use of $\sum $ for uncountable indexing set

I was wondering whether it makes sense to use the $\sum $ notation for uncountable indexing sets. For example it seems to me it would not make sense to say  $$ \sum_{a \in A} a \quad \text{where A is some uncountable indexing set e.g. some $A \subset \mathbb{R}$ } $$  Would it be better to avoid the above notation in general for uncountable indexing sets ? Any help in making better sense of this would be very appreciated.


TeXstudio \includegraphics file not found

\documentclass{article}  \usepackage{amsmath, amssymb} \usepackage{graphicx}   Inside \begin{document} I have:  \begin{figure}     \centering     \includegraphics{supremum} \end{figure}   supremum.gif is a gif file inside the same file as this .tex file. I have looked into other solutions but none have worked for me so far.


How to disable command block logging into the log files in minecraft

Hi, I have a single player world which is opened to LAN to let my friends play while I am AFK. I have a lot of command blocks running in that world and those commands are all logged in the log files.  So, my question is, how to only log player commands and chat?  Correct me if I am wrong, thank you.


proof of a^2 + ab + b^2 >0; a,b, both are not zero, both are real

Show that for any reals a,b, both of which are not zero, it holds true that a^2 + ab + b^2 >0


Where should I ask a question about a programming interface for a game?

I wanted to ask about the documentation for the programming interface of the game  since I can't find it anywhere. I first was about to ask on Gaming.SE, where I found similar questions that were closed as off-topic and recommended to be asked again on Super User. But I don't think it's on-topic on Super User either (or is it?).  Where should I post this question?


Seeking book or site for help with ArcGIS Desktop?

I am new to the field of GIS and use Trimble Pathfinder and TerraSync.   I just started with ArcGIS 10.3 and was wondering if anyone can recommend a entry level "Q&A" book or site for ArcGIS 10?


Wordpress Themes Categories for the Admin pannel

I am working on this project and I'll have 200+ and even more by the end of the project.  I need to have all these themes show up in Admin > Appearance ?  All themes will be installed on the same wordpress site Is there any way to arrange the themes in Categories (ex. Financial, Arts etc).


I had 1440 tga files and I wanted to convert them to a 24 fps mov.  Here's the command I used:  /usr/local/homebrew/bin/ffmpeg -y -f image2 -pattern_type glob -i '/Users/ninhenzo64/Documents/Projects/Insta 18/shots/common/images/train/spiral_v023/masterLayer/common_spiral_v023.*.tga' -c:v libx264 -preset veryslow -crf 0 -pix_fmt yuv420p -r 24.0 -s 640x640 '/Users/ninhenzo64/Documents/Projects/Insta 18/shots/common/images/train/spiral_v023/masterLayer/common_spiral_v023.mov'   The mov that was generated is 24 fps but it's missing some frames, ffprobe says it's only 57.67s - it should be 60.0s. Also the motion in the file isn't smooth, it's jilty like there are dropped frames.  ~> ffprobe '/Users/ninhenzo64/Documents/Projects/Insta 18/shots/common/images/train/spiral_v023/masterLayer/common_spiral_v023.mov' ffprobe version 2.3 Copyright (c) 2007-2014 the FFmpeg developers   built on Jul 19 2014 11:52:35 with Apple LLVM version 5.1 (clang-503.0.40) (based on LLVM 3.4svn)   configuration: --prefix=/usr/local/homebrew/Cellar/ffmpeg/2.3 --enable-shared --enable-pthreads --enable-gpl --enable-version3 --enable-nonfree --enable-hardcoded-tables --enable-avresample --enable-vda --cc=clang --host-cflags= --host-ldflags= --enable-libx264 --enable-libfaac --enable-libmp3lame --enable-libxvid --enable-libfreetype --enable-libtheora --enable-libvorbis --enable-libvpx --enable-librtmp --enable-libopencore-amrnb --enable-libopencore-amrwb --enable-libvo-aacenc --enable-libass --enable-ffplay --enable-libspeex --enable-libschroedinger --enable-libfdk-aac --enable-libopus --enable-frei0r --enable-libopenjpeg --extra-cflags='-I/usr/local/homebrew/Cellar/openjpeg/1.5.1_1/include/openjpeg-1.5 '   libavutil      52. 92.100 / 52. 92.100   libavcodec     55. 69.100 / 55. 69.100   libavformat    55. 48.100 / 55. 48.100   libavdevice    55. 13.102 / 55. 13.102   libavfilter     4. 11.100 /  4. 11.100   libavresample   1.  3.  0 /  1.  3.  0   libswscale      2.  6.100 /  2.  6.100   libswresample   0. 19.100 /  0. 19.100   libpostproc    52.  3.100 / 52.  3.100 Input #0, mov,mp4,m4a,3gp,3g2,mj2, from '/Users/ninhenzo64/Documents/Projects/Insta 18/shots/common/images/train/spiral_v023/masterLayer/common_spiral_v023.mov':   Metadata:     major_brand     : qt       minor_version   : 512     compatible_brands: qt       encoder         : Lavf55.48.100   Duration: 00:00:57.67, start: 0.000000, bitrate: 25460 kb/s     Stream #0:0(eng): Video: h264 (High 4:4:4 Predictive) (avc1 / 0x31637661), yuv420p, 640x640, 25459 kb/s, 24 fps, 24 tbr, 12288 tbn, 48 tbc (default)     Metadata:       handler_name    : DataHandler       encoder         : Lavc55.69.100 libx264   Can anyone tell me what's going wrong?


QGIS 2.6 summarizing area (m²) for current atributes

If I have a code for each polygon and I have counted the area in m² for each of them (all this information is in single columns). How can I summarize these areas by codes (for example summarize all areas with code 100 etc.) in QGIS 2.6.1.?


Deep neural networks require lots of examples to learn tasks like image classification, and object recognition. On the other hand, we humans can learn and identify object just by looking at it once. Is there any method that allows us to do object detection just with one example? I tried to search for it, but couldn't get any satisfactory solution.


Is it possible to set optimization level on Microsoft SQL server?

I would like to ask if there is a way to set the optimization level for SQL Server like it can be done on DB2/Sybase ASE/Oracle. The reason for this question is that I belive that SQL Server may not be choosing hash join for some cases.  Examples for other DBMS:   DB2 -  Sybase ASE -   Oracle -


Letter U in American English vs British English

Why was the letter 'U' dropped from many words such as colour, odour etc?  And also why is the letter 'l' spelt as a singular, when in British English it's used as a double 'll' in most words, cancelled, traveller, modelled etc?


How can I check using a script that CD-drive is connected to USB port?  I don't want to allow cd-rom to be used as usb device under any circumstance in my system. Is there a way to check this?


How to install OpenLayers plugin on QGIS 1.8?

After having installed QGIS 1.8 I am not able to find the OpenLayers Plugin. In "the old days" I know I was supposed to check "add 3rd party repositories", but that button has disappeared. I tried adding the following repositories without luck:  http://pyqgis.org/repo/contributed ..openlayers.org/api/2.12 ..github.com/sourcepole/qgis-openlayers-plugin.git ..github.com/nvkelso/qgis-openlayers-plugin.git ..plugins.qgis.org/plugins/plugins.xml ..plugins.QGIS.org/plugins/plugins.xml ..github.com/openlayers/openlayers   I hope someone can help me locate the OpenLayers plugin as I desperately need it.


I just cannot figure out why this keeps pointing to null. I am a fairly new programmer. But here I have made a Dice class and a commands class. I have tried changing variables and all sorts of stuff. I guess I'm just not sure why it's pointing to null.      package com.rs.game.player;  /**  * Created by Kevinpro0 on 2/26/2015.  */ public class Dice {     public int die2;     public int die3;     public int die4;     public int die6;     public int die8;     public int die10;     public int die12;     public int die14;     public int die16;     public int die18;     public static int die20;      public void d2() {         die2 = (int)(Math.random()*2) +1;     }     public void d3() {         die3 = (int)(Math.random()*3) +1;     }     public void d4() {         die4 = (int)(Math.random()*4) +1;     }     public void d6() {         die6 = (int)(Math.random()*6) +1;     }     public void d8() {         die8 = (int)(Math.random()*8) +1;     }     public void d10() {         die10 = (int)(Math.random()*10) +1;     }     public void d12() {         die12 = (int)(Math.random()*12) +1;     }     public void d14() {         die14 = (int)(Math.random()*14) +1;     }     public void d16() {         die16 = (int)(Math.random()*16) +1;     }     public void d18() {         die18 = (int)(Math.random()*18) +1;     }     public static int d20() {         die20 = (int)(Math.random()*20) +1;         return die20;     } }   /***** i am ONLY using d20 for this right now...****/  DM.java  package com.rs.game.player; import com.rs.game.player.*; import com.rs.game.World;  import java.util.Arrays;  /**  * Created by Kevinpro0 on 3/1/2015.  */ public class Dm {     public static Dice init = new Dice();     public static int worldSize = World.getPlayers().size();     public static int[] PlayerInt = new int[worldSize];     //     public static Player player;     public static int initRoll  = init.die20;     public static String playersName;     public static int i = 1;       public static void initiative(){          for (i = 1; i < World.getPlayers().size() + 1; i++) {             //Dice = new Dice();             init.d20();             PlayerInt[i] = initRoll;             player.getPackets().sendPanelBoxMessage(Integer.toString(Dice.d20()));             //player.getPackets().sendPanelBoxMessage("Player " + i + " is " + playersName + " and initiative roll: " + Integer.toString(initRoll));          }     } }    Commands.java   case "init":                 case "initiative":                     Dm dmaster = new Dm();                     //String currentPlayer = player.getUsername();                     //Player Dm = World.getPlayerByDisplayName("Dm");                     if (player.getUsername().equalsIgnoreCase("Dm")) {                         if (World.getPlayers().size() <= 1){                             player.getPackets().sendPanelBoxMessage("Not enough players logged in.");                         } else {                             Dm.initiative();                             player.getPackets().sendPanelBoxMessage(Dm.playersName + " and initiative roll: " + Integer.toString(Dm.initRoll));                          }                      }                  return true;


Can anybody recognize the font or symbol for this . It is used as font for alphabetic letter S, in my text. I did check almost all fonts and symbols but couldn't succeed in finding a good match. I need this symbol in Latex math mode. Or a way, to design this symbol by myself to be use in Latex. thanks


No writeable permissions when mounting Windows folders

So I have a Windows machine and a number of folders that I want to share my network. I've no problem mounting the folders and they have the correct permissions set in Windows. I'm mounting them using the following  sudo mount.cifs '//WINDOWS_MACHINE/WINDOWS_FOLDER' /mnt/windows_folder/  -o uid-1000,gid=1000,username=$USRN,password=$PASS


is there a simple way to make a monthly donation to Ubuntu ? I would like to do so but i don't want to do it manually every month. Federico


How to keep font preferences in TexWorks 4

The default font is too small on my screen at the resolution I have it, so I like to reset the font to size 12, but it appears I have to do this everytime I launch the program.  How do I make it remember my preferences?


Can I travel to Cyprus using Schengen Visa?

Hi I've got a Schengen multiple entry visa issued from Switzerland to visit my sister in July however I'd like to go to Cyprus first with my friends. Will I need an additional visa if I will be staying in Switzerland for 15 days and Cyprus for 7 days? I am a holder of a Cameroonian passport.


cannot scan QR code for login whatsapp web version

using 3 inch display phone, cannot scan QR code for login. any idea to solve this?


Is there a reason why British use me instead of my in their sentences? For example, I'm going to call me mom. Is it just a slang in Britain? Is the usage grammatically correct?


Computer with Ubuntu 20.04 installed was working. Now boots to a black screen. Lights on the keyboard show the computer is on. Tried to reboot with a ubs from which the system was first loaded. Cannot get to terminal. Any suggestions welcome.


Percentage of tenure track positions promoted to full professors

I wonder if there are statistics on the overall percentage of people promoted from tenure track positions (assistant professor) to full professor in fields like mathematics and science (first-rate institution is OK).


Let $X$ and $Y$ be iid real-valued random variables. Show $P[|X-Y| \le 2] \le 3P[|X-Y| \le 1]$.

Found this question in The Probabilistic Method and tried for hours to prove it, but I'm not getting anywhere. Can anyone walk me through it? I see that if we can show $P[1 \le X - Y \le 2] \le P[|X -Y| \le 1]$ the claim will follow. This is intuitively appealing but I don't see how to proceed.


If $\mu$ is semifinite measure and $\mu(E) = \infty$, for any $C > 0$ there exists $F\subset E$ with $C < \mu(F) < \infty$.   Attempted proof - Suppose $E\in M$ with $\mu(E) = \infty$ then there exists $F\in M$ with $F\subset E$ and $0 < \mu(F) < \infty$, $\mu$ is called semifinite. This is the definition from Folland. I am guessing that we have to set $C$ equal to something where the definition still holds true but I am not sure how to do this. Any suggestions is greatly appreciated.


What R packages do you find most useful in your daily work?

Duplicate thread:   What are the  packages you couldn't imagine your daily work with data? Please list both general and specific tools.  UPDATE: As for 24.10.10 ggplot2 seems to be the winer with 7 votes.  Other packages mentioned more than one are:   plyr - 4 RODBC, RMySQL - 4 sqldf - 3 lattice - 2 zoo - 2 Hmisc/rms - 2 Rcurl - 2 XML - 2   Thanks all for your answers!


I have the following go code:  s := `prefix<b>Group ID:</b><br/> G123<br/>temporary<br/>suffix`  re := regexp.MustCompile(`(?s)(.*)<b>Group ID:</b><br/>(.*)<br/>(.*)`)  m := re.FindAllStringSubmatch(s, -1) fmt.Println(m[0][2])   playground link:   The above program prints \nG123
temporary because the last/second
 after the pattern is matched, as per the regex. Is there a way to get the first
 to be matched so that the output will be, just: G123. In addition to the first br match, the newline/whitespace in the beginning should also be stripped. Any suggestions ?


Proving a statement in the distributional sense

I am trying to solve a problem, but am really confused on what I'm supposed to prove. The question is:     Prove in $2$D that $\Delta \log(|x|)=2\pi\delta_0$ in the distributional sense.   Now, let $x=\langle\alpha,\beta\rangle$. Then I figured out: $$\langle\Delta\log(|x|),\phi\rangle = \iint_{\mathbb R^2}\log(\sqrt{\alpha^2+\beta^2})(\phi_{\alpha\alpha}+\phi_{\beta\beta})d\alpha d\beta$$ But where am I supposed to go from here? Do I use integration by parts?


Login screen appears in a much older style

The login screen appears in a much older style:    Output of cat /etc/X11/default-display-manager:  /usr/bin/xdm   How can I change it back to normal?


People I walk by in the game are always mentioning that I look "sick." Is that something they just say or is that a problem? If it's a problem, how can I fix it


What is a good discussion forum for iOS developers

I assume that the below question would be inappropriate for Stack Overflow, as it is asking for well informed opinions, not specific answers. Am I right? Is there a good forum for this that anyone can recommend? Would this be appropriate any other Stack Exchange sites, like this one or Programmers?     Is the iOS 6 auto layout too complex? I am just learning it, but at first look it seems far more complex than manually setting frames. I'd love to hear from experienced iOS developers who have embraced or rejected the new auto layout features for complex layouts.


Let us imagine lightning striking you so hard it disintegrates all your atoms and then, simultaneously, lightning strikes just a few meters from where you stood, somehow happening to rearrange all the atoms as you were before you disintegrated. The question now is did you really 'shut off' and then 'reappear' in the second instance? Or did you shut off and never reappear? Or did you experience two different realities? What if the lightning struck 10 different places, each time rearranging your body? Will you have 10 different perspectives of one body or will there be ten different bodies each with its own perspective ?


Manipulating a String's content with an Integer

I'f you're familiar with Python, I'm sure you're aware that you can multiply a String by an Integer to get that desired amount of Strings back.     Example:  'J' * 3 --> 'JJJ'     What's the most efficient way to do this in JavaScript?  I was looking for an inline method; similar to that of Pythons behaviour    A few of my ideas:  var str = 'J',     strOld = str,     timesToExtend = 3;  for(var i = 0; i < timesToExtend; i++){     str += strOld; }  = 'JJJ'     var str = 'J',     timesToExtend = 5,     strOld = str;  while(!timesToExtend){   str += strOld;   timesToExtend--; }     These are just rough ideas, so don't expect them to be 100% accurate and working. I assume this MUST contain a loop; however any method without a loop will be praised!  Thanks for reading; thank you for your response in advance!


Now that we can unfollow deleted posts, there is an issue with being unable to unfollow answers which were locked due to being rude or spam. There is a button on the answer and when clicked it changes state, but I get a red popup with the message:  This post has been locked; locked posts can't be voted on  Also, the unfollow/following button on the questions is gone, I can only unfollow it by going through the profile. If the answer was deleted by the owner then I can both unfollow and follow it again without issues. I haven't tried it with locked questions yet, but I can't even follow a deleted question again from my profile page. I get this error message:  Following not enabled for this post.  To summarize:  I can unfollow deleted questions, but only from profile page I can't follow deleted questions I can unfollow and follow deleted answers. Both from post view and profile I can't follow/unfollow locked posts  P.S. Filtering doesn't work with paging. When I select answers only and go to second page the filtering turns off.


Citation warnings - Citation 'bibtexkey' on page 7 undefined.

Hey so I am having issues with my citations.  I am getting multiple warnings for a number of my citations saying: Citation `Bibtexkey' on page 6 undefined.  Some of my citations are fine while others will not work and show up as ( ?) in the pdf.  There is nothing wrong with my bibtex file within JabRef that I can see, so I do not no what is causing this to happen.  I am using TeXStudio.  Here is a MWE.  nuthesis is a class designed for my universities graduate students.  I don't believe it has anything to do with the issue as I know many many people who have used this document class successfully.  I've tried using different styles as well but no luck.  I have a lot of other packages involved, but not sure if they may be affecting the bib.  I've seen people talk about how you compile matters, but I'm not sure what is meant by this.    \documentclass[print,double]{nuthesis} \usepackage{amssymb} \usepackage{natbib} \usepackage[   unicode=true,   urlcolor = blue,   colorlinks = true,   citecolor = blue,   linkcolor = blue]{hyperref}  \begin{document}  \cite{Mero}  \cite{Schaffer} \cite{Keldysh}  \end{document}  \bibliography{Thesis_BIB} \bibliographystyle{aipnum4-1}   Any and all help is greatly appreciated! Thank you!


Can anyone help me on how I could make a better render to my scene? No matter what I do it always shows these fireflies and never render with the quality i need...   I´m using filmic color management, 128 samples (and even when I increase this number I still get noise), and Filter Glossy: 2. For lighting, I´m using a sky hdr.    Thanks!


Suppose that $\|f\|_p &lt \infty$ for all $1\leq p &lt p'$, I want to know if the the following is true and in that case how to show it     $p \mapsto \|f\|_p$ is continuous on $[1,p')$   Or maybe we need to impose some more constraints such as finite measure space. In case of finite measure space, I tried to use .


How can I check if a file exist in a index file?

How can I check if a physical file is located in index file?  For example:  Let's say we have 5 files in the folder C:\Users.  I have a file with a link to this location  C:\Users\1.txt C:\Users\2.txt C:\Users\3.txt C:\Users\4.txt  We can see that we are missing 1 file from C:\Users in that index file?  How can I do it? If you could give me some way to do it, it would be great. Is it even possible to do such thing?


Stack Exchange user reputation leagues drop-down bug

when on the  page, I noticed that the drop-down was not functioning correctly. When selecting , the drop-down keeps showing Stack Overflow:    I noticed the same behavior for some other sites, but not all. Even some weird combinations show up:


Unable to update software centre from terminal

Unable to update software centre via terminal and update software via centre is very slow and not able to download software from centre. Please help.    vineshnair@vineshnair-Lenovo-G580:~$ sudo apt-get install gnome-software packagekit [sudo] password for vineshnair:  E: Could not get lock /var/lib/dpkg/lock - open (11: Resource temporarily unavailable) E: Unable to lock the administration directory (/var/lib/dpkg/), is another process using it?


Updating the arXiv version of paper after it is published in ACM proceedings

Before submitting my paper to one of ACM's conferences, I uploaded the earlier version of the paper on arXiv. The paper has now been accepted and published in ACM proceedings. I plan to update the arXiv version of the paper with the final version of the paper that has been published in ACM proceedings. I wanted to ask if:  1) Am I allowed to do this? 2) Do I have to make any changes to the format of the draft. i.e the paper contains a copyright block from ACM now.   When granting licence to ACM, I did NOT opt for open-access. Also the paper was published in 2018.


The $L^p$ norm in $\mathbb{R}^n$ is \begin{align} \|x\|_p = \left(\sum_{j=1}^{n} |x_j|^p\right)^{1/p}. \end{align} Playing around with WolframAlpha, I noticed that, if we define the "scaled" $L^p$ norm in $\mathbb{R}^n$ to be  \begin{align} \| x \|_p = \left(\frac{1}{n}\sum_{j=1}^{n} |x_j|^p\right)^{1/p} \end{align} then \begin{align} \lim_{p \to 0} \|x\|_p &= \left( \prod_{j=1}^{n} |x_j| \right)^{1/n}, \end{align} which is the geometric mean of the coordinates' absolute values. This is interesting maybe because the $L^p$ norm doesn't have a nice limit at zero.  My questions:   How do I prove this? Is this definition of "scaled $L^p$ norm" interesting, or known by another name, or used anywhere? Is there any interesting reason to define the $L^0$ norm as the geometric mean, as above? Further reading?   Thanks!


Plotting recursive function using pgfplots \addplot

Is it possible to plot a recursive function using pgfplots \addplot command?  I tried like this;  \documentclass{article} \usepackage{pgfplots}  \pgfmathdeclarefunction{fac}{1}{   \pgfmathparse{(#1<=1)+                 (#1>1)*#1*fac(#1-1)   } }  \begin{document} fac(5) is \pgfmathparse{fac(5)}\pgfmathresult  \end{document}   But the result seems to be an infinite recursion, as the entire function is being evaluated.


What do we call a person who is obsessed with cleanliness?

Is there any word for a person who is very , very much concerned about cleanliness and keeping things hygienic and even point out faults in clean things and explaining that they were dirty ?


How do I prove that $m(TE)=\left|\det(T)\right|m(E)$?

Let $m$ be the $n$-dimensional Lebesgue measure and $T$ be a linear operator on $\mathbb{R}^n$. Let $\Sigma$ be the sigma-algebra of Lebesgue measurable sets. How do prove that (1) $\forall E\in\Sigma, T(E)\in \Sigma$ and $m(T(E))=\left|\det(T)\right|m(E)|$? Since the $\sigma$-algebra of Lebesgue measurable sets is strictly larger than the borel algebra, I think it cannot be proven by showing that $T$ is continuous. How do I prove this formally? I have a script from UC Davis and every thing is proven precisely here, except for one lemma which is critical for rest proofs in the script. That is,  Define $\mathbb{B}=\big\{\prod_{i=1}^n [a_i,b_i) : a_i,b_i\in\mathbb{R}\big\}$. Let $T$ be a unitary operator on $\mathbb{R}^n$. Let $A\in \mathbb{B}$ and $\{A_k\}_{1≦k≦m}$ be a finite disjoint sequence such that $\bigcup_{1≦k≦m} A_k \subset T(A)$. Then $\sum_{1≦k≦m} m(A_k) ≦ m(A)$.  It's written in the script: "This result is geometrically obvious, but a formal proof seems to require a fuller discussion of the volume function on elementary geometrical sets, which is included in the theory of valuation in convex geometry. We omit the details" It's okay to me to go through full discussion of volume function if that is precise. If it cannot be proven another easier way(so I can prove it in a day), please recommend me a "convex geometry" text which explains this.


How do I convert html page to SharePoint 2013 master page?

There is functionality provided in SP2013 for converting html page to SharePoint master page. I have tried this functionality but each time it convert nothing. Is there any specific method that I need to follow? Or is there any specif layouts of html page need to be converted into SP 2013 master page?


Task: find all values of the parameter, such that integral converges. $$\int_0^{+\infty} \frac{dx}{1+x^a \sin^2x}$$ I tried a lot and I used Cauchy and Weierstrass method but it was useless. And now I know that I must use $$\sum_n \int_{\pi n}^{\pi(n+1)}$$


Handling a conditional statement in a single line

Is it possible to write following C# code in a line without if and else?   string res = "";  if (!string.IsNullOrEmpty(var1))     res = string.Format("{0}/{1}", var1, var2); else     res = var2;


How many rectangles are in a dodecagon? I am unsure how to approach this. I've counted 12 so far but none more


In which countries are the visitor's first name and last name compulsory?

My name consists of just a first name and no surname.  Will there be a problem regarding my name in the country I visit with a tourist or employment visa? Are there countries in the world where this might be a problem?


how to add numbering to subsubsection-level headers in a chapter?

I am a beginner latex user,  I wonder if you could help me to add subsubsection level 1.1.1.1 in my report, the code is:  \documentclass[12pt]{report}  \begin{document}  \chapter{the name of chapter}  \section{section test}  \subsection{subsection test}  \subsubsection{subsubsection test}  \end{document}  \end{document}


What are some interesting sole exceptions or counterexamples?

Many theorems assert that a particular property holds for all objects in a class except those in a given list of exceptions. Examples of rules that admit precisely one exception include:   All primes are odd, except for $2$ All automorphisms of $S_n$ are inner for all $n$ except $6$ All simple Lie algebras have abelian outer automorphism group except for $D_4$ ($\text{Out}(D_4) \cong S_3$, which leads to the exceptional phenomenon of )   What are some other interesting examples of results that admit (essentially) one exception?  Edit (modified from a comment below): Read strictly this question is subordinate to , but that question asks (more or less) about classifications of exceptional objects more generally, and not specifically about the case of a single exception. Partly because of this, very few of the answers to that question are admissible answers to this one (and two of them are actually already given in the question here).


Is ArcMap's Fixed Zoom In/Out algorithm documented anywhere?

I only occasionally use the Fixed Zoom In/Out buttons on the Tools toolbar of ArcMap and had always assumed that they zoomed in/out by a set scale factor.  However, using ArcGIS for Desktop 10.2, I just set my scale to be 1:10,000,000 and then hit the Fixed Zoom In button 10 times while recording the subsequent scale each time and was surprised to see:  10,000,000 8,000,000 6,000,000 5,000,000 4,000,000 3,000,000 2,500,000 2,000,000 1,500,000 1,250,000 1,000,000   Dividing each scale denominator by its successor shows a sequence of: 1.25, 1.33, 1.2, 1.25, 1.33, 1.2, 1.25, 1.33, 1.2  Curious about what happened in between the scales above I experimented a little to discover that the first issuance of the Fixed Zoom In button simply takes the scale to the first of those listed above and then starts following the same pattern.  Try starting with 1:8,000,001 to see ...  8,000,001 8,000,000 6,000,000 5,000,000 4,000,000 3,000,000   This seems like quite a neat solution, but not one that I had realised was in place - does anyone know if it has been documented anywhere?    I've looked in the Online Help without success.  In answer to @DevdataTengshe, the scales currently in my available list (see below) seem to bear no relation to those used by Fixed Zoom In/Out.    However, when I add 1:7,500,000 into my available list it does seem to insert that as an additional scale step ...  10,000,000 8,000,000 7,500,000 6,000,000 5,000,000 4,000,000   This makes the algorithm being used even more mysterious to me.


Why does a rolling thunder always starts with a high pitch and ends with a deep, low sound?

Rolling thunders always come cracking in with a high frequency, and the sound grows more deep as the rolling advances, ending with the deep sound of a roaring lion. Why? This is not the same question than the one of the extended sound but about the way we hear the rolling thunder from the beginning till the end. The sound starts with a higher frequency than that with which it ends and I was wondering why.


Italian keyboard: entering tilde (~) and backtick (`) characters without changing keyboard layout

Here is what the layout of an Italian keyboard looks like:  As you can see, the curly braces, which are absolutely necessary to write code in any of C, C++, JavaScript, Java, Objective-C, and others, appear in purple in this picture. This is because while the other characters can be seen visually as printed characters on most Italian keyboards, these purple characters are actually usually not printed on the keyboard's keys. These characters, found in the upper right corners of the given keys, can usually be generated with the following key combinations: (RIGHT SHIFT or LEFT SHIFT) + (RIGHT CTRL or LEFT CTRL) + (Alt or AltGR) + ([ or ]) (Actually as the MSKLC application shows, SHIFT + AltGr + [ and SHIFT + AltGr + ] are enough to generate the curly braces.) Characters such as the at (@) sign (called 'chiocciola' in Italian) and the hash (#) key (called 'cancelletto' in Italian) found in the lower right hand corner of the keyboard can be generated easily as follows (AltGr + @) or (AltGr + #). Such characters are also fundamental to programming as they can, for instance, be found in CSS, namely with media queries and with selectors referring to the id html attribute. Upon further inspection, we can see that all of the US ASCII keyboard / programmer's keyboard are covered by the keys of the Italian keyboard, except for the following, which are the tilde, which is especially useful on the Linux command line and is used to refer to a user's home directory on such system, as well as the back-tick (`), also known as the back-quote, which is also very useful on the Linux shell when we want to turn the output of a command into a command-line input. So, here comes the question: With all those empty upper-right hand corners of keys, why isn't there a better way of generating these characters, perhaps through a CTRL-ALT-SHIFT modifier key combination? All I've been able to find regarding generation of these characters are the following ALT-codes:  ALT code 96  corresponds to ` ALT code 123 corresponds to { ALT code 125 corresponds to } ALT code 126 corresponds to ~  and to generate a character via an ALT code, you make sure that the NumLock key on your keypad is toggled on, hold down the ALT key, enter the keycode, and release the ALT key. ALT code are documented at:  If someone knows of a better way of inserting these characters from an Italian keyboard without switching the keyboard layout in the Control Panel, then please let me know. Thanks.


How to Install Viber on Ubuntu 13.10, 32bit

I hope everyone is OK  I would like to know if someone knows how to install Viber on Ubuntu 13.10, 32 Bit.  Best Regards,


Are 401(k) contribution limits for employee & employer separate? What about hitting the limit?

I am 29 years old and have a 401(k) already with my company. I just started contributing 10% to my 401(k), up from my 8%. My company does not match but they do put 10% of my salary into my 401(k) as their contribution every February, once per year. I make between 95k and 110k a year and as stated started to put 10% of my pay into my 401(k). My current 401(k) balance is at $53k-ish.  My question is: When do I max out in the year 2012? I read at $17,000, but does that cover only my contributions, or both mine and my employer's? If I do max out with mine and my employer's, how do I know that, and how will I be notified? If I do max out, what do I do with the extra funds beyond the max? Should I put that into a Roth IRA? I am concerned as I get paid more year after year when I will be maxed out. What penalties or options do I have?  Thanks in advanced for the information and I look forward to reading more on this forum!


Cast to date is sargable but is it a good idea?

In SQL Server 2008 the  datatype was added.  Casting a datetime column to date is  and can use an index on the datetime column.  select * from T where cast(DateTimeCol as date) = '20130101';   The other option you have is to use a range instead.  select * from T where DateTimeCol >= '20130101' and       DateTimeCol < '20130102'   Are these queries equally good or should one be preferred over the other?


Ajax example dependent dropdown callback

I have two custom Drupal modules moduleA and moduleB. moduleA has all the functions for Ajax calls i.e. ajax_example_dependent_dropdown_callback and _ajax_example_get_second_dropdown_options.  I create a content type in moduleB called content_type_b. I am using Ajax calls in moduleB to populate drop down in content_type_b.  While creating content for content_type_b, I try to choose a value from the drop down. The first time, it works fine. The second time I get an error saying "An Illegal choice has been selected. Please contact the administrator". All these events happen before a node insert.  When I looked into the logs, the hook_node_validate of moduleA is getting called. The node insert must happen in moduleB. So node_validate of moduleB must be called. I think since the Ajax functions were present in moduleA, the node_validate of moduleA is being called.   Please advice how to proceed in this situation.


Parameters passed to a sourced script are wrong

A script on AIX which checks the number of parameters passed and complains if they are not correct:-  if [ "$#" -ge 1 ]; then   ... else   echo 'Usage: myscript <a> [b] [c]' fi   The script sets some environment variables so it is sourced. By that I mean I type the following on my command line. There is no second script, I am not sourcing a script from within another script.  . ./myscript.sh   If I pass it no parameters, I expect it to print out the usage statement but instead it runs using the parameters passed to the previous command that was sourced (not necessarily even this script!).  To double check this I added this line at the beginning of my script to prove that this was the case.  echo $# $@   If I pass it no parameters, it prints out the number and the list of parameters from a previously sourced script.  How do I get it to say $# is zero when I pass it zero parameters and source it?  The smallest possible recreate is a script thus:-  myscript.sh  echo $# $@   and then run it thus:-  . ./myscript.sh a b c   which prints out  3 a b c   then run it again without any parameters thus:-  . ./myscript.sh   which prints out the same  3 a b c   when you would expect it to print out  0   If you don't source the script and just run it thus:-  ./myscript.sh   then it works as expected and prints out  0   I hope that clarifies the issue at hand.  Since I seem to be getting lots of answers to explain why the above doesn't work and no answers to tell me what I should do instead, I thought I would have one more attempt at trying to explain what I am trying to do.  Requirement  I need to write a script that expects at least one parameter and complains if it is not invoked with a said parameter (see the first block of code in my question above), and this script needs to set some environment variables. Because of this second requirement I have assumed that I need to source the script so that the environment variables are still set when the script completes. How can you write a script that can tell when it has not been passed parameters that is also able to set an environment variable?


There are vector logos for five of the sites: .  I was wondering if there were also vector logos for the other sites that are available for download? (I am looking, in particular, for Mathematics, but ideally I'd like them all!)  Edit: Thanks to IBUG's answer, I've gotten a few of them and can share these few logos in SVG and PDF format - .  Unfortunately I don't know any programming and this takes me a bit of work. Hopefully someone else who knows better can easily get them all and share all of them with everybody.


How can I write a regex which matches non greedy?

I need help about regular expression matching with non-greedy option.  The match pattern is:     The text to match is:    abc     I test on   This expression matches all text from . I need it to match with the first encountered > after the initial <img, so here I'd need to get two matches instead of the one that I get.  I tried all combinations of non-greedy ?, with no success.


Another take on canonical answers: Add a "canonical" vote

When closing a question as a duplicate, it is becoming harder and harder to search for a good original as the pool of questions and answers grows and grows.  While the new dupe closing dialog is a huge step forward, it doesn't always work - if you've spent some time on the site, you know there are perfect answers to many new questions but you can't always find them. Or can't be bothered to, as your time is limited.  A way to further improve this could be introducing a vote for canonical answers.  It could, for example, work like this:   Answers get a new icon, the "canonical vote" (signified here by a cannon because I can't think of anything that makes sense right now.)     Only users with a certain minimum rep (maybe 1k+ or 2k+) see this icon. The icon would work like the favourite icon: You can toggle it on or off at any time. The hover message for the icon could read e.g.      This is a "canonical answer": It answers the question asked in the most extensive and general way, and is very likely to benefit other users with the same problem.    Questions that contain an answer with three or more canonical votes get special  treatment:      They show up on the top in search results; maybe even under a special heading ("Questions with canonical answers")  They show up prominently in the "close as dupe" dialog (i.e. the canonical votes influence the metric that is used to determine the questions shown there).  There could be some rewards for users whose answers receive "canonical" votes - maybe a badge if ten of your answers get at least three canonical votes, or a counter of canonical answers in your profile. It would be really interesting as it's a badge that you can't game your way to, but this whole rewarding part is entirely optional.  would be a great safeguard against over-use of this feature.    Dupe (but sans cannon):       Related:


How to create A list of blackJack cards(method) with Factory class method. enums have been created for the values and suitsC#

I want to create deck of cards using a for loop and my Factory class method. I have setup the suit and face values as enums. How should i aproach this? public static class FactoryClass {     public static Card CreateCard(CardFace face, CardSuit suit) {           return new Card(face, suit);             }     }        public enum CardFace {     A, _2, _3, _4, _5, _6, _7, _8, _9, _10, J, Q, K }       public enum CardSuit {     Spades, Hearts, Clubs, Diamonds }   public void Deck() {                 for (int i = 0; i < 13; i++) {             for (int j = 0; j < 4; j++) {                 _cards.Add(FactoryClass.CreateCard();             }         }     }


I don't want to see any Windows 10 security stuff anywhere. I already disabled UAC, and made my account Admin.  However, I still get security prompts with networking my three PCs together as well as pop-ups that say I don't have access to this or that until I select "continue".  How do I rid my PC of this stuff? No one uses my PC, there is nothing of value on my PC, and it is hard for me to read stuff about how to do this and that with the security features of Windows 10.  I miss the ease on Windows 3.1 and how i could simply right click a drive on other PC and select map.   Thank you, DReeves  Tried to look at the "exact duplicate this was marked as, but then i remember, i have never been on this site before and therefore, it cannot be an "exact duplicate". Someone may have asked a similar question of which i was unable to locate, and would gladly look at it and try and get the answers i need. Thank you.


I wonder whether it is possible to perform within R a clustering of data having mixed data variables. In other words I have a data set containing both numerical and categorical variables within and I'm finding the best way to cluster them. In SPSS I would use two - step cluster. I wonder whether in R can I find a similar techniques. I was told about poLCA package, but I'm not sure ...


How can I bulk replace the suffix for many files?  I have a lot of files like   NameSomthing-min.png NameSomthing1-min.png NameSomthing2-min.png   I would like to change all them to   NameSomthing.png NameSomthing1.png NameSomthing2.png   i.e., remove the characters -min from the name.  How would I do this?


Looking for a short story title about a "weird house"

A man's house gets altered by some rat-like creatures, so it is somewhat bent in on itself.  It has become a portal to another part of the universe.  He pokes around on the "other side" because he is after his dog that wandered off.  He meets up with some aliens (seemingly friendly) moving around on some anti-gravity saddles.  He tries to barter with them! Very weird and original story!  Anyone know what this is?


Graphics Bug? Not rendering faces and Objects that were there stuck on my screen

Object is invisible in the 3rd render mode and if I go to the last render mode from up right it shows a grey thing that stucks in the same position even if i move my camera to another angle like this:  I already tried creating new project , creating new object , repairing blender.


Suppose you have this code:  static void Send(byte[] buffer, int offset, int count) {     while (count > 0)     {         int size = sock.Send(buffer, offset, count);          if (size == 0) throw new EndOfStreamException();          offset += size;         count -= size;     } }   vs.  static void Send(byte[] buffer, int offset, int count) {     int size;      while (count > 0)     {         size = sock.Send(buffer, offset, count);          if (size == 0) throw new EndOfStreamException();          offset += size;         count -= size;     } }   My teacher told me the second one would be more efficient, but is that true?  I did some testing and compared the assembly code and it was equal.  But will this always be the case?   What if instead of a primitive type you used a reference type? (assuming you don't allocate) What about using multiple variables? Will there ever be differences between the two possibilities?   Thanks in advance for any answers, I apologize if this has been asked before but I didn't really know how to call it.


Can every semi-algebraic set be written as a finite union of disjoint Nash submanifolds?

Can we write every semi-algebraic set $A \subset \mathbb{R}^m$ as the disjoint union of finitely many Nash submanifolds of $\mathbb{R}^m$? By Nash submanifolds are meant those manifolds that are smooth and semi-algebraic.


At my school, the Panasonic interactive "SmartBoard" show a different message on the Windows 7 login screen. Instead of:     Press CTRL + ALT + DELETE to log on   It reads:     Press CTRL + ALT + DELETE or use the Windows Security Button to log on   What is this "Windows Security Button", and where is it located?


When I use \vdots within the align environment, its size is bigger than of the rest of characters. I want to get rid of the gap (purple colour on the picture below) or somehow move \vdots upward (\vspace{-Xmm} didn't work at all). My code is \documentclass[12pt]{article} \usepackage{amsfonts, amsmath}  \begin{document} \begin{align}     A &= B \nonumber\\       &=  C \nonumber \\       &=  \vdots \nonumber \\       &=  Z \nonumber \end{align}  \end{document}  which gives you  Cheers!


Keras "Set" identifier not learning as expected

I am using Keras to make a "set" identifier for the card game "set":   Here is my script (some code may be unnecessary but was used during experimentation):  from keras.models import Sequential from keras.layers import Conv2D from keras.layers import MaxPooling2D from keras.layers import Activation from keras.layers import Flatten from keras.layers import Dense from keras.layers import Dropout from keras.callbacks import EarlyStopping from keras.optimizers import SGD from keras.utils import to_categorical from keras.layers.advanced_activations import LeakyReLU from keras.regularizers import l2  import os import glob import shutil  import numpy as np from keras.preprocessing.image import load_img, img_to_array from keras.applications.imagenet_utils import preprocess_input  earlystop = EarlyStopping(monitor='val_acc', min_delta=0.001, patience=5,                           verbose=1, mode='auto')  callbacks_list = [earlystop]  # opt = SGD(lr=0.01)  setIdentifier = Sequential()  setIdentifier.add(Conv2D(32, (3, 3), input_shape = (64, 64, 3), activation = 'relu'))  setIdentifier.add(MaxPooling2D(pool_size = (2, 2)))  setIdentifier.add(Conv2D(64, (3, 3), input_shape = (64, 64, 3), activation = 'relu'))  # setIdentifier.add(Conv2D(64, (3, 3), input_shape = (64, 64, 3), activation = 'relu'))  setIdentifier.add(MaxPooling2D(pool_size = (2, 2)))  setIdentifier.add(Flatten())  setIdentifier.add(Dense(units=256, activation = 'relu'))  setIdentifier.add(Dropout(rate=0.5))  setIdentifier.add(Dense(units = 2, activation = "softmax"))  setIdentifier.compile(optimizer = "adam", loss='categorical_crossentropy', metrics = ['accuracy'])  from keras.preprocessing.image import ImageDataGenerator  train_datagen = ImageDataGenerator(rescale=1./255,                 shear_range = 0.2,                  zoom_range = 0.2,                  horizontal_flip = True)  test_datagen = ImageDataGenerator(rescale=1./255)  training_set = train_datagen.flow_from_directory('Data_Training',                                                  target_size = (64, 64),                                                 batch_size = 32,                                                 class_mode = 'categorical')  test_set = test_datagen.flow_from_directory('Data_Testing',                                             target_size = (64, 64),                                             batch_size = 32,                                             class_mode = 'categorical')  setIdentifier.fit_generator(training_set,                                  steps_per_epoch = 486,                                 epochs = 50,                                  validation_data = test_set,                                 validation_steps = 60,                                 callbacks = callbacks_list)  setIdentifier.save("setIdentifier.h5")   The file 'Data_Training' has a folder "notSet" and a folder "Set", and the file 'Data_Testing' likewise. There are two times as many "notSets" than "Sets" in each category.  No matter what I do, in both training and testing phases, the output is always notSet. I am not sure what is the cause for this.  I have tried a binary_classifier with the sigmoid activation function and final density layer with 1 node. I have tried changing activation functions and using leakyRelus.  I have double checked my training steps and test steps. I have 5184 sets + 2 * 5184 notSet = 15552 train images, which when divided by a batch size of 32 gets me 486 steps. I have 648 sets + 2 * 648 notSet = 60.75 >> rounded to 60 validation steps.  I am confused by what is going on with the neural network - why isn't anything approving and why is it labelling everything with one class?  For more info, here is the Github repo which includes the training images:   Any help is appreciated!


why does this anacron job run hourly, not daily?

I'm running zulip on a virtual private server, and have created a script backup-zulip on my laptop (with ubuntu 20.04) to back up zulip via ssh. I want to run this script daily, so I put the line @daily  10      backup-zulip    sudo -u username /home/username/bin/backup-zulip  into /etc/anacrontab/. However, now the backup seems to run hourly whenever the laptop is turned on, filling up my drive far too fast. What's going on? I wondered whether the script gets rerun each hour by anacron since it exits on error, but running it by hand returns 0. Is there a log file that I can look into? Searching for cron in /var/log/ gives nothing. My complete /etc/anacrontab looks as follows: # /etc/anacrontab: configuration file for anacron  # See anacron(8) and anacrontab(5) for details.  SHELL=/bin/sh PATH=/usr/local/sbin:/usr/local/bin:/sbin:/bin:/usr/sbin:/usr/bin HOME=/root LOGNAME=root  # These replace cron's entries 1       5       cron.daily      run-parts --report /etc/cron.daily 7       10      cron.weekly     run-parts --report /etc/cron.weekly @monthly        15      cron.monthly    run-parts --report /etc/cron.monthly  @daily  10      backup-zulip    sudo -u username /home/username/bin/backup-zulip  (If this is not the correct stack exchange for this question, where should I post it to?)


I have a folder on Windows that contains files whose name contain unicode extended characters (simplified chinese). I'd like to grab a list of these files. Of course, cmd won't display them correctly, but I was hoping Powershell could.  Unfortunately, the result of the dir command isn't any better. When I search existing questions, everything is about the file encoding, not displaying the file name.  I'm not looking to make any system-wide change like changing the system locale or the default code-page, but I would expect PowerShell to be able to handle unicode output on screen.


Why are people so trigger happy with close as duplicate?

I have asked  which I don't honestly think is a duplicate of the question linked as motivation for closing. They are both about java, but one is about the language and the other one about its applications in the real world. They are sure related but not exact duplicates by any means. Yet it took just a few minutes to find 5 people willing to close it.  Why is it so? Do similar questions really pollute SO so much? Is closing a question like that so urgent that you can't leave it open for a while and see if it meets interest in the community? Do people just do it because they have the power to do so and they like to use it?  SO should be a community site about programming, not about who's the quickest sheriff.  EDIT: edited subject as I meant "close" instead of "delete"


How to add new column as external data type in SP2013 designer?

When i click on add new column i don't see option to add  External data type


I have to prove: $||x|-|y||\leq |x+y|\leq |x|+|y|$ I have already proved $|x+y|\leq |x|+|y|$.  I saw proofs for $||x|-|y||\leq |x-y|$, can I use the proof for  $||x|-|y||\leq |x-y|$ and just add that $|x-y|\leq|x+y|$?


How does Darth Vader eliminate waste from his body?

I've always wondered what the deal was with Darth Vader's "crotch door". Does he use a catheter (due to all his injuries) or does he simply flip the door up and whip it out? I've never really seen the the back of his suit under his cape to see if there a corresponding "back door".   It doesn't look like he carries a catheter bag nor a colostomy bag in his suit or anything.     Is this addressed anywhere either in canon or legends sources?


How to prove that  is not a topological manifold.I think I have to do something with the meeting point of the two cones.


.substring() throws a nullPointerException

I am creating a Chess program on NetBeans using jButtons as squares, and my java knowledge is limited to what I have learnt at school.  So this line  int verticalValue = Integer.parseInt(newButton.substring(1,1));   returns a nullPointerException and I can't figure it out whatsoever. Here is the relevant code:  static void pawnMovement(JButton but){     String buttonName = but.getName();     String newButton = buttonName;     int verticalValue = Integer.parseInt(newButton.substring(1,1));   The names of all buttons are in the format letterNumber, so I don't see why this shouldn't work.  Thanks!


Suppose that $G$ is finite and that $g\in G$ . If $h\in G$, show that $o(hgh^{-1})=o(g)$.   Solution:  We have that $(hgh^{-1})^{o(g)}=hgh^{-1}hgh^{-1}...hgh^{-1}=hg^{o(g)}h^{-1}=h1_Gh^{-1}=1_G$, so $hgh^{-1}$ has finite order and $o(hgh^{-1}) \leq o(g)$.   Now, what I don't understand is "A similar argument shows that $$ g^{o(hgh^{−1})} =h^{−1}(hgh^{−1})^{o(hgh^{−1})})h = 1_G ."$$  Which shows that $o(g) \leq o(hgh^{-1})$ and then $o(g) = o(hgh^{-1})$  I don't understand how to get $ g^{o(hgh^{−1})} =h^{−1}(hgh^{−1})^{o(hgh^{−1})})h = 1_G $, what argument do you use to get this?


How to protect an external hard disk files from accidental deletion?

I had a bit of problems in the recent months with the data I have on my External hard disk. I have large content in each folder.   If you think about it, it takes only two keys to delete a folder - del and enter. Is there anyway to protect files from accidental deletion?


When a permanent has a "When a creature dies" ability, and gets destroyed at the same time as creatures, does that ability trigger?

Say I control , which states:     Whenever a creature dies, that creature's controller may draw a card.   If I control 2 creatures and my opponent controls one creature, and I cast  to wipe the board (including Fecundity), what happens?  Do I get to draw 2 cards?  Does my opponent get to draw 1 card?  Or do neither of us get to draw any?


How do I stop Ubuntu One from telling me its file service will be shutting down two weeks ago?

I have Ubuntu 12.04 LTS.  Starting a few weeks ago, every time I boot a message would pop up in the notification area and say that Ubuntu One's file services will be shutting down June 1st, 2014.  This makes no sense because:   I've never used Ubuntu One's file services. In fact, I uninstalled Ubuntu One over a year ago. It's good that the service will be shutting down on June 1st, but it's June 16th now. These messages didn't start until after June 1st anyways.   How do I make this message stop?


In a tennis tournement of 128 players, elimination system, what is the probability that two twins will meet at some point?

Needs to be solved using conditional probability. I was thinking using the formula for total probability and having the hypothesis $H_i$ - they get to the $i$-th round and ($A$-they meet) $$P(A)=\sum P(A|H_i)P(H_i)$$ I reach a dilemma when trying to find these values, unsure whether to take into account which part of the tournament tree do they meet..  each player has an equal chance of winning.


How do I keep the narrative alive during combats?

For years, I've had trouble keeping the players engaged in the narrative of combat and what happens during their turns. After the first 4 turns or so, it becomes hard to imagine what everyone does and even my players forget about their allies, and I forget about the villain's allies as well. After a couple rounds it starts becoming a "you hit with a raise, well, throw 1d6 more", and I'm left wondering how I can make things seem more dynamic and cool, however I find it very hard to wait for players to end turns, throw dices, and then proceed to imagine and narrate what they do, it also makes players frustrated as they just want me to be down with other player's narrative and move on to their own turn.


General info:  SO:  Ubuntu 18.04  Script folder:  /home/Emby/Anime/canon_vids   Serie folder:  /home/Emby/Anime/Goblin Slayer   I normally execute the script at folder like this:  ./canon_vids [folder]  ./canon_vids Goblin\ Slayer/   Problem:  I want to execute the script with crontab every 10 minutes as root.  I tried adding like this but isnt working.  */10 * * * * root sh /home/Emby/Anime/canon_vids /home/Emby/Anime/Goblin\ Slayer/


Case insensitive terminal completions in macOS Big Sur

I am totally new in MacOS environment and I can't get my terminal completions to work case insensitive. I've tried almost all google search results for this question, like editing ~/.zshrc, /etc/inputrc, and many other solutions... I am trying to achieve this for more than 5 days now, so I really appreciate if someone could help!!


Is it possible to shoot tethered with a preview on the screen?

I had to shoot self-portraits today, and it didn't go well. I first tried shooting tethered, but it was so hard to get composition & focus right, that I just did it with a mirror. Which of course introduced a whole new set of problems. Not only is using a strobe with a mirror an extremely dumb idea (and I don't have real continuous lightning, so ended up using an anti-SAD lamp), but my infrared remote has to be pointed at the front panel of the camera. While I managed somehow, the results are far from thrilling.   So I searched a bit and landed at good old DPS, which has an article about self-portraits. This includes following advice:      Shoot tethered; most digital cameras have a mini video if not a HD video out. I borrowed my son’s DVD player (the one he watches movies in the car with) on multiple occasions for the sole purpose of shooting self portraits. This is where the remote comes in great; you can fine tune the composition by watching that little monitor, without having to run back and forth. If you have a newer DSLR with an HD out then you could hook up your laptop or HD monitor.   (source )  This made me wonder. I have a D90, which has both LiveView and a HDMI output. I have shot with it tethered using DarkTable, but I cannot see the image on the monitor the way I would be seeing it on the camera back in LiveView mode. Instead, I can just make some changes with the mouse (and that doesn't work perfectly, as some settings are overridden by the position of the controls on the camera) and then click on a button to shoot, effectively using the wireless mouse as a wireless remote. And then the picture is visible on the big colour-calibrated monitor. This is, of course, much better than shooting camera-only and later noticing that what looked OK on the camera back is not so hot at normal resolutions, but it still isn't enough for very demanding situations like self-portraits.   The quote from DPS, on the other hand, sounds as if it is possible to send a video to the monitor, which I imagine like a kind of LiveView on the monitor. Which would be, of course, perfect. So, is this possible, and if yes, which software supports it? (preferred platform is Linux with Gnome, but if there are Windows options, I want to hear about them too). Or did I just misunderstand the quote and does he mean that he is only tethering the same way as I do, but using a HDMI instead of a USB cable?


I am trying to remove Ubuntu and reinstall Windows 10, can someone help me?

So I'm in love with Ubuntu. It's fast, clean, and efficient. However there are certain things that I can't do that I used to love to do on my Windows 10. I tried creating a bootable USB using UnetBootin, however it failed to actually do anything, and killed my USB drive (Not that I'm mad, I got it specifically with the intention of reinstalling windows, so it was cheap). Now I need to reinstall Windows and I'm in dire need of assistance.  When I tried booting from my USB (before it died on me) it took me straight to the UnetBootin boot page (granted I had to hit F2). However there was no option to boot from USB, and the one thing that happened when I hit enter was that it would start the 'automatic boot' count down again. I let the count down run, and it just simply restarted again. I remember being smart enough when I was younger to dual boot (Back when I had Vista) but this time I just didn't (maybe because I thought I wouldn't want to go back?)  Anyway, I really really really need help.


Undoing an old vote cannot be recast because vote is too old

Undoing a Vote  There is a very brief window where you can undo a vote which allows you to take back a vote you accidently cast. After a brief time, it is "locked in" until the post is edited.  The Bug:  I see an old vote where the answer has been edited. I accidently click which undoes the vote. Oops. I can't immediately click again to re-do the vote. The system says the vote is too old.


Can an app make phone calls in the background

I saw a number of apps that require "Services that cost you money" permissions, my question is if I install such an app and that app will make a phone call, is that call visible to the user or the app can make the call in the background without the user knowing ?  I usually don't install apps that require extending permissions and I haven’t found anything googling, I prefer not to install it unless I'm sure I won't have a surprise when my phone bill comes.  Specifically I was invited to join a conference via GoToMeeting and their Android  is requesting the above permission.


Set a default segment for Google Analytics

I set up a segment that contains the data that my colleagues and I will want to be looking at 90% of the time. The All sessions segment contains superfluous data that we will generally not be interested in. However, every time I go to the GA, the All sessions segment is selected. I already know how to change/add the segments that I am looking at but is there a way for my segment to already be selected each time I arrive at GA?


Tighten vote-to-close conditions for high-score questions

I've seen some questions with score 5+ on the verge of getting closed and sometimes I thought "Mmmh that's a shame".  I know I can vote to re-open but perhaps we don't have to go through that. Surely a high score is indicative of a "question of interest" and should perhaps be taken into account in the vote-to-close system.  Allow me to nuance that though: closing a high-score question as a duplicate is perfectly fine to me (and is the right thing to do) but apart from that, is it ok for me to close a question I think is off-topic and ignore everybody who think otherwise?  Couple of suggestions:   Increase VTC threshold Has to be VTCed by a relevant bronze tag badge holder   Something similar to  but the other way round ;)


When you are saying The Johnson Family is is The Johnsons or The Johnson's?


How Do I Update Ubuntu Linux Software Using Command Line?

I'm new and I want to know how do I update Ubuntu Linux for security and application fix/upgrades using the ssh command line? How can I install updates via the command line option?


Like it or not, Meta Stack Exchange favicon was changed recently to , however in the app the old icon is still showing:        Can it please be updated?


Consecuence of the existence of isomorphism $\mathbb{R}^3\rightarrow \mathfrak{o}(3)$

I have already proved that there exists a vector isomorphism $f$ between $\mathbb{R}^3$ and the set of $3\times 3$-antisymmetric matrix $\mathfrak{o}(3)$, that satisfies  $f(u\times v) =[f(u),f(v)]$ where $\times$ denotes the  vector cross product. I wonder if I can deduce something interesting of the Lie algebra $\mathfrak{o}(3)$ from the fact that there is such isomorphism with $\mathbb{R}^3$?  Any idea is welcome.


How to fix column does not exist error in Postgres?

I'm getting the following error when attempting an insert in Postgres: psycopg2.errors.UndefinedColumn: column "bac" does not exist I am not sure why. This is the command I'm trying: cur.execute("INSERT INTO t43407779_positions(ticker, shares) VALUES(BAC, 40);") I'm wondering if I shouldn't have variable names the same as column names, because perhaps Postgres can mix them up. But that doesn't seem right. Here is a larger snippet of the code in case its helpful: try:     start = text.index('$')     stop = text.index(':')     letters = ['a', 'b', 'c', 'd', 'e', 'f', 'g', 'h', 'i', 'j', 'k', 'l', 'm', 'n', 'o', 'p', 'q', 'r', 's', 't', 'u', 'v', 'w', 'x', 'y', 'z']     if text[start+1].lower() in letters:         ticker = text[start+1:stop]         #if words after ticker..         '''         if ' ' in text_2:             for i in text_2[:text_2.index(' ')]:                 ticker = ticker + i         #if there are no words after ticker..         else:             for i in text_2:                 ticker = ticker + i         '''         ticker = ticker.upper()         print("TICKER =", ticker)         r = requests.get(alpaca_base+ticker, headers=headers)         res = json.loads(r.text)         price = res['last']['price'] except:     msg = 'No price found for ticker {}. Check for an alternative ticker that is traded on NYSE, Nasdaq, or IEX.'.format(ticker)         if 'buy' in text:     #buy     shares = text[text.index('buy:')+4:]     print(shares)     shares = int(shares)     cost = shares*float(price)     print('cost=',cost)     cur.execute("SELECT cash FROM "+tablename+" WHERE player = " + gmuser +";")     cash = cur.fetchone()[0]     print(cash)     print(cash > cost)     if cash>cost:         #valid buy         cur.execute("SELECT * FROM " + "t" + gmuser +"_positions;")         portfolio = cur.fetchall()         print(portfolio)         print(type(portfolio))         #for i in portfolio:         #   print(i)         command = "INSERT INTO "+ pos_table +"(ticker, shares) VALUES("+ticker+", "+str(shares)+"); "         print("Command:")         print(command)         cur.execute(command)         conn.commit()


I would be very grateful for some advice on how to decide whether to use an attributive noun or the "of genitive" (periphrastic genitive).  It seems to me that an attributive noun is generally preferable, except when it leads to ambiguity, often due to the combination of several modifiers with mixed dependent relationships.  Additionally, the of-genitive, when used stand-alone, seems to impart a more formal tone, a higher register.  Simple examples (preferred first, less-preferred second):  The department secretary vs. the secretary of the department.  But:  The excellent secretary of the department vs. the excellent department secretary.  Any additional guidelines would be most welcome.


Is there a name for the category containing the words trans and cis?

Gender is the name of the category that contains the words male, female, and others. The words trans and cis are not genders, rather they describe the state of one's gender: i.e. trans refers to one whose gender has changed from that which they were assigned at birth, while cis refers to one whose gender has not changed.  Is there a word that describes the category of words that includes trans and cis? In other words, similarly to how one could say "My gender is female", is there a word that fills the blank in "My ____ is cis?"


How to divide up utilities amongst tenants?

Let's say I have two tenants who share my apartment with me. It is agreed that utilities shall be divided equally amongst us. However, one tenant has, as part of his lease, a stipulation that all utilities are provided free with his rent.  My question is this, how do I calculate the utility charge for me and the other tenant? Do I divide by 2, or 3?


Minecraft LAN isn't working from one computer

Trying to LAN and my son can come into my world but I can't go into his. No firewalls, both MACs IP addresses match. This just started since the 1.9 update. Any ideas to fix this?


Are there any dictionaries that be able to look up words in word families?

I was wondering there are any dictionaries/a dictionary that if I search for a word, for example: news, the dictionary will provide its word family or any types of usages related to this word, for example: news -> {reading, magazine, politics, amusing, global warming, accident, ..}.


I am having two batteries of different specs (both, dry cell, UPS/inverter batteries)  Battery A: 12 V, 26 Ah  Battery B: 12 V, 7.2 Ah  I need a 24 V output so I have connected them in series.  My question is, will it damage my batteries?  If the configuration is okay, can I charge the 12 V 26 Ah battery alone? Wouldn't it push a higher current to battery A and keep the voltage at a steady state?  I don't have a 24 V charger, but I do have a 12 V charger. Yes I can charge them both parallely but I don't want to do that as I would have to open up my robot to access the batteries.  P.S. Sorry if it's a silly question. I am not much of an expert in this.


What is the quickest way to check if a list is empty, and in what scenarios would one method be preferred over the other?

I would like to know what would be the best way to check if a list is empty. I know this question seems silly, but I realize that sometimes when you are working with others and others read your code, using certain functions may look better than others, and would be more understandable for people coming from different programming languages. Say I have a list: names = ["Bob", "Billy", "Samuel", "Adam", "Rob"]  This is one way I can check if the list is empty: is_empty = bool(names)  This is another: is_empty = any(names)  I do realize the any function checks if there is at least 1 true value inside a list. What would be the best and quickest way to check if the list is empty? Which would look the best and in which scenarios? Are there any faster ways that I do not know of?


Currently as soon as I reach him I get destroyed. I've tried ranged attacks, summoning, teleporting, and using my massive enchanted spoon, but to no avail. What is the tactic for beating the devil?


Is lemonade better when made with simple syrup?

On a hot summer day and with a basketful of lemons I often want a nice cold glass of lemonade. A lot of recipes suggest making lemonade with simple syrup, which requires cooking, whereas other recipes just have stirred-in sugar.  What exactly are the benefits of making lemonade (or limeade) with simple syrup versus just stirring in sugar?


Do I use a period or a question mark at the end of a statement that presents a question?

Let's say I have a statement like this:  I just saw you come online, and I wanted to see how your day was going.   Now, am I right to use the . at the end of that sentence? I've written it like this in the past because I thought the . was wrong:  I just saw you come online, and I wanted to see how your day was going; how's it going?   Is the latter more appropriate? I mean at least it asks the question.


2 separate lights on two separate switches on one line - issue

I have an issue where the far left 12/2 coming from the circuit has been used to power a dimmer switch to a light  Carry power from light to another light  The second light is controlled by another switch at the end of the run. Issue - if 1st switch is off, the 2nd light will work from its switch. If 1st switch is on, the 2nd light wont work at all from its switch Based on the diagram is there anyway to fix this issue without current wiring setup?


Is the low-light advantage of larger sensors attributable to the sensor itself or to the larger aperture of the lenses?

Let's say I take a photo using an APS-C camera and using an FF camera, from the same position, with the same ISO and shutter speed.  Let's say I use a 50mm focal length for the FF camera. To match the field of view, I use a 50/1.5 = 33mm focal length for the APS-C camera.  Now, let's say that both lenses have the same aperture of f/2.8. But since the focal length is different (50 vs 33), the actual value of f/2.8 will be higher for the FF lens, which means it's letting in more light [1].   Am I correct in understanding that the FF system performs better not because of the sensor but actually because of the wider opening of lens? If we measured aperture in sq mm, and if I take a photo using the same actual aperture, like 20 square mm, with an FF and an APS-C camera, won't I get the same amount of noise?  In other words, the supposed advantage of the FF system is merely an artefact of the way we measure aperture, as f-numbers. If we chose to measure aperture in sq mm, the advantage of the FF sensor goes away.  I'm assuming we are comparing lenses of FF-equivalent focal length, and we don't have a mismatched system like mounting an APS-C lens on an FF body or vice-versa (unless you use something like the MetaBones Speed Booster).  There are two ways of measuring aperture:   As an f-number, which is the conventional way of measuring aperture. As a total area, in square mm.   (1) measures the light per unit area and (2) measures the total light incident on the sensor.  (1) is useful to determine aperture in relation to shutter speed and ISO (the so-called exposure triangle).  (2) is useful when you're interested in noise under low-light. Since noise is caused by lack of light, so you want to measure the total light coming in to the sensor, not the amount of light coming in per unit area of the sensor. (I'm assuming you're viewing both photos at the same size on your monitor.)  Since (2) assumes that you don't have a mismatched system, where you mount an FF lens on an APS-C camera or vice-versa (without something like the MetaBones Speed Booster adapter), and also assumes you're not comparing lenses of different FF-equivalent focal lengths, it may not be a very useful measurement of aperture in photography in general. But it helps to determine noise, taking sensor size out of the question.  Let's say you're trying to buy a camera + lens for low-light work, and you've identified two options within your budget:   An NEX body with a Sony f/2.8 lens. An Olympus µ 4/3 body with an Olympus f/2 or an f/1.4 lens.   The f-number measurement makes it hard for you to see which system performs better under low-light. Whereas, if we measured aperture in square mm, you'd instantly see which system worked better under low-light -- the one with the bigger aperture in square mm. (Again, let's assume both lenses have the same FF-equivalent focal length.)  A comment below says that it's an academic question whether we attribute the advantage of the FF system to the bigger sensor or to the wider entrance pupil of the lens. The existence of the MetaBones Speed Booster disproves that statement, since you can now mount an FF lens on a crop-factor sensor without losing light or, more formally, without having an image circle larger than the sensor. When you can mix and match FF and APS-C lenses and bodies, it's no longer academic whether you attribute the advantage of the FF system to the body or to the lens.


Equivalence of conditions for Convergence of Non-negative Random Series

Question  Let $X_n\geq 0$ be independent for $n\geq 1$. The following are equivalent.  $\sum_{n=1}^\infty X_n<\infty$ a.s. $\sum_{n=1}^\infty[P(X_n>1)+E(X_nI(X_n\leq 1)]<\infty$ $\sum_{n=1}^\infty E(X_n/(1+X_n))<\infty$   My attempt I was able to prove $(1)$ implies $(2)$ and $(2)$ implies $(3)$ but not $(3)$ implies $(1)$. For $(1)$ implies $(2)$, observe that by Borel-Cantelli $\sum_{n=1}^\infty P(X_n>1)<\infty$, else $X_n>1$ infinitely often w.p.1 so that $(1)$ is violated. To see that $\sum_{n=1}^\infty E(X_nI(X_n\leq 1)]<\infty$, apply Kolmogorov three-series theorem (I think). For $(2)$ implies $(3)$ we can write that $$ \begin{align} \frac{X_n}{1+X_n}& =\frac{X_n}{1+X_n}I(X_n\leq 1)+\frac{X_n}{1+X_n}I(X_n>1)\\ &\leq X_nI(X_n\leq 1)+ I(X_n>1). \end{align} $$ Now take the expectation of both sides and sum on $n$ using $(2)$ to conclude $(3)$. For the last implication $(3)$ implies $(1)$, I tried to use Kolmogorov three series theorem. To this end put $Y_n=X_nI(X_n\leq 1)$. First note that $\sum_{n=1}^\infty P(X_n>1)<\infty$ since $$ P(X_n>1)\leq P\left(\frac{X_n}{1+X_n}>\frac{1}{2}\right)\leq 2E\frac{X_n}{1+X_n} $$ by Markov's inequality. But I am unable to show that $\sum EY_n<\infty$ and $\sum\text{Var}(Y_n)<\infty$. Any help is appreciated.


Given the very simple integral  \begin{equation} \int -\frac{1}{2x} dx \end{equation}  The obvious solution is  \begin{equation} \int -\frac{1}{2x} dx = -\frac{1}{2} \int \frac{1}{x} dx = -\frac{1}{2} \ln{|x|} + C \end{equation}  However, by the following integration rule \begin{equation} \int \frac{1}{ax + b} dx = \frac{1}{a} \ln{|ax + b|} + C \end{equation}  the following solution is obtained \begin{equation} \int -\frac{1}{2x} dx = -\frac{1}{2}\ln{|-2x|} + C \end{equation}  Why are these solutions different? Which is correct?   The second solution can be simplified \begin{equation} -\frac{1}{2}\ln{|-2x|} + C = -\frac{1}{2}\ln{|-2|} -\frac{1}{2}\ln{|x|} + C= -\ln{\frac{1}{\sqrt{2}}} - \frac{1}{2}\ln{|x|} + C \end{equation} but they still differ.


'Your understanding my sense of humour...' vs 'Your understanding OF my sense of humour...'

Are both of the above phrases correct or only the latter?   For example, if saying, 'Your understanding (of) my sense of humour was the only thing that made the dinner enjoyable'. Is the 'of' necessary?  Similarly: 'Your support of the project was invaluable'. vs 'Your supporting (of) the project was invaluable'.   I know, in this case, use of the gerund 'supporting' would be unlikely since it sounds clumsy in comparison to 'support', but for the sake of argument I was curious whether it sounded correct to use the 'of' in the gerund phrase - to me 'Your supporting the project was invaluable' sounds more natural than 'Your supporting of the project...' but I find this difficult to reconcile with the necessary use of 'of' when using 'support' (you obviously can't say 'Your support the project was invaluable.').   I suppose, 'Your supporting the project was invaluable' could be justified grammatically since 'supporting the project' is a gerund phrase. Referring back to the first part of the question, 'Your understanding my sense humour was...' would also be correct since 'understanding my sense of humour' is again a perfectly good gerund phrase - but here, the inclusion of 'of' sounds more natural.   Curious what others would tend to use/regard as correct in these sentences (or for similar phrases)


$2^n<n!$ for some $n>3\in\mathbb Z^+$  Basic step is true with $n=4$.  So induction step assume $2^n<n!$ for some $n>3\in\mathbb Z^+$ is true.   Will show that $2^{n+1}<(n+1)!$ for some $n>3\in\mathbb Z^+$.  Consider $2^{n+1}=(2)2^n$


Weak convergence of product of random variables

Suppose $X_n$ and $Y_n$ are random variables defined on the same   probability space. Prove that if $X_n$ converges weakly to a random   variable $X$ and $Y_n$ converges weakly to a constant $c$, then $X_n  Y_n$ converges to $cX$.   I'm new to weak convergence, and I've recently learned about theorems like Prokhorov's Theorem. I'm studying for an exam, and this is one problem that I have been stuck on for some time now. I saw a similar question on this website, but it was different since the convergence was not weak convergence.   I would greatly appreciate your help in solving this problem as I revise for my exams since I have been stuck for quite some time now.


Is there a way to root an Android phone without unlocking the bootloader?

I've tried almost any method to root my ASUS ZenFone Live, but no one seems to work. Also I only need root, no unlocked bootloader (don't want to wipe data) or custom recovery (not essential ATM).


Is 'I was climbing down the road' correct?

My friend Thomas asked me to come in his home with my brother Solomon. So me and my brother were on the way to his house. Thomas called me (on the phone) while I was on my way over and asked me "where did you reach?"   Then I replied, "I'm climbing down the road". As soon as I said that sentence, my brother started laughing and pointed me out that it is not a correct sentence.   Actually at that moment I was very tired and that road was also very steep (hard slope). And I was having difficulty walking down that road. So I was trying to express my tiredness to my friend. My question is whether it is correct to use 'climbing down' instead of 'walking down' in a sentence?


NullPointerException When starting from constructor

The program is running without any error when i'm trying to start Thread from main() but Why i'm getting NullponterException when i'm trying to start Thread from constructor.  class MyThread extends Thread {      static MyThread obj;     MyThread()     {         obj.start();          for(int i=1;i<20;i++)         System.out.println("getName:"+obj.currentThread().getName());     }     public void run()    {        for(int i=1;i<20;i++)      System.out.println("getName:"+obj.currentThread().getName());    }      public static void main(String... s)    {       obj=new MyThread();     } }


Hint to find a Closed Form of $\sum_{1 \leq k \leq n}\frac{1}{k(k+1)}$

This problem is the Exercise from . The problem says      Find the a closed form of $$S_n = \sum_{1 \leq k \leq n}\frac{1}{k(k + 1)}$$   I tried these ways with no luck  Re-index and plus themself   Replace k with k + 1  From $$S_n = \sum_{1 \leq k \leq n}\frac{1}{k(k + 1)}$$ Replace k with k + 1 $$S_n = \sum_{1 \leq k + 1 \leq n}\frac{1}{(k + 1)(k + 2)}$$ Add -1 all through the inequation $$S_n = \sum_{0 \leq k \leq n - 1}\frac{1}{(k + 1)(k + 2)}$$ The range is not matched with original. So, I think I cannot go further. Replace k with k - 2  From $$S_n = \sum_{1 \leq k \leq n}\frac{1}{k(k + 1)}$$ Replace k with k - 2 $$S_n = \sum_{1 \leq k - 2 \leq n}\frac{1}{(k - 2)(k - 1)}$$ Add +2 all through the inequation $$S_n = \sum_{3 \leq k \leq n + 2}\frac{1}{(k - 2)(k - 1)}$$ The range is not matched with original. So, I think I cannot go further. Replace k with n - k + 1  From $$S_n = \sum_{1 \leq k \leq n}\frac{1}{k(k + 1)}$$ Replace k with n - k + 1 $$S_n = \sum_{1 \leq n - k + 1 \leq n}\frac{1}{(n - k + 1)(n - k + 2)}$$ Tune the inequation $$S_n = \sum_{0 \leq n - k \leq n - 1}\frac{1}{(n - k + 1)(n - k + 2)}$$ $$S_n = \sum_{-n \leq -k \leq -1}\frac{1}{(n - k + 1)(n - k + 2)}$$ $$S_n = \sum_{1 \leq k \leq n}\frac{1}{(n - k + 1)(n - k + 2)}$$ Try adding them together $$2S_n = \sum_{1 \leq k \leq n}(\frac{1}{k(k + 1)} + \frac{1}{(n - k + 1)(n - k + 2)})$$ $$2S_n = \sum_{1 \leq k \leq n} \frac{(n - k + 1)(n - k + 2) + k(k + 1)} {k(k + 1)(n - k + 1)(n - k + 2)}$$ I decide not to go further. Is this the dead end?   Plus with extra boundary  From  $$S_n = \sum_{1 \leq k \leq n}\frac{1}{k(k + 1)}$$ Add $$\frac{1}{(n + 1)(n + 2)}$$ to both side $$S_n + \frac{1}{(n + 1)(n + 2)} = \sum_{1 \leq k \leq n}\frac{1}{k(k + 1)} + \frac{1}{(n + 1)(n + 2)}$$ $$S_n + \frac{1}{(n + 1)(n + 2)} = \sum_{1 \leq k \leq n + 1}\frac{1}{k(k + 1)}$$ Adjust the inequation $$S_n + \frac{1}{(n + 1)(n + 2)} = \frac{1}{2} \sum_{1 \leq k - 1 \leq n}\frac{1}{k(k + 1)}$$ Replace k with k + 1 $$S_n + \frac{1}{(n + 1)(n + 2)} = \frac{1}{2} \sum_{1 \leq k \leq n}\frac{1}{(k + 1)(k + 2)}$$ From this point, I have no idea to go next.  Can anyone give me a clue? Every suggestion will be appreciated.


Detecting that a fraction is a repeating decimal

Given any fraction where both the numerator (N) and denominator (D) are both positive and are both whole numbers.  Without manually dividing N by D, is it possible to pre-determine if the resulting value represented in decimal would be a repeating value? (e.g. 44÷33 is 1.3333333333....)  I believe the value of N ÷ D will NOT be a repeating decimal if and only if D is any of the following   D is equal to 1 OR D's prime factors only consist of 2's and/or 5's. (includes all multiples of 10)   Otherwise, if none of the two rules above hold true, then the positive whole numbers N and D will divide into repeating decimal.  Correct, or am I missing a case?


I'm doing complex analysis out of Gamelin, and I'm stuck on a problem in section V.7 on zeros of analytic functions.  Problem:  Show that $\int_{-\infty}^{\infty}e^{-zt^2 + 2wt} \ dt = e^{w^2 / z} \sqrt{\frac{\pi}{z}}$ for $z,w \in \mathbb{C}, Re(z) > 0$.  Gamelin gives a hint to start with $z$ as a real positive number, and I was able to show this is true when $z$ is a positive real number.  But I do not see how to extend this result to general $z$.


I'm writing a formal legal memo and could not find any explicit form of writing a plural letter grade (as in the example below).  Timmy made one C. His other grades were all As and Bs. (A's and B's?)


I need to provide real-time, or almost real-time, data for SSRS and Tableau reporting. I don't want the production OLTP system to be negatively impacted by long running queries. Will running a large query on a secondary database in an availability group affect transaction performance in the primary database?


javascript regex find words contains (at) in text

I've got a bunch of strings to browse and find there all words which contains "(at)" characters and then gather them in the array.   Sometimes is a replacement of "@" sign. So let's say my goal would be to find something like this: "account(at)example.com".   I tried this code:   let gathering = myString.match(/(^|\.\s+)((at)[^.]*\.)/g;);   but id does not work. How can I do it?  I found a regex for finding email addresses in text:   /([a-zA-Z0-9._-]+@[a-zA-Z0-9._-]+\.[a-zA-Z0-9._-]+)/gi)   I think about something similar but unfortunately I can't just replace @ with (at) here.


I'm creating a C# .net WebAPI using the following route mapping   config.MapHttpAttributeRoutes(); config.Routes.MapHttpRoute(     "DefaultApiWithId",     "api/{controller}/{id}",     null,     new { id = @"\d.+" }); config.Routes.MapHttpRoute(     "UI",     "{*url}",     new { Controller = "UI", Action = "Index" }     );   I have several actions of the format /action/{name} where the name could end with a dot (.). If the dot is anywhere, but at the end of the name, the URL gets resolved properly, but if the dot is at the end, the application says The resource cannot be found.  URLs that get resolved   https://foobar.com/foo/ https://foobar.com/foo.bar/ https://foobar.com/.foobar/ https://foobar.com/......a/ https://foobar.com/./ (gets converted to https://foobar.com/)   URLs that don't get resolved   https://foobar.com/foo./ https://foobar.com/foo.bar./ https://foobar.com/.foo.bar./ https://foobar.com/foo.bar


Since all particles also show wave like nature. Do we know that which type of waves they are? I know they are matter waves but is it an electromagnetic or mechanical waves?


How do I create a cursor (.cur) image file in Photoshop CS4?

I'm using Photoshop CS4 and I need to create a .cur image.  The actual process of doing so is simple enough but I cannot find the necessary Photoshop CS4 plug-in to do so.  Can anybody help me either find the plug-in or show me how to create the .cur file without it?


Remove sudo privileges from a user (without deleting the user)

If you give a user sudo privileges how can I remove the sudo privileges and make the user become just a regular user?  I used:  sudo adduser username sudo   Now I've changed my mind.


My Dell XPSl521x is very warm. The temperature sometimes reaches 90°C. Psensor shows that the laptop is hot: it has a red colour.  What should I do?


How does quantum entanglement help us communicate?

I do understand how quantum entanglement works, but I don't understand how this can help us communicate. Just because you know the value of the other, there's no way to change it (as far as I know), so it would be the same, so you couldn't send a bit. I know there's something I'm missing, but I'd really like to understand this, so it would be very helpful. If you could, please break it down for me and maybe use an example, too. Thanks in advance! EDIT: So from what I'm getting from some of the comments, I realize that it's not exactly what I'd imagined, and you can't really send data through entangled particles.


I am having difficulty adding code fragment to my slides in beamer with listings package. My code: \documentclass{beamer} %\usepackage[utf8]{inputenc} \usetheme{Warsaw} \usepackage{listings}  \title{My slies} \author{Me } \date{October 2020}  %slide number \expandafter\def\expandafter\insertshorttitle\expandafter{%   \insertshorttitle\hfill%   \insertframenumber\,/\,\inserttotalframenumber}  \begin{document}  \begin{frame}{Slide 1}   \begin{lstlisting}[basicstyle=\footnotesize] def LosScore(y_pred, y_test):   mse = []   for i in range(len(y_test)):      mse.append(np.mean(np.square((y_test[i]-y_pred[i])))) return mse \end{lstlisting}  \end{frame}  \end{document}  Error: Runaway argument?  ! Paragraph ended before \lst@next was complete. <to be read again>                     \par  l.27 \end{frame}                  I suspect you've forgotten a `}', causing me to apply this control sequence to too much text. How can we recover? My plan is to forget the whole thing and hope for the best.


Winter Bash dropdown doesn't appear on sites I haven't joined

When I go to a site I haven't joined, I can see my personal Stack Exchange SiteSwitcher™, inbox, and reputation dropdown. However, I can't see my (or any, for that matter) Winter Bash dropdown:    Could it be put there?


How would you integrate $\sqrt{1+\frac{1}{x^2}}$

I need to integrate $\sqrt{1+\frac{1}{x^2}}$  I've tried to let $u=1/x^2$ but end up with, $\int \frac{\sqrt{1+u^2}}{u^{3/2}}du$ . I attempted to then substitute $u=\tan\theta$ and lead me to $-\frac{1}{2}\int \frac{1}{(\sin\theta\cos\theta)^{3/2}}d\theta$.  Not sure how to progress from here. Is there any alternative way of doing this?


How to make a link to a chapter in a local pdf file?

The title is self-explanatory.  Anything of that sort  \href{run:path/to/file.pdf#chapter2}{go to chapter 2 of file.pdf}   ?


is log1p the "correct" way of doing log scale transformation of charts?

when transforming data to log scale for charting purposes, is it more "correct" in some way to always transform using log(x+1) (henceforth referred to as  log1p following numpy/python convention) than with log(x) and does it break any common user expectations? I understand that log(x+1) will have better numerical stability if the numbers are close to 0, for instance if they are say a loss metric in DL. in such cases log1p could be a better choice. which of these design choices are more valid?  always use log1p to compute the transformation use some heuristic to select between log1p and log depending on the name of the metric and/or the range of values (how close to 0 the values get) put the burden on the user to select between log1p and log (I've never seen any code-free software do that)


Is it possible to get a combined flair like the ones on Area 51?  See follower list on the right side of an  for examples.


Let $R > r > 0$ and $a,b\in B(0,r)\subset R^n$ where $n \geq 2$. Construct a diffeomorphism $f$ of $R^n$ satisfying $f(a)=b, f(x)=x $ for all $||x|| > R$ and $det(Df_x) =1 $ for all $x\in R^n$.  I was trying with $f(x)=\rho(x) g(x) + x$ where $\rho$ is a bump function and $g$ is smooth function with $g(a)=b-a$. But problem is that this type of function may not be diffeomorhism and also jaccobian of $f$ is not necessarily 1.


I just started using the STM32 F401VC Discovery Evaluation board and I'm trying to get the maximum GPIO toggling frequency without assambler. So my tought process is following:  The code I was planning to use is:  #include "stm32f4xx_gpio.h" #include "stm32f4xx_rcc.h" #include "stm32f4xx.h" #include "stm32f4xx_spi.h"  void initializeGreenLed(void){     GPIO_InitTypeDef GPIO_InitStructure;      RCC_AHB1PeriphClockCmd(RCC_AHB1Periph_GPIOD, ENABLE);     GPIO_InitStructure.GPIO_Pin = GPIO_Pin_12;     GPIO_InitStructure.GPIO_Mode = GPIO_Mode_OUT;     GPIO_InitStructure.GPIO_Speed = GPIO_Speed_50MHz;      GPIO_InitStructure.GPIO_OType = GPIO_OType_PP;     GPIO_InitStructure.GPIO_PuPd = GPIO_PuPd_NOPULL;     GPIO_Init(GPIOD,&GPIO_InitStructure); }   int main(void) {     //RCC_CFGR;     initializeGreenLed();     //initialiseSysTick();     GPIO_SetBits(GPIOD,GPIO_Pin_12);     while(1)     {         GPIO_ToggleBits(GPIOD,GPIO_Pin_12);     } }   The max pin toggle frequency I get is around 230 KHz. Since the MCU can be run at 84 MHz, I have a feeling, that it's possible to increase the max toggle frequency beyond 230 KHz.  So I tought that I need to change/modify the clock source for RCC_AHB1Periph_GPIOD in RCC_AHB1PeriphClockCmd(RCC_AHB1Periph_GPIOD, ENABLE);. For that I used the STM32 F4 reference manual.  So my plan was to use PLLCLK as SYSCLK. The PLLCLK would be sourced from 8MHz HSE.  Browsing through , found a nice example:  #include "stm32f4xx_gpio.h" #include "stm32f4xx_rcc.h" #include "stm32f4xx.h" #include "stm32f4xx_flash.h"  void initializeGreenLed(void){     GPIO_InitTypeDef GPIO_InitStructure;      RCC_AHB1PeriphClockCmd(RCC_AHB1Periph_GPIOD, ENABLE);     GPIO_InitStructure.GPIO_Pin = GPIO_Pin_12;     GPIO_InitStructure.GPIO_Mode = GPIO_Mode_OUT;     GPIO_InitStructure.GPIO_Speed = GPIO_Speed_100MHz;      GPIO_InitStructure.GPIO_OType = GPIO_OType_PP;     GPIO_InitStructure.GPIO_PuPd = GPIO_PuPd_NOPULL;     GPIO_Init(GPIOD,&GPIO_InitStructure); }   int main() {    //---------------------------down is clc stuff---------------------------      RCC_DeInit();      ErrorStatus Errsts;     RCC_HSEConfig(RCC_HSE_ON);     Errsts = RCC_WaitForHSEStartUp();      if (Errsts == SUCCESS) {         //external clc is ok         RCC_PLLConfig(RCC_PLLSource_HSI, 8, 336, 2, 7);         RCC_PLLCmd(ENABLE);         RCC_GetFlagStatus(RCC_FLAG_PLLRDY == RESET);          FLASH_SetLatency(FLASH_Latency_5);          RCC_HCLKConfig(RCC_SYSCLK_Div1);         RCC_PCLK1Config(RCC_HCLK_Div4);         RCC_PCLK2Config(RCC_HCLK_Div2);          RCC_SYSCLKConfig(RCC_SYSCLKSource_HSE);          initializeGreenLed();         while(1){             GPIO_SetBits(GPIOD,GPIO_Pin_12);                 }           }     else {         //External clc no ready          while(1);     } }   But it doesn't work, as in it just stays in one state.    So I have two questions:   Why isn't my code working? If my abovementioned strategy is incorrect, how to increase the toggle frequency beyond 230 KHz?


As of December 2017, the largest known prime number was the Mersenne prime $2^{77232917} – 1$.  For such a large Mersenne prime, what are the techniques available for one to verify that it is in fact a prime?  Is it simply a matter of brute force checking, or are there other more elegant techniques available?


Intuition of the meaning of homology groups

I am studying homology groups and I am looking to try and develop, if possible, a little more intuition about what they actually mean. I've only been studying homology for a short while, so if possible I would prefer it if this could be kept relatively simple, but I imagine it is entirely possible there is no real answer to my query anyway.   As I said above, I want to gain a little deeper understanding of what the n-th homology group actually means: I can happily calculate away using Mayer-Vietoris but it doesn't really give me a great deal of intuition about what the n-th homology group actually means. For example, with homotopy groups, the fundamental group is in some sense a description of how loops behave on the object in question, and it is obvious to me why that is what it is for say, the torus or the circle. However, I have no idea what, if anything, I am actually saying about a triangulable object when I talk about it having 0-th homology group this or 1st homology group that.  The best I have been able to find online or in my limited book selection is the brief description "intuitively, the zeroth homology group counts how many disjoint pieces make up the shape and gives that many copies of $\Bbb Z$, while the other homology groups count different types of holes". What 'different types of holes' are there, roughly speaking? I appreciate that it may often be completely non-obvious what the low-order homology groups are for some complicated construction, but perhaps in simpler examples it might be more explicable. Are there (simple) cases where I could say, just from looking something like e.g. the torus, what its zero-th or first or second etc. homology group was based on the nature of the object? I guess in the zero-th case it is, as my source () above says, related to the number of disjoint pieces. Can we delve deeper than this for the other homology groups?   Any book/website suggestions would be welcomed (preferably websites as I am nowhere near a library!) - I have Hatcher but not a great deal else, and I haven't gleaned as much as I wish to from that alone. Of course I know that there is a great deal we don't know about homology groups even today, so I don't expect some magical all-encompassing answer, but any thoughts you could provide would be appreciated. I hope this question is appropriate for SE Mathematics, apologies if not! -M