Does anyone know how to make a table of contents page separately from the others?  For instance: creating a section on table of contents without generating a next page containing this section.

I'm trying to make table of contents manually, I mean I set the page of each of sections one by one. Here's my target:  and I'm using book class here.  Here's the code that I found   \documentclass[oneside]{book} \renewcommand\contentsname{CONTENTS} \renewcommand\listtablename{LIST OF TABLES} \renewcommand\listfigurename{LIST OF FIGURES} \addtocontents{toc}{{\bfseries Contents\hfill Page No.\bigskip\par}} \addtocontents{lot}{{\bfseries No.\hfill Title\hfill\hfill Page No.\bigskip\par}} \addtocontents{lof}{{\bfseries No.\hfill Title\hfill\hfill Page No.\bigskip\par}}  \usepackage[titles]{tocloft} \usepackage{xcolor,xpatch} \renewcommand\cftbeforechapskip{0ex} \renewcommand\cftchapfont{\mdseries} \renewcommand\cftchappagefont{\mdseries} \renewcommand\cftchappresnum{Chapter~} \renewcommand\cftchapaftersnum{. } \newlength\tocindent \settowidth\tocindent{\cftchapfont\cftchappresnum9\cftchapaftersnum} \edef\cftchapnumwidth{\the\tocindent} \edef\cftsecindent{\the\tocindent} \advance\tocindent2.3em \edef\cftsubsecindent{\the\tocindent} \advance\tocindent3.2em \edef\cftsubsubsecindent{\the\tocindent} \renewcommand\cftsecdotsep{\cftnodots} \renewcommand\cftsubsecdotsep{\cftnodots} \renewcommand\cftsubsubsecdotsep{\cftnodots} \newcommand\tocmainmatter {\renewcommand\cftchappagefont{\color{white}}% } \xapptocmd\mainmatter{\addtocontents{toc}{\protect\tocmainmatter}}{}{}   \newif\ifschaptertoc \makeatletter \renewcommand\@makeschapterhead[1]% {{\parindent \z@ \centering     \normalfont     \interlinepenalty\@M     \Large \bfseries  #1\par\nobreak     \vskip 20\p@ }% \@mkboth{\MakeUppercase{#1}}{\MakeUppercase{#1}}% \ifschaptertoc \addcontentsline{toc}{chapter}{#1}% \fi } \makeatother  \usepackage{blindtext}  \begin{document} \frontmatter  \tableofcontents \schaptertoctrue  \chapter*{ACKNOWLEDGEMENTS} \blindtext  \chapter*{ABSTRACT} \blindtext  \listoftables  \listoffigures  \chapter*{ABBREVIATIONS} \Blindtext  \chapter*{NOTATIONS} \Blindtext  \mainmatter  \chapter{INTRODUCTION} \blindtext  \section{General Background} \blindtext  \section{Objective} \blindtext \subsection{Objective 1} \blindtext \subsection{Objective 2} \blindtext \subsection{Objective 3} \blindtext  \section{Scheme} \blindtext \end{document}


yesterday when I visited  and  there was a banner of unicoins in right sidebar     after mining and collecting unicoins I purchased “No downvotes, please” Unicoins power and also got some downvotes on this question   and upvotes on this question  now where all my powers and unicoin has gone? was it a  ?


Problem 1: I'm trying to create subfolders for the projects that started at certain year. To do that,I tried to use the spread operator but the result was simply {<start_year>..<end_year>}.  I tried with the comma operator,and it worked. Maybe i'm missing something.     └── projects         ├── 2018         ├── 2019         ├── 2020         └── 2021   ## The code  declare -i START_DATE=$(date --date="3 years ago" +'%Y')   declare -i END_DATE=$(date +'%Y')  mkdir -p projects/{$START_DATE..$END_DATE}   ________________________________________ result:               projects          └── {2018..2021}   Problem 2: If I try to use a variable SUB_PROJECTS={$START_DATE,$END_DATE} to be readable and easier to change values, the bash command cannot distiguish the symbols, only assume as a whole string. How I can solve this? SUB_PROJECTS={$START_DATE,$END_DATE} mkdir -p projects/$SUB_PROJECTS ________________________________________  result:               projects          └── `{2018,2021}`

How do I iterate over a range of numbers in Bash when the range is given by a variable?  I know I can do this (called "sequence expression" in the Bash ):   for i in {1..5}; do echo $i; done   Which gives:     1    2    3    4    5   Yet, how can I replace either of the range endpoints with a variable? This doesn't work:  END=5 for i in {1..$END}; do echo $i; done   Which prints:     {1..5}


Good morning all , I must configure an automated backup to an azure blob storage in the backup script I have correctly configured the credential now what right is needed for the sql server agent startup account to access the storage azure blob thank you for your help

RESTORE FILELISTONLY FROM URL = '' WITH CREDENTIAL = '' fails in SQL Server 2016.  Copied script from SQL Server 2012 environment, successfully restoring from Azure Storage Container, with create credential statement, and it failed in 2016.  Error message "Forbidden".  Only after logging into the Azure Portal, creating a Shared Access Signature for the container, could I execute the restore, and only by not specifying the credential did the restore work.  No documentation advises that a SAS (Shared Access Signature) is required in SQL Server 2016 for Azure container backup / restore.  Is there another way to use T-SQL to access blob backups on Azure storage containers in SQL Server 2016, than using SAS?    Looking at the MSDN tutorial on how to configure the backup service SQL 2016 introduces, a SAS is used. Refer


Given any irregularly shaped large polygon, I'd like to be able to subdivide it into as many (full) smaller rectangular polygons as possible (like a grid, but rectangular and with user-specified dimensions).  I know of the Tesselate function in ArcGIS Pro, and of the Fishnet function, but I'm not totally sure those would have the outcome I'm after.  I can manage writing something in ArcPy to facilitate this, I'm just not familiar with the built-in functions in Arc well enough to know what functions to look into leveraging.  The workflow I'm envisioning is something along the lines of:   Create a grid that has the user-specified cell dimensions (a x b) Clip the grid to the size of the polygon, and create shapefiles for each cell.    All of the space from the original polygon needs to be accounted for in the final output.    A good example use case for this would be, you have an area of irregularly shaped  parcel of land and want to subdivide it into equal rectangular lots and create polygons for each of them.  Have access to ArcGIS Pro, ArcGIS 10.3, and can build arcpy toolboxes if needed.  Image:   - "Grid" in red  - Original irregularly shaped polygon in black.  - Output polygons in blue

I have a task that sounds simple, but I just can't get through the last step. I need to find suitable areas where wind farms that have a size of 500x150 meters, could be placed. The restrictions are slope - best areas are form 0-2 degrees and 2-3 degrees are worth considered - and a 3 km buffer from the selected location. Data used here was SRTM as this is preliminary study. My workflow was to buffer the locations, clip the DEM, create slope, reclass into 3 categories and convert to shapefile.  My categories of reclass are as follows:   First category - 1 = 0-2 degrees - green; Second category - 2 = 2-3 degrees - orange; Third category - 3 = all other data - red.   The issue that I am facing is that I would like know many 500x150 meters polygons can I fit in the green area, without overlapping the orange and red areas and without overlapping the polygon itself. The end result should be a shp with the possible positions for the aforementioned 500x150 meters polygon.   I should also specify that the 500x150 meters polygon can have any position/orientation and that I have access to ArcGIS Desktop 10.6/ArcGIS Pro 2.2/Global Mapper 19 and QGIS and my coding skill relate to very simple tasks that I replicate from other users.  I had a look at  where a similar things is described, but with circles and using ETGeowizard, also an older version of Arcmap.  Also,  is almost what I need, but the answers are just to above my level.  EDIT: the purple area is an existing possible location drawn by hand. I am  trying to figure out the maximum number of 500x150m polygons that can be mosaic-ed into the green area. They don't necessarily have to touch each other.


With all the new ____.stackexchange.com sites coming up, I wonder if there is some reasoning on which questions do belong on stackoverflow.com.  The  says a question belongs there if it covers:   a specific programming problem a software algorithm software tools commonly used by programmers a practical, answerable problem that is unique to software development   However as far as I understand for example a "specific programming problem" would belong to    , if it is about specific code the person wrote , if it is about a design question , if it is about what library to use , if it is about user interaction.   Similar sites can be found for the other three points as well.  So my question is: Is there some kind of masterplan what stackoverflow is for? Or is it in fact meant to be the site, where everything that is not exactly covered by another site, belongs?

There seems to be more than a few computer science/programming Stack Exchange networks (is that the correct term?). Stack Overflow, being the first, has by far the most users, questions, and answers.  What is the reasoning for creating the others, and are there clear guidelines for which kinds of questions should be posted? I can see a large amount of potential overflow, many cases of people not getting a good answer to their question, because the person who has the answer isn't browsing that particular network at the moment.  I understand that they were probably created for organizational purposes, but wouldn't it almost make more sense to just have them as categories under Stack Overflow, keep them separated but still connected, instead of making people have to create multiple 'account's, one for each network?  I am sure there was a very good reason to break them up, but as someone that is new to SE, it can be somewhat intimidating to decide which one to post in to ensure you get a good answer. For example, if I am a computer science student, my first instinct might to be to post in the computer science network, until I see that it literally has 1% of the users as the Stack Overflow network, which still seems to be for programming/computer science related questions.  So my second instinct would then to be to post it into the Stack Overflow site on the basis that I have a significantly higher chance of my question being seen and getting a good answer. Then I notice that there is also a 'programmers' network, and I don't even begin to know where that fits in. I, and I am assuming most people, will probably just post on Stack Overflow to be safe.  My question is, other than the short little description blurb of each one, is there a clear cut set of guidelines which what each network is intended for, what kinds of questions should go to each one, and is anything being done to encourage people to post in these newer, smaller (more specialized?) networks as opposed to just posting in big daddy Stack Overflow?  Now again, this is for computer science/programming/"why isn't this code doing what I want?" related questions, I am not saying that if I had a question about Linux or WordPress or something I would have the same confusion.


I added something in visudo and now when I want to run sudo it gives me the following error: Sorry, user reza is not allowed to execute '/bin/su' as root.  What should I do?

How do I edit an invalid sudoers file? It throws the below error and it's not allowing me to edit again to fix it.  Here is what happens:  $ sudo visudo >>> /etc/sudoers: syntax error near line 28 <<< sudo: parse error in /etc/sudoers near line 28 sudo: no valid sudoers sources found, quitting


I am not that familiar with regulators, so, I want to know what happens if the input voltage is under the rated minimum voltage? Does it give zero volts or something under the rated voltage? If it's not zero volts, is there any type that gives 0v or acts like an open circuit in that case ?  there is another similar question but it's not that specific. what I want here is a mention of any type that goes open circuit when the input voltage is under the rated minimum voltage

I know that for a linear regulator to go into regulation, it is necessary to maintain (at least) a specific dropout voltage between its input and output.  But what happens if the input voltage drops so much that it will be closer to the intended output value than the dropout? What will be the "new" output voltage?


Fermat's little theorem states that if $p$ is prime, then $\forall a\in\mathbb N \quad a^p\equiv a \quad \text{mod} \quad p$. Is the converse true ?

If $a^n\equiv a \pmod n$ for all integers $a$, does this imply that $n$ is prime?  I believe this is the converse of Fermat's little theorem.


App Version: 1.0.85 Device Manufacturer: htc Device Model: Nexus 9   OS Version: 6.0.1 (2960889)    Activity is missing layout_weight in <RelativeLayout> from GroupView for JUST NOW,EARLIER TODAY,etc.

The lines wrap so much on v1.0.85 that only a few items can be displayed.  Edit: This is on the world's most low end tablet, Azpen A727.  Screenshots of the old:    and new, showing loss of quality


We have several fields on the Article content type such as field_headline (plain text field). When we try to access the value of this field in a module hook such as mymodule_preprocess_page (mymodule.module), we have found several ways to do it.   What is the correct way to get the value of the fields?   Example:  function mymodule_preprocess_page(&$variables) {   $node = $variables['node'];    // These both work.    $node->get('field_headline')->value;   $node->get('field_headline')->first()->getValue()['value']; }

For example  Drupal\Core\Entity\Entity::id() returns $this->id(or NULL) Drupal\Core\Entity\ContentEntityBase::id() returns $this->id->value Drupal\Core\Entity\ContentEntityBase::uuid() returns $this->get('uuid')->value Drupal\node\Entity\Node::id() returns $this->get('nid')->value  Also in some methods there are setValue() and getValue() utilised but sometimes there are just $this->field->value. So what is the reason for this inconsistent behavior? From my understanding all the "fields" are TypedData fields hence the setValue() and getValue() methods should be used instead of directly access $this->field->value. Besides it's strange because $value is private.


I opened the terminal of blender suite and typed:  youtube-dl -f22 youtubeaddress   The specifics of format 22 of the youtube-dl program is as follows:     22           mp4        1280x720   hd720 , avc1.64001F,  mp4a.40.2@192k (best)   I have no expertise in video-or audiocodes, I thought to recognize mp4 is sufficient.  I played the file with the parole movie player, I got video but no sound. When I imported the file into the Openshot movie editor I also got video, but no sound.  I guess, the answer to my problem is somewhere in the format description:      hd720 , avc1.64001F,  mp4a.40.2@192   I am clueless what this mean and how I can use this information to get the right audio codecs or something like this.

./youtube-dl https://www.youtube.com/playlist?list=PLVqBLRhC9UzGX1BRbF53zsJE8Jw_eiLRK   It produce following output with warning  [youtube:playlist] PLVqBLRhC9UzGX1BRbF53zsJE8Jw_eiLRK: Downloading webpage [download] Downloading playlist: Fear Files [youtube:playlist] PLVqBLRhC9UzGX1BRbF53zsJE8Jw_eiLRK: Downloading page #1 [youtube:playlist] PLVqBLRhC9UzGX1BRbF53zsJE8Jw_eiLRK: Downloading page #2 [youtube:playlist] playlist Fear Files: Downloading 223 videos [download] Downloading video 1 of 223 [youtube] R8lNWOGJ5cg: Downloading webpage [youtube] R8lNWOGJ5cg: Downloading video info webpage [youtube] R8lNWOGJ5cg: Extracting video information [youtube] R8lNWOGJ5cg: Downloading MPD manifest  WARNING: Requested formats are incompatible for merge and will be merged into mkv.  [download] Resuming download at byte 206757946 [download] Destination: Fear Files - Episode 44 - September 28, 2014-R8lNWOGJ5cg.f137.mp4  Because of waring youtube-dl download video without audio. How to solve that issue. I also try command  youtube-dl -f 22 URL_link but still not work.


For example 11 and 101 are primes, but apart from them, can we determine how many primes on the form $100\cdots 00 1$ there exist (in decimal number system)?

Is there a prime which is the form of $10^n + 1$ except $2, 11, 101$?  I confirm there isn't such prime for $n < 64$.


I've got a TI LM3S Cortex-M3 Development board with USB host. I've done quite a bit of TCP/IP programming through the Ethernet and using SPI/UART GSM modems, but I was wondering the feasibility of getting web access through a USB 3G 'dongle'.  From my brief bit of research, I can see most of the modern modems support this through CDC-ACM and/or RNDIS but having only 256k flash and 96k of RAM am I being a bit too ambitious? So far I've only found commercial libraries for this and I haven't looking into the complexities of doing myself.  Should I just be looking at ARM9 and Linux?

In my country (Nigeria) we have very few wireless hotspots, most people connect to the internet via private USB dongles.  I was wondering if it is possible to use these dongles to allow an embedded system connect to the internet.  I know that involves knowing some form of USB protocol with which these devices communicate with a system, but I don't know if there is some standard for that or something to make it generic.


I know this issue is well known, I just wanted to know whether there is a real fix for this issue and not just a workaround.   Minimizing the mail window didn't work. Unchecking "Prefer opening messages in split view when in full screen" in mail preferences didn't work. Reconfiguring the gmail account in the System Preferences didn't work.   BTW, one of the causes for this behaviour is when the mail client can't connect to the mail server of one of my emails so it's not only related to gmail.  Again, I know this issue was asked repeatedly but there was no real solution to the problem.  I found a temporarily workaround for now,  I had to literally keep mac mail open in full screen in a different space just to stop its annoyance but I don't like seeing it there all the time when I switch between screens.  I have checked the following questions but none of them helped.       Note, I'm using macOS Mojave (10.14.6), if upgrading to Catalina would solve the issue please let me know. Although I don't want to upgrade I will do it anyway to get rid of this issue.

When I am doing some work on my macbook pro, Mail app's main window keeps popping up in the background, it even pops up when I watch movies by interrupting full screen. This is so frustrating, I can't find out solution to this, googled and went to many discussion forums, no luck, suggestions that I found are very old and outdated. Has anyone faced similar issues or does anyone knows solution to this?


Determine the general form of $u_0, u_1 ~\text{and} ~ u_2$ if a system of difference equations of the form  $$x_{n+1} = Ax_n  + Bu_n,$$  where:  $A = \begin{pmatrix}   3 & 2 & 2  \\   -1 & 0 & -1 \\    0 & 0 & 1   \end{pmatrix}$  and:  $B = \begin{pmatrix}   0 & 0  \\   0 & 1 \\   1 & 0   \end{pmatrix}$  is to be controlled for $x_0 = 0 ~ to ~ x_3 = [2, 1, 2]^T$ .  Show this target could have been achieved at  $x_2$   Solution So far I have caculated the controlability matrix to be $ C =\begin{pmatrix} 0&0&2&2&6&6\\ 0&1&-1&0&-3&-2\\ 1&0&1&0&1&0 \end{pmatrix}. $ Thus the system is controlable Now putting Cv=x3 i have the 3 equations $$ 2c+2d+6e+6f=2\\ b-c-3e-2f=1\\ c+e+f=2\\ $$ which i have then put into  row echleon form which i have found to be $$ a+c+e=2\\ b-c-3e-2f=1\\ c+d+3e+3f=1\\ $$  I proceeded to put these in terms of c,e and f to get the general terms  $a=2-r_1-r_2  ,  b=1+r_1+3r_2  , c=r_1   , d= 1-3r_3-3r_2-r_1  ,  e=r_2   ,  f=r_3,$  however when i substitue this back into my equation to check by doing  $$x_1=Ax_0+Bu_0, x_2=ax_1+Bu_1, x_3=Ax_2+Bu_2$$  i dont get $x_3=(2,1,2)^T$

Determine the general form of $u_0, u_1 ~\text{and} ~ u_2$ if a system of difference equations of the form  $$x_{n+1} = Ax_n  + Bu_n,$$  where:  $$A = \begin{pmatrix}   3 & 2 & 2  \\   -1 & 0 & -1 \\    0 & 0 & 1   \end{pmatrix}$$  and:  $$B = \begin{pmatrix}   0 & 0  \\   0 & 1 \\   1 & 0   \end{pmatrix}$$  is to be controlled for $x_0 = 0 ~ to ~ x_3 = [2, 1, 2]^T$ .  Show this target could have been achieved at  $x_2$   Solution So far I have caculated the controlability matrix to be $$ C =\begin{pmatrix} 0&0&2&2&6&6\\ 0&1&-1&0&-3&-2\\ 1&0&1&0&1&0 \end{pmatrix}. $$ Thus the system is controlable Now putting Cv=x3 i have the 3 equations $$ 2c+2d+6e+6f=2\\ b-c-3e-2f=1\\ c+e+f=2\\ $$ which i have then put into augmented matrix row echleon form which i have found to be $$ a-d-2e-3f=1\\ b+d+f=2\\ c+d+3e+3e=1\\ $$  How do I now solve with so many unknowns? also can you please check my working so far is correct. many thanks


So I have the following: $\sum_{n=1}^x (\frac76)^{n-1}  *n $  When I plug it into wolfram alpha it gives me the following equation: $6^{1-x}(7^xx-6*7^x+6^{x+1}) $ I have no idea where this came from. I'm guessing it involves taking the derivative to make it a normal geometric series, but I have no idea. Any help would be appreciated.  In general, how would could I find an equation for $\sum_{n=1}^x a^n*p(n) $ where a is a rational number and p is a polynomial?

How can I evaluate $$\sum_{n=1}^\infty\frac{2n}{3^{n+1}}$$? I know the answer thanks to , but I'm more concerned with how I can derive that answer. It cites tests to prove that it is convergent, but my class has never learned these before. So I feel that there must be a simpler method.  In general, how can I evaluate $$\sum_{n=0}^\infty (n+1)x^n?$$


I have Ubuntu 13.10 on my desktop.I wanted to install the "D-Link DWR-730" 3G modem drivers, but the default autoplay software for Ubuntu says "kernel not supported" for this.  I ran the dpkg -i command to install the .dep files manually, but after this every apt-get command returns an error and tells me to run apt-get -f install to correct this.  I ran apt-get -f install, but it still returns an error, and I can't install anything from apt-get. The apt-get error is as follows:      Errors were encountered while processing:   flashplugin-installer   E: Sub-process /usr/bin/dpkg returned an error code (1)   I ran apt-get remove flashplugin-installer, but that also returns an error.  sudo apt-get -f install gives the following output:  Reading package lists... Done Building dependency tree Reading state information... Done  0 upgraded, 0 newly installed, 0 to remove and 3 not upgraded. 1 not fully installed or removed. Need to get 0 B/7,008 B of archives. After this operation, 0 B of additional disk space will be used.  dpkg: error processing flashplugin-installer (--configure): Package is in a very bad inconsistent state - you should reinstall it before attempting configuration. Errors were encountered while processing: flashplugin-installer E: Sub-process /usr/bin/dpkg returned an error code (1)

I can't update my system because it freezes while installing a third-party update (zramswap-enabler)! Sometimes I get the following message in Update manager:  Could not initialize the package information An unresolvable problem occurred while initializing the package information. Please report this bug against the 'update-manager' package and include the following error message: E:The package zramswap-enabler needs to be reinstalled, but I can't find an archive for it.  I tried to remove the zramswap-enabler, but it's impossible because I get the following message: dpkg: error processing zramswap-enabler (--remove):  Package is in a very bad inconsistent state - you should  reinstall it before attempting a removal. Errors were encountered while processing:  zramswap-enabler E: Sub-process /usr/bin/dpkg returned an error code (1)  Actually I would really reinstall that package, but it is unable to do it! If I remove this third-party PPA then the system is warning me about a very very serious problem. So why can I not install/reinstall/remove/update this package and why freezes the updater if I try to update?


Why .openPopup() is not working in case of GeoJSON data in Leaflet? I want to use this as labeling in my map.      ////////////// for Popup label  function onEachFeature(feature, layer) {     // does this feature have a property named popupContent?     if (feature.properties && feature.properties.Name && feature.properties.Lat && feature.properties.Lon) {         layer.bindPopup(feature.properties.Name+"("+feature.properties.Lat+","+feature.properties.Lon+")");     } } /// for Show in map marker style and popup     L.geoJSON(geojsonFeature, {     pointToLayer: function (feature, latlng) {         return L.circleMarker(latlng, geojsonMarkerOptions);     },      onEachFeature: onEachFeature  }).addTo(map);

When I try to label the polygon on my Leaflet map I always get the error:     t is undefined   I am trying to do it as shown below:        <title>Page Title</title>     <link rel="stylesheet" href="https://unpkg.com/leaflet@1.0.0-rc.3/dist/leaflet.css" />

        I want to show some text inside the polygon. I've tried to accomplish it using label but unable to do it.


I am writing my thesis on latex but I do not know how to write Itô's in latex with the symbol on the 'o' . Could someone tell me how can I do it? Do I need a special package?

How to type these special letters from European languages in latex? ä, é, and L'?


i created my first app and I would ship it with a local database that contains about 600 entries. I tried to hard-code this data in my class but i think it is not a good idea. So is it possible to copy a database to phone on first start of an application?

If your application requires a database and it comes with built in data, what is the best way to ship that application? Should I:   Precreate the SQLite database and include it in the .apk? Include the SQL commands with the application and have it create the database and insert the data on first use?   The drawbacks I see are:   Possible SQLite version mismatches might cause problems and I currently don't know where the database should go and how to access it. It may take a really long time to create and populate the database on the device.   Any suggestions? Pointers to the documentation regarding any issues would be greatly appreciated.


For PCs, cantrip damage increases with their total character level and not their class level ().  However, NPCs do not normally have class levels, and their stat blocks don't state a total character level.    How can I determine the number of damage dice to roll for an NPC's cantrip?   Should I use their number of hit dice as their total character level?   Should I use their stated Spellcaster level? (What if they don't have one?)   Some other method?     A couple of examples to illustrate my concern:    An Archmage (SRD p. 395) has 18d8 + 18 hit dice and is an 18th level spellcaster, so methods 1 & 2 here would produce the same result. Nezznar the Black Spider (LMOP p.59) has 6d8 hit dice and is a 4th level spellcaster, so methods 1 & 2 would produce different results.   The fact that Nezznar has more hit dice than spellcasting levels implies to me that Nezznar has, in some unspecified way, multiclassed - and that 6 would be his total character level - and the number I should use for cantrips, not 4 (his spellcasting level).   A good answer would also cover NPCs with Innate Spellcasting and no spellcasting level. See for instance:    A Green Hag (SRD. p 319) has 11d8 + 33 hit dice but no spellcasting level.

A 9 HD Yuan-ti Pureblood can innately cast the poison spray cantrip 3 times per day. The monster description says the save is DC 12, but it does not go into damage. So does it do 1d12 or 2d12 damage?


Today we were studying vector and scalar products, when my teacher gave an example of them and told us that area is a vector quantity.   I Have studied previous class’s physics books (two years ago) which defined vector as any quantity that has both direction and magnitude while scalar is defined as any quantity that has only has magnitude and not direction.  And if I remember my high elementary mathematics then:   Area is equal to length x width. Both of these quantities have SI units meter. So we have meter as length, then knowing that length is a scalar quantity:   Scalar quantity x scalar quantity = scalar quantity   Example :  Speed: $$    Speed = v = \frac{d}{t}$$ Where $d$ is distance and $t$ time, which are both  scalar quantities but knowing  Unit is : m/s  Velocity:   $$Velocity = \mathbf v = \frac{\mathbf D}{t}$$  where $\mathbf D$ is displacement (a vector) and $t$ the time (a scalar).  Unit is : m/s.  So the question is why did my teacher say that area, a product of two scalar quantities, is vector in nature?

My professor told me recently that Area is a vector. A Google search gave me the following definition for a vector:  Noun: A quantity having direction as well as magnitude, esp. as determining the position of one point in space relative to another.  My question is - what is the direction of area? I can relate to the fact that velocity is a vector. The velocity of a moving motorbike for example, has a definite direction as well as a definite magnitude assuming that the bike is moving in a straight line & not accelerating. My friend gave me this explanation for the direction of Area vector. Consider a rectangular plane in space. He argued that the orientation of the plane in space can only be described by considering area as a vector & not a scalar. I still wasn't convinced. Suppose the plane was placed such that its faces were perpendicular to the directions, North & South for example. Now the orientation of the plane is the same irrespective whether the so called vector points to north or to the south. Further what is the direction of a sphere's area? Does considering area as a vector have any real significance? Please explain. Thanks in advance.


I have$$\lim_{n\to \infty} \frac{1^p+2^p+\ldots+n^p}{n^{p+1}}=$$ I managed to simplify it down to $$=\lim_{n\to \infty}\left( \left(\frac1n\right)^p \cdot \frac1n + \left(\frac2n\right)^p \cdot \frac1n + \ldots + \left(\frac{n}{n} \right)^p \cdot \frac1n \right)=$$ $$=\lim_{n\to \infty} \sum_{i=1}^{n} \left(\frac{i}{n}\right)^p \frac{1}n$$ How should I calculate this limit?

What is the result of the next limit:   $$ \lim_{n \to \infty} \frac{ \sum^n_{i=1} i^k}{n^{k+1}},\ k \in \mathbb{R} $$  Why (theorem)?


I have the following javascript function with one argument     How can i put function argument text inside this regex rather than YYYYYYYYY  innerHTML = innerHTML.replace(/YYYYYYYYY/gi, '' + text + '');

I would like to create a String.replaceAll() method in JavaScript and I'm thinking that using a regex would be most terse way to do it.  However, I can't figure out how to pass a variable in to a regex.  I can do this already which will replace all the instances of "B" with "A".  "ABABAB".replace(/B/g, "A");   But I want to do something like this:  String.prototype.replaceAll = function(replaceThis, withThis) {     this.replace(/replaceThis/g, withThis); };   But obviously this will only replace the text "replaceThis"...so how do I pass this variable in to my regex string?


Is one more correct than  the other?  Make sure the part is connected to the widget.   Make sure that the part is connected to the widget.

He will understand that I was not joking.   He will understand I was not joking.  Which of the sentences is correct? Are there any specific rules about the use of "that" in the sentences I reported as example?


If the distance between the center of the lens and the film is called Focal length, does that mean the focal point of the camera lens is located on the film?

This  opens with the following statement (bold emphasis added by myself):     In camera design, a focal-plane shutter (FPS) is a type of photographic shutter that is positioned immediately in front of the focal plane of the camera, that is, right in front of the photographic film or image sensor.   Other references concerned with photography almost universally seem to equate focal plane and film plane. This statement is from the  (bold emphasis added by myself):     When a photographic lens is set to "infinity", its rear nodal point is separated from the sensor or film, at the focal plane, by the lens's focal length. Objects far away from the camera then produce sharp images on the sensor or film, which is also at the image plane.   In both of these references the meaning of focal plane and image plane appear to be interchangeable when the distance from the lens' rear nodal point to the film/sensor plane is equal to the lens' focal length.  Yet in physics references that discuss the field of optics (such as this ) the focal plane is defined differently. It seems the front focus plane is defined as what photography refers to as the plane of focus. The back focus plane seems to be defined as the point behind the lens where the aperture is ideally situated. Yet the charts and diagrams on the same page seem at times to use the terms rear focal plane, back focal plane, and image plane interchangeably. Sometimes it seems they are referring to the plane where the image is brought into focus (such as  and the text beneath it in ). At other times it seems to be referring to the crossover point between the lens and the image plane (such as  and the text next to it in ).  When speaking in the context of Photography that uses film or a digital sensor to record an image projected onto that film or image sensor is it legitimate to refer to the film or sensor as occupying the Focal Plane? Is there a nomenclature that allows one to distinguish between the plane occupied by the objects depicted as in focus in the image (plane of focus?, front focal plane?) and the plane the in-focus image is projected on (rear focal plane)?


Is the following true?  ————————————————–  Primes are uniformly distributed  Let p, r, n are positive integers with p>1.  U(p, r, n) denotes the number of primes less than n that are equal to r (mod p).  For any prime p and pair of integers r1, r2 between 1 and p-1, we have:  The ratio U(p,r1,n) / U(p,r2,n) has limit 1 as n goes to infinity.

Let $n\geq 2$ and let $k$ be "considerably larger" than $n$ (like some large multiple of $n$). Then for each $i$ such that $0<i<n$ and $\gcd(i,n)=1$ let's define $$c_i=\left|\{p_j\;|\; p_j\equiv i \mod n,\;\mbox{where $p_j$ is the $j$-th prime, $1\leq j\leq k$}\}\right|$$ so $c_i$ represents how many of the first $k$ primes are congruent to $i$ modulo $n$.  What can we say about $c_i$s, that is about the distribution of the first $k$ primes modulo $n$?  I thought the distribution will be seemingly random, and that is mostly true - for example $c_i$s are always very close together. But there are observable non-random patterns. For example for $n=3$, for various $k$s I've tried  (up to $10^6$) I always got $c_2>c_1$. If this were just some kind of random discrepancy due to distribution of small primes, it would eventually vanish for large $k$s, which I don't observe.


I'm brand new to Blender. Had used KDenlive for video editing a couple times, but it wouldn't handle the large file (30 minutes) I'm working with now. I keep web-searching & keep finding adjacent things or old answers to different versions of Blender.  So I have the 30 minute video. I deleted the first minute. I cut out a 2-3 minute section, and I want to export that section as a .mp4 or... webm or whatever is recommended nowadays.    So I just keep poking around and getting overwhelmed. What/where do I click to export this first little section to video? (and I assume it would be similar for exporting the full thing as a video file?)  Thanks

Yesterday I was working on a simple animation, an animated logo.   Here is an image of the progress:    I already have the animation working and everything is okay with the project, but I can't figure out how I can render the animation and turn it into an AVI format video.  How do I render an animation in Blender?


Please clarify if what I have mentioned below is correct.   I like painting. - Gerund?  I like painting pictures. - Present participle?

This is a follow-up to a previous question which I am still trying to understand. I think I'm making progress in my understanding, but I would appreciate feedback to help me refine my thinking.  Here is the sentence:     Good writing requires hard work.   Originally, I thought that "writing" was acting as a gerund in this phrase.  After reading through the replies to that question along with back posts related to gerunds, I've since concluded that "writing" in this sentence is a , also termed a deverbal noun.  My reasoning?  —In the sentence above "writing" is modified by "good" and is thus acting more like a noun than a verb. —It has no direct object.  Is my thinking correct here?  If not, could someone politely help me to refine it?  However, what if I had written the following?     Writing well requires hard work.     or   To write well requires hard work.   In these examples, I'm thinking that "writing" would be a different kind of verbal noun—a non-finite verb acting as a gerund or infinitive, which is one piece of a larger complement noun clause.  The last bit is muddy for me, but I will leave it at that. Thank you in advance for your patience and insight.


Good morning guys, I'm trying to write some application in C#, where I like to update the UI (A progress bar in this case) from another thread and class.  But I just can't get it to work, I googled and search around but I'm afraid I just don't get it. I have a windows form application, I start a thread when I click a button, and somewhere in this thread I would like to update my UI.  I either get: An object reference is required for the non-static field, method, or property or something in the direction of the object being created by a different thread.  (At the location where I try to call Form1.UpdateProgressBar(value); in fileReader).  I have no experience in object orienting programming, I usually stick with C. If anyone could tell me the right way to do this, I would be very happy.  Edit_1: Alright.. Combinations of errors, the answer so far might have helped if I didn't have he static issue. And fixing the static issue by making the entire class static creates another X amount of errors on its own, including:  Static classes cannot have instance constructors    namespace TestCode {    public partial class Form1 : Form   {     static fileReader SourceReader;     public Thread SearchThread { get; set; }      public Form1()     {         InitializeComponent();      }      private void button1_Click(object sender, EventArgs e)     {         folderBrowserDialog1.ShowDialog();         Console.WriteLine(folderBrowserDialog1.SelectedPath);          this.SearchThread = new Thread(new ThreadStart(this.ThreadProcSafe));         this.SearchThread.Start();     }       public void UpdateProgressBar( int value)     {         progressBar1.Value =value;      }      private void ThreadProcSafe()     {         SourceReader = new fileReader(folderBrowserDialog1.SelectedPath);     }   } }   Class 2:       namespace TestCode      {          class fileReader          {               public fileReader(String path)              {                 int value = 20;                 /*Do some stuff*/                   Form1.UpdateProgressBar(value);               }            }       }

I have a scenario. (Windows Forms, C#, .NET)   There is a main form which hosts some user control. The user control does some heavy data operation, such that if I directly call the UserControl_Load method the UI become nonresponsive for the duration for load method execution. To overcome this I load data on different thread (trying to change existing code as little as I can)   I used a background worker thread which will be loading the data and when done will notify the application that it has done its work.   Now came a real problem. All the UI (main form and its child usercontrols) was created on the primary main thread. In the LOAD method of the usercontrol I'm fetching data based on the values of some control (like textbox) on userControl.    The pseudocode would look like this:  CODE 1  UserContrl1_LoadDataMethod() {     if (textbox1.text == "MyName") // This gives exception     {         //Load data corresponding to "MyName".         //Populate a globale variable List<string> which will be binded to grid at some later stage.     } }   The Exception it gave was     Cross-thread operation not valid: Control accessed from a thread other than the thread it was created on.   To know more about this I did some googling and a suggestion came up like using the following code  CODE 2  UserContrl1_LoadDataMethod() {     if (InvokeRequired) // Line #1     {         this.Invoke(new MethodInvoker(UserContrl1_LoadDataMethod));         return;     }      if (textbox1.text == "MyName") // Now it wont give an exception     {     //Load data correspondin to "MyName"         //Populate a globale variable List<string> which will be binded to grid at some later stage     } }   BUT BUT BUT... it seems I'm back to square one. The Application again  become nonresponsive. It seems to be due to the execution of line #1 if condition. The loading task is again done by the parent thread and not the third that I spawned.  I don't know whether I perceived this right or wrong. I'm new to threading.  How do I resolve this and also what is the effect of execution of Line#1 if block?  The situation is this: I want to load data into a global variable based on the value of a control. I don't want to change the value of a control from the child thread. I'm not going to do it ever from a child thread.   So only accessing the value so that the corresponding data can be fetched from the database.


The sentence below is extracted from vocabulary for IELTS book (recording scripts part).     But nowadays all we seem to do is argue and that causes a lot of conflict between us.   Can we use 'argument' instead of 'argue' here? Why?

This sentence below is extracted from vocabulary for IELTS book (recording scripts part).     But nowadays all we seem to do is argue and that causes a lot of conflict between us.   Why she's saying argue? Shouldn't it be arguing or argument? And why conflict is not plural?


I want to check if my text file contains data or not. If the file contains a data I want to read it. My problem is I don't know the right condition to write in the if statement. Hint: I tried to use the functions of fseek & ftell, but without any benefit. I want to know why this condition in the if statement doesn't work properly?      FILE *fptr;   if(ftell(fptr)!=0){   //check if the file is not empty.     if ( !( fptr = fopen( "saving.txt", "r" ))){         printf( "File could not be opened to retrieve your data from it.\n" );     }     else{         while ( !feof( fptr ) ){             fscanf( fptr, "%f\n", &p.burst_time );             AddProcess(&l,p.burst_time);         }         fclose( fptr );     }    }

How can I figure out the size of a file, in bytes?  #include <stdio.h>  unsigned int fsize(char* file){   //what goes here? }


I can't create a list of abbreviations. I have been using nomencl package.  I put \makenomenclature and   \nomenclature{symbol}{name of symbol} \printnomenclature   But nomenclature doesn't appear.  Thanks

I have used the package nomencl. In my code I have incorporated the \nomenclature as well. But when I compile, it is not showing me any results. My code is :  \documentclass[pdftex,12pt,a4paper]{report} \usepackage{nomencl} \makenomenclature \begin{document} ---page numbering and other things included----- \include{symbols} -----others--- \end{document}   symbols.tex  \chapter*{NOTATIONS} \addcontentsline{toc}{chapter}{Notations} \nomenclature{$G_e$}{Equivalent Shear Modulus} \printnomenclature   Shall I use \nomenclature while explaining the chapter. Will It give me the same results? like  \documentclass[pdftex,12pt,a4paper]{report} \usepackage{nomencl} \makenomenclature \begin{document} ---page numbering and other things included----- \include{symbols} \include{chap3-calculate_w} -----others--- \end{document}   symbols.tex  \chapter*{NOTATIONS} \addcontentsline{toc}{chapter}{Notations} \printnomenclature   chap3-calculate_w.tex  \chapter{SETTLEMENT RESPONSE OF GEOSYNTHETIC REINFORCED GRANULAR FILL SOFT SOIL} \label{chap:W} \section{INTRODUCTION} In this thesis, the methodology to determine an  Equivalent single layer shear modulus \nomenclature{$G_e$}{Equivalent Shear Modulus},$G_e$ value for a...etc   I am not getting the output in both these. Can someone help me with this?


How does a FIFO (named pipe) differs from a regular pipe (|)? As I understand from , unlike a regular pipe, a FIFO pipe "keeps living" after the process has ended and can be deleted sometime afterwards.  But if f the process is based on a shell command containing a pipe (cat x | grep y), we could "keep it alive after the process" if we store it in a variable or a file, isn't it then a FIFO?  Also, a regular pipe also has the first stdout it gets, as stdin for another command, so isn't it also a kind of first in first out pipe as well?

From APUE     FIFOs can be used to duplicate an output stream in a series of shell   commands. This prevents writing the data to an intermediate disk   ﬁle (similar to using pipes to avoid intermediate  disk  ﬁles).       But  whereas  pipes  can  be  used  only  for  linear  connections   between processes, a FIFO has a name, so it can be used for   nonlinear connections.      Consider  a  procedure that  needs  to  process  a  ﬁltered  input    stream  twice.   mkfifo fifo1 prog3 < fifo1 & prog1 < infile | tee fifo1 | prog2       We create the FIFO and then start prog3 in the background, reading   from the FIFO. We then  start prog1 and  use tee to  send  its  input    to  both  the  FIFO  and prog2.    How does a FIFO "duplicate an output stream in a series of shell commands"? Isn't this done by tee instead of a FIFO? In the example, mkfifo fifo1 creates a file in the current directory, and fifo1 seems replaceable with a regular file . So what is the point of a FIFO "prevent writing the data to an intermediate disk file"? What do "linear connections" and "nonlinear connections" between processes mean? What does it mean that a FIFO can be used for nonlinear connections, while a pipe can be only used for linear connections between processes?   Thanks.


Is there an  (terminal application for Mac OS) equivalent for Ubuntu?  Amongst the many features it adds the one I'm after is the "hotkey window", where you can overlay/hide a translucent terminal window at the touch of a button on the keyboard.

My terminal choice has always been Guake, but at my job they have some Macs and I've started to use iTerm2 and I really love the split-functionality.  So I was searching for something similar in Ubuntu. I've tried with Guake + screen, but that is definitely not the same experience, because screen has to be executed as a command.  Yes, I could put it into my bash config, but if I split the screen I cannot move the scroll bar with the mouse (maybe there's a shortcut for this?). The other thing is that my bash config is completely screwed up with screen, I have a function to make an ls after each cd and another to show some info in my prompt when I enter a git repository.  Both don't work for me.  I really would like to know about a program with the iTerm2 functionalities for Ubuntu or, in the worst case, try to emulate them the most similar possible.


Assume that $F: \mathcal{P}A \to \mathcal{P}A$ and that $F$ has the monotonicity property: $$X \subseteq Y \subseteq A \implies F(X) \subseteq F(Y)$$ Define $$B = \bigcap \{ X \subseteq A | F(X) \subseteq X \} \; \mathtt{and} \; C = \bigcup \{ X \subseteq A | X \subseteq F(X) \}$$ Show that $F(B)=B$ and $F(C)=C$.      So far I can get: 1. $F(A) \subseteq A \;\&  \; \varnothing \subseteq F(\varnothing)$ 2. given any $X_1 \subseteq F(X_1)$ and $F(X_2) \subseteq X_2$ $(X_1 ,X_2 \subseteq A)$     I have  $B \subseteq X_2 ,F(B) \subseteq F(X_2) \subseteq X_2$ and  $X_1 \subseteq C, X_1 \subseteq F(X_1) \subseteq F(C)$    But: I cannot find a way to show the relation between $F(B)$ and $B$.What should I do?

Let $P(X)$ denote the power set of $X$ (the set of all subsets of $X$) with a partial order given by inclusion.  If $F: P(X) \to  P(X)$ is monotone (order preserving), then $F$ has a fixed point.  How are we going to prove that without using the term (complete lattice)?!


I want a software for blogging like Live Writer in Linux and GNOME.  Do you have any idea?

I´m searching for a good blog editor like Windows Live Writer something similar.


The question has already been asked as  but the answers did not fit my own trouble.   I am trying to create a plug-in. I followed the Qgis Cookbook and when I start the OSGeoW4 shell I type the following code (xxx is the name of the Beta plugin) :  cd c:\Users\Guillaume\.qgis2\python\plugins\xxx   then       make   which doesn't work nor  pyrcc4 -o resources_rc.py resources.qrc   They are not recognized as internal or external command.   So little research lead me to look after the /bin from qgis and I found pyrcc4.exe but no pyrcc4.bat   I have two python version (2.7) one from the ArcGIS package which is working nicely as a shell on pyzo python interpreter, and one downloaded from the python.org.   I'm working with QGIS 2.18.23

C:\Users\Department\.qgis2\python\plugins\np>pyrcc4 -py2 resources.qrc -o resources.py      'pyrcc4' is not recognized as an internal or external command,      operable program or batch file.   How do I solve this problem?


I really need someone's help. I don't know what else to do, I've read all forums trying all sort of manipulations without managing to solve my problem.   After my login my desktop is empty. I don't know exactly what happend, everything was working well but I think it was after an upate. I cannot access the terminal with Alt+Ctrl+T only with Alt+Ctrl+Fx.   I'm running under Ubuntu 14.04 LTS with Virtual Box (Windows 8 host).   I've tried (among others) :  unity --replace   and I have the following error :  compiz (core) - Error: Plugin 'opengl' not loaded   I'm not an expert with Linux but I can do some basic stuff. :)

When I login, nothing happens.   I am presented with my desktop wallpaper.    No Dash, no Launcher, nothing.


i was working on an algorithm of sub sequences. please tell me the meaning of this statement. program is as below.  void printSubsequences(int arr[], int n) {     unsigned int opsize = pow(2, n);      for (int counter = 1; counter < opsize; counter++)     {         for (int j = 0; j < n; j++)         {             if (counter & (1<<j))                 cout << arr[j] << " ";         }         cout << endl;     } }

I've been attempting to learn C in my spare time, and other languages (C#, Java, etc.) have the same concept (and often the same operators) ...   What I'm wondering is, at a core level, what does bit-shifting (<<, >>, >>>) do, what problems can it help solve, and what gotchas lurk around the bend? In other words, an absolute beginner's guide to bit shifting in all its goodness.


I want to get the above diagram in Latex, but I don't know how to edit it. Any help will be appreciated. I know I had better post my effort here, but I really can not get it by tikz. I find an example written by Stefan Kottwitz. I try to modify his example to get what I want. But I am failed.  % A simple Tree % Author: Stefan Kottwitz % https://www.packtpub.com/hardware-and-creative/latex-cookbook \documentclass[border=10pt]{standalone} \usepackage{tikz} \begin{document} \begin{tikzpicture}[sibling distance=10em,   every node/.style = {shape=rectangle, rounded corners,     draw, align=center,     top color=white, bottom color=blue!20}]]   \node {Formulas}     child { node {single-line} }     child { node {multi-line}       child { node {aligned at}         child { node {relation sign} }         child { node {several places} }         child { node {center} } }       child { node {first left,\\centered,\\last right} } }; \end{tikzpicture} \end{document}

I am writing a paper on numerical solutions for ODEs. For the representations of B-series I want to use binary tree-like symbols. I know how to produce them with TiKZ; however, just as in the given picture, i need to use them also within the text or a mathematical expression. As these trees can be represented by a bracket expression, e.g. in the given picture t=[[.,.], [[.]]], it should be possible to write a macro doing this. However, I failed so far - or is there an alternative approach?


I have a problem where when I click shift, space, w and x at the same time it does not work. I use this when playing a game and it it will not work. It allows me to click shift, space, w and c, but not 'x'. I cannot find a way to fix it and believe it might be a limitation of some sort but I want to be sure. I am also using a laptop running Windows 10 and it's a 64-bit system. If you have any ideas on what is going on or what I should do if I want to fix it, please do speak.

Whenever I play a PC game with the directional keys, I can only press two buttons at a time.  For instance if I am playing a shooter like R-Type, I cannot hold down the fire button while moving diagonally at the same time.  The computer simply ignores the extra button press.  How do I remove this limit so I can shoot while moving diagonally?  This limitation seems to apply for every game.  I am running Windows 7 if it makes any difference.  I noticed the same problem back when I used Windows XP.


What is $\prod$ and how can I use it? I have seen it used under numerous occasions and on the  graphing calculator keyboard-menu. I could not get it to work, and wanted some pointers.

This is one of those cases where I would google if I could, but I don't know what to search for.  I've come across this symbol a few times, but I have no clue what it means or what it is called.  $$\prod$$  Furthermore, what are the $\coprod$ and $\amalg$ symbols for?  I could not list all the places I found it, but the one that sparked it was a discussion on solving the Diophantine equation, $\frac{1}{x} + \frac{1}{y} = \frac{1}{n}$.


So that I will be able to see where people that used my bit.ly link come from? I already checked it with Chrome dev tool in Network tab but there is no info.

Traffic coming form shortened URLs like bit.ly, do they show up in Google Analytics as direct or do they keep their real referrer?  Ex.: if someone types in a bit.ly link it counts as direct, but if someone clicks a bit.ly link from Twitter, it counts as referral traffic from Twitter?


I was looking for a way to see what was edited in one of my questions on the Android app, but there doesn't seem to be a way of viewing the edit history.  Is there a way to fo this and if not can we add it in?

Basically this suggestion for the Android app:   Many times I'll see that a post has been edited on the Android app. I'll want to see exactly what was edited, and the Android app doesn't show this. Can the revision history be added to the Android app?


It could be a misprint or typo in what I'm reading, but I just want to make sure.  I'm reading Loring Tu's "An Introduction to Manifolds", and at the end of the first chapter, one of the problem states:  $\textbf{1.3 A diffeomorphism of an open interval with}\,\,\mathbb{R}$  Let $U\subset\mathbb{R}^n$ and $V\subset\mathbb{R}^n$. A $C^\infty$ map $F: U\rightarrow V$ is called a diffeomorphism if it is bijective and has a $C^\infty$ inverse $F^{-1}:V\rightarrow U$.  (a) Show that the function $f: \,\,\,]-\pi/2, \pi/2[\rightarrow \mathbb{R}, f(x)=\tan(x)$ is a diffeomorphism.  To be clear, I'm not asking for help with the problem, just the notation he uses. Elsewhere in the text, it appears that every time he mentions an open interval, he uses this $]a,b[$ notation, but for closed intervals he uses the traditional $[a,b]$.  Is this notation commonly used, or likely some sort of misprint with the pdf I'm reading from?

I have frequently encountered both $\langle a,b \rangle$ and $[a,b]$ as notation for closed . I have mostly encountered $(a,b)$ for open intervals, but I have also seen $]a,b[$. I recall someone calling the notation with $[a,b]$ and $]a,b[$ as French notation.   What are the origins of the two notations?  Is the name French notation correct? Are they used frequently in France? Or were they perhaps prevalent in French mathematical community at some point? (In this  Bourbaki is mentioned in connection with the notation $]a,b[$.)      Since several answerers have already mentioned that they have never seen $\langle a,b \rangle$ to be used for closed intervals, I have tried to look for some occurrences for this. The best I can come up with is the article on , where these notations are called Czech notation and French notation. Using $(a,b)$ and $[a,b]$ is called English notation in that article. (I am from Central Europe, too, so it is perhaps not that surprising that I have seen this notation in lectures.) I also tried to google for  or . Surprisingly, this lead me to a  where this notation is used for open interval.


In MySQL table definitions is there a different between INT(5) and SMALLINT(5)?  Or do they both represent the same size?


I play on Xbox One, and I do commands to give heads, like  /give @s skull 1 3{SkullOwner:MrCrainer}, but it doesn't work. (MrCrainer was a real player example.)  I don't use internet on Xbox, because it'll force an update that won't work. I have 1.14.

This question was recently split into different questions for each workaround. See   meta posts for more information.   Can you use NBT tags in commands? I’ve tried commands that normally work in Java Edition like: give @s minecraft:planks 30 1 {display:{Lore:["Wooden planks"]}} give @s stone_pickaxe{Unbreakable:1b} give @s item_frame{EntityTag:{Invisible:1b}} summon villager ~ ~ ~ {Offers:{Recipes:[{buy:{id:"emerald",Count:5b},sell:{id:"diamond_sword"}}]}} summon tnt ~ ~ ~ {Fuse:20s}


I’m working on this limit I guess it had to do with the Riemann sums type of exercise so I am trying to compute it: $$\lim_{n\to\infty} \left(\frac{(2n)\,!}{n^n\,n \,!}\right)^{\frac{1}{2n}}$$  Here is what I have got so far:  $$\lim_{n\to\infty} e^{\frac{1}{2n}{\ln\left(\frac{(2n)\,!}{n^n\,n \,!}\right)}} $$ Now I try to reduce the factorial division: $\frac{(2n)\,!}{n \,!}=\frac{2n(2n-1)(2n-2) \cdots(2n-(n-1))(n)(n-1)\cdots2\cdot1}{(n)(n-1)\cdots2\cdot1}=2n(2n-1)(2n-2) \cdots(2n-(n-1))=\prod_{k=1}^{n-1}(2n-k)$  Therefore I can write the logarithm as : $\ln\left(\frac{\prod_{k=1}^{n-1}(2n-k)}{n^n}\right)=\ln \left(\prod_{k=1}^{n-1}(2n-k)\right)-n\ln(n)$   And I also transform the logarithm into a sum like that should looke like this: $\sum_{k=1}^{n-1}\ln(2n-k)$  So, in the end I got this: $$\lim_{n\to\infty} e^{\frac{1}{2n}{\sum_{k=1}^{n-1}\ln(2n-k)-n\ln(n)}}$$  Now what I can't figure out is how to continue, I want to get some kind of $k/n$ inside the sum and also the limits of the sum I got don't convince me... can someone help me out, or point out any mistakes I could have done?? Thanks in advance ;)

I'd like a hint to show that:  $$\lim \frac{1}{n} \sqrt[n]{(n+1)(n+2) \cdots 2n} = \frac{4}{e} .$$  Thanks.


I get a linking error when I am trying to build and compile a class which uses template class. I am using smart pointer to create an instance of this template class.   I have tried removing the int from main class instead of template T, and it seems to help but doesn't fixes the issue.  My vehicle class -   #ifndef VEHICLE_H #define VEHICLE_H  template <class T>   class Vehicle {  private:      T m_x;     T m_y;  public:       Vehicle(T x, T y);      Vehicle();      ~Vehicle();      T add();  };  #endif   My vehicle.cpp  #include <iostream>  #include "pch.h" #include "Vehicle.h"  template <class T> Vehicle<T>::Vehicle(T x, T y): m_x(x), m_y(y) {     std::cout << "Parameterised constructor called" << std::endl; }  template <class T>  Vehicle<T>::Vehicle() {     std::cout << "Calling default constructor" << std::endl; } template <class T> Vehicle<T>::~Vehicle() {     std::cout << "Calling destructor" << std::endl; }  template <class T>  T Vehicle<T>::add() {     return m_x + m_y; }   Here is my main()  #include <iostream> #include <memory.h>  #include "Vehicle.h"  int main() {     std::cout << "Hello World!\n";       auto vehicle_ptr = std::make_unique<Vehicle<int>>(10,20);     std::cout << vehicle_ptr->add()<<std::endl;       return 0;  }   Linking Error I get, I expect it to compile and build.

Quote from :     The only portable way of using templates at the moment is to implement them in header files by using inline functions.   Why is this?  (Clarification: header files are not the only portable solution. But they are the most convenient portable solution.)


I know $[0,1]$ denotes the interval between 0 and 1 with the boundary. And $(0,1)$ denotes the interval between 0 and 1 without the boundary. Today, I encounter some expressions as $]0,1]$, $]-\infty,+\infty]$. What does $]0,1]$ mean? Thanks.


Old movie where staying out in the sunlight causes death since it is too hot. The protagonist gets chained up outside during the day but somehow manages to survive. Wish I had more details on this, but it's been at least 15 years since I've seen it.

Okay, this is a hard one as I don't remember very much, and can't figure out what to Google, but here goes. This is one of those 1990 straight to VHS type movies (probably) with decent production value.   From what I remember, a family moves to a dangerous, hot environment where you would be burned outside in the day in a short period of time. The father is possibly a scientist, and is working with plants (maybe reptiles) in the family's basement. The boy becomes affected by his father's work and is an outcast at school. One scene involved him being left outside to burn tied to a post, where he survived due to his affliction. His dad may form into a planet like creature in the end, or the planet is eating his family..possibly.  This may be all in my head, but I am pretty sure it was a movie.


How are pokemon's individual values calculated? Simple question, I'm trying to make an app for personal use.

I'm trying to understand how to calculate IVs range in order to calculate Pokémon Max CP. I have the following info:  Pokemon: Exeggcute His base stats are 110/132/120 (Atk/Def/Sta) CP now: 176 HP now: 42 Dust cost: 600 -Not powered up Trainer level 11   What's the formula and calculations I have to do in order to get the Pokémon's INDIVIDUAL stats?  I'm trying to figure out the formulas used in      I'm not looking for automatic tools! I'm looking for the formula used for this calculations.


Let $f: R \to S$ be a surjective ring homomorphism. Let $M \subset S$ be maximal, and let $f^{-1}(M) \subset I$ for some ideal $I \subset R$. Then $M=f(f^{-1}(M)) \subset f(I)$ since $f$ is surjective. Since $M$ is maximal in $S$, then either $f(I)=M$ or $f(I)=S$. If $f(I)=M$, then $I \subset f^{-1}(f(I)) =f^{-1}(M)$, hence $I=f^{-1}(M)$.  Now, I'm having trouble showing that if $f(I)=S$, then $I=R$.

Let $f :R \to S$ be a surjective ring homomorphism , $M$ be a maximal ideal of $S$ , I am writing a proof showing $f^{-1}(M)$ is a maximal ideal of $R$ , Please verify whether it is correct or not .   Proof :- Let $J$ be an ideal such that $f^{-1}(M) \subset J \subseteq R$ , we want to show $J=R$ i.e. $R \subseteq J$. Now as  $f$ is surjective , $M=f(f^{-1}(M)) \subseteq f(J) \subseteq S$ . As $f$ is surjective , $f(J)$ is an ideal of $S$ . Now if it were possible that $M=f(J)$ , then $x \in J \implies f(x) \in f(J)=M \implies x \in f^{-1}(M)$ , so $J \subseteq f^{-1} (M)$  ,contarry to our assumption $f^{-1}(M) \subset J$ . Thus $M \ne f(J)$ , $f(J)$ is an ideal of $S$ containing $M$ ; since $M$ is maximal ideal in $S$ , so $f(J)=S$ . Then $x \in R \implies f(x) \in S=f(J) \implies \exists j \in J : f(x)=f(j) \implies f(x-j)=0_S \in M $  $\implies x-j \in f^{-1} (M) \subset J \implies x=x-j+j \in J$ , so $R \subseteq J$   Is the proof correct . Please comment .


I am using sqlDatareader to read and assign variable value. The variable datatype is string.  string displayUnits = dr["DisplayUnits"].ToString(); // the variable value "DisplayUnitType.DUT_GENERAL"   Variable value is used to assign formatOptions.DisplayUnits.  formatOptions.DisplayUnits = displayUnits;   However, I am getting an error message cannot implicitly convert type string to Autodesk.Revit.BD.DisplayUnitType. I know I assigned a value to another type.   How do I casting and type conversions?

What's the best way to convert a string to an enumeration value in C#? I have an HTML select tag containing the values of an enumeration. When the page is posted, I want to pick up the value (which will be in the form of a string) and convert it to the corresponding enumeration value. In an ideal world, I could do something like this: StatusEnum MyStatus = StatusEnum.Parse("Active");  but that isn't a valid code.


I loove Harry and all, but why is he so popular?

In Harry Potter and the Chamber of Secrets, why is Dobby helping Harry Potter? What are his motives?


On page 150 of the book Introduction to Mathematical Statistics, there's the following passage:     Let the symbol $o(h)$ represent any function such that $lim_{h→0}[o(h)/h] = 0;$ for example, $h^2 = o(h)$ and $o(h) + o(h) = o(h)$.   I can understand how $h^2 = o(h)$ fits the description. But I couldn't understand the function $o(h) + o(h) = o(h)$.

This question is about asymptotic notation in general. For simplicity I will use examples about big-O notation for function growth as $n\to\infty$ (seen in algorithmic complexity), but the issues that arise are the same for things like $\Omega$ and $\Theta$ growth as $n\to\infty$, or for little-o as $x\to 0$ (often seen in analysis), or any other combination.  The interaction between big-O notation and equals signs can be confusing. We write things like $$\tag{1} 3n^2+4 = O(n^2)$$ $$\tag{2} 5n^2+7n = O(n^2)$$ But we're not allowed to conclude from these two statements that $3n^2+4=5n^2+7n$. Thus it seems that transitivity of equality fails when big-O is involved. Also, we never write things such as $$\tag{3} O(n^2)=3n^2+4,$$ so apparently commutativity is also at risk.  Many textbooks point this out and declare, with varying degrees of indignation, that notations such as $(1)$ and $(2)$ constitute an "abuse of notation" that students are just going to have to get used to. Very well, but then what are the rules that govern this abuse? Mathematicians seem to be able to communicate using it, so it can't be completely random.  One simple way out is to define that the notation $O(n^2)$ properly denotes the set of functions that grow at most quadratically, and that equations like $(1)$ are just conventional abbreviations for $$\tag{4} (n\mapsto 3n^2+4)\in O(n^2)$$ Some authors even insist that writing $(1)$ is plain wrong, and that $(4)$ is the only correct way to express the estimate.  However, other authors blithely write things like $$\tag{5} 5 + O(n) + O(n^2)\log(O(n^3)) = O(n^2\log n)$$ which does not seem to be easily interpretable in terms of sets of functions.  The question: How can we assign meaning to such statements in a principled way such that $(1)$, $(2)$ and $(4)$ are true but $(3)$ is not?


I have to import a csv table whose entries contain underscores. A simple example is the following table:  FirstCol, SecondCol Item_A, Item_B   I am trying to solve my problem with the csvsimple package with the "respect underscore=true" option. Here is a minimal working example:  \documentclass[10pt,a4paper]{article} \usepackage[utf8x]{inputenc} \usepackage{longtable} \usepackage{csvsimple} \usepackage{array,booktabs} \usepackage[T1]{fontenc}  \begin{document}  \begin{longtable}{|l|l|}    \hline    \csvreader[respect underscore=true, head to column names,      late after line=\\\hline]{Test.csv}{}{\FirstCol & \SecondCol} \end{longtable}  \end{document}   This code produces the following result:    How do I get rid of the obviously wrong column separators just below the table? To be clear, what I would like is this:    Note that the two separators only appear if the "respect underscore=true" option is present. If I remove this option (and delete the underscores from the input file), then all works as expected.

I try to print a .csv file using csvsimple. The column headers of that CSV file contain underscores.   Within the csvsimple documentation, I found the option respect underscore=true option that is supposed to make LaTeX handle the underscores correctly.   So far, my code can be compiled, but the underscores are rendered in the pdf as an unknown character:    Here is a minimal working example:  \documentclass[10pt,a4paper]{article} \usepackage[utf8x]{inputenc} \usepackage{csvsimple} \usepackage{array,booktabs}  \begin{document}      \csvautobooktabular[respect underscore=true]{data.csv}  \end{document}   And here the respective CSV file:  test_col,col_test 1824,4 1892,3 1948,3 1968,3


I'm learning calculus, and I was given this information:  $$\lim_{x \to a} (f(x))^n = (\lim_{x \to a} f(x))^n$$ $$\lim_{x \to a}(f(x) + g(x)) = \lim_{x \to a} f(x) + \lim_{x \to a} g(x)$$ $$\lim_{x \to \infty}\frac{1}{x}=0$$ And I have to find this limit: $$\lim_{x \to \infty} \left(1 + \frac{1}{x}\right)^x$$ Why can't I just use my first rule to get: $$\left(\lim_{x \to \infty} \left(1 + \frac{1}{x}\right)\right)^x$$ then... $$\left(\lim_{x \to \infty} 1+\lim_{x \to \infty} \frac{1}{x}\right)^x$$ finally... $$(1 + 0)^x=1^x=1$$ I know the limit is actually equal to $e$ which is around $2.71828$, so why am I able to manipulate the limit to make it 1?

I am trying to identify what the flaw is exactly when reasoning about a limit such as the definition of $\mathbf e$:  $$ \lim_{n\rightarrow \infty}\left(1+\frac{1}{n}\right)^n={e} $$  Now, I know there are ways of proving this limit, such as by considering the binomial expansion of $(1+\frac{1}{n})^n$ and comparing that to the Maclaurin series of $e$. So to make this clear, I am not looking for a proof of the limit definition of $e$.  I tried searching for "limit laws/rules" but none of the rules I found described the above case. Hence, I am looking for a specific rule (or perhaps a certain perspective) that will help me realize why the above does not in fact evaluate to 1.  My train of thought is as follows: at a first glance, if I wasn't already familiar with what the limit evaluates to, I probably would evaluate the expression inside the brackets first, and then apply the limit to the power. So, $$\displaystyle\lim_{n\to\infty}\frac{1}{n}=0\quad\text{and then}$$  $$\displaystyle\lim_{n\rightarrow \infty}\left(1+0\right)^n=\lim_{n\to\infty}1^n=1$$  Why is my reasoning flawed?


Ex.: 8, 1, 15, 10, 6, 3, 13, 12, 4, 5, 11, 14, 2, 7, 9, 16 The sums are: 9, 16, 25, 16, ... In fact I want to know for which numbers N the numbers 1, 2, 3, ..., N has this property. Maybe the sum not being a square but a cube or k-th power, or maybe arranging in a circle... Is there any sequence of N's on oeis or something?

Inspired by this  and in order to solve an old problem, I have the following question:      Can we construct a strictly increasing sequence $(N_i)_{i\in \mathbb{N}}$, such that for every integer $i$, we can arrange all the numbers from 1 to $N_i$, in a row such that the sum of every two adjacent numbers is a perfect square.   The first term of the sequence cannot be less than $14$, so we can take  $N_0=15$: $$8,1,15,10,6,3,13,12,4,5,11,14,2,7,9$$ And we can take also $N_1=16$ because we can add $16$ at the end, and $N_2=17$ by adding $17$ in the beginning (@mathlove). And as pointed by @gnasher729  in his answer we can not take $N_3=18$.  This is related to the connectedness  of a graph, if we consider the graph $G_N = (V, E)$ with $V=\{1,\cdots,N\}$ and $\{i,j\}\in E$ if and only if $i+j$ is a square, The question is equivalent to prove that $G_N$ have a Hamiltonian path for large integers $N$.  Edit I updated the question, I hope it's very clear and more direct.


I've recently been using my iPad with TexPad to do a lot of tex work.  One thing that I do not know how to deal with is the issue of animations on the iPad, as my current method for embedding animations (usually mp4's) in the document is to use the media9 package which accomplishes this with flash.  Since iOS does not support flash, none of the standard PDF readers, including Acrobat, are capable of displaying the animation.  I was wondering if anyone had a strategy for putting animation in beamer in a way that the iPad can render it?  Note, I am really asking for alternatives to using a flash based solution entirely, rather than just querying how to run flash content on iOS.  I am open to using image sequences, other media formats, etc.

Is there a bug in the media9 package that causes H-264 mp4 files to embed properly and play properly on a computer, but not an iPhone? I embedded the exact same mp4 video file in Acrobat X Pro (Mac OS 10.6.8) using the video tool under Multimedia, in which case the video played perfectly in Acrobat X Pro and ezPDF Reader on the iPhone. However, when I embedded the exact same video file via media9 (testing both VPlayer.swf and StrobeMediaPlayback.swf), the file played in Acrobat, but showed up as a blank media folder icon in ezPDF Reader. Clicking on that folder threw up an error message of   Media playback failure. Can not play format.   My LaTeX2e distribution is MacTeX 2012. I am using the LaTeX engine in TeXShop.


I am working on some presentation with beamer. However, I need a specific frame size (not the default values of aspect ratios). What I need is to crop the frame around its content and control the padding size. For example:  \documentclass{beamer}  \beamertemplatenavigationsymbolsempty  \begin{document} \begin{frame} \begin{tikzpicture}  \draw (0,0) circle(3cm);  \end{tikzpicture} \end{frame} \end{document}   And here is what I got:    What I am looking for is to get:

I'm programming a presentation in LaTeX using the beamer class.  However, it defaults to 4:3 aspect ratio slides, while everything I use is 16:9. Is there an easy way to change this using a command or two?


I am using Ubuntu 16.04. I am doing copy and paste of large data from one drive to another. It took over 30 minutes.  When I am trying to see the status using right click to see show copy dialog nothing is happening.  I tried by double clicking on File Manager but no success.  Any idea?

When I make long copy operations (which usually is to USB-flash memories), the progress window often disappears completely if I put it out of focus. I have tried some hints using alt/tab and wmctrl, but I can't get the progress window back.  I can see a very small grey bar on top of the corresponding launcher icon. But there is no way to terminate the copy operation or to see details.  Can I bring the copy progress window back somehow?  I use v 16.04 default setup. (I hope it is correct to use the Nautilus tag.)


I'd like to do something similar to \boxed{whatever}, but with the box open one side. Something like the following.  \documentclass{article}  \begin{document}  \[ \overline{\underline{abc |}} \]  \end{document}   which results in the following output (ugly, but conceptually close to what I want):    I suppose there is a simple way to do what I need, but I couldn't find it.

I am trying to draw a partial box around one or more words within a paragraph--that is, a rectangle with one or more sides missing. I have read the documentation for the fancybox package and it doesn't seem to be able to do what I want. I was able to produce thus ugly hack:    That's just a vertical bar | followed by a word with \overline and \uline. The trick is to connect the vertical and horizontal lines so that you have a rectangle missing just one side.  Is there an easy, general way to do this, perhaps with Tikz? I don't know enough about that package to be able to do this myself, but I'm wondering if there might be other solutions too.


If a model predicting 'days to payment etc.' has an RMSE of 25 days and MAE of 20 days. How to explain RMSE of 25 days easily to them, just like the MAE of 20 days (which is average prediction error) I have looked at various posts, but with no luck. Is there a simple explanation o rmse like the mae to explain to business folks (not an elaborate one). MAE is the average difference in the prediction from the true value. can we explain RMSE as the 'spread of predictions', or is it 'spread in the errors of the predictions'? By spread I mean standard deviations. can someone please clarify, spent hours at this already.

My company is in the process of switching equipment from one vendor to another. We measured several metrics from the existing and new equipment and compared the time series. The ideal is to have no difference between the old and new equipment. For that, we use Root Mean Square Error (RMSE) to measure the difference.  We are to present the findings to upper management and employees at the plant, many of whom have no background in statistics. How should I explain the concept of RMSE to those audiences? If series X and Y have an RMSE of 5, how should I explain that 5 in layman's terms?


$$\text{ If } a,b \geq 3, \text{ show that } \  2^b-1 \text{ does not divide } 2^a+1$$  How can I do this? Could you give me a hint?

I'm trying to prove $2^b-1$ does not divide $2^a + 1$ for $a,b>2$. Can someone give a hint in the right direction for this?


Yeah, like in the title, how do Regular Conditional Probabilities assign values to $P(A|B)$ when $P(B) = 0$? Because I am not trained in advanced probability, please explain it as simply as possible. It'll be great if you can demonstrate with an example. Let $X$ be a random variable between $[0, 1]$. What is the $P(X=\frac{2}{3}|X=\frac{2}{3})$?  Also, can it also assign values to $P(A|B)$ in finite spaces? For example, imagine you throw a die, and you observe that the die landed on an odd number at 12 noon. So letting $O$ be the event that the die landed odd, $P(O)$ changes from $\frac{1}{2}$ to $1$ after noon. Hence, after noon, letting $E$ be the event that the die landed even, $P(E)$ changes to $0$. But even after 12 noon, I still intuitively want to say that $P(E|E)$ is still $1$. It seems to me that for any non-empty set $A$ in the sigma-algebra, $P(A|A) = 1$. Can regular conditional probabilities assign $P(E|E)$  a value of $1$? Is it possible? Or do I need to give that intuition up? Thanks for your help.  Edit: I think my question is different from this:   Because I'm asking about finite spaces too. Also, I'm asking for a demonstration of how regular conditional probabilities assign value to $P(X=\frac{2}{3}|X=\frac{2}{3})$.  Edit 2: Let the sample space in the dice example be {1, 2, 3, 4, 5, 6}.  Edit 3: The sample space for the dice example is {1, 2, 3, 4, 5, 6}. The initial probability function before noon is $P$. After noon, the probability function becomes $P'$. So $P(O)$ = $P(E)$ = 0.5. But $P'(O) = 1$ and $P'(E) = 0$. Still, I want to say that $P'(E|E) = 1$.

Is there a way to resolve probability of an event, given another event that never happens? Mathematically speaking the problem is:  Given that $P(B) = 0$,  $$P(A|B)=\frac{P(A \cap B)}{P(B)} = \frac{0}{0}$$  Is this probability vacuously $0$ of $1$? Can we show that it's one or the other?


I've had the game for 10 days and I want to know if I can upgrade nookling junction.

How can you upgrade Nookling Junction into T&T Mart in Animal Crossing: New Leaf? I don't know how to upgrade Nookling Junction.


My MacBook Pro’s battery is swollen and it don’t turn on nor charge? It’s 13 inch early 2015. I found my MacBook dead suddenly . Later I opened it up but found that the battery is swollen and after that I tried to unplug the battery and turn on the Mac using AC POWER but it didn’t turn on?

I bought the MBP around 2016 April. Few months ago, around 2018 Nov, bottom of the device appears a bit uneven, with slight gap with my desk. Over past few months, it wobbles more and more serious. Today I brought it to Apple Store Singapore for diagnostic, specialist at Genius Bar confirmed that it's caused by swollen battery. Consider it was just after about 2.5 years use, I find it hard to believe. According to the staff, it depends on usage. If under heavy usage or often charge it overnight, it's normal that MacBook Pro's battery can become swollen pretty soon.   My battery charge cycle is under 300, battery life drops a bit but still strong (9 hours instead of 10). I rarely charge overnight, normally turn AC power off and leave my MBP in sleep mode. I do use my MBP heavily though, say 10 to 13 hours a day. However, I still find it hard to accept the explanation given by Apple Singapore.  I wonder if other MBP 15" users experience the same? Or... am I the isolated case?  -- edit  To make the question more specific, is it generally expected that, Macbookpro battery will start swelling after 2-3 years use if laptop usage is heavy, e.g. 10-13 hours a day? The concern is not about the slightly reduced battery life (the battery life is still strong), but the physical expansion. I'm asking this because I've used few other laptops before, among which I never experience battery swelling except one (after near 5 years use). If the experience with my MBP is aligned with most other users, which means it's just a matter that I should adjust my expectation, and include the near SGD300 battery cost per 2-3 years into my next purchaser's consideration; Otherwise, I will try to ask them to consider replacing without me paying the full cost.   -- update 2019/6/21  Apple has just announced a battery recall for Macbook Pro 15" mid-2015 model. They confirmed that these batteries may pose fire safety risk:


Beamer seems to clash with pstricks-add:  \documentclass{beamer} \usepackage{pstricks} \usepackage{pstricks-add}  \begin{document}  Lorem Ipsum \end{document}   Gives the following error:  ! No room for a new \dimen . \ch@ck ...\else \errmessage {No room for a new #3}                                                   \fi  l.1895 \newdimen\pst@chartHeight   But it runs smoothly without pstricks-add or replacing beamer with article.

I have this error message:  ! No room for a new \dimen . \ch@ck ...\else \errmessage {No room for a new #3}                                                 \fi   which I can not find a cure for.


I would like to ask you for a help with align of symbolic x-coords. Now it is align like middle of the bar with middle of the word (IT, Elektrotechnické, Strojírenské, etc.). Is there some way, how I can align middle of the bar with end of the word?   Cause this way it is little bit confused.  Thank you so much for any help.    \begin{tikzpicture} \begin{axis}[     width  = 16cm,     height = 8cm,     major x tick style = transparent,     ybar=2*\pgflinewidth,     bar width=6pt,     ymajorgrids = true,     ylabel = {Run time speed},     symbolic x coords={IT,Elektrotechnické,Strojírenské,     Architektura,Ekonomické,Sociální,Jiné},     xtick = data,     scaled y ticks = false,     enlarge x limits=0.10,     x tick label style={rotate=45},       ymin=0,     legend cell align=left,     legend style={             at={(1,0.5)},             anchor=south east,             column sep=1ex     } ]     \addplot[style={bblue,fill=bblue,mark=none}]         coordinates {(IT,3) (Elektrotechnické,3) (Strojírenské,3) (Architektura,2) (Ekonomické,2) (Sociální,1) (Jiné,1)};      \addplot[style={rred,fill=rred,mark=none}]          coordinates {(IT,5) (Elektrotechnické,3) (Strojírenské,2) (Architektura,0) (Ekonomické,0) (Sociální,2) (Jiné,1)};      \addplot[style={ggreen,fill=ggreen,mark=none}]          coordinates {(IT,2) (Elektrotechnické,2) (Strojírenské,1) (Architektura,2) (Ekonomické,0) (Sociální,1) (Jiné,1)};      \addplot[style={ppurple,fill=ppurple,mark=none}]          coordinates {(IT,3) (Elektrotechnické,3) (Strojírenské,3) (Architektura,2) (Ekonomické,2) (Sociální,1) (Jiné,1)};       \addplot[style={zluta,fill=zluta,mark=none}]          coordinates {(IT,3) (Elektrotechnické,3) (Strojírenské,3) (Architektura,2) (Ekonomické,2) (Sociální,1) (Jiné,1)};       \addplot[style={oran,fill=oran,mark=none}]          coordinates {(IT,3) (Elektrotechnické,3) (Strojírenské,3) (Architektura,2) (Ekonomické,2) (Sociální,1) (Jiné,1)};      \legend{SG ResearchGroup,21.CentTech,SmartTech,SmartTechRG,SmGrigLab,ISCA} \end{axis} \end{tikzpicture}

I have a figure where one of my labels is very long. I would like this label to be split to two rows. Currently my code is like this  \documentclass{article}  \usepackage{pgfplots} \pgfplotsset{compat=1.10}  \begin{document}  \begin{tikzpicture} \pgfplotsset{width=10 cm} \begin{axis} [ symbolic x coords={0, Label 1, Label 2, This is a very very very long label, Label 4, Label 5, Label 6, Label 7,Label 8}, xtick={Label 1, Label 2, This is a very very very long label, Label 4, Label 5, Label 6, Label 7}, x tick label style={rotate=45, anchor=east, align=center}, axis lines*=left, ymajorgrids = true, legend style={at={(0.5,-0.30)},anchor=north}, ymin=0, ymax=175, bar width=5mm, ybar=-0.5cm,  enlarge x limits={abs=0.6cm}, nodes near coords,         every node near coord/.append style={color=black}, ] \addplot [red,fill=red]  coordinates{ (Label 1,100) (Label 2,90) (This is a very very very long label,80) (Label 4,140) } ; \addplot [blue,fill=blue] coordinates{ (Label 5,80) (Label 6,25) (Label 7,66) } ; \addlegendentry{Legend 1} \addlegendentry{Legend 2} \end{axis} \end{tikzpicture}  \end{document}   Which produces this:   Now if I try to change the x tick label style to be  x tick label style={rotate=45, anchor=east, align=center,text width=3.5cm}   This happens:   So the anchor=east command doesn't seem to go along with the text width command. Other anchor commands like anchor=west, anchor=base seem to be working perfectly normal. Does anyone know why the anchor east command doesn't seem to work with the text width command and is there a way to go around this?


Today in my math class I presented a counter example to the theorem: "if any infinite sequence in X has an adherent point in X, then X is compact."  Let $X=(-1,2)$. Choose $\{X_{n}\}= \frac{1}{n} = \{1,\frac{1}{2}, \frac{1}{3},\cdots \}$. Then $0$ is an adherent point of $\{ X_{n} \}$ in $X$. But X is not compact.   My professor told me that "if any" is synonymous with "if every" in this instance so my counter example doesn't work but I can't see how that is the case. Can anyone give me some insight into how these statements are equivalent?  Sorry about any poor formatting I am on mobile.

This is a really basic question, but it is one I never really thought about until now.   Let $\mathscr{G}$ be a tree. Then every pair of vertices in $\mathscr{G}$ is connected by a unique walk.   We are asked to prove the converse which is worded as:  If any two vertices of  $\mathscr{G}$ are joined by a unique walk, then $\mathscr{G}$ is a tree.   My question is whether the author means that if we can find a single pair of vertices that are joined by a unique walk in a graph (that may not be a tree), then we know $\mathscr{G}$ is a tree (which obviously is not true), or if he means something more a long the lines of "for all pairs of two vertices in $\mathscr{G}$".   Similarly, he asks us to prove:  If $\mathscr{G}$ is connected but becomes disconnected by the removal of any one edge, then $\mathscr{G}$ is a tree.   Again, in one case it is easy to find counterexamples of graphs with cycles (not trees) that can become disconnected by the removal of one of their edges, but if he wants us to prove that "if, for every edge, the removal of that edge will result in a disconnected graph, then the graph is a tree", the proof while also simple is very, very different.   I come from a more applied background and am not used to this kind of wording. Any insight would be much appreciated.


During last week, I tried to install Ubuntu for few newcomer friends. I know two method to make a bootable Flash USB through Linux. One is famous method of "DD" and other one is Unetbootin. But I got failed for each time I tried one of these methods to bring system in EFI mode up(and when it starts in UEFI mode it fails to install because of different reasons such as having another distro installed in EFI). So I had to use the software "Rufus" in windows to make a bootable flash USB and it worked in EFI mode. But I don't want to use Windows each time just only to make a Flash USB bootable properly. Do you have any serious advice?

Having live media that can boot both ways can be a problem when installing Ubuntu onto currently available Windows 8 computers.  In other words the key advantage to creating UEFI-only bootable USB live media is: You know that it definitely booted and installed via UEFI.   Since Valve has already been doing UEFI-only booting USB installers with their Debian-based Steam OS and UNetbootin — the top voted alternative to Ubuntu's Startup Disk Creator — isn't UEFI compatible and therefore misleading, I think we should have a separate topic for creating UEFI-only bootable USB live media.


I just suggested to regard the  tag as a synonym for the  tag (on WordPress Development SE), because in practice these terms are interchangable. Now I need 4 votes to support it (or 2 downvotes to kill it).  I thought somewhere in the interface (for instance under 'reviews') there would be a prompt that this vote is open. I can't find anything. Am I overlooking something? Or am I supposed to draw attention to it myself by telling everyone that the vote is ?

I almost never even think about synonymization. Why? Maybe because the link is almost hidden on the bottom of the :  Can we please make that feature more prominent? Maybe put it on the review page. I am sure there are some  waiting to be voted on. Let's get the tag jungle organized.


Short version  Imagine I run the exact same experiment $n$ independent times and get $n$ times the same result. Can you put a lower bound on the probability of getting the same result the $n+1$ time I run the experiment?    Long version  I'd like to check that a computer program is deterministic and I don't want to read the code to go looking for potential bugs (race conditions ...). I'd like to estimate the probability of the code being error free. If I run it $n$ times and get $2$ different answer or more, I know something went from at some point.  However, if I get $n$ times the same answer, what is the probability of the code being error free?   I'm sure someone somewhere did some math on it, I just don't know how to find it.

What is the best technique to calculate a confidence interval of a binomial experiment, if your estimate is that $p=0$ (or similarly $p=1$) and sample size is relatively small, for example $n=25$?


I've seen a lot of ciphers with variants that use 80-bit keys, like Grain, Trivium, KLEIN, KATAN & KTANTAN, Piccolo, PRESENT, RC4, Skipjack, and TWINE. Some of these designs are younger than six years old, making me wonder if an 80-bit key size is "secure", be it against brute force attacks or as a buffer in the case of weaknesses in a cipher's design. Is 80-bit security not enough anymore? Is it only on the edge of being insecure? If it is on the edge, by what time will 80-bit keys be obsolete?

I came across the  family of ciphers for small domain input blocks. They cipher arbitrary block lengths: 32, 48 and 64, but their key size is 80 bits only.   Is 80 bits of key size considered safe against brute force attacks with current state of the art processors?


I have following javascript that I came across. I don't understand the process flow of the code execution.  var val = 'ap';  function func() {     if (!val) {         var val = 'ple';     }     console.log(val); } func(); console.log(val);   The output that I thought would be was, 'ap' then 'ap'. But I get 'ple' and then 'ap'. How is this happening?

What is the scope of variables in javascript? Do they have the same scope inside as opposed to outside a function? Or does it even matter? Also, where are the variables stored if they are defined globally?


I'm working on a book project using LaTeX and am stuck on a very fine point of style in the index. The publisher wants page ranges in the index to appear in the form 145--52 (rather than 145--152), page range elision. I have no idea how to to get a LaTeX indexing package to do this. At the moment I'm using imakeidx and the project has two indices (Names and Subjects). I've put together a minimal working example. I'd be grateful for any advice,  \documentclass{article} \usepackage[utf8]{inputenc}  \title{Index elision problem} \date{July 2019}  \usepackage{imakeidx}  \makeindex[name = person,title=Name Index,columns=2] \makeindex[name = subject,title=Subject Index,columns=2]  \begin{document}  \maketitle  \index[person]{Mr. T} \index[subject]{vans} \clearpage Space \clearpage filler \clearpage Space \clearpage filler \clearpage Space \clearpage filler \clearpage Space \clearpage filler \clearpage Space \clearpage  Mr. T, vans \index[person]{Mr. T|(} \index[subject]{vans|(} \clearpage filler \clearpage Space \clearpage filler \clearpage Space \clearpage filler Mr. T, vans \index[person]{Mr. T|)} \index[subject]{vans|)}  \printindex[person] \clearpage \printindex[subject]  \end{document}

This is a followup question to egreg's answer to  The answer runs into a problem if an index topic occurs in more than one page range. The following MWE, based on egreg's answer:  \begin{filecontents*}{subjind.ist} delim_0 ", \\checkrange{" delim_t "}" \end{filecontents*}  \documentclass{book} \usepackage{xparse} \usepackage{imakeidx}  \makeindex[title=Subject Index,options=-s subjind]  \ExplSyntaxOn \NewDocumentCommand{\checkrange}{>{\SplitArgument{1}{--}}m}  {   \formatrange#1  } \NewDocumentCommand{\formatrange}{mm}  {   \IfNoValueTF { #2 }    { % no --, it's not a range     #1    }    { % it's a range     \egreg_range:nn { #1 } { #2 }    }  }  \bool_new:N \l__egreg_range_compare_bool  \cs_new_protected:Nn \egreg_range:nn  {   % print the start number   #1--   \int_compare:nNnTF { \str_count:n { #1 } } = { \str_count:n { #2 } }    {% same number of digits, remove equal ones at the start     \__egreg_range_compare:nn { #1 } { #2 }    }    {% different number of digits, print both     #2    }  } \cs_new_protected:Nn \__egreg_range_compare:nn  {   \bool_set_true:N \l__egreg_range_compare_bool   % do a loop on the digits in the first number   \int_step_inline:nn { \str_count:n { #1 } }    {     \bool_if:NTF \l__egreg_range_compare_bool      {       % if the digits coincide, print nothing       \str_if_eq:eeF { \str_item:nn { #1 } { ##1 } } { \str_item:nn { #2 } { ##1 } }        {         \str_item:nn { #2 } { ##1 }         % at the first differing digit, don't compare any longer         \bool_set_false:N \l__egreg_range_compare_bool        }      }      { \str_item:nn { #2 } { ##1 } }    }  } \ExplSyntaxOff  \begin{document} \setcounter{page}{95}\index{Topic0|(}Text\newpage \setcounter{page}{101}\index{Topic0|)}Text\newpage \setcounter{page}{124}\index{Topic1|(}\index{Topic2|(}Text\newpage \setcounter{page}{126}\index{Topic1|)}Text\newpage \setcounter{page}{134}\index{Topic2|)}Text\newpage \setcounter{page}{141}\index{Topic0}Text\newpage \index{Topic0}Text\newpage \index{Topic0}Text \printindex \end{document}   yields the following error message:  ! LaTeX3 Error: Too many '--' tokens when trying to split argument.  For immediate help type H <return>.  ...                                                l.3   \item Topic0, \checkrange{95--101, 141--143}   Entering non-stop yields the following output:    which omits "-3" from the second index entry of Topic0. The question is how to get around this.  Edit following up on egreg's ingenious solution.  I don't know if I should ask a new follow up question, so I'm posing it first here in this edit.  egreg's solution doesn't seem to handle index sub-topics.  If one adds the following 4 lines  \setcounter{page}{135}\index{Topic0!sub0|(}Text\newpage \setcounter{page}{136}\index{Topic0!sub0!subsub0|(}Text\newpage \setcounter{page}{139}\index{Topic0!sub0!subsub0|)}Text\newpage \setcounter{page}{140}\index{Topic0!sub0|)}Text\newpage   after  \setcounter{page}{134}\index{Topic2|)}Text\newpage   in the solution, one gets the following errors:  Output written in mwe.ind. Transcript written in mwe.ilg.  (mwe.ind ! Extra }, or forgotten \endgroup. l.4     \subitem sub0, 135--140}  ? r OK, entering \nonstopmode... ! Extra }, or forgotten \endgroup. l.5       \subsubitem subsub0, 136--139}  ) [145] (mwe.aux) )   and this output:    Alas I don't understand egreg's code well enough to make the required changes.


Looks like SO's code formatting has a bug and it's ignoring first few lines no matter what I do. Not sure who to contact but if you know the solution or can tell how to forward to SO's developers that would be great.  Answer that has bad code formatting bug:

Possible Duplicate:         If there is a list immediately followed by a code block the code block is not recognized as code (Even though there is a newline between the two).  int answer = 42;  Note: This happens both in the WMD preview and in the final (server rendered) post.


I've been looking for a textbook in classical mechanics that's readily available (like can be found in the library of James Cook University of Townsville, Australia) and full of fully-answered questions in the Lagrangian/Hamiltonian formalisms yet I can't find any. My first port of call was the Schaum's Outlines and Demystified series but the only member of these series I could find that was relevant was  which is difficult for me to track-down in real-life.   It would be particularly helpful if one could point me to a free eBook with this material.

Need to brush up on my late-undergrad and early-grad physics and was wondering if anyone can recommend books or lecture notes (hard copy, or on-line) that also have solutions.   Two that I have come across are:  Princeton Problems in Physics with Solutions - Nathan Newbury  University of Chicago Graduate Problems in Physics with Solutions - Jeremiah A. Cronin  Spacetime Physics - Taylor & Wheeler (favorite book on special relativity; has a lot of problems with solutions at the back; a lot of the problems really enforce the material and discuss paradoxes)  If possible, please also provide a reason why you like the books as opposed to just listing them.