Proving that any closed subset $U \subset \mathbb{R}$ is a countable intersection of open sets

I got stuck in this proof.  First, we know that if $U$ is closed, then the complement $U^c$ is open.  Therefore, what I tried to do is use one of my previous results in another question. This is, that every open set in $\mathbb{R}$ is a countable union of disjoint open intervals.  Using the previous statement, simple set theory and De Morgan's Laws, we get  $$U = (U^c)^c = \bigg( \bigcup_{x\in U^c} I_x\bigg)^c = \bigg( \bigcap_{x\in U^c} I^c_x\bigg)$$  where $I_x$ are the intervals of the open set $U^c$. My problem is that we know that the intervals $I_x$ of $U^c$ are open, and, therefore the intervals $I^c_x$ are closed, which is the opposite of what I was trying to obtain.  I know there's another answer. Nevertheless, it is completely different to what I am trying to do. I want to know why this method does not work.


I made a weapon model in blender, I can't remember exactly when or how I ended up with these edges because I made the model a few days ago, however I came back to the model to use it as something to learn how to UV map with. That's when I noticed these edges on this face, the face is not meant to be separated like this, on the other side it appears normal but on the side with the bolt two edges appear, when I try to dissolve them nothing happens, if I completely delete them the whole face disappears.    In wire frame view in case it helps:    If I fully delete one edge it makes the faces invisible but the other edge stays, as shown here:    Alright so, started messing around with the model trying to figure out what went wrong, it appears that the un-dissolvable lines appear after putting a hole in the model using the Boolean difference modifier, no idea why or how to avoid this but thought this might help in finding a way to get rid of the edges.  SOLUTION: Othoap Proto suggested that while in edit mode I select the faces that are separated by the two edges and then press "P/Seperate", by selection. The edges that where an issue then disappeared, all I had to do then was rejoin the two objects (Select the objects and press CTRl+J.) This worked for me and hopefully will for anyone else with the same issue.


Commnication between mobiles which are in range of 100 meters without using any mobile tower for free

Every mobile radiates its signal to its nearest tower during phone call.Then is it possible for two mobiles to communicate with out using any tower with in range of 100 meters or more .If it is possible then we call a person who is beside me for free of cost . Thanks in Advance.


Why is the p-value written with a supremum?

I noticed that there is a definition of the pvalue in my textbook is defined says the following:    I have no idea why it is written with a supremum. I've spent hours pondering this, does anyone have enough of a background to help me with this? Thank you!


How to include python with script package?

I'm working on rewriting a software package my employer uses for system health checks from Windows Batch to Python. Is there an easy way to include a Python 2.7 installation with this package, that can be moved around? Or will I have to install Python on the machines I'm running the scripts on each time?  I've looked into Portable Python, but it seems like more of a portable dev environment then a portable installation I can run scripts off of.


How do commitees evaluate candidates from foreign / unknown universities?

I'm asking out of curiosity / because I think the answer may be of general interest:  A bit of context: When I applied to PhD programs, I had degrees from two institutions. One (let's call it "A") is more selective and trains students a little more in depth than the other (which we'll call "B"), but doesn't really have a great international reputation (being very teaching-focused).   During interviews abroad, it felt like I was considered as a "serious" applicant because I studied in the other institution, B, which is much more famous because of its research programs, but actually didn't contribute as much to my training. Clearly, nobody had ever heard of institution A. During one of my interviews, an interviewer even saw my grades from university A, where grading is very strict, and asked me: "do you think your grades are good enough to go to [our prestigious university]?". In a live interview, I had the opportunity to explain these grades, but what about the other programs that did not invite me for interviews? I can't help but think that this kind of misunderstanding may have played a bigger role than it should have.   Fortunately I joined the program that I wanted the most. But I started wondering: what if I had only studied in institution A?  So here's the question: Those of you who, at some point, were part of selection commitees (for college, grad school etc.), how did you evaluate candidates who studied in small, foreign and/or unknown universities/high schools, as opposed to big, local, well-known universities/high schools?   In particular, how did you take into account :   Different grading standards - in institution A, the equivalent of a 70% was considered an unusually good grade, whereas in some prestigious universities, an A or a B is quite normal; that difference does not always appear on transcripts. Different curriculum structures - some universities may require that students in their first/second years take classes  that do not seem very relevant for certain grad school applications Different opportunities to perform research - this time in university B, a students would only perform research once at the end of their masters, so significant undergrad research experience is unusual and would require a lot of extra commitment Different prestige - the "best university of the country" may not be as famous as MIT or Harvard, depending on the country. For example are you familiar with the best university in, say, Kazakhstan (no offense meant, Kazakhstani friends)? Would you "trust" a degree more if it came from a more famous institution? Different academic culture - Europeans, for example, do not typically have a long list of "dean's list", "undergaduate award for (XXX)" etc.; it's simply not a thing there, so even exceptional students just don't have these. Writing SOPs is also not common in certain countries, so students are not trained to "modestly praise themselves" and might seem a little clumsy when they try to do so. Anything else?    Have you ever faced this kind of issues when evaluating candidates? Did you at any point take extra steps to make sure this kind of differences would not penalize international applicants?  Edit: this question is not entirely similar to other questions like "?". Indeed, this question focuses on applications within a single country, with a priori homogeneous definitions of what a "good" university is, with known grading standards... Answers to this question clearly assume that it is possible to define "good" and "bad" grades by looking at a transcript, for example. My questions challenges the notion that the application documents (SOP, GPA etc) are meaningful, because unless a commitee member knows the high school / university of origin of an applicant, they really have no way to tell whether grades are good or not, because standards are not uniform.


How to install XnViewMP in Ubuntu 18.04 and later

Is there a way to install Image viewer and converter XnViewMP (or Xnview and XnConverter) in Ubuntu 18.04 and later? Other described ways (, , ) seem not to work for me.


For example:  A question was closed with this:     "closed as not a real question by Will May 14 at 17:55"   It could be a UP and DOWN marker in left side of this decision. So the users could vote if it was a good or bad decision. If it receives too many negative votes, it could be reversed.


When bitbanging I2C, rather than switching the LOW/HIGH states of the pin, switch between LOW/HiZ by simply altering the DDR/DIR registers.Why is it like this? Why can't we switch LOW/HIGH states of data pin? My controller is communicating with only one slave.


Making reference using \ref{name} rather than directly name

This is continuation of . The answer by @samcarter works, but there is a loose end: making reference to Example 1 in the continuing example is done by "[myexample]". I was wondering if we can replace it with "[\ref{myexample}]" by modifying the preamble. This makes life a little easier because WinEdt then suggests a list of label after typing the first few letters. Thanks!


What I am trying to do is to set a date in my date field and also update the object. I am using the class below to do so which works just fine in my sanbox but in production I am getting this error:      System.LimitException: Too many query rows: 50001   public with sharing class updateObject{     public  List<NRProducts__c>  values;     public PageReference updateObject() {         values=[SELECT Refreshed_Date__c FROM NRProducts__c ];         for (NRProducts__c s :values){            s.Refreshed_Date__c =Date.today();          }          update values;         return null;                       }     }   VF Page:  <apex:page showheader="false" controller="updateObject" sidebar="false"> <apex:form>  <apex:commandButton action="{!updateObject}" value="Update"/> </apex:form> </apex:page>


Defining the appropriate Projected Coordinate System

I am a beginner at ArcGIS and have a technical question.  I need to assign a projected coordinate system to my boundary/polygon data in order to calculate square miles.  There are many to choose from.  Which should I be using?  Here are my geographic coordinate system details:    Angular Unit: Degree (0.017453292519943295) Prime Meridian: Greenwich (0.000000000000000000) Datum: D_North_American_1983                         Spheroid: GRS_1980                          Semimajor Axis: 6378137.000000000000000000                         Semiminor Axis: 6356752.314140356100000000                          Inverse Flattening: 298.257222101000020000   Thanks in advance for any consideration.


Why does adding a capacitor increase voltage gain?

I'm trying to get a bit of intuition when dealing with transistor amplifiers. I recently watched  , and wanted a bit more elaborate explanation about why adding the cap circled in blue greatly increases gain.   I am aware that caps block dc signal, so adding the cap shorts the ac signal to ground, but why does that drastically increase the gain?


To + verb in sentence without any other verb

From time to time I come across a sentence with to + verb, but with no other verb in it. I see it often in news titles. For example:     Squall, Tina and Lightning to appear in Final Fantasy Explorers   But what does it mean? What is the difference between this form, and that:     Squall, Tina and Lightning are appearing in Final Fantasy Explorers   The first time I saw that, I thought it was a mistake.


Location of Georeferencer in QGIS Las Palmas

I can't find the georeferencer in qGIS las Palmas 2.18


I am following a tutorial and it says to do: var original_UpdateInWater = typeof(Player).GetMethod("UpdateInWater"); var postfix_noSwim = typeof(Myclass).GetMethod("Patch_UpdateInWater");  Line 2 works, but line 1 returns null. Here is the referenced method. public class Player : Being, ISaveLoad, IInputsReceiver, IPeerWorldRepresentation {private void UpdateInWater()}  It seems to pick up the Player class correctly, unless their is a second class with the same name it is getting, but fails when it tries to get the method. What is going on? Is their some other method of getting the MethodInfo?


Why over/under-sampling could not help my model fitting?

I fit random forest to my imbalanced dataset with minority class 1. I found that the AUC under the imbalanced data was better than that of re-sampled dataset (over/under sampling). Can someone help to put forward some theoretical explanation to justify this observation or please help to point out the underlying problem which caused this spurious output?


After the wedding ceremony in Riften, before my wife left, I asked her where we should live. After I told her, me and her left and I can't find her at the house, OR at the Temple of Mara. Where can I find her?


Evaluate if series with exponential diverges or converges

The task is to evaluate for what values of $a \in \Bbb R_+$ does the series $$\sum_{n=1}^\infty \frac{a^n \times n!}{n^n}$$ converge. I've already checked with the ratio test that it converges for $ a < e $ and diverges for $a > e$, but I can't seem to find the answer what happens for $a = e$: $$\sum_{n=1}^\infty \frac{e^n \times n!}{n^n}$$  What test should I apply?


How can we define convexity in one dimension?

Definition of a convex set: A set $S\subset\mathbb R^n$ is said to be convex if for each $x_1, x_2\in S$ the line segment $\lambda x_1 + (1-\lambda)x_2$ for $\lambda\in (0,1)$ belongs to $S$. This says that all points on the line connecting two points in the set are in the set. My question is: how can we define convexity in one dimension?


I am currently stuck with the following partition function   Let the action be $$S(X, \psi^1, \psi^2) = \frac{1}{2} (\partial h)^2 - \partial^2h\psi^1 \psi^2 ,$$ where $h$ is a real function of the bosonic variable $X$, $\partial h = h'$ and $ \psi^i$ are Grassmann odd variables. The action is invariant under $$ \delta X = \epsilon^1 \psi_1 + \epsilon^2 \psi_2$$ $$ \delta \psi_1 = \epsilon^2 \partial h$$ $$ \delta \psi_2 = -\epsilon^1 \partial h,$$ with $\epsilon^i$ Grassmann odd variables.  Now Suppose $\partial h$ is nowhere $0$, i have to show that the corresponding partition function  $$ Z = \int dX d\psi^1 d\psi^2 e^{-S}= 0$$  After a change of variables $$ \hat{X} = X - \frac{\psi^1 \psi^2}{\partial h}$$ $$ \hat{\psi}^1= \alpha(X) \psi^1$$ $$ \hat{\psi}^2= \psi^1 + \psi^2,$$  such that $S(X,\psi^1,\psi^2) = S(\hat{X}, 0,\hat{\psi}^2)$ ,with $\alpha$ an arbitrary function of X, and some Grassmann integration  i get that $$Z = -\int e^{-S(\hat{X}, 0, \hat{\psi}^2) } \frac{\partial^2h}{(\partial h)^2} \hat{\psi}^1 \hat{\psi}^2 d \hat{X} d \hat{\psi}^1 d \hat{\psi}^2$$ which should be zero. But i can not see why ? I got the hint that the integrand is a total derivative in $ \hat{X}$ but that didnt help me.


I have learnt that depending on the various gases those are involved in the reaction that produces fire, different colors (yellow, red or blue) of flames become visible.  I have a question .. what are the possible colors that fire can possess? and do they (how, if yes) relate to the intensity? like I know blue is more intense than red, etc..


Light interference with light and other EM waves

Lets assume a room with one or two sources of light (normal light bulbs or fluorescent lamps). So if we look at lamp from any direction we see it. We also see different objects in the room because of light reflected from it from the source. So I would like to visualize that at any point in space inside the room there is a EM wave with a particular E and H component. Also the room might be filled with Radio waves, Microwaves and other EM waves. So at any point in space the Electric and Magnetic field components are the sum of all these individual wave components at that point.   Also if we specifically assume light then it will be sum of light directly coming from the source  and other reflected components of that light. If that being true how are we able to see clearly, meaning we are able to see individual objects in a room distinctly without any interference from these reflected component. Also how these Radio waves, microwaves etc do not impact the images we see in any way. They are just Electric and magnetic fields oscillating at different frequencies but still they will have an impact on the the E and H components of visible light at all points in space inside the room.


Is there an easy way to disable this laptop's touchpad?

Specifically, I'm on a . I'd like to disable the  so that I can re-enable if my mouse were to run out of batteries (so physically breaking the connection to the motherboard or uninstalling the driver will not be the best options). In the Control Panel, when I go to "Mouse" and find the touch pad, there is no disable option. Any ideas?  Edit: I am on Windows 7. There is a driver on the Dell site that might allow an option to disable it, but I cannot install it on Windows 7.


Does minecraft servers scale well on multi thread CPU?

I'm going to run small, heavily modded server and I can't find this anywhere. How many threads can an MC server use efficiently?  I'm choosing between 5GHz 2/4t and 4Ghz 6/12t.  Edit:  I'm asking about production data of an up to date server and if it can utilize more than 4 heavy threads. The question everybody flaging as duplicate is quite old (10 versions back) and it only tells me: How can I force JVM Garbage Collector to use more threads.  Im concerned about world loading, tick handeling, dimension handeling, entities managment and so on. Not about GC.


I am trying to make a simple request on my database, whoever, my attempts with binding something to the query doesn't work. I tried both codes and none seems to work      $query = $this->prepare("SELECT * FROM :table");     $query->bindParam(":table", $this->table);     $query->execute();     return $query->fetchAll();       $query = $this->prepare("SELECT * FROM :table");     $query->execute(array(":table" => $this->table));     return $query->fetchAll();   However, When I try to just concatenate it, it works just fine      $query = $this->prepare("SELECT * FROM " . $this->table);     $query->execute();     return $query->fetchAll();   Does anyone know what might be happening? What am I doing wrong? Is that any standard that I'm not aware here? I've done something similar before and it worked fine  OBS: The $this reffers to this:    class Db extends PDO{}


Bibliography as \section and included in Table of Contents

Previous questions ( et al.) have considered how to include bibliographies at the end chapters. This question concerns bibliographies at the end of chapters when natbib is used as a citation package.  In the preamble, I wrote  \usepackage{chapterbib} \usepackage[sectionbib]{natbib} \usepackage{etoolbox} \patchcmd{\thebibliography}{\chapter*}{\section}{}{}   with  \bibliographystyle{unsrtnat} \bibliography{biblio}   in each \include(d) file.  I ran LaTeX on the main file (test2.tex) and bibtex on each auxillary file (chap1.aux and chap2.aux), and then LaTeX again, twice, on test2.tex. This gave:   The correct style (from \bibliographystyle{unsrtnat}) The references inserted as a numbered section (from \usepackage{chapterbib) and using \patchcmd) BUT, the section that includes the references is excluded from the Table of Contents   What is the correct way to use natbib to have references placed as a section within a chapter and included in the Table of Contents? If \usepackage{natbib} is excluded, the code generates references that are included as a numbered section as well as being included in the Table of Contents, but (of course) the natbib style is not applied.  I have read the chapterbib (Arseneau 2010) and natbib (Daly 2010) reference material entirely.  Here is my minimum non-working example:  \documentclass{report} \usepackage{filecontents} \usepackage{chapterbib} \usepackage[sectionbib]{natbib} %\usepackage{natbib} \usepackage{etoolbox} %patchcmd from https://tex.stackexchange.com/questions/158871/bibliography-as-section-instead-of-section \patchcmd{\thebibliography}{\chapter*}{\section}{}{} \begin{filecontents*}{chap1.tex} \chapter{First Chapter} \section{First chapter, first section} Watson and Crick \citeyearpar{watson53} proposed the structure of DNA. \bibliographystyle{unsrtnat} \bibliography{biblio} \end{filecontents*} \begin{filecontents*}{chap2.tex} \chapter{Second Chapter} \section{Second chapter, first section} This is Einstein's famous paper \citep{einstein05}. \bibliographystyle{unsrtnat} \bibliography{biblio} \end{filecontents*} \begin{filecontents*}{biblio.bib} @article{ watson53, Author = {Watson, J. D. and Crick, F. H. C.}, Title = {Molecular Structure of Nucleic Acids: A Structure for Deoxyribose Nucleic Acid}, Journal = {Nature}, Volume = {171}, Number = {4356}, Pages = {737-738}, Year = {1953} } @article {einstein05, Title   = {{Zur Elektrodynamik bewegter K{\"o}rper}.        ({German})     [{On} the electrodynamics of moving bodies]}, Author  = {Albert Einstein}, Journal = {Annalen der Physik}, Year    = {1905}, Number  = {10}, Pages   = {891--921}, Volume  = {322}} \end{filecontents*} \begin{document} \tableofcontents \include{chap1} \include{chap2} \end{document}


What happens if I combine Ur-priest and prestige class to exceed 10 effective spellcasting levels?

Suppose I have a human character who invested 5 levels on Wizard, 2 on Ur-priest(by appropriate feat chain), and 8 levels of Mystic Theurge, net level of 15. This allows you to cast spells as stated in 10th level Ur-priest Spells per day table. Now, assume that I leveled up, and I choose Mystic Theurge as the next level class. This makes me to look up Ur-priest table for Level 11, which does not exist. In this case, what happens to my divine spells per day? Does it continue to progress "in the same pattern", as Hellfire Blast progresses with Hellfire Warlock-Legacy Champion build? Does it stop and I only get Wizard spells per day? Or, isn't it allowed to do so?  I am totally aware that although the answer is "yes", it does not mean it means spells over 9th level will be granted to my character unless I take Improved Spell Capacity, which requires me to be epic. What I am curious is the progression of spells per day of existing spells.  P. S. Don't ask me how to satisfy the requirements. This is possible by combining Apprentice (Criminal), Iron Will and Great Fortitude as level-up feat, and Spell Focus (evil) as a Wizard bonus feat (RAW, it is a "Spell Focus" feat, anyway.)


Most advisable way of checking empty strings in C#

What is the best way for checking empty strings (I'm not ) in C# when considering code performance?(see code below)  string a;  // some code here.......   if(a == string.Empty)   or  if(string.IsNullOrEmpty(a))   or  if(a == "")   any help would be appreciated. :)


My website title shows up slightly different from what's in my title tag, only in Google search

I've included my page title in the title tag in this format: " blah blah blah | sitename ". But for some reason it's showing up on Google search results as " sitename: blah blah blah ".  It shows up right on the actual tab itself, and even right on both Bing and Yahoo search, but different on Google search. Can't figure out why.  EDIT: Let me clarify: I really doubt that this is due to Google having not crawled my website yet. The title it previously had was very different from this (several different words), and the title that currently shows up on the search is not even remotely similar to my old one. Hence the confusion. And I've already submitted it and a sitemap to the Google webmasters tool.


getting started with apache mod_rewrite on a virtual host

hey SO I am attempting to use apache's  mod_rewrite module to do some basic rewrting of url on my website so they become a little more seo friendly   basically I have a virtual host file that look like this       <VirtualHost *:80>         ServerAdmin morrison.brendan17@gmail.com         ServerName mind-knowledge.com         ServerAlias www.mind-knowledge.com          DocumentRoot /var/www/tagmenu         <Directory />                 Options FollowSymLinks                 AllowOverride All         </Directory>         <Directory /var/www/tagmenu>                 Options Indexes FollowSymLinks MultiViews                 AllowOverride All                 Order allow,deny                 allow from all                 <IfModule mod_rewrite.c>                         RewriteEngine on                         RewriteRule /video/([0-9]+) /PlayVideo/index.php?videoID=13424                 </IfModule>         </Directory> </VirtualHost>   now from what I understand the rewrite rule should allow  http://www.mind-knowledge.com/PlayVideo/13424/  to be rendered as the page http://www.mind-knowledge.com/PlayVideo/index.php?videoID=13424 is this correct?  As currently I get  404 , and i have run sudo a2enmod rewrite and reloaded apache.   Can anyone help me in what I am doing wrong or suggest some ways to troubleshoot the problem thanks in advance.  brendan


What is the meaning of $\mathbf{Q}(\sqrt{2},\sqrt{3})$

I know that : $\mathbf{Q}(\sqrt{2}) = \mathbf{Q}+ \sqrt{2} \mathbf{Q}$ , but then what is $\mathbf{Q}(\sqrt{2},\sqrt{3})$?


Best singleton pattern for thread safe object

Whats the best pattern for singleton? I frequently use  + (SomeManager *)shared {     static SomeManager * _SomeManager = nil;     if (_SomeManager) {         return _SomeManager;     }      _SomeManager = [[SomeManager alloc] init];      return _SomeManager; }   Is this thread safe? If not, hot to make it safe?


Prove: $\displaystyle\liminf_{n\to\infty}(-a_n)=-\limsup_{n\to\infty}(a_n)$   My general idea was: if $a$ is partial limit (PL) of $a_n$, then $-a$ is a PL of $-a_n$ so it follows that $s$ is the maximal PL iff $-s$ is the minimal PL.   But how do you show it rigorously ?


If we use the book class, the output looks like the following screenshot.    But if we use the article class, the output looks better as follows.    The MWE is given as follows. Note: please enable -shell-escape!  \documentclass[12pt]{article}% please change to article and compare the output.  \usepackage{filecontents} \begin{filecontents*}{"article sample.tex"} \documentclass{article} \usepackage{lipsum} \begin{document} \lipsum[1-20] \end{document} \end{filecontents*}  \usepackage{showexpl}  \lstset {     breaklines=true,     breakindent=0pt,     tabsize=2,     columns=flexible,     language={[LaTeX]TeX},     basicstyle=\small\ttfamily\hbox{}, }  \newcount\x  \newcommand\MyLTXinputExample[2][2mm]{% % #1: length of gap, % #2: filename with .tex,      \lstinputlisting[caption=\url{#2.tex}]{"#2.tex"}     \bgroup         \parskip=#1\relax         \fboxsep=0pt         \pdfximage{#2.pdf}%         \x=0         \loop             \ifnum\x<\pdflastximagepages                 \advance\x by 1                 \noindent\hfill                 \fbox{\includegraphics[width=0.5\dimexpr\linewidth-4\fboxrule-#1\relax,page=\x]{"#2"}}%                                  \ifnum\x<\pdflastximagepages                 \advance\x by 1                 \hfill                 \fbox{\includegraphics[width=0.5\dimexpr\linewidth-4\fboxrule-#1\relax,page=\x]{"#2"}}%             \fi                 \hfill\null\par         \repeat     \egroup }  \PassOptionsToPackage{obeyspaces}{url} \usepackage{hyperref}  \begin{document} \immediate\write18{pdflatex "article sample"} \MyLTXinputExample{article sample} \end{document}   How to prevent book class from vertically justifying the contents? In other words, I want to use the book class but its output (only the justification is under consideration) must look like the output that article class produces.


I'm currently building a website that is not targeted to an English speaking audience. So my thoughts are that if I were to make the URLs in the language of choice (in this case Spanish) then would this help or hinder my SEO for the website? Is it always better to have english URL paths for getting picked up by search engines?


Can every test be done by automation?  Or is there anything that cannot be done by automation?


Use drush to put a site in maintenance mode

drush @mysite cget system.maintenance shows:     message: '@mysite is currently under maintenance. We should be back shortly. Thank you for your patience.'       langcode: en   Drupal 8 uses state values to record transient state, so drush @mysite sget system.maintenance_mode gives me a 1 or a 0.  But, try as I may, I cannot see how to set the boolean. I've tried:  $ drush @mysite sset system.maintenance.mode "TRUE" --format=boolean $ drush @mysite sget system.maintenance_mode 0 $ drush @mysite sset system.maintenance.mode "TRUE" --format=auto $ drush @mysite sget system.maintenance_mode 0 $ drush @mysite sset system.maintenance.mode true --format=auto $ drush @mysite sget system.maintenance_mode 0 $ drush @mysite sset system.maintenance.mode true --format=boolean $ drush @mysite sget system.maintenance_mode  0     What's the secret?


Just as the title indicates my PATH variable resets after every reboot. I read that I have to edit my bashrc file's PATH variable, but I don't have anything there that suggests anything related to the PATH variable.


Why does this wget command fail to download this file?

I was wondering why the following command fails to download a pdf file, while pasting the URL in browser's address bar can? (I am trying to learn a little about HTTP, web services, or web applications from this question)  How shall I use wget to download the pdf file?  Thanks.  $ wget https://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.99.598&rep=rep1&type=pdf [1] 5696 [2] 5697  Redirecting output to ‘wget-log.1’. [2]+  Done                    rep=rep1  $ cat wget-log --2019-11-25 13:30:42--  https://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.99.598 Resolving citeseerx.ist.psu.edu (citeseerx.ist.psu.edu)... 130.203.136.95 Connecting to citeseerx.ist.psu.edu (citeseerx.ist.psu.edu)|130.203.136.95|:443... connected. HTTP request sent, awaiting response... 200 OK Length: 5641 (5.5K) [text/html] Saving to: ‘download?doi=10.1.1.99.598’  download?doi=10.1.1.99.598                   100%[============================================================================================>]   5.51K  --.-KB/s    in 0s        2019-11-25 13:30:42 (453 MB/s) - ‘download?doi=10.1.1.99.598’ saved [5641/5641]  [1]+  Done                    wget https://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.99.598


Why the optimal classifier is called "Bayes". I do not see the connection with being Bayesian or so.  Edit: This question asks about naming. Not about math.    Another phrasing of the question:  Given that the Bayesian classifier is optimal (under certain constraints) does not explain why that particular classifier is called "Bayesian."  Why do we call such a classifier "Bayesian" rather than some other name?


How to prove that order of a field is a power of its characteristic?

How to prove that order of a field $\mathbb{GF}(q)$ is a power of its characteristic $\lambda$?  What I can say is that every field has a subfield of order $\lambda$ if it helps


I have ran these codes:  sudo chown -R / sudo chmod 755 /   And now my server is not working. I need to get backup copy of MySQL database How can I fix it?


Like materialise is to turn something into real. Is there a word to mean turn something into money?  e.g. Please don't give me any medal, I would rather want you to [the word] it.  Bet there is no moneilise?


Which process knows what applications are open?

I'm trying to find the process that takes care of what applications are open. For example, an app I closed stills shows as open in Dock and Force Quit, so I want to kill/restart that process (which takes care of what processes are open). Logging out would solve it too, but I can't right now. Restarting Dock does not work.  For example, I'm 100% sure I have killed Safari, using kill -9, but it still shows up in the Dock and in Force Quit. The process is definitely killed, but the Dock and Force Quit haven't got that, because the process that lists which applications are open have frozen. I want to know the name of that process.


Save static version of a webpage to be available offline

Is there a way to save a webpage as static HTML, available for offline viewing, editing etc.?  I want to remove all JavaScript files. Leave only HTML, CSS and images.  For example, if this web page has a Facebook Like button, I want the image of the button to be part of the HTML as a regular image (and not be loaded as some JavaScript code runs after I load the page).  I'm trying to prepare a webpage for an offline demo. When I use the standard "save as HTML complete" like tools, all the JavaScript is saved as well, and when viewed offline, all the dynamic content is blanks.  Note- I don't expect the dynamic content to work, of course, with no JavaScript. I just want the web page to LOOK as though it was just loaded from the interwebs.


Enumerating integer solutions to quadratic equations

Consider a quadratic equation with integer coefficients in two variables.  $$ax^2+bxy+cy^2+dx+ey+f=0$$   I would like to know how to find the number of integer solutions $(x,y)$ to this equations. Is there some closed formula?


SFDX error for LiveChatTranscript object

I have added LiveChatTranscript object in my unlocked package but while versioning getting error  LiveChatTranscript: Invalid fullName, must end in a custom suffix ( for ex. __c )  Can anyone help me to resolve this error.


How to transfer only several apps data from old iPhone to new iPhone?

I just buy new iPhone. I want to transfer only Whatsapp chat history, and none of all the other apps. I want to start with clean slate. I don't want to going through each app to delete them one by one on the new iPhone. But I still need all the Whatsapp chat history. How can I do that using  Finder? I presume I have to use the backup on Finder to backup just the selected app (Whatsapp), and then use the backup to restore on the new iPhone. But how do I do that (backup just the selected app)? I don't see any selection on the Finder iPhone management to do that. Only "Back Up Now" button.


Do we always use "were" with the 3rd person in imaginary situations?

Do we always use were with the 3rd person in imaginary situations?   If only she were here ...  If only she was here ...    Are we supposed to use were every time there is an if in the beginning of a sentence?


What happens to a short seller, who wants to close his position, but there are no shares available for sale?

For the sake of argument, let's assume a scenario, where the company is very illiquid, and there are no shares for sale and even increasing the buy order doesn't produce sellers. What happens to the short seller, who wants to cover his short position in this scenario?  Or a second scenario: A company like Tesla goes private. The short sellers are not able to buy enough stock in time and they end up unable to cover their short positions.  Does something like this need to be settled between the lender and the shorter or is there a mechanism for this type of situation?


I came across this on the internet. What is the correct form? Singular or plural?  "Here is a pen and a ball."  or  "Here are a pen and a ball."  And please give me your thoughts on the contradiction in 'Here's some ideas about what you can do:'  Does it mean 'here are' or 'here is'? Thank you.


How to use biblatex with IEEE bibtex style?

http://mirrors.ctan.org/macros/latex/contrib/IEEEtran/bibtex/IEEEfull.bib   defines a bibliography style.  How to use that if I want to use biblatex to format my bibliography?


How to Convert 0 to 10V analog signal to 0 to 2.5V for ADC input?

I have an analog signal which ranges between 0V and 10V.  I want to linearly scale it down to 0 to 2.5V for my ADC.     I'm concerned that using a resistive voltage divider will affect signal quality.  Is this true?  If it's not true, what value resistor should I use for voltage divider?


How can i see a statistics about when the number of views increased over time?  I would like to find out if at a certain date there were a significant increase of views to one of my "famous" questions.


A word the encompasses errors, issues and inaccuracies

I'm writing a document on software testing and am looking for a word that means errors, misunderstandings and inaccuracies. For example when testing you are looking for an error e.g. error in formula, or misunderstandings in the data you are using or that the data is inaccurate. All of these will negatively affect the end results. The sentence reads " We will be looking at three types of ______ covering ...." Is there such a word or phrase, would it be 'issues'?


Why are mirrorless cameras much slower than DSLRs?

This is a follow-up to a .  I've been comparing cycle times (or shot to shot times in single shot mode) of mirrorless cameras with interchangeable lenses with traditional DSLRs and all of them, even the highest end ones (like the Olympus OM-D EM-5 or Panasonic GH3) are slower than even entry level DSLRs.  How's that possible? The electronics should be the same and they don't have the burden of a mirror going up and down between each shot. I think that there must be a technical reason for that (maybe some cpu time is going to feed the live-view before the image is encoded?), because from a commercial point of view it does not make sense.  I've seen the cycle times under the performance tab in the reviews pages of .  The average CSC has cycle times around 0.7~1.2s, the flagship ones around 0.5s. The average DSLR has cycle times around 0.4s and the flagships around 0.25s.


I got virus on my computer. This is a list of executables of the virus:  Name              |Size  |Description ------------------+------+-------------  B06A.exe          |162   |B06A D3F2.exe          |217414|wYtRBdGyks E3DA.exe          |357190|TWunHOlqmZ NTDETECT.COM      |177152|Mail.Ru Агент ScreenSaverPro.scr|177152|Mail.Ru Агент temp.bin          |177152|  (none) ViewFiles.cmd     |177152|Mail.Ru Агент Zafgff.exe        |177152|Mail.Ru Агент   I have found the virus had done the following, but I haven't find actual damage yet:   Folders in my USB disk became hidden and system. Links with the same name with those folders were spawned. Clicking those links cause virus to run. Registry HKEY_CURRENT_USER\SOFTWARE\Microsoft\Windows\CurrentVersion\Run was set to run this virus when I login.   Do anyone know this virus? What does it actually do? Or is it a new one? How can I report it?


What is the difference between HAL and udev?

As far as I understand, if I have 3 different network cards, then HAL will cal each of them eth0, eth1 and eth irrespective of their brands, manufacturerers etc. But it seems to me that udev precisely performs similar operations based on its rules. What is their essential difference(except that HAL is deprecated)?


Shell script runs with bash but not with sh. Why and how to fix it?

I have the following shell script that sums up all the arguments passed to it (space separated):  sum=0 for arg in "$@"; do     (( sum += arg )) done echo $sum   I have saved it as SumAll.sh. So, its supposed to function as follows:  sh SumAll.sh 2 4 6 8 20   or  bash SumAll.sh 1 -2 3 -3 -1   Both work on my local machine (MacBook), but when I try the same in a linux server, running the script with bash works, but with sh does not work. I get the following error:  sum: '+=': No such file or directory sum: arg: No such file or directory   Why is that? And how do I fix it?


Migrating Thunderbird Profile from Windows 7 to Ubuntu

I'm very new to this. I've trawled the forums to try to find out how to set up Thunderbird in Ubuntu and transfer my existing profile from Windows but I can't work it out. Please help.   Step-by-step instructions like you're talking to the impaired (because you are)  would be most appreciated.


What is the best techniques to photograph large rugs?

I am trying to take pictures of small and large rugs. I have Canon 6D with 24-70mm lens. Could you please suggest the best way for mounting the camera to the ceiling, and any other recommendations for my camera/lens setup?  The ceiling has steel supports with height around 12ft (3.6 metres).  There are about 4000 rugs, small and too large. the use case for photos is for uploading in website for customers


Redirect port 80 to 8080 and make it work on local machine

I redirected traffic for port 80 to 8080 on my machine with  sudo iptables -A PREROUTING -t nat -p tcp --dport 80 -j REDIRECT --to-ports 8080   It works fine for all the world except my own machine. I am a developer and I need to redirect port 80 to 8080 for myself.  My IP is 192.168.0.111  My web server runs on port 8080  I wish to open website from http://192.168.0.111/ instead of http://192.168.0.111:8080/ from same machine where server runs.


How do I find the   How do I find the transfer function of Gd(s)?  I am able to find the transfer function of Gr(s) but I am not really sure about Gd(s)? and how do i determine which order is this closed system?


How I can wrap the rope around cylinder?

I want to wrap this rope, based on curve around cylinder:


How to trigger one app from another app in iOS Swift

I want create an app using ios Swift, where first app can launch second app on click of the button. I am able to launch web Url's on click of the button but not the application. Please guide me through how to provide the URL scheme for the same.  Thanks in advance.


What is the degree of the zero polynomial and why is it so?

My teacher says-     The degree of the zero polynomial is undefined.   My book says-     The degree of the zero polynomial is defined to be zero.    says-     The degree of the zero polynomial is $-\infty$.   I am totally confused and want to know which one is true or are all true?


Is there a way of proving that if $A$ is an infinite set and $x\not\in A$ then $|A|=|A\cup\{x\}|$ without relying on the axiom of choice.

Let $A$ be an arbitrary infinite set and $x\not\in A$. I want to find a bijection between $A$ and $A\cup\{x\}$.  Proof 1: A possible proof of that is to play with cardinal numbers as follows: Let $\kappa,\lambda$ be cardinal numbers such that $\kappa$ is infinite and $\lambda\leq \kappa$. Then  $$ \kappa\leq\kappa+\lambda\leq\kappa+\kappa=\kappa $$  and hence, Schroeder-Bernstein Theorem implies that $\kappa+\lambda=\kappa$, which for $\lambda=1$ implies the desired result.  Proof 2: Another way of proving it is the following: We know that since $A$ is infinite there exists a countably infinite proper subset of $B\subseteq A$. Then, it is easy to see that $B$ can be partitioned as $B=B_{1}\cup B_{2}$, where $B_{1},B_{2}$ are countably infinite subsets of $B$. In particular, there exists a bijection $g:B\to B_{1}$. Hence, by writing $A=B\cup(A\setminus B)$, we see that the map $f:A\to B_{1}\cup(A\setminus B)$ where  $$ f(x)=\left\{\begin{matrix} x, & x\in A\setminus B \\ g(x), & x\in B\end{matrix}\right. $$  is a bijection between $A$ and its proper subset $B_{1}\cup(A\setminus B)$. Then, using this fact we proceed of proving the desired result. Let $C\subseteq A$ be a proper subset of $A$ such that $|C|=|A|$. Let $h:A\to C$ be a bijection. Let also $y\in A\setminus C$. Obviously, we have that $|A|\leq|A\cup\{x\}|$. For the other direction observe that the map $f:A\cup\{x\}\to A$ where  $$ f(a)=\left\{\begin{matrix} h(a), & a\in A \\ y, & a=x\end{matrix}\right. $$  is 1-1 and so $|A\cup\{x\}|\leq |A|$. Then, again from Schroeder-Bernstein Theorem, we derive the equality.  Question: My question is whether I can prove this fact without relying in the axiom of choice. I know that Schroeder-Bernstein Theorem is independent from AC but the proofs of the facts:   if $\kappa$ is an infinite cardinal then $\kappa+\kappa=\kappa$, and if $A$ is an infinite set then it contains a countably infinite proper subset   rely in AC (as far as those proofs that I know). However, it seems to me that the statement $|A\cup\{x\}|=|A|$ is very simple to rely in AC and can be proven without it, though I may be completely wrong. Any comments?


Is there a way to calculate the time taken by a falling object to reach terminal velocity?

I know it is possible to calculate terminal velocity using air density, mass, and drag coefficient, but is there any way to calculate the time taken until that speed is reached (assuming air density is constant for simplification purposes)?


How to stop the pointer jumping around due to the touchpad?

When searching for solutions to cursor jumping around, I found a lot of references to touchfreeze - a package that disables the touchpad while typing. But it is no longer part of any repository that I can find. All links to it are invalid.  How can I disable the touchpad while typing?


How do I pipe each command given to the shell?

I'd like to edit my .bashrc so that every command executed on the shell is piped to something, for example:   $ sudo apt update   _________________ < sudo apt update >  -----------------     \   ^__^      \  (oo)\_______         (__)\       )\/\             ||----w |             ||     ||   I have managed something rather similar, but not entirely:  $ bash $ exec > >(cowsay) $ echo "Hello AU!" $ exit  _______ < Hello AU! >  -------     \   ^__^      \  (oo)\_______         (__)\       )\/\             ||----w |             ||     ||   It is not the desired result, as it only happens after exiting the current shell.  It's mainly for fun/learning purposes.


What's an easy way to view formatted Markdown files?

When I tap spacebar on a .markdown file in the finder, Quick Look shows me a very nicely formatted view of that file. But the view doesn't act like a normal window, I can't select text from it, etc. All the apps I have that can open Markdown files show them in edit mode, without the pretty formatting.  Short of buying an app like , is there some way to open Markdown files with pretty formatting?


normality of subgroup of odd prime index

It is known that any subgroup of a group having index 2 is normal. Note that here 2 is a prime.   Is such a result true for some other odd prime ?. That is, "does there exist an odd prime $p$ such that whenever a subgroup $H$ of a group $G$ has index $p$, then $H$ is normal in $G$ ?"


How to save temporary variables in Google Sheets formula?

I'm trying to create a formula in a Google spreadsheet which looks like this:  if (x < 0, x + 1, x)   It means if x is smaller than 0, return x + 1, else return x.  However, x itself is an expression, e.g. A1 + B1. So I ended up with:  if ((A1 + B1) < 0, (A1 + B1) + 1, (A1 + B1))   How can I save the expression (A1 + B1) into a temporary variable x such that I can do this? :  x = (A1 + B1); if (x < 0, x + 1, x);   The current expression in my spreadsheet looks like this:  if(     timevalue(Sheet1!$D10)-timevalue(min(filter(Sheet1!$D$2:$D$99,Sheet1!$A$2:$A$99=A10,Sheet1!$E$2:$E$99=E10))))     < 0,     1 +     timevalue(Sheet1!$D10)-timevalue(min(filter(Sheet1!$D$2:$D$99,Sheet1!$A$2:$A$99=A10,Sheet1!$E$2:$E$99=E10))))     ,     timevalue(Sheet1!$D10)-timevalue(min(filter(Sheet1!$D$2:$D$99,Sheet1!$A$2:$A$99=A10,Sheet1!$E$2:$E$99=E10)))) )   I'm trying to get it to look shorter and more manageable like this:  x = timevalue(Sheet1!$D10) - timevalue(min(filter(Sheet1!$D$2:$D$99,Sheet1!$A$2:$A$99=A10,Sheet1!$E$2:$E$99=E10)))); if(     x     < 0,     1 +     x     ,     x )


Method of finding all non-trivial homomorphism $\mathbb{Z_{14}}\rightarrow \mathbb{Z_{21}}$

I have the following question :  Find all non-trivial homomorphism $\mathbb{Z_{14}}\rightarrow \mathbb{Z_{21}}$  I wonder how to solve such problems when the groups are pretty big to check the definition of each possibility.  Any ideas?  Thank you.


How to explain mismatch between the Announced size and real size on my USB?

I am struggling with this free space issue on my USB  sudo f3probe --destructive --time-ops /dev/sdd    shows   Good news: The device `/dev/sdd' is the real thing  Device geometry:              *Usable* size: 14.65 GB (30728832 blocks)             Announced size: 14.65 GB (30728832 blocks)                     Module: 16.00 GB (2^34 Bytes)     Approximate cache size: 0.00 Byte (0 blocks), need-reset=no        Physical block size: 512.00 Byte (2^9 Bytes)  Probe time: 4'36"  Operation: total time / count = avg time       Read: 547.7ms / 4814 = 113us      Write: 4'33" / 4192321 = 65us   On the other side df -h output   Filesystem                      Size  Used Avail Use% Mounted on  /dev/sdd                        1,9G  1,4G  442M  77% /media/miki/05DB-E2AB     file -s /dev/sdd /dev/sdd: DOS/MBR boot sector, code offset 0x58+2, OEM-ID "mkfs.fat", sectors/cluster 8, Media descriptor 0xf8, sectors/track 32, heads 64, sectors 3815136 (volumes > 32 MB), FAT (32 bit), sectors/FAT 3720, reserved 0x1, serial number 0x5dbe2ab, unlabeled   And  mount | grep /media/miki/05DB-E2AB /dev/sdd on /media/miki/05DB-E2AB type vfat (rw,nosuid,nodev,relatime,uid=1000,gid=1000,fmask=0022,dmask=0022,codepage=437,iocharset=iso8859-1,shortname=mixed,showexec,utf8,flush,errors=remount-ro,uhelper=udisks2)   How to explain this?  How can I know the free space?


I am using Ubuntu 12.10.  Please outline the different ways I can upgrade to 13.04.


I want to calculate a customer age based on his birth date.   public List<ProductView> GetProductsByStoreAndCategoryID(string storeId, string categoryId) {     Authenticate();     int _storeId = Convert.ToInt32(storeId);     int _categoryId = Convert.ToInt32(categoryId);      //selecting customerid     var _customerId = (from cs in context.customerstores.Where(cs => cs.StoreId == _storeId && cs.IsDefault.Equals(true)) select cs.CustomerId).FirstOrDefault();      //getting customer date of birth for calculating age and excluding regulated product from the list     var _DateOfBirth = (from c in context.customers.Where(c => c.CustomerId == _customerId && c.IsBlocked.Equals(false)) select c.DateOfBirth).FirstOrDefault(); }   Here I am getting the date of birth, after that I want to calculate age based on that date of birth. How to do that?


Which odd primes can divide the integers of the form $k^2-5$ ?   My try: odd prime means $p>2$ and if $$p\mid k^2-5$$ then $$k^2\equiv5 \mod p$$ hence 5 is quadratic residue mod p


I have cooked a kilo of black eye beans and made a meal with half of them. I intend to freeze the rest (the other half) to make another meal next week and freeze them for later meals. This last step means that the frozen beans are going to be cooked and refreeze them again. Is this procedure a safe one to take? I regularly cook full meals and freeze them in portions for later meals but not from already frozen ones.


I know this question asked here before, and I've seen all your answer but it didn't  work with me  just \includegraphics[width=0.8\textwidth,natwidth=610,natheight=642]{first.png}work, but if I do that then I can't control on the position of graph, so could you help ?


this most likely has a very simple answer but i can't find the answer anywhere online. I'm trying to get the reflection from the standard blender hdri on an object. It shows it perfectly in Look Dev mode, but in Rendered it just doesn't show up. I tried shifting the lighting, increasing light strength, etc etc. basically everything i could find but it's just not changing. What am I doing wrong?


I noticed that when I plug in an external NTFS HDD something is reading it and it doesn't stop for a long time... I checked with fs_usage and saw this:  23:26:54.189404  read              F=5    B=0x28                                                                                0.000048 W tuxera_ntfs.242048 23:26:54.189465  writev            F=5    B=0x80                                                                                0.000007   tuxera_ntfs.242048 23:26:54.189476  getattrlist                            /Volumes/REDSTAR/Kindle/Kindle books/Dean R. Koontz/Shadowfires (880)                                                                         0.000093 W mds.242039 23:26:54.189490  getattrlist                                 /Volumes/REDSTAR/Kindle/Kindle books/Dean R. Koontz/Shadowfires (880)                                                                       0.000008   mds.242039 23:26:54.189511  read              F=5    B=0x28                                                                                0.000046 W tuxera_ntfs.242048 23:26:54.189540  writev            F=5    B=0x80                                                                                0.000006   tuxera_ntfs.242048 23:26:54.189549  getattrlist                            /Volumes/REDSTAR/Kindle                                                                                0.000054 W mds.242039 23:26:54.189579  read              F=5    B=0x28                                                                                0.000038 W tuxera_ntfs.242048 23:26:54.189616  writev            F=5    B=0x80                                                                                0.000006   tuxera_ntfs.242048 23:26:54.189626  getattrlist                            /Volumes/REDSTAR/Kindle/Kindle books                                                                                0.000066 W mds.242039 23:26:54.189656  read              F=5    B=0x28         etc.  So the Tuxera driver is scanning the drive each time. Why? Is this normal?  UPDATE: it's not Tuxera's fault... it's Spotlight indexing the drive via a Tuxera NTFS driver


What word or phrase best communicates the idea that a human (or other sentient being) is easily swayed, particularly between moral good and evil? Words I have found that are close are:   Impressionable - Easily influenced because of a lack of critical ability.   Implies that the subject lacks critical skills, and misses the concept of good and evil.  Gullible - Easily persuaded to believe something   Misses the concept of good and evil    I created a typical angels and demons scenario to demonstrate the polar extremes of the the spectrum. In this scenario, I lack the word to describe the humans, who can be influenced towards either end of the spectrum if impressed upon by an external entity.     The angels are devoted to good, and are immovable in their ideals. The demons are wicked, and will feign morality only to manipulate others. Both prey upon the humans, who are ____________.   I think that the key here is the spectrum of good an evil. Here are examples of other spectra and their associated words, for comparison.   Easily pushed from calm to angry: Temperamental Easily moved from determined to hopeless: Weak-willed Easily influenced by propaganda:


I have a class named Point that overloading "==" and "!=" operators to compare two Point object. How can I compare my Point object with "null", this a problem because when I call ==  or != operator with null a problem inside Equals method. Please open a console application and see what I want to say.How can  I fix it.   public class Point     {         public int X { get; set; }         public int Y { get; set; }           public static bool operator == (Point p1,Point p2)         {             return p1.Equals(p2);         }          public static bool operator != (Point p1, Point p2)         {             return !p1.Equals(p2);         }           public override bool Equals(object obj)         {             Point other = obj as Point;              //problem is here calling != operator and this operator calling  this method again             if (other != null)             {                 if (this.X == other.X && this.Y == other.Y)                 {                     return true;                 }                 return false;             }              else             {                 throw new Exception("Parameter is not a point");             }         }     }  class Program     {         static void Main(string[] args)         {             Point p1 = new Point { X = 9, Y = 7 };             Point p2 = new Point { X = 5, Y = 1 };              p1.X = p2.X;             p1.Y = p2.Y;              bool b1=p1==p2;              Console.ReadKey();         }     }


Gradient of a quadratic form — row or column?

I am taking derivative of  $$X^TAX, X \in {\rm I\!R}^n$$  using Frechet Derivative where  $$f(x + h) = f(x) + <\nabla f(x), h> + O||h|| $$.   So I have   $$f(x + h) = X^TAX + X^TAh + h^TAX +h^TAh$$   and with the two terms in between, I have   $$<X^T(A+A^T), h> $$  and I think this $X^T(A+A^T)$ is the derivative of $X^TAX$. However, since $X$ is a $n \times 1$ vextor, while $X^T(A+A^T)$ is a $1 \times n$ vector. Am I doing anything wrong here? I saw some matrix calculus instructions also have this answer. I don't know what is happening.   So the problem is if I am doing gradient decent, I will have to do $x - \nabla f(x)$, but the dimensions don't match, so I think there must be something wrong.


Combinatorial Proof Of A Number Theory Theorem--Confusion

I came across a combinatorial proof of the Fermat's Little Theorem which states that    If $p$ is a prime number then the number ($a$$p$-$a$) is a multiple of $p$ for any natural number $a$.  Let me write down the proof.    PROOF  We have pearls of $a$ colours . From these we make necklaces of exactly $p$ pearls .   First,we make a string of pearls . There are $a$$p$ different strings.If we throw away  the $a$ one one -coloured pearls  ($a$$p$-$a$) strings will remain.We connect the ends of each string to get necklaces.We find that two strings that differ only by a cyclic permutation of its pearls result in indistinguishable necklaces.But there are $p$ cyclic permutations of $p$ pearls on a string . Hence the number of distinct necklaces is    [($a$$p$-$a$)/$p$].  Because of this interpretation this is an integer.Thus ($a$$p$-$a$) is a multiple of $p$ for any natural number $a$. [HENCE PROVED]     MY CONFUSIONS    What is the use of the fact that $p$ is a prime in this proof?  If this proof is true then why is this not true for every positve integer $p$?


Switched from bash to zsh and now I can't login as root

I have changed my shell from bash to zsh and set it as default in Ubuntu 20.10 and now every time I run the command su i get this: su Password: (entered correct password) su: Authentication failure  Does Anyone knows why?


Given a matrix A of order $n$, then how many possible order of minor's exists and how to calculate it

Let A be a square matrix of order 3 over $R$ then minor of $a_{11}$ is determinant of the square submatrix of order 2 which is the result of leaving $1st$ row and $1st$ column, like that we calculate minors of all elements of matrix A, so there are $9$ minors of order $2$, similarly minor of order $3$ in A is the determinant of A, also does there are minor of order $1$ in $A$? My questions are "for an n by n matrix"  what are the possible order minors and how to calculate those?


My two original controllers no longer connected to my ps4 so I set out and bought a brand new controller, in which then that controller will not connect to the console either. It will only flash for a few seconds then return to orange, I have searched numerous forums for answers and none have worked, I have also callled PlayStation but they said only my two older controllers could be damaged but doesn’t explain the new controller problem, please help.


What happens to wheels of a car moving near speed of light?

Let's take a standard ACME Thought Experiment Division car with a max speed of a leisurely, constant 0.75c in a straight line.  So, for an external observer, the body of the car behaves like a typical Thought Experiment Car, it's shorter than at rest, the dashboard clock goes slower than the clock in the observer's pocket, and so on.  Thing is, the car uses oft-neglected in thought experiments, wheels.  The surface of the wheel in contact with the road surface remains at rest relative to the road (friction etc). But from the classical mechanics point of view, the upper surface of the wheel would be moving at 1.5c relative to the ground (and the external observer). Obviously this is impossible.  What gives? What shape will the wheels be to the external observer? Will they shatter as the shearing forces grow towards infinity? What shape will they have to the driver of the car?    Just to avoid trivial answers ( e.g. "wheels explode in all directions torn apart by centrifugal force") let's impose some limits:  The wheels are extremely (though, let's say, not infinitely) durable, and quite (though not infinitely) flexible and stiff: you need a very strong force to distort them - certainly more than the their centrifugal force alone. And once that force is exerted it doesn't instantly break them - they distort flexibly for an observable while before an eventual critical failure.  They move over the surface without slipping, and the car's motor provides just enough torque (if any) to keep the car moving at constant speed despite any flexibility/friction/other forces the wheels might exert on it; the car retains its 0.75c no matter what the cost to the wheel integrity or such.


Best Statistical Test for Median Comparison

I just have a very quick question on some data I have. I was asked to collect data for tumor emergence in two groups of mice. One treated with PBS and another treated with PBS plus Matrigel. The one with matrigel had a median day appearance of 183 days post implantation, while the PBS one had a median day appearance of 298 days post implantation. How would I test if the medians between the two is significant. I know what tests to use for the mean number of days, but my PI wants the median number of days and the corresponding significance of the difference between the two groups. Searching online it seems like the Mann-Whitney U test would be appropriate, but some are saying that it isn't meant purely for medians. The data I have is quite simple and I'd like to do everything on excel if possible. See below  Thank You!


How can I create an advanced addon with a GUI and multiple settings for Blender 2.8x?

How can I create an advanced addon for Blender 2.8x that is displayed in the n menu (right panel of the viewport) with multiple settings. What are the most important GUI scripts, how to add settings, how to access settings between multiple files, how to add icons, how to read the documentation to find lines of code?


using lapotop as hotspot using windows 7

I'm using windows 7 with a wireless internet connection and i want to share the internet to mobile devices.for this I set a "set up a new connection or network " in network and sharing centre in control panel but it's not working.is there any other possible ways to share the network.


Is there a way to generate individual uniformly distributed points on a sphere from a fixed amount of random real numbers per point?

The obvious solution of Lattitude & Longitude doesn't work because it generates points more densely near the poles, and the other thing I came up with (Pick a random point in the unit cube, if it's in the unit sphere map it to the surface, and restart if it's outside) doesn't always find a point within a fixed number of tries.


Let $f$ be a function which is continuous on an open interval $I$. Let $c$ be a point of $I$. Suppose that $f$ is differentiable at every point of $I$ other than $c$, and that $\displaystyle\lim_{x\to c} f'(x)$ exists. Let $L$ denote this limit. Prove that $f$ is differentiable at $c$, and that $f'(c) = L$.   If $e > 0$ is given, choose a $\delta > 0$ such that $|f'(x)-L|<e$ whenever $e \in I$ and $0<|x-c|<\delta$. Now I need to apply the mean value theorem. Can someone help?


In most languages, the word used for a single caryopsis seed is a good equivalent of grain — it is not only the translation for this kind of seeds, but also the translation for other meanings of the word, such as a grain of sand. In English, this is used for grain of rice and other cereals, and even for botanical non-grains like amaranth. But then suddenly, other similar seeds are called by other words whose primary meaning is much less suited than that of grain. The examples I have in my head are kernel of maize and wheat berry.   Why this strange mixing of words? A grain is well aligned with maize and wheat not only in its meaning as a caryopsis seed, but also the other meanings like grain of salt exhibit some similarity, as this is a single very small discrete dry piece of something encountered as a large mass, which has fluid-like dynamics as a whole (you can pour salt, and you can even have phase separation with two different sizes of grains). Many other languages follow this logic.   A kernel as I understand it is something which is at the middle of a thing, somehow giving it definition. If you want a look at it, you have to extract it from its outer layers. Also, there is definitely only one of it, just like a human has many bones, but only one skeleton. This is true to some extent for both “normal” plant kernels (like peach kernels) and the new meaning of an OS kernel. I think that the mathematical meanings of kernel follow this metaphor, like the kernel of a matrix. But maize — which should logically have grains — has kernels, which are unlike all the other objects I have heard being called kernels.   A berry is a word I like, too. While I am aware that botanically, the fruits we call berries belong to different categories of fruit, they have very similar culinary properties. They are always juicy, taste best when raw, combine a sweet and a sour taste, are small, not starchy at all, and make good jams. The color is also mostly somewhere between red and blue. But they don't have a shape in common — compare the classically heart-shaped strawberry, the round blueberry, and the agglomeration called a raspberry. And then we have wheat, which differs from true berries in all points I listed — and somebody calls its grains wheat berries.    Edit: I was probably too mired in descriptions to state the question clearly. While there probably isn’t an all-encompassing reason for all existing cases (but if there is one, I’ll be glad to hear it), I’d like to hear the reasons for the two specific cases I listed, as in kernel of maize and wheat berry. Why was an exception made for exactly these two, and why was the specific word chosen for them?


how do I use the fourier series formula to find the fourier series for this function?$f(x)=\frac12(\pi-x), 0 \lt x \lt 2\pi$

Find the fourier series representation of  $$f(x)=\frac12(\pi-x), 0 \lt x \lt 2\pi$$ to calculate $a_0, a_n \text{ and } b_n$ I have to use the integrals $\int_{-L}^L$ but is $-L=0 \text{ and } L=2\pi \text{  or is } -L=-\pi \text{ and } L=\pi$ for this problem? I think the period is $2\pi$ I am not sure if I use the bounds of the interval as the bounds of the integral or the fact that the period should be 2L?


how to run .jar software on ubuntu (17.04)?

Despite following  for .jar file :   java -jar imker-cli.jar   It doesn't work for me :   me@pc:~/Documents/imker$   java -jar imker-cli.jar The program 'java' can be found in the following packages:  * default-jre  * openjdk-8-jre-headless  * gcj-4.8-jre-headless  * gcj-4.9-jre-headless  * gcj-5-jre-headless  * gcj-6-jre-headless  * openjdk-9-jre-headless Try: sudo apt install <selected package>   What is going on ? What should I do to run this .jar file ?


I am reading Schwartz's book on Quantum field theory. In the chapter anomalous magnetic moment (chapter 17) he mentions that Dirac equation naturally implies that the electron spin $g$-factor is 2. Can anyone please explain why does the Dirac equation implies that $g_s=2$?


So me and my friends downloaded pokemon go yesterday.  We got drunk, walked 3km and found 0 pokemon, not even one pokemon showed up in the 'pokemon near you' thing.   Is this normal for remote areas?(nearest pokestop is ~15km away)  Thanks.


how to set static ip from bash scriptlinux

I want to set static IP using bash script what I would to achieve I want to set the same IP to static which is come from DHCP, for example, my eth0 set to DHCP and it picks IP 51.89.84.82 for eth1 it pick 10.0.0.1 I want to set the same IP to static how can I achieve this in centos7. 1 ) find interface name and its ip , subnet mask , gateway. 2 ) loop each interface and set the same ip , subnet and gateway.


Hint on computing the series $\sum_{n=2}^\infty \frac{1}{n^2-1}$.

I'm supposed to determine whether this sum diverges or converges and if it converges then find its value:  $$ \sum_{n=2}^\infty \frac{1}{n^2-1}. $$  Using the comparison test I eventually showed that this converges.  But I can't figure out how to show what this sum converges to.  The only sums we actually found values for in my notes are geometric series which this clearly isn't.  I saw that I could use partial fraction decomposition to represent the terms as  $$\frac{1/2}{n-1}- \frac{1/2}{n+1} $$ but that just gets me $\infty - \infty$, so this isn't the way to do it.  I'm not sure how to find the value of this sum.  I don't need the full solution but a hint would be appreciated. Thanks. :)


Iterating over Java collections in Scala

I'm writing some Scala code which uses the  API. I would like to iterate over the rows contained in the java.util.Iterator that I get from the Sheet class. I would like to use the iterator in a for each style loop, so I have been trying to convert it to a native Scala collection but will no luck.  I have looked at the Scala wrapper classes/traits, but I can not see how to use them correctly. How do I iterate over a Java collection in Scala without using the verbose while(hasNext()) getNext() style of loop?  Here's the code I wrote based on the correct answer:  class IteratorWrapper[A](iter:java.util.Iterator[A]) {     def foreach(f: A => Unit): Unit = {         while(iter.hasNext){           f(iter.next)         }     } }  object SpreadsheetParser extends Application {     implicit def iteratorToWrapper[T](iter:java.util.Iterator[T]):IteratorWrapper[T] = new IteratorWrapper[T](iter)      override def main(args:Array[String]):Unit =     {         val ios = new FileInputStream("assets/data.xls")         val workbook = new HSSFWorkbook(ios)         var sheet = workbook.getSheetAt(0)         var rows = sheet.rowIterator()          for (val row <- rows){             println(row)         }     } }


Just out of curiosity: When I open the GNOME System Monitor, there is always a  of the window. It doesn't disappear when I drag the window around or close and relaunch the application. It does not affect the functionality by any means, but I wondered how it comes that I observe this phenomenon always and exclusively for this application. I'm using Ubuntu 18.04.3 LTS, System Monitor version 3.32.1-3-g0ea89b4922


Found  link to a c script that claims to take a screenshot of the running machine, so I copied it and installed all that libraries needed for compiling this file you can find info on how to to install the cairo lib I am using gcc to compile the script and I tried compiling using the following commands gcc -I/usr/include/cairo -lcairo -lX11 pic.c gcc -I/usr/include/cairo -lX11 pic.c gcc -Wall -I/usr/include/cairo -lm -lX11 pic.c  This is what i get when compiling /usr/bin/ld: /tmp/ccOh9u2g.o: in function `main': pic.c:(.text+0x91): undefined reference to `XOpenDisplay' /usr/bin/ld: pic.c:(.text+0x15e): undefined reference to `cairo_xlib_surface_create' /usr/bin/ld: pic.c:(.text+0x175): undefined reference to `cairo_surface_write_to_png' /usr/bin/ld: pic.c:(.text+0x181): undefined reference to `cairo_surface_destroy' collect2: error: ld returned 1 exit status   this is what i am using Target: x86_64-linux-gnu gcc version 9.3.0 (Ubuntu 9.3.0-17ubuntu1~20.04)


Expected value of times we roll a pair of dice

I am trying to solve this using a geometric series. Pretty much the question goes like this: We roll a pair of fair dice repeatedly and independently and stop as soon as the sum of the dice is equal to 7.   My random variable is: $X =$ the number of times we roll.  To calculate the expected value of time we will roll I do somehting like this:  $$E(X) = X_1P_1+X_2P_2+X_3P_3+...+X_nP_n$$  The probability or rolling a 7 using 2 dice is $\frac 6 {36}=\frac1 6$ so then,  $$E(X)=1*\frac 1 6+2*\frac 1 6+3*\frac 1 6+...+n*\frac 1 6$$  Not to sure about this:  $$E(X)=\frac 1 6 \sum_{n=1}^{\infty} n*\frac 1 6$$  And if this is the correct sequence what can I do with it next?


How to prevent the command prompt from closing after execution?

My problem is that in Windows, there are command line windows that close immediately after execution. To solve this, I want the default behavior to be that the window is kept open. Normally, this behavior can be avoided with three methods that come to my mind:   Putting a pause line after batch programs to prompt the user to press a key before exiting Running these batch files or other command line manipulating tools (even service starting, restarting, etc. with net start xy or anything similar) within cmd.exe(Start - Run - cmd.exe) Running these programs with cmd /k like this:  cmd /k myprogram.bat   But there are some other cases in which the user:   Runs the program the first time and doesn't know that the given program will run in Command Prompt (Windows Command Processor) e.g. when running a shortcut from Start menu (or from somewhere else), OR Finds it a little bit uncomfortable to run cmd.exe all the time and doesn't have the time/opportunity to rewrite the code of these commands everywhere to put a pause after them or avoid exiting explicitly.   I've read  about changing default behavior of cmd.exe when opening it explicitly, with creating an  and manipulating its content in these locations:  HKEY_LOCAL_MACHINE\SOFTWARE\Microsoft\Command Processor\AutoRun HKEY_CURRENT_USER\SOFTWARE\Microsoft\Command Processor\AutoRun   (The AutoRun items are _String values_...)  I put cmd /d /k as a value of it to give it a try, but this didn't change the behaviour of the stuffs mentioned above at all... It just changed the behaviour of the command line window when opening it explicitly (Start-Run-cmd.exe).   So how does it work? Can you give me any ideas to solve this problem?


Will there be conflict if there is two account with the same domain?

What will happen if more than one account on the same server is using the same domain? For instance in shared hosting, I have two user using the same domain name (Add-ons). Since this two accounts are on the same server, the domain is pointed to the same nameserver, will there be a conflict? and how to resolve this?


What should be the size of a Diffie-Hellman private key?

I'm implementing the SRP-6 protocol, which relies on discrete logarithms for it's security (essentially Diffie-Hellman).  The  state:     The private values $a$ and $b$ SHOULD be at least 256-bit random numbers, to give   approximately 128 bits of security against certain methods of calculating discrete   logarithms.   I can't seem to find any info on this – is it still valid advice?  Is the reason for this simply that the best known method for calculating discrete logs of $n$-bit numbers requires $2^{n/2}$ steps?


It is not clear to me if the disjoint union of a $d_{1}$-manifold and a $d_{2}$-manifold is still a manifold?

While it is clear that a disjoint union of two $d$-manifolds is a $d$-manifold, it is not clear to me if the disjoint union of a $d_{1}$-manifold and a $d_{2}$-manifold is still a manifold and if yes under some conditions then what is its dimension?


I have following sample PHP to print special characters in output. But its not printing any special character.  <head> <meta http-equiv="Content-Type" content="text/html; charset=utf-8" /> </head>     <?php     $string = "½ Kg";     ?>   Outputs:   <p>� Kg</p>   I have tried htmlspecialchars() or htmlentities() which is also not helping !!  Then tried setting header inside php.   header('Content-Type: text/html; charset=utf-8');   it says,     Warning: Cannot modify header information - headers already sent   kindly suggest how to print Special Characters


Is logical implication always determinable from just the given statements?

I am reading introductory texts on logic and am having a hard time understanding intuitively logical implication.  Specifically, I am wondering if logical implication can always be determined by two statements, P and Q alone? I'll try to give an example to clarify my question.  For example if the statement P is $x = 2$, and the statement Q is $x^2 < 6$, then determining the truth of P $\Rightarrow$ Q is fairly straightforward:   If $x$ does equal 2, then $4<6$ and Q is true, so $P \Rightarrow Q$ is true. And if $x$ does not equal 2, $P \Rightarrow Q$ is vacuously true.  In this example, with two statements P and Q, I can evaluate the truth/falsity of the statement P implies Q. However, what if the statement Q is changed such that it is now the statement $y = 5$?  So now I am trying to prove from that $$x = 2 \Rightarrow y = 5$$  Here is where things get murky for me. Say $x$ is not equal to 2, then $P \Rightarrow Q$ is vacuously true. But what about when $x$ does equal 2, now the statement Q could be true, but it could also be false, depending on some 'context'.   For example, if I said at the start: "Here are two statements, P and Q. Know that x = 2 and y = 4." Given this 'context', $P \Rightarrow Q$ is false. But if I say "Here are two statements, P and Q. Know that x = 2 and y = 5", then now $P \Rightarrow Q$ is true.  My discomfort here is that I assumed with two statements P and Q, I can determine the truth/falsity of $P \Rightarrow Q$ with just this information. Is this the wrong assumption?  As a secondary question, how can the truthfulness of the statement $P \Rightarrow Q$ be variable, depending on context? I have read on some other questions that implication can be interpreted as a promise. So how could it be that depending on some context the promise is sometimes true but sometimes false? Wouldn't this actually mean the promise is not always consistent and is therefore always false?  Some further information in case it is relevant, I recognise that in the first example, the statement Q is 'dependent' in some way on the statement P, since the object under examination in both statements is $x$, whereas in the second example there are two different objects which I am trying to make a logical connection between, which I am thinking may not be valid for some reason. I also recognise that there is still 'context' in the first example, in that we need information on whether $x$ is equal to 2 or not, however in that case it doesn't matter, since $P \Rightarrow Q$ is always true anyway.  Thanks very much in advance.


How to get a div to fill the remainder of the screen height

I've got a div, I need the bottom div to fill the remainder of the screen and show a scroll bar. The bottom div is not showing a scroll bar.      .page {   position: fixed;   top: 0;   width: 100%;   height: 100%;   margin: 0;   padding: $menu-height 0 0 0;   box-sizing: border-box; }  .sidebar {   width: 500px;   float: left;   height: 100%;   box-sizing: border-box;   background: #ddd;   border-right: 1px solid red; }  .top {   height: 200px;   background: #eee; }  .bottom {   background: #ccc;   overflow-y: auto; }  .filler-content {   height: 2000px; }

       top

         bottom


Does SQL check each And condition if first condition fails?

For a query of below kind does sql process data for each And condition if first And condition fails? If Emp_ID is not 12 for a row then does it check condition of Emp_Name? So how SQL process this kind of queries?  SELECT [Emp_ID],[Emp_Name],[Emp_Sal] FROM [gyh].[dbo].[Employee_Demo] where Emp_ID='12' And Emp_Name like '%ab%'


Are the aperture, ISO and shutter speed stops perfectly interchangeable?

Imagine you have an scene with shutter speed 1/60, f/8 and ISO 200. Then you change the configuration to get an equivalent exposure: speed 1/120, f/5.6, ISO 200 (plus one stop in speed, minus one stop in aperture).  My question is, apart from the obvious changes in the depth of field due to the aperture change, and less blur for the speed change, would there be any effect in brightness, contrast, color or other? And what if the change is 3 or more stops?


A strange phenomenon on ST_Intersection() in PostGIS


My LUbuntu 18.04's lxpanel is not working. Which command can I run to   adjust brightness of my screen? Thanks.


How do I set my level, unlocked weapon equip slots and playthrough mode?

I would like to play with the same level and questlines as my friend's characters, which are mostly Level 30+ and in True Vault Hunter Mode, but some of my characters that I'd like to play are in a low level and are not yet in True Vault Hunter Mode. I would also like to have all weapon slots unlocked.     I'd rather not play through the game again to be near the same level as them.  I've checked out  but I am unsure on what fields to edit or toggle to make my characters be like what I described.


How to exclude package from apt --fix-broken install (redux)

My  got closed as duplicate, and I don't know how to delete that duplicate mark. If you think this is duplicate or already answered please comment first, don't immediately mark as duplicate. Because these threads are not resolved my problem and I can't comment on these threads:   .     Because I can install and the packettracer works properly, but the package manager detected the packettracer has a dependency error (at-at-spi). So when I want to install another package, the package manager requires me to delete packettracer (--fix-broken). And in this case I use ubuntu 20.04 and packet tracer 7.3.  Package packettracer is refer to . My OS is ubuntu 20.04.  I have a package packettracer that not clearly installed, but the package is working.  $sudo dpkg -i PacketTracer_730_amd64.deb Selecting previously unselected package packettracer. (Reading database ... 199702 files and directories currently installed.) Preparing to unpack .../PacketTracer_730_amd64.deb ... Unpacking packettracer (7.3.0) ... dpkg: dependency problems prevent configuration of packettracer:  packettracer depends on qt-at-spi; however:   Package qt-at-spi is not installed. dpkg: error processing package packettracer (--install):  dependency problems - leaving unconfigured Processing triggers for gnome-menus (3.36.0-1ubuntu1) ... Processing triggers for desktop-file-utils (0.24-1ubuntu2) ... Processing triggers for mime-support (3.64ubuntu1) ... Processing triggers for shared-mime-info (1.15-1) ... Errors were encountered while processing:  packettracer   Even the packettacer need qt-at-spi, but the packettracer is working, can run properly without error. However, when I tried to install another package (whatever is it), there is dependency error:  packettracer : Depends: qt-at-spi but it is not installable E: Unmet dependencies. Try 'apt --fix-broken install' with no packages (or specify a solution).   So, I must run "apt --fix-broken install" first and uninstall packettracer before install another package. Then when that another package installed, I reinstall the packettracer again. It is annoying.  $ sudo apt --fix-broken install Reading package lists... Done Building dependency tree        Reading state information... Done Correcting dependencies... Done The following packages will be REMOVED:   packettracer 0 upgraded, 0 newly installed, 1 to remove and 1 not upgraded. 1 not fully installed or removed. After this operation, 0 B of additional disk space will be used.   Why I didn't fix the dependency qt-at-spi? Because there is no official package qt-at-spi for ubuntu 20.04 repository. I just found package for ubuntu 19.10 it requires many more packages that I have to install one by one. See details explanation about this on my another thread:    The question is: Can I exclude packettracer from apt --fix-broken install? So, when I run that command, package packettracer not be uninstalled.


Problem with solving a conditional-probability question

I have a problem with a statistics question.  The question is as follows:  I want to go to location B, but I am lost. To find this location I will ask random people where it is. There are two kind of people. 1/3 of the people will always lie where the location is, and 2/3 of the people have the probability ¾ that they are telling the truth, also they have a really bad memory, the moment that they told you the answer they will forget what they have said, so the answers will be independent.   I’ve drawn a tree diagram to show probabilities: T=true F=false   I need to answer the following questions:   You ask a random stranger where location b is. He says: "South". What is the chance this is the correct answer? You ask for the second time to the same random stranger the same question. He gives the same answer. Show that the chance that this answer is correct equals to 1/2. You ask the same question for the 3rd time to the same strangers. He gives the same answers. What is the chance that “South” is correct? The 4th time you will ask the same random stranger if location B is in the North or South. He gives the same answer. Show that the chance that this answer is correct equals to 27/70 Lets say he didn't said the 4th time "South", but he said "North". Show that the chance that this answer is correct equals to 9/10    I got the following answers:  1): $$ {2\over3}*{3\over4}={1\over2} $$ 2) $$ {({2\over3}*{3\over4} + {2\over3}*{3\over4})\over2}={1\over2} $$ 3) $$ {({2\over3}*{3\over4} + {2\over3}*{3\over4} + {2\over3}*{3\over4})\over3}={1\over2} $$ 4) I do not know  5) I do not know  I hope that someone can tell me the solution of the questions.


If I compile the following:  \begin{multicols}{2}  \begin{enumerate}      \item Math      \item Is       \item Quite      \item Fun  \end{enumerate}  \end{multicols}   Then it will compile as:       (a) Math   (c)  Quite       (b) Is     (d) Fun   I would like (b) to be to the right of (a).  Is there any way to get Mulitcols to do this automatically?  I know I can just rename things or type them in a different order.


I calculated my inductance value and current rating but I can't decide which inductance I have use. for example 10uH, max 800mA my inductance values but there is other variables.in this topic I have some questions .What type of inductance should be? Multilayer,Wirewound or Molded.what Material - Core of inductance shoul be?Ferrite or Powdered Iron? how can i choose inductance? for example i want to use step down or step up converter or LC filter? what kind of situtaion i should think? If anyone has information about this topic i will glad. By the way i am so sorry for my english.


Assume Black 10, Blue 10, Red 10 and Joker are on the board as a set of four: The Joker, at this point has to be an orange 10. Questions:  Can you take one of the three non-joker 10's from the set to use elsewhere on the board? Leaving a three tile set. This would have the effect of now making that joker one of two colors, instead of just orange. Can you split up all four 10's keeping the joker an orange 10 elsewhere on the board?


What cause the "from review" links to appear in comments?

I sometimes see comments ending in "From Review" (hyperlinked to a review page) on questions and answers, e.g.        I spend a good bit of time in the review queues (on Unix & Linux), but comments I make do not come with these "From Review" links. Note that I only have access to the "First post" and "Late answer" queues.  Do these links only appear for the higher-rep queues?


Let $f\in H(B(0,1))$, $f(0)=0$, $f(B(0,1))\subset B(0,1)$. Suppose there are 2 different points $z_1$,$z_2\in B(0,1)$, s.t. $|z_1|=|z_2|$, $f(z_1)=f(z_2)$. Show that $|f(z_1)|=|f(z_2)|≤|z_1|^2=|z_2|^2$.    I have used the Schwarz-Pick Proposition to prove that $|f(z_1)|=|f(z_2)|≤|z_1|=|z_2|$ directly, but that is not enough. Thank you for help!


How to install/run an AppImage on Lubuntu

I installed an AppImage on my laptop with Lubuntu 18.04.5 but I can't get it to run. When I click on the "properties" tab of the AppImage, I can't see the setting that says "Allow executing files as program" so I'm not sure what I should do. If anyone is wondering, the AppImage I am trying to install is Ripcord, a rewritten version of discord meant for 32-bit systems.


There is a mathematical model. Model can give a forecast for some duration (hours, days, years). But the forecast will not be equally accurate for different periods of time. How should I ask for what period of time the forecast is most accurate?    What is duration, the model can give most accurate forecast.  For whatduration....  What is duration for....   Which of the above is correct? Where can I read about this rule?


Custom .bst file : Does not process entries of type "@book"

I have created a custom .bst file using  makebst such that it is as per my univeristy PhD guidelines. When I run BibTex, it works perfectly for articles, conference proceedings etc. cited. However BibTeXfails when I am citing a book. The error I get is    This is BibTeX, Version 0.99d (TeX Live 2015)  The top-level auxiliary file: example.aux  The style file: thbibstyle.bst  Database file #1: books.bib  You can't pop an empty literal stack for entry Arnett96  while executing---line 1720 of file thbibstyle.bst  You can't pop an empty literal stack for entry Spitzer78  while executing---line 1720 of file thbibstyle.bst   An example .tex file is as follows:  \documentclass[a4paper,11pt]{tanvirTU} \begin{document} \title{Title} \maketitle Read \cite{Spitzer78, Arnett96}  \bibliography{books}   \bibliographystyle{thbibstyle} \end{document}   Here is my .bst file:   Also the bibliography entry are as follows   @BOOK{Spitzer78,    author = {{Spitzer}, L.},     title = "{Physical processes in the interstellar medium}", publisher = {New York Wiley-Interscience, 1978.~333 p.},     year = 1978,    adsurl = {http://adsabs.harvard.edu/cgi-bin/nph-bib_query?  bibcode=1978ppim.book.....S&db_key=AST},  adsnote = {Provided by the Smithsonian/NASA Astrophysics Data     System} }    @BOOK{Arnett96,     author = {{Arnett}, D.},     title = "{Supernovae and Mucleosynthesis: An Investigation of the History of Matter from the Big Bang to the Present}",     publisher = {Supernovae and Mucleosynthesis: An Investigation of the History of Matter, from the Big Bang to the Present, by D.~Arnett.~Princeton: Princeton University Press, 1996.},      year = 1996,     adsurl = {http://adsabs.harvard.edu/abs/1996snih.book.....A},    adsnote = {Provided by the SAO/NASA Astrophysics Data System}    }   Also the document class is customized which is:   Can anyone tell me why this is happening and how to fix it?  For a solution, please refer to this


How to decide which execution time is more reputable while using System.nanoTime ()

When i try to measure the performance execution speed time of my method below:    public static int FFMulFast(int firstPol, int secondPol){   int temp = 0;    if (firstPol == 0 ||secondPol == 0)    return 0;   /*The multiplication is done by using lookup tables. We have used both logarithmic and exponential table for mul  the idea is firstly look to Logarithmic table then add their powers and find the corresponding of this to exponential table */     temp = (Log[(firstPol & 0xff)] & 0xff) + (Log[(secondPol & 0xff)] & 0xff);      if (temp > 255) temp = temp - 255;      return Exp[(temp & 0xff)];   }    Now when i measure the performance speed of this method as below   public void runABunch() {      long start = System.nanoTime();     int a=0x59;    int b=0xb4;      for (int i = 0; i < 5000000; i++)         FFMulFast(a,b);     long end = System.nanoTime();     System.out.println("Time in nanoseconda: " + (end-start));   }   The result of this one is approximately 0.1 seconds .   But when i run the same method runABunch but omitted for then i get totally different results and i do not understand why these results are totally different and which one is more reputable the one with for or the one without for  public void runABunch() {  long start = System.nanoTime(); int a=0x59;   int b=0xb4;      FFMulFast(a,b); long end = System.nanoTime(); System.out.println("Time in nanoseconda: " + (end-start)); }   Also when i put some println statements the time of execution increased a lot.Anyone know why?  I tried to use profiler like java visualvm but the problem is that i can not see anything there since it disappeared to me as soon as my application finished to run.


Grub rescue can't write outside of disk "hd0"

I tried to install Ubuntu 13.04 from a Live USB, and it said it was successfully installed, and after the reboot I got an error message that said:  error: attempt to read or write outside of disk "hd0" grub rescue   I am new to Ubuntu. Please help.


How to set default footnote linespacing? Now for each footnote I have to write  \footnote{\onehalfspacing ...}   But I would like to set the line spacing once.  I guess its possible to use \renewcommand{\footnote}{...}. But I don't know how to redefine the command.


Where are MTP mounted devices located in the filesystem?

I have an Android phone that connects with my computer via MTP. This works fine; I can see and transfer files with Nautilus. However, I often want to use the terminal to move large numbers of files, and I cannot seem to find the device anywhere in the filesystem tree. Nautilus reports the location as mtp://[usb:003,007]/, but it's not under /media or /mnt.  Does anyone know where it is?


Prove that $$\frac{1+\sin\theta+i\cos\theta}{1+\sin\theta-i\cos\theta}=\sin\theta+i\cos\theta$$   I tried to rationalize the denominator but I always end up with a large fraction that won't cancel out. Is there something I'm missing?  Thanks in advance


Leaving gold and elixir uncollected to prevent losing when raided

In Clash of the Clans, to minimize loss of resources when your base is attacked is it better to store loot in clan castle and not collect it? Also is it better to leave resources in elixir collectors/mines for as long as possible before collecting it (at what point is it necessary)?


I am a frequent Stack Exchange user and often ask questions, especially on Stack Overflow. Today it happened to me that I asked three questions and answered them myself shortly after thinking about the problem a while longer.  I am not sure if this is okay or if I am violating a best practice here. It happens to me from time to time that I answer my own question, but never before that frequently.  Is there anything I can/should do to prevent this in the future or is it perfectly normal and accepted to answer one's own questions?


Why can't we have simple HTML in comments?

Why can't we have simple HTML in comments; or at least newlines and tabs?  I think it would be good if we had such functionality.


Can it be proven in ZF that $\mathbb{N}$ is a universal size comparator?

This is a follow-up to my previous question several years ago about whether every finite set is a universal size comparator. Now I am asking, can it be proven in ZF without the axiom of choice that the set $\mathbb{N}$ of natural numbers is a universal size comparator, meaning, it can be compared with every set in terms of cardinality?


Incorrect wording in protected question status

Similar (but different, please read on) questions have been asked dozens of times, so I'll try to be concise about this one.  The wording on protected questions "posting an answer now requires 10 reputation on this site" is incorrect. I have 60 reputation on the Physics SE site, but when I tried to post an answer on  I was greeted with the protected message warning:     Thank you for your interest in this question. Because it has attracted   low-quality answers, posting an answer now requires 10 reputation on   this site.   This is buggy documentation. I do have more than 10 reputation. If the origin of those points affects whether or not they're counted this should be clarified in the message (in this case the association bonus is not included, so the word earned might be appropriate, although still subjective). Previous gripes with this message were posted in these questions:      There are probably more. In these posts, the questioners were asking to improve the wording to clarify that the association bonus is not included. Since then, the word earned has been removed, so now the wording is not just confusing (as pointed out in those questions), it's simply wrong.  A previous question with the same message was posted, but this question is not a duplicate because it requests to change the feature, I'm asking for it to be correctly documented:    I posted a physics meta question about this here:    Unfortunately it was closed as duplicate, which I do not believe to be warranted. A commmenter suggested I post it on Meta SE.


Why is normal contact force acting on a person in an elevator during a free fall 0?

Since normal contact force between two surfaces depends on molecular interaction between them, then why does its value change with the acceleration of the elevator?


So I'm doing a search method and my HashSet<GameBoard> explored has all the explored states. I need to add more states to "explored" so I don't check the same state over and over again. I need to compare states with a copy of itself and if the VALUE of them are the same, I don't check it again.  I know I have to override the .equals()method in Obj class for it to do a deep search and I did just that. Below is my equals method.   public boolean equals  (GameBoard a){     for(int j = 0;j < a.len;j++){         if(a.boardArr[j] != this.boardArr[j]){             return false;         }     }     return true; }   I add GameBoard to explored using explored.add(state);. But this doesn't seem to do anything. I even commented out the equals method completely and the result is the same. It keeps adding the same state to the explored state and hence I have an infinite loop. Really need some help here does anyone know how to solve this?


Create Vector Grid from a features Extent with PyQGIS

NOTE: THIS IS FOR QGIS 2.14.1 and uses VectorGrid instead of CreateGrid also though the question How to generate a grid programmatically in Python without GUI? is answered fantastically the PyQGIS language is outdated  We have a .txt file  "Extent.txt", in this example this file contains the coordinates of 4 points formatted like so;     Point,Lat,Lon   TL,-29.788254, 30.820720   TR,-29.788254, 30.825372   BL,-29.790710, 30.820720   BR,-29.790710, 30.825372   We want to add this shapefile in our QGIS Map Document, and then create a vector grid that has the same extents of this .txt file, all using PyQGIS.  We add the .txt file with a PyQGIS script  import csv, ctypes, os, sys, datetime, string import processing from PyQt4.QtGui import * from PyQt4.QtCore import * from qgis.core import * from qgis.utils import iface  #Load CSV gridSettings = QSettings() gridoldValidation = gridSettings.value( "/Projections/defaultBehaviour") gridSettings.setValue( "/Projections/defaultBehaviour", "useGlobal" ) gridInFlnm='Extent.txt' gridInDrPth='PATH_TO_CSV_FOLDER' gridInFlPth="file:///"+gridInDrPth+gridInFlnm griduri = gridInFlPth+"?delimiter=%s&xField=%s&yField=%s" % (",","lon","lat") gridbh = QgsVectorLayer(griduri, gridInFlnm, "delimitedtext") gridbh.isValid() gridbh.setCrs(QgsCoordinateReferenceSystem(32365,  QgsCoordinateReferenceSystem.EpsgCrsId)) QgsMapLayerRegistry.instance().addMapLayer(gridbh) gridSettings.setValue( "/Projections/defaultBehaviour", gridoldValidation )   This produces our point vector layer from our .txt file!   So...How do we get our Vector Grid?  NOTE: THIS IS FOR QGIS 2.14.1 and uses VectorGrid instead of CreateGrid also though the question  is answered fantastically the PyQGIS language is outdated