How to define a member function outside class in python?

import numpy as np  class MyClass:          a = int()         b = float()         c = np.array([0 for i in range 10])          def Memberfunction():              print("Hii")


Continuous homorphisms between topological groups.

Let $G,H$ be topological groups and let $\rho: G \rightarrow H$ be a homomorphism of topological groups.  I understand this to mean that $\rho$ preserves group structure and is a map between the topologies.    If we say $\rho$ is continuous I understand that this means the map between the two topologies must be a continuous map i.e. the preimage of open sets will be open etc.  However I have come across the following claim, which in my eyes using the definitions above seems trivial. It goes as follows:  Let $G,H$ be topological groups and let $\rho: G \rightarrow H$ be a homomorphism of topological groups. Then $\rho$ is continuous if and only if $\rho^{-1} (V)$ is open for each $V$ in a basis of neighbourhoods $\mathcal{V}$  of the identity $1_h$.   Maybe I have not fully grasped one of the definitions.


Why am I not notified for edits on answers and posts?

There's a question I answered some time ago (about 2 weeks) and now I see there were some edits introduced a week ago by another person to the question and to my answer. Why am I not notified of these edits? I'd like to be because for instance if the question was changed, maybe my answer is no longer valid (I mean it doesn't answer the updated question and I can loose reputation). And if my answer was changed, maybe it doesn't answer the original question, maybe it's changed completely (at least I can't guarantee the opposite). I assume people with great reputation edit posts and answers only slightly and if there are some mistakes that can easily be fixed, but you don't need to have 10 thousands of rep to make edits, so how am I protected from people trolls or people who accidentally made my answer invalid? I feel uncomfortable with such rules and I'd like to be at least notified of changes.


I installed Ubuntu 16.04 I'm getting this error:  E: The package ubuntu-mono needs to be reinstalled, but I can't find an archive for it.   I haven't found the solution. What should I do?


What are the biggest disadvantages of using a 64bit version of linux over a 32bit and vice-versa

I've been using Ubuntu 12.10 for some time now, but I am very limited when it comes to installing some software such as wine that won't run on a 64bit. I want to know what are the biggest disadvantages/advantages of both the 32 and 64 bit. Will it be worth switching to a 32bit? If using a 32bit will my programs still work?   Will this command change completely the architecture from 64 to 32bit, or will it just add support to 32bit while keeping the 64bit?  sudo dpkg --add-architecture i386


How do i make the edges sharp without adding loop cuts?

Hi I have added a sub surf modifier to my car and the edges have curved and I would like to sharpen them.I have tried to use loop cuts but that causes a slight crease in the geometry. Is there another way of sharpening the edges while keeping geometry smooth.    I have tried using edge crease and it has definitely helped, however it only gets rid of part of the curve if that makes sense. There is still a bend visible.


I am having a list box, and its item template is having one check box.  Now, when I click on the check box in the listbox, it sets the checked status of the check box. If I use keyboard "Space" key, I cannot change the checkbox state.   Note: Keyboard is shortcut is working once I set focus to the check box by clicking it.


My girlfriend is Swiss and has the ESTAVisa. We landed in the US over 3 months ago and were in NYC for just 4 days. Then, we have been in Canada for the past 3 months+. I just read that a visit to Canada doesn't count as "leaving the US".  She is not a resident of Canada, but we've been here for over 3 months so it's obviously not a border jump. Any ideas?


I used to be able to rotate upon the origin of any given item that I was working on, but now blender just wants to rotate around the cursor, which i usual have at the world origin. This is a little annoying!! Any ideas or am i missing something? I have searched the web and not had any joy. Tried the full stop, still the rotation is of.


What did I do wrong to get this FIBONACCI error?

I am working on a program that I am having trouble with it. I have been working with this program for a day and did not work. The output came only letters, @ symbol and numbers. Here is the description of the program.  Generate a Fibonacci sequence. Each number in the Fibonacci series is the sum of the two preceding numbers in the sequence. The first two numbers in the sequence are both 1. The third number is 2, the fourth number is 3, the fifth number is 5, and the sixth number is 8. The program should be able to return a specified amount in the fibo sequence. If a number is specified that is out of range, a -1 should be returned.  I have done the code and the runner code. My output will be similar to this.  1  1  2  3  5  8  89  987  10946  1346269  165580141  1836311903  1  1  1  -1  Here is my code   public class Fibonacci {     int[] fibArray;     public Fibonacci()     {         fibArray = new int[50];         this.setFibo();     }     public void setFibo()     {         fibArray[0]=1;         fibArray[1]=1;         for(int idx = 2; idx<fibArray.length; idx++){             fibArray[idx] = fibArray[idx-1] + fibArray[idx-2];         }     }     public int[] getFibo()     {         return fibArray;     }     public String toString()     {         return this.getFibo() + "\n";     } }      Here is my runner code.   public class FibonacciRunner {     public static void main(String[] args) {         int[] fibArray = {1,2,3,4,5,6,11,16,21,31,41,46,1,1,2,1,2,11};         Fibonacci fibo = new Fibonacci();         System.out.println(fibo.getFibo());         System.out.println(fibo.getFibo());         System.out.println(fibo.getFibo());         System.out.println(fibo.getFibo());         System.out.println(fibo.getFibo());         System.out.println(fibo.getFibo());         System.out.println(fibo.getFibo());         System.out.println(fibo.getFibo());         System.out.println(fibo.getFibo());         System.out.println(fibo.getFibo());         System.out.println(fibo.getFibo());         System.out.println(fibo.getFibo());         System.out.println(fibo.getFibo());         System.out.println(fibo.getFibo());         System.out.println(fibo.getFibo());      } }


What is the value of this series? $$ \sum_{k=1}^\infty \frac{1}{k^k} = 1 + \frac{1}{2^2} + \frac{1}{3^3} + \frac{1}{4^4} + \cdots $$  I found the answer to be equal to $1.29$ by converting the sum to an integral.


What is Inflow and Outflow of money in the context of ETFs

There are   and  that talk about cash flowing in and out of ETFs. The last link also hints at what that might mean, but I want to know more in detail. If they are exchange traded, how/when are new units added? I presume capital gain isnt what is meant when "Inflow" is used.


Let $(X, \mathcal A)$ be a measurable set, $Y$ a subset of $X$    Show that $\mathcal A_Y$$= { A \cap Y : A \in \mathcal A }  $ is a $\sigma$-algebra on $Y$


Is there a constructive approach to creating a distribution achieving the Chebyshev lower bound?

I came across the following question and am wondering if there's a simple way to cook up a distribution achieving the Chebyshev lower bound:  Suppose $X$ has $\mu_X = \sigma^2_X = 9$. Define the lower bound for  $$\mathbb{P}[3 \leq X \leq 15]$$  Chebyshev tells us the answer is $\frac34$.  Can we come up with a specific distribution for $X$ that follows this?  More specifically, I'd prefer $X$ be discrete and restricted to take non-negative values.  A more general constructive proof would of course be more instructive!


How is depth-of-field affected on micro format cameras?

One of my favorite qualities of large apertures (besides the low light capability) is their characteristic shallow focus that can offer dramatic background blur.  I've been considering how a micro format camera such as a micro four-thirds or even something like a Canon G16 or S120 (with 1/1.7" sensor) might perform with regards to depth-of-field. Both of those cameras boast an f/1.8 ratio. I am of the understanding that the lens won't be as fast as an f/1.8 on an APS-C or fullframe sensor as it obviously won't be capturing nearly as much light, but how does depth-of-field scale down?  To clarify my question consider these scenarios:   a camera body with a fullframe sensor and an appropriately matching f/1.8 lens a camera body with a micro 4/3 sensor and an appropriately matching f/1.8 lens a camera body with a 1/1.7" sensor and an appropriately matching f/1.8 lens   How would the depth-of-field compare? Let's also assume for the sake of argument, that all lenses have focal lengths that correspond to the same field-of-view.


Get unique combinations of elements from a python list

Edit: This is not a exact duplicate of   This topic is about finding unique combinations while the other topic is about finding ALL combinations.  If I have a python list:   L = [1,2,3,4]   what's the best way to get all the possible unique combinations of 3 elements from the list like below:  ["1,2,3", "1,2,4", "2,3,4", "3,4,1"]   The order of the elements in the combinations doesn't matter. For example, "1,2,3" and "3,2,1" will be considered the same combination.  I can probably write a few loops to do this but I think there might be a one-liner which can do the same.


Object is not updated (by Lambdas filter) when passing it (by reference) to a method

I'm using java8, SpringBoot 2, and JPA2 and I'm run in a strange problem. Suppose the following code: public void doSome() {     List<Integer> arr = new ArrayList<>(Arrays.asList(1,2,3,4,5));     List<Integer> arr2 = new ArrayList<>(Arrays.asList(1,2,3,4));      otherMethod(arr, arr2);     System.out.println(arr); }  In the same class I have the otherMethod() and with this version: public void otherMethod(List<Integer> arr, List<Integer> arr2) {     arr = arr.stream().filter(x -> !arr2.contains(x)).collect(Collectors.toList());     System.out.println(arr); // here print just 5 }  When code flow bring me back to doSome(): System.out.println(arr); // print [1,2,3,4,5]  If I change my otherMethod() as follows: public void otherMethod(List<Integer> arr, List<Integer> arr2) { //    arr = arr.stream().filter(x -> !arr2.contains(x)).collect(Collectors.toList());     arr.removeIf(x -> x < 3);     System.out.println(arr); // print [3,4,5] }  and the changes affect the Object I have passed by reference, in doSome() method I see: System.out.println(arr); // print [3,4,5]  I don't understand why with arr.stream().filter(x -> !arr2.contains(x)).collect(Collectors.toList()) changes doesn't affect my Object passed by reference. where am I wrong?


I'm new in Linux and I'm trying to make my first bash script to improve  my work at college. Im working with a software called GROMACS and I'm trying to make a script to perfom a bunch of codes at the same time, but in one of the lines I need needs an input (number) from the keyboard. What can I do to make this script work?  Here are my lines:  !#/bin/bash gmx pdb2gmx -f protein_name.pdb -o protein_name_processed.gro -water spce   And that last line needs the keyboard input (number 15)  Thanks for your help.


How to add a line break into my batch script below?

I'm trying to figure out how to add a line break so the echo command prints the output for each computer line by line.  FOR %%X IN ("pc1", "pc2",) DO for /F "tokens=2 delims= " %%A in ('qwinsta /server:%%X ^| find "Active"') do (echo %%X %%A Active) >> c:\temp\pcinfo.html   Thanks  PS: modified:  @echo off  break > c:\temp\hdinfo.html echo ^ >> c:\temp\hdinfo.html echo ^ >> c:\temp\hdinfo.html  echo ^ >> c:\temp\hdinfo.html echo ^ >> c:\temp\hdinfo.html FOR %%X IN ("pc1", "pc2", "pc3", "pc4",) DO for /F "tokens=2 delims= " %%A in ('qwinsta /server:%%X ^| find "Active"') do (     echo %%X %%A ^ Active ^ ) >> c:\temp\hdinfo.html  "c:\program files\internet explorer\iexplore.exe" c:\temp\hdinfo.html  exit


Our civilization on Earth collapses; subsequent civilization discovers our technology

I'm looking for a science fiction book that is about the discovery of an ancient technological civilization on Earth in the far future .  The discoverer's civilization is not highly technological, and they awaken an artificial intelligence.   I don't know much more about the book - hopefully my description is not too vague. Thank you for any help.


I am curious as to how much time it takes to hear about desktop rejection from editors of Journal of Marketing, Journal of Marketing research, Journal of Consumer Research, Management Science etc. What does it mean if it says "awaiting COE decision"?


mathematical induction proof of a square vs factorial

So lets say I have $$ n^{2} \le n! $$  For what positive integers is this not true? $n=2$ and $ 3$  Base case? $$n=4 \implies  16 \le 24 $$  What is the inductive hypothesis and how do I show the inductive proof? Thanks


Can someone show the work with some details that $f^{-1}$ is not continuous at $(1,0)$?

Show that the function $f: [0, 2 \pi) \to S^1$ defined by $f(t)=e^{it}=(\cos t, \sin t)$ is not homeomorphic.  Answer:  This function is bijective and continuous. But $f^{-1}$ is not continuous at $(1,0)$.  But how to show that $f^{-1}$ is not continuous at $(1,0)$.  From definition of continuous function, we call $f:X \to Y$ a continuous function if for $x \in X$ there are neighborhoods $U$ in $X$ and $V$ in $Y$ with $x \in U$ and $f(x) \in V$, then $f(U) \subset V$.  Following this definition,  We have $f^{-1}(1,0)=0 $.  Let $U$ be any open set containing $(1,0)$ and $V$ be any open set containing $0$, we have to show that $f^{-1}(U) \not\subset V$.  But I can not show it.  Can someone show the work with some details that $f^{-1}$ is not continuous at $(1,0)$ ?  There is a explanation in Wikipedia as below:  The function $f^{-1}$ is not continuous at the point $( 1 , 0 )$ because although $ f^{-1}$ maps $( 1 , 0 )$ to $0$,  any neighbourhood of this point also includes points that the function maps close to $2 \pi $, but the points it maps to numbers in between lie outside the neighborhood.   But I could not understand it clearly. How they choosing neighborhood?


How to change a float into a String in Java?

Is it possible to change a float value to a String? If possible, is it also possible to converting it to a String while rounding the number to the nearest integer?  For example if I have a float such as 2.335 then, can I change it to a String of value "2.335" or "2" (by rounding it)?


Excel. How to join tables by a column with sum?

I need to obtain column F in the following example    Basically, I need to match the index, and return the value in column B, with the complication of having to return the sum in case there is more than one match for my index. I would normally just use VLOOKUP, but that only returns the first match, and I can think of some manual ways to deal with this, but I was wondering what the cleanest way is.


Momentum conservation in ball and massive wall collision

I know momentums definition (p=mv) and how to calculate problems involving it, but there are bits I don't understand.   Take a ball thrown at a wall for instance with mass value (5) and velocity (5). This would mean the total momentum of ball is (25). The wall is attached to the earth so the mass is huge and the wall doesn't move (momentum of (0)). Total momentum in system is now (25). This ball hits a wall and bounces back in the opposite direction.   The ball now has a momentum of (-25) so its moving in the opposite direction from which it started. The wall doesn't 'move' due to its high mass (and undetectable gain in velocity). THe total momentum of the system still has a magnitude of (25) but there has been a change in momentum of (50) for the ball. Where did the extra momentum come from? I would think that the ball would transfer all its momentum to the wall in the collision so it would stop moving (as its its momentum drops to 0) but it actually gains momentum to go in the opposite direction.   Where is this extra momentum coming from? Is it linked to newtons 3rd? But then there is a gain of acceleration...


Is there a feasible way to invite flatmate to Stack Exchange?

I rent a room, I don't need a whole apartment for myself and I prefer to save some money to party ;) Same with internet connection, we are rarely at home at the same times, so no need to pay separate fees for separate connection.  Now, if he will join SE, we will share IP. And I probably would feel the urge to find answers for his questions - he asks me questions already, only outside SE network. Given the ability to talk IRL, I'll probably spend more time on his questions than on anyone else, and the other way around. And there are votes.  Now - it seems it would look like sockpuppeting. I don't want it. And I don't want to get punished for it if I will not do it. But I understand there is no easy algorithm to distinguish it. Is there any solution except keeping him out of SE or moving out?  Not sure if it should be  or . Guess it's kinda both.


How feasible is a hyperdrive-based weapon? (Star Wars 8 spoiler)

After the battle in The Last Jedi when the ship activated its hyperdrive and tore through the Star Destroyer, I immediately began wondering why weapons weren't being made that utilized hyperdrives to push something really fast to be used as a projectile. What I'm wondering is how much it would cost to develop a weapon like this compared to other weapons in the Star Wars universe, and why such a weapon had not been created hundreds of years ago.


How can I get this 'Version: 0.1.0 - 94" value from the  tag in selenium webdriver?

How can I get this Version: 0.1.0 - 94 value from the <div> tag in selenium webdriver? and here is my code:  <div _ngcontent-qbk-c3="" style="text-align: center;">Version: 0.1.0 - 94</div>


If $\gcd(a,b)=d$ then prove that $\gcd(\frac{a}{c},\frac{b}{c})=\frac{d}{c}$

My attempt:  $ax+by=d$(as gcd(a,b)=d).  Dividing by c  $\frac{a}{c}x+\frac{b}{c}y=\frac{d}{c}$  Let $k$ be the gcd of$ (\frac{a}{c},\frac{b}{c})$ so $k|\frac{a}{c}$ and $ k|\frac{b}{c}$ then $k|\frac{a}{c} x + \frac{b}{c}y$  and so $k|\frac{d}{c}$.  As $d|a $ implies that $\frac{d}{c}|\frac{a}{c} $ similarly it divides $\frac{b}{c}$ . Hence $\frac{d}{c}|k$(as $k$ is the greatest common factor). Thus $k= \frac{d}{c}$


Understanding how the german tax system works

I hope that you can help me understand how the German tax system works.  I recently found a job in Berlin with a yearly gross salary of 68000. I am married (we are both Spanish) but my husband is still working in the UK with a yearly gross salary of 47000 pounds.  My questions are:   In which tax classes do we belong?  If he moves to Berlin, registers here and we live together with him being unemployed will we pay less for taxes?  Which case (1st or 2nd) is the most favourable for us in order to pay less taxes?


Showing cardinality of all infinite sequences of natural numbers is the same as the continuum.

So I'm trying to show that these two sets have the same cardinality, i.e. there is a possible bijection between the two. I'm trying to use the Cantor-Schroeder-Bernstein theorem as I can't explicitly think of a bijection that will work. For this I need to find an injective map each way. I can find an injective mapping between $R$ and the set of infinite sequences of natural numbers. E.g., for each real number $x$, I can associate it with the sequence $S$, where the first element is $2^{n}$ (where $n$ is the greatest integer less than or equal to $x$) if x is nonnegative, and $3^{n}$ if x is negative. Then the rest of the sequence can be the decimal expansion of x in single digits. E.g. the sequence associated with pi through the function would be $(2^{3}, 1,4, etc)$. This is injective, so the first half of Cantor-Schroeder-Bernstein is satisfied. If I can find an injective function going the other way then I am done.  I first thought of something involving turning the digits of the sequence into a real number, but that failed to be injective as my function would not be able to differentiate between the sequences $(1,0,1,0,1,0,...)$ and $(10,10,10,...)$.   Any hints or help? I'm trying to figure it out without resorting to proofs based on cardinal arithmetic or related to the power set of N.


When I open Terminal I expect it to show what my PS1 is set to \h:\W \u\$.  However it's not displaying my hostname Eriks-MacBook, as displayed in System Preferences.  Instead, it's showing a random string unknownb88d120cd4b2.   How can this be fixed or reset?  This machine is brand new, and the preferences/settings haven't been changed.


Constant morphism from $\mathbb{P}^m_k$ to $\mathbb{P}^n_k$ as schemes

Let $k$ be a field and $m>n \in \mathbb{N}$. Then any morphism of schemes $\mathbb{P}^m_k \rightarrow \mathbb{P}^n_k$ is constant.  What I know is that every morphism from a scheme $X$ to $\mathbb{P}^n_k$ corresponds $1:1$ to isomorphism classes of invertible sheaves $\mathcal{L}$ on $X$ and generating sections $s_0,...,s_n \in \Gamma(X,\mathcal{L})$.  What I'm thinking is also that $\mathbb{P}^m_k$ cannot be generated by $n+1$ sections.


Redirect the output of a command in `time command`

I am trying to time something using:  /usr/bin/time myCommand   However, since /usr/bin/time writes to stderr, if myCommand also writes to stderr, I will get more than just time's output on the stream. What I want to do is, redirect all of myCommand's output to /dev/null, but still write time's output to stderr. Using an example myCommand that writes to stderr of ls /nofile, we see that (obviously) there is no output at all with the following:  $ /usr/bin/time ls /nofile 2> /dev/null $   Without any redirection, we see both the output from ls (to stderr) and the output from time (also to stderr):  $ /usr/bin/time ls /nofile ls: cannot access /nofile: No such file or directory 0.00user 0.00system 0:00.00elapsed 0%CPU (0avgtext+0avgdata 3776maxresident)k 0inputs+0outputs (0major+278minor)pagefaults 0swaps   What I want is something that simply produces:  $ /usr/bin/time ls /nofile > RedirectThatImAskingFor 0.00user 0.00system 0:00.00elapsed 0%CPU (0avgtext+0avgdata 3776maxresident)k 0inputs+0outputs (0major+278minor)pagefaults 0swaps   Any ideas?


Is it useful to have your company name as an  on every page?

I saw a (quite okay) website where every page has the logo/title of the company as an . I was wondering if that is actually usefull or just ruining your SE(o)-score?  The full HTML line is
Company name here
  And I got to add: Not the , but the  gets, via CSS, updated with a background image.


I am using a script to automatically set up a computer. I need to assign a password to the vnc server for the user, which is normally done using the vncserver command. However, it prompts for the user to enter and re-enter their password, neither of which the script is capable of doing. So, how can I set up the VNC password without an interactive prompt?   Thanks.


I'm trying to install offline g++ software on Ubuntu 14.04:  $ sudo dpkg -i g++-4.4.4_4.4.3-4ubuntu5.1_i386.deb  [sudo] password for ecil:  dpkg: error processing archive g++-4.4.4_4.4.3-4ubuntu5.1_i386.deb (--install):  cannot access archive: No such file or directory Errors were encountered while processing:  g++-4.4.4_4.4.3-4ubuntu5.1_i386.deb ecil@ECIL-HP:~$ sudo dpkg -r g++-4.4 (Reading database ... 164836 files and directories currently installed.) Removing g++-4.4 (4.4.3-4ubuntu5.1) ... Processing triggers for man-db (2.6.7.1-1) ... ecil@ECIL-HP:~$ sudo dpkg -i g++-4.4.4_4.4.3-4ubuntu5.1_i386.deb  ecil@ECIL-HP:~$ sudo dpkg -i g++-4.4.4_4.4.3-4ubuntu5.1_i386.deb  dpkg: error processing archive g++-4.4.4_4.4.3-4ubuntu5.1_i386.deb (--install):  cannot access archive: No such file or directory Errors were encountered while processing:  g++-4.4.4_4.4.3-4ubuntu5.1_i386.deb ecil@ECIL-HP:~$ sudo dpkg -r g++-4.4 dpkg: warning: ignoring request to remove g++-4.4 which isn't installed ecil@ECIL-HP:~$ sudo dpkg -r g++-4.4 dpkg: warning: ignoring request to remove g++-4.4 which isn't installed ecil@ECIL-HP:~$ sudo dpkg -r g++-4.4 dpkg: warning: ignoring request to remove g++-4.4 which isn't installed ecil@ECIL-HP:~$ cd Desktop/ ecil@ECIL-HP:~/Desktop$ sudo dpkg -i g++-3.3_3.3.5-13_i386.deb  Selecting previously unselected package g++-3.3. (Reading database ... 164820 files and directories currently installed.) Preparing to unpack g++-3.3_3.3.5-13_i386.deb ... Unpacking g++-3.3 (1:3.3.5-13) ... dpkg: dependency problems prevent configuration of g++-3.3:  g++-3.3 depends on gcc-3.3-base (>= 1:3.3.5-13); however:   Package gcc-3.3-base is not installed.  g++-3.3 depends on gcc-3.3 (>= 1:3.3.5-13); however:   Package gcc-3.3 is not installed.  g++-3.3 depends on gcc-3.3 (<< 1:3.3.6); however:   Package gcc-3.3 is not installed.  g++-3.3 depends on libstdc++5-3.3-dev (>= 1:3.3.5-13); however:   Package libstdc++5-3.3-dev is not installed.  dpkg: error processing package g++-3.3 (--install):  dependency problems - leaving unconfigured Processing triggers for man-db (2.6.7.1-1) ... Errors were encountered while processing:  g++-3.3


How can I copy all the data from certain colored cells in a Google Spreadsheet to a single cell?

I've only just started using a spreadsheet and I'm wondering how to take all the data from cells of a certain color, then place that data in a single cell?


Language sites and pronunciation questions

The following feature request would be useful for the language sites in general if implemented. A discussion took place in a chatroom dedicated for  it started:    the discussion went on from there.  Among the mentioned is that basically no language can be used to show how to pronounce an Arabic word, at least not properly, and because of this transliteration would not be very viable.  It was suggested that perhaps we can ask SE for a feature for when Arabic Language goes into beta that would enable users to upload sound files into their answer.  And if we had to, we can resort to using an outside host and request a feature that would enable us to embed the files within a post from that host. I hope I was clear enough in describing what we are trying to request, my question is would such a feature be possible for when we go to beta? if not, then would it be possible to have a feature enabling users to embed sound files from outside  hosts?


Conditional convergence, Mertens theorem

If $\sum a_n$ and $\sum b_n$ both converge and one of them absolutely then the Cauchy product $\sum c_n$ converges to $\sum a_n \sum b_n$. ($c_n = \sum_{k = 0}^n a_k b_{n - k}$), by Mertens Theorem.  Now, if both converge conditionally then the product does not have to converge as $a_n = b_n = (-1)^n/n$ shows. My question now is: What if $\sum a_n$ and $\sum b_n$ both converge conditionally and $\sum c_n$ converges, then is it always true that $\sum c_n$ converges to the product?  By the way, this is not homework, I'm already past the real analysis part.


prove that if $a_1 a_2\cdots a_n=1$ implies $a_1^{n-1}+a_2^{n-1}+\cdots a_n^{n-1}\geq \frac{1}{a_1}+\frac{1}{a_2}+\cdots+ \frac{1}{a_n}$

Let us consider $a_1,a_2,\cdots a_n>0$ such that  $a_1 a_2\cdots a_n=1$ then show that  $a_1^{n-1}+a_2^{n-1}+\cdots a_n^{n-1}\geq \frac{1}{a_1}+\frac{1}{a_2}+\cdots \frac{1}{a_n}$.  Attempt 1(definition) Since the the inequality is equal to $(\frac{a_1^n}{a_1}-\frac{1}{a_1})+(\frac{a_2^n}{a_2}-\frac{1}{a_2})+\cdots +(\frac{a_n^n}{a_n}-\frac{1}{a_n})\geq 0$ but the inequality $$\frac{1}{a_1}(a_1^n-1)\geq 0$$ can´t be true for each $a_i$. Attempt 2 (by substitution) Now from our hypothesis $\frac{1}{a_i}=a_1a_2\cdots \hat{a_i} a_{i+1}\cdots a_n$ and putting it in our inequality $a_1^n(a_2a_3\cdots a_n)+a_2^n(a_1a_3\cdots a_n)+\cdots + a_n^n(a_1a_2\cdots a_{n-1})\geq (a_2a_3\cdots a_n)+(a_1a_3\cdots a_n)+\cdots +(a_1a_2\cdots a_{n-1})$ but each $a_i>0$ and hence $\frac{1}{a_i}>0$ and then our assertion is true. Attempt 3 (rearrangement inequality) WLOG assume that $a_1\leq a_2\cdots \leq a_n$ I need find a collection of ordered numbers  $b_1\leq b_2\cdots b_n$ for use that $a_1b_1+a_2b_2+\cdots a_nb_n\geq a_1b_{\sigma(1)}+a_2b_{\sigma(2)}+\cdots+a_nb_{\sigma(n)}$ where $\sigma\in S_n$. But I cant figure out how should be $b_i$ for each $i$. Any advice or hint was helpful.


Application of Green's Theorem when undefined at origin

Problem:  Let $P={-y \over x^2+y^2}$ and $Q={x \over x^2+y^2}$ for $(x,y)\ne(0,0)$.  Show that $\oint_{\partial \Omega}(Pdx + Qdy)=2\pi$ if $\Omega$ is any open set containing $(0,0)$ and with a sufficiently regular boundary.   Working:  Clearly, we cannot immediately apply Green's Theorem, because $P$ and $Q$ are not continuous at $(0,0)$. So, we can create a new region $\Omega_\epsilon$ which is $\Omega$ with a disc of radius $\epsilon$ centered at the origin excised from it.   We then note ${\partial Q \over \partial x} - {\partial P \over \partial y} = 0$ and apply Green's Theorem over $\Omega_\epsilon$. Furthermore, $\oint_C(Pdx + Qdy)=2\pi$ if $C$ is any positively oriented circle centered at the origin.  I get the general scheme of how to approach this problem, however I am unsure of how to argue it in a rigorous manner.


tikz: number precision when incrementing by 0.01

When I increment the y axis by 0.01, the numbers encounter a rounding error for some weird reason.  \documentclass[tikz]{standalone} \begin{document} \begin{tikzpicture}   \foreach \y in {0.01, 0.02, ... 0.1}{     \draw (0, \y cm) -- (-0.1cm, \y) node[left] {$\y$};   } \end{tikzpicture} \end{document}


I'm trying to get a figure in my LaTeX document, but I struggle to set the search-path  I use  \addplot[blue] table {invcum.dat};   from the example, however it keeps saying  ! Package pgfplots Error: Could not read table file 'invcum.dat'.   After trying around with various things I looked at the reportings from Process Monitor (Sysinternals) and it shows, that the file is only looked for in the temporary directory.  In LyX I found the TEXINPUT option and it was set to "." I added my working directory to it (where the data file lies) but I keep getting the same behaviour.  I will continue by inserting the data into the documents directly, but I'd really like to see what I missed to get things working.


I want to prove that  $(n-1)^n>n^{n-1}$, for $n>4$, $n$ is an integer.  So I divided by $n^n$ and got:  $(1-\frac{1}{n})^{n}>\frac{1}{n}$  I know that $(1-\frac{1}{n+1})^{n+1}$>$(1-\frac{1}{n})^{n+1}=(1-\frac{1}{n})^n(\frac{n-1}{n})>\frac{1}{n}(\frac{n-1}{n})$.  How can I continue?  Thanks.


PCA on a rank-deficient matrix using SVD of the covariance matrix

I have a high-dimensional data matrix X where sample size is smaller than the variable size. I want to use PCA as a dimensionality reduction method, but I cannot call it directly in R since the matrix X is rank-deficient. I saw below technique in an R code to get the principal component representation from a rank-deficient matrix:  1) Get U from svd(XXT)  2) Get the principal component representation C by solving X = UC  I am new to PCA, and I have no idea how that makes sense. Could someone clarify how those 2 steps is equivalent to applying PCA on X?


Convert Numerical Digits in Vocabulary Forms

How can I convert final amount of billing to it's related vocabulary form?  I am trying to develop a function which convert it in vocabulary form.  For, ex. 12345 Rs. then it's output should be like this  TWELVE THOUSAND THREE HUNDRED N FORTY FIVE ONLY  is it possible with few easy steps in C# ?


What is the story behind ${n+1 \choose k} = {n \choose k} + {n \choose k-1}$?

By exploring the inductive proof from   I came to the point where I did not understand this step:  $${n+1 \choose k} = {n \choose k} + {n \choose k-1}$$  There is a  article but it does not make much sense to me.  What is the idea behind this "trick"?


Why using X in tabularx inserts new line

Why newline is inserted in the first row and why \noindent fixes it in the second row? \documentclass{book}  \usepackage{colortbl} \usepackage{tabularx} \usepackage{xcolor}  \begin{document}     \begin{tabularx}{\textwidth}{lX lX}         \rowcolor{gray}         cell1 & \color{white}{cell2} \\         \hline         \rowcolor{gray}         cell1 & \noindent\color{white}{cell2} \\     \end{tabularx} \end{document}


Different standards for writing down logical quantifiers in a formal way

What are standard ways to write mathematical expressions involving quantifiers in a (semi)formal way ? In different posts of mine concerning similar question I have encountered for a generic expression of the type "for all $x\in I$ and $y\in J$ holds $P(x,y)$" the following writing conventions  1) $\forall y\in J \ \ \forall x \in I: P(x,y)$ (this was how I would usually write statements in a formal way; sometimes also as  $\forall y\in J: \ \ \forall x \in I: P(x,y)$ ;don't know if it standard)  2) $(\forall y)(\forall x)(x \in I \land y\in J \Rightarrow P(x,y))$  (in the accepted answer from  question)  3) $(\forall y: \ y \in J) (\forall x: \ x \in I) (P(x,y))$ (form the same answer as above)  4) $\forall y \ \forall x\ (x \in I \land y \in J \Rightarrow P(x,y))$  (in the accepted answer from question)  5) $(\forall y\in J )(\forall x \in I) [P(x,y)] $  (in the accepted answer from  question).  ( (I hope I "generalised" them correctly, because at some points, they where written only for one variable, for example 3) was written just as $(\forall x: \ x \in I) (P(x))$ )  Could you tell me which ones are generally accepted an if there is a standard to how these should be written ?  (I think unique readability should be a criterion and I'm not sure the way I'm used to writing mathematical expression satisfies that)


Allow me to explain: There is a famous quote from the movie      "All work and no play makes Jack a dull boy"   I can also paraphrase it: Jack was dull because he didn't play enough.  My question is, what if I intentionally modify the original quote and turn it into the following?     All work and no play makes Pouya a dull boy   This is neither a quote nor a paraphrase. Is there any word for these kinds of phrases?


How to change default settings on installation disk?

I am wanting to install Lubuntu on a bunch of computers and laptops. I would rather not through each individual installation and change the settings to how I want them. Is there a way to set the settings prior to installation on the installation disk (which is a USB)?


I have been taught that the $\pi^0$ particle contains either an up quark and an anti-up quark or a down and an anti-down. How can these exist without annihilating?  Also, it is its own antiparticle, but it doesn't make sense that the up version and down version would annihilate when they meet.  Or is what I've been taught a simplification - if so, in what state does this particle exist?


Robust method to extract "pure" part of a variable

I am trying to perform a multi linear regression model:  $$y_i = β_0 + β_1x_{i1} + β_2x_{i2} +... + β_px_{ip} + ε_i$$  where $$x_{i1}, x_{i2}, ..., x_{ip}$$ are highly correlated with each other (VIFs can be as low as 5 and high as 30).  I am just wondering if there exists a procedure with the following properties:  1) extracts the pure part of each independent variable, where pure is defined as a part of the variable which is uncorrelated with other variables.  2) the pure part and the original variable should be similar to each other, whether similar is defined as moments such as mean and variance and correlation coefficient (ideally >0.90)


Automount when clicking on disks in GUI file manager suddenly stopped working in Ubuntu. ("Unable to mount...Not authorized to perform operation.")

I'm using Ubuntu 18.04 with nemo as the file manager, and out of nowhere I can no longer mount disks or partitions which show up just by double-clicking them, when just a few weeks ago this worked perfectly fine! Any idea what changed? Perhaps an update messed it up?  The error is:      Unable to mount NAME_OF_DISK. Not authorized to perform operation.   Screenshot from nemo file manager:    This answer doesn't seem to help me either, as I just booted up and have nothing open really. Repeated reboots don't solve the problem. How would I find out which application might be holding the lock? .  Note that the work-around is to manually do it with sudo, but I really don't like having to use sudo! Ex:  sudo mkdir /media/mydisk sudo mount /dev/sdb1 /media/mydisk   Or this works too:  sudo gnome-disks   Then use the gnome "Disks" utility to mount via the GUI.  If I do this though I cannot view the mounted partition unless I also run my file manager as root. Ex:   sudo nemo   Then navigate around in a GUI file manage window with elevated permissions.    Update:    possibly related to Polkit?? -    Related    to Polkit and plugdev group?


I ssh on remote host but terminal performance is poor. Symbols I am typing are not shown immediately, but with some delay. Sometimes two symbols are shown at one time after delay.


Why does zero derivative imply a function is locally constant?

I've been trying to prove to myself that if $\Omega$ is an open connected set in $\mathbb{R}^n$, then if $f\colon\Omega\to\mathbb{R}^m$ is a differentiable function such that $f'(x)=0$ for all $x\in\Omega$, then $f$ is constant.   I've reduced the problem to just showing $f$ is locally constant on $\Omega$. Given $x_0\in\Omega$, I know that  $$ \lim_{x\to x_0}\frac{\|f(x)-f(x_0)-f'(x_0)(x-x_0)\|}{\|x-x_0\|}=\lim_{x\to x_0}\frac{\|f(x)-f(x_0)\|}{\|x-x_0\|}=0. $$  This implies $\lim_{x\to x_0}\|f(x)-f(x_0)\|=0$. So for any $\epsilon>0$, there exists some open ball $B(x_0,\delta)$ around $x_0$ in $\Omega$ such that $\|f(x)-f(x_0)\|<\epsilon$ for $x\in B(x_0,\delta)$. But since the choice of the open ball changes with $\epsilon$, I don't think I can conclude $\|f(x)-f(x_0)\|=0$ for $x\in B$. So this doesn't convince me that there actually exists a neighborhood of $x_0$ on which $f$ is constant.   How can you make the leap from zero derivative to locally constant?


On a site with premium user account subscriptions, I'd like to be able to limit logins to one computer at a time. The most straightforward way to accomplish this would be to limit by IP, but I haven't had any luck finding a plugin to accomplish this. Does anybody know of one I can use to get this functionality?  Related:


Black is Back! New update with Achievement shows black backgrounds with black text

Update: This is fixed on version 1.0.43 as per the accepted answer below.  Already saw ,  and . They are old and seem to be about previous versions.  I just updated to the version 1.0.41 of the Android app that brings the new feature - Achievements. Sadly, I think the stress of World Cup has made you guys not do a good job with it. It's buggy.  When I open my Achievements panel and tap on any post, I get this:    After I get this, it persists throughout the rest of the app. For example, if I go to the feed and open another question, I get this too.  Detailed reproduction steps are available in AD7six's answer.  My Device: Samsung Galaxy SIII LTE GT-I9305 Android: Stock ROM 4.3 Jelly Bean  Other Devices: - Device model, Android version, Reported by - HTC Desire, 4.2.2, xd6_ - Huawei Ascend, 4.2, Manu343726 - LG Optimus F3, 4.1.2, Rocket Hazmat - LG Optimus G, 4.3, Canadian Luke - Samsung Galaxy Nexus (Sprint), 4.3, Chrono Kitsune - Samsung Galaxy Note II, 4.3, Katja Christiansen - Samsung Galaxy SII GT-I9100, 4.1.2, AD7six - Sharp SH837W, 4.1.2, timrau - Sony Xperia SP, 4.3, pepoluan - Sony Xperia Z1, 4.3, user2313067 - Unknown, 4.2.1, Deer Hunter


Is it math for studying logic or logic for studying math? I'm confused on what it really is.


How to find modulo of large numbers like $9801\! \pmod {\!32}$

It is easy to calculate small examples like $26\pmod {5}$ but how do you calculate examples like $9801 \pmod {32}$ without a calculator.


I am confused about the notation.  What's the differences between $(\frac{1}{2},\frac{1}{2})$ and $(\frac{1}{2},0)\bigoplus  (0,\frac{1}{2})$, or maybe $(\frac{1}{2},0)\bigoplus  (\frac{1}{2},0)$ ?  (1) $so(1,3)=su(2) \bigoplus su(2)$ has different representations, I don't understand why  $(\frac{1}{2},\frac{1}{2})$ is irreducible, since we already have direct sum  $\bigoplus$ between two $su(2)$, and direct sum usually means reducible.   The Schwartz book (page 163) says $(\frac{n}{2},\frac{n}{2})$ These are each irreducible representations of the Lorentz algebra, but reducible representations of the $su(2)$ subalgebra corresponding to spin.  (2) The group elements are acting on some space, then $\bigoplus$ means the direct sum of these spaces, like $(\frac{1}{2},0)\bigoplus  (0,\frac{1}{2})$. Then what does $(\frac{1}{2},\frac{1}{2})$ means, a direction product $(\frac{1}{2},0)\bigotimes  (0,\frac{1}{2})$ ?


I think its supposed to be simple, but somehow, I don't get what I'm doing wrong.  I have this code:  var currentPosition = {     x:10000,     y:10000 };  var directions = "v>v<"; var housesVisited = [{x:10000, y:10000}];  function createHouseCoordinates(data){     for(var x = 0; x<4; x++){         if(data[x]=="^"){            currentPosition.x += 1;           } else if(data[x]=="v"){            currentPosition.x -= 1;         } else if(data[x]==">"){            currentPosition.y += 1;         } else if(data[x]=="<"){            currentPosition.y -= 1;           }     housesVisited.push(currentPosition);     } }  createHouseCoordinates(directions); console.log(housesVisited);   It is supposed to take directions in the form of symbols, modify the current location, and create an array of objects that lists all locations that were visited. The result of the above, when I run it, gives me this (basically the end position):  [ { x: 10000, y: 10000 }, { x: 9998, y: 10000 }, { x: 9998, y: 10000 }, { x: 9998, y: 10000 }, { x: 9998, y: 10000 } ]   I was expecting:  [ { x: 10000, y: 10000 }, { x: 9999, y: 10000 }, { x: 9999, y: 10001 }, { x: 9998, y: 10001 }, { x: 9998, y: 10000 } ]   What am I doing wrong? What should I read up on to understand this better..? Thanks in advance!


num1 and num2 both are 3.5 and num1 == num2 gives True, but for is operator it is False.  Look at the below code,  Input:  num1 = 3.5 num2 = float(input('num2:'))  # num2 stands for 2nd number print(num1 == num2) print(num1 is num2)   Output:  num2:3.5 True False      num1 and num2 both are 3.5 and num1 == num2 gives True, but   for is operator it is False.   Why is id(num1) != id(num2) ?


Why do I sometimes see a downloading 'pie' icon when viewing photostream photos?

it normally shows in the bottom corner as a sort of 'pie' that fills up as the picture is downloaded, similar to the 'app downloading' pie when viewing a downloading app on the home page/s  prior to this the picture resolution is terrible


let $k$ be a complete, non-Archimedean field, $R$ the corresponding valuation ring, $m$ its maximal ideal. If $u\equiv 1$ mod $m$ and $n$ any natural number $\neq$ char$(K)$, then $u$ is a $n$-th power in $K$.  I am stuck at the condition $u\equiv 1$ mod $m$. What does it mean?


Optimal software package for bayesian analysis

I was wondering which software statistical package do you guys recommend for performing Bayesian Inference.  For example, I know that you can run openBUGS or winBUGS as standalones or you can also call them from R. But R also has several of its own packages (MCMCPack, BACCO) which can do bayesian analysis.  Does anybody have any suggestions as to which bayesian statistics package in R is best or about other alternatives (Matlab or Mathematica?)  The main features I am looking to compare are performance, ease of use, stability and flexibility


Select an element whose id matches href attribute jQuery

I want to select an element whose id matches the href of an  element  HTML

   jQuery  $('a').on('click', function(e) {    e.preventDefault();    var $href = $(this).attr('href');    var $id = $('div').attr('id');    $(this).addClass('active');    //HERE I WANT TO SELECT THE DIV WHOSE "id" MATCHES THE "href" of the  clicked     $('div').id($href).addClass('active'); });


Time taken to empty a hemispherical shaped tank

The tank has a radius of $2$m when initially filled and has an outlet of cross section $12$ cm2  Outlet flow as I calculated goes according to the law $V(t)=0.6\sqrt{2gh(t)}$.  Having found out the general description of the tank and the volume flowing out in time $dt Qdt=A v(t) ; Q=A v(t)$ in time $T$  After attempting further calculations, I do not know how to proceed to find the time taken to actually empty the tank


How could I know how much CPU time is used by all threads?

I have a few threads in my program - run on Windows and write in C++. How can I know in the end of the running how much CPU time is used by all or one of them?


Android app crashes when rotating the "Getting preview" or "Posting edit" dialog

App version: 1.0.52  When you edit a question and rotate the screen while the "Getting preview" or "Posting edit" dialog is showing the app will crash.  12-25 21:38:07.033 E/AndroidRuntime(4768): FATAL EXCEPTION: main 12-25 21:38:07.033 E/AndroidRuntime(4768): Process: com.stackexchange.marvin, PID: 4768 12-25 21:38:07.033 E/AndroidRuntime(4768): java.lang.IllegalArgumentException: View=com.android.internal.policy.impl.PhoneWindow$DecorView{42440ba0 V.E..... R......D 0,0-684,192} not attached to window manager 12-25 21:38:07.033 E/AndroidRuntime(4768): at android.view.WindowManagerGlobal.findViewLocked(WindowManagerGlobal.java:370) 12-25 21:38:07.033 E/AndroidRuntime(4768): at android.view.WindowManagerGlobal.removeView(WindowManagerGlobal.java:299) 12-25 21:38:07.033 E/AndroidRuntime(4768): at android.view.WindowManagerImpl.removeViewImmediate(WindowManagerImpl.java:84) 12-25 21:38:07.033 E/AndroidRuntime(4768): at android.app.Dialog.dismissDialog(Dialog.java:329) 12-25 21:38:07.033 E/AndroidRuntime(4768): at android.app.Dialog.dismiss(Dialog.java:312) 12-25 21:38:07.033 E/AndroidRuntime(4768): at com.stackexchange.marvin.core.OperationThatCanFail$1.onPostExecute(OperationThatCanFail.java:81) 12-25 21:38:07.033 E/AndroidRuntime(4768): at com.stackexchange.marvin.core.OperationThatCanFail$1.onPostExecute(OperationThatCanFail.java:67) 12-25 21:38:07.033 E/AndroidRuntime(4768): at android.os.AsyncTask.finish(AsyncTask.java:632) 12-25 21:38:07.033 E/AndroidRuntime(4768): at android.os.AsyncTask.access$600(AsyncTask.java:177) 12-25 21:38:07.033 E/AndroidRuntime(4768): at android.os.AsyncTask$InternalHandler.handleMessage(AsyncTask.java:645) 12-25 21:38:07.033 E/AndroidRuntime(4768): at android.os.Handler.dispatchMessage(Handler.java:102) 12-25 21:38:07.033 E/AndroidRuntime(4768): at android.os.Looper.loop(Looper.java:136) 12-25 21:38:07.033 E/AndroidRuntime(4768): at android.app.ActivityThread.main(ActivityThread.java:5097) 12-25 21:38:07.033 E/AndroidRuntime(4768): at java.lang.reflect.Method.invokeNative(Native Method) 12-25 21:38:07.033 E/AndroidRuntime(4768): at java.lang.reflect.Method.invoke(Method.java:515) 12-25 21:38:07.033 E/AndroidRuntime(4768): at com.android.internal.os.ZygoteInit$MethodAndArgsCaller.run(ZygoteInit.java:785) 12-25 21:38:07.033 E/AndroidRuntime(4768): at com.android.internal.os.ZygoteInit.main(ZygoteInit.java:601) 12-25 21:38:07.033 E/AndroidRuntime(4768): at de.robv.android.xposed.XposedBridge.main(XposedBridge.java:132) 12-25 21:38:07.033 E/AndroidRuntime(4768): at dalvik.system.NativeStart.main(Native Method) 12-25 21:38:07.035 W/ActivityManager(27384):   Force finishing activity com.stackexchange.marvin/.ui.AskOrEditQuestionActivity


Pronunciation of a (article) /ə/ vs /eɪ/

When to use the weak form /ə/ and when to use the weak form /eɪ/ of the article "a"? I figure if I would emphasize anything I wouldn't emphasize an article like "a", but rather, the noun (phrase) following it. But still I've heard people occasionally use /eɪ/. What's the point of that?


How can I search an Excel spreadsheet in SharePoint?

Looking to be able to search an Excel spreadsheet from the SharePoint mobile app.  I have a spreadsheet with Postal Codes/Zip Codes with corresponding information. I would like to be able to search as you would in Excel.  When I upload a test spreadsheet, it opens as like a PDF. User has "Read" permissions for the document library the spreadsheet is located in.  Thanks in advance,


"Nobody will help you but me" vs. "Nobody will help you but I"

As has been shown , in comparisons with than both the accusative and the nominative are possible and grammatical:        He loves you more than I.   He loves you more than me.      However, when we use but only the accusative seems possible:     Nobody will help you but me. [Not I]   What I think is that the nominative case could be justified as well.     Nobody will help you but I [will].     Why I am wrong? Any other examples and references will be appreciated.


I am looking for a book (English only) that I can treat as a reference text (more colloquially as a bible) about probability and is as complete - with respect to an undergraduate/graduate education in Mathematics - as possible. What I mean by that is that the book should contain and rigorously address the following topics:   Measure Theory (As a mathematical foundation for probability)   It is of course fine if this theory is addressed with an emphasis on probability and not only for the sake of mathematical measure theory, although the latter would be great too.  Introduction to Probability, i.e. the most common theory a student is exposed to when taking a first course in theoretic Probability. For example: distributions, expected value, modes of convergence, Borel Cantelli Lemmas, LLN, CLT, Gaussian Random Vectors More advanced topics such as: Conditional Expectation (defined through sigma-Algebras), Martingales, Markov Processes, Brownian Motion   I want it to be one book so I can carry a physical copy of it with me and work through the material in my spare time.   Examples:   The book by Jean-Francois Le Gall which can be found here:  but (unfortunately for me) is written in French.  Rick Durrett's book on Probability which can be found here  - the  for this book seems a bit mixed, uncertain about how to weigh that.   I am well aware that it's not easy to meet all of the above criteria simultaneously, but I would be grateful for any recommendation.


Difference between "people" and "persons"?

At least 5 people died in Bangladesh and more than 200 are injured.  At least 5 persons died in Bangladesh and more than 200 are injured.


I have Ubuntu 16.04 and my gnome-terminal does not work (I cannot do "run from terminal"). I have xterm, and when I try to run:  gnome-terminal   I get:  Traceback:    File "/usr/bin/gnome-terminal", line 9, in <module>      from gi.repository import Glib, Gio ModlueNotFoundError: No module named 'gi'   I tried to reinstall:  sudo apt update sudo apt install gnome-terminal   but it did not help.  What can I do?


What determines a "year" in SW Universe, for age?

In The Mandalorian, it's said that the package that the Mandalorian is to pick up is "50 years old".  Given how many different planets, stars, etc. there are in the Star Wars universe, what is the "baseline" for a Year?    This discussion does point out that a "year" is certainly relative:     "Wait. They said fifty years old."   "Species age differently. Perhaps it could live many centuries."   - "The Mandalorian" and IG-11 upon discovering an infant of the species   I found a reference to a :     On Coruscant, a year was made up of twelve months[source?] spanning 365 days of 24 hours each, with no leap years. The galaxy used a standardized dating system based off of the galactic capital Coruscant. By the time of the New Republic, the Galactic calendar would use the Battle of Yavin as the epicenter on which to date years   So would it all, even in the time-frame of the Mandalorian, and beyond, still be a Corsucantian year?


How can I label my equations as:  a = b+c (1(a)) d = f+g (1(b))   Please advice as I have used simple labeling structure \label but don't know how to handle the letters.


Virtualbox kernel vboxdrv not loaded on ubuntu 19.10

i have installed virtualbox with repo  deb [arch=amd64] https://download.virtualbox.org/virtualbox/debian aeon contrib  sudo apt-get install virtualbox vagrant -y   but use   VBoxManage --version   this error below      WARNING: The vboxdrv kernel module is not loaded. Either there is no module      available for the current kernel (5.3.0-45-generic) or it failed to      load. Please recompile the kernel module and install it by           sudo /sbin/vboxconfig  You will not be able to start VMs until this problem is fixed. 6.0.18r136238   i have tried step 1  sudo /sbin/vboxconfig   output below     vboxdrv.sh: Stopping VirtualBox services.   vboxdrv.sh: Starting VirtualBox services.   vboxdrv.sh: Building VirtualBox kernel modules.   This system is currently not set up to build kernel modules.   Please install the gcc make perl packages from your distribution.   This system is currently not set up to build kernel modules.   Please install the gcc make perl packages from your distribution.   There were problems setting up VirtualBox.  To re-start the set-up process, run     /sbin/vboxconfig   as root.  If your system is using EFI Secure Boot you may need to sign the   kernel modules (vboxdrv, vboxnetflt, vboxnetadp, vboxpci) before you can load   them. Please see your Linux system's documentation for more information.   step 2 :  sudo /usr/lib/virtualbox/vboxdrv.sh setup vboxdrv.sh: Stopping VirtualBox services. vboxdrv.sh: Starting VirtualBox services. vboxdrv.sh: Building VirtualBox kernel modules. This system is currently not set up to build kernel modules. Please install the gcc make perl packages from your distribution.   after i have install library with command  sudo apt-get install build-essential gcc make perl dkms  but still not working . kernel vboxdrv still not loaded. somebody helpme .


Any of y'all have any suggestions on books/websites that give an intuitive intro to abstract algebra/basic algebraic structures?


I'm really confused on this. I have no idea on several things:   When do elections begin?   Is there a set time each year?   Do elections actually take place each year?   Can I vote?   Where do I vote?     Etc.  Can someone please help me?


Switch between workspaces with mouse (not trackpad / magicpad and not keyboard)

Is there a way I can switch between workspaces with a mouse? I know I can configure keyboard shortcuts for this, and I can also configure trackpad 3/4 finger swipe up for mission control then select workspace from there. But is there a method for switching workspaces with only mouse?


How to evenly unwrap / texture long extruded objects with folds and uneven segments?

I've some difficulties to find a satisfactory unwrap solution for this kind of long angled object with uneven segments:      I'm only interested in the brown faces which are delimited by two seams.   The solution must preserve the relative length of each straight segment, so that the texture containing a repeated pattern can be mapped evenly on the whole length (the sample is a ceramic ).  Here is the result with a cube projection and a checker texture, other methods provide different results, but the distortion is always present:      I can't find a solution, except purely manual, to create the UV map while ensuring all segments:   Are oriented in the same direction on the map, Have their length proportional to their actual size, to prevent texture distortion.   These constraints seem quite common, is there a standard approach?  Intuitively, I'm expecting the most simple method to lead to overlapping variable length rectangles, in the same direction, anchored at a corner (or a very large single rectangle).


How to change login id without using another provider?

I use an email address as my user name to get into Stack Exchange (along with various child sites). I do not use Facebook, Yahoo, Google, OpenID or any of the other myriad of logon providers, and I am not interested in signing up.  The email address I use has long since been deleted, and I'm cleaning up my web accounts. How do I change the user name to an email address that I currently use?


Adding a line break in the title attribute

i would like to find out how to add a break in the title attribute, i would like to have breaks in the title attribute to differentiate the names. how can i add a break in the title attribute?  i have something like this  Some Text
   what comes out is:


How to properly use `vim-airline` package

After installation of the vim-airline and vim-airline-themes packages, what is the best way to use / activate them?  I can manually copy the .vim-files over, but this defeats the purpose of package management with eventual updates. Using vim 8, so I think the answer  is outdated for the new vim 8 package management.


How to see http requests made on a network?

I have an Android phone, which have an app. This app uses an API. Now, I want to know the URL of this API. I sure the mobile phone connects with the app using some HTTP requests. I also want to know what kind of HTTP requests and its parameters.  The easiest way to get that URL, I guess, is to connect my Android phone to my own private WiFi network, and then get a list of all HTTP requests made, and then pick out the one my phone is using.  So my question is: How do I see all HTTP requests made on my wifi network? Is it WireShark? And if so, how do I see the actual posts?  (Is this the right forum? It was definetely not StackOverflow and I guess this is a "network" question...)


Subspace of the real matrices generated by the matrices of the form $AB-BA$

Let $S$ be the subspace of vector space of all real $n\times\ n$ matrices generated by all matrices of the form $AB-BA$ with $A$ and $B$ in vector space all $n\times\ n$. What is the dimension of $S$?


Reflexive love: where does "love me some ..." come from?

It seems trendy to use a reflexive-like construction with love or hate plus some, like this:   You know I love me some cheese! I hate me some cold and the temperature is dropping.   Where did this come from and why has it become popular?


Screen Time shows 24hr usage for several weeks

Screen Time on my iPhone 8 (iOS 14.2) is reporting that the Wikipedia app has been running 24hrs a day for a few weeks. I don’t even have the Wikipedia app installed on my phone. What’s going on and how can I fix it? I’m trying to use Screen Time to limit my usage, but now the statistics are completely messed up.


$2$ out of $3$ property of the unitary group

I am trying to understand the . I have almost got it, but I am not completely sure about the interaction between an inner product and a symplectic form to obtain an almost complex structure.  Let $V$ be a real vector space. An inner product on $V$ is a positive definite symmetric bilinear form $g$. An endomorphism $T \in \operatorname{End}(V)$ preserves $g$ if $g(T(u), T(v)) = g(u, v)$ for all $u, v \in V$; the collection of all such endomorphisms forms a group $O(V, g)$ called the orthogonal group. An almost complex structure on $V$ is an endomorphism $J \in \operatorname{End}(V)$ such that $J^2 = -\operatorname{id}_V$. An endomorphism $T \in \operatorname{End}(V)$ is complex linear if $T \circ J = J\circ T$; the collection of all such endomorphisms forms a group $GL(V, J)$ called the complex general linear group. A symplectic form on $V$ is a skew-symmetric non-degenerate bilinear form $\omega$. An endomorphism $T \in \operatorname{End}(V)$ preserves $\omega$ if $\omega(T(u), T(v)) = \omega(u, v)$ for all $u, v \in V$; the collection of all such endomorphisms forms a group $Sp(V, \omega)$ called the symplectic group.  Almost Complex Structure & Inner Product For an inner product $g$ and a compatible almost complex structure $J$ (i.e. $J \in O(V, g)$), we obtain a symplectic form by defining $\omega(u, v) := g(u, J(v))$. It follows that $O(V, g)\cap GL(V, J) \subseteq Sp(V, \omega)$.  Almost Complex Structure & Symplectic Form For a symplectic form $\omega$ and a compatible almost complex structure $J$ (i.e. $J \in Sp(V, \omega)$) which tames $\omega$ (i.e. $\omega(u, J(u)) > 0$ for all $u \in V\setminus\{0\}$) we obtain an inner product by defining $g(u, v) := \omega(J(u), v)$. It follows that $Sp(V, \omega)\cap GL(V, J) \subseteq O(V, g)$.  Inner Product & Symplectic Form This is the part I am unsure about. Denote by $\Phi_g$ the isomorphism $V \to V^*$ induced by $g$; that is $\Phi_g(v) \in V^*$ is defined by $\Phi_g(v)(u) = g(u, v)$. Likewise, denote the isomorphism $V \to V^*$ induced by $\omega$ by $\Phi_{\omega}$; that is $\Phi_{\omega}(v) \in V^*$ is defined by $\Phi_{\omega}(v)(u) = \omega(u, v)$.   Is there any compatibility restriction that we must impose on $\Phi_g$ and $\Phi_{\omega}$?  Is $J = \Phi_g^{-1}\circ\Phi_{\omega}$ an almost complex structure on $V$?  How do we use this to deduce $O(V, g)\cap Sp(V, \omega) \subseteq GL(V, J)$?    For question 3, I can use the previous relationships between the three groups, but I'd like to be able to deduce it from the structures themselves.


Why does the exif data show a max aperture 1.6 when I am using a f/1.8 lens?

I am looking at exif data of one of my image that i took with Nikon 35mm f/1.8 lens. While the exif information of my actual aperture is correct, max aperture displayed is 1.6 for the lens which is actually f/1.8!  I am wondering how this is possible ?


Need to convert string to DateTime format in C#

I have a string stored in table "13/12/1985 12:00:00 a.m." when i tried to convert this to Datetime, i am getting an exception saying "String is not a valid DateTime Format". It is because the first part of the string(13) is month. Is there any way to convert the above string to (mm/dd/yyyy hh:mm:ss am/pm) format?. Actually the string saved in table is in the format of "dd/mm/yyyy". I want to convert to "mm/dd/yyyy" in Datetime


How to hide certain objects in reflection in Eevee

Hello, I want to make the kettlebell shiny but without those reflections of other objects. Is there a way to make certain objects not visible in the reflection in Eevee?


Confusion about definition of manifold with boundary

Consider this definition:     A space $M$ is a manifold with boundary if each point $x\in M$ has a neighborhood $U_x$ that is homeomorphic to $\mathbb R^n$ or to $\mathbb R^n_+=\{(x_1,\cdots,x_n)\;|\; x_n \ge 0\}$; the points which have neighborhoods homeomorphic to $\mathbb R^n_+$ form the boundary $\partial M$ of $M$.   I want to understand how precise this definition is. Indeed, a point that has an open neighborhood homeomorphic to $\mathbb R^n$ can also have another open neighborhood that is homeomorphic to $\mathbb R^n_+$ and in that case is this point on the boundary $\partial M$ or in $M\setminus \partial M$  ? How to choose? Is my definition incomplete so that I have to say: "In a manifold with boundary, a point in $M$ has an open neighborhood homeomorphic to $\mathbb R^n$ but if it doesn't have such neighborhood then it has to have an open neighborhood homeomorphic to $\mathbb R^n_+$"  Thank you for your help!


FFMPEG video from images comes out same (yet incorrect) duration regardless of frame rate

When creating a video from an image sequence using ffmpeg, I'm finding that I get a same length video whether encoding it as 30fps or 60fps. Given, in my current case, 6329 image files, the following two commands produce video files of the same length:  1. ffmpeg -pattern_type glob -i '*.png' -r 30 -pix_fmt yuv420p out-30fps.mp4 2. ffmpeg -pattern_type glob -i '*.png' -r 60 -pix_fmt yuv420p out-60fps.mp4   With the above, ffprobe shows video 1 is 00:04:13.17 and encoded at 30fps, while video 2 is 00:04:13.15 and encoded at 60fps. When loaded into Quicktime Player, both videos have the same length and speed.  So, two questions:   I'm confused by the total video duration, as 4m13s is a total of 253 seconds. At 30fps, 253 seconds should require 7590 frames, not 6329. What is required to use the existing frame sequence as if it's 60fps source instead of 30? Or, put another way, how to make the final video have twice as many frames/second during playback?


Can anyone explain reverse bias pn junction using only electrons as charge carriers

In forward bias condition p-type semiconductor is connected to positive side and ntype semiconductor to negetive side and the electrons flow from n-type to p-type to cathode of battery.  But imagine the same situation when the situation is reverse biased so now p-type is connected to negetive terminal of battery and n-type to positive terminal of battery.  Now there is excess of electrons in n-region and it is connected to positive terminal of the battery.So electron can flow from n-type region to positive terminal of the battery due to potential difference created by battery whereas in p-type electrons can flow from one covalent bond to another as they do in forward biasing.  Only difference is,here electron move in opposite direction (from one covalent bond to another) i.e. from n-region to depeletion region whereas in forward bias they move from depeletion to n-region.Which shouldn't be a problem   Now in this manner current must flow regardless of biasing so what's the correction?


How is an EEPROM different from a Flash memory?

I am trying to understand the terminology used for various non-volatile memory chips for example as  and .     Is there any preference to use the word EEPROM or Flash for specific type of memory chips or is it some specific technology difference in the two types?


Im brand new to Linux in general, ive only been using it a few days, and I keep getting a huge amount of 404 errors when running sudo apt-get update here are some examples  Err http://security.ubuntu.com oneiric-security/universe i386 Packages         404  Not Found [IP: 91.189.88.152 80] Ign http://extras.ubuntu.com oneiric/main Translation-en                       Err http://security.ubuntu.com oneiric-security/multiverse i386 Packages       404  Not Found [IP: 91.189.88.152 80]   that then gives me failed to fetch errors like this  W: Failed to fetch http://security.ubuntu.com/ubuntu/dists/oneiric-security/multiverse/source/Sources  404  Not Found [IP: 91.189.88.152 80]   Im using ubuntu 11.10 ( the reason im running on an old version is because im using amd legacy drivers)


Where/When can I find Xur in Destiny tower and what does he sell?

I've heard many people talk of an exotic vendor named Xur who only comes on the weekends, but I couldn't find him anywhere in the tower, and he wasn't on the map either this weekend. I was wondering if someone could just clear this up. Also, does he always have the same stuff, is it random, or is it a cycle of some sort.


Move the edit widget on the left side on the mobile app

On the web interface when Alice edits Bob’s question, the Alice’a profile widget will appear on the left. On the mobile app it appears on the right, pushing the Bob’s widget on the left.  I found this quite confusing because I usually use the web interface and I know what’s on the left is the widget of the user who edited the question.  I’ve been using the mobile iOS app for about an year and still didn’t get used to it.  Here is a screenshot of the components I’m referring to:    To me it seems like a small inconsistency, but I’m wondering what you think.  Is there a specific reason to keep it this way?


Determining size of grid cells created by vector grid tool of QGIS?

I am working with QGIS 1.8.0 and Im making a vector grid on a map. Does someone know how big are the squares if the grid settings look like in the picture?


When I open the Unity Dash from the launcher, the Dash takes up the whole screen and doesn't give me the ability to resize it. This makes it impossible to see my desktop and drag and drop icons to it in order to create shortcuts. I've seen some screen where the dash has maximize and minimize buttons, but I do not have anything like that on my 11.10 install.


Pacman: error: duplicated database entry

On Arch Linux, I've backed up my system with rsync and restored it again, but it seems that my way of doing it (which I did get from the Arch Wiki but must be wrong?) has kept old files deleted by Pacman.  This results in the error duplicated database entry when I try to upgrade my system with pacman -Syu.  What should I do?


Proof of $e^x - 1 \geq x$ for ${x: -1 \leq x < 0}$

Is this valid, and how can i prove that it holds.  Proof of  $$e^x - 1 \geq x \text{ for } {x:-1 \leq x < 0}$$


How can I make a shortcut to close all the windows of the same application?

When I right click on an application's icon in the Unity launcher, I can press Quit to close all the windows corresponding to that application. Is it possible to do the same with a keyboard shortcut which operates on the active window (and all the other windows corresponding to the same application)?  I could do something similar with xkill, but in that case I do not have the message that remembers me of unsaved files.


Is a spontaneous decrease in entropy *impossible* or just extremely unlikely?

I was reading  and I got some doubts about a sentence about entropy, specifically when Ethan explains the irreversibility of the conditions of the hot-and-cold room, as in this figure:  In his words:  It's like taking a room with a divider down the middle, where one side is hot and the other is cold, removing the divider, and watching the gas molecules fly around. In the absence of any other inputs, the two halves of the room will mix and equilibrate, reaching the same temperature. No matter what you did to those particles, including reverse all of their momenta, they'd never reach the half-hot and half-cold state ever again.  My question is: Is the spontaneous evolution from the equilibrium temperature (right side of the image) to the half-hot and half-cold state (left side) physically and theoretically impossible/forbidden, or is it simply so astronomically unlikely (from a statistical perspective) that in reality it never happens? The article seems to suggest the former, but I was under the impression of the latter.


What factors determine enemy levels or: How do enemy levels scale to the player character's?

When I finished Normal Mode at around Level 30 and went back to the  (still at Normal mode), I found that all enemies there are now very easy to kill, meaning they didn't level up (or hit a level cap).  When I went to  as a Level 36 character in True Vault Hunter Mode, I noticed that the enemies are the same level as me.  What factors determine enemy levels?   Specifically, I would like to know:       Are enemies affected by what level a character accepted a mission?      Or is it what level a character is when they first entered an area?      How does Normal Mode, True Vault Hunter mode, and the Ultimate True Vault Hunter Mode affect enemy levels?     Are there enemies that will scale to the player level, as the player levels up? Any enemy leveling differences specific to the DLC areas?         EDIT:   There is now  that explains how this works generally: "In playthrough 1, outside of the DLC, there's no such thing as scaling. Enemy levels are determined solely by the area they're in and your mission." Can anyone expound on that, and comment or provide an answer on what are the specific enemy levels on specific areas and/or missions?    states that "enemies do not actually "scale", or at least from what we know of..." and lists specifics for enemy levels on certain areas in the game (sans DLC areas). Can anyone expound on that and/or add specifics for enemy levels in the DLC missions or areas in TVHM (PT 2.0) and/or UTVHM? The  update has just been released, can anyone provide info about enemy levels on that mode, including the DLC areas or missions?


Prove that a convex function on $\mathbb{R}^n$ is continuous

Let $f: \mathbb{R}^n \rightarrow \mathbb{R}$ be a convex function on $\mathbb{R}^n$. How to prove that $f$ is continuous?


Does MariaDB Support Materialized views?

Before I even try to experiment with MariaDB, could anyone tell me if MariaDB supports Materialized views? I can't seem to find it in their documentation.  This is one of my major issues with MySQL (the fact that it does not have materialized views out of the box). This is a major feature for me in a database, and I would like to know if MariaDB supports it.


Upgrade to an unsigned version of iOS - possible or not?

I have an iPhone 5s (A1453). It is currently running iOS 9.x.  I need to upgrade it to iOS 11.x to perform testing of apps on this particular iOS version/device combination.  I've read couple of articles about a method with Prometheus, SHSH2, etc. But it seems that I'm out of luck, because this device never had iOS 11 installed on it, so there's no SHSH2 for this version, and it is already unsigned.   Am I right with my guess, or is there some way to do such an upgrade?


Please help me to write the function drawing code  polynomial function f(x) = x^3 – 5*x.  polynomial function f(x,y) = x^3 – 5*y^2.


If $A,B,C$ are the angle of a triangle, then show that $\sin A+\sin B-\cos C\le \dfrac3 2$

If $A,B,C$ are the angle of a triangle, then show that $\sin A+\sin B-\cos C\le \dfrac32$ I tried substituting $C=180^\circ-(A+B)$ and got stuck. I also tried using the formula $\sin A+\sin B=2\sin \frac{A+B}{2}\cos \frac{A-B}{2}$ without any progress. Please help!


Get ID for each single v.to.points point in GRASS?

How do I get for each  point an ID in the database (DB).  So far I splited the line (each 10m) but it returns only one DB entry for each original line.   v.db.select line cat|Id|Name 1|1|Line 1 2|2|Line 2  # split the lines every 10m v.to.points in=line out=line_points dmax=10  # check the result v.db.select line_points cat|Id|Name 1|1|Line 1 2|2|Line 2   Each point should have its own DB entry. The result should be:  v.db.select line_points cat|Id|Name 1|1|Line 1 2|1|Line 1 3|2|Line 2 4|2|Line 2     Workaround: So far my workaround is, to export (v.out.ogr) the points as shape and import (v.in.ogr) it again. Then each point has his own ID. But there must be a smarter way to do that!


Proving upper bound for $\binom{n}{k}$ directly from given fact

Given the fact: for every $n\in\mathbb{N}$ $$e\left (\frac{n}{e}\right)^n\leq n!\leq en\left (\frac{n}{e}\right)^n $$ Prove directly: $$\binom{n}{k}\leq \left (\frac{en}{k}\right )^k $$  Yes, this inequality is as obvious as obvious gets ($\binom{n}{k}\leq \frac{n^k}{k^k}$), but how do we utilize fact to come to desired result? Have attempted to manipulate the upper/lower bounds of $n!$ so that we get: $$\frac{1}{k!}\geq \frac{1}{e}\left (\frac{e}{k}\right )^k\qquad \frac{1}{(n-k)!}\geq\frac{1}{e}\left (\frac{e}{n-k}\right)^{n-k} $$ combined, results in $$en\left (\frac{n}{e}\right)^n\cdot \frac{1}{e}\left (\frac{e}{k}\right )^k\cdot \frac{1}{e}\left (\frac{e}{n-k}\right)^{n-k}\geq \binom{n}{k}$$ If we extract the part of interest from the above product, we may ask: $$\left (\frac{en}{k}\right )^k\overset{?}\geq \frac{1}{n^k}\left (\frac{n}{e}\right )^{n+1}\left (\frac{e}{n-k}\right )^{n-k}\cdot \left (\frac{en}{k}\right )^k\geq \binom{n}{k} $$ Hence, we ask whether: $$n^{n-k+1}\leq e^{k+1}(n-k)^{n-k} $$ i.e remains to show for $1\leq k\leq n$ $$n\left (\frac{n}{n-k}\right )^{n-k}\leq e^{k+1} $$  Unnecessary work. Begin by evaluating one piece at a time.


How do you prevent Apple Photos from opening on connecting a camera.  I prefer to download all my work to Lightroom 3.


I am Getting NullPointerException When Converting JSON to HashMap, The Code is Given Below

I am Really Struggling with this code Trying different ways to Convert JSON to HashMap but still no Progress any help regarding the code would be appreciated.I have tried Searching for the problem but it still Gives me other Exceptions like not a JsonObject and already tried a different lib but Google.gson works best for me please let me Know if you have any fix regarding this...      import java.util.HashMap;     import java.net.*;     import java.io.*;     import java.util.Map;      import com.google.gson.*;     import com.google.gson.reflect.*;      public class Weather {         private static Map<String, Object> jsonToMap(String str){             Map<String, Object> map = new Gson().fromJson(                     str, new TypeToken<HashMap<String, Object>>() {}.getType()             );             return map;         }          public static void main(String[] args){             String apiKey = "API not Provided";             String urlString = "http://api.openweathermap.org/data/2.5/forecast?id=1174872&APPID=" + apiKey + "&units=metric";             try{                 StringBuilder result = new StringBuilder();                 URL url = new URL(urlString);                 URLConnection connection = url.openConnection();                 BufferedReader reader = new BufferedReader(new InputStreamReader(connection.getInputStream()));                 String line;                 while ((line = reader.readLine()) != null)                 {                     result.append(line);                 }                 reader.close();                 System.out.println("json print: ");                 System.out.println(result);                  Map<String, Object> respMap = jsonToMap(result.toString());                 Map<String, Object> mainMap = jsonToMap(respMap.get("main").toString());                 Map<String, Object> windMap = jsonToMap(respMap.get("wind").toString());                  System.out.println("Current Temperature: " + mainMap.get("temp"));                 System.out.println("Current Humidity: " + mainMap.get("humidity"));                 System.out.println("Current Wind : " + windMap.get("speed"));                 System.out.println("Current Wind Direction : " + windMap.get("deg"));              }catch(NullPointerException e){                 System.out.println("Null Pointer Exception Occurred!");             }catch (IOException e)             {                 System.out.println("Input Output Exception Occurred!");             }         }     }


Any case where simultaneous multithreading is worse than normal case?

Is there any chance of SMT (simultaneous multithrading) giving worse performance than normal CPU?  For example, is it possible for normal CPU to two programs one by one to have better performance than running these two programs simultaneously on CPU that supports 2-way SMT?  Thanks in advance.


In an abelian group, the elements of finite order form a subgroup.

I need to show that elements of finite order in an abelian group form a subgroup of that group. Where do i start ?


Integers coprime to $n$ are closed under multiplication

I have just began learning number theory and I wanted to prove the following statement:   'if $x$ is coprime with each $p_i$ then $x$ is coprime with $p_1...p_n$'   This was actually a statement from a proof within CRT and they also had the condition that $p_i$ are pairwise coprime but I am not sure if that was used in proving the above statement.  Here is my attempt.  Suppose for a contradiction that $x$ is coprime with each $p_i$ and $x$ is not coprime with $p_1...p_n$, then there exists a prime number $q$ such that $q\mid x$, $q\mid p_1...p_n$. By the property that $q$ is prime we must have $q\mid p_i$ for some $i$. Hence $\operatorname{hcf}(x, p_i)\geq q$ for that specific $i$ and so there is a contradiction.   As I said, since I didn't use at all the pairwise coprime property of $p_i$, I am not sure if my proof was correct, could someone please let me know if there were any flaws in my argument?


If $x+y+z \equiv 1 \pmod{17}$, where $x,y,z$ are irrationals, then is it true that $x^n + y^n +z^n \equiv 1 \pmod{17}$ for odd $n$?

Original problem:  If $\alpha$ be the greatest positive root of $x^3-3x^2+1=0$, then show that $[\alpha^{1996}]$ is divisible by 17. ($[x]$ denotes the greatest integer less than or equal to $x$)  My work: It is easily found that if the roots are $\gamma < \beta <\alpha$, then $-1 < \gamma < 0 < \beta < 1$ and $2 < \alpha < 3$, and that they must be irrational. We also have, $\begin{align*} \alpha + \beta + \gamma &= 3 \\ \alpha\beta + \beta\gamma + \gamma\alpha &= 0 \\ \alpha\beta\gamma &= -1 \\ \alpha^2 + \beta^2 + \gamma^2 &= 9 \\ \alpha^4 + \beta^4 + \gamma^4 &= 81-12 = 69 \equiv 1 \pmod{17}\\ \end{align*}$ Now, we also note that $-\beta < \gamma < 0 < \beta < 0.9$, and using the inequality $(1+x)^r \leq e^{rx}$, we have that $0 < \beta^{1996} + \gamma^{1996} < 0.5$. From Newton's identities, we know that $\alpha^{1996} + \beta^{1996} + \gamma^{1996} \in \mathbb{Z}$. Hence, from the definition of the greatest integer function, $$[\alpha^{1996}] = \alpha^{1996} + \beta^{1996} + \gamma^{1996} = \left(\alpha^4\right)^{499} + \left(\beta^4\right)^{499} + \left(\gamma^4\right)^{499}$$ But we have that $\alpha^4 + \beta^4 + \gamma^4 \equiv 1 \pmod{17} \implies (\alpha^4 + \beta^4 + \gamma^4)^{499} \equiv 1 \pmod{17}$. To prove the required result, we must show that the rest of the terms of the expansion must sum to a multiple of 17. Although we know that the sum must be an integer, as the terms themselves are irrational, I can't think of any way to show this, or even if it is true or not. Any help or hint regarding this will be appreciated. I am also grateful to any hints on how to solve the original problem in any other easier way.


Assigning null value to a nullable enum through :? operator

I am trying to initialize the following object:  return new ObjectNaturalPerson             {                 Initials = entity.Initials,                 FirstName = entity.FirstName,                 LastName = entity.LastName,                 Gender = GetGender(entity.Gender),                 BirthPlace = entity.Birthplace             };   So far there is no problem with the code. But focus on the line:  Gender = GetGender(entity.Gender)   What I want to achieve is that I would like to set Gender to null or GetGender(entity.Gender) depending on entity.Gender, which is a string. Moreover, Gender is a nullable property, named indeed Gender and of type Gender, which is an enum.  public Gender? Gender { get; set; }   What I don't understand is that, if during the object initalization I try to set directly Gender = null, there is no problem! Instead, if try to use the operators :? in the following way then I receive an error:  Gender = entity.Gender.IsNullOrEmpty() ? null : GetGender(entity.Gender)   The error is: type of conditional expression cannot be determined because there is no implicit conversion between Null and Gender. But again, if I set Gender directly to null then there is no problem! Thanks in advance.


It's now a week since I have reported  bug on Chess Meta, and the question has received only 13 views. I would like to share this question, but I am also afraid this would be considered spamming. Since it is on a meta site, I can't open a bounty. However, this does not seem to be the problem. The problem is that not much people visit Chess Meta. Nothing posted  can help, because the question is already on the top of the . The bug is very annoying to me. Some even don't know it is a bug.  How do I draw attention to this question, without causing chaos to the community?


Why do I get different results when printing out z as shown in the following code snippet?  It seems that the compiler cuts in the second "print" all positions after '2'... Thank you for help!   double z = 1.0; z = z + 0.1; z = z + 0.1; System.out.print("z := "+z); System.out.print(" # z:= "+((0.1+0.1)+(1.0)));   Output:  z := 1.2000000000000002 # z:= 1.2


Question getting downvoted, but unable to delete the question, 2 years later

I've started getting downvoted, for some reason, on a 2-3 year old question here:    It is 2 years later, and I now agree that the question sucks. However, I can't remove the question because it has answers. While I understand that we want to prevent question askers from nuking things in the general case, is there any recourse for the asker if they're randomly getting downvoted 2 years later?


How do I install Firefox ESR from a command line?

How do I install  from a command line?  Mozilla is releasing a new major version of Firefox . With each release, there's a possibility of bugs, unwelcome new features and interface changes (as well as bugfixes, welcome new features and interface changes; of course)  For those of us who don't have the time and effort to cope with change on a six-week cycle, yet still need security updates from the newer versions, Mozilla is maintaining  (ESR) versions, which have major updates approximately every eight rapid (non-ESR) releases, yet still receive security fixes.  How do I install the latest ESR release of Mozilla Firefox, and stay on the ESR channel, so that I will only get major update to a new ESR version?  I need a robust command-line solution that can be automated. Currently I'm installing Firefox with  sudo apt-get install firefox -y


Find a counterexample that $f(x)$ is Gateaux differentiable and $\lambda(x)$ is not continous

I've learned that function $f:\mathbb{R}^n\rightarrow \mathbb{R}^p$, at $x \in \mathbb {R}^n$, $f(x)$ is Gateaux differentiable, then exits a linear operator $\lambda (x):\mathbb{R}^n\rightarrow \mathbb{R}^p$ such that $D_uf(x)=\lim_{t \rightarrow 0}{\frac{f(x+tu)-f(x)}{t}}=\lambda(x)(u),\forall u \in \mathbb{R}^n$. If $\lambda(x)$ is continous, $f(x)$ is Frechet differentiable.   I want to find a counterexample that $f(x)$ is Gateaux differentiable and $\lambda(x)$ is linear, not continous, but it's hard for me, help me, thank you!


How get content of a dynamically appended  on click?

I have a php file:  $sql = mysql_query("SELECT id, name FROM table") or die(mysql_error()); if (mysql_num_rows($sql) > 0){     while($row = mysql_fetch_array($sql)){       echo "

".$row['id']."

".$row['name']."

;    } }   In JS file:  success: funxction(data){ $(".content").html(data); }   In HTML file I have:
     // Here the ajax put the divs
   How can I get the content of

 or

 when I click on a button?  The button is situated out of .content area. I clicked on a row, it is lighted and I click on button. When a clicked on button, I want to get the id and name div content where the row is lighted.  ............................................. Update: I have this js code:   when I click on the button, check if a row was selected; if is not selected i receive an notification, if the row is selected i want to receive div content :)


Do Brunei Darussalam passport holders require transit visa in Brussels?

A colleague with Brunei Darussalam passport is flying from Delhi to Manchester and will transit in Brussels fro a few hours? Does he need a transit visa in Brussels?


How about blogs for Stack Overflow users?

There are times when I'd like to communicate something to the Stack Overflow community but it doesn't fit a question.  Right now, I have the product of many answers (a bunch of code) I'd like to share back but can't.  If each user had a blog or wiki (or something) they could create articles / blogs on and then link the related SO questions to it. You could then add an icon to those questions to show there is also more expansive information available.  By linking to the questions, this means anyone could author articles addressing a question outside of the scope of the more simple Q/A scenario.  Of course, many people have blogs but they must link that in a not so immersive fashion and not everyone has a blog (and also many blogs are inadequate in displaying text from a coding viewpoint (e.g. formatting code). Folding such a mechanism into SO would open up all sorts of creative opportunities and make the site even more sticky for users.  I think it's a winner and I'd use it for sure.


20GB of Temporary Files, Only 50MB in Temp Folder

I recently discovered that the Settings app is showing around 20GB of space used by temporary files. But when I go to remove them I can only remove about 28MB. When I open the temp folder by using Run and then %temp% it only shows around 40-50MB of files right after boot. How can I remove these 20GB of invisible files? I only have a 240GB SSD so space is quite scarce. Here are a few photos:    I run Windows 10 Home Activated. I have tried Disk Cleanup but this removed only around 30MB of files.  UPDATE: After turning on hidden items I found a folder name WINDOWS-BT, after doing some research it turned out to be a folder for the previous windows version. I deleted it using TakeOwnerShip pro and this removed around 12GB of temporary files, but 8GB still remain. I am currently downloading TreeSize free to find out where the other 8GB is.  UPDATE 2: Hi, I downloaded TreeSizeFree and I didn't really find anything there.   The biggest folder is 87GB of Program Files which mainly consists of my GTA V install. The Program Files (x86) folder was mainly made up of my Steam games (CS:GO, Besiege, etc). The 5.5GB [3 Files] location was noted as being my pagefile.    The Windows folder shows up as 25GB when in Settings it is only 18GB, this could explain where the other 8GB are coming from. What are some things I should look for in there?  FINAL UPDATE: After deleting the Windows-BT folder it reappeared a few hours later. I decided to check from system updates and surely enough one was downloaded and pending to be installed. After installing the update the Windows-BT folder disappeared on it's own and a new folder taking up 20GB called Windows.old was created. I then followed this  to remove the .old folder and I had all my disk space back! NOTE: Disk Cleanup wasn't able to find the Windows.old folder, this is why I had to delete it from the settings app.


Can a Tourist from a VWP country carry (Rent/ Borrow) a gun in say Florida

Looking to find out if it is legal to borrow or rent a gun from an individual(s) or company to use to either visit the various gun ranges or wildlife hunting in Florida.  I have a shotgun licence in the UK for hunting etc... but looking to do something similar in Florida without falling foul of any gun carrying laws in transit to any gun range or hunting area?  I know various friends in the US that would lend the guns while there but are they required to be with me while attending any event? Basically not looking to be tethered to any third party...


When I'm running sudo apt-get update I am getting following errors/exceptions. Give me some solutions..   W: Failed to fetch http://mirror.kavalinux.com/ubuntu/dists/trusty/multiverse/source/Sources  404  Not Found W: Failed to fetch http://mirror.kavalinux.com/ubuntu/dists/trusty-updates/main/source/Sources  404  Not Found E: Some index files failed to download. They have been ignored, or old ones used instead. E: dpkg was interrupted, you must manually run 'sudo dpkg --configure -a' to correct the problem.


Vim in tmux does not correctly determine background color

I connect to a server via SSH from xfce4-terminal.  When I open vim outside of tmux, colors in vim are very bright (which is good):   When I start tmux with default config, and open vim from there, it displays normal colors (t_Co=8):   However, if I set default-terminal to "whatever-256colors" (or start tmux with -2) , and start vim from tmux, some colors are very dim:   Vim does recognize that this is a 256-color terminal, since t_Co gets set to 256.  I found out that entering :set background=dark in vim fixes the colorscheme, however, that isn't the proper fix, because this only inverses the problem (i.e. it causes vim to use bright colors with a terminal with light background).  How do I make vim correctly determine background color while in tmux, without setting it explicitly?    Ouside of tmux, $TERM is equal to xterm-256color.  .tmux.conf contains:  set -g default-terminal "screen-256color"   Inside tmux, $TERM is screen-256color. Changing terminal type to xterm-256color didn't help.


Why does GNU find suppress printing -prune'd directories when another "-or" test is applied?

I have a directory with the following files and a .git directory, e.g.  . ├── .git │   ├── branches │   ├── COMMIT_EDITMSG │   ├── packed-refs │   └── refs ├── readme.md ├── server_build.sh └── tags   If I run GNU find command with the -prune test, find prints the directory which is prune'd:  % find . -name '.git' -prune ./.git   If add another OR option, then the directory which is pruned not longer appears in the output:  % find . -name '.git' -prune -o -name '*.md' -print ./readme.md   In this case, both -name '.git' and -name '*.md' tests must be returning true, it can't be possible that adding another OR test suddenly makes the -name '.git' -prune test untrue. Is there some implicit switch being added to the first statement? In other words is find turning  find . -name '.git' -prune   into   find . -name '.git' -prune -print   at run time? and the implicit -print is taken away  when the next test when is added? Why doesn't find print the -prune'd directory when another "-or" test is applied?


Internal pull up resistors in a micro-controller vs external pull ups

Micrcontrollers such as PIC describe their pull up resistors as weak pull up resistors, what does weak signify?  When/why would I want to use external pull-up resistors on I/O pins that support internal pull up?


Multiple keyboard shortcuts for same command

Is it possible to assign multiple keyboard shortcuts for same default command. I want to switch between workspaces using CTRL+NUMPAD_1 and using CTRL+1 too.  Or how to add custom command for switching?


How can I download price data given the ISIN?

Give the ISIN of a stock I would like to download the stock prices of, for example, the last 30 days. Is there a simple way to do this?   Requirements - Must take the ISIN as input - Should be available as simple web download (wget, curl) or via a simple python script


Do we have any proof that  are always  or is it just a fact that hasn't been violated  till date? If there is a proof then please provide a link.


This may seem like a basic question, but I have a small screen without a lot of real estate. When I have a website (Like Stack Exchange) open, about 20% of the screen is taken up by menus, bars, and empty space. I would love to find a way to combine some of these empty spaces. For example, having the tabs combined with the title bar, or the title bar combined with the menu bar. Are there any steps I can take to make this a little more manageable?


I understand that once a game is in the library it cannot be removed, only hidden.  My question is, can I gift an uninstalled copy of a game to a friend?  I understand that this may be impossible due to legal issues, and that once a game is in the library it stays.


As the title goes,   Does Stackoverflow (the website) use any Bootstrap?


Is there a way to create a new command with 9 arguments ({a_{11}},{a_{12}},{a_{13}},{a_{21}},{a_{22}},{a_{23}},{a_{31}},{a_{32}},{a_{33}}) that has as output a matrix with the Sarrus Rule? For instance: to obtain     just use the command that we will call sarrus:  \sarrus{-k}{k-1}{1}{0}{k-1}{k}{2}{0}{1}.   If it is possible i want to use the command sarrus in math mode just like matrix for istance.


Tabularx line break with long space between words

I'm a problem when using the package tabularx.   Here is how I use the table:  \documentclass{report} \usepackage{tabularx} \usepackage[margin=3.5cm]{geometry}  \begin{document} \noindent \begin{tabular}[H]{|l|c|c|c|} \hline Simple text & A simple long text maybe very long or not i dont know c: & Simple text & Another simple long text maybe very long or not i dont know c:\\ \hline \end{tabular} \bigskip \noindent\begin{tabularx}{\textwidth}{|c|X|X|X|} \hline Simple text & A simple long text maybe very long or not i dont know c: & Simple text & Another simple long text maybe very long or not i dont know c:\\  \hline \end{tabularx} \end{document}   I was using the the regular taular but I need to have auto linebreak. I get theses long space when he breaks line. How can I have normal space ?    Thanks in advance, MYT.  SOLUTION by leandriis The 'long spaces' are due to X columns being based on justified p columns. To get rid of them you could define your own column type as follows: \newcolumntype{Y}{>{\raggedright\arraybackslash}X}


stack.imgur.com was created to avoid link rotting of images. Images not uploaded with an Imgur Pro account may be . Inferring from the  and ,  images at i.stack.imgur.com should be kept forever regardless of views while images at i.imgur.com that were not uploaded with a pro account may be deleted due to inactivity.  This means that anyone can upload to stack.imgur.com through the  button (CtrlG) and keep images there forever unless they are  or discovered to be unconnected to Stack Exchange and deleted. My questions are:  Is this behavior expected? Does it not matter to Stack Exchange and Imgur? Is there already an active process keeping irrelevant i.stack.imgur.com images out of Imgur?


Question about correlations and independence

My professor was discussing correlation and when it implies independence. It was fairly clear to me that, if $X$ and $Y$ are independent, then their correlation is zero. The reverse direction is less clear. Correlation being zero doesn't imply independence. This makes some sense to me because correlation measures linear association in some sense, but I am having trouble coming up with a concrete example of this. He also stated that, if $X$ and $Y$ are bivariate normal and correlation is zero, then $X$ and $Y$ are independent. Can someone provide a proof/intuition about this?


There is no model for a contradiction M $\models \phi \land \lnot \phi$

Let $L$ be  a languague. How can I show that there is no model ($L$-structure) $M$ for a contradiction?  M $\models \phi \land \lnot \phi$  It seems very intuitive to me but how do I prove it?


Sqlite: CURRENT_TIMESTAMP is in GMT, not the timezone of the machine

I have a sqlite (v3) table with this column definition:  "timestamp" DATETIME DEFAULT CURRENT_TIMESTAMP   The server that this database lives on is in the CST time zone.  When I insert into my table without including the timestamp column, sqlite automatically populates that field with the current timestamp in GMT, not CST.  Is there a way to modify my insert statement to force the stored timestamp to be in CST?  On the other hand, it is probably better to store it in GMT (in case the database gets moved to a different timezone, for example), so is there a way I can modify my select SQL to convert the stored timestamp to CST when I extract it from the table?


I need to flash a stock ROM to my Samsung Captivate i897 as a part of unbricking process, but I can't find one. Odin one click roms don't work for me as Odin one click doesn't see my phone (regular ODIN does see the phone so I assume the drivers are ok). I need a rom that I can either install in recovery or using regular ODIN