Factor into irreducibles in $\mathbb{Z}[\omega]$ (Eisenstein Integers).

$\mathbb{Z}[\omega] = \{a + b\omega : a, b\text{ are integers}\}$  $\omega = e^{2πi/3} = -\frac12 + \frac{\sqrt3}2i$  My task is to factor the numbers $2, 3, 4, 5, 6, 7, 8, 9, 10, 11$ into irreducibles in $\mathbb{Z}[\omega]$.  I don't know if I'm overthinking this, but I do not even know where to start.  I'm used to doing this in $\mathbb{Z}[i]$ and $\mathbb{Z}[\sqrt2]$, but I have no idea how to approach $\mathbb{Z}[\omega]$.  EDIT: I am not supposed to use the norm in this exercise.  My biggest struggle right now is just figuring out how to factor these numbers.  Using guess and check I was able to find:  $$3 = (2 + \omega)(1 - \omega)$$  $$7 = (3 + \omega)(2 - \omega)$$  I'm plugging and chugging into Wolfram Alpha right now. Is there any better way to do this?


HTML: Why there is no native support to restrict state change in check-box without disabling it?

In HTML, only text controls like text-box, text-area, password-box have read-only property. Why didn't they support check-box/radio-button?  I know I can achieve this feature using script by putting onclick="return false;". (I don't want any workaround, I want to know only the reason for not providing native support to achieve this)  But my question is there any specific reason for not supporting read-only in check-box/ radio button even-though it accepts input from user.  EDIT 1: I found  but it doesn't answer my question - Why there is no native way to restrict the user to change the state without disabling it?


In the aftermath of the space shuttle Challenger explosion, where seven crew members were killed, the NASA program underwent a massive examination of priorities.   My SAT grammar book claims that where is incorrect and should be replaced with in which.   I tried googling the difference, and the answers have been saying those two are practically the same. I was wondering if it was not the case with this sentence?


I want to group every element in the list with all other elements in the list  for ex -   l1 = [1,2,3] l2 = [(1,2),(1,3),(2,3)]   I try using zip:  l2 = list(zip(l1,l1[1:]))   but it gives me:  l2 = [(1, 2), (2, 3)]   DESIRED OUTPUT:  [(1,2),(1,3),(2,3)]   for   [1,2,3]


Any hints on parsing / converting / operating on hex values in c# ?  In particular I want to cast a decimal int to hex and then output as a string...


wpa_supplicant store password as hash (WPA-EAP with phase2="auth=PAP")

Is there a way to store my password in /etc/wpa_supplicant/wpa_supplicant.conf as some hash instead of plaintext?  By "password" I refer here to the password used for phase2 authentification. I do not refer to the Preshared Key (PSK) which could be hashed using wpa_passphrase.  For phase2 MSCHAPv2 or MSCHAP authentification I could store the password as MD4 hash using nt_password_hash (see example wpa_supplicant.conf line 659).  Is there any way to store my PAP password as hash?  Or: Is there a way to store the password in some sort of external storage? The example wpa_supplicant.conf suggests the use of such an external storage (using ext:????) but I could not find any documentation about it.  I am aware that storing the password as hash does not increase wifi security. But as the password MUST be the same as the password for other services (account management, subscriptions, payments ...) I don't want it to be stored as plaintext.


Travel to Cuba as dual citizen (USA+other)?

Suppose I am a U.S. citizen with dual citizenship with another country.  Citizens of this second country are allowed to travel to Cuba.  Suppose further that I live and work outside the United States and have a non-U.S. bank account containing funds in a currency other than dollars.  If I travel to Cuba using my passport from this 2nd country and using my non-U.S. financial resources, could I get into trouble upon return to the United States?  When I return, could I list Cuba under "countries visited" on the customs form without fear of repercussions, using the explanation that I traveled on a foreign passport and paid for my trip from foreign resources?  Are U.S./dual citizens subject to the Cuban embargo when traveling on their non-US passport?


Using induction to prove that $2 \mid (n^2 − n)$ for $n\geq 1$

Use induction to prove that, for all $n \in \mathbb{Z}^+$, $2\mid (n^2 − n)$.   That is, I am supposed to use induction to prove that $(n^2 − n)$ can be divided by $2$ when $n$ is a positive integer.  I've tried the following: $$\begin{split} (n+1)^2 − (n+1) &= (n+1)(n+1) - (n+1)\\ &=(n+1)(n-1)+2 - (n+1)\\ &=n^2 +n -n -1 +2 -n -1\\ &=n^2 -n, \end{split}$$ but I'm not particularly good at maths so I have no idea if this is even correct, and if it is, what it even means.


Should external link open in same tab or new tab?

What is best case scenario for external link to open in new tab or same tab? and Why?  When do we use external link? Is it when the data is linking to some external page other than your existing page.


Clicking a HNQ "ad" in the sidebar opens the link in the ad instead of changing the current page

, but I didn't have evidence of it, so it was dismissed. I'm not crazy though, and here's proof!:    When clicking on a HNQ in the side-bar, the link appears to open within the ad itself (an iframe? I'm not a web-dev so I'm not sure the terminology).  This happens consistently. I can't reproduce it often because the ads don't appear very often. Every time I try to reproduce it though, I'm able.  This was done on Edge 44.18362.329.0, but as the link above shows, a year ago I did it in Chrome.


List all hidden folders/files in Windows (7)?

A long time ago, I remember hiding some really personal files on my computer. Something that nobody could ever find, so I buried them down pretty darn good.  Now to my problem, I don't remember where.   Do anyone know a way to scan a drive and list all hidden folders and/or files?   I know how to view hidden files in Windows, but as far as I know, there is no way to search for them? I've been looking for a program, but I couldn't find one - and now I'm here, asking the experts. ;)  I'd really appreciate any tips.


What type of factor is practice of motor skills?

I recently asked a question about the cause of motor laterality:  I understand that there can be genetic factors, epigenetic factors, or environmental factors. But in terms of continuous practice of motor skills, what type of factor will that be? Physical factors? Thank you!


Why is double encryption that's equivalent to single encryption no better than single encryption?

In the "Introduction to Cryptography: With Coding Theory" by Trappe and Washington, in the chapter about DES algorithm the authors say that:     "if a cryptosystem is such that double encryption is equivalent to a single encryption, then there is no additional security obtained by double encryption"   Why is this?


How do I use tab stops in enumerate or itemize?

Current code is:  \begin{enumerate}[label=LEVEL \arabic{*},leftmargin=*]     \item Description of Level 1 \quad L1 \\ \emph{more text}     \item Description of Level 2 \quad L2 \\ \emph{more text}  \end{enumerate}   but the \quad does not align L1 and L2 uniformly vertically. I want to replace \quad with a tab but the tabbing environment does not allow mixing with an enumerate!


Updates problem giving a PPA not found error

I am on Ubuntu 14.04 and it always show me the little icon for updates, I do it and every time it show me this message :   W:Failed to fetch (http)://ppa.launchpad.net/c-korn/ppa/ubuntu/dists/trusty/main/source/Sources 404 Not Found , W:Failed to fetch (http)://ppa.launchpad.net/c-korn/ppa/ubuntu/dists/trusty/main/binary-amd64/Packages 404 Not Found , W:Failed to fetch (http)://ppa.launchpad.net/c-korn/ppa/ubuntu/dists/trusty/main/binary-i386/Packages 404 Not Found ,       E:Some index files failed to download. They have been ignored, or old ones used instead.   I googled and didn't find any "accurate" solution for this error, do you think is my nvidia driver the problemes ( I use the nvidia driver giving in software and updates : proprietary, tested) ? Because I have some little problems to make my Nvidia drivers work well.


EDIT Thanks to user , this issue boiled down to Templates, and my understanding of how they work.  I had to move function implementations into the class header, otherwise they would not be compiled for some arbitrary type.  See     I'm writing a template class, Tensor, which can be ininitalised to hold elements of type T, whose constructors takes some arguments.  I've found that if I try to create an object of class Tensor in any other file, it fails with undefined reference.  I made sure that I'm including the header correctly, and even created a function unrelated to the class called test_boi() which can be called successfully by other files.  I won't go into the details of my testing setup, but I have a MWE with 3 files: tensor.cpp, tensor.h, and main.cpp.  In tensor.cpp I have a main() which works when uncommented.  It is identical to the one in main.cpp, which fails with the undefined reference error.  For building (with CMake), I make a library using tensor.h and tensor.cpp and add it to my executable.  I think this might be my problem, but I'm not sure what I'm doing wrong.  Making libraries is something I've just started doing, and there's a deluge of info out there.  The fact that I am able to call test_boi() from Main.exe (when I don't create objects) tells me that tensor.cpp has been compiled, and is accessible by Main.exe.  The fact that I can create these objects when I put main() in tensor.cpp tells me that there isn't something broken in my classes.  "Undefined reference" stackoverflow posts are rampant, so I haven't been able to find anything that fits my particular issue.  Relevant portion of my CMake script  add_library (libTensor tensor.h tensor.cpp)  add_executable(Main.exe test_main.cpp) target_link_libraries(Main.exe libTensor)  #add_executable (Tensor.exe tensor.cpp) #target_link_libraries (Tensor.exe Tensor)   My Class definition (tensor.h)  #ifndef TENSOR_H #define TENSOR_H #include <vector>  template<typename T> class MyClass {   int width, height;  public:   MyClass(int n, int m)   {     height = n;     width = m;   };   MyClass(int n, int m, std::vector<T> elems); };  int test_bois(); #endif   My function implementations (tensor.cpp) ```  #include <iostream> #include "tensor.h"  template<typename T> Tensor<T>::Tensor(int n, int m) {   //  shape = (height, width);   height = n;   width = m; }  template<typename T> Tensor<T>::Tensor(int n, int m, std::vector<T> elems) {   //  shape = (height, width);   height = n + 100;   width = m + 100; }  int test_bois() {   return 42; }  // int main() // { //   std::vector<int> elems(10); //   int height = 2; //   int width = 2; //   Tensor<int> *my_obj_zero = new Tensor<int>(height, width); //   Tensor<int> *my_obj_one= new Tensor<int>(height, width, elems); //   std::cout << my_obj_zero->shape() << std::endl; //   std::cout << my_obj_one->shape() << std::endl; //   std::cout << "Hello World!!" << std::endl; //   return 0; // }   main.cpp  #include <iostream> #include "tensor.h"  int main() {   std::cout << test_boi() << std::endl;    // this block commented out to get successful run   std::vector<int> elems(10);   int height = 2;   int width = 2;   Tensor<int> *my_obj_zero = new Tensor<int>(height, width);   Tensor<int> *my_obj_one= new Tensor<int>(height, width, elems);   std::cout << my_obj_zero->shape() << std::endl;   std::cout << my_obj_one->shape() << std::endl;   std::cout << "Hello World!!" << std::endl;    return 0; }


How is this possible ?? can someone explain this?

iam making easy battleship game. but there is something that doesnt make sense for me. when there is strictly append in the first loop it has different output than if i wrote the same thing with variable..  import random  BOARD = []  for i in range(5):     BOARD.append(["O"]*5)  x = random.randint(1,5) y = random.randint(1,5)  while True:     for i in BOARD:         print(" ".join(i))      row = int(input(": "))     column = int(input(": "))      if x == row and y == column:         print("you win")     else:         BOARD[x - 1][y - 1] = "X"   in case of miss there is output like this  O O O O O O X O O O O O O O O O O O O O O O O O O   but if i wrote this code.. which is similar to previous.. only difference is a variable in the first loop... it has totaly different output..  import random  BOARD = []  Q = ["O"]*5  for i in range(5):     BOARD.append(Q)  x = random.randint(1,5) y = random.randint(1,5)  while True:     for i in BOARD:         print(" ".join(i))      row = int(input(": "))     column = int(input(": "))      if x == row and y == column:         print("you win")     else:         BOARD[x - 1][y - 1] = "X"   but there is output like this.. it doesnt make sense for me  O x O O O O X O O O O x O O O O x O O O O x O O O   is there on this site anyone who can explain this ??? nobody can help


Calculating conditional entropy given two random variables

I have been reading a bit about conditional entropy, joint entropy, etc but I found this: $H(X|Y,Z)$ which seems to imply the entropy associated to $X$ given $Y$ and $Z$ (although I'm not sure how to describe it). Is it the amount of uncertainty of $X$  given that I know $Y$ and $Z$? Anyway, I'd like to know how to calculate it. I thought this expression means the following:  $$H(X|Y,Z) = -\sum p(x,y,z)log_{2}p(x|y,z)$$  and assuming that $p(x|y,z)$ means $\displaystyle \frac{p(x,y,z)}{p(y)p(z)}$, then  \begin{align} p(x|y,z)&=\displaystyle \frac{p(x,y,z)}{p(x,y)p(z)}\frac{p(x,y)}{p(y)}\\&=\displaystyle \frac{p(x,y,z)}{p(x,y)p(z)}p(x|y) \\&=\displaystyle \frac{p(x,y,z)}{p(x,y)p(x,z)}\frac{p(x,z)}{p(z)}p(x|y)\\&=\displaystyle \frac{p(x,y,z)}{p(x,y)p(x,z)}p(x|z)p(x|y) \end{align} but that doesn't really help.  Basically I wanted to get a nice identity such as $H(X|Y)=H(X,Y)-H(Y)$ for the case of two random variables.  Any help?  Thanks


Getting the group of text between two strings using regular expression

I have a string like this  1) /* This is the Start for the Test : 1 */ 2) Lu8_Ret = GetStatus_1(); 3) Lu8_Ret = Lu8_Ret + 1; 4)/* This is the End for the Test : 1 */ 5) 6) /* This is the Start for the Test : 2 */ 7) Lu8_Ret = GetStatus_2(); 8) Lu8_Ret = Lu8_Ret + 1; 9) /* This is the End for the Test : 2 */ 10)  11) /* This is the Start for the Test : 1 */ 12) Lu8_Ret = GetStatus_1(); 13) /* This is the End for the Test : 1 */   By using following regular expression I am reading the content between the start and end comment lines  regex = r"This is the Start for the Test : 1(([\S\s])*) This is the End for the Test : 1" for match in re.finditer(newrx, content):     print(match.group(1))   But it's giving the content between the start comment of Test: 1 to last end comment of Test: 1(line number 2 to 12).  How to get the content as a separate group (from line 2-3 as one group and line 12 as another group)? (My program will take care of unwanted /* , */ )


Groups in derived series are normal in the whole group

I am considering a finitely generated, solvable group $G$ which has subexponential growth. Let $G=G_0\vartriangleright G_1\vartriangleright....\vartriangleright G_d\vartriangleright G_{d+1}=1$ denote the derived series of G.  It should be the case that $G_d$ is normal in $G$. Does anyone know why this is true? I don't know whether all of the assumptions above are necessary for the result.


Why is Random.nextInt() and Math.random going out of the range I set?

So I needed to get random numbers between 25 and 75 and I tried two things:  System.out.println(random.nextInt(75)+25); System.out.println((int)(Math.random()*75) + 25);   From what I understood, the "75" I wrote in both lines should be the greatest number I get and the "25" should be the smallest number. However, I got numbers like:  84,94,82,79,98 // these are only the numbers that went out of range   I guess I misunderstood the rules of nextInt and Math.random. How can I get the numbers I want(between 25 and 75)?


I am reading the Hidden Markov Model note  from Stanford and have problem finding the meaning of the notation described below.  What does the semicolon (;) means in below (Page 2 in above link)?  $$P( z_t, z_{t-1},\ldots, z_1; A )$$  $A$ is the transition matrix.  How should it be read?  For example, I know $P( x | y )$ is "probability of $x$ GIVEN $y$"; $P( x=s_1 | y=o_1 )$ is "probability of $x$ being $s_1$ GIVEN that $y$ is $o_1$".  Thanks in advance for any help for this possibly trivial, but surprisingly hard to find answer.  Further question on same notation issue.  In Wikipedia article on , They have  $$L( \theta;X ) = p( X,Z | \theta )$$  In the above, X is the set of observed data, Z is the set of observed data and $\theta$ is a vector of parameters.  Based on my current understanding of the notation, I will read the above as "the likelihood of theta given X is equal to the joint probability of X and Z given theta".  In this context, X contains observed data, which to me appears to be random variables rather than fixed parameters.  Why is semicolon ';' used here?  Update  I have just noticed a few other threads asking the same question, when these threads shown up as related threads on right pane.  My apology that I couldn't find them earlier.  The following two threads have elaborated answers, in agreement with the accepted answer of this thread.


Make listing look normal (ttfamily and character spacing)

listings seems to like protrude characters. Every time I see that I have this strange urge of killing a kitten. How can I get rid of it?    \documentclass{article}  \parindent0pt  \usepackage{listings} \lstset{basicstyle = \ttfamily}  \begin{document}  \texttt{test test test}  \begin{lstlisting} test test test \end{lstlisting}  \end{document}


I started by searching guides. I found  but neither of the main methods works anymore in 11.10.   The first solution, I have created the desktop file, however the file location given as .gconf-> desktop-> unity-> launcher -> favourites no longer exists. I can get to /home/sayth/.gconf/desktop but there is no longer a unity folder. The second solution described right-clicking the desktop and creating a launcher. Right-clicking the desktop no longer produces a "create a launcher" option.   I manually installed geany 0.21 as the one in the repo's is outdated. It's installed and working correctly, and is executing from /usr/local/bin/geany.  How can I add it to the launcher?


What are the differences between a HashMap and a Hashtable in Java?

What are the differences between a  and a  in Java?  Which is more efficient for non-threaded applications?


How to find the limit of $ \dfrac{n! e^n}{n^n} $?

How can we find limit of the sequence $\dfrac{n!e^n}{n^n} $? I know its limit is infinity. First, I showed it is strictly increasing(by taking ratio of terms) and then showed it is not Cauchy sequence. I want to prove this by some other method, like comparing with other sequence. Can any one give some hint?


Making a three phase voltage source to drive a gyroscope

I'm trying to drive a gyroscope that needs a 3 phase 400Hz 32v 1A power supply. How can I provide that supply? It's one part of my university project and I'm a beginner in this field. I'd like to find the best way  to provide a suitable supply. thanks


If $f(x)=(\int_0^x e^{-t^2}dt)^2$ and $g(x)$=$\int_0^1{e^{-x^2(1+t^2)}\over(1+t^2)}dt$ then $f'(\sqrt\pi) + g'(\sqrt\pi)$ is equal to?? i tried to use Leibniz rule and differentiate with respect to x but got got stuck in between could someone help me


Windows update causing system high CPU on Windows 10

Over the last few days I have been having issues with my machine running very slow. The problem seemed to be with the System process consuming about 20% CPU (more specifically ntoskrnl.exe!MmProbeAndLockPages).  Many attempts to reset and/or reinstall where unsuccessful. The only options that eventually worked was to reinstall windows (fresh) with the Network cable unplugged. This prevented Windows updates during the installation.  Now, I'm quite certain it's one of the device driver updates that's causing this issue. I have Windows Updates disabled for now but I would like to turn it back on but run the updates in stages.  Is there a way to selectively approve updates one by one? I am running Windows 10 Pro on a home network (if it makes a difference).  Thanks!   EDIT: I think I have managed to find the problem. I've enabled Windows Update again and it went through the same process of updating drivers. Checking the list of drivers I went to the Lenovo support website (M93p in my case) and started downloading alternative drivers and install them one by one. The Intel Gfx Driver fixed the problem and now the computer is responsive again. The high CPU from the System process may have been unrelated.


Factorize $X^p+1$ in a field of characteristic $p$.

How can I factorize $X^p+1$ in a field of characteristic $p$ ?  If the field is $\mathbb Z/p\mathbb Z$, then $$X^p+1=X^p+1^p=(X+1)^p,$$ but if the field is $\mathbb F_{p^n}$ or if the characteristic is $q\neq p$, I don't know how to do it.    It's not duplicate, but it solve my problem for $\mathbb F_{p^n}$. But what happen for a field of characteristic $q\neq p$ ?


Is there a normal subgroup $H$ such that $S_6/H$ is isomorphic to $S_5$

My attempt : By Lagrange's theorem the order of $H$ should be 6.So $H$ should be generated by ($a$)6 cycle,  ($b$) 3cycle and 2 cycle. I think these are the only cases of $H$. Now, if $H=<(a_1...a_6)>$ , then $gHg^{-1} \in H$.As $H$ is a normal subgroup, we see that $g(a_1)..g(a_6) \in H$.Now,  there are $120$ elements of  6 cycle.As the elements of cycle $6$ are conjugates of each other, we can pick up an element $c$ such that $g(a_1..a_6)g^{-1} =c$  where$ c \ne\in H$ .We are done. Now,$<(a_1 a_2)(a_3 a_4 a_5)>=H$ so how do we progress with this case.


Could someone please explain how to solve this : $x^4 - 10x^3 + 21x^2 + 40x - 100 = 0$ - not the answer only, but a step-by-step solution.  I tried to solve it, with the help of khanacademy, but still I have no idea how to correctly solve it.  Thank you so much in advance!


What could happen if I use 2 cycle fuel in a 4 cycle engine?

First off, this is NOT to be confused with the following question:    2 cycle oil is used for my weed eater. There is no way I could use a whole gallon in a year.  Sometimes I run out of gasoline for my 4 cycle lawn mower, and that 2 cycle mix fuel is sitting there getting really old.  If I run that in the lawn mower, am I simply going to create extra pollution or could the 2 cycle fuel cause any damage to the 4 cycle engine?


Computer makes mistake over a late library book

I'm looking for a short story about a man who forgets to return his library book.  A computerised system takes over and everything goes from bad to worse.  The book he did not return is 'Kidnapped' by Robert Louis Stevenson, so the man ends up on a kidnapping charge, which changes to a murder charge when the computer learns that RLS is dead.  It must be from the 60s or 70s.


I just installed Ubuntu 14.4 instead of windows (now this is the only OS on my laptop) I have Broadcom bcm9506 card. How can I fix this? I already looked at a lot of similar questions but non of them help me.    lspci -vnn | grep Network 04:00.0 Network controller [0280]: Broadcom Corporation BCM4312 802.11b/g LP-PHY [14e4:4315] (rev 01)   Thanks


Proving left-invariance (and proof-verification for right-invariance) for metric constructed from left-invariant Haar measure

$\newcommand{\diff}{\mathrm{d}}$ TL;DR   Having read  I know something about Haar measures, in particular that a left-invariant one exists and is unique on any Lie group $G$. I know that defining:  $$\langle x,y\rangle_g=\langle(\mathrm{d}_gL_g)^{-1}(x),(\mathrm{d}_gL_g)^{-1}(y)\rangle,$$  where $\langle\cdot,\cdot\rangle$ is any inner product on the Lie algebra $T_eG$ and $L_g$ is the map $L_g(h)=gh$, one obtains a left-invariant metric for $G$. I know that if $G$ is compact we can define the metric:  $$(u,v)_g=\int\limits_G\langle\diff_gR_h(u),\diff_gR_h(v)\rangle_{gh}\diff\mu(h),$$  where $\mu$ is the unique left-invariant Haar measure on $G$; I believe the following proves right-invariance for that metric:     \begin{align*} (\diff_gR_ku,\diff_gR_kv)_{gk}={}&\int\limits_G\langle\diff_{gk}R_h\diff_gR_ku,\diff_{gk}R_h\diff_gR_kv\rangle_{gkh}\diff\mu(h)={} \\ {}={}&\int\limits_G\langle\diff_g(R_h\circ R_k)u,\diff_g(R_h\circ R_k)v\rangle_{gkh}\diff\mu(h)={} \\ {}={}&\int\limits_G\langle\diff_gR_{kh}u,\diff_gR_{kh}v\rangle_{gkh}\diff\mu(h)=\int\limits_G\langle\diff_gR_\ell u,\diff_gR_\ell v\rangle_{g\ell}\diff\mu(k^{-1}\ell)={} \\ {}={}&\int\limits_G\langle\diff_gR_\ell u,\diff_gR_\ell v\rangle_{g\ell}\diff\mu(\ell)=(u,v)_g. \end{align*}      Steps thus justified:         Definition of the metric.   $\diff_g(R_h\circ R_k)=\diff_{R_kg}R_h\circ\diff_gR_k=\diff_{gk}R_h\circ\diff_gR_k$ by the chain rule.   $R_h\circ R_k=R_{kh}$.   Set $\ell=kg$ and change variables. $h=k^{-1}\ell$.   This is where I use the invariance. I used it in the form $\diff\mu(k^{-1}\ell)=\diff\mu(L_{k^{-1}}\ell)=\diff\mu(\ell)$. Is that right?   Definition of the metric again.       So my question is: is the proof in 4. correct? And how do I prove left-invariance?  (For those wishing to delve deeper into the history of this post and its earlier exact duplicate, see edit history)


Why are the largest land/air animals today smaller than in the Mesozoic?

. Was the Mesozoic somehow more hospitable to large animal species than today's world? Have subsequent evolutionary innovations shifted the balance towards smaller species?  Interestingly .


Probability that the last passenger seats in the correct place .

Consider there's a flight from some place to another. The flight has $100$ passengers. The passengers alight the plane one by one. The first passenger doesn't have his boarding pass so he goes and seats on a random seat. The next passenger then goes to his seat if its unoccupied otherwise takes a random seat. Find the probability that the last person  seats in the seat assigned to him. $$\text{Approach 1}$$  The seat can either be occupied or unoccupied so the last person seats in his place is $\frac{1}{2}$. However I felt this logic had a flaw so I took another route. $$\text{Approach 2}$$ first consider the case that the first person seats in the correct place then the probability is $\frac{1}{100}$ the probability that last person seats in correct place is just $1$ as its mentioned in the question. Now consider the case where the first person doesn't seat in his or last person's seat is $\frac{1}{98}$. Let the last person get the correct seat so the number of ways of $98$ de arrangements is $98!\sum_0^98 \frac{(-1)^n}{n!}=p$ . The total no of ways of placing 98 passenger is $98!$ hence total probability $\frac{1}{100}+\frac{1.p}{98.98!}=0.01+\frac{0.3678}{98}\neq 0.5$ . Where is the flaw in the $2$and approach?


How can I generate random number in range?

I have 2 EditText. The user will enter the minimum number in the first EditText and the maximum in the second EditText.  There is one TextView to show  the generated number and a Button to click after entering the minimum and maximum numbers   How to generate a number between 2 numbers the user entered and show it in TextView ?


If the Universe reaches the state of heat death scenario, could it produce a new Big Bang?

So in heat death of the Universe time stops, matter is degraded, only quantum vacuum remains and the universe no longer expands?  Aren't those conditions similar to what physicists say about the quantum field from which the Big Bang happened?  So is there possibility that the current Big Bang before 14 billion years happened "after" an already heat death state of previous instance of the Universe?  Or quantum fluctuations can't happen in such scenario and the Universe will remain dead for an eternity.


The sentence "you only can dream of the stars" - it's in a song lyric. I have tried singing it "you can only dream of the stars" which I think is semantically correct... but the emphasis sounds wrong, & having "only" as the second word just sings better. I would welcome opinions about just how unacceptable this is grammatically.  Thanks, robb


12 or 16 column grid for a full width website?

So I'm looking for the right answer for my grid system:  1) Should I use 12 or 16 column grid for a full width website similar to these websites:    2) Can I use bootstrap for 16 column width  3) what are the challenges for a 16 columns grid vs traditional 12 column grid?


combining two arraylist into a single linked list in one go

I am getting an list as shown below    List<String> tr = newdatamap.get("B1").getRef();  List<String> tr2 = newdatamap.get("B1").getMS();   now as you can see that we have two arraylists but I want to store it contents into single a list itself. Something like that:  List<String> tr = newdatamap.get("B1").getTradeRef() + newdatamap.get("B1").getTMS();   but it is showing an error. Please advise how we can combine them into a single linked list.


How do I prevent identity spoofing in a multiplayer game?

I'm thinking about clients spoofing IP addresses, tricking other clients that they are the server; that sort of stuff. (I don't know much about this, so if this is completely wrong, please correct me.)  What should I do to prevent this? Because it is a real-time game, if I were to use encryption, I would use something fast and secure like RC4. Should I encrypt packet data with a key, that the server gives to the client?   If it makes any difference, I'm using UDP.


How do I install wallpapers from older releases?

I have currently installed 12.04 and I really like the wallpapers of 11.10. How do I install it in 12.04?


How can I tell if a retail box of Windows 7 is genuine, especially from the Certificate of Authenticity (COA) seal? The COA has 3 barcodes: left, right, and bottom. The left one has 2 number sequences, the right one has 1, and the bottom one has none (unless it refers to the alphanumerical sequence in the center of the sticker). How can I verify these sequences?


Transformerless rectification is giving out AC component

I want to convert 240V AC 50hz to 12V DC without transformer.I want the output (12V) to drive 25 white LEDs.The circuit is giving an output of ~14V DC.But the problem is that it is also giving out ~30V AC.Is it OK to use this for my task or is it harmful (for LED's).What should be done to eliminate the AC component?I even tried using an extra 1N4007 diode at the O/P but no use. Following is the circuit diagram.   EDIT: My Multimeter shows 0V AC for a 12V 1A power source.So that means my Multimeter is working fine.Is it not?


What is the probability a random number I select is a perfect square

I have been thinking about this problem  Yes, let's simplify the problem by assuming the set of only positive integers $Z$ I know if I take a range of numbers say $1$  to  $10$ , there are only three perfect square existing here; which are $1$ , $4$ and $9$  So the probability is $3/10$  If I increase my range the probability becomes lesser, so I can conclude there are more imperfect-square numbers than perfect squares.  My question Is there any fixed value assign to this, can I know the minimum and maximum value of this probability


Can I replay a whole kingdom in Mario odyssey? My brother completed one and. I wanted to do it myself

My brother did a kingdom for me, the luncheon kingdom and I want to do it myself so is there a way I can delete the progress just for 1 kingdom?


Assume I have a Theorem with number 1.2 in my paper. After that some other numbered content follows. Now, in a new section I want to cite Theorem 1.2, i.e. want to make some kind of copy paste. How would you do this?


If won't is the contraction of will not, where did the "wo" come from in won't? Why is this convention over willn't?


Does anyone know if these work together? I see there are dedicated iPhone +altimeter apps for the iPhone, but I can't find info if there is an altimeter built into the iPhone that works with these Endomondo/Strava apps.  So my fear is that my gps is not tracking the correct altimeter information. Should I be worried?


How to print large numbers in javascript

I am trying to print 1538409725339216503 this number in javascript console but it gives me output 1538409725339216400 [console image]


Is there a "standard" quantum simulator/animator for pedagogy?

I'm having a hard time finding animations for 1D or 2D square well, SHO, free particle with barriers, etc, that I'm sure are "trustworthy". It's the sort of thing I would do in python in my spare time if I had any, and I know plenty of people have done it, but I don't like trusting someone's random github repo or youtube channel. Is there a recommended Youtube channel or PC/Mac program that is maintained, trustworthy, and somewhat user-friendly? I'm aware of some of the pedagogy outfits like QuiLT and Phet that make flash programs for teaching, but I find those a bit clunky/old/low-level; I'm looking basically for a more general Schrodinger equation solver for a user-specified potential, or just a repository of animations.


What's the difference between Fermi Energy and Fermi Level?

I'm a bit confused about the difference between these two concepts. According to Wikipedia the  and  are closely related concepts. From my understanding, the Fermi energy is the highest occupied energy level of a system in absolute zero? Is that correct? Then what's the difference between Fermi energy and Fermi level?


If $x$ and $y$ are not both $0$ then $ x^2 +xy +y^2> 0$

Can't quite finish this proof:     Prove that if $x$ and $y$ are not both $0$ then $ x^2 +xy +y^2> 0$   $ x^2 +xy +y^2 +xy -xy> 0$  $ (x +y)^2 -xy> 0$ Without loss of generality define $x\geq y$  Firstly the case where $y<0$ and $x>0$ is trivial as both $ (x +y)^2$ and $-(xy) >0$.   I want to say by transitivity  as each are >0 that there sum must be ${}> 0$ can I do that?  The second trivial case is $y=0$ as we simply have $ x^2 >0 $ where $x>0$.  Lastly we have define $c= x+y$  since both $x$ and $y$ must have the same sign we know $|c|>x$ since $x\geq y$ we know that $ x^2 \geq xy$ finally since  $ |c|^2 = c^2$ $ \forall c \in \mathbb{R} $  We have $ c^2 >x^2 \geq xy$ hence $c^2 -xy >0$  I feel like I have all the pieces but it doesn't feel finished how do I fix it?  Edit: I am really glad i asked this question love the variety of different good answers no idea what a discriminant is but im going to go look that up. I wanted to give the accepted answer to Edward as he actually answered my question but Anurag s proof was just so much better then my attempt. ^^


Option clash for package hyperref while Compiling in TexLive for arXiv submittal

I am getting the option clash error and I can't seem to figure out why.  Here is my preamble:  \documentclass[preprint]{elsarticle} \usepackage{amssymb} %for \mathbb{} \usepackage{amsmath} % for underbrace annotations \usepackage{mathtools} % for underbrace annotations \usepackage{enumitem} % for command "\begin{enumerate}[noitemsep]" \usepackage{color} % for command "{\color{blue} TXTTXTTXT} \usepackage[normalem]{ulem} % for command \uwave{TXTTXT} \usepackage{float} % for \begin{figure}[H] \usepackage{graphicx} \usepackage{epstopdf} \usepackage[colorlinks]{hyperref} \usepackage{setspace} \usepackage{verbatim} \usepackage{pseudocode} \usepackage{natbib} \bibliographystyle{plainnat} %\bibliography{Refs} %\bibliographystyle{agsm}  \usepackage{lipsum}       % for sample text \usepackage{changepage}  \usepackage{pstricks-add} % for crazy drawings \usepackage{tikz}


NullPointException from Codename One code

Since a few days ago and out of nowhere, I sometimes get this NullPointException error:     Exception: java.lang.NullPointerException - Attempt to invoke virtual   method 'boolean java.util.ArrayList.add(java.lang.Object)' on a null   object reference 03-19 09:08:47.785 22799-22820/? W/System.err:   java.lang.NullPointerException: Attempt to invoke virtual method   'boolean java.util.ArrayList.add(java.lang.Object)' on a null object   reference           at com.codename1.r.an.cj(TextArea.java:1199)           at com.codename1.r.an.ci(TextArea.java:865)           at com.codename1.r.an.H(TextArea.java:879)           at com.codename1.r.an.F(TextArea.java:824)           at com.codename1.r.g.b.a(DefaultLookAndFeel.java:907)           at com.codename1.r.an.a(TextArea.java:1259)           at com.codename1.r.l.J(Component.java:2942)           at com.codename1.r.l.K(Component.java:2981)           at com.codename1.r.l.aa(Component.java:1340)           at com.codename1.r.l.af(Component.java:1430) 03-19 09:08:47.786 22799-22820/? W/System.err:     at   com.codename1.r.e.a.b(BorderLayout.java:480)           at com.codename1.r.n.a(Container.java:2224)           at com.codename1.r.l.J(Component.java:2942)           at com.codename1.r.l.K(Component.java:2981)           at com.codename1.r.l.aa(Component.java:1340)           at com.codename1.r.l.af(Component.java:1430)           at com.codename1.r.e.b.a(BoxLayout.java:155)           at com.codename1.r.n.bP(Container.java:1715)           at com.codename1.r.n.K(Container.java:1707)           at com.codename1.r.n.bP(Container.java:1720)           at com.codename1.r.n.K(Container.java:1707)           at com.codename1.r.n.bP(Container.java:1720)           at com.codename1.r.n.K(Container.java:1707)           at com.codename1.r.n.bP(Container.java:1720)           at com.codename1.r.n.K(Container.java:1707)           at com.codename1.r.n.a(Container.java:1606)           at com.codename1.r.v.a(Form.java:4046)           at com.codename1.r.l.b(Component.java:2214)           at com.codename1.r.v.b(Form.java:4056)           at com.codename1.r.l.d(Component.java:2187)           at com.codename1.r.l.a(Component.java:2162) 03-19 09:08:47.787 22799-22820/? W/System.err:     at   com.codename1.r.l.d(Component.java:2130)           at com.codename1.r.l.c(Component.java:2421)           at com.codename1.r.l.i(Component.java:2365)           at com.codename1.impl.a.s(CodenameOneImplementation.java:613)           at com.codename1.r.q.l(Display.java:1161)           at com.codename1.r.q.k(Display.java:1070)           at com.codename1.r.aj.run(RunnableWrapper.java:120)           at com.codename1.impl.b$1.run(CodenameOneThread.java:60)           at java.lang.Thread.run(Thread.java:776)   It doesn't come from my code and I have no idea how to resolve this intermittent error.  Please help me!


I'm trying to prove that $\frac{\mathrm{d} }{\mathrm{d} x}\ln x = \frac{1}{x}$.  Here's what I've got so far: $$ \begin{align} \frac{\mathrm{d}}{\mathrm{d} x}\ln x &= \lim_{h\to0} \frac{\ln(x + h) - \ln(x)}{h} \\ &= \lim_{h\to0} \frac{\ln(\frac{x + h}{x})}{h} \\ &= \lim_{h\to0} \frac{\ln(1 + \frac{h}{x})}{h} \\ \end{align} $$ To simplify the logarithm: $$ \lim_{h\to0}\left (1 + \frac{h}{x}\right )^{\frac{1}{h}} = e^{\frac{1}{x}} $$ ^This is the line I have trouble with. I can see that it is true by putting numbers in, but I can't prove it. I know that $e^{\frac{1}{x}} = \lim_{h\to0}\left (1 + h \right )^{\frac{1}{xh}}$, but I can't work out how to get from the above line to that. $$ \lim_{h\to0}\left ( \left (1 + \frac{h}{x}\right )^{\frac{1}{h}}\right )^{h} = e^{\frac{h}{x}} $$ Going back to the derivative: $$ \begin{align} \frac{\mathrm{d}}{\mathrm{d} x}\ln x &= \lim_{h\to0} \frac{\ln(e^{\frac{h}{x}})}{h} \\ &= \lim_{h\to0} \frac{\frac{h}{x}\ln(e)}{h} \\ &= \lim_{h\to0} \frac{h}{x} \div h\\ &= \frac{1}{x} \\ \end{align} $$  This proof seems fine, apart from the middle step to get $e^{\frac{1}{x}}$. How could I prove that part?


Is there a verb for making (appreciative/agreement/attentive) sounds during conversation?

Is there a verb for giving feedback to someone with non-word sounds during conversation, including not specifically using filler words, in order to indicate attentiveness, agreement or appreciation, etc.?  I have searched for this word in all kinds of places and understood it to be a form of vocal (non-verbal) communication and as a subset of paralanguage. However, none of it helped finding a verb.


Wifi connected but no ping (narrowed down to Ethernet interface somehow interfering with Wifi functionality)

I've recently been getting into Linux (Debian - Gnome shell) and am currently having trouble with my WiFi.  Basically when I reboot the WiFi works fine for about a minute or two, after that it remains connected but I can't ping any external IP (8.8.8.8 is my test IP address). After googling similar issues I tried a few of the tools I saw suggested.  running route -n on boot (when WiFi is working) gives the following:  Destination    gateway        Genmask       Flags  Metric Ref Use Iface 0.0.0.0        192.168.178.1  0.0.0.0       UG     1024   0   0   wlan0 169.254.0.0    0.0.0.0        255.255.0.0   U      1000   0   0   wlan0 192.168.178.0  0.0.0.0        255.255.255.0 U      0      0   0   wlan0   After a minute or so when the internet access cuts out if I run the same command I get:  Destination    gateway        Genmask       Flags  Metric Ref Use Iface 0.0.0.0        0.0.0.0        0.0.0.0       U      1002   0   0   eth0 0.0.0.0        192.168.178.1  0.0.0.0       UG     1024   0   0   wlan0 169.254.0.0    0.0.0.0        255.255.0.0   U      0      0   0   eth0 169.254.0.0    0.0.0.0        255.255.0.0   U      1000   0   0   wlan0 192.168.178.0  0.0.0.0        255.255.255.0 U      0      0   0   wlan0   so I tried shutting down eth0 with: ifconfig eth0 down and voila the internet works again. for another minute or so only for eth0 to somehow come back online and mess it up again.  I really have no idea what's going on being so new to Linux, so if anyone could shed some light on why eth0 keeps coming online and clashing with my WiFi would be appreciated.   ---- EDIT ----- Found the ACTUAL solution for gnome-shell  So all of the solutions I found on the suggested threads (and supposedly duplicate questions) didn't actually help me in the long run. Or they were sub-optimal solutions that forced annoying manual reconfiguration of network devices every time devices are changed.  what I ended up doing was simply removing the eth0 interface from /etc/network/interfaces  so by commenting the following:  # allow-hotplug eth0  # iface eth0 inet dhcp  This allows the network manager that comes with Gnome to take control of eth0 and stops the clashing of the interfaces. meaning the standard GUI networking tools acted as expected.


I keep hearing people say things like:     I took off the quote unquote lid.   That is, they say "quote unquote" followed by what they meant to quote. In reality, it means that they quoted an empty string and then said the next word outside of the quotes.  Why don't they say it like this?     I took off the quote lid unquote.   ?


Find the determinant of the following matrix in the terms of $a_1,a_2,\cdots,a_n$ explicitly, $$ \begin{bmatrix} a_1 & a_2 & a_3 & \cdots & a_n\\ a_2 & a_3 & a_4 & \cdots & a_1\\ a_3 & a_4 & a_5 & \cdots & a_2\\ \vdots & \vdots & \vdots & \ddots & \vdots\\ a_n & a_1 & a_2 & \cdots & a_{n-1}\\ \end{bmatrix} $$ When the determinant is zero?


Using a return ticket as a one way ticket to Mexico from the UK?

My boyfriend will buy two return tickets in Mexico to travel to the UK. One for him to travel to the UK and back to Mexico, and one for me (I am already in the UK) to travel to Mexico. Is it possible for me to use the return ticket that he buys me as a one way, or am I not allowed to do that because I haven't actually come from Mexico to the UK and back to Mexico again?  Am I able to travel to Mexico from the UK (on the return ticket that my boyfriend bought for me, using it as a one way ticket) if I haven't actually flown from Mexico on it?


How do I prove that a polynomial F[x] of degree n has at most n roots

It's a really basic question,in these days, I've been thinking why a polynomial $p(x)\in F[x]$ ($F$ a field) with degree $n$ can have at most n roots. It seems easy to prove, but I've been trying to prove this since yesterday, maybe I forgot some important details necessary to prove, I don't know. I'm solving some questions about Field Theory and I noticed that almost every question I should use this theorem, I need help.  Thanks


Is there a software utility to adjust screen gamma/brightness/contrast?

I use to work at night and it is eye-hurting to watch at lightbulb-bright screens (I've got two - laptop's built-in panel and an external 18-inch CRT) in a dark environment. So I adjust my screens to be darker.  Can I do this a software way instead of pressing monitors' buttons that many times every time?


I am trying to install Ubuntu into my laptop. Will the option 'Erase and use the entire disk' delete all my data in my hard disk? I don’t want to loss my data in the D drive.


Is SuperSU a "rooting app" or is it an "app that requires root"?

There are so many guides that say SuperSU is a "rooting app".  A method of rooting a phone is to install SuperSU as a .zip:   Then, SuperSU shows up as an app in Play store that requires root:    says that the way to root zenfone 2 is to install SuperSU.zip   is another guide where installing SuperSU is a way to root a phone.  Who is correct? Is it a way to root or is it an app that requires root?


Will completing Dawnguard stop Vampire Attacks?

Windhelm has had more Vampire Attacks than Whiterun which i have been in the most and i thinkl they're messing up the game as when i arrived to do the quest about "The Butcher", after killing the vampires i went to where the dead body was about however only 3 people where there and no guard came running up to me, one of the casualties of the Vampire Attack was a Windhelm Guard.  Given that i am also roleplaying in the game and have joined the Stormcloaks these attacks on Ulfric's City are unforgivable  so i am wondering, if i complete the Dawnguard quest line will these vampire attacks stop?


My minecraft game has been crashing alot lately, and i dont kow why. It also happens with other games and i frequently get blue screen errors. I believe it is a hardware problem but does  The error i usually get it "exception_access_violation" but i sometimes get "exception_illegal_instructuion" A few things:  My system can run minecraft, i used to be able to play Minecraft with no issues at an amazing frame rate (usually 90 to 160)  I have updated my Intel Graphics drivers to the latest one and even tested the previous version  I have the latest version of the Minecraft launcher  I have the latest version of Java installed


Unbelievable reputation for a new member

I've just looked at the stats for a relatively new member and cannot believe the rep he supposedly made in one day, being a relative rookie.   Can this accumulation of rep for June 11 be explained? Was there something going on in the back end?   I posted a comment on one of his , which contained only links, advising that he should summarize the solution in the post, as per SO best practice. He replied with a very cocky "Sure ..." -  Where/How did he get that many reputation in one day? Hard to believe it's not a system error.


What's the maximum actual bit rate of an 802.11g connection?

Using a wired connection, I get a 38 Mbit/s download speed. When I switch to wireless one (Linksys WRT54GL router with Tomato firmware), the speed drops to 23 Mbit/s even if the distance between the router and the computer is 2 or 3 meters.  Is that a maximum effective bit rate I can expect from an 802.11g connection? Are there any settings I can tweak to to increase the download speed?


Where can I ask questions about failed tests when compiling PHP?

I compiled PHP and compilation went fine (no errors). On the make test step I get one test that doesn’t pass. Should I ignore it since the compilation went right anyway or should I do something about it?  Relevant test output is:   ===================================================================== FAILED TEST SUMMARY --------------------------------------------------------------------- bool checkdnsrr ( string $host [, string $type = "MX" ] ); [ext/standard/tests/checkdnsrr.phpt] =====================================================================   The following communities don’t seem to fit:   Stack Overflow is for programming questions Server Fault is for sys-admin stuff, I guess Unix & Linux is for sys-admin stuff for Unix-like OSes Super User is for help with apps or userland OS questions.   Any suggestions?


I know , but what tier are the various Pathfinder classes? This is about Pathfinder only, no 3.5 material is relevant.  An ideal answer would cover all available (non-prestige) classes, but an answer covering the PHB, ACG, APG, and UM would be sufficient. Answers do not need to take into account especially good/bad archetypes that might change the tier of a class (but if you want to list archetypes that are that impactful, feel free to do so).


How do i enter my numeric password in iPhone 4 in VoiceOver mode?

My iPhone 4 is in VoiceOver mode. It`s currently locked and not accepting my passcode which is absolutely correct. And now it's saying iPhone is disabled.  Any solution?


Is possible do this in latex by tikz? Any idea?


As you may or may not be aware, Stack Overflow's close vote review queue . I felt like graphing the progress of the queue historically, and attempted to persuade the Stack Exchange Data Explorer to give me the data. I was, however, stymied by the lack of a Reviews table. The current SEDE query is a 32-line monster with three CTEs and six INNER JOINs - which still can't account for  or  due to limitations of SEDE.  Seeing as expired close votes , and metadata on deleted posts has been heavily protested, I would like to propose that some data on reviews (of all types, because why not) be added to SEDE. I'm not asking for much - something like the following:  Id INT NOT NULL, PostId INT, ReviewTypeId TINYINT NOT NULL, CreationDate DATETIME NOT NULL, CompletionDate DATETIME, PossibleDuplicateId INT, SuggestedEditId INT, IsAudit BIT   (As suggested by @Rachel on the deleted-questions-metadata question, maybe null out PostId for deleted posts.)  Even this minimal data (it doesn't include reviewer stats or individual review timestamps) would allow my use case:  WITH CreatedCVReviews(CreationDate, CreationCount) AS (   SELECT CAST(CreationDate AS DATE), COUNT(*)   FROM Reviews   WHERE ReviewTypeId = 5 -- or whatever ID   GROUP BY CAST(CreationDate AS DATE) ), CompletedCVReviews(CompletionDate, CompletionCount) AS (   SELECT CAST(CompletionDate AS DATE), COUNT(*)   FROM Reviews   WHERE ReviewTypeId = 5   GROUP BY CAST(CompletionDate AS DATE) ) SELECT   Cr.CreationDate AS [Date],   Cr.CreationCount - Co.CompletionCount AS [Net Tasks Added] FROM CreatedCVReviews AS Cr INNER JOIN CompletedCVReviews AS Co   ON Cr.CreationDate = Co.CompletionDate ORDER BY Cr.CreationDate   Other related posts   to  postulates that tables with review data may be added in future. That was eight months ago.  The question  is a possible duplicate from last month. I feel that the question you're reading now better presents the evidence; posting this as an answer to the possidupe didn't feel right, and editing the possidupe with this amount of new stuff is just plain frowned upon. (If you disagree, vote it is a duplicate... as desired.)


Minimum system requirements for ubuntu 18.04

I want to run Ubuntu 18.04 in my machine.  Here are my system specs:  Cpu : Intel core 2 duo Hard disk : 160 gb RAM : 2GB DDR3  Please anyone help. Thanks in advance. ..


I want to change the order of a webform component. This creation of a webform component:  $component = array(       'name' => key($question_name),       'form_key' => $key,       'type' => $form_type,       'mandatory' => 0,       'weight' => $weight,       'pid' => 0,       'extra' => array(           "items" => "1|1\n2|2\n3|3\n4|4",           "multiple " => FALSE,           "aslist" => FALSE,           "description" => $question['description'],         ), );   Gives me the following display result:   Name of component  1 - 4 radiobuttons Descriptiontext   But I want to move the description text over the radiobuttons:   Name of component Descriptiontext 1 - 4 radiobuttons   How can I change the order of the output?


Suppose $\sum a_n$ converges conditionally and $\sum b_n$ converges absolutely, then will $\sum a_nb_n$ converge absolutely?  I know that $\sum|a_n|$ does not converge while $\sum a_n$  does and that $\sum|b_n|$ does converge, and also that $\lim_{n \to \infty} |a_nb_n|=0$ but I'm not sure how to proceed from here.


Should you always use the accent in foreign words like "résumé"?

You can see in the  that the word resumes is mentioned — not résumés or résumés.  What should be the common practice here? What about other words like café?


Why does my Mantaflow waterwheel not work?

Apologies if this doesn't light correctly, I omitted the HDRI I was using to save space for upload and download of the .blend. Plug in your HDRI of choice and the scene should look fine (or turn off HDRI and light as you desire!).  I'm trying to turn a physics object through contact with the Mantaray liquid simulation and it's not working.  The simulation particle system is set to render as a simple object with a sphere rigidbody with sphere collision.  The domain also has a passive rigidbody and collision system - added this out of desperation, and it doesn't seem to be doing much.  The water wheel is a Fluid effector set to collision.   The water wheel also has an active rigidbody and collision system set to mesh - which doesn't seem to be doing much.  The wheel attached to the pole behind it with an empty set to Generic physics constraint (having some problems getting that to rotate reliably on the Y axis, but that's not the main problem).  Can anybody tell me how to get this waterwheel spinning with Mantaflow?


I read in the DND 5e player's handbook about AC and I'm confused if my build is ok or not.  I'm trying to create lvl 4 character with a lot of AC with a light armor.  So here it is: A Tabaxi, Fighter Eldritch Knight with Defense archetype.  My Dex add +3 AC  /  I use a shield +2 AC  /  Wear a studded leather +12 AC  /  Defense Archetype +1 AC / Get the feat Defensive duelist + 2 AC (in reaction) / And maybe use the spell Shield.  So is there anything that I cannot mix together or use at same time?


How to access object instance from property instance? (in `update` callback)

I am trying to create an add-on to create parametric objects (Blender 2.8rc1)  I have defined a custom PropertyGroup, i.e.:  def _update(self, context):     print(repr(self))  class FurnigenProperties(types.PropertyGroup):     width: FloatProperty(         update=_update,         unit='LENGTH'     )     length: FloatProperty(         update=_update,         unit='LENGTH'     )   When I change property I can see out of _update:  bpy.data.objects['GeneratedObject'].parametric_properties  What I essentially want to get access to would be bpy.data.objects['GeneratedObject'] however I am unclear how to get from self in callback function to actual object that property we just modified.  Looking at documentation for  there isn't much detail on what I should expect context to be.  I.e. would context be the place to retrieve object reference? I was thinking about context.object, but I am not clear how object is determined. Is that object selected by user in viewport? In which case it wouldn't work if I modified property from some other Python code (as it would be most likely for a collection of objects of which none would be selected by user). Or is context.object in callback guaranteed to point to object that self belongs to in above callback?  edit:  context.object doesn't seem to work. I just tried setting value of one of my properties through Python console and the object that I get from context.object is (as I expected) object selected in viewport and not the object I modified property of.


Equivalence between CH and existence of certain sets in $\mathbb{R}^2$

The problem is to prove the following equivalence:  $$2^{\aleph_0}=\aleph_1 \iff \exists\ A,B\in\mathbb{R}^2:\\ \textrm{a)}A\cup B=\mathbb{R}^2 \\\textrm{b)}\ \forall\ \textrm{lines } l\ \textrm{parallel to x-axis, } |A\cap l|\leq\aleph_0 \\\textrm{c)}\ \forall\ \textrm{lines } l\ \textrm{parallel to y-axis, } |B\cap l|\leq\aleph_0$$  I think I know how to prove "$\impliedby$":  Let's assume the RHS and that $2^{\aleph_0}\geq\aleph_2$. Now let's take a sequence $\langle x_{\alpha}:\ \alpha<\omega_1\rangle$. Since $\bigcup_\limits{\alpha<\omega_1}|B\cap x_{\alpha}|\leq \aleph_1\cdot\aleph_0=\aleph_1$ there is such a $y$-coordinate that neither of $(x_{\alpha},y)$ is in $B$. But hence we obtain $\aleph_1$ point which all lie on the same line parallel to $x$-axis. Since $A\cup B=\mathbb{R}^2$ they all must be contained in $A$ $-$ a contradiction as $A$ has at most countably many of those points.  But what about the other implication? Do I contruct these sets by induction? Over all lines or something else? I haven't come up with anything yet, perhaps you could help me.


Can you make Games with Pygame that are transparent?

so your sprites could look like this, in front of a transparent background (this is actually a icon, just for illustration) i thought about a minigame that you could play while a movie or whatever is playing in the background


Why does the question's closed status disappear when clicking to load a new edit?

I've come across a small issue which occurs when a question has been closed but the question itself or one of its answers are being edited.  Steps to reproduce:   Visit a closed question. (even closed years ago)   In a different tab or browser, edit the question or one of its answers. "an edit has been made to this post; click to load" message will appear above the edited post in the first tab/browser, click it. The .question-status div becomes hidden, which includes the closed notice below a question and, for a duplicate-closed question, the list of duplicates above the question body. This gives the appearance that the question is no longer closed (until you refresh).   Some screenshots:                I know it isn't common/important but it did confuse me when looking at a particularly bad question - I thought it had been reopened.   Is this an intentional feature? If so, what was the thinking behind it?    Another example  Before    After


How can I shoot with a fast aperture in sunlight?

I have Nikon D7000 with 50 mm lens and like to shoot my family with 1.8 aperture. But, in sunlight it looks so bright. I am a beginner and had try to increase the shutter speed in manual but it's still so bright. When I change to auto, it chooses the f/8 aperture, which I don't like. What can I do?


Who knows the truth about Jon Snow's parentage (father & mother)

There are a lot of great theories telling us that Eddard Stark couldn't be the father of Jon Snow, like this one:    But, who could tell the truth about him, who knows this (that is still alive) that could confirm these theories?


$\mathrm{gcd}(a+nb,b)=\mathrm{gcd}(a,b)$ for all $n\in\mathbb{Z}$

I have a question: Let $n\in\mathbb{Z}$, then $(a+bn,b)=(a,b)$, $(a,b)$ being the greatest common divisor.  Is this a correct approach?  Let $e=(a+bn,b), \quad n\in\mathbb{Z}$, then $e$ is expressible as the smallest linear combination of $an+b$ and $b$ so there exists $u,v\in\mathbb{Z}$ such that $$ e=u(a+bn)+vb $$ and $e$ is the smallest positive such number. Rearranging on the right hand side we get $$ e=ua+(un+v)b $$ which gives a linear combination of $a$ and $b$. Since $e$ is still the smallest such we get that $(a,b)=e$. If this is correct is there a more elegant solution?


Difference between if () { } and if () : endif;

Are there any differences between...  if ($value) {  }   ...and...  if ($value):  endif;   ?


I was trying to prove that a surjective Endomorphism $f:A \to A$ of a noetherian ring is also injective. I would like to know why this argument is not correct? $A/\rm{Ker}f \cong \rm{Im}f=A \Rightarrow Kerf=\{0\}$


shelf life question regarding mayonnaise based sauce

I make this mayonnaise based sauce that my friends all rave over and I wanted to make a large batch, can it (which I've never done before) and give it out as a gift. I'm nervous about giving away something without understanding how long it can be preserved in the refrigerator.  The sauce has 1 part white wine vinegar, 1 part water and 6 parts mayonnaise, in addition to minced garlic and other spices. Any ideas on how long this might last, or where I can find better literature about preserving in general?


> can do it.  echo "text" > file   tee can do it.  echo "test" | tee file    Can sed do it without using either of the above? Is it possible to save the output of a sed command to a file without using either > or tee?


$n=\dim V$. Then $V=\ker(T^n)\oplus\mathrm{range}(T^n)$

I trying to solve the following problem. The question is from a past exam.     Suppose that $V$ is a finite dimensional vector space over a field $K$. Let $T: V\rightarrow V$ be a linear operator. If $n=\dim V$, then $V=\ker(T^n)\oplus\mathrm{range}(T^n)$   Attempt/Thoughts. If I can show that $\ker(T^n)\cap \mathrm{range}T^n={0}$ then we are done. To show this I need the following claim. (At least this is what I think). I claim that $\ker(T^{2n}) \subseteq \ker(T^n)$. I am stuck on trying to prove this. I know that     $\ker(T) \subseteq \ker(T^2) \subseteq \ker(T^3) \subseteq \cdots$   So this set of inclusions has to stop at some point since we are in the finite dimensional case(?). If there is some $r\geq0$ such that $\ker(T^{r})=\ker(T^{r+1})$ then I can easily prove my claim. But I don't know how to make this precise.   Can somebody help?  Thanks


Best practice when implementing numbered lists in columns?

I often implement numbered list for both print and web projects. At times it is just more efficient to break the list into two, three, or four columns.  How should item ordering be handled?  Should numbers start at 1 in the top left then move down the column, then jump to the next column to continue numbering? (Option A)  Or should numbers start at 1 in the top left the move sideways to #2, #3, etc., jumping columns for each number? (Option B)    In terms of web responsiveness, Option B provides better break points (at times with 3 or 4 columns).  Should this be handled the same in both print and web?


The formula $\exists x[x=a]$, where $a$ is a constant, is always valid in first-order logic. See discussion and proof . The formula $\exists x[f(x)=a]$ is not valid, since the universal set, defined as the set that contains all elements, does not exist. Discussion . Now, I would like to know if the formula $\exists y[y=f(a)]$ is valid. Since $y$ belongs to the universal set, I would assume we can substitute it by $f(a)$ and since $f(a)=f(a)$, the formula is valid. If that's the case, I infer that the formula $\exists y[f^{-1}(y)=a]$ is valid as well.


Integrated voltage regulator chip versus discrete circuit utilizing op-amps and power BJTs for DIY bench power supply

After using the simple LM317 on breadboard variable power supply for a while, a need for a more rugged and reliable bench power supply has arose.    Short on money, i decided to build it as many other amateurs like me did. The thing is that, for my current needs i don't need a giant digitally controlled multi-channel 500 watt beast or something like that.  Instead what i really want is a low wattage positive and negative low voltage ouput -12v-0v-12v for example. However i really like that my power supply to be safe, reliable and fool-proof as far as possible. So after searching the web here and there, i found many designs that from my point of view fell in one of two divisions:-   Ones that use discrete op-amps and transistors. And ones that use integrated voltage regulators.   So -at least for me- i think that the ones with discrete op-amps and transistors are more prone to malfunctions and issues compared to the integrated ones with all of their internal over current and thermal protection circuits which would need to be discretely implemented in the bench power supplies that utilize discrete op-amps, however those designs have the advantage of ease of customization and more importantly that it is easier to have 0V output compared to 1.2V in integrated voltage regulator ones.    So i like advice to help me choose between circuits that utilize discrete op-amps like this circuit for example:-  Or ones that use integrated voltage regulators with their intrinsic robustness and low form factor.    Also as a side but related question i have seen many designs on the web that utilize negative voltage fed to the adjust or like pins to achieve 0V output from integrated voltage regulators like this single positive power supply:-     Or a positive and negative channels power supply that i really like its design because of simplicity (not because of laziness but to avoid the drawbacks that may come with complex designs especially when implemented by an amateur like me):- And the question is      Is it wrong or a system safety and reliability lowering act to feed negative voltage to adjust pin for LM317 for example?     I ask this question because the datasheet clearly states that the working output range is 1.2V-37V for LM317 for example, also no similar circuit is mentioned in the Typical Applications section except for the following one:- And even in that circuit, however the adjust pin is tied to the negative rail, it does't regulate during this interval instead it is shut until the next half wave at least that what i understand.    So at last to sum it up which alternative is best suited for my needs, its pros and cons and suggested circuits if possible.


"Recent Badges" list is displayed without margins on "Home" page

When the "Hide Hot Network Questions" preference is enabled (i.e. HNQ sidebar is hidden), we see "Recent Tags" and "Recent Badges" in the homepage instead of the HNQ. However, the "Recent Badges" list is displayed with no margins. ex.)   I think that the appropriate margins were set in the past. cf.)


Find the limit $\lim\limits_{n \to \infty} \left ( \left (1 + \frac {1} {2} + \cdots + \frac {1} {n} \right ) - \ln n \right ).$

Prove that the following limit exists and find the limit $:$ $$\lim\limits_{n \to \infty} \left ( \left (1 + \dfrac {1} {2} + \cdots +  \dfrac {1} {n} \right ) - \ln n \right ).$$  I know that the above sequence is strictly decreasing and bounded below by $0$ and hence by monotone convergence theorem it has to converge to it's infimum which is known as Euler-Mascheroni's constant. But how do I evaluate the limit? Any help or suggestion in this regard will be highly appreciated. Thanks in advance. Source $:$ ISI (Indian Statistical Institute) PhD entrance test in Mathematics, TEST CODE : MTA (FORENOON SESSION) (Question No. $1$) held in $20$th September this year.


Looking for recommend. Tire pressure for a 26in MTN bike. Im around 185lbs.   I am fixing my bike up, and I want to make sure not to over inflate as I do not want to blow a tire.


Ubuntu 16.04 software center not working

Just installed the UBUNTU 16.04 LTS. I just noticed that the software center is not working. I did installed the older version of it (sudo apt-get install software-center) but I want the new software center.  How can I install the new version of the software center?


How do I create this effect in Photoshop?  It appears to be something dripping downwards and is sourced directly from the V-Sauce3's youtube channel.     Could someone let me know? Thanks!


Is $\mathbb{Q}[\sqrt{n}]$ ever isomorphic to $\mathbb{Q}[\sqrt{m}]$ where m,n are not perfect squares?

I was doing some abstract algebra exercises and I noticed that we if we assume there exists some homomorphism $\phi : \mathbb{Q}[\sqrt{n}] \rightarrow \mathbb{Q}[\sqrt{m}]$. Then if we want an isomorphism then $\phi$ must be surjective which means that $\phi(1) = 1$. Which means that $\phi (a) = a $ for some $a\in$ $\mathbb{Q}$.  Then for some $(a + b\sqrt{n})$ we get that  $$\phi(a + b\sqrt{n}) = a +b\phi(\sqrt{n})$$ Now we also have that, $$\phi (n) = n = \phi ((\sqrt{n})^2) = (\phi(\sqrt{n}))^2$$ Then if $\phi(\sqrt{n}) = c + d\sqrt{m}$ we get that $$n  = (\phi(\sqrt{n}))^2 = (c + d\sqrt{m})^2$$ $$ n = c^2 + 2\sqrt{m}cd + md^2$$ we get that $cd = 0$ so we have that if $c = 0 $ $$ n = md^2 \Rightarrow  d  = \sqrt{\dfrac{n}{m}}$$ which is a contradiction as $d\in \mathbb{Q}$ similarly we get that if $ d = 0$ $$ n  = c^2 \Rightarrow c  = \sqrt{n} $$ which again contradicts that $c\in \mathbb{Q}$ which means that we cannot construct an isomorphism. Is there something that I am assuming that I shouldn't be or is this correct?


How do I stop a bash script until a user has pressed Space?  I would like to have the question in my script     Press space to continue or CTRL+C to exit   and then the script should stop and wait until Space is pressed.


Are cards that are both Land and Creature affected by summoning sickness?

Are cards that are both Land and Creature affected by summoning sickness with regard to:   Possibility to attack Activating special abilities with the TAP symbol?


Trying to connect to the internet, no WiFi symbol in the top right

Title says it all. I'm trying to connect to my WiFi network, but the WiFi icon that's supposed to be in the top right corner is no where to be seen.


Is there any significant difference between Nikon and Canon?

I'm considering purchasing a DSLR for the first time here in the next couple of months. The two "big boys" seem to be Canon and Nikon. I've looked at both companies, and I can't really see significant differences between the two.  Are there any?  (Please don't go into a flame war here -- I'm looking for factual differences between the cameras, not "I enjoy X because of Y...")    Also see   for another important part of the story.


Why bosons have integer spin and fermions have half-integer ones?

Due the fact that the fermions are the "block particles" and the bosons are the "carriers" I just came out with the question that, why the "block particle" have half-integer spin and the "carriers" have an integer spin?


Show that, for square matrices $A$ and $B$, $A+B=AB$ implies $AB=BA$.

Let $A$ and $B$ be two $n$-by-$n$ real matrices such that $A+B = AB$.   How do I prove that $AB= BA$?   I have tried using the trace function on $A+B-AB$. But I could not get any Ideas. Kindly provide me with hints.


can lights in blender influence image sequence?

I have a image sequence imported in blender and I want it to be influenced by the lights in blender, not just the shadow but also the amount of light and color of light.


Using Named Credentials With 3rd Party Authorization Token

Trying to use point and click      External Services   but unsuccessful with      Named Credential authorization.   A 3rd party service just requires the Authorization Token be sent with request. Not seeing any options in Named Credentials to use this? Before being pointed to creating an Apex Class or Connected App I want to confirm that the point and click approach for this is NOT possible today.   which seems to confirm the above but not clearly.  API I'm trying to use is pretty basic . Seems like rest of External Service piece may be working when used in a Flow.


Finding limit of a sequence in product form

\begin{equation} \prod_{n=2}^{\infty} \left (1-\frac{2}{n(n+1)}  \right )^2 \end{equation}  I need to find limit for the following product..answer is $\frac{1}{9}$.  I have tried cancelling out but can't figure out.  Its a monotonically decreasing sequence so will converge to its infimum.. how to find the infimum?


How can I prove this:       Finite rings without zero divisors are division rings.   I know how to prove it when the ring has $1$, but I have no idea if my ring needs to have an unity.


A gray 'pyramid' appeared that limited my model to what was inside that 'pyramid', but only in solid and wireframe view

I was editing in material preview, but when I switched to solid view, most of my scene did not show, just the parts that fell into a dark rectangular pyramid.  The pyramid itself is positioned and rotated arbitrarily.


How much do monsters get from Change Shape?

If you have a dragon or a couatl and have it change shape into, say, the CR 3 knight, what among brave, multiattack, leadership, and parry is "not a class feature" and would therefore be available to the creature?  And, does it get racial benefits on top of the knight's stats? In which case, if you have it turn to a variant human with the Tough feat, would you count its "level" as its CR or its number of hit dice? If that feat is just unavailable, then what if it turns into a mage that specifies it's an "x-level spellcaster"?


I bit the bullet and upgraded to iOS 9.1, and the phone now moves like it's an iPhone 3GS. I can see iOS 8.x is no longer signed, but fortunately I have SHSH of iOS 8.2 saved.  How can I downgrade without losing my warranty? I've heard jailbraking will void warranty, but I guess jailbraking then flashing an iOS version that removes the jailbreak should allow my phone to still be in warranty.  PS: This is not a duplicate of , because it talks about restoring from IOS9 to usinged IOS8 version with SHSH blobs.


So I made this structure by subdividing a plane and elevating parts to make hallways:    Then I realized that I wanted to make the walls have a certain thickness.  Is there a way to do this?  Extruding didn't really work for me.


Why is the shape of lightning or an electric spark a zig-zag line?

Why is the shape of the  (or an electric spark) always of a zig-zag nature? Why is it never just a straight line?     .


Proof that Hadamard matrices of order $4k+2$ don't exist

It's known that Hadamard matrices can only exist for orders $1$, $2$ and $4k$. It's easy to show that there are no Hadamard matrices of order $2k+1$. But what is the proof that there are no Hadamard matrices of order $4k+2$?


Are both ground pins on the ATMEGA internally connected?

I think the title is self-explanatory but should I make the connection on PCB or they are already connected? If so, should I still connect them externally? Why? I'm working on ATMEGA328p-pu if it matters.  (source: )


When I first installed Ubuntu 13.04 from a USB stick I was asked to fill in for user username and password so I set one on my own. When I run Ubuntu I click log in but it automatically logs me in as user so I can't type my username. As a result, in order to run certain apps or set up my network I'm asked to type the root password for authentication. I don't wanna log in as a superuser. Please note that I'm a newbie to Ubuntu.


Where can I find or download ANT Landscape?

I'm using blender2.79 and I have looked for ANT Landscape for a long time (it doesn't exist in add-ons). I have also searched the question and I found the link:   but it writes"There is currently no text in this page." So I wonder does anyone know where can I download ANT Landscape. Thanks!


Using right-hand Riemann sum to evaluate the limit of $ \frac{n}{n^2+1}+ \cdots+\frac{n}{n^2+n^2}$

I'm asked to prove that $$\lim_{n \to \infty}\left(\frac{n}{n^2+1}+\frac{n}{n^2+4}+\frac{n}{n^2+9}+\cdots+\frac{n}{n^2+n^2}\right)=\frac{\pi}{4}$$ This looks like it can be solved with Riemann sums, so I proceed:  \begin{align*} \lim_{n \to \infty}\left(\frac{n}{n^2+1}+\frac{n}{n^2+4}+\frac{n}{n^2+9}+\cdots+\frac{n}{n^2+n^2}\right)&=\lim_{n \to \infty} \sum_{k=1}^{n}\frac{n}{n^2+k^2}\\ &=\lim_{n \to \infty} \sum_{k=1}^{n}(\frac{1}{n})(\frac{n^2}{n^2+k^2})\\ &=\lim_{n \to \infty} \sum_{k=1}^{n}(\frac{1}{n})(\frac{1}{1+(k/n)^2})\\ &=\lim_{n \to \infty} \sum_{k=1}^{n}f(\frac{k}{n})(\frac{k-(k-1)}{n})\\ &=\int_{0}^{1}\frac{1}{1+x^2}dx=\frac{\pi}{4} \end{align*}  where $f(x)=\frac{1}{1+x^2}$. Is this correct, are there any steps where I am not clear?


Unable to install windows 7 over ubuntu 14.04. ( to remove ubuntu )

I want to install win 7 over ubuntu but the windows installation has stopped when appear the "Starting Windows" screen (for the first time). I convert my hard disk to mbr, from gpt and I deleted all partition, but the same problem. The screen is just froze.  Now I don't have an operating sistem on my hp envy laptop, just an ubuntu live usb.  What can I do ?


What is this globe icon with blue down arrow in my menu bar?

At far left of my top bar you can see a globe-like network sort of icon with what I interpret as a blue download arrow. This icon appeared recently for the first time for unknown reasons. Clicking it, right-clicking it, double-clicking it, etc all produce no effect. It's not interactable. What is this and how can I learn more about it and/or remove it if appropriate?


Projection of a point onto a simple convex polytope

I have a convex polytope described by the intersection of a hypercube and two parallel lower and upper hyperplanes cutting through the hypercube. I want to find the projection of a point onto the polytope. I read the question  and see that the general problem of finding a projection onto a convex polytope can be solved with quadratic programming. However, taken alone, projection onto a hypercube or a hyperplane is trivial. For the hypercube, each dimension is defined by a lower+upper bounds and we just pull each dimension within those bounds, which take $O(n)$ time in $n$ dimensions. For the hyperplane just find the projection onto it. So I'm wondering whether there is simpler method for finding such a projection, maybe somehow combining the two independent projections.


While statement ends no matter what the input is

Below is my code, basically what I want the program to do is loop the while statement every time the enter key is hit, and then when "q" is submitted to the console, I want the program to end. What did I do wrong? With this code, it only runs once, and if i change  if (moreEmps != "q") break;    to  if (moreEmps == "q") break;   then it will continue no matter what is entered. can someone steer me in the right direction? Thanks!      import java.text.NumberFormat;     java.util.Scanner;     /**     * Input a number of hours and calculate the pay at $10.00 per hour     * Pay time and one half for any hours over 40.     */     public class PayCalc     {     public static void main (String[] args)     {     // Declare constants to be used in payroll calculation     final double RATE = 10.00;     // hourly rate     final int REGULAR_HOURS = 40; // hours paid at regular rate      double pay = 0.0;     Scanner input = new Scanner (System.in);      System.out.println("Employee Payroll Program");     System.out.println("Press enter to begin.");      String moreEmps = "";      while (moreEmps != input.nextLine())     {          System.out.print("Enter employee name: ");          String employee = input.next();          System.out.print("Enter hours worked:  ");          int hours = input.nextInt();           if (hours > REGULAR_HOURS)              pay = RATE * REGULAR_HOURS + (hours - REGULAR_HOURS) * RATE * 1.5;           else             pay = hours * RATE;           NumberFormat formit = NumberFormat.getCurrencyInstance();          System.out.println();          System.out.print("Total Pay for ");           System.out.print(employee);          System.out.println(" : " + formit.format(pay));           System.out.println("Any more employees?");          System.out.println("Press enter to input another employee's information, or q to quit.");          moreEmps = input.next();          moreEmps.toLowerCase();             if (moreEmps != "q") break;     }    } }


UBUNTU 14.04LTS Wi-Fi hotspot is not detected by android phone

Default creation of HotSpot in network manager is not able to detected on andriod phones of any version. There is a answer for this question in given link below but its need to install third party repository    How can one make the ubuntu default setting of a hotspot creation to be detected on smartphones ?


I'm trying to make an array of some objects (another array or dict), like:  a = {"authorName" : 0} b = [a] * numOfAuthors     # numOfAuthors = 300, predefined   My objective is that each element in b should be a copy of a, such that they can be modified independently without affecting each other, but clearly the code shown will result in: modifications to any element in b will be reflected to all others due to the assignment. Hence I tried changing it to:  b = [copy.deepcopy(a)] * numOfAuthors   from this . But it's still behaving in the old way. If I do:  b[0]["Ben"] = 12   then b will be a list of {"Ben": 12}. How should I resolve this?


How can I check if I have Thunderbolt x4 or x2?

I have a Dell XPS 13 on which I have installed Ubuntu. I would like to know if it has PCIe x4 or x2.  Edit 1: I already know that it is Thunderbolt, just don't know how many PCIe lanes it has.   Edit 2: This is what I got after trying the suggested command.  $ sudo dmidecode | grep PCI PCI is supported Type: x16 PCI Express Type: x1 PCI Express Type: x1 PCI Express Type: x1 PCI Express Type: x1 PCI Express Type: x1 PCI Express Type: x1 PCI Express Type: 32-bit PCI     SA - PCIe Version   Edit 3: After trying, sudo lspci -vv | grep -E 'PCI bridge|LnkCap'  00:1c.0 PCI bridge: Intel Corporation Sunrise Point-LP PCI Express Root Port (rev f1) (prog-if 00 [Normal decode])     LnkCap: Port #1, Speed 8GT/s, Width x2, ASPM not supported, Exit Latency L0s unlimited, L1 <16us 00:1c.4 PCI bridge: Intel Corporation Sunrise Point-LP PCI Express Root Port #5 (rev f1) (prog-if 00 [Normal decode])     LnkCap: Port #5, Speed 8GT/s, Width x1, ASPM L1, Exit Latency L0s <1us, L1 <16us 00:1c.5 PCI bridge: Intel Corporation Sunrise Point-LP PCI Express Root Port #6 (rev f1) (prog-if 00 [Normal decode])     LnkCap: Port #6, Speed 8GT/s, Width x1, ASPM L1, Exit Latency L0s <1us, L1 <16us     LnkCap: Port #0, Speed 2.5GT/s, Width x1, ASPM L0s L1, Exit Latency L0s <4us, L1 <64us     LnkCap: Port #0, Speed 5GT/s, Width x1, ASPM L0s L1, Exit Latency L0s unlimited, L1 <64us


What's the significance of this passage from "The Goblet of Fire"

For a fleeting instant, Harry thought he saw a gleam of something like   triumph in Dumbledore's eyes. But next second Harry was sure he had   imagined it, for when Dumbledore had returned to his seat behind the   desk, he looked as old and weary as Harry had ever seen him.   This happens right after...      Dumbledore questions Harry about the events in the graveyard and the coming back of the Dark Lord.   Why would Dumbledore display a "gleam of triumph" in that specific moment? Is there any references in canon explaining what was going on in Dumbledore's mind?


How do I use the Natural Earth SQLite DB with QGIS?

I just downloaded the Natural Earth data in SQLite format from . I had assumed that this would be a SpatiaLite database, but it appears not to be! QGIS is failing to recognize it as a spatial database. OGR supposedly supports reading geometries even when stored in a plain SQLite database, but maybe QGIS doesn't use OGR for SpatiaLite?  The SQLite database does have geometry_columns and spatial_ref_sys tables. Is there some way to convert it to a full SpatiaLite database?


I just came onto a project with a pretty huge code base.   I'm mostly dealing with C++ and a lot of the code they write uses double negation for their boolean logic.    if (!!variable && (!!api.lookup("some-string"))) {        do_some_stuff();  }                                      I know these guys are intelligent programmers, it's obvious they aren't doing this by accident.   I'm no seasoned C++ expert, my only guess at why they are doing this is that they want to make absolutely positive that the value being evaluated is the actual boolean representation. So they negate it, then negate that again to get it back to its actual boolean value.   Is this correct, or am I missing something?


Maximum and minimum of $f(x)=\cos(\sin(x))-\sin(\cos(x))$

Given the function: $$f(x)=\cos(\sin(x))-\sin(\cos(x))$$ it has absolute maxima at $x=(2k+1)\pi$ with $k=0,1,..N$ and relative maxima at $x=2k\pi$. It is not clear where are the minima. Putting the derivative to zero doesn't help. Any suggestion on how to find the minimum value and where is it? Thanks.


How to install VirtualBox Guest Additions for Ubuntu 16.04

What is the best way to install Guest Additions with all the resize and clipboard and file sharing features on Ubuntu 16.04?


Do magnets lose some form of energy while attracting each other?

Consider two very strong magnets, one above a wooden table, one below a wooden table. As the two magenets clamp together, wedging the tableplate between them, at least the bottom magnet will experience a force that is stronger or equal to the gravitational force pulling it down. This means that some form of energy must be expended while the two magnets attract each other. How would this expenditure of energy be affecting the system? Heat through pressure in the tableplate? Loss of magnetism in the magnets? Consider the magnets and table being made of such a material that deformation does not need to be considered.


Show that are logically equivalent (without truth table)  (p → r) ∧ (q → r) and (p ∨ q) → r My solution:  (p→r)∧(q→r) ≡(¬p∨r)∧(¬q∨r)  ≡(¬p∧¬q)∨(r∨r) ≡(¬p∧¬q)∨r    ≡¬(p∨q)∨r ≡(p∨q)→r   (p → r) ∨ (q → r) and (p ∧ q) → r  (p→r)∨(q→r) ≡(¬p∨r)∨(¬q∨r)     ≡(¬p∨¬q)∨r ≡¬(p∧q)∨r    ≡(p∧q)→r   Is it correct ?


I have a CentOS server (release 6.7). In order to do tmux shortcuts more quickly (ctrl-b), I thought of mapping the caps lock key as another ctrl key. How do I go about doing this?  I have looked up this up on Google and have tried adding XKBOPTIONS="ctrl:nocaps" to /etc/sysconfig/keyboard to no avail.


Hello would anybody here know how to fake animate a texture/material? I would recreate a waterfall similar to this video and have a fake flowing via textures just like how it is done here without using fluid simulation. Thank you very much.    at 0:49    If you must know I would recreate the animation to this scene..


If the set of natural numbers is closed under addition, how can we have the result that the sum of all the natural numbers to infinity is -1/12

As seen  and on this wikipedia page the sum of all the natural numbers to infinity is -1/12.    $\sum_{n=1}^\infty n = \frac{-1}{12}$  but the set of natural numbers is closed under addition and $\frac{-1}{12}$ is not a natural number.  In addition the series is clearly divergent, so how can we get away with "assigning" is a value as described on the wikipedia page.


Wifi Automatically Turning ON after iOS 11 Update

I'm facing this issue after updating iOS11 in my recently bought iPhone 7  I usually turn off wifi during the night and found it ON in the morning. It automatically turns ON resulting in unnecessary battery drains.  Would appreciate a fix !!


Can solar panel charging slow down the draining of phone battery?

I have made a solar panel charger, it consists of a 1.2 watt panel connected to a buck converter, then to the phone.  Now, when I connect it, it charges the phone and in the battery settings it shows it is charging as "plugged ac" and slow charging.  I wanted to test if it can slow down the discharge rate, so I came up with a test procedure where I:   Downloaded "battery drainer" app (which essentially turns on cpu stress, gps, vibrator, full brightness etc);   Measure the time it take for the phone to get to 90% from 100% with solar panel attached and without solar panel attached.   But the time it takes to discharge is almost the same. I am wondering what am I missing. Wouldn't the solar charging increase the discharge time?  When I measured the solar panel output it was 5 V and around 110 mA.   Thank you, any help will be appreciated.


What does the blue pill in The Matrix actually do?

During the first meeting between Neo and Morpheus in The Matrix, Morpheus states that if Neo takes the blue pill,  Does this mean that the blue pill acts as a selective amnesiac? A program to make Neo feel as though he dreamed the meeting, similar to his experience of having a bug implanted by the Agents? Would it include something that makes him no longer of interest to the Agents? Since, technically, all that Neo has to do, if he refuses Morpheus' offer, is get up and leave the room, why have a blue pill at all?


Do characteristic functions characterize the independence of random variables? [Solved]

It is well known that the probability density function characterizes the independence of random variables in the following sense.  $$X,Y \quad\text{independent}\iff f(x,y)=f_x(x)f_y(y)$$  where $f$ is the pdf of the random variable $(X,Y)$ and $f_x$ and $f_y$ are the pdfs of the marginal distributions of $X$ and $Y$, respectively. My question is, seeing as there is a bijection between characteristic functions and probability distributions, do characteristic functions also characterize independence? In the following sense  $$\varphi_{(X,Y)}(t_1,t_2)=\varphi_X(t_1)\varphi_Y(t_2)$$  where again $\varphi$ is the characteristic function of the random variable in its subscript.


I sometimes see a speaker saying: I'm going to disagree with you. I'm going to have to agree with you.   How does "going to" work in the above sentence?


I meet a problem when  using mingw32-g++ to compile a pj in codeblocks.       error msgs  obj\Debug\main.o||In function `main':| E:\project\test\main.cpp|15|undefined reference to `Stack<char>::Stack()'| E:\project\test\main.cpp|23|undefined reference to `Stack<char>::shiftL()'| E:\project\test\main.cpp|28|undefined reference to `Stack<char>::shiftR()'| E:\project\test\main.cpp|33|undefined reference to `Stack<char>::Del()'| E:\project\test\main.cpp|36|undefined reference to `Stack<char>::push(char)'| ||error: ld returned 1 exit status| ||=== Build failed: 6 error(s), 0 warning(s) (0 minute(s), 0 second(s)) ===|   Stack.h  #ifndef STACK_H_INCLUDED #define STACK_H_INCLUDED  template <class Type> struct List {     Type content;     List<Type> *head;     List<Type> *end; };  template <class Type> class Stack { public:     Stack();     ~Stack(){};     void push(Type x);     void Del();     void shiftL();     void shiftR();     List<Type> *Front(){ return front; }     List<Type> *Back(){ return back; } private:     List<Type> *front;     List<Type> *back;     List<Type> *operate;     List<Type> F;     List<Type> B;     int pos; }; #endif // STACK_H_INCLUDED   Stack.cpp  #include"Stack.h" #include<stdio.h> template<class Type> Stack<Type>::Stack() {     F.head = B.end = NULL;     front = &F;     back = &B;     front->end = &B;     back->head = &F;     operate = back;     pos = 0; } template<class Type> void Stack<Type>::Del() {     if (pos>0)     {         List<Type>* temp;         temp = operate;         operate = operate->end;         operate->head = temp->head;         temp->head->end = operate;         pos--;     } } template<class Type> void Stack<Type>::shiftL() {     if (pos>0)     {         operate = operate->end;         pos--;     }  } template<class Type> void Stack<Type>::shiftR() {     if (operate->head != front)     {         operate = operate->head;         pos++;     } } template<class Type> void Stack<Type>::push(Type x) {      List<Type>* temp;     temp = new List<Type>;     temp->content = x;     temp->end = operate;     temp->head = operate->head;     operate->head->end = temp;     operate->head = temp;     operate = operate->head;     pos++; }   mian.cpp  #include<stdio.h> #include<iostream> #include"Stack.h" using namespace std;  int main() {     char c;     int k;     cin >> k;     getchar();     for (int j = 0; j < k; j++)     {         Stack<char> password;         while (1)         {             c = getchar();             if (c == '\n')                 break;             if (c == '<')             {                 password.shiftL();                 continue;             }             if (c == '>')             {                 password.shiftR();                 continue;             }             if (c == '-')             {                 password.Del();                 continue;             }             password.push(c);         }              List<char>* i;             for (i = password.Back()->head; i != password.Front(); i = i->head)                 printf("%c", i->content);             printf("\n");     }     return 0; }     But  If I add #include"Stack.cpp" in main.cpp(this is illegal,right?),the complier don't show any errors or warnings. Can you tell me why?Thanks a lot!  :)


How to install the Web Apps in Ubuntu 16.04

Can't Install the Web Apps in Ubuntu 16.04 I tried to do this to resolve the problem but got error message saying,  E: Could not get lock /var/lib/dpkg/lock - open (11: Resource temporarily unavailable) E: Unable to lock the administration directory (/var/lib/dpkg/), is another process using it?


I would like to start Xterm terminal with "Always on Top" option enabled rather than right-clicking and setting it on manually each time. How can I do it ?


How can I adapt a 3-pin PC fan connector to a 4-pin connector?

My computer's motherboard uses all four pin fan connectors with no support for speed controlling the older three pin fan connector. The problem is, all the PC fans that I have use a three pin connector. As fan as I know there are no premade solutions available, so I was thinking of building an adapter that sits in an unused drive bay.   I can't seem to find much information on how the four pin fan connecter works. Apparently, it looks something like this:   12 V 0V Tachometer PWM   The three pin header is numbered similarly:   Vcc 0V Tachometer   Could I simply use a logic level MOSFET to do the following?


jQuery css "click" doesn't work after change in selected month in calendar

I'm working on a dynamic calendar that allows user to click on individual days to change whether they're available or unavailable. It works as it's supposed to up until I select another month or year. Once that happens the "click" event on individual cells/days doesn't work.   // Changes cell background of the calendar var changeColor = function(temp) { // if cell background is white -> change to green if(temp.css('background-color') == "rgba(0, 0, 0, 0)") {     temp.css('background-color', 'green');     // if cell background is green -> change to red } else if (temp.css('background-color') == "rgb(0, 128, 0)") {     temp.css('background-color', 'red'); } else {     // else change back to white     temp.css('background-color', ''); } };   Here is were it's used   $(document).ready(function() { // When a date-cell is clicked - changes color to green -> red -> white $(".calCell:not(.empty)").click(function() {     changeColor($(this)); });  });   The two buttons that change the whole calendar to red or green seem to work fine with each month selected.   // When Available button is click -> changes whole calendar to available $("#yes").on("click", function() {     $(".calCell:not(.empty)").css('background-color', 'green'); });  // When Unavailable button is clicked -> changes whole calendar to unavailable $("#no").on("click", function() {     $(".calCell:not(.empty)").css('background-color', 'red'); });   Example:


I was wondering whether the antisymmetry of cardinality (expressed in the Shroeder-Bernstein Theorem) carries over to homomorphisms. That is, if A and B are algebraic structures of the same type, and there is an injective homomorphism from A to B, and there is an injective homomorphism from B to A, then are A and B necessarily isomorphic?


Can wizards/witches change their Animagus?

Animagi are the spirit animal of a magical person. So what if a person's personality changes, will their Animagus form change as well, as Nymphadora Tonks' Patronus did? Or will it remain?


Laptop turned on from sleep automatically

I found my laptop powered on from Stand by mode about 6 hours later. I did a research around the site to find out the reason why it would automatically turn on from sleep. So, it told me to go into the power management of the devices and disable the wake up of computer sleep. I'll do that.  What I want to know is: Can I know exactly what made my computer wake up from sleep? Does it keep track of it the logs or events?  Update:  I have looked into the Event viewer to figure out the time when my computer came out from sleep:  The system has returned from a low power state.  Sleep Time: 2013-09-10T11:46:31.927985300Z Wake Time: 2013-09-10T16:46:38.116075100Z  Wake Source: Unknown   It clearly says that the Source was Unknown. Is there still possibility I might get to know?


Possible Duplicate:          How do you convert a C++ string to an int?  Assume you are expecting the string to have actual numbers in it ("1", "345", "38944", for example).  Also, let's assume you don't have boost, and you really want to do it the C++ way, not the crufty old C way.


Illustrating op amp feedback without control theory

We are teaching op amps in a high school class, before calculus.  So we can't use control theory to teach how op amps respond.  All the same, I would like to have an intuitive explanation for how a feedback circuit works.  Take the negative feedback, for instance.  Is there a clear way to show how an initial difference of delta between V+ and V- leads to a very large (G(V+ - V-)) difference in the output, which then leads to ...  I'd like to be able to take that argument and show how the voltage of the output converges in addition to the standard virtual short argument.  Can anyone explain it clearly?


I need a square polygon to clip layers to, in QGIS, a perfect square perhaps. It needs to be a certain size. Anyone have any experience or any good ideas?


I am making a game in python. At the beginning, the User enters his name and when he finishes the game, the Programm is saving the name and the playing time in a text file, like this: Playerx: 12:04 Playery: 4:54 Playerz: 7:12  The program converts the text file to dictionary, like this: scorelist = {'Playerx': '12:04', 'Playery': '4:54', 'Playerz': '7:12'}  Now I am searching for a possibility to sort the elements and print the 3 lowest at the end (highscore). Can you help me?


how to integrate sqrt(sin(x)).without using elliptic integration .

How do you solve  $$ \int\sqrt{\sin(t)}dt  $$ using the substitution method.


Suppose p(x) is a polynomial with integer coefficients. Show that if p(a) =1 for some integer a then p(x) has at most two integer roots.

Problem :   Suppose $p(x)$ is a polynomial with integer coefficients. Show that if $p(a) =1$ for some integer $a$ then $p(x)$ has at most two integer roots.   Let $p(x)$ be a cubic polynomial such that $p(x) =ax^3+bx^2+cx +d =0 $  Let $p(\alpha) =a\alpha^3 +b \alpha^2 + c\alpha +d =1 $  ( as per the question) .  where $a,b,c$ are integers.   Now how to prove the  given problem please suggest thanks.....