with several customizations.  Our Value-Added-Reseller (VAR) for GP has setup most of these customizations in a separate database from the GP data called DYNCUSTOM.  In the DYNCUSTOM database is a View that is merely a SELECT * FROM a table in the GP company database (called PARTS).  I was approached by a user having problems trying to select on this view.  The error he was getting:  Msg 229, Level 14, State 5, Line 2 SELECT permission denied on object 'BM010415', database 'PARTS', schema 'dbo'   I looked at how his login was mapped and he had a database user in the DYNCUSTOM database belonging to a database role that was granted select on the view.  However, he did not have a database user in the PARTS database.    Usually the intent of a view is so that one can grant select permissions on the view without exposing access to the underlying table.  With SQL Server however, if the view crosses databases does it then change the security context being used?  Therefore, the user would also need a database user in the PARTS database as well as granted select access to the underlying table? When the phrase is used as an object, why so many native speakers are saying "you and I" instead of "you and me"? I'm not a native speaker but I thought "you and me" is correct. Not sure if this falls into the same category, but "Just between you and me" sounds more natural than "Just between you and I". how to get the last character of a string? can we have a parallel earth made of dark matter? I am considering purchasing a Mac for my godson who will be using it to run Blender 2.8.  I know very little about this program.  All I can find are requirements for a Mac that will run earlier versions of Blender.  Would someone please recommend a list of requirements for a Mac (or a link to a list of requirements) that I could use to find a model that can run 2.8?  Thank you in advance for all your help! Sincerely, M. Lap $ d_1,d_2\mid n\iff {\rm lcm}(d_1,d_2)\mid n\ $ [LCM Universal Property] Is $$d_1\mid n,d_2\mid n\iff [d_1,d_2]\mid n$$ true ? And if yes, how can I prove it ? I recall that $[d_1,d_2]$ is the least common multiple.  My tries  For the implication : Let $d_1\mid n$ and $d_2\mid n$. Then, $d_1d_2\mid n^2$. By the way, since $d_1,d_2\mid n$, we have that $(d_1,d_2)\mid n$ where $(d_1,d_2)=:\gcd(d_1,d_2)$  and thus $$[d_1,d_2](d_1,d_2)\mid n^2.$$  Question: How can I get $[d_1,d_2]\mid n$ from this?  For the converse, since $d_1,d_2\mid [d_1,d_2]\mid n$, the claim follow. Kontact in Kubuntu 16.10 will not start because the Akonadi server will not start Is it: My apples and orange are/is wrong? Simple question:     My apples and orange are wrong   or     My apples and orange is wrong   I am not a native English speaker, and I am having some trouble choosing between plural are or singular is for that kind of example. How do I achieve this kind of light star effect? I'm kinda new to Blender. Currently playing around with version 2.8 to practice some rendering. Is there a way to achieve this 'light-star' effect for the blooming objects with the emission? If there is an alternative way then it's fine too. See these images below for references. Thanks in advance: No module named numpy I am trying to run Jupyter notebook from my Ubuntu subsystem in Windows 10. I've installed numpy, scipy, and pandas using the following commands:  pip install scipy numpy pip install pandas   When I load python in Ubuntu, there is no issue importing numpy in Ubuntu cmd.   But, when I run my Jupyter Notebook from Ubuntu terminal, and try to import numpy as np, or import pandas as pd, they report  ModuleNotFoundError                       Traceback (most recent call last) &lt;ipython-input-1-a9340201ed9f&gt; in &lt;module&gt;       5 import dash_html_components as html       6 import plotly.graph_objs as go ----&gt; 7 import numpy as np       8 from dash.dependencies import Input, Output       9   ModuleNotFoundError: No module named 'numpy'   Is there anyway to solve this issue? Thanks a lot. Play audio with Python Recurrence relation for number of ternary strings that contain two consecutive zeros The question is: Find a recurrence relation for number of ternary strings of length n that contain two consecutive zeros.    I know for ternary strings with length one, there are 0. For a length of 2, there is just 1 (00), and for a length of 3, there are 5 (000,001,002,100,200).    I did a similar problem, finding a relation for the number of bit strings of length n with two consecutive zeros: $$a_n = a_{n-1} + a_{n-2} + 2^{n-2}$$    Since you can add "1" to the end of all the $a_{n-1}$ strings, "10" to all the $a_{n-2}$ strings, and "00" any string of size $n-2$.    For the ternary string problem, I'm pretty sure you would replace the $2^{n-2}$ with $3^{n-2}$, but confused about the other terms of the relation. My guess is that it would have the coefficient $2$ in front of the other terms, since you can add either $1$ or $2$ to the end of $a_{n-1}$ and either $01$ or $02$ at the end of $a_{n-1}$.    So I believe the answer for the relation is: $$a_n = 2a_{n-1} + 2a_{n-2} + 3^{n-2}$$    How does that look? "They are quite full up this year." How to print without newline or space? Getting a black screen when installing or Live booting Ubuntu (any version) in my laptop I have an ACER Aspire laptop. Model number is E5-573G-56RG. I bought it only 15 days back. There is no DVD drive in it. I have tried various versions of Ubuntu- 14.04.2, 14.04.3, 15.10, 12.04.5. Tried disabling secure boot, fast startup. I current have Windows 10 Home and Windows 10 PRO (not-activated) installed with GPT partition in UEFI bios. I actually want only the Home edition and Ubuntu 14.04.3 (preferably because of LTS) or 15.10. In case more information is required, kindly ask me..  I tried installing through Wubi, when booting if I choose Ubuntu it automatically restarts and goes into Windows 10 Home! (I didn't have Windows 10 PRO at that time)  NONE OF THE SOLUTIONS I REFERRED HELPED ME.  I have spent 5 days (literally at least 20 hours reading all of them and trying out all kinds of editing in the grub command line, like removing quiet splash, adding and replacing with nomodeset, no splash, acpi_osi=off, acpi_osi=Linux, acpi_backlight=vendor,  acpi_backlight=legacy, noveau.modeset=0, i915.i915_enable_rc6=1 and such things! But I was not able to succeed installing which is why I doubt if there is some more thing to be done or know exactly what has to be done. Four tasks in parallel... how do I do that? I have a bunch of PNG images on a directory. I have an application called pngout that I run to compress these images. This application is called by a script I did. The problem is that this script does one at a time, something like this:  FILES=(./*.png) for f in  "${FILES[@]}" do         echo "Processing $f file..."         # take action on each file. $f store current file name         ./pngout -s0 $f R${f/\.\//} done   Processing just one file at a time, takes a lot of time. After running this app, I see that the CPU is just 10%. So I discovered that I can divide these files in 4 batches, put each batch in a directory and fire 4, from four terminal windows, four processes, so I have four instances of my script, at the same time, processing those images and the job takes 1/4 of the time.  The second problem is that I lost time dividing the images and batches and copying the script to four directories, open 4 terminal windows, bla bla...  How do that with one script, without having to divide anything?  I mean two things: first how do I from a bash script, fire a process to the background ? (just add &amp; to the end?) Second: how do I stop sending tasks to the background after sending the fourth tasks and put the script to wait until the tasks end? I mean, just sending a new task to the background as one tasks end, keeping always 4 tasks in parallel? if I do not do that the loop will fire zillions of tasks to the background and the CPU will clog. Is Dirichlet function Riemann integrable? "Dirichlet function" is meant to be the characteristic function of rational numbers on $[a,b]\subset\mathbb{R}$.   On one hand, a function on $[a,b]$ is Riemann integrable if and only if it is bounded and continuous almost everywhere, which the Dirichlet function satisfies.  On the other hand, the upper integral of Dirichlet function is $b-a$, while the lower integral is $0$. They don't match, so that the function is not Riemann integrable.  I feel confused about which explanation I should choose...