Suppose $f: X \rightarrow Y$, and is one-to-one, and let $A \subseteq X$, prove that $f^{-1}[f[A]] = A$.  EDIT: Actually, this identity should hold even if $f$ is not one-to-one (injective), right?  This is completely intuitive and logical, but I can't think of a proof strategy to use to prove it? I'm familiar with induction and element chasing, but they don't seem to work here.  Here is the beginning of my element chasing proof to prove that $f^{-1}[f[A]] \subseteq A$.  Start with arbitrary element: $a \in f^{-1}[f[A]]$ \  Apply definition of preimage: $a \in \{x \in X | f(x) \in f[A] \}$ \  Simplify and convert to boolean expression: $a \in X \land f(a) \in f[A]$ \  Apply definition of image: $a \in X \land f(a) \in \{y \in Y | y = f(x), x \in A \}$ \  I'm stuck here...

Let $f: A \rightarrow B$ be a function. How can we show that for all subsets $S$ of $A$, $S \subseteq f^{-1}(f(S))$? I think this is a pretty simple problem but I'm new to this so I'm confused.  Also, how can we show that $S = f^{-1}(f(S))$ for all subsets $S$ iff $f$ is injective?


Is it possible to have the following sample correlation matrix for $x$, $y$, $z$?  $\begin{pmatrix} 1 & 0.8 & 0.2 \\ 0.8 & 1 & 0.7\\ 0.2 & 0.7 & 1\end{pmatrix}$  Where a 3 by 3 correlation matrix is $\begin{pmatrix} 1 & p_{xy} & p_{xz} \\ p_{yx} & 1 & p_{yz}\\ p_{zx} & p_{zy} & 1\end{pmatrix}$, and the $p$'s (partial correlations) are unequal, making this different more general than a similar question with equal partial correlations posed .  My answer is yes, and my reasoning is: all the diagonal entries have value $1$, the matrix is symmetric and all entries are between $-1$ and $1$  Is my reasoning good enough? Are there other points that I'm missing?

There are three random variables, $x,y,z$. The three correlations between the three variables are the same. That is,  $$\rho=\textrm{cor}(x,y)=\textrm{cor}(x,z)=\textrm{cor}(y,z)$$  What is the tightest bound you can give for $\rho$?


What is the command to completely disable the weather in minecraft? I currently use /weather cycle 1000000 but it only works for a couple minutes. After that it resumes raining. I need the command to ensure it is permanently disabled for this world until I use a different command to make it resume. Thank you!

The arrival of Minecraft Beta 1.5 brought weather conditions. However, it can at times be inconvenient when you're trying to screenshot something and show it off (as it reduces lighting and obstructs your view slightly). Is there anyway to turn weather off?  Alternatively, is there a way to speed up the duration of weather or "skip" it?


I've been trying to get a VirtualBox VM set up with Xubuntu on my Windows 10 Home laptop for web development (working through The Odin Project if any of you are familiar with it). However, I can't seem to install any applications from downloaded .deb files. For reference, I've been trying to get Google Chrome and VSCode. I've tried using the software installer and all the methods listed here:  (tl;dr sudo apt install gdebi-core then sudo gdebi _.deb, sudo dpkg -i _.deb, sudo apt install _.deb) None of those seemed to work. After getting some help, I tried the following: sudo apt install _.deb  sudo apt-get install -f then sudo apt install _.deb  sudo apt update and sudo apt upgrade then the same commands from before   Sorry if the images are difficult to read. I don't have the original terminal output anymore, so those are the screenshots of error messages I sent while getting help. At this point, I'm at a loss for what I should do. It took me ~15 tries of uninstalling and reinstalling Virtual Box and Xubuntu to get the VM up and running, so maybe this installation isn't functional either? I'd greatly appreciate any suggestions.

How do I install a .deb file via the command line?


My character is a bard and I'm planning on taking a level in Warlock. Do I get the 2 cantrips and 2 spells from the Warlock spell list that a new Warlock character would get in addition to the Bard cantrips and spells that I already have access to?

If I multiclass into 2 or more classes/subclasses that can cast spells, how do I determine what spells I know or can prepare?  For instance, if I am playing a multiclassed character with 1 level in warlock, 2 levels in bard, and 3 levels in paladin, how do I determine which spells I know/have prepared?    Related:


I have been searching the forums and web with no working solutions. I tried almost every solutions found here but so far no luck.... Here is it: I have a website  http://example.com/user=me and I want that when the user enter  me.example.com he gets the content of  http://example.com/user=me . note that I do not have a me.example.com subdomain, how can I achieve this? Maybe relevent if I add that I'm on a shared server. I've seen many .htaccess script, copied and pasted them but so far no luck.  here is my htaccess (for removing the .php)  RewriteCond %{REQUEST_FILENAME}.php -f RewriteRule !.*\.php$ %{REQUEST_FILENAME}.php [QSA,L] AddHandler application/x-httpd-php55  .php55 .php   any help?

I am looking to create a system which on signup will create a subdomain on my website for the users account area.   e.g. johndoe.website.com  I think it would be something to do with the .htaccess file and possibly redirecting to another location on the website? I don't actually know. But any information to start me off would be greatly appreciated.  Creating a sign up area is not the problem - I have done this many a time. I am just unsure where to start with the subdomain.


What's the difference between  buf = (char*)std::malloc(aSize * sizeof(float));   and  buf = new char[aSize * sizeof(float)];   I have seen both used, and I usually use the first. However today I noticed that the second one has started sometimes throwing std::bad_alloc and crashing. Changing it to the first fixed the issue.  What exactly does each line do?

I see in C++ there are multiple ways to allocate and free data and I understand that when you call malloc you should call free and when you use the new operator you should pair with delete and it is a mistake to mix the two (e.g. Calling free() on something that was created with the new operator), but I'm not clear on when I should use malloc/ free and when I should use new/ delete in my real world programs.  If you're a C++ expert, please let me know any rules of thumb or conventions you follow in this regard.


Suppose there is sphere which is completely made of ideal mirror. What if a light particle is induced in it by a source of light? Does the light particle remains there by bouncing or disappear after removing the source of light?

Let's say you have the ability to shine some light into a perfectly round sphere and the sphere's interior surface was perfectly smooth and reflective and there was no way for the light to escape.  If you could observe the inside of the sphere, what would you observe? A glow? And would temperature affect the outcome?  Seems silly, it's just something I've always thought about but never spent enough time (until now) to actually find an answer.


I am not sure if this is the right place to post this but I am unaware  of any other stack to get such issue into notice.  I came across this site today from google search  Which mirrors SO site. Thought its better to get this into the SO team's notice.

of Stack Overflow, all content posted on Stack Exchange sites by their users (i.e. you wonderful people) has been provided to the whole universe under . For my fellow non-lawyers, that license basically means:   Anyone can use any Stack Exchange posts at any time without having to ask for permission Making money off of the copied content is permitted You don't even have to copy stuff from here verbatim; you can just use it as a starting point and make whatever edits you want There are just two rules you have to follow:   You have to provide . Simple links to the original post and author info are just fine. You have to  and allow other people to use your content, as long as they follow these very same rules. How meta!    (If you ever forget any of that, and want to refresh your memory, the license info is linked to in the footer of every page.)  There are, in fact, a lot of people who republish varying amounts of our content for assorted reasons. Unfortunately, there are some Stack Content Republishers Attributing Poorly and/or Excelling at Ranking (SCRAPERs, for short).  In this context, "attributing poorly" means any use that doesn't follow our attribution rules or make any other reasonable attempt at give credit. This can get pretty egregious; I've seen SCRAPERs that not only don't link back to SE originals, but also use fake author info and post dates to make it harder to find originals. By "excelling at ranking," I'm referring to copycat sites that end up higher in Google results than the original SE sites do for the same content. That's not necessarily wrong, but in some cases, it indicates inappropriate SEO hackery.  So, the question is: what can you do if you spot a SCRAPER?


If $\ x$ is an arbitrary real number, prove that there is exactly one integer $n$ which satisfies the inequalities $n\leq x < n + 1$.

Show given any $x\in\mathbb{R}$ show there exists a unique $n\in\mathbb{Z}$ such that $n-1\leq x <n$. I already know that there exists a $n\in\mathbb{N}$ such that $x<n$ by the archimedean property. But to prove that $n-1\leq x$ part I'm not sure. I think I have to create some set such that $n-1$ is a lower bound. But I'm not sure.


I would like to create an empty (objects and data) sandbox with the same license and features than my prod org to test new implementations.  I know that we can use and new dev org. However, this will have more features than our prod org (like connect, service cloud, etc.). We don't want to use a feature that then, is not available in our prod org.  Is there any way to achieve this? Someone already ask this on 2013 (). But three years later something must have changed  Any thoughts?

We want to have a plain empty sandbox - one without any configuration metadata or data from Production.  Is it possible to have such a sandbox?  Please advise.


How do I make my friend list invisible to my other friends on my facebook? I thought making my friend list private did the job. But it didnt.

I don't want the entire world to see who I am friends with on Facebook.  How do I control who can see my list of friends?


I created a table with the following sql:  CREATE TABLE fens_mng_people_utf8 (   pidm varchar(16) NOT NULL default '',   fname varchar(32) NOT NULL default '',   mname varchar(32) default NULL,   lname varchar(32) NOT NULL default '',   KEY pidm (pidm) )CHARACTER SET utf8  DEFAULT CHARACTER SET utf8  COLLATE utf8_general_ci  DEFAULT COLLATE utf8_general_ci;   And some Turkish characters such as Ş appears as a html code &#350; even if I insert it directly with an sql not from a text document. And I am viewing it from phpmyadmin.  As a result, when I try to do such operations in my php:  SELECT * FROM  fens_mng_people_utf8 WHERE fname = '$fname' and lname = '$lname'   It returns null because $fname and $lname both displays Turkish characters properly.  I either want to correctly display Turkish characters in my table or convert $fname as it would match the value in my database.  Thanks for the help!

I'm setting up a new server and want to support UTF-8 fully in my web application. I have tried this in the past on existing servers and always seem to end up having to fall back to ISO-8859-1.  Where exactly do I need to set the encoding/charsets? I'm aware that I need to configure Apache, MySQL, and PHP to do this — is there some standard checklist I can follow, or perhaps troubleshoot where the mismatches occur?  This is for a new Linux server, running MySQL 5, PHP, 5 and Apache 2.


I'm only new to java and trying to make an equals code, but it won't work with ==, only with .equals() not sure why.      import java.lang.*;     import java.util.*;      public class password     {         public static void main(String args[])          {             Scanner Keyboard = new Scanner(System.in);             String guess = Keyboard.newLine();              String password = "1password";              if (guess == password) {                 System.out.println("Welcome");             } else {                 System.out.println("Login Failed");             }          }     }

I've been using the == operator in my program to compare all my strings so far. However, I ran into a bug, changed one of them into .equals() instead, and it fixed the bug.  Is == bad? When should it and should it not be used? What's the difference?


I am running a flask application and connecting to database with Flask-mysqlAlchemy when I am running my script with python 2.7 I am getting below error.  Traceback (most recent call last):   File "app2.py", line 8, in <module>     from database.dbconfig import db, myAccounts2 ImportError: No module named database.dbconfig   whereas this is running fine in python3 I need this running in python 2.7 as my server is pre-installed with it. I am not able to figure out what the issue is. I have installed all dependencies in my server and keep getting this where as it works in my local machine with python3.  Here is my main script  My directory is like this  Main folder | +--->database |   | |   +------> dbconfig.py |    +----->app2.py     Here is my app2.py  #!usr/bin/python import boto3 import json import urllib2 import urlparse #import urllib.request #import urllib.parse from database.dbconfig import db, myAccounts2 from flask_sqlalchemy import SQLAlchemy from flask import Flask,render_template,jsonify,json,request  application = Flask(__name__)   Here is my dbconfig.py  from flask import Flask from flask_sqlalchemy import SQLAlchemy  app = Flask(__name__) app.config['SQLALCHEMY_DATABASE_URI'] = 'mysql+pymysql://root:password@pushbuttontest.us-east-1.rds.amazonaws.com:3306/test_pb' app.config['SQLALCHEMY_TRACK_MODIFICATIONS']= 'False' app.config['SECRET_KEY'] = "random string22" db = SQLAlchemy(app)  class myAccounts2(db.Model):     #__tablename__ = 'myAccounts'     id = db.Column(db.Integer, primary_key=True)     account_name = db.Column(db.String(45), primary_key=True)     vpc = db.Column(db.String(55))     subnet = db.Column(db.String(55))     instance_type = db.Column(db.String(90))      def __init__(self,  account_name, vpc, subnet, instance_type):         #self.id = id         self.account_name = account_name         self.vpc=vpc         self.subnet=subnet         self.instance_type=instance_type

What is __init__.py for in a Python source directory?


I have a simple latex picture I want to align with the text. Here is a sample of code.  \begin{tabular}{ p{10em} p{20em} }   \includegraphics{images/jouer.png}  &  Prevailed sincerity behaviour to so do principle mr. As departure at no propriety zealously my. On dear rent if girl view. First on  smart there he sense. Earnestly enjoyment her you resources. Brother chamber ten old against. Mr be cottage so related minuter is.  Delicate say and blessing ladyship exertion few margaret. Delight herself welcome against smiling its for. Suspected discovery by he  affection household of principle perfectly he. \\  \end{tabular}

is there a way to create a table with 2 columns, in the left column should be some text, in the right column should be a picture.  The problem is - to align both to the left, top corner. The image seems to be inserted as an inline object, so it pushes the text down, from the top.                            _____________________                          |                     |                              |                     | Some text is pushed down |                     |   What i want is:  Some text is pushed down  _____________________                          |                     |                              |                     |                          |                     |   Here is the code:  \begin{tabular}{\textwidth}{ l l } Some text & \includegraphics{images/image.png} \\ \end{tabular}


global static List<String> checkEmailExists(String emailtocheck, String phone,String memberId){                  OmniOperations.PhoneNumberValidation emailObj = new OmniOperations.PhoneNumberValidation();         if(memberId.trim() !=null)             emailObj.memberId = memberId;                  if(emailtocheck.trim() != null)             emailObj.emailAddress  = emailtocheck.trim();                  //if(phone.trim() !=null)         emailObj.mobilePhoneNumber = null;                  emailObj.ThrowErrorIfExistsOnOtherAccounts = true;                  OmniOperations omniOps = new OmniOperations();         String reqBody = JSON.serialize(emailObj,true);         HttpResponse res = omniOps.CheckEmailExists(reqBody);         LIST<String> retVal = new LIST<String>();        /* if(res != null && res.getStatusCode() == 200)         {             string status = Utils.extractFieldFromJSON(res.getBody(), 'Status');             If(status != null && status != '')             {                 if(status == 'EXISTS'){ //API returns 'EXISTS' if email address is already existing and shows the warning                     System.debug('Status : '+status);                     retVal.add('EXISTS');                     omniOps.logAllHttpRequests();                     return retVal;                 }                 else if(status == 'Error'){ // new email address not set. Warning shown                     System.debug('Status  :'+status);                     retVal.add('Error');                     omniOps.logAllHttpRequests();                     return retVal;                 }                 else if(status == 'Success'){ // new email address is set instantly on sumbit                     System.debug('Status  :'+status);                     retVal.add('Success');                     omniOps.logAllHttpRequests();                     return retVal;                 }                 else{ // API error                     System.debug('Status  :'+status);                     omniOps.logAllHttpRequests();                     retVal.add('APIERROR');                     return retVal;                 }             }             else             { //API Error                 System.debug('Status NULL');                 omniOps.logAllHttpRequests();                 retVal.add('APIERROR');                 return retVal;             }         }         else         { // API ERROR             System.debug('Error in Email number API');             omniOps.logAllHttpRequests();             retVal.add('APIERROR');             return retVal;                      }*/

This is a canonical question and answer developed by the community to help address common questions. If you've been directed here, or your question has been closed as a duplicate, please look through the resources here and use them to shape more specific questions. To browse all canonical questions and answers, including more unit test resources, navigate to the  tag.  This canonical question is intended to address several classes of common questions by providing a quick summary and links to comprehensive resources:   How is code coverage obtained and calculated? How do I increase my coverage?  Why can't I cover these lines? Why isn't the body of my loop or conditional statement covered?


I've set up my SPF record at improvedemployees.com as follows:  v=spf1 a mx ptr ip4:84.40.9.177 mx ip4:84.40.9.11 ~all   I've set up my SPF record at affiliatewebdesigners.com to point to using improvedemployees.com as this is the reverse lookup name of the server. The SPF for affiliatewebdesigners.com is as follows:  v=spf1 a mx ptr ip4:84.40.9.177 mx ip4:84.40.9.11 include:improvedemployees.com ~all   I'm still getting bounced emails unless I'm on a whitelist and I can't figure out why. I've tried to analyse my SPF record using mxtoolbox:      This error seems pretty useless. Can anyone help me figure out where I'm going wrong?

This is a  about setting up .     I have an office with many computers that share a single external ip (I'm unsure if the address is static or dynamic). Each computer connects to our mail server via IMAP using outlook. Email is sent and received by those computers, and some users send and receive email on their mobile phones as well.  I am using  to generate an SPF record and I'm unsure about some of the fields in the wizard, specifically:   Enter any other domains who may send or relay mail for this domain Enter any IP addresses in CIDR format for netblocks that originate or relay mail for this domain Enter any other hosts which can send or relay mail for this domain How stringent should SPF-aware MTA's treat this?   the first few questions i'm fairly certain about... hope i have given enough info.


I'm writing an iPhone application which needs to have an option to call our office. However, the phone number that needs to be dialed has a 5 digit extension.  I know that to call a regular phone number we can use openURL using something like:  [[UIApplication sharedApplication]      openURL:[NSURL URLWithString:@"tel:1-800-555-5555"]];   Can I get this to work with an extension? If so, how?  The  link to , which describes the URL scheme for tel: and it seems as though extensions are supported, but I can't figure out the syntax from the RFC.

How do you programmatically do the following from the iPhone SDK:   Programmatically Dial a Phone Number through the iPhone SDK Bypass the dial / cancel prompt that the iPhone brings up Send additional DTMF after the number is dialed just like how you would program pauses into a regular phone.    I know you can make a tel:// call but the issue is that it brings up the dial / cancel prompt and after that it prevents any future DTMF from being sent.


Hi¡ I have some troubles with the next problem.   Let $(X,\tau)$ be a topological space. Prove that $X$ is $T_1$ if and only if there exists a family $U$ of open sets such that $\bigcap U=\Delta$ where  $\Delta=\left\{(x,x): x\in X\right\}\subseteq X\times X$ (the diagonal)   My attempt.  $\Rightarrow)$ We know that $X\times X$ is $T_1$ because $X$ is $T_1$. Moreover, we have the next theorem for $T_1$ spaces  Theorem Let $X$ be a topological space. The next conditions are equivalent.  1) $X$ is $T_1$  2) For all $B\subseteq X$, $B=\bigcap \left\{ U: B\subseteq U, U\in\tau\right\}$  3) For all $x\in X$, $\left\{x\right\}=\bigcap\left\{U : U\in\tau,  x\in U\right\}$  Then, the implication follows from 3).  But, what can I do for $\Leftarrow)$? I have tried to prove that $\left\{x\right\}$ is closed, but I have failed.  My best attempt was consider two distinct points $x$ and $y$. Clearly, $(x,y)\notin\Delta$, then, $(x,y)\notin\bigcap U$, so, there exist some basic open set such that $(x,y)\notin A\times B$. Then, my idea was use the projection $\Pi_X$, but, from here, I'm so confused.   Thanks in advance.

Let $X$ be a topological space and let $\Delta = \{(x,x) : x\in X \}$ be the diagonal of $X\times X$ (with the product topology).     I was asked to prove that $X$ is ${\rm T}_1$ if and only if $\Delta$ can be written as intersection of open subsets of $X\times X$.   I think is better (maybe easier) to use the well-known result "$X$ is ${\rm T}_1$ if and only if $\{x\}$ is a closed set $\forall x\in X$".  What I've done:  Assuming that $X$ is ${\rm T}_1$, let $Y=(X\times X) \setminus\Delta$ and note that (trivially) $$Y = \bigcup_{y\in Y} \{y\}.$$ Then $$\Delta = (X\times X) \setminus Y = (X\times X) \setminus \left(\bigcup_{y\in Y} \{y\} \right) = \bigcap_{y\in Y} (X\times X)\setminus \{y\},$$ where $(X\times X)\setminus\{y\}$ is open since each $\{y\}$ is closed.  The other direction seems be a bit harder, I've tried unsuccessfully. Any ideas?  Thanks in advance.


I have 2 activities.  In first activity there are some text fields and two buttons. In text fields I'm entering some data, and by clicking the first button I'm calling second activity that displays a ListView with checkboxes.   And from second activity after clicking a button over there I'm calling the first activity again. But by the time I move to that page, all data that have been entered earlier have disappeared.  I would need that data to reside even if I move back and forward between two activities.

I've been working on the Android SDK platform, and it is a little unclear how to save an application's state. So given this minor re-tooling of the 'Hello, Android' example:  package com.android.hello;  import android.app.Activity; import android.os.Bundle; import android.widget.TextView;  public class HelloAndroid extends Activity {    private TextView mTextView = null;    /** Called when the activity is first created. */   @Override   public void onCreate(Bundle savedInstanceState) {     super.onCreate(savedInstanceState);      mTextView = new TextView(this);      if (savedInstanceState == null) {        mTextView.setText("Welcome to HelloAndroid!");     } else {        mTextView.setText("Welcome back.");     }      setContentView(mTextView);   } }   I thought it would be enough for the simplest case, but it always responds with the first message, no matter how I navigate away from the app.  I'm sure the solution is as simple as overriding onPause or something like that, but I've been poking away in the documentation for 30 minutes or so and haven't found anything obvious.


Let $S$ be a subspace of $C([0,1])$ whose elements satisfy $\|f\|_{L^\infty}\leq K\|f\|_{L^2}$. Prove that it's finite dimensional.  The obvious observation is that the $L^\infty$ and $L^2$ norms are equivalent (since the space is finite), but I can't see how to directly exploit this. The only way I know to prove a subspace is finite dimensional is to show the unit ball is compact. Using the equivalence of the norms it then seems like it'd be sufficient to prove that a sequence with $\|f_n\|_\infty$ has a subsequence converging in the (usually weaker) $L^2$ topology. I'm not sure this is true, am I on the right track?

Let linear $S$ be a subspace of $C([0,1])$, i.e., the continuous real-valued   functions on $[0,1]$. Assume that there exists $c>0$, such that   $\|\,f\|_\infty\leq c \|\,f\|_2$, for all $f\in S$. Then show that $S$ is finite-dimensional.   This is equivalent to proving that the closed unit ball in $(S,\|\|_\infty)$ or in $(S,\|\|_2)$ is compact, but I can't derive this.   Another thought is that the $L^2$ closure of $S$ is a subset of $C([0,1])$. Indeed, if $f_n\to f\in L^2$, then the given relation $\|f_n-f\|_\infty \leq c\|f_n-f\|_2$ implies that $f_n\to f$ in $L^\infty$, so $f$ is continuous. Therefore we have the inclusion $$S\subset \overline{S}^{L^2}\subset C([0,1])\subset L^2$$ If $S$ was infinite dimensional, then $\overline{S}$ would be an infinite dimensional hilbert space, proper subset of $L^2$.   Another thought is that all the $L^p$ norms on $S$ are equivalent (by Holder). If ALL norms are equivalent, then $S$ has to be finite dimensional.


I have found this sentence in a dictionary. Section 17 provides that all decisions must be circulated in writing. Do you think it can be reworded like this? Section 17 provides that all decisions be circulated in writing. SUBJUNCTIVE or like this Section 17 provides that all decisions are to be circulated in writing. INDICATIVE

It is to me a curious fact that the  of verbs in English has so nearly disappeared in modern times. In fact, even the correct form and usage of the subjunctive in Modern English barely distinguishes itself from the indicative! In many regions and dialects, the subjunctive would appear to be entirely obsolete, replaced by the indicative in all cases. (Educated speakers, certainly in Britain at least, do however still make good use of it.)  The present subjunctive form in  is (in almost all cases) virtually identical to the third-person plural present indicative (e.g. 'He were', 'She own'). This is markedly different from , where the subjunctive form a form was . Even by the advent of Early Modern English in the 16th century, the subjunctive was already converging with the indicative.  Other Modern European languages, not only Romance ones such as French and Spanish, but Germanic languages related to English (e.g. Dutch/German) have a much more pronounced subjunctive form. From what I remember of my Classical Latin, word suffixes for a variety of tenses are hugely obvious in the subjunctive.  My question is: why is this convergence of the subjunctive and indicative so strongly the case in Modern English? Is it a general trend in other Germanic/Romance (or more generally Indo-European) languages? Why is its disappearance so much more apparent in English than other related languages?


I would like to freeze, or in any way disable Google Play on my Android 2.3.6. I tried to prevent the autorun: it always finds its way. I tried to freeze it with Gemini App Manager: even blocked it starts.  How can I definitely block or even uninstall this damned application ? Has someone succeeded in doing so ?  The reason: every time it starts, my whole phone becomes extremely slow, barely usable.

Believe it or not, but I want to remove a few Google Apps which I have no use for and want to free up space, resources and mobile data usage by not having them on my phone at all.  These include:   Google Currents Google Play Music Google Play Movies Google Play Newsstand Google Keyboard Google+   I have ‘uninstalled’ them via the Play Store, but they still appear in my ‘Installed’ items in ‘My apps’ in the Play Store and instead of ‘UPDATE' and ‘UNINSTALL’ for any other app in my ‘Installed’ list, they stubbornly remain and only have ‘OPEN’ AND ‘UPDATE’ options.  Also going in the ‘All’ list in ‘My Apps’, all these apps are also different from other ones, where unlike other locally uninstalled apps that have their payment status (‘FREE’ or ‘PURCHASED’) and a ‘X’ at the top to remove it from your Google Account entirely, these Google Apps that I don’t want on my Android and want to be completely optional for my Android experience, only have an ‘UPDATE’ and no X up the top of their listing.  I don’t mind them remaining on the Google Account if Google insists on this, but I just want listings to ‘update’ them in my Google Play updates list to be removed, given this is Google basically forcing me to reinstall them against my will.  Is there a way to do this?  I’m on stock 4.3 Gnex.


I'm a little embarrassed to ask this question because it should be easy but it's stumped me for over a week now. The answer will determine how I write some code, so it matters.  According to  the coordinates of an n-sphere in $n$ coordinates is given as  \begin{align} x_1 &= r \cos(\phi_1) \\ x_2 &= r \sin(\phi_1) \cos(\phi_2) \\ x_3 &= r \sin(\phi_1) \sin(\phi_2) \cos(\phi_3) \\     &\vdots\\ x_{n-1} &= r \sin(\phi_1) \cdots \sin(\phi_{n-2}) \cos(\phi_{n-1}) \\ x_n &= r \sin(\phi_1) \cdots \sin(\phi_{n-2}) \sin(\phi_{n-1}) \,. \end{align}  By this formula, the coordinates of an n-sphere in 4 coordinates should be  \begin{align} x_1 &= r \cos(\phi_1) \\ x_2 &= r \sin(\phi_1) \cos(\phi_2) \\ x_3 &= r \sin(\phi_1) \sin(\phi_2) \cos(\phi_3) \\ x_4 &= r \sin(\phi_1) \sin(\phi_2) \sin(\phi_3) \end{align}  Whereas  gives coordinates as (allowing for a change of notation and ordering)  \begin{align} x_1 &= r \cos(\phi_1) \\ x_2 &= r \sin(\phi_1) \cos(\phi_2) \\ x_3 &= r \sin(\phi_1) \sin(\phi_2) \sin(\phi_3) \\ x_4 &= r \sin(\phi_1) \sin(\phi_2) \cos(\phi_3) \end{align}  Which is correct? Note that $x_3$ and $x_4$ are swapped in my version and wolfram's.

I was wondering how one would proceed to convert between coordinate systems in $ \mathbb R^n $.  For $ \mathbb R^2 $ the conversion is easy and just basic trigonometry. Given $(r, \theta)$ we can convert these polar coordinates to cartesian coordinates to $(x=r\cos\theta, y=r\sin\theta)$  The same follows for $ \mathbb R^3 $. Given $(r,\theta_1,\theta_2)$ in spherical coordinates we can convert the spherical coordinates to cartesian coordinates with the following transformation $(x=r\cos\theta_2\cos\theta_1,y=r\cos\theta_2\sin\theta_1, z=r\sin\theta_2)$, just so my point of reference is clear:$\theta_1$is the angle lying in the x-y plane, and  $\theta_2$ is the angle the vector makes with the x-y plane.  So what about for four dimensions and up? For the sake of simplicity we can define the n-sphere vector as $(r,\theta_1,\theta_2,...,\theta_n)$ and the cartesian vectors $(x_1,x_2,...,x_n)$ and maintain the same reference of $\theta_1,\theta_2$ as before.  How do we define a transformation in $ \mathbb R^4 $?  A look into this wikipedia page under the  gave me something that I don't believe is quite right.  As according to the section  $(x_1=r\cos\theta_1,x_2=r\sin\theta_1 \cos\theta_2,x_3=\sin\theta_1 \sin\theta_2\cos\theta_3,...)$ which is already in contradiction to my statement about $ \mathbb R^3$ transformations.   What is the general transformation rule? Am I missing something that I should know from linear algebra that I might be forgetting because my linear algebra is rusty? If so, please let me know what I should review or point me in the right direction.


I learned C++ in my highschool on Borland C++, and used textbooks which referred to the same. So the basic C++ I know doesn't even work on most IDEs I have tried. For example, I was using hackerrank the other day and I got an error because I used cout<<""Hello!"; which is what I learned in school. But the only way the program started working was after I changed it to std::cout<<"Hello";.    I am stuck here wondering what I should do now.    I want to get back to C++ programming and this time the right way. So any suggestions?    Also, explain the difference in the above code samples and in standard way of C++ programming and Borland way of programming.

This question attempts to collect the few pearls among the dozens of bad C++ books that are published every year. Unlike many other programming languages, which are often picked up on the go from tutorials found on the Internet, few are able to quickly pick up C++ without studying a well-written C++ book. It is way too big and complex for doing this. In fact, it is so big and complex, that there are very many very bad C++ books out there. And we are not talking about bad style, but things like sporting glaringly obvious factual errors and promoting abysmally bad programming styles. Please edit the accepted answer to provide quality books and an approximate skill level — preferably after discussing your addition in . (The regulars might mercilessly undo your work if they disagree with a recommendation.) Add a short blurb/description about each book that you have personally read/benefited from. Feel free to debate quality, headings, etc. Books that meet the criteria will be added to the list.  Books that have reviews by the Association of C and C++ Users (ACCU) have links to the review. *Note: FAQs and other resources can be found in the  and under .


I want to grant a newly created user sudo privileges in Ubuntu.  I tried  sudo adduser hduser admin   but it says no admin group exists. How can I do it?

After I add a user using adduser, I can't see it via System > Administration > Users and Groups unless I log out and then log in again. Is that normal?  Also, can I set a newly added user as a sudoer or do I have to change that only after adding it? How can I do that via the shell?  Finally, can I delete the original user that was created upon initial installation of Ubuntu, or is this user somehow 'special'?


As mentioned in the title, i want to get started with number theory and I am searching for a book fitting my purposes. Ive just finished Calculus 1. I'd be glad if you could recommend a book written in English or German. Thank you in advance.

I'm in Grade 11. I'm interested in elementary number theory and would like properly study it. I'm not intending to enter any competitions.


What is the preferred way to refer to la Wallonie in English -- Wallonia or Walloon Region?

Many place names have different form/spelling in English and in the original language of the country, in which they lie, e.g. Lyons x Lyon, The Hague x Den Haag, Munich x München. Most of them are used so commonly that there is no question about their usage in English (e.g. I would definitely write Cologne and not Köln); however, there are also cases, which are more ambiguous because they are not used often. Specifically, I came across an English variant Ratisbon for Regensburg in Germany. I never encountered this variant before and I wonder whether I should use it in a list of publications, if all other places of publication in this case are anglicized (e.g. Cologne, Munich). What is the general rule for using anglicized versions of place names versus the use in the original language?


Normally Indian dishes are spiced up with chilli, turmeric, coriander and pepper and that seems enough for most cases. However when I go to the supermarket these days, there seem to be too many exotic spices packed into little bottles (jalapeno, basil, white pepper). I would like to know whether these spices go well with Indian cooking. What are some of these spices that I should consider putting in my shelf.?

I'm interested in slowly getting started with Indian cooking and building up my store of spices. However, I generally don't have as much time to cook as I would like and really don't have enough space to go out and binge spend on cooking materials for Indian food.  What are the bare minimum ingredients / spices / etc that I would need, to make some tasty  dishes for a wide array of palettes (in case I can convince friends to try my cooking).


I am looking for a product.  Basically exactly stack exchange but for a custom internal application.   We want to implement a Q&A site with reputation into our existing customer base.   I'm open to paying or open source solution.   Self hosted or cloud

Is the Stack Exchange engine that powers Stack Overflow available to download or install internally for an enterprise or company?  I think Stack Exchange's engine is very great and could be very cool to use for internal enterprise patterns and practices, like the engine of Wikipedia.


A cubic equation $x^{3}+ax^2+bx+c$ has all negative real roots and $a, b, c\in R$ with $a<3.$ Prove that $b+c<4.$  My attempt : Let the cubic be $f(x)$ Plotting graph we see that , $f(x\geq 0)>0$. So we can see that a relation between $a, b, c$ can be established by putting $x=1$, so, $1+a+b+c> 0$. So $b+c>-4$. Also by using Vieta's Formula we get $a, b, c > 0$. Now I'm uncertain how to proceed, any help will be appreciated. This is a problem of a maths olympiad. Thanks.

let $a,b,c \in\mathbb{R} ,a<3$    and all roots $p(x)=x^3+ax^2+bx+c=0$ be negative .    then prove that $b+c\neq 4$   MyTry :   we have $x_1<0 ,x_2<0,x_3<0$ So: $$x_1+x_2+x_3=\dfrac{-a}{1}=-a \to a\in (0,3)$$ and :  $$x_1\cdot x_2\cdot x_3=\dfrac{-c}{1}=-c$$  now what ?


When I first saw:  $$\frac{\pi}{4}=1-\frac{1}{3}+\frac{1}{5}-\frac{1}{7}+\frac{1}{9}\mp\cdots.$$  I was puzzled that such an expression could have anything to do with circles. There are tons more and it seems like a very large amount of summations will end up having to do with $\pi$. My question is how come $\pi$ finds its way into so many formulas, and could the above equation be thought of geometrically.

Following reading this great post : , Vadim's answer reminded me of something an analysis professor had told me when I was an undergrad - that no one had ever given him a satisfactory intuitive explaination for why this series definition should be true (the implied assumption being that it is so simple, there should be some way to look at this to make it intuitive).  Now it follows simply from putting $x=1$ in the series expansion $$ \tan^{-1}(x) = x - \frac{x^3}{3} + \frac{x^5}{5} - \cdots $$  but I don't see anything geometrically intuitive about this formula either!


You roll a fair, six-sided die 4 times. what is the probability of getting at least 2 sixes?   How do you answer this question using combination rules?

What is the probability of rolling at least two 6's on twelve rolls of a fair 6-sided die.  I am using the complement to solve the question  $$1-\frac {5^{12}+(_{12}C_ 1)5^{11}}{6^{12}}$$  $5^{12}$ is the probability of not rolling a six  $6^{12}$ is the sample space  My question is why does the binomial coefficient have to be multiplied $5^{11}$ where the binomial coefficient is a "6" on the die.  This method I find difficult but intriguing.


I have one task that I want to do: def task(body):     # some logic that which can throw an exception     # if something goes wrong     do_task(body)   and the logic inside this task can throw an exception And I have execute method with executor: def execute():     executor = ThreadPoolExecutor(max_workers=4)     future1 = executor.submit(task, body1)     future2 = executor.submit(task, body2)     future3 = executor.submit(task, body3)     future4 = executor.submit(task, body4)          result1 = future1.result()     result2 = future2.result()     result3 = future3.result()     result4 = future4.result()  And I want if at least one task crashes - do not wait for the completion of other tasks and stopped everything. How can I do this correctly?

Is it possible to terminate a running thread without setting/checking any flags/semaphores/etc.?


I bought a laptop with 4GB RAM. Im planning to upgrade it to 8GB later (not in a short time) but i dont want to waste my time in reinstalling windows (if possible).  So, i think i will install windows 64bit for now, with a hope that i dont have to reinstall my windows when i upgrade my RAM to 8GB.  My questions are :   Is it possible? Is it good to have 64bit windows running on 4GB RAM?Does having 64bit on 4GB RAM effect laptop's performance?   Thanks for your help :D

I've recently purchased Windows 7 Ultimate.  I have an AMD Athlon64 X2 5000+ with 2GB DDR2 RAM.  I know RAM has gotten much cheaper, I know, I know, but I am not going to be able to upgrade my RAM for about a year.  My question is obviously this; will I get any benefit from installing 64-bit Windows over 32-bit if I'm only using 2GB of RAM?    As I understand, the minimum requirement is 2GB & max is 192GB so if the minimum for 64-bit is 2GB & the minimum for 32-bit is 1GB will I lose performance if I chose to install 64-bit at it's minimum requirement over 32-bit whose minimum is half the amount?  I would like to install the 64-bit edition if only because it's the future.  192GB of RAM! that's incredible! Plus I've heard it simply performs better.  But that is with a larger amount of RAM.  I've tried to make this question as easy to decipher as possible.  Any advice would be greatly appreciated.


I'm reading about inacessible cardinals. I don't know anything about them, I just know basic set theory, cardinal operations etc., but I am too curious to leave this question that now I'm (probably) not able to totally understand...  So, a (strongly) inacessible cardinar is a regular uncountable cardinal $\lambda$ such that  $\kappa < \lambda \implies 2^{\kappa}<\lambda$. I know that if the hypothesis of being uncountable is dropped then $\aleph_0$ satisfy the other 2 properties (regular and $\kappa < \aleph_0\implies 2^{\kappa}<\aleph_0)$. But I can't think what happens if we drop the hypothesis of $\lambda$ being regular. Does exist a uncountable singular cardinal $\lambda$ such that $\kappa < \lambda \implies 2^{\kappa}<\lambda$? Why?

A cardinal $\kappa$ such that $2^{\lambda}<\kappa$ for all $\lambda<\kappa$ is regular?  I would appreciate very much an answer


I am following the  and am using Unity 5.  I just completed this video (linked) and I tested played it to see my animations worked but it seems like it will only transition from idle to walking after the entirety of the idle animation completes. The idle animation is quite long so my character will move around when it looks like its idling since the movement responds right away.  Did I mess up something in my transitions? I followed the directions exactly and didn't change anything in the inspector that I wasn't told to do.

I'm trying to make a simple idle-walk transition in Animator using Unity. I've set a script that changes the Speed value from the Animator, and it works perfectly when I move the character forward when the game is on.  The transitions work well between both animations, except that they don't start automatically after the speed has changed to greater than zero.  I've found out that it waits until the animation loop gets to it's end, which makes the game feel dull and not fluid at all.    I don't think there's an issue with the code, but I'm attaching it anyway:  #pragma strict var anim : Animator;  function Start () {     anim = GetComponent("Animator"); }  function Update () {     var move : float = Input.GetAxis ("Vertical");     anim.SetFloat("Speed",move);     transform.Rotate(0,Input.GetAxis("Horizontal"),0);     transform.Translate(0,0,(Input.GetAxis("Vertical")*Time.deltaTime*move)); }


Developing a python script in QGIS 2.2, I can run algorithms from the Processing plugin fine such as those from QGIS geoalgorithms and SAGA.   Can you do the same for the algorithm "Merge shapefiles to one" from the Vector menu and how can you call it from the Python console?  The "Merge shapefiles to one" algorithm is from the Ftools plugin.  Found a link which might be useful:

I know how to make Hub Lines using the GUI, I want to know how to do the same using the Python Console, a tutorial would be great.


For instance if there was a galaxy, assume it to be made up of antimatter (isolated from other "normal" galaxies), how would we, or rather, would we be able to distinguish if it was made up of matter or antimatter? If not then why is not considered that half of the universe out there might be made up of antimatter but we think there is an abundance of matter over antimatter just because we can't detect any difference among the two?  Are there any cases in which antiparticles act differently than their corresponding particles would?

Since the spectra of hydrogen and  are the same, how do astronomers know which one they're detecting? Is, perhaps, the  in antihydrogen different?


The problem is finding the sum of the numbers:  $$\arctan{\frac{1}{2}} + \arctan{\frac{1}{3}}$$  I've tried expressing $\frac{1}{2}$ and $\frac{1}{3}$ as tangent functions of some angles but I wasn't able to find a valid solution.  Any help would be much appreciated.

Show that $\arctan\frac{1}{2}+\arctan\frac{1}{3}=\frac{\pi}{4}$.   Attempt:  I've tried proving it but it's not equating to $\frac{\pi}{4}$. Please someone should help try to prove it. Is anything wrong with the equation? If there is, please let me know.


If $X_1,X_2...X_N$ are independent Poisson variables with parameters $\lambda_1,\lambda_2...\lambda_3$, then given $\sum_iX_i=N$, we have that   $X_i \sim \mathrm{Binom}(N,\frac{\lambda_i}{\sum_j\lambda_j})$ (straight from !)  I am looking for a proof of this -- I haven't really studied the relevant stats to know how to attack  this problem. Any help would be great. Cheers!

I need help thinking about and identifying the kind of regression analysis that would be appropriate for this problem. Nothing I've discovered so far seems quite right. Referrals to articles or examples would be helpful. Thank you.  The data look like this:   The data are observational. The sampling unit is a geographic location (EDIT: let's assume units are independent); I'm just trying to understand the basic analytical problem here). At each sampling unit, there are events of two types: the event type of interest (A) and all other types (B). EDIT: In other words, each event is a binary outcome (success, failure). The outcomes are aggregated to the to the location level (Location 1: Success 3, Failure 2. Location 2: Success 0, Failure 1. Location 3: Success 0, Failure 0. Location 4: Success 4, Failure 9 .... etc.  Often, A=0 and, somewhat less often but still frequently, A+B=0.    I am interested in testing a hypothesis about A, somehow controlling for the total count of events (A+B), so either a proportion A/(A+B) or a count model that controls for the total count.  If I understand correctly, if the counts were large, proportions could be calculated for all units, and I could do beta regression. But that definitely can't happen when the total number of events for a unit is zero.  If all I cared about was the count, I could use a ZIP or other count model (and maybe still can). But the research question regards the frequency of A relative to the total number of events.  But how to control for the total number of events? Does it just go in the predictors of a ZIP or similar model? I suspect it's more complicated than that.  It seems obvious to me that the individual events could be modeled directly using multi-level logistic regression (EDIT: or another model for clustered data), but I'm wondering if there is a simpler way to examine what I'm interested in, and I just somehow haven't seen an example of this.


Quite often I see code like this (C, C++ and sometimes Java):  return (value);   I don't see any benefit of these parentheses. So my question is, have the programmers assumed return to be some kind of function with the return value as argument or are there really cases where these parentheses make sense?  I understand that a similar question has already been asked , but this is related to ANSI C only. I wonder if there are aspects specific to C++ or Java that have not been answered there.

Quite often in ANSI C code I can see parenthesis sorrounding a single return value.   Like this:-  int foo(int x) {   if (x)     return (-1);   else     return (0); }   Why use () around the return value in those cases? Any ideas? I can see no reason for that.


Trying to place a background image into the scene that renders with the scene. The camera view shows the image nut it's not there when rendered. Any clues?

First time I've used cycles rendering engine.  I'm using a movie clip as the background in short animation. Selected RBGA under Property Tab, and Transparent under Film Tab.  It looks good and individual frames in OpenGL active viewport render, and looks fine.  When I try to get it to spit out PNG files of the finished animation the objects render out fine, except no movie clip background as Blender Render engine did when using Paper Sky setting.  Operator error, or am I trying to do something Cycles won't do?  Haven't found an answer in my searches so far.  Can anyone point me in the right direction please.   Addition:  I think I found my problem after a couple more hours of research.  Post should read "operator ignorance" instead of operator error.  Too tired to try the solution tonight, everything looks better in the morning. Thanks anyway.  Sorry, I just saw your posts.  Really tired.  Much appreciation.


Given,  $U_t-U_{xx}-2U_x=0$  Using method of separation of variables, find ALL possible solution.  My answer :  $U(x,t)=X(x)T(t)$  $T'(t)/T(t)$=$[X''(x)+2X'(x)]/X(x)$=$\lambda$  From here I'm stuck. Could someone show me some working steps for me to proceed further.

Hi could someone guide me this problem  It says ,  $ u_t - u_{xx}-2 u_x=0  $  Use the method of separation of variables to find all possible solutions.   Could someone help me out for this problem. I'm beginner at PDE. I would be much appreciated if you able to show some partial work so that I can understand.  Thanks in advance for taking my consideration


In other words, are the white walkers able to cross the Narrow Sea? We do know that they cannot swim, but could the freeze it?

The white walkers are a constantly-looming threat over Westeros, but in a worst-case scenario where the wall is breached and Westeros falls to the white walkers, would Essos be similarly doomed? Would the Narrow Sea protect Essos from the white walkers, or do they know how to build / pilot ships?


Evaluate $$\lim_{n \to \infty} \frac{1}{n}[(n +1)(n+2) \cdots (n+n)]^{\frac{1}{n}}$$  We can write as $\displaystyle\lim_{n \to \infty} \frac{1}{n}[(n +1)(n+2) \cdots (n+n)]^{\frac{1}{n}}$ $$= \lim_{n \to \infty}\left[\frac{(n +1)(n+2) \cdots (n+n)}{n^n}\right]^{\frac{1}{n}} = \lim_{n \to \infty}\left[(1+\frac{1}{n})(1+\frac{2}{n})\cdots (1+\frac{n}{n})\right]^{\frac{1}{n}}$$  I have used this result if $\{a_n\}$ is a sequence of positive term which is convergent to $l$ and $b_n = (a_1. a_2 . \cdots a_n)^{1/n}$ ,thhen $b_n$ converges to $l$  here $a_n = 2$, but i think it is not right,how to use this result in this question. Give me hint how to proceed . Thank you

Evaluate $$\lim_{n \rightarrow \infty~} \dfrac {[(n+1)(n+2)\cdots(n+n)]^{\dfrac {1}{n}}}{n}$$  Attempt: Let $$y=\lim_{n \rightarrow \infty} \dfrac {[(n+1)(n+2)\cdots(n+n)]^{\dfrac {1}{n}}}{n}$$  $$\implies \log y = \lim_{n \rightarrow \infty} \dfrac {1} {n} [\log (n+1) +\cdots+log(n+n)-log(n)] $$  How do I move forward?  Thank you very much for your help.


Ok, I just installed Ubuntu 12.04 and I was an administrator, but then someone made a standard user and deleted the admin account. How do I make a new admin user without it asking me to enter a password? Or, is deleting the OS and reinstalling it the only option?

I clean-installed Ubuntu 11.10 today, and then installed VirtualBox.  This required me to add myself to the vboxusers group, and since 11.10 seems to no longer have a graphical app to add users to a group, I ran the following command:  sudo usermod -G vboxusers stephane   This is a problem.  I now see what I should have run instead is:  sudo usermod -aG vboxusers stephane   The end result is I'm no longer in the groups I should be in.  Including whatever group is required to run "sudo".  When I run any command as sudo now, I get the following:  $ sudo ls [sudo] password for stephane:  stephane is not in the sudoers file.  This incident will be reported.   Is there a way to fix this, or do I need to re-install from scratch again?


There's not a ton of evidence to support this, but the intro to the show seems to imply the world exists inside a sphere rather than on the outside of it:    This seems like the sort of hint GRRM would drop; additionally, this could be the source of the strange season cycles that the world experiences. It's at least plausible that the inhabitants of this world would never notice due to atmospheric effects. Also, I don't recall any references in the books to a ship appearing on the horizon (which would be a nail in the coffin for my theory).  Of course, perhaps the animators for the intro simply did not want to render a sky...  EDIT: forgot to include:   In  GRRM is quoted as saying the world is "round", which neither confirms nor denies my suspicions.

The HBO series  and the book series it's from, , offer no examples or suggestions that the world is set in a hollow world. But the television show's  strongly suggest this very thing. Has there been an official word about the shape of the Song of Ice and Fire world?


When I was re-watching the well-known movie about the boy who lived I noticed that the tenses in the note from Dumbledore (spoiler, sorry ><) don't really correspond, or do they?   Here's what I mean:     It is time it was returned to you.   Shouldn't it be:     It is time it is returned to you.   Of course, Dumbledore is not dumb (or movie creators, if you will :P), and I'm just wrong, but could you explain why?

I'm watching Suits TV Series, and there was something that caught my attention. 2 guys meet, have a drink, chat, and then one guy says:     I mean it's time I told you. I made a deal with Darby to take over the   firm from Jessica.   Why is "told you" in paste tense? What exactly does it mean? He is saying that news right now. If I were to say that, I would say "it's time to tell you" or "it's time I'm gonna tell you".  Thanks!


I was drawing a diagram and trying to resolve all the forces. It seems to me that because of gravity, centrifugal force will produce a sort of "dragging" motion along the surface of the earth. The centrifugal force is quite small (I got around 2.5 N at the equator). This force is easily neutralized by friction. Is this right?  EDIT: I did not consider any complexities that may arise due to revolution, I just considered rotation.

Let us say a block of mass is placed on the surface of earth. Then while drawing the forces on that body, we say:   Force $F = mg$ acting towards the center of Earth. Normal reaction $N$ offered by the surface of Earth.   If no other forces are acting, we say $F=N$. But what about the centrifugal force $m\omega^2R$ . Why don't we ever bring that into picture? What am I missing?


I'm new at Latex, and I'm trying to make a photo diagram.     And i have found the program "Dia" and wants to know how it works, i have tried to read the Manuel, but I'm not entirely sure of how it works, - So my questions is, how can i convert the Diagram to Latex, and then how do i include it in Latex?, And if i include a photo ind the diagram, where should i put the photo-file (in which folder)?

What packages do you use and recommend for creating graphics in your LaTeX documents?     As this is a community wiki post, please add your package to the accepted answer (or add a comment, and someone with >100 rep will add it to the CW answer), and include a brief description of what differentiates it from others and how it can be used (GUI drawing tool which generates code, type in raw text, or generates image for inclusion in document).   We'll eventually sort these answers under headings.


Main program  public class signin{      public static void main(String[] args) throws Exception {      util.OpenBrowser();      b.closebrowser();   }   1st method is in class util: openbrowser is one method  public class util{  public static WebDriver OpenBrowser(){      System.setProperty("webdriver.chrome.driver",                         "D:\\Selenium\\selenium3.1\\chromedriver.exe");      driver = new ChromeDriver();      driver.manage().timeouts().implicitlyWait(10, TimeUnit.SECONDS);      driver.get("https://www.google.com/");     return driver;  }   2nd method(closebrowser) is in another class b  public class b  {       static WebDriver driver;      public static void Execute(WebDriver driver){         homepage.phonenumber(driver).sendKeys(constant.Phonenumber);         homepage.proceedbutton(driver).click();     }        public static void closebrowser(){          driver.close();      }  }   I am trying to call 2 methods of different classes  in another class and  I am getting null pointer exception and pointing the line to closebroweser method. Why null pointer exception occured while calling the second method?  closebrowser method is working only when I am not calling openbrowser method from different class. It is working if i am writing openbrowser code in main program itself.

What are Null Pointer Exceptions (java.lang.NullPointerException) and what causes them?  What methods/tools can be used to determine the cause so that you stop the exception from causing the program to terminate prematurely?


Here is the full question. Lots of struggles:  Let $p(t)$ belong to $P(R)$. a) If $(x − \alpha)$ is a factor of $p(t)$ over the complex numbers (i.e. $p(t) = (x − \alpha)\cdot q(t)$, for $\alpha$ equal a complex number and for $q(t)$ a polynomial with coefficients in the complex numbers), then show that  $(x − \alpha)(x - \overline{\alpha})$ is a also a factor of $p(t)$ over the complex numbers (where $\overline{\alpha}$ denotes the complex conjugate of $\alpha$)  and  b) Use the fundamental theorem of algebra to show that every polynomial with real number coefficients is the product of real polynomials of degree 1 or 2.  I've tried reading the book (Friedberg) and looking through my lecture notes to figure this out. I've tried using the unique factorization theorem for a) and, needless to say, have not had any luck (but this could also be because of the fresh "understanding" of the theorem). Anyone able to help? I just no idea how to go about proving this.

So I understand how to do integration on rational functions with a linear and a quadratic denominator, and I understand how to do a partial fraction decomposition, but I was wondering what happens if the polynomial is higher degree and can't be factored. Later in the page, it says this:     However, it can be shown that any polynomial with real coefficients is a product of linear and/or irreducible quadratic factors with real coefficients.   And I was wondering, how do we know this and is this definitely true?


private static double round (double value, int precision) {     int scale = (int) Math.pow(10, precision);     return (double) Math.round(value * scale) / scale; }   I would like this code to not only be able to round to any given decimal place, but also to either always round up or down, this could be given as another paramter. But I am having trouble with how to implement this.  For example, I want to round 11.1436 to 11.15. Please help.

What I would like is a method to convert a double to a string which rounds using the half-up method - i.e. if the decimal to be rounded is 5, it always rounds up to the next number. This is the standard method of rounding most people expect in most situations.  I also would like only significant digits to be displayed - i.e. there should not be any trailing zeroes.  I know one method of doing this is to use the String.format method:  String.format("%.5g%n", 0.912385);   returns:  0.91239   which is great, however it always displays numbers with 5 decimal places even if they are not significant:   String.format("%.5g%n", 0.912300);   returns:  0.91230   Another method is to use the DecimalFormatter:  DecimalFormat df = new DecimalFormat("#.#####"); df.format(0.912385);   returns:  0.91238   However as you can see this uses half-even rounding. That is it will round down if the previous digit is even. What I'd like is this:  0.912385 -> 0.91239 0.912300 -> 0.9123   What is the best way to achieve this in Java?


While going through javascript course on codecademy.com, I've become slightly confused.  So first we've been learning how to add method to a Class:  function Dog (breed) {     this.breed = breed;     this.sayHello = function () {         console.log("Hello this is a " + this.breed + " dog");     } }; var someDog = new Dog("golden retriever"); someDog.sayHello();   Then we started the "prototype". And there was this example:  function Dog (breed) {     this.breed = breed; }; Dog.prototype.sayHello = function () {     console.log("Hello this is a " + this.breed + " dog"); } var someDog = new Dog("golden retriever"); someDog.sayHello();   Both examples are giving the same result.  Are these two examples are just two ways doing same thing? Or there is a practical difference between two of them?

What's the difference between  var A = function () {     this.x = function () {         //do something     }; };   and  var A = function () { }; A.prototype.x = function () {     //do something };


I have the same problem but can still login to my account on my friends computer. i logged out and now cant log in as it says to connect to the internet and all my other stuff works because i am connected to the internet. help

Similar to  on the bugs in Minecraft, I would like a complete list of what error codes exist in Minecraft and how they occur, as well as how they can be resolved.


I was trying to solve some algorithms when I found out that one could leverage a simple stupid linear Diophantine equation, but I cannot figure out how solve it (I'm pretty sure I would have been able to do that back in high-school but I guess I am getting rusted).  Basically, I ended up on this equation: $ax+by=c$, where $a=3$, $b=5$ and the triplet $\lbrace a, b, c\rbrace \in ℕ$  Which is to say the least the most "basic" Diophantine equation.  Obviously, I am trying to find out the value of $x$ and $y$ according to $c$ that are .   The equation has a solution upon the condition that $c$ is a multiple of $gcd(a,b)=gcd(3,5)=1$   I noticed that there is an obvious solution here, which is the couple: $\lbrace x=2c, y=-c\rbrace$  Supposedly other solutions are of the form: $\lbrace x + kv, y − ku\rbrace$ where $k$ is an arbitrary integer such as: $u=\frac{a}{gcd(a,b)}=\frac{3}{1}=3$ and $v=\frac{b}{gcd(a,b)}=\frac{5}{1}=5$.  Therefore other solutions are more specifically $\lbrace 2c = x + 5k, -c = y − 3k\rbrace$  Equivalent to: $\lbrace x = 2c - 5k, y = -c + 3k\rbrace$  At that point I cannot manage to find the value of $k$ that would make $x$ and / or  $y$ positive.   The replacement strategy seem to lead to nothing.  I am pretty sure it might be really easy but cannot get my head around it.  Any idea?  [Edit]  My point is how to find out $k$. If I'm just replacing $x$ and $y$ with their respective values found above in the former equation, I am going to end up with:  $3(2c+5k) + 5(-c+3k) = c$  $\Rightarrow 6c + 15k -5c + 15k = c$  $\Rightarrow c + 30k = c$  $\Rightarrow 30k = c - c = 0...$  I don't think $k$ is equal to $0$... so I might be wrong.

I want to find a set of integer solutions of Diophantine equation: $ax + by = c$, and apparently $\gcd(a,b)|c$. Then by what formula can I use to find $x$ and $y$ ?   I tried to play around with it: $x = (c - by)/a$, hence $a|(c - by)$.     $a$, $c$ and $b$ are known. So to obtain integer solution for $a$, then $c - by = ak$, and I lost from here, because $y = (c - ak)/b$. I kept repeating this routine and could not find a way to get rid of it? Any hint?  Thanks, Chan


My family and I are traveling from Auckland to Los Angeles via a stop in Honolulu. Will we have to clear customs in Honolulu or LAX or even both? Will we need to allow extra time in Honolulu for this? Or will the HNL-LAX be considered domestic? Flying Hawaiian; it appears to be different flight numbers for each leg.

I'm a British citizen travelling from London Heathrow (LHR) to the Hartford, Connecticut airport, and have a two hour stopover in Newark, New Jersey (EWR) on my itinerary. At what stage would I clear immigration and customs on arriving in the USA?


CERN claims that there's a possibility of formation of tiny 'quantum' black holes inside the LHC. So, if that ever happens (or have already happened), will the observers ever know about it? Can in any way a quantum black hole be visible within the LHC?

Last week, I went to Switzerland and visited the LHC. I took a tour, and the guide told us that it is possible for black holes to appear in the LHC, but they will be so small, that they would evaporate away due to Hawking Radiation and there would be virtually no time for the black hole to "suck up" anything. I suddenly remembered something I read on  that said a "a 100 tonne black hole would evaporate in 8.4×10−2 s, emitting approximately E=Mc2=9×1021 joules of energy as it does so – equivalent to more than a million megatons of TNT. I guess you could call this an explosion!"  If Mount Everest was condensed into a black hole, it would be smaller than a hydrogen atom. Mount Everest is 357 trillion pounds. 357 trillion pounds converted into energy would be a mind-boggling amount.  If a black hole formed in the LHC, wouldn't it completely annihilate it due to the spontaneous energy release due to Hawking Radiation? I'm new to the topic of Hawking Radiation, so I do not know if I have been misinformed in any way.


Here's Prob. 7 in the Exercises of Chapter 3 in the book Principles of Mathematical Analysis by Walter Rudin, 3rd edition:      Prove that the convergence of $\sum a_n$ implies the convergence of $$ \sum \frac{\sqrt{a_n}}{n}$$ if $a_n \geq 0$.    How to show this? I have no clue! Can anybody here please be of any help?  Is this result a special case (or application) of a more general result about infinite series?

Ch.3 #7. Prove that the convergence of $\sum a_n$ implies the convergence of $$\sum \frac{\sqrt{a_n}}{n},$$ if $a_n \geq 0$.      My attempt. If $\sum a_n$ is convergent, then by the root test, $\lim_{n \rightarrow \infty} sup \sqrt[n]{|a_n|} < 1$. This means $|a_n|^{1/n} < 1$. Because $a_n \geq 0$, this means $a_n ^{1/n} < 1$. Now apply the root test to $\sum \frac{\sqrt{a_n}}{n}$ by considering $$\lim_{n \to \infty} sup \sqrt[n]{|\frac{\sqrt{a_n}}{n}|}.$$ $$\sqrt[n]{|\frac{\sqrt{a_n}}{n}|} = \frac{\sqrt{{a_n}^{\frac{1}{n}}}}{\sqrt[n]n}.$$ Because  $a_n ^{1/n} < 1$, certainly the numerator on the left-hand side of the equation above is $<1$. And because $n$ tends to $\infty$, and $n > 1 \rightarrow \sqrt[n]n > 1,$ the denominator is $>1$. Therefore the limit is $<1$ and the root test implies that $\sum \frac{\sqrt{a_n}}{n}$ converges.     If there are any errors in my proof, I think they come from 1) my assumption of the converse of the root test theorem and 2) my misunderstanding of $\lim_{n\to\infty} sup$. Thanks in advance for your help.


Can I use or "cast" the type of a class, for instance type of the class CustomClass, therefor typeof(CustomClass), to execute a method which relies on providing its corresponding class CustomClass as an "argument"?  Method<CustomClass>();   How could I achieve this by only knowing typeof(CustomClass)?  Detailed question:  I'm developing a Web API in ASP.NET 4.5. I have access to an extension method, that I cannot change, for the Startup's IAppBuilder app:  public static class AppExtensions {     public static void AddExceptionTranslation<TException>(         this IAppBuilder app,         HttpStatusCode statusCode,         Func<TException, ApiErrors> messageGenerator))         where TException : Exception; }   This extension method is used to convert custom exceptions, which extend Exception, to its appropriate status codes. I'm using it as follows:  public static void SetUpExceptionHandling(IAppBuilder app) {     app.AddExceptionTranslation<CustomException>(HttpStatusCode.BadRequest, e => e.ToApiErrors());     app.AddExceptionTranslation<CustomUnauthException>(HttpStatusCode.Forbidden, e => e.ToApiErrors());     // ... }   Right now I have to manually add an entry for every single custom exception, providing the TException in each case. I'm already maintaining a data structure which contains the typeof for each custom exception class, alongside with its appropriate status codes, unique ids and other properties that I only want to maintain in one place.   I'd like to use this existing data structure to iterate through it and execute AddExceptionTranslation<TException> for each custom exception, where I know their Type.   Is this possible? If not, would it be possible if my data structured contained something else? Sure, I could just bite the bitter apple and add each new custom exception to the data structure and manually add an entry for the method execution but I'd really like to automate the latter.  Please let me know if I can clarify. Thanks!  Edit  AddExceptionTranslation actually accepts a second argument, a lambda expression, that's applied to the custom exception:  app.AddExceptionTranslation<CustomException>(HttpStatusCode.Forbidden, e => e.ToApiErrors());  I didn't think it would be relevant to the question but since it's interfering with the suggested solution/duplicate I'm in quite the pickle. Can I still invoke the method in some way?

What's the best way to call a generic method when the type parameter isn't known at compile time, but instead is obtained dynamically at runtime?  Consider the following sample code - inside the Example() method, what's the most concise way to invoke GenericMethod<T>() using the Type stored in the myType variable?  public class Sample {     public void Example(string typeName)     {         Type myType = FindType(typeName);          // What goes here to call GenericMethod<T>()?         GenericMethod<myType>(); // This doesn't work          // What changes to call StaticMethod<T>()?         Sample.StaticMethod<myType>(); // This also doesn't work     }      public void GenericMethod<T>()     {         // ...     }      public static void StaticMethod<T>()     {         //...     } }


I have a very basic program in Android Studio that gets a Json-Object from a website ("") and the just displays it on screen, without parsing it. The Json-object is transmitted correctly, but at onPostExecute the String result seems to be null and the Log.e("setText") is throwing a NullPointerException, while Log.e("String") is correct and neither the IOException nor the MalformedURLException is thrown:       try {             url = new URL("https://jsonparsingdemo-cec5b.firebaseapp.com/jsonData/moviesDemoItem.txt");             connection = (HttpURLConnection) url.openConnection();             connection.connect();              InputStream stream = connection.getInputStream();              reader = new BufferedReader(new InputStreamReader(stream));             Log.e("TRY", "trybracket");             StringBuffer buffer = new StringBuffer();              String line = "";             while ((line = reader.readLine()) != null) {                 buffer.append(line);             }              String result = buffer.toString();             Log.e("String", result);             return result;          } catch (MalformedURLException e) {             e.printStackTrace();             Log.e("MUE", "Malformed");         } catch (IOException e) {             e.printStackTrace();             Log.e("IOE", "IOException");         } finally {             if (connection != null) {                 connection.disconnect();             }             if (reader != null) {                 try {                     reader.close();                 } catch (IOException e) {                     e.printStackTrace();                 }             }             return null;          }     }      @Override     protected void onPostExecute(String result) {         super.onPostExecute(result);         tvData.setText(result);         Log.e("setText", result);     } }   Also this my Logcat:   E/TRY: trybracket E/String: {  "movies": [{"movie": "Avengers","year": 2012}]} D/AndroidRuntime: Shutting down VM E/AndroidRuntime: FATAL EXCEPTION: main                Process com.stasiak.jsonparsing, PID: 20061               java.lang.NullPointerException: println needs a message                     at android.util.Log.println_native(Native Method)                     at android.util.Log.e(Log.java:238)                     at com.stasiak.jsonparsing.MainActivity$JSONTask.onPostExecute(MainActivity.java:96)                     at com.stasiak.jsonparsing.MainActivity$JSONTask.onPostExecute(MainActivity.java:39)                     at android.os.AsyncTask.finish(AsyncTask.java:695)                     at android.os.AsyncTask.-wrap1(Unknown Source:0)                     at android.os.AsyncTask$InternalHandler.handleMessage(AsyncTask.java:712)                     at android.os.Handler.dispatchMessage(Handler.java:105)                     at android.os.Looper.loop(Looper.java:164)                     at android.app.ActivityThread.main(ActivityThread.java:6541)<1 internal calls>                     at com.android.internal.os.Zygote$MethodAndArgsCaller.run(Zygote.java:240)                     at com.android.internal.os.ZygoteInit.main(ZygoteInit.java:767)

What are Null Pointer Exceptions (java.lang.NullPointerException) and what causes them?  What methods/tools can be used to determine the cause so that you stop the exception from causing the program to terminate prematurely?


I'd like to create a smoother version of the navigable and quite natural-looking random tunnel found in .  It should ideally be...   infinite, so more can be generated as the player progresses; parametrised, allowing control of its thickness over time; made of smooth curves, not rectangles as in the above game; precomputable, as knowing its bounds in advance allows collision detection for e.g. positioning powerups inside the tunnel.   I'm looking for a generic method I could implement myself. Further parameters and optimizations are welcome.  Asking here was suggested . I think this fits in both places, as it's as much about the algorithm as about gamedev.

I'm looking into adapting the classic "helicopter" game (i.e. ), but I haven't yet figured out how to create the walls-generation engine.  Any pointers into the pseudocode? I'm not so interested in the objects in the middle- only the methodology for generating the sides in a way which increases with difficulty (closes in more, has more unexpected curves) as the game progresses.


Circles $c_1$ and $c_2$ with origins $O_1$ and $O_2$ are on plane. $O_1Z$ and $O_1X$are tangents to Circle $c_2$.These tangents intersect $c_1$ in $A$ and $B$.$O_2Y$ and $O_2T$are tangents to Circle $c_1$.These tangents intersect $c_2$ in $C$ and $D$. Prove $AB=CD$   Figure   Things I have done: I was able to Prove that quadrilateral $JO_1LO_2$ is Kite (Triangles $O_2J O_1$ and $O_2L O_1$ are congruent by Angle-Side-Angle). So  $JO_1=LO_1$ and $CO_2=DO_2$. $O_1A=O_1B$ because Both of them are radius.So $JA=BL$.Similar to this,$CJ=DL$. So By Side-Angle-Side, $CJA$ and $DLB$ are congruent.So $AC=BD$. So if I Prove that $AC ||DB$,then $CABD$ will be a Parallelogram So $DC=AB$ will be true.This where I stuck.    I would Appreciate if someone could edit title to something better.

Let $\Gamma_1$ and $\Gamma_2$ be two non overlapping circles with centers $O_1$ and $O_2$ respectively. From $O_1$, draw the two tangents to $\Gamma_2$ and let them intersect $\Gamma_1$ at points $A$ and $B$. Similarly, from $O_2$, draw the two tangents to $\Gamma_1$ and let them intersect $\Gamma_2$ at points $C$ and $D$.  Prove that $AB=CD$.  I've done some extensive angle chasing on this but have been unable to make any real progress. Can't decide whether $ABCD$ is supposed to be rectangle (as in my diagrams), a parallelogram or even a trapezium. There is a homothety taking one circle to the other but as far as I can see this doesn't help as we don't have a clearly defined center to this.  Any help/hints would be greatly appreciated.


I have thousands of buildings blocks in ArcGIS. I want to select a half of this blocks randomly.   How can I do it?

What methods are available in ArcGIS 10.2 to randomly subset a selection of points.  For example, in the attached screenshot I am interested in keeping 20% of the selected points and deleting the rest.


In beamer, how can I make a colored text with black boreder?  I am currently using \textcolor to have colored text, but I need a black border, so the text can be read more easily.  EDIT I want the border of the letter black I do not want this:

How could I produce characters which are outlined when the character itself is in some color. A picture to illustrate what I'm after:   The problems with the above are that:   the outline is of no consistent width around the letter. the way I've done it (using tikz with a upscaled black node below the colored one), there is no easy way to control the width of the outline.   Do you know of a way to accomplish this with TeX? I am using plain-format with XeTeX, but I'm interested in all ways to accomplish this.


I've downloaded a blender file off Sketch-fab and I knew it was created with an older version of blender. I opened the file and every texture except for some blue emission thing.

I made a character, and its one of my first times texturing, and I saved my character into a new folder, and when I came back to the model ALL the textures were pink, I used to know what to do, but I stopped texturing, how do I bring my textures back?


Let thing of a bird standing still in a box on top of a weighing machine that shows a mass $m_0$. Now, imagine that the bird is flying, still in the same box and the same weighing machine shows a mass $m_1$. As the bird when flying, is applying a force towards the weighing machine, could we deduce that $m_0 = m_1$? I'm asking this question because saying that these masses are equal makes me as uncomfortable as saying that they are not equal and can't figure the right answer. So does $m_0 = m_1$ and why?

suppose there is a scale able to measure weight with an uncertainty of $10^{-9}kg$ . On the scale, an airtight plastic chamber is placed. Initially, a fly of mass $10^{-5}kg$ is sitting at the bottom of the chamber, which sits on the scale. At a later point in time the fly is flying around the chamber. Will there be a difference in the observed weight as measured by the scale when the fly is sitting at the bottom of the chamber compared to when it is flying around the chamber at some point in time? If so, what does the value of this difference depend on (I am most concerned with the case where the fly has not touched any surface of the container in enough time for the scale to reach some equilibrium value (or do the pressure variations induced from the flies wings cause constant fluctuations in the scale)?


An intermediate step in a problem I was working on was to find a closed form for the sum $$\sum_{i=1}^n i2^i.$$  WolframAlpha returns $2^{n+1}(n-1) + 2$, but didn't provide any step-by-step solution.  I would usually provide progress that I made, but I wasn't sure how to proceed(although I solved the problem by bashing out small values).

I want to know the general formula for $\sum_{n=0}^{m}nr^n$ for some constant r and how it is derived.  For example, when r = 2, the formula is given by: $\sum_{n=0}^{m}n2^n = 2(m2^m - 2^m +1)$ according to   Thanks!


I have followed the instructions in  and I have created a template class:  // ConfigItems.hpp #pragma once     #include <memory> #include <string>  template< typename T > class ConfigItem : public IConfigItem // here IConfigItem is the class that has the virtual members { private:     T m_value;  public:     ConfigItem< T >(const T& valueIn = 0);      std::ostream &printTo(std::ostream &outIn) const;     operator T() const; };  template< typename T, typename ...Args > std::unique_ptr< T > make_unique(Args&& ...args);   Implementation is here:  // ConfigItems.cpp #include "ConfigItems.hpp"  template< typename T > ConfigItem< T >::ConfigItem(const T& valueIn) : m_value(valueIn) {}  template< typename T > ConfigItem< T >::operator T() const {     return m_value; }  template< typename T > std::ostream& ConfigItem< T >::printTo(std::ostream& outIn) const {     return outIn << m_value; } template< typename T, typename ...Args > std::unique_ptr< T > make_unique(Args&& ...args) {     return std::unique_ptr< T >(new T(std::forward< Args >(args)...)); }   And I have created a ConfigFile class:  // ConfigFile.hpp #pragma once class ConfigFile { private:     static const std::string sm_inputFolderPath;      std::map<std::string, std::unique_ptr< IConfigItem > > m_configMap;  public:     ConfigFile(const std::string& nameIn);     ~ConfigFile();  };   Implementation:  // ConfigFile.cpp #include "ConfigFile.hpp"  const std::string ConfigFile::sm_inputFolderPath = "input_folder_path";  ConfigFile::ConfigFile(const std::string& nameIn) {     PTree tmpPT;     json::read_json(nameIn, tmpPT);      m_configMap.emplace(         ConfigFile::sm_inputFolderPath,         make_unique< ConfigItem< std::string > >(tmpPT.get< std::string >(ConfigFile::sm_inputFolderPath))); // here I get the error }   I am getting a linking error (not compiling):  undefined reference to `std::unique_ptr<ConfigItem<std::string>, std::default_delete<ConfigItem<std::string> > > make_unique<ConfigItem<std::string>, std::string>(std::string&&)'   I am not sure what is the problem here. I am using c++11, that is why I have added the function of make_unique. Can anyone help me to fix this? What am I doing wrong?

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


The phrase "" was first used on TV by the 10th Doctor in the episode "Blink".  However, it then appears as if the Doctor had invented this phrase long before that in-universe, as it is used by the 5th Doctor in the mini-episode "".  But in the 50th anniversary episode "Day of the Doctor", when the 11th Doctor says "timey wimey" the War Doctor appears as he has never heard this phrase.  Is there any explanation for this? In his own timeline, when did the Doctor invent or first hear this phrase?  Edit:  This question is different from  because I'm not asking about the first “use” of that phrase in a television serial or the first broadcast of the phrase, but when it was invented (or known) by the Doctor in his personal timeline. And if the 5th Doctor was aware of it, then why didn’t the War Doctor recognise it?  I thought this was clear in the question.

Was the phrase "timey-wimey" (or time-y wimey) used in Doctor Who, or elsewhere,  before it appeared in the script of the 2007 episode "Blink"?


Say, I am trying to predict likelihood to buy ice cream (event =1 , non-event = 0) using logistic regression.   I have only one variable "Gender" (2 value= Male/Female), so, the formula would be like this.   $logit(p)=β_0+β_1∗female$  Odd ratio for female with reference to $male (A)  = \frac{odd(female)}{odd(male)}$  Next, I added in "TodayWeather" (2 $value = \frac{Sun}{Rain}$).   $logit(p)=β_0+β_1∗female+β_2*SUN$  Q1) Why does the Odd ratio for A with reference to male change? Shouldn't my Odd ratio for female still be the same as (A) above? Since it is still comparing female and male (i.e. the odd of female to buy ice cream if increase by one unit)?  Q2) Say (A) above is < 1, is it possible that once i added "TodayWeather", the odd ratio become > 1? Why?

I'm somewhat new to using logistic regression, and a bit confused by a discrepancy between  my interpretations of the following values which I thought would be the same:    exponentiated beta values  predicted probability of the outcome using beta values.    Here is a simplified version of the model I am using, where undernutrition and insurance are both binary, and wealth is continuous:  Under.Nutrition ~ insurance + wealth   My (actual) model returns an exponentiated beta value of .8 for insurance, which I would interpret as:     "The probability of being undernourished for an insured individual is .8 times the probability of being undernourished for an uninsured individual."   However, when I calculate the difference in probabilities for individuals by putting in values of 0 and 1 into the insurance variable and the mean value for wealth, the difference in undernutrition is only .04. That is calculated as follows:   Probability Undernourished = exp(β0 + β1*Insurance + β2*Wealth) /                              (1+exp(β0 + β1*Insurance + β2*wealth))   I would really appreciate it if someone could explain why these values are different, and what a better interpretation (particularly for the second value) might be.     Further Clarification Edits As I understand it, the probability of being under-nourished for an uninsured person (where B1 corresponds to insurance) is:  Prob(Unins) = exp(β0 + β1*0 + β2*Wealth) /               (1+exp(β0 + β1*0+ β2*wealth))   While the Probability of being under-nourished for an insured person is:  Prob(Ins)= exp(β0 + β1*1 + β2*Wealth) /            (1+exp(β0 + β1*1+ β2*wealth))   The odds of being undernourished for an uninsured person compared to an insured person is:  exp(B1)   Is there a way to translate between these values (mathematically)? I'm still a bit confused by this equation (where I should probably be a different value on the RHS):  Prob(Ins) - Prob(Unins) != exp(B)   In layman's terms, the question is why doesn't insuring an individual change their probability of being under-nourished as much as the odds ratio indicates it does?  In my data, Prob(Ins) - Prob(Unins) = .04, where the exponentiated beta value is .8 (so why is the difference not .2?)


[I attempted this question but just wanted to check if I'm on the right track.   I started the question by :  Let { ($a_o$+$a_1$$x^2$), ($a_o$-$a_1$$x^2$), ($a_1$$x^2$-$a_0$), ($a_1$$x^2$-$a_2$x) ∈ $P_2$  Followed by putting in vector form and into a matrix, reducing it to row echelon form and comparing the rank to the number of columns to determine it is lenearly dependent. Am I right to do it this way?

I was looking for a short snazzy proof on the following statement:     n+1 vectors in $\mathbb{R}^n$ cannot be linearly independent   A student of mine asked this today morning and I couldn't come up with a proof solely from the .  From a higher level perspective, I explained that if I put the vectors in a matrix then if the only null space entry is the zero vector, then the vectors are independent but since we have one extra column than row and that the row and column rank are equal, there is no way we can have $n+1$ as the rank of the matrix and hence from Rank-Nullity theorem, the dimension of the Nullspace is at least one which implies that there is a combination of the vectors where not all the scalar multiples in the definition are 0 but yet we get a zero as the linear combination. The student hasn't completely learnt the fundamental subspaces yet so I am not sure he grasped what I was saying.  Is there a cleaner proof?  EDIT: I am stunned how many beautiful answers I got with so much diversity.


Why does a simple do-release-upgrade not upgrade from 17.04 to 17.10 if . I have to add the -d flag which treats 17.10 like a development version. It doesn't have any side effects, i.e. the upgrade is performed as expected, but it doesn't seem to be correct and most users might not catch this and complain that the upgrade to 17.10 doesn't work. As far as I remember the same happened when 17.04 was released.  Does do-release-upgrade have an update function I'm missing and which isn't listed in the manpage?

I have a laptop with Ubuntu 17.04 desktop installed. And I noticed that Ubuntu has just announced their new version (17.10). However, when I'm trying to open update-manager, it just tells me that I have the newest version.  Also, when I type the sudo do-release-upgrade command on the terminal, it tells me the same thing (No new release found.)  Is there any reasons for that, and what can I do? or should I just wait for that version, to get to the server?


I am using these below versions   VMWare Workstation 15 Player Ubuntu 18.04 LTS as guest os Windows 10 Pro as Host os vmware-tools-cmd version (10.3.0.5330 (build-8931395))   I have created the shared folder in VMWare options in GUI. Powered on my Ubuntu Guest. But there was not hgfs under /mnt.  So I used the command below  sudo mount -t fuse.vmhgfs-fuse .host:/ /mnt/hgfs   after this my shared folder appeared under /mnt/hgfs but can't cd into my shared folder. I restarted the VM. But now I can't find my shared folder under /mnt/hgfs.  Can anybody please provide complete steps how to debug this issue and a solution for this?

Experts. I've successfully installed VMware tools for Ubuntu. Everything seems to work fine, but shared folders were not mounted automatically. How do I get them to work?  If I run vmware-hgfsclient in terminal, I get the list of shared folders, but ls -l /mnt/hgfs is empty. Actually there's no hgfs dir in /mnt. I know I should probably use the vmware-hgfsclient tool, but I realy don't know how.   P.S. I wouldn't ask if I could understand the vmware-hgfsclient help I've read.   Any suggestions?


A diagram of the project:   It is working under Putty with its GUI configuration, but it is not working if using command line through Putty.  how to replicate the GUI settings in putty with command line?

I am able to do a reverse port forwarding through the PUTTY GUI with settings similar to below. Once I apply this setting, I am able to run to the server box and run wget http://localhost:8080 <-- a quick and dirty way to verify that the port is being forwarded.    However I am unable to make it working when I am using the command line.    --  When I tried using the most basic reverse port forwarding commands in ssh, it just does not work  the few examples which I have tried  ssh -R 8080:localhost:80 root@debian-tunnel-a1 ssh -g -R 8080:localhost:80 root@debian-tunnel-a1  ssh -f -g -R *:8080:localhost:80 root@debian-tunnel-a1 -p 22   Basically I've tried all samples I can find online for the past two days and they all don't work.  If I use the most commonly used commands which I've show above, I always get the error in the picture below:    As I try use a basic wget http://localhost:8080  On the SERVER machine (I am using wget http://localhost:8080 as a way to verify that Device #1 's port 80 is being forwarded to the Server device #2's port 8080, and that I can access it directly), the device #1 which I use the reverse port command basically spit out this error above.  It seems like the connection LINK is established, but the reverse port machine is not allowing it to go through.  But the puzzling thing is I am able to get it working under GUI, but just not command line.    To have a full picture of what the goal is:  device #1 share port 80 to------> server device #2 --------->  device #3 (talks to device #1 through server with server being the middleman)  I am still stuck on the first portion of  (device #1 ---> server device #2)   once I am completed, then I will   relay device #1  to  device #3  with server device #2 acting as middleman.


I'm stuck in solving this limit  $$ \lim_{x\to0} \frac{(1+x)^{\frac1x} - e}{x}. $$   Here I can must use Taylor expansion. My idea is to obtain the form $e^y-1$ on the numerator and then use Taylor expansion on it stopping on the first grade but I continue to fail. I also tried to stop on the second grade but no results. Note that I started using Taylor a few hours ago so I'm not so familiar. Can you help me? Thank you in advance. (sorry for my english)

I tried to evaluate $$\lim_{x\to0}\frac{(1+x)^{1/x}-e}x$$but all my efforts were in vain . L'Hospital rule becomes very complicated.


Just bought an older home that has a 3 prong dryer outlet.  It is right above an unfinished crawl space so it would be easy to run a good grounding cable to a grounding rod and/or an iron water pipe in the crawl space.  Unfortunately, the service wire does not have 4 conductors all the way back to the panel and would be difficult to replace.  Is this a good idea and would this be the equivalent of modern wiring assuming the proper installation of the grounding rod?  Thanks

A contractor looked at our house and told me that you can't fix a house (with old wiring) that has some outlets that are not grounded.  He said that you can go on YouTube and search the internet and it will tell you that you can.  He says that the only way to properly fix and ground everything is to do a whole house rewire.  Is he correct?  If, theoretically, you have an old house that has no ground whatsoever, can you run a grounding wire from the panel to all of the outlets to fix this?  updated  We have BX/AC wiring. And also apparently we have "...old-style AC (BX) with cloth insulated wires in a paper overall wrap under the spiral armor (no bonding tape)" Courtesy of @ThreePhaseEel.


In Example 5 , the authors discuss polling. Voting for candidate 'A' is given the numerical value of 1, and voting for 'B' has the value of 0. The CLT says that the average of a sample of $n$ people has the approximate distribution $$\overline{X} \approx N(p_0,\sigma/\sqrt{n}) $$ where $p_0$ is the true proportion of people who would vote 'A'. From this, and some general knowledge of the normal distribution they write:     This   means that we can conservatively say that in 95% of polls of $n$ people the sample mean   $\bar{X}$ is within $1/\sqrt n$ of the true mean. The frequentist statistician then takes the interval $\bar{X} ± 1/\sqrt n$ and calls it the 95% confidence interval for $p_0$.   I'm fine with this. However they write further     A word of caution: it is tempting and common, but wrong, to think that there is a 95%   probability the true fraction $p_0$ is in the confidence interval. This is subtle, but the error   is the same one as thinking you have a disease if a 95% accurate test comes back positive.   It’s true that 95% of people taking the test get the correct result. It’s not necessarily true   that 95% of positive tests are correct.   This remark has me puzzled. Earlier they said that in 95% of polls (of $n$ people) the confidence interval would contain $p_0$. Why doesn't this mean that $p_0$ would be in the interval with a probability of 95%?   Also, I can't see the analogy with the disease/test scenario (which sounds like the base rate fallacy). I'd appreciate some elaboration on that too.  Thank you!

It seems that through various related questions here, there is consensus that the "95%" part of what we call a "95% confidence interval" refers to the fact that if we were to exactly replicate our sampling and CI-computation procedures  many times, 95% of thusly computed CIs would contain the population mean. It also seems to be the consensus that this definition does not permit one to conclude from a single 95%CI that there is a 95% chance that the mean falls somewhere within the CI. However, I don't understand how the former doesn't imply the latter insofar as, having imagined many CIs 95% of which contain the population mean, shouldn't our uncertainty (with regards to whether our actually-computed CI contains the population mean or not) force us to use the base-rate of the imagined cases (95%) as our estimate of the probability that our actual case contains the CI?   I've seen posts argue along the lines of "the actually-computed CI either contains the population mean or it doesn't, so its probability is either 1 or 0", but this seems to imply a strange definition of probability that is dependent on unknown states (i.e. a friend flips fair coin, hides the result, and I am disallowed from saying there is a 50% chance that it's heads).  Surely I'm wrong, but I don't see where my logic has gone awry...


I am trying to remove a directory that has the name --crm. When I do   rm -f -R '--crm'   I get the following error:  rm: illegal option -- - usage: rm [-f | -i] [-dPRrvW] file ...    unlink file   I have also tried  rm -f -R *crm   but the directory is not removed.  Any clue how can I do that?

How do you remove a file whose filename begins with a dash (hyphen or minus) -?  I'm ssh'd into a remote OSX server and I have this file in my directory:  tohru:~ $ ls -l total 8 -rw-r--r--    1 me  staff  1352 Aug 18 14:33 --help ...   How in the world can I delete --help from a CLI?  This issue is something that I come across in different forms on occasion, these files are easy to create, but hard to get rid of.  I have tried using backslash  rm \-\-help   I have tried quotes  rm "--help"   How do I prevent the minus (dash or hyphen) character to be interpreted as an option?