Suppose $Y\subset X$ and $X,Y$ are connected and $A,B$ form separation for $X-Y$ then, prove that $Y\cup A$ and $Y\cup B$ are connected

Question is :  Suppose $Y\subset X$ and $X,Y$ are connected and $A,B$ form separation for $X-Y$ then, Prove that  $Y\cup A$ and $Y\cup B$ are connected.  What i have tried is :   Suppose $Y\cup A$ has  separation say $C\cup D$ then all i could see is that   Either $Y\subset C$ or $Y\subset D$ as $Y$ is connected and $ C\cup D$ is separation for a subset that contains $Y$.  Without loss of generality we could assume $Y\subset C$  As $Y\cup A=C\cup D$ and $Y\subset C$  i can say $D\subset A$ (I do not know how does this help)  I have $X-Y=A\cup B$ with $A\cap B=\emptyset$  I have not used connectedness of $X$ till now, So i thought of using that and end up with following :   $X-Y=A\cup B\Rightarrow X=Y\cup A\cup B=(Y\cup A)\cup (Y\cup B)$  I do not know what to conclude from this...   I would be thankful if some one can help me by giving some "hints"  Thank you


Find and prove a formula for $1\pmod{3}\cap 1\pmod{7}$.   I have tried looking at similar problems where $A$ is a subset of $B$ iff $A \cap B =A$. But it does not seem to work.   What type of formula should I be looking for and proving?


How to set up Windows 10 partiton on Ubuntu?

I've downloaded the .iso image for the Windows 10 OS, and have imaged it to /media/windows and made it bootable and am using FAT16, and with the bootable option ticked. I restarted my computer, and the UEFI isn't showing and when i start the partiotion on disks, nothing happens. What am i doing wrong?


I have a large collection (hundreds) of partially quite old xfig pictures. Though I really like the xfig program I would like to move to some more up-to-date picture format like TikZ. So I would like to ask if someone has a good idea for an automatic conversion tool. Ideally, some shell srcipt or so... Then problem (?) is that many of the xfig pictures have LaTeX overlays. EDIT: this might be too long for a comment on Mark's answer, so I post it here as an edit: Here is a sample of a xfig which simply produces an error FIG 3.2  Produced by xfig version 3.2.5b Landscape Center Metric A4 52.00 Single -2 1200 2 3 0 0 3 0 7 50 -1 -1 0.000 0 1 0 3 1 1 4.00 60.00 150.00 7650 3375 6975 4275 7650 5625 0.000 1.000 0.000  the script gives some tikz command requesting an error  Package pgf Error: Arrow end type ``triangle 45'' unknown.  So, of course, I can edit now by hand several arrows and so, but I would like to have it more automatic... :(


Is it acceptable to transform an accepted paper (tier-1 conf.) as a patent?

Recently I have a paper acceptance from a tier-1 conference in our field of telecommunication. I have also submitted the extended version in IEEE Transactions as well.  Is it ok (and acceptable) for me to write the patent out these papers? (I understand that paper acceptance does not guarantee patent acceptance)  What will be the academic/career benefits for me to write the patent at this stage when I am writing my thesis?


How many town ordinances can I enact at a time?

In Animal Crossing: New Leaf, how many town ordinances can I enact concurrently? (I figure the early/late ordinances would conflict, but what about the others?)


How does different ways of scaling/ normalising variables in K -Means clustering effect clustering

There are different ways of scaling variables in k-means clustering. I can divide all variable by sum of that column, I can take z score,I can have (max(var)-value)/(max(var)-min(var) etc. How selection of variable scaling/normalising would change clustering result? I have done clustering on 1 million rows with 20 continuous variables. And the wss/tss  is different for different scaling methods.      What is the reason from Algo perspective ?


Why is the fundamental group of the plane with two holes non-abelian?

I know $\pi_1(\mathbb{R}^2\setminus\{x,y\}) = \mathbb{Z}\ast\mathbb{Z} = \langle a,b\rangle$, but its non-abelian-ness isn't obvious to me.   Specifically, I draw a box and two points to represent $x$ and $y$. I call the clockwise loop around $x$ $a$, and the clockwise loop around $y$, $b$.   If I draw the loops $ab$ and $ba$ they look `obviously homotopic' to me (they are both a single clockwise loop containing both $x$ and $y$), so should be the same element in $\pi_1$, which is clearly not the case if we take the free product of $\mathbb{Z}$ with itself.   It seems that I must be making a big mistake somewhere. What is the obstruction to $ab \simeq ba$? I would prefer something concrete, I know this fundamental group follows from standard theorems (van Kampen's theorem), but I want to see the homotopy fail, because I think they are pretty clearly homotopic - so there is something wrong with my intuition which I'd like to fix.


Error : friend function not declared in this scope

/****************pair.h******************/   #include<iostream>     using namespace std;     template<class T1,class T2>     class Pair     {     private :       T1 first;       T2 second;     public  :       Pair(T1,T2);       Pair(){};       Pair<T1,T2>  make(T1  a , T2  b);       void operator=(const Pair& other);       friend ostream& operator<<(ostream& out ,const Pair<T1,T2>& A);      };   /*******************main.cpp*********************/  #include<iostream> #include<utility> #include"Pair.h" using namespace std;  int main()  {   Pair<int,int> A=make(10,20);  cout << A ;   return 0; }   /***********************pair.cpp******************/  #include"Pair.h"  #include<ostream>  using namespace std;  template<class T1, class T2>  Pair<T1,T2>::Pair(T1 a,T2 b){    this->first = a;    this->second = b;  }   template<class T1, class T2> void  Pair<T1,T2>::operator=(const Pair& other)  {     this->first = other.first;     this->second = other.second;  }   template<class T1, class T2> ostream& operator<<(ostream& out ,const Pair<T1,T2> A) {   out<<"("<<A.first<<" , "<<A.second<<")";   return out; }   template<class T1, class T2>  Pair<T1,T2> make(T1   a , T2   b) {   return (Pair<T1,T2> (a,b)) ;     }   it gives me an error in function make ; as it was not declared in the scope of main and i don't understand why.     Also there is a problem when it comes to all friend functions and template. The program doesn't want to be compiled.


An entire function $f(z)$ is real iff $z$ is real

Let $f$ be an entire function s.t. $\forall z \in \mathbb{C}, f(z)\text{ is real}\iff z\text{ is real}$. Prove that $\exists a,b \in \mathbb{R}$ s.t. $a\neq 0$ and $\forall z \in \mathbb{C}, f(z)=az+b$.  I think I have a proof for this using some advanced theorems, but I want to find one that can be done by elementary means (by a student in undergraduate complex analysis).


The infinite hat guessing problem and the axiom of choice, is it necessary?

This question is based on this . Consider the problem of having $\mathbb N$ players. Each is wearing a hat (white, or black), and has to guess his own hat color; however player $i$ can only see the hats of players $j$ with $j>i$. Here's the proposed solution from the blog:  If they can make a strategy before hand, they can make equivalence classes of functions $f: \mathbb N \to \{0,1\}$ with the relation $f \sim g$ iff they agree in all but a finite number of coordinates. Using AC, pick a representative of each equivalence class. Once on the line, since player $i$ can see all players $j$ with $j>i$ then he can tell in which equivalence class they ordering is. Player $i$ the just guesses his hat according to the representative previously picked. Since the representative agrees in all but a finite number of coordinates, then all players guess correctly except a finite number of players.  My question is if the use of the axiom of choice is necessary here. Naively, since these equivalence classes have a lot of structure inside them, it seems to me that I can pick each representative by other means. For example, it's possible to pick a countably infinite number of these representatives: If $\langle 0,1,0,1,0... \rangle$ is in that equivalence class then pick it. If $\langle 0, 0,1,1,0,0,1... \rangle$ is in that equivalence class then pick it. And so on. Of course this is not enough as there are uncountably infinite of these sequences. I would like a prove that AC is necessary here, or if not which weaker version of AC is necessary. (Maybe DC?)


Is there any way to jump to the ground floor?

When you tap at the top of the screen, you jump to the very top floor. Is there an equivalent to jump to the ground floor (i.e. not the quick button for the elevator, but something which is there all the time)?


Why doesn't using the approximation $\sin x\approx x$ near $0$ work for computing this limit?

The limit is $$\lim_{x\to0}\left(\frac{1}{\sin^2x}-\frac{1}{x^2}\right)$$ which I'm aware can be rearranged to obtain the indeterminate $\dfrac{0}{0}$, but in an attempt to avoid L'Hopital's rule (just for fun) I tried using the fact that $\sin x\approx x$ near $x=0$. However, the actual limit is $\dfrac{1}{3}$, not $0$.  In this , the approximation reasoning works out.


Im using fontspec to have Arial in my scrartcl -document. For some reason this Arial is not applied to sectiontitle/subsectiontitle. Compiling with Xelatex  \documentclass[a4paper]{scrartcl} %%%%%%%%%%%%%%%%%% Font %%%%%%%%%%%%% \usepackage{fontspec} \setmainfont{Arial}  %%%%%%%%%%% header %%%%%%%%%%%%%%%%%% \usepackage[headsepline=0.75pt]{scrlayer-scrpage} \renewcommand*{\headfont}{\normalfont} \clearpairofpagestyles \automark[section]{section} \ihead{\headmark} \ohead{\pagemark}  \begin{document}  \tableofcontents \section{Section 1} 11111111111111111111111 \subsection{Subsection 1} 11111111111111111111111 \subsubsection{Subsubsection 1} 11111111111111111111111 \end{document}


Deriving the speed of the propagation of a change in the Electromagnetic Field from Maxwell's Equations

I've been told that, from Maxwell's equations, one can find that the propagation of change in the Electromagnetic Field travels at a speed $\frac{1}{\sqrt{\mu_0 \epsilon_0}}$ (the values of which can be empirically found, and, when plugged into the expression, yield the empirically found speed of light)  I'm really not sure how I would go about finding $v = \frac{1}{\sqrt{\mu_0 \epsilon_0}}$ simply from Maxwell's equations in the following form, in SI units --  $$\nabla \cdot \mathbf{E} = \frac {\rho} {\epsilon_0}$$  $$\nabla \cdot \mathbf{B} = 0$$  $$\nabla \times \mathbf{E} = -\frac{\partial \mathbf{B}} {\partial t}$$  $$\nabla \times \mathbf{B} = \mu_0 \left( \mathbf{J} + \epsilon_0 \frac{\partial \mathbf{E}} {\partial t} \right)$$  Is what I believe true? (that the speed of propagation is derivable from Maxwell's Equations)  If not, what else is needed?  If so, can you provide a clear and cogent derivation?


I want to write this 1 in latex, could anyone help me, please?


Which is correct "A huge unattractive block of flats" or "An unattractive huge block of flats". What is the word "huge" - an opinion or a size?


What is exactly the non-normality requisite for nonparametric tests?

As the title says, what is exactly what is being tested before deciding to use a non-parametric alternative  test (as Kruskal-Wallis for ANOVA, or Mann-Whitney's U for student's t)?  Most sources are not specific on this issue, being content with just referring to the "normality of the data" (e.g. ). This leaves us with two options, either the normality of the residuals or the normality of the response variable, and looking online both arguments are used.  For "data normality" as "response normality" we have other sources (e.g. , and ). For example, in the Biostatistics Handbook by John McDonald which on his  section refers to the , which gives a sequence of examples of normality testing on histograms and distributions of different response variables:     Parametric tests assume that your data fit the normal distribution. If your measurement variable is not normally distributed, you may be increasing your chance of a false positive result if you analyze the data with a test that assumes normality.   Also stating that residuals come as a second option:     If there are not enough observations in each group to check normality, you may want to examine the residuals (each observation minus the mean of its group).   On the other hand, for "residual normality",  is on board with it:     Since it is a non-parametric method, the Kruskal–Wallis test does not assume a normal distribution of the residuals, unlike the analogous one-way analysis of variance.   As well as other answers on this website ()  I am inclined to think it is residual normality what matters, but I am actually curious on why it seems to be such a common error—that actually makes its way into academic contexts, handbooks and "general knowledge"—and if there's some weight or sense into the "response variable normality" position.


Why is apt-get unable to locate bitcoin and bitcoin-qt package?

when i run these: sudo apt-get install bitcoin  OR sudo apt-get install bitcoin-qt  i get "E: Unable to locate package" what do i do?


How can I get back a working GUI on 16.04.1?

Recently I upgraded a computer from Ubuntu 16.04 to 16.04.1 using the command line. After a reboot, there was no more GUI. I managed to install the default GUI with agt-get, and now I do have a graphical login. However, once I am logged in I only have a completely empty desktop, so I need to switch to a console to do anything. Is there a simple way to get back a working GUI?


When playing with progressive Draw 2 and Draw 4 and (say that there are 2 players playing) and    Player 1 goes out with a Draw 2  Player 2 puts down a Draw 2    Does player 1 have to pick up 4 cards?


Setting to stop LaTeX from fitting content to page by stretching spacing

I'm using a template for my thesis and now that I'm all done I want to set a formatting parameter different from the one in the template. When an image is supposed to show and it doesn't fit in the end of a page, it goes to the next page and the content in that previous page doesn't occupy a full page. The problem is that when that happens, LaTeX strecthes the spacing in the page so that the content fits the whole page, like so:  When I want it to keep the normal spacing, like so :  What command could be causing this? Or what would avoid it? I've Ctrl+F'ed \flushbottom and \raggedbottom and the only two entries I found made no difference so I really don't know what's causing this. Any tips?


On this site I usually see very amazing techniques to solve integrals; contour integrals, differentiating under the integral sign, transforming the integral into a series and son on and so forth.  What I really like is that seemingly difficult integrals become very easy to evaluate; you just need this "a-ah" moment and the right technique.  I know that this skill must be trained, so I would like to find a book or a website which has a collection of such integrals.  I don't mean just difficult integrals, for which you have to work through pages of calculations; I want integrals that are easy to solve if you know how to apply the right technique  Can somebody point me in the right direction?


Can a zombie have orphans? Will the orphan children be disturbed by reaping the zombie?

As I understand it, a zombie process has died but still exists as a placeholder in the process table until its parent (or init if the zombie is itself an orphan) checks its exit status.  And my understanding of orphan processes is they are processes that are still alive and running but whose parent has died.  Since a zombie is already dead, its children would be considered orphans, wouldn't they?  Would they be affected be reaping the zombie?  Specifically, would init adopt them as its children only once the zombie was reaped, or would they be adopted as soon as the parent became a zombie?


Please help me " java Exception in thread main java.lang.nullpointerexception"

I would like to ask help for my project. I am a newbie programmer and I don't get this error "exception in thread main java.lang.nullpointerexception"   this is my code:      public class Slumbook{      public String codeName;      public Slumbook(){         //     }      public Slumbook(String codeName){         this.codeName = codeName;     }      public String getCodeName(){return codeName;}      public void setCodeName(String codeName){this.codeName = codeName;}    }   And the Driver Program code is:-  import java.util.*;  public class SlumbookD{     public static void main(String[] args){          Scanner sc = new Scanner(System.in);         Slumbook[] slum = new Slumbook[20];          for(int n=0; n<10; n++){             slum[n].setCodeName(sc.nextLine());         }     } }


Cannot do passwordless SSH from Mac to Ubuntu VM

I am trying to setup password less login from my Mac OS X to to Ubuntu VM created by Virtual-box. I am using NAT->port forwarding option in VM and have host port as 3022. When I do      ssh -p 3022 ubuntu@127.0.0.1   from my local and I can able to login to ubuntu with password, and this works vice versa.  Now I have created public/private key file in my Mac and copied the pub key to VM (ubuntu/.ssh/authorized_keys)  So now when I do:  ssh -p 3022 ubuntu@127.0.0.1   and it's asking for the password again.  I verified the key from id_rsa.pub vs VM authorized_keys and key is same in both places  Can someone tell me if I am making any mistake in my steps?


I am writing a lot of survey reports in which I need to answer specific questions. I stumbled upon \usepackage[shortlabels]{enumitem} and \begin{enumerate}[a)], respectively, which does exactly what I want.    However, at the moment, I need to input pagebreaks by hand if the question and the corresponding answer gets to the next page and was wondering if this could be corrected "automatically". Let me explain this with the help of some code and a picture.  Code:  \documentclass[12pt]{scrartcl} \usepackage[shortlabels]{enumitem} \usepackage{lipsum}  \begin{document} \begin{enumerate}[a)] % a), b), c), ...  \item \textbf{Lorem ipsum 1?}  \lipsum ...  \item \textbf{Lorem ipsum xxx?}  \lipsum  \end{enumerate} \end{document}   As you can see in the attached image, the item does not use a new page even if it does not fit as a whole on the actual page. How can this be changed?    Picture:


There is a coin with a probability $p$ of heads, and $1-p$ of tails. Tosses are independent of each other. When you bet an amount of money $x$, you receive $2x$ if it lands heads, and you lose what you bet if it lands tails.  We are going to use the following strategy:  You start betting an initial amount $x_0$. Every time you lose, you bet twice what you bet in the previous throw. You keep doing this, until you win, at which point you retire, or start again, betting $x_0$.  The interesting case of course is when $p < 0.5$.  The question is: How profitable is this strategy? Intuitively I feel that eventually I can always win an arbitrarily large amount of money. But that can't be entirely right ("the house always wins!"). So what am I missing here? What's the expected win in each run?  Also, does this sort of strategy have a name in the literature?  P.S.: Found this later,


Children's sci-fi series from 70's/80's with a pink blob as a pet

I remember a connected series of science fiction children's books at my library from when I was a kid. This was 1983-1986, and the books might have been a few years old. These were not long books - maybe 25-35 pages each. Hardcover, and several illustrations per book. I remember the title font being that very traditional "computer font" from the early 80's.  The stories concerned the multi-ethnic crew of a space station dealing with various sci-fi tropes, such as plague in space, loss of life-support, etc. I remember it as being kind of a cross between Star Trek and Space 1999. The tone was serious, not cartoony. I remember the space plague book because they thought the plague was smallpox, but then solved it by using an old library book to identify the symptoms as chicken pox. I remember them carrying the library book out of the archive in a special container so it wouldn't crumble to dust.  One other standout detail that might jog someone's memory: one of the crew members had a pet. It was a semi-intelligent pink blob, about the size of a small dog, that could change its shape. It had a small box attached to itself that it could use to communicate via ticker tape. In one story the blob stretched itself out into a rope to climb through a pipe to rescue someone or perform some vital task.


Can a third type of electrical charge exist?

Upon reading my book on physics, it mentions that there are only two discovered types of electric charges. I wonder if there could be a third type of elusive charge, and what type of effects could it have upon matter or similarly?


What is the difference between $* and $@?

Consider the following code:  foo () {     echo $* }  bar () {     echo $@ }  foo 1 2 3 4 bar 1 2 3 4   It outputs:     1 2 3 4       1 2 3 4   I am using Ksh88, but I am interested in other common shells as well. If you happen to know any particularity for specific shells, please do mention them.  I found the follwing in the Ksh man page on Solaris:     The meaning of $* and  $@  is   identical  when  not  quoted  or  when  used  as a parameter   assignment value or as a file name. However, when used as  a   command argument, $* is equivalent to ``$1d$2d...'', where d   is the first character of the IFS variable,  whereas  $@  is   equivalent  to  $1 $2 ....   I tried modifying the IFS variable, but it doesn't modify the output. Maybe I'm doing something wrong?


Why don't appear categories items in Ubuntu Software?

I recently installed the 20.04 LTS version of Ubuntu. Because all data present in the previous version has been erased and installed, I believe this issue is not a result of the previous data.  It worked normally in Ubuntu 18.04 and 19.10 versions.   Categories appear, but items contained in categories do not appear. And I can't find the search window.  Also, when I trying to     install software placed on the recommendation list, an error message     "Unable to install" occurs. This issue was also found in 18.04 and 19.10 versions.


How do I prevent apt-get from upgrading packages built from source with apt pinning?

I have a package installed (xcp-xapi) which is prone to a bug. The fix is very simple (only a couple of lines in the code) so what I do is the following:  apt-get source xcp-xapi   Then I find the source file to apply the fix and then I run again  apt-get -b source xcp-xapi   This will produce some .deb files that I install using  dpkg -i *.deb   Now the problem is that every time I try to run an apt-get upgrade, apt tries to fetch the packages from the repositories. I guess this can be fixed using pinning, but I cannot find the proper configuration to put in high priority the packages I compiled on my own.  So the question is how can I configure pinning to put the following already installed packages on higher priority than any existing in the repositories?  # apt-cache policy xcp-networkd xcp-v6d xcp-xapi xcp-xapi-debug xcp-networkd:   Installed: 1.3.2-5ubuntu0.1   Candidate: 1.3.2-5ubuntu0.1   Version table:      1.3.2-5ubuntu0.1 0         500 http://ftp.uninett.no/ubuntu/ precise-updates/universe amd64 Packages         500 http://security.ubuntu.com/ubuntu/ precise-security/universe amd64 Packages  *** 1.3.2-5ubuntu0.1 0         100 /var/lib/dpkg/status      1.3.2-5 0         500 http://ftp.uninett.no/ubuntu/ precise/universe amd64 Packages xcp-v6d:   Installed: 1.3.2-5ubuntu0.1   Candidate: 1.3.2-5ubuntu0.1   Version table:      1.3.2-5ubuntu0.1 0         500 http://ftp.uninett.no/ubuntu/ precise-updates/universe amd64 Packages         500 http://security.ubuntu.com/ubuntu/ precise-security/universe amd64 Packages  *** 1.3.2-5ubuntu0.1 0         100 /var/lib/dpkg/status      1.3.2-5 0         500 http://ftp.uninett.no/ubuntu/ precise/universe amd64 Packages xcp-xapi:   Installed: 1.3.2-5ubuntu0.1   Candidate: 1.3.2-5ubuntu0.1   Version table:      1.3.2-5ubuntu0.1 0         500 http://ftp.uninett.no/ubuntu/ precise-updates/universe amd64 Packages         500 http://security.ubuntu.com/ubuntu/ precise-security/universe amd64 Packages  *** 1.3.2-5ubuntu0.1 0         100 /var/lib/dpkg/status      1.3.2-5 0         500 http://ftp.uninett.no/ubuntu/ precise/universe amd64 Packages xcp-xapi-debug:   Installed: 1.3.2-5ubuntu0.1   Candidate: 1.3.2-5ubuntu0.1   Version table:      1.3.2-5ubuntu0.1 0         500 http://ftp.uninett.no/ubuntu/ precise-updates/universe amd64 Packages         500 http://security.ubuntu.com/ubuntu/ precise-security/universe amd64 Packages  *** 1.3.2-5ubuntu0.1 0         100 /var/lib/dpkg/status      1.3.2-5 0         500 http://ftp.uninett.no/ubuntu/ precise/universe amd64 Packages


Are Love Potions actually banned at Hogwarts?

Rita Skeeter's Witch Weekly article states that Love Potions are banned at Hogwarts.     Love Potions are of course banned at Hogwarts, and no doubt Albus Dumbledore will want to investigate these claims. In the meantime, Harry Potter's well-wishers must hope that, next time, he bestows his heart upon a worthier candidate.   (Goblet of Fire, Chapter 27, Padfoot Returns)   Obviously Skeeter has been known to print the odd untruth in her time. I wonder if this one of them. There certainly seem to be plenty of Love Potion-brewers and -users at Hogwarts:   Gilderoy Lockhart encourages students to ask Snape to brew a Love Potion for them. Molly Weasley brewed a Love Potion as a student. Romilda Vane repeatedly tries to dope Harry during Half-Blood Prince. Slughorn brews Amortentia, "the most powerful love potion in the world", in front of his sixth-year Potions class. The Weasley twins brew the "best range of love potions you'll find anywhere." These are banned by Filch along with the rest of the Weasleys' Wizard Wheezes products. Whether the Love Potions in that range were contraband on multiple counts is up for debate I think.   Pottermore only features  summary of the examples listed above. There's no JKR feature.  Are they actually banned? If so, why are they so commonly used with no disciplinary consequences? If not, why did Skeeter claim that they were as if it were obvious?  ( Note that I'm not asking about whether Love Potions were banned by the Ministry of Magic but whether they were banned at Hogwarts.)


I have 10 custom settings in my org . I need to fetch all and need to use in apex class


I've always never fully understood pointers. I'm writing this dinky blackjack game for fun on the side of my studies, and I need confirmation that this use of pointers is legitimate so I can fully understand what they do.  currently this is an example of the program and function i'm using:  void dealcard(int hand){     hand+=rand()%10+2;  }  int()main{    int playerHand;    ...    *blackjack stuff*    ...    if(hit){       deal(hand);         }   now if I'm correct, the above would not work as I intend because the function uses a copy of the variable that is cleared before it can be applied to the original, and hand would never be changed.  if I changed it to something like             int b;      int *hand;      hand=&b;   and changed the function declaration to include the *, then that would be correct.  I'm really trying hard to understand pointers and i'd appreciate any help or confirmation on this so I can understand the basic usefulness of them.


I honestly have no idea how to approach this question. I have done easier questions eg. show $gcd(a,b)lcm(a,b)=ab$ by letting $a=Alcm(a,b)$ and $b=Blcm(a,b)$ and then using the fact that $A$ and $B$ are coprime. However this approach only works in two variables. Any help with the question in the title would be greatly appreciated, as well as the thought process behind the answer so that I can approach similar problems.


Are international transfer zones typical around the world?

Most, if not all, European airports have international transfer zones, meaning that if you don't have to pass customs and immigration check of the country the airport is located in. On the other hand in US airports do not have international transfer zones. (Note that in case of Schengen zone countries "international" would mean out-of-Schengen).   How about rest of the world, which case is more typical?   Note: I'm not expecting full list of countries, just general indication what's the case in other regions.


My company is trying to improve the UX in our system. It's web based app, full with features.  The system development started 8 years ago, but it was never documented, and our programmers/support team can't remember every small thing about the features, that causes our clients who need support to wait while we dig into the source code to find things.  We want to document it, first for ourselves but later to publish some parts of it to our clients.  Since it's a big app, going through everything without a system/app could take forever and we probably won't be able to cover everything.   I was wondering if anyone knows about such system/app?  I need it to be easy to use for out support/sales teams and for the users but also efficient for the documenting process.


Variable Returns Are Blank Using Defined Function in Python

I am trying to have a user defined function that refers to a data set and groups costs by state. The function that I created pulls a list from a list of lists and runs it through the function. While the function works perfectly for the first state, the second time the function is run all of the variables return blank. The function is not adding the proper variables in which is leading to a divide by zero error in my code.  import csv Patient_File = open('Patient_Data.csv') reader = csv.reader(Patient_File)    State_Averages = [] States = [['Alabama','ALcost','AL'],['Alaska','akcost','AK']] def State_Data(State_list,State_Cost,Abbreviation):     State_list = []     State_Cost = []     for row in reader:         if Abbreviation in row[5]:             State_list.append(row)     for item in State_list:         State_Cost.append(item[9])     State_Cost = [elem.strip('$').replace(',','') for elem in State_Cost]     State_Cost=map(float,State_Cost)     #State_Average = sum(State_Cost)/len(State_Cost)     #State_Average = round(State_Average,2)     #State_Averages.append(State_Average)     print Abbreviation     print State_Cost     print State_list  State_Data(States[1][0],States[1][1],States[1][2]) State_Data(States[0][0],States[0][1],States[0][2]) #print State_Averages   The quoted out part of the code is what is causing the divide by zero error but the real core of the problem is the variables State_Cost and State_list are completely empty lists the second time the function is used.


Proving the exponential inequality: $x^y+y^x\gt1$

How can the following inequality be proven? $$x^y+y^x\gt1$$ for $(x\gt0,y\lt1)$


How to propagate uncertainty to $\tan(x)$?

As a lab assignment I have to replicate experiment with spring oscillations, and eventually calculate spring constant. The measurements I took are: spring displacement from equilibrium $x$, mass of weights $m$, and period $T$. And presumed uncertainties: $\Delta_\alpha(x)=1[mm]$, $\Delta_e(x)=2[mm]$,  $\Delta_\alpha(t)=0.1[s]$,  $\Delta_e(t)=1[s]$. Where $\alpha$ stands for uncertainty of used equipment, and $e$ is readings uncertainty made by me.  I calculated the standard uncertainty using this formula: $$\sqrt\frac{\Delta_\alpha(x)^2+\Delta_e(x)^2}{3}$$ Which produced $u(x)=1.29[mm]$. Then using the following substitutions:  $$F=kx$$ $$mg=kx$$ $$x=\frac{g}{k}m$$ I assert that:  $$tan(a)=\frac{g}{k}$$  Because in this part of experiment I plotted $x=f(m)$, using excel's linest, I get the slope $s$  $$tan(a)=\frac{g}{k}=s$$  Now, my question is, since I had uncertainty for $x$ introduced, and it is used to compute $tan(a)$, then the latter is affected and should have uncertainty of itself? How in this case should I go about propagating uncertainty to $tan(a)$?


What is the gnome on ubuntu 18.04 and 18.10 and where can I find it?

Which git can I find the gnome on ubuntu 18.04 and see the source code of the applications?


Suppose $p$ and $q$ are odd primes and $p = q + 4a$ for some $a$. Prove that $(\frac ap) = (\frac aq)$ holds.

This problem also had me prove that $(\frac pq) = (\frac aq)$, but I've already managed to do that. I've tried messing around with the Law of Quadratic Reciprocity but can't get anything. I've also tried using the first identity by proving that $(\frac pq) = (\frac ap)$, but again I've got nothing.


Getting the class name of an element that was clicked

I have a class in jQuery, I want to get the class of the element that has been clicked. (The element is in the same Class).  <!DOCTYPE html>   <title>Try jQuery 2.0.0 Online</title>

Superman

Hulk

Spiderman

Batman

      Heres a fiddle -


Prove with the mean value theorem that $x-\frac{x^2}{2} < \ln(1+x)$

Prove with the mean value theorem that $x-\frac{x^2}{2}<\ln(1+x)<x$ in $(0,\infty)$  Approach $f(x) := \ln(1+x) $ with the mean value theorem in $[0,x]$  $\frac{1}{1+\xi}= \frac{\ln(1+x)-0}{x-0}$  $\frac{1}{1+\xi}$ takes the biggest value when $\xi$ is $0$  and so $1 <\frac{\ln(1+x)}{x}$ multiply with x and you get $x<\ln(1+x)$  I can't prove the second part.


Please see following image,   Both the reputation refer to exact same question. But I see 2 rows, instead of them grouped together. Is it a bug? or am I missing something?  Edit:  I saw it again and it got grouped. :| So, Is there a lag in grouping logic?


Disk Partitioning while installing Ubuntu 12.04

I am an absolute beginner in Linux and I have problems with partitioning my disk space while installing Ubuntu 12.04. I have 300 GB of unallocated space on my hard disk. How can I divide the available space? My music collection is almost 170 GB and how can I make space for these music files (Like D: drive in Windows)


Does the 14 day self-isolation period in the UK end if a travel-corridor starts during the 14-day self-isolation period?

From 8th June there's been a  period for people entering the UK. From 10th July, travellers from  via a travel-corridor. If more countries are added to the list of exemptions then the date for each country will be later than the 10th July. If a traveller entered the UK from a country that is not on the exempt list and that country is added to the exempt list prior to the end of the 14 day self-isolation period does the self-isolation period end early? For example, if an individual entered the UK from France on the 5th July, should they remain in isolation for 14 days or does the isolation end on the 10th when France is added to the list of exempt countries?


User  answered the wonderful  question by mentioning the using keyword. Can you elaborate on that? What are the uses of using?


Please, I can't log into my Ubuntu account. I have tried logging in using the right password. But can gain access to my account.


i had used linux once when i was 8 back in 2001 and i used to love it as i played the games that came with the OS, then i left linux until recently since i have been hearing about all this new linux hype so i decided to give it a try.  I have used this OS since one semester now, It lives upto its hype and i am seriously in love with it and i had downloaded wine and have been playing games on it even tho all my games do not work "I'll remain patient and hope it soon becomes better"  Now the only Issue with the operating system is that the games i used to play was slower, then i went to settings and details and noticed that the laptop was using Intel instead of Nvidia GPU and optimus was not supported. I understand that there might be some devs here and experts so could any one write a tutorial for serious noobs it would help me and all the new people starting to use linux.  Also i wonder why ubuntu devs do not integrate Wine into the OS ?.  "Sorry for my english and also if i had asked a question that already had been answered as i didn't find any of them fit to work for my laptop, i bricked the OS multiple times"  P.S i also always get an error when i boot the OS and unity shows.


What is the sum of internal angles of a triangle around a black hole?

Around Earth spacetime is curved but what about space? It's still Euclidean around Earth but what about more massive bodies.  geometrically how different is space around a massive body.   NO COORDINATES.


Is plural-possessive needed before "organization"

I'm not sure which one is correct: "The Physical Therapist Organization" or "The Physical Therapists' Organization".  I'm leaning more towards without the plural-possessive but will I be grammatically wrong? Please don't respond with saying that I can use "Therapy" instead. I need to use the word "Therapist" or "Therapists'". Any help will be well appreciated.


How many "$1$" can be selected at most, provided that only one from each row and column of the attached matrix $A$ is selected?(That is, when one "$1$" is selected, no other element can be selected than the row and column where that "$1$" is located.)  Answer: I think $6$ can be chosen.  How can I give this answer in connection with graph theory? I think it has to do with the Latin Square(or Rectangle). But I can't connect and explain. Please help me. I thought a lot, but I could not establish the relationship completely. Thanks...


clean up value without rounding up or down

There is an input to my software for processing: float totalPurchased. I am coding with C++11/GCC/GDB/Linux.  The totalPurchase price informed is 14.92 as it is read from a file.  However, when the program runs, it shows 14.920001 out of no where. I don't want to  the value 14.92 to up 15.00 or down 14.00; the only thing I really need is to have the input right, without the compiler adding up things that does not exist as input.   The problem is that this 0.000001 is breaking a part the whole software calculation in the long run.  How to get rid of this 0.000001, and make sure that it appears the actual value that was read from the file into my float variable: 14.92?  All comments and suggestions are highly appreciated.


How do airports differentiate supplements from drugs?

I was just packing for an international flight, and realized that my little plastic bags of protein powder and creatine look an awful lot like the bags of cocain I see on tv. Does the airport have some way to identify drugs, or should I leave it at home?  I make my own mix of BCAAs creatine CLA etc. so I can't just bring it in the original packaging, it's all in carefully measured individual bags which look a lot like what I imagine a drug dealer might be carrying to sell, along with a bunch of vitamin pills.


Considering ditching windows 10 altogether..  But one of my main concerns is losing adobe acrobat.  What is the best free and paid pdf editors for ubuntu? Need to be able text. Also is there anything that can compete with photoshop?


Why do mesons like the J/Psi or Y exist? Shouldn't the quark/anti-quark pair annihilate?

q/qbar->photon is part of Drell Yan, so it's kinematically allowed. Is this somehow related to the difference in speed phenomenologically between a strong and a weak decay? As in is this annihilation what a strong decay means in this case?  Additionally, should a q/qbar pair necessarily be able to annihilate? If they form a color-anitcolor pair, they should be allowed to go to a photon, but otherwise, shouldn't they need to go into a gluon of the appropriate color preserving flavor? Should we expect q/qbar -> gluon to occur ~2x as frequently in proton-antiproton collisions due to this color preserving argument?


Periodic wifi network interuption : Realtek RTL8723be wifi adapter

This problem has occured to me many times before. I connect to my home wifi network and then i can browse pages and download stuff. But after sometime suddenly pages stop loading and downloads get interuppted. I updated to 16.04 lts but problem still persists. I searched this site for answers but it seems that this problem can occur due to multiple reasons and hence I cannot determine mine. Since i am a total newbie in using ubuntu I do not know how to exaclty present my problem. Any help in cornering up the problem and finding the solution would be a great help.   One more thing. The temporary thing which i can do now is to disconnect the wifi and then connect again. But the problem returns back within 10-15 min.


The news is shocking to me.   vs     The news is shocking for me.   and     For me, the cooking style is useless   vs     To me, the cooking style is useless.    I think these two sentences are exactly the same. Is there anyone who can help me to tell the difference?


I'm confused about the resistance of superconductors. It is known that the resistance at the the critical temperature goes exactly to zero (the resistance is not very small, its really zero, right?). But in a superconducting state, not all electrons form Cooper pairs right? so why then is the resistance exactly equal to zero? Greetings


Which SSL certificate would support external and internal domain names?

This is a school-network.  Official (outside reachable domain name) is  bgschwechat.ac.at (www.bgschwechat..., mail.bgschwechat... and ftp.bgschwechat..)  Internally the windows domain is named bgs.ac.at  We need (possibly cheap) SSL certificates for Webserver and Exchange-Server  From our firewall (www.bgschwechat.ac.at) (Sophos UTM9) requests get NATed to virtual machines - some of them need SSL   Webserver (running CENTOS - www.bgschwechat.ac.at) Exchange Server (named xch.bgs.ac.at) should be reachable via NAT as mail.bgschwechat.ac.at WSUS Server (dc2.bgs.ac.at) - only for internal clients   My question: What kind of SSL-Certificate would we need to secure eg. both domains (bgschwechat.ac.at AND bgs.ac.at) so that they appear secured from outside when NATTING for example mail.bgschwechat.ac.at to xch.bgs.ac.at ?  Or do we need to rename the interior domain to the official domain name?  ...recommandations where to purchase such certificate?


A year long Schengen visa but I have passed the three months maximum stay

I have been granted a Schengen visa for one year with the condition of staying a maximum of 90 days in Spain back in April, now, I have exceeded that period without calculating. I flew out of Spain for work but then returned, I got held in the airport because the police did calculate how long I stayed and did not allow me in.   I hold a Saudi passport and my visa is still valid until April next year, can I "refresh" my visa to enter Spain again? As I have another work trip before the date that I will be allowed to enter Spain again.


How to find the prime factorization of a very large number.

I want to know if there are any tricks or shortcuts to write the factorial of a large number, like $20!,$ as the product of its prime factors.  For example, $5!= 5 \times 3 \times 2^3$


Is there a way to edit files on a Linux ext partition in Windows?

Many times one wants to edit files on a Linux ext partition from Windows. Is there a way to view and edit files in Linux partitions in Windows 7 or 8?


Why is light, that was emitted right at the big bang (same time/place), arriving to us at different times

I understand the big bang to have (at least mathematically) started our universe at a virtually precise moment and within a virtually infinitesimal volume. Yet some of the light from that moment/volume reached us in the distant past, some is reaching us now, and more will reach us in the distant future (expanding particle horizon).   That seems strange to me.   I am thinking that maybe the big bang really is sort of the limiting case of the event horizon approaching $0$ distance from us. That is, if time began at the big bang ($t=0$ at the moment of the big bang), then at any $t>0$, there is a finite event horizon (albeit very tiny for $t \approx 0$) and, if object A is closer to it than object B, then object A's light will reach us later than object B (and object A will reach the particle horizon later than object B). But, at $t=0$, the actual big bang, I think all this breaks down. However, perhaps we can talk about  how and when we receive light emitted as $ t \to 0$, and interpret light "emitted at the big bang" in that way?    Or maybe there is some kind of quantum uncertainty regarding the moment of the big bang, so that the event horizon was never (with no uncertainty) exactly $0$ distance from us? Then, at $t=0$, we have a non-trivially uncertain event horizon.   In any case, talking about "light emitted at (or during, if you prefer) the big bang" sounds problematic.


How to deal with a figure that is really a table?

I have a table already set as a PDF, and I need to include it, so the question is: how do I include it as a figure, but call it a table? I'd also like to move it from the list of figures to the list of tables.


How to prove for $x>0$, $\dfrac{x}{1+x^2}<\arctan x<x$?   I started with saying $0<\arctan x<\frac{\pi}{2}$  when $x>0$  I'm just not sure how to proceed with this proof, it works when I take random  values but I cant see how to prove that it works for any $x$.


How do I replace a text file using regex package in python?

I am finding patterns within a large text file, then I remove the patterns, and print the text. But, I am trying to replace the old text within the file (with the patterns) with the new_text without the patterns.   Im using the regex package, and no matter what i try it doesnt work   My command .replace is not working.   import re  rgx_list = ['Read More',             'Read',             'And follow us on Twitter to keep up with the latest news and and acute and primary Care.',...]  txt_path = '/Users/sofia/Documents/src/fakenews1/data/news-data/war_sc_r.txt'  with open(txt_path) as new_txt_file:     new_text = new_txt_file.read()  for rgx_match in rgx_list:         new_text = re.sub(rgx_match, '', new_text)  new_text.replace(txt_path, new_text)  print(new_text)   Thank you !


I have huge file 100M, that has the text (few lines below,) stack of lines are unique scaffold1_, scaffold2_ and on.   I would like to have a new file that is specific to each scaffold.1...txt tried few sed and grep commands but they didn't help.  scaffold1_2,C,C,C,C,N,C,N,C,G,G,C,N,C,C,G,N,N,C,G,N,C,C,C,G,C,N,N,C,C scaffold1_113,T,T,T,T,T,T,T,T,T,C,T,T,T,T,T,T,C,T,T,T,T,T,C,T,T,N,T,T,T scaffold1_149,G,G,G,G,C,G,C,G,C,G,G,C,C,G,C,C,G,C,G,G,C,G,G,G,G,C,G,G,G scaffold1_160,G,G,G,T,G,T,T,T,N,T,T,T,G,T,G,G,T,T,T,T,T,N,T,T,G,G,T,T,G scaffold2_315,C,C,C,G,C,C,C,C,C,C,C,G,C,C,G,G,G,C,C,C,C,C,C,G,C,C,C,C,G scaffold2_318,G,A,A,A,A,A,A,G,A,A,A,A,A,A,A,A,A,A,G,A,A,A,A,A,A,A,A,A,A scaffold2_323,T,T,T,T,T,C,C,T,T,T,T,T,T,T,T,T,T,T,T,C,T,T,T,T,T,T,T,T,T scaffold2_397,A,A,A,A,A,A,C,A,A,A,A,A,A,A,A,A,C,A,A,A,A,A,A,A,A,A,A,A,A scaffold3_402,C,C,C,C,C,T,C,C,C,C,C,C,C,T,C,C,C,T,C,C,C,C,C,C,C,C,C,C,C scaffold3_465,G,G,G,G,G,G,G,G,G,C,G,G,G,G,G,G,G,G,G,G,G,G,G,G,G,G,C,C,G scaffold3_502,C,C,C,C,C,C,C,C,C,G,C,C,C,C,C,C,C,G,C,G,C,G,C,C,C,C,C,C,C scaffold3_508,G,G,G,C,G,G,G,G,G,C,G,C,C,C,C,C,G,C,G,C,G,C,C,C,C,C,C,C,C scaffold3_533,G,G,G,G,A,A,A,G,A,G,A,G,G,A,G,G,A,A,G,A,A,G,G,G,G,G,G,G,G scaffold4_555,T,T,T,T,T,T,T,T,T,T,T,T,T,T,A,A,T,T,T,T,T,T,T,T,T,T,T,T,T scaffold4_586,T,T,T,T,T,T,T,T,T,T,T,C,C,T,T,T,T,T,T,T,T,T,C,T,C,T,T,T,T scaffold4_593,A,G,G,G,A,A,A,A,G,G,A,A,A,A,G,G,A,A,G,A,G,G,A,G,A,G,A,A,G scaffold4_598,C,C,C,C,C,C,C,C,C,C,C,C,C,C,C,C,C,C,C,C,C,C,C,C,C,C,A,A,C scaffold4_664,G,A,A,G,G,G,A,G,G,G,G,G,G,G,G,G,A,G,G,G,G,G,G,G,G,G,G,G,G scaffold5_667,C,C,C,C,C,C,C,C,T,C,C,C,C,C,C,C,C,C,T,C,T,T,C,C,C,C,T,T,C scaffold5_670,A,A,A,A,A,A,A,A,G,A,A,A,A,A,A,A,A,A,G,A,G,G,A,A,A,A,G,G,A scaffold5_679,T,C,C,C,C,C,C,T,C,T,C,C,C,C,C,C,C,C,C,C,C,C,C,C,C,C,C,C,C   resulting files should look something like  cat scaffold1.txt  scaffold1_2,C,C,C,C,N,C,N,C,G,G,C,N,C,C,G,N,N,C,G,N,C,C,C,G,C,N,N,C,C scaffold1_113,T,T,T,T,T,T,T,T,T,C,T,T,T,T,T,T,C,T,T,T,T,T,C,T,T,N,T,T,T scaffold1_149,G,G,G,G,C,G,C,G,C,G,G,C,C,G,C,C,G,C,G,G,C,G,G,G,G,C,G,G,G scaffold1_160,G,G,G,T,G,T,T,T,N,T,T,T,G,T,G,G,T,T,T,T,T,N,T,T,G,G,T,T,G   cat scaffold2.txt  scaffold2_315,C,C,C,G,C,C,C,C,C,C,C,G,C,C,G,G,G,C,C,C,C,C,C,G,C,C,C,C,G scaffold2_318,G,A,A,A,A,A,A,G,A,A,A,A,A,A,A,A,A,A,G,A,A,A,A,A,A,A,A,A,A scaffold2_323,T,T,T,T,T,C,C,T,T,T,T,T,T,T,T,T,T,T,T,C,T,T,T,T,T,T,T,T,T scaffold2_397,A,A,A,A,A,A,C,A,A,A,A,A,A,A,A,A,C,A,A,A,A,A,A,A,A,A,A,A,A


Express in gamma/beta functions $\int_{0}^{\pi/2}\tan^n x \ dx$

Express in gamma/beta functions and find n's that intergral converges.  $\int_{0}^{\pi/2}\tan^n x \ dx$  i am stuck a little bit


Linux shell script: Run a program only if it exists, ignore it if it does not exist

I am programming a Linux shell script that will print status banners during its execution only if the proper tool, say figlet, is installed (this is: reachable on system path).    Example:  #!/usr/bin/env bash echo "foo" figlet "Starting" echo "moo" figlet "Working" echo "foo moo" figlet "Finished"   I would like for my script to work without errors even when figlet is not installed.    What could be a practical method?


Is use of function return values for error checking and/or exception handling good and proper technique?

I've inherited a C system which makes use of function return values to check for errors and exceptions; something like this:  #define OK 1  int create_cheese(const char * myType, float myCost, char * myCheese) {    // Do Stuff...     if // everything looks good        return 1;    else        return // error/exception code }  int main() {     rc = create_cheese("cheddar", 12.99, &cheese);     if (rc != OK) { exit(rc); }      return 1; }   Is this considered proper C technique?  These functions are not very, well, functional. In other words, they don't use the function return values as meaningful data relevant to program execution; they're used for error and exception handling. Thank you, Keith :^)


My JQUERY can't see echo PHP.  Here is the php statement that I echo in an external PHP file -   `echo ("<a href='#' id='bb'>hello</a>");   Here is the JQUERY also in an external js file -   $('a').click(function() {     var linkId;     linkId = $(this).attr('id');     alert(linkId);`   And finally I have an HTML file with a <div> that my php is being sent to via ajax. Now my php echo statement above shows in the HTML file, but when I click it the JQUERY      doesn't see it. I tested it by adding an anchor tag in the html file and it works fine. Any help would be appreciated. Thanksenter code here


Fantasy novel where the character had to collect pendants

I remember reading a fantasy novel as a teen, so it would have been a young-adult novel. In it the main character had to collect pendants to ward off an evil.   I remember him getting the first pendant early, and it had a cross type shape on it. I think perhaps a wizard granted him the first pendant so that the character would have the power to find the others. I don't think the character was granted any special powers, other than specific protection from an evil force.   I recall ravens and "cold" being themes... maybe a change in temperature and ravens signaled an imminent attack?


How to become a professional photographer

I have a great passion for photography. I own a normal Canon digital camera of 10 megapixel. I would like to learn more about the various techniques, tips for taking great pictures so that I an enthusiast currently can become a professional someday. Please let me know how this can be achieved.


Draw dimension of a line as a decoration in TikZ

Is it possible to define in TikZ a new decoration or something like that, such that it is possible to write something like:  \draw[dim={text,above}] (A) -- (B); \draw[dim={text,below}] (C) -- (D);   or even better  \draw (A) dim[text,above] (B); \draw (C) dim[text,below] (C);   to get something like this:    It's important that the text is sloped.  If possible I would prefer the second syntax, because then I could easily combine such path's:  \draw (A) dim[text,above] (B) -- (C) -- (D) dim[text] (E) dim[text,below] (F) -- circle;


Generate a command block with variable data

I'm trying to setblock a command block with variable data in it. I want to make a variable sized array with an armor stand, and read a custom tag at a variable position. This position should be stored in a scoreboard as well.    Further information:     Minecraft version 1.13.2   Singleplayer mode   I've already tried this command:    /setblock ~ ~2 ~ minecraft:command_block{Command:{"text":"execute store result score posN replay run data get entity highfrequent Pos["},{"score":{"name":"#this","objective":"replay"}},{"text":"]"}} replace   But it doesn't work. It couldn't place the block, and I think I did something wrong with the JSON syntax.    My objective is to have an array which I can read at a variable position.  If anybody has an idea of how to do this, I would be glad to hear it.


Lebesgue-measurable sets requiring the Axiom of Choice to construct

Every known construction of the  relies on the Axiom of Choice. It happens to not be Lebesgue-measurable.     Must every set whose construction relies on the Axiom of Choice not   be Lebesgue-measurable?   I'm not sure if "relies on the Axiom of Choice" is mathematically meaningful, in which case I'll rephrase the question as asking whether there are any sets for which there is an existence proof with AC but no known existence proof without AC, which are known to be Lebesgue-measurable.  This  asks whether there exists a Lebesgue non-measurable set that can be constructed without AC. The answer to that question is no.


Instantly detect client disconnection from server socket

How can I detect that a client has disconnected from my server?  I have the following code in my AcceptCallBack method  static Socket handler = null; public static void AcceptCallback(IAsyncResult ar) {   //Accept incoming connection   Socket listener = (Socket)ar.AsyncState;   handler = listener.EndAccept(ar); }   I need to find a way to discover as soon as possible that the client has disconnected from the handler Socket.  I've tried:   handler.Available; handler.Send(new byte[1], 0, SocketFlags.None); handler.Receive(new byte[1], 0, SocketFlags.None);   The above approaches work when you are connecting to a server and want to detect when the server disconnects but they do not work when you are the server and want to detect client disconnection.  Any help will be appreciated.


I'm trying to find the sum of :   $$\sum_{i=1}^n\frac i {2^i}$$  I've tried to run $i$ from $1$ to $∞$ , and found that the sum is $2$ , i.e :   $$\sum_{i=1}^\infty\frac i {2^i} =2$$  since :  $$(1/2 + 1/4 + 1/8 + \cdots) + (1/4 + 1/8 + 1/16 +\cdots) + (1/8 + 1/16 + \cdots) +\cdots = 1+ 1/2 + 1/4 + 1/8 + \cdots = 2 $$  But when I run $i$ to $n$ , it's a little bit different , can anyone please explain ?   Regards


Insert multiple rows into a table with only an IDENTITY column

I have a table called dbo.Groups defined like this:  CREATE TABLE dbo.Groups (   GroupID int NOT NULL IDENTITY (1,1) PRIMARY KEY );   The table really consists of just the one IDENTITY column.  Sometimes I want to insert into it multiple rows at once and get the generated IDs. (I already have a pre-defined table variable called @output with a single ID column to be used in the OUTPUT clause.)  Now I know how I would proceed if it was a single row:  INSERT INTO   dbo.GroupID OUTPUT   inserted.GroupID INTO @output (ID) DEFAULT VALUES ;   But I want to be able to insert two or more in one go. The actual number is determined by the number of rows returned by this query:  SELECT   * FROM   dbo.MySource ;   So if the query returns one row, I want to insert one row into dbo.Groups and return the generated GroupID. If it is a hundred rows, then I would expect a hundred rows inserted and a hundred IDs generated and returned at once.  One obvious method is to insert one row at a time in a loop. I would like to avoid that and use a set-based approach instead, something along the lines of  INSERT INTO   dbo.GroupID OUTPUT   inserted.GroupID INTO @output (ID) SELECT   ...  -- what? FROM   dbo.MySource ;   Is there a way to insert multiple rows into a table with just an IDENTITY column in (preferably) a single statement?


In Edit Mode, is it possible to invert selection?

I wish to select areas of a mesh, but it would be much simpler to just select the ones I don't want selected (because they are easier to access), and then inverse the selection.  Is this possible?


I'm an engineer who recently became a member of a county Grand Jury in California.  For those who don't know what that means, it's a body of 19 people who - for a year - have the responsibility to investigate various aspects of the county and the cities and special districts, etc., in the county.  The object of an investigation is to create a report containing research, findings, recommendations and such which is then provided to the entity or entities mentioned in the report who then must respond.  The set of all reports during the year is then included in the full report of the Grand Jury. OK, that's the background.  In reading past reports (which are online) I have found pretty much all of them to be profoundly uninteresting as far as layout and design are concerned.  What I expect has occurred in the past is some juror starts using Microsoft Word pretty much straight out of the box with no eye towards the niceties of layout and design - probably due to not having any background (or, in my case, talent) for layout and design. I do, however, understand the need of separating layout and design from content - something Microsoft Word doesn't do well.  I admit I have no particular skill at graphic design but would still like to produce a product at the end of our service which not only has properly formatted citations, an index, good typography and excellent content, but which also looks good.  Can anyone offer advice as to where I might find help along these lines?  That is, is there (for example) a Graphic Design class that might wish to give us a design (and get it published by the County) that I can use?  I don't know that I have any actual budget for this but someone might want to do it for the publicity. Is there a significant possibility that I might succeed in getting some help?


Short story about humans marooned on high gravity planet

I'm trying to find a short story that I read years ago.  There were a group of humans marooned on a high gravity planet by an alien species.  On the planet they encountered saber-tooth cat-type animals that they eventually became allies with. There were also telepathic squirrel-like creatures that allowed them to communicate over distance.  The aliens that marooned them returned generations later, but the high gravity and hardships of the planet made the offspring of the original humans become superior warriors, which allowed them to destroy the aliens.


Can I have multiple background images using CSS?

Is it possible to have two background images?  For instance, I'd like to have one image repeat across the top (repeat-x), and another repeat across the entire page (repeat), where the one across the entire page is behind the one which repeats across the top.  I've found that I can achieve the desired effect for two background images by setting the background of html and body:  html {     background: url(images/bg.png); }  body {     background: url(images/bgtop.png) repeat-x; }   Is this "good" CSS?  Is there a better method?  And what if I wanted three or more background images?


Remove a specific extension from all the files in a directory

I have a couple of files with ".old" extension. How can I remove the ".old" extension without remove the file?    I can do it manually but with more work:    mv file1.key.old file1.key mv file2.pub.old file2.pub mv file3.jpg.old file3.jpg mv file4.jpg.old file4.jpg  (etc...)   The command will work with other extensions too?  example:    mv file1.MOV.mov file1.MOV mv file2.MOV.mov file2.MOV mv file3.MOV.mov file3.MOV  (etc...)   or better:    mv file1.MOV.mov file1.mov mv file2.MOV.mov file2.mov mv file3.MOV.mov file3.mov  (etc...)


Modern Firefox Extension Which Allows Text Editing With Vim Keybinds?

I would like to be able to edit text fields in Firefox with the vim keybinds.    I searched for addons in   but all the provided solutions did not work with the most recent version of firefox.  A popular recommendation was an extension named . I ran into issues using this addon due to all the links to this addon being broken.   Another recommendation was . However a note on the website indicates that newer versions of firefox are no longer compatible with this version.    Similar issues were encountered with .    Another popular recommendation was , unfortunately the author of this extension had to stop maintaining it for work reasons.    pentadactyl was also recommended, however  was dead.


Comma after or before "parenthetic" and?

After showing me the house, Nana led us to the living room, and with Mongai's Take Me Somewhere Nice playing on in the background, we started on the Scotch we'd bought at the 7-Eleven. The dim light and the soft   Is the comma correctly positioned before the italics in the example above? Or I should place the comma after and?


Installing Vbox Guest Additions in Ubuntu Server

I am running Ubuntu Server in a Windows 8 host. When I click the "Devices>>Insert Guest Additions CD image", I am greeted with a prompt that says:  "Unable to insert the virtual optical disk : Would you like to try to force insertion of the disk?"  What should I do with this? Should I "Force Mount" or "Cancel"?


"Wow, what a car!" - Is it okay if I say 'Wow, what the car!"

I have been struggling with articles for quite a long time. Most of the times, I understand but then the more I understand them, the more it's getting perplexed!   For this particular question, I'm keeping in mind that the definite article 'the' is used for the one and only, a unique thing. Known to both - the listener and the speaker. If I say there was a table, it means there was some table but then if you and me are standing in a hall and we see a table, I won't use an indefinite article. There, it's Do you see the table? Quite clear.   Let's extend this further...  You and me are standing on a footpath. And we see a sexy Bentley...     "Wow, what a car!" is generally what we hear. But...   why not the? I'm talking about that Bentley only --that particular car, in front of us (like the table).   And to argue, I'm not talking about the same model by German Volkswagen AG (or else 'a car' is justified!) because it has a beautiful sticker of Spiderman on it. Volkswagen does not make it that way!   Same case with...     "What the beautiful pair of legs!" - She's right in front of me!   "What the movie it is! Awesome!" - Telling someone in the interval.   Though I'm asking this question, What a beautiful... and What a movie... seems correct.   Ah, I am trying to come up with What the [countable noun]... examples but finding it difficult. Is it that weird?


Is there a review process for rejected suggested edits?

I edited the only answer to a question I asked, and the edit was rejected.       It seems like a very fair edit to me. The guy has the right answer in there, and should get credit for it, but to find the right answer, you have to dig to the bottom.   He also answers several questions I did not ask when I specifically stated in my question I did not ask. This leads to confusion for folks finding this question later.   I tried to clarify by moving the correct portion of his answer to the top and marking the rest as "Background Information". The diff tool makes it seem like a lot has changed, but it's mainly moving the answer to the top. I wonder if the rejection was from a quick glance instead of an actual read.  I want to accept his answer, but can't in its current form, as it muddies the waters around GPS to UTC leap seconds vs Unix epoch to GPS epoch.  Is there a rejection review process?


If magnetic force do no work at all then how do magnets attract or repel each other?


Just bought an used xs specialized sirrus sport in great condition. I am 5'8 and just realized that is too small. Just wondering if there anything that I could to do to make it fit me? Got it today so I haven't try anything yet


Well vs good........proper vs conversational

Proper answer friendly greeting, "How are you?" I am "well" or I am "good"  "I am well" sounds like I'm saying I'm not sick. "I'm good," or "good" accompanied by a friendly nod sounds much better.


How do we prove that $$1+\frac{2^3}{2!}+\frac{3^3}{3!}+\frac{4^3}{4!}+\cdots=5e$$ I'll post the answer to this question as a knowledge share.


In Ubuntu Software there are duplicates listed for some applications like: Calendar; GNOME Software; ImageMagick; Online Accounts; Software & Updates; UXTerm/XTerm.  I believe they should not be listed twice as most other applications aren't.  My system is a fresh install of Ubuntu 17.04. Is there a good reason for this issue with Ubuntu and does anyone else encounter it?


Astronaut can't stop counting things. Terrible consequences

Here are things that you may need to know:   I first read this in an anthology which was used for a college class ca. 1995. I remember that the cover was a picture of a starscape; nothing fancy, just a background of black with white stars.  And the anthology title, too, was on there, I'm sure.  This anthology also had the story of "In the land of the blind, the one eyed man is king". Aldous Huxley?     The plot goes something like this:  A spaceman from Earth (astronaut) experiences a collision and needs to make repairs.  But he's by himself (it is a "he"), and he needs to time things. To do this, he starts counting in seconds and then does quick math to determine different timers.  Then he needs to keep counting to track numerous things, like objects, processes, and time.  He gets to a point where he realizes after a while that he can't stop counting.  It's automatic and unending.  The story goes on to describe the consequences, good and bad (and terrible) of his ability to do this.   Anybody remember anything like this? Thanks for your time.   Edit 1:  The story I read was in English.   Edit 2:  I do not know the original publication date.  No clue actually, other than before 1995.  Edit 3:  I do not recall anything about the author's name or gender.  Sorry.  Edit 4:  Trying to recall, but I remember that the astronaut returns to Earth and talks with a person from the ground crew involved in the mission; the Director, maybe.  And I think it is the same person that talked to the protagonist right after the collision at the beginning of the story.


How to find the smallest number with just $0$ and $1$ which is divided by a given number?

Every positive integer divide some number whose representation (base $10$) contains only zeroes and ones. One can easily prove that using pigeonhole principle.  Some examples: 2 -> 10 3 -> 111 4 -> 100 ...   But how to find the smallest answer? Is there any way to find it efficiently?


Linear congruence $8x\equiv 21\pmod{24}$

$8x\equiv 21\pmod{24}$  I am having problem solving this linear congruence because 8 is even and 21 is odd.


How to determine how many times an area was burnt?

In arcgis I want to find from various forests fires shp files how many times parts of a particular forest were burnt during the last 70 years. Is there a way to count overlapping polygons?


ArcPy saveACopy method saving copy of MXD to wrong path?

I have a script that looks through datasets in a geodatabase and copies a mxd document to a folder. The programs works, however it is saving the map documents to my desktop and not the specified folder on my desktop (PATH2). This is the code I have so far:  import arcpy import os PATH1 = r"C:\Users\Daimon Nurse\Desktop\DFMPROJECT\DFM.gdb" PATH2 = r"C:\Users\Daimon Nurse\Desktop\DFMPROJECT\" arcpy.env.workspace = PATH1 arcpy.env.overwriteOutput=True  zones = arcpy.ListDatasets("Zone*")  for zone in zones:     mxd = arcpy.mapping.MapDocument(r"C:\Users\Daimon Nurse\Desktop\DFMPROJECT\Complete Final Capstone Map\Complete Z2 Campus Map_Landscape1.mxd")     print zone     mxd.saveACopy(PATH2 + zone)


Covariance between sum of iid random variables and sum of indicator functions

The question is-     Let $X_1,X_2,..,X_n$ be iid random variables from a continuous distribution whose density is symmetric about $0$. Suppose $\mathbb{E}(|X_1|)=2$ and define $Y=\sum_{i=1}^{n}X_i$ and $Z=\sum_{i=1}^{n}I(X_i>0)$. Then calculate covariance between $Y$ and $Z$.   My attempt:  $E(X_i)=0$ for all $i=1(1)n$ because $X$ is symmetric about $0$ and $E(|X|) $ exists.   Now,  $Cov (Y,Z)=E(YZ)-E(Y)E(Z)$ $=E(YZ)-0$ $=E[(\sum_{i=1}^{n}X_i)(\sum_{i=1}^{n}I(X_i>0)]$  $=(\sum_{i=1}^{n}E[(X_i.I(X_i>0))]$ $+\sum\sum_{i \neq j}E(X_i)E(I(X_j>0)$ as $X_i,X_j$ are independent.   $=\sum_{i=1}^{n}E[(X_i.I(X_i>0)] +0 $ as $E(X_i)=0$  $ =\sum_{i=1}^{n}\{E[X_i.I(X_i>0)|I(X_i>0)=1]×1/2] + E[X_i.I(X_i>0)|I(X_i>0)=0]×1/2]\}$  $=\sum_{i=1}^{n}E[X_i.I(X_i>0)|I(X_i>0)=1]×1/2] +0$  $=\sum_{i=1}^{n}E[X_i|X_i>0]×1/2]$  $=2n×(1/2)$ $=n$  Is my reasoning correct ? Thanks in advance!


oracle SQL subquery: using the minimum but getting all columns

MIN(A.price)  CustomerID     TripID travelby                                      25  x05               66 train                                  66  x07               21 train                                 100  x07               12 train   Trying to figure this one out. the above results is from a query of 2 tables. However, I need to modify it so that it gives me the result of min price with all of its 4 columns.  this was my original sql:  (select min(price) from trips a, customers b where a.tripid = b.tripid and c.travelmode = 'train')  I can only get the row with 25, but that is only if i request the price column. How would you go about this, but get all columns? Thank you for all input


I'm learning about iterative methods to solve the system $Au = f$, and I came across the following in my book:     To construct an iterative scheme, we assume that a non-singular matrix $M$ exists and define the matrix $N$ as $N = M - A$. We can then write $$A = M - N$$ The linear system $Au = f$ can then be written as $Mu = Nu + f$. By multiplying to the left and right with $M^{-1}$ we can define an iterative scheme $$\begin{split}u^{k+1} &= M^{-1}Nu^k + M^{-1}f\\&=M^{-1}(M-A)u^k + M^{-1}f\\&=u^k + M^{-1}(f - Au^k)\\&=u^k + M^{-1}r^k\end{split}$$   Question: This all makes a lot of sense to me, except for one thing; why is it allowed to write $u^{k+1} = M^{-1}Nu^k + M^{-1}f$ with the superscripts $k+1$ and $k$ over $u$? The construction of an iterative method goes from $Mu = Nu + f$ to $u^{k+1} = M^{-1}Nu^k + M^{-1}f$ and I don't understand how.  Thanks in advance!


When stumbling across a great answer, it would be vastly nicer to be able to bookmark it than have to do a screen capture.   Otherwise: Kudos to the developers of the iOS app. It may say alpha, but it's solid, smooth, and a joy to use!


retrieving special characters from mysql database, php

I've inserted some data to a mysql database. Set up the utf-8 cz. And it looks fine.   But when I echo a row from the table, special characters are not shown. Meta utf-8 included.   Any ideas how to fix it? Thank you


Exists intel graphics for ubuntu 15.10? If not, when is the launch date?


Is Fantastic Beasts a self supporting story?

I was thinking of watching Fantastic Beasts and Where to Find Them but have so far avoided watching any of the Harry Potter series (mostly because I don't want to see them until I can get access to the entire series - to watch in chronological order).  Is enjoyment of Fantastic Beasts dependant on knowing details of the Harry Potter universe?  Note: from seeing various bits around here & the larger internet / real world I am familiar with some of the most basic parts of the HP universe, but only a small amount & at a very basic level (you'd have to be living under a rock not to have taken in some HP lore). Familiar with the existence of Hogwarts, Horcruxes, Quidditch ..  (Yes, I am aware that FB&WtFT is set before HP, but just want to check.)


We write when we need to remember something, be it an idea, a quote or the outcome of a study.  In the second clause, the beginning is be. What is the grammatical rule behind it?


lately it has been very irritating for me because I almost have a fully functioning site about to be launched. This may not seem like a problem, however my web host is running an old version of PHP so I cannot use MySqli_* or PDO, so I am stuck with the deprecated version (MySql_). A user here on S.O has told me that it is IMPOSSIBLE to prevent sql injection attacks whilst running MySql_.   Question: Is it impossible to secure my website from sql injection whilst using MySql_*?


Show that $x_n \rightarrow x \Rightarrow (1+\frac{x_n}{n})^n \rightarrow e^x$

My approach so far:   Using  I'm expressing the above limit as $((1+\frac{1}{\frac{n}{x_n}})^\frac{n}{x_n})^{x_n}$ and then using the property (?) that if $x_n \rightarrow x$ and $a_n \rightarrow a$, then $x^{a_n}_n \rightarrow x^{a}$. But I'm proving this last property by taking log on both sides (suppose $a,x > 0$). My question is isn't that somehow using the property I'm required to prove and hence is this valid?


Workaround for exceeding governor limits using COUNT_DISTINCT in Batch Apex Class?

So I have the following query that I am running through Batch Apex. I get the error:  System.LimitException: Too many query rows: 50001  I am receiving this because COUNT_DISTINCT() is subject to the same governor limits as other SOQL Queries. Basically I cannot think of a solution here, which is why I am posting this. The goal of the query is to see how many unique accounts an SDR is in contact with over a given time period. In this case, it is over a 120 day period. Would love some advice on how to achieve this.  String Contacts_Reached_TR_120_Query = 'SELECT Ownerid SDR_ID, COUNT_DISTINCT( whoid ) result FROM Task Where ActivityDate = LAST_N_DAYS:120 AND OwnerId in :ListOfIDs GROUP BY Ownerid';  DynamicBatchApexAR batch3_TR120      =   new DynamicBatchApexAR('SDR_ID', 'result', 'Contacts_Reached_TR_120__c', Contacts_Reached_TR_120_Query, SDR_IDs);   Then here is the batch class  global class DynamicBatchApexAR implements Database.Batchable<AggregateResult> {  public String sObjectIdKey; public String sObjectResultKey; public String sObjectFieldToUpdate; public String query; public List<Id> ListOfIDs;   global DynamicBatchApexAR(String arIdKey, String arResultKey, String fieldToUpdate, String soqlQuery, List<Id> whereInClause )  {       sObjectIdKey            = arIdKey;     sObjectResultKey        = arResultKey;     sObjectFieldToUpdate    = fieldToUpdate;     query                   = soqlQuery;     ListOfIDs               = whereInClause; }  global DynamicBatchApexAR(String arIdKey, String arResultKey, String fieldToUpdate, String soqlQuery )  {       sObjectIdKey            = arIdKey;     sObjectResultKey        = arResultKey;     sObjectFieldToUpdate    = fieldToUpdate;     query                   = soqlQuery; }  global Iterable<AggregateResult> start(Database.BatchableContext BC)  {     return ListOfIDs == null ? new BulkIterable(query) : new BulkIterable(query, ListOfIDs); }  global void execute(Database.BatchableContext BC, List<sObject> scope)  {     DynamicSObjectUpdater sObjectUpdater = new DynamicSObjectUpdater();      for(sObject sObj: scope)     {          AggregateResult ar      = (AggregateResult)sObj;         ID sObjectId            = (ID)ar.get(sObjectIdKey);         Decimal arResult        = (Decimal)ar.get(sObjectResultKey);         Map<String, Object> sObjectFieldsToUpdate = new Map<String, Object>{             sObjectFieldToUpdate => arResult         };          sObjectUpdater.getUpdateSObject(sObjectId, sObjectFieldsToUpdate);     }      sObjectUpdater.updateSObjects();   } global void finish(Database.BatchableContext BC)  {  }   }  Here is the iterable    global with sharing class BulkIterable implements Iterable<AggregateResult> {         String query;         List<Id>   ListOfIDs;      global BulkIterable(String soql, List<Id> WhereInClause)     {         query = soql;         ListOfIDs = WhereInClause;     }      global BulkIterable(String soql)     {         query = soql;     }      global Iterator<AggregateResult> Iterator(){         return ListOfIDs == null ? new BulkIterator(query) :  new BulkIterator(query, ListOfIDs);     }  }   Here is the iterator      global class BulkIterator implements Iterator<AggregateResult> {        AggregateResult[] results { get;set; }       Integer index { get;set; }   List<Id> ListOfIDs;      global BulkIterator(String query, List<Id> WhereInClause)      {     index = 0;     ListOfIDs = WhereInClause;     results = Database.query(query);        }    global BulkIterator(String query) {     index = 0;     results = Database.query(query);      }    global Boolean hasNext(){     return results != null && !results.isEmpty() && index < results.size();    }        global AggregateResult next() {      return results[index++];   }      }   Is the error because I am running too many batches?


Blender glitches and a cube show up inside the cube model and shows no materials plus it doesn't render anything

Blender doesn't show materials and it has a model inside model effect thingy. Solid view works fine materials view doesn't show materials and rendered view shows this glitch effect thing (in EEVEE, in Cycles rendered view works fine but in materials view the cube is again blank). Today i installed 2.91 and it still occurs. Any ideas on how to fix it? Screenshot in rendered view:  Screenshot of when i scroll to zoom:  Screenshot when i rotate view:  Also screenshot of render in Eevee:


I was going through the chapter of  "Newton's Laws of Motion", where I was introduced to the concept of inertia in Newton's First Law. I saw that all objects that have mass  will have inertia. But I do not really get it. What is the reason behind objects having inertia? And why is it that only those objects that have mass have inertia? I tried researching on the matter a bit, but until now I have not found any satisfactory answer.


Using intersect method of ItopologicalOperator gives error 0x80040239?

I would like to intersect a polygon and a polyline to know if the polyline is in the polygon.  The code works but when i do it on more than 100 000 times in a for, there is this error :  System.Runtime.InteropServices.COMException (0x80040239): Exception de HRESULT : 0x80040239     à ESRI.ArcGIS.Geometry.ITopologicalOperator.Intersect(IGeometry other, esriGeometryDimension resultDimension)   My code :  ITopologicalOperator4 topoOperateur = secteurPsr.Shape as ITopologicalOperator4; topoOperateur.IsKnownSimple_2 = false; topoOperateur.Simplify(); IGeometry geomPsr = currentPsr.Value.Shape; IPolyline polylinePsr = geomPsr as IPolyline; (geomPsr as ITopologicalOperator2).Simplify(); IGeometry geomResult = null; try  {     geomResult = topoOperateur.Intersect(geomPsr,esriGeometryDimension.esriGeometry1Dimension);  }


Show that the equation $a_1e^{\alpha_1x} + a_2e^{\alpha_2x} + \cdots + a_ne^{\alpha_nx} = 0$ has at most $n - 1$ real roots.

For non-zero $a_1, a_2, \ldots , a_n$ and for $\alpha_1, \alpha_2, \ldots , \alpha_n$ such that $\alpha_i \neq \alpha_j$ for $i \neq j$, show that the equation $$a_1e^{\alpha_1x} + a_2e^{\alpha_2x} + \cdots + a_ne^{\alpha_nx} = 0$$ has at most $n - 1$ real roots.  I thought of applying Rolle's theorem to the function $f(x) = a_1e^{\alpha_1x} + a_2e^{\alpha_2x} + \cdots + a_ne^{\alpha_nx}$ and reach a contradiction, but I can't find a way to use it.


If I am using a channel only for morse code (CW), with one frequency and interruptions for dots and dashes, is the necessary bandwidth of the channel twice the audio frequency of the tone used for CW?


Problem:  Let $A_{n.n}$ be square complex matrix. Prove the following: $$\left \| A \right \|=\left \| A \right \|_{HS}\Leftrightarrow  rank(A)\leqslant 1$$. Where $\left \| . \right \|_{HS} $ is the Hilbert Schmidt Norm.  Please read my solution and tell me whether it is correct. If not, let me know where the mistake is.  Proof of the implication $\Leftarrow $:   If $rank(A)=0$, then in this case $A=0$. It follows that $\left \| A \right \|=\left \| A \right \|_{HS}=0$ If $rank(A)=1$, than: $ A=\begin{pmatrix} A_{1}\\  \alpha _{2}A_{1}\\  ...\\  \alpha _{n}A_{1} \end{pmatrix}$ where $A_{1}$ is the first row of $A$   and in this case: $\left \| A \right \|=\left \| A \right \|_{HS}=\left \| A_{1} \right \|\sqrt{1+\alpha _{1}^{2}+...+\alpha _{n}^{2}}$  Proof of the implication $\Rightarrow $   We know that $\left \| A \right \|=max_{\left \| x \right \|=1}\left \| Ax \right \|$  On the other hand: $ A=\begin{pmatrix} A_{1}\\  A_{2}\\  ... \\ A_{n}  \end{pmatrix}$. So, $$\left \| Ax \right \|=\left \| \begin{pmatrix} \left \langle A_{1},x \right \rangle\\  \left \langle A_{2},x \right \rangle\\  ...\\   \left \langle A_{n},x \right \rangle\end{pmatrix} \right \|=\sqrt{\left \langle A_{1},x \right \rangle^{2}+\left \langle A_{2},x \right \rangle^{2}+...+\left \langle A_{n},x \right \rangle^{2}} $$  Where $ \left \langle A_{i},x \right \rangle$ is the inner product of $A_{i}$ and $x$  Using the Cauchy-Schwarz inequality: $\left \langle A_{i},x \right \rangle^{2}\leq \left \| A_{i} \right \|^{2}\left \| x \right \|^{2}$, we get: $\left \| A \right \|=max_{\left \| x \right \|=1}\left \| Ax \right \|\leq max_{\left \| x \right \|=1}\left \| x \right \|\left \| A \right \|_{HS}=\left \| A \right \|_{HS}$. In order to have the equality: $\left \| A \right \|=\left \| A \right \|_{HS}$, we should have: $\left \langle A_{i},x \right \rangle^{2}=\left \| A_{i} \right \|^{2}\left \| x \right \|^{2} $ which occurs only if $A_{i}=\lambda _{i} x$. So, the rows of A are dependent, which implies that $rank(A)=1$. Note that the case $rank(A)=0$ happens when $A=0$  Please let me know if my solution makes sense.


Show that if G is a group with $G = p ^ n$

Show that if G is a group with $$|G| = p ^ n,$$ where p is prime and $n ∈\mathbb N$, then Z (G) (i.e. the center of G) must have at least p elements.   It is not an assignment question I only saw a similar exercise in a book and I want to know how it would be solved.  I think it can be done with the Orbit-Stabiliser Theorem because each orbit has size a power of p, and the orbit sizes sum to $$p^n$$ So,the number of elements not in Z(G) is divisible by p, whence the number in Z(G) is also. But there is at least one element in Z(G), namely the identity; so there are at least p such elements.Now, if g is an element of order p in Z(G), then  is a normal subgroup of G of order p. I do not know if it is so, thanks in advance.  I would like to know how it would be using the class equation...


What is the best USB file system format for linux?

I want to format a 2TB USB which I plan use for storing media (some of which may go over 10+GB). As I don't plan on using it on any other system aside from Linux-based system I don't really care about compatibility. So, as mentioned in the title, what is the best file system format (NTFS, FAT32, exFAT etc...) I can go for?


I'm trying to dual boot my laptop with windows 8 and linux. Can someone supply me with instructions of an easy way to do this? Thank you.


What is right preposition to use before a location?

What preposition should I use here?  Your initial place of posting shall be in the office located ____ A. Bonifacio St. Brgy. Canlalay Biñan City.


How to select the best/correct site for a question?

For some issues it is not clear to which SE site they belong. Either they "match" more than one, or none. Or you don't know all existing sites and miss the correct one. Is there some recommended way to solve this problem? I just try to do a quick search on SE for some keyword and the see what I get, but the search returns questions and answers instead of sites. Should just go with the one appearing most on the first page of results? Is there a way to get a list of sites sorted by relevance (by number of matching posts or other metric)? Or simply search thru the descriptions of the sites at  ? (probably too terse)


Find the minimal maximal distance in a $n\times n$ square grid?

Write $1,2,\dots,n^2$ into a $n\times n$ square grid. If $u,v$ are adjacent, call $\max_{u,v}|u-v|$ the maximal distance of this grid. So what is the minimal maximal distance? I feel like that it is $n$, the construction is to write $1,2,\dots,n^2$ in order, but I do not know how to prove it, and I cannot find any results on it either.


$[F(t):F(t^n)]=n$ where $t$ is trascendental

Let $F$ be a field and let $t$ be trascendental over $F$. Prove that $[F(t):F(t^n)]=n$. Obviously $[F(t):F(t^n)]\le n$ since the polynomial $f(x)=x^n-t^n \in F(t^n)$ has $t$ as a root. But I don't know how to prove that it's irreducible over $F(t^n)$. I tried to consider that $t$ is trascendental to deduce some algebraic relations over $F$ on $t$. But it did not work.


I am having an issues with my ~/.xsession-errors file filling up my entire drive (128G) in a couple of days. Infact, once it was in a few hours. I run this machine as a server, so it runs for days with out reboot.  I have read some solutions about how to remove the file via cron, or redirect it to /dev/null. My concern though is that my home is on a SSD and I don't want to waste the drive i/o with a bunch of writes I don't want.  How can I prevent it from writing?? Also, if anyone could explain what this file is, and why it has so many errors, I would appreciate it. Does it have to do with my remote sessions vnc/ssh.  UPDATE: It seems to go up in size every time I remote VNC in using "Desktop Sharing".


Was Salazar Slytherin's whole "Don't teach muggle-born" idea less-than-brilliant?

Leaving aside ethical and moral considerations, the whole policy of Salazar Slytherin's "we should not teach muggle-born magic-capable children" seems to be completely counter-productive to the whole "Let's not allow Muggles to know about existence of magical world" idea.  To wit, muggle-born wizards are obviously capable of performing magic (there were several examples in the book) even without wands/training, and many of them are powerful enough as far as their magical ability that it's likely to get noticed.   So, short of killing off every child that has latent magical abilities (or at least those with abilities beyond some threshold) or charming them so they are unable to do any magic, wouldn't refusal to teach them all how to PROPERLY use magic and what the rules are merely get a lot more chances for Muggles to see magic being performed which totally goes against the whole "Let's not allow Muggles realize that there are magic users around" that drives a lot of the Wizarding rules?  UPDATE Just to clarify - this question is about the idea of Salazar Slytherin himself and not the modern-day Death Eaters/Voldemort.


Let $P$ be a set of primes, such that for each nonnegative integer $n$, $19⋅8^n+17$ is divisible by some prime $p$ in $P$. Find the smallest possible number of elements in $P$. How do I start the problem? Thanks.


I had a  over what seems like a simple question:     Is $\sin \infty$ an ?   What do you think? :)    I'm labelling this as (soft-question) to be safe, but it should have a clear answer depending on the definition of indeterminate form used. The term "indeterminate form" is seldom used in post-calculus mathematics, but I believe it has one or more accepted definitions, which are either informal or formal. So any answer which takes a standard definition and argues the case would be interesting to me.  How to make a good answer:   State the definition of indeterminate form, either from an online or textbook source, or a definition you came up with on your own. Determine, using your stated definition, whether $\sin \infty$ is indeterminate or not.   EDIT: What do I mean by $\sin (\infty)$?  It's not a well-defined expression, but neither are any of the other indeterminate forms: $\frac{0}{0}$ doesn't exist, $1^\infty$, doesn't exist, and so on. So the question is whether this expression -- which is not well-defined, just like any other indeterminate form -- is an indeterminate form.


How to change color of command prompt, only the first line?

I want to change color of the main command line. Just the first and last ones.  The command I've called and the prompt line that waits to new command.  When I've called a command and it returns some stuff, I'm lost in those! I want to highlight the main line and the new line.  If I can reposition the main line it would be great too! I'm not sure if it's clear enough, sorry for my bad English.


Regular Expression for number with prefix 65+?


Where can I find the application executables in the filesystem?

Where are executables for programs stored in Ubuntu?  An application (Komodo Edit) is asking me to identify an application to be used as a web browser. I've become used to just entering the application name as a command for situations such as these, but this scenario got me thinking.   I know in Windows it would just be the relevant application folder in the 'program files' folder, but I'm assuming things are a bit different on Linux?  I thought somewhere like bin would be logical but this appears to standard Linux/Unix applications. Where would I find the binary executable for applications stored on my system?


The problem is from  Algebra by Artin, Chapter 1, Miscellaneous Problems, Exercise 8. I have been trying for a long time now to solve it but I am unsuccessful.      Let $A,B$ be $m \times n$ and $n \times m$ matrices. Prove that $I_m - AB$ is invertible if and only if $I_n - BA$ is invertible.    Please provide with only a hint.


if (cond1 and cond2) or (not cond1 and not cond2):  Is there a simpler way to write this in Python?


Uniform convergence of $\sum_{n=1}^{\infty} \dfrac{z^{n}}{1+z^{2n}}$

Show that the series $\sum_{n=1}^{\infty} \dfrac{z^{n}}{1+z^{2n}}$ converges uniformly over the compact subsets of $\{z\in \mathbb C : |z|\neq 1\}$.  if we assume $|z| = 1$. Then, by the limit test, $$\lim_{n\to \infty}\frac{1}{1^n+1^{-n}}=\frac{1}{2}\neq 0$$ therefore, the series diverges.   but, I don't know how to bound the series to use Weierstrass M-test.


Detect desynchronization in HOTP authentication

In HOTP authentication, is there a way for a system to detect that the token has been desynchronized? If so how does it know that the OTP was generated from a desynchronized (but valid) token and is not just a fake/random OTP?


Show Pad Nets Seemingly Not Working in Altium

For some reason, the PCB is not showing net names on the pads  I have all connections (rats nests) visible I have checked the "Show Pad Nets" and "Show Via Nets" under the View Configurations > View Options Panel  I have checked layer colors and everything is on  What other setting might there be which is preventing the net names from displaying within the pads/vias on the PCB layout?  I am running AD15 on Windows 8.1 and this is really bugging me!   This is an example screen shot of the PCB environment, you can see that despite the option for "show pad nets" being enabled, they are not showing.   Thanks for the help  This question is not the same as another related question "Show Pads with their Name on PCB altium " which discussed adding silkscreen designators. It is about why the Altium feature "show pad nets" does not seem to be working to show the 'virtual' net names in the PCB tool within the pads


Describe all ring homomorphisms of:  a) $\mathbb{Z}$ into $\mathbb{Z}$  b) $\mathbb{Z}$ into $\mathbb{Z} \times \mathbb{Z}$  c) $\mathbb{Z} \times \mathbb{Z}$ into $\mathbb{Z}$  d) How many homomorphisms are there of $\mathbb{Z} \times \mathbb{Z} \times \mathbb{Z}$ into $\mathbb{Z}$  Note: These were past homework questions and my professor already gave out answers. I just need someone to help me understand and approach this type of problem.  Thank you.


Is there any way to display the package contents using `apt-get` without first downloading the package?

I know I can list the files in a package using the following command, which first download the package (.deb) into /var/cache/apt/archives and then list its contents:  apt-get --download-only install <pkg> dpkg --contents <pkg> (.deb)   Does apt-get support any way of listing the package contents without first downloading the package?  Extra: Furthermore, how can I download a package using apt-get --download-only ... without all of its dependencies?


Formula field change doesn't cause trigger fire

Assume we have ObjectA__c with Field1__c and ObjectB__c with formula field Field2__c which is formula to ObjectA__r.Field1__c.  I expected change of record field Field1__c of ObjectA__c would cause trigger on ObjectB__c to fire with changed Field2__c field, but this doesn't happen.  Can anyone explain why? Alternatively, can anyone share link to docs where is behavior is explained?


How do you give an object a solid color in the render?

I want to have a part of my render be a very specific color, for the whole object. Is there a way to do this?


What is the best way to install Python packages?

What is the best way to install Python packages in Ubuntu 11? I am a recent convert to Ubuntu and want to learn best practices.  For context, I am looking to install the tweeststream package, but I did not see it in my Synaptic package manager. Also, I am very new to programming, but I usually can follow along with code samples.


How can i select where i install the ubuntu aplications?

I want to download programs like Cmap tools or Geany to a removable drive, but I don't now how.


Having ssh tunneling itself for remote access from a third machine

I am struggling with understanding if and how the following is possible.  Say that I have a machine T (target) which I want to access from remote (ideally via ssh).  T is behind a router/firewall R and I cannot forward port (e.g.) 22 of R to port 22  of T.  In a word, no direct ssh access to T is possible.  Now say that    I have a machine A on which I have full control.  I can ssh from T to A, i.e.    T:  ssh user@A   succeeds.   Q1: can I use this to access shell of T from A? I.e., can I use the connection created from T to A, to use T from A?     T ---> ssh ----> A          # this is possible                    T <--- ? shell ? <---- A    # is this possible?   Q2: If Q1 is possible:  Let's say that I have a third machine L (e.g. my laptop), and I aim at having access to the shell of T from L. Can I ssh-tunnel A access to L?     T ----> ssh ----> A <---- ssh < ---- L     T <-------  ?? %&£€ ?? <------- L       # is this possible?   any help appreciated.


From Oersted experiment we know " When an electric current is passed through a conducting wire, a magnetic field is produced around it." An electric current is a flow of electric charge or electron. My question is "How does a flow of electron or electric charge create magnetic field?"


A few days ago my hard drive died and now I have a problem.  I installed Ubuntu 15.04 on my 16GB pendrive. When I use Ubuntu it acts very slowly.  I tried my best to solve this problem but can't. My PC has 3GB RAM and 2GB video RAM. The processor is an Intel dual-core @3GHz and the motherboard is an Intel dg41wv. Why is my computer so slow?


I'm 100% sure I saw  about HDMI which may not have been asked more than 4 hours ago, but it was not in the result list when I entered HDMI in the search field.  Then I noticed: when I enter "HDMI" as search term, it searches for the tag  instead. Is this the expected behavior? And is it really my task to find out that I have to enter "HDMI" to get other results?  Can we at least have an indicator that some magic happened, e.g.     You entered HDMI. We're looking for questions tagged  instead. Search for "HDMI" instead.


initializing std::string from char* without copy

I have a situation where I need to process large (many GB's) amounts of data as such:   build a large string by appending many smaller (C char*) strings trim the string convert the string into a C++ const std::string for processing (read only) repeat   The data in each iteration are independent.  My question is, I'd like to minimise (if possible eliminate) heap allocated memory usage, as it at the moment is my largest performance problem.  Is there a way to convert a C string (char*) into a stl C++ string (std::string) without requiring std::string to internally alloc/copy the data?  Alternatively, could I use stringstreams or something similar to re-use a large buffer?  Edit: Thanks for the answers, for clarity, I think a revised question would be:  How can I build (via multiple appends) a stl C++ string efficiently. And if performing this action in a loop, where each loop is totally independant, how can I re-use thisallocated space.


Tips on how to freeze a no-bake cheesecake

Good day! I have made a no-bake cheesecake in a glass container. Since I could not find the parchment paper, I used a substitute- aluminium foil. Now, the dish has been in the freezer for past two days and still the cake is not firm. On the top, it's a little firm but from the corners, it's runny because of which, I cannot take the cake out of the foil. What should I do to ensure that my cake turns out like a normal cheesecake?


Existence of $x$ such that $2^x =a,3^x=b,5^x=c$ for some integers $a,b,c$

Conjecture:     There does not exist a non-integer $x$ such that      $$2^x=a$$ $$3^x=b$$ $$5^x=c$$      where $a,b,c$ are all integers.     I'm aware that the similar question      There does not exist a non-integer $y$ such that      $$2^y=A$$ $$3^y=B$$      where $A,B$ are all integers.   is a famous unsolved problem.  (evidence in the corrolaries  or )  My idea was that the addition of the condition $5^x$ made the problem easier and therefore solvable.


String artifacts from history on commandline

When I scroll through the bash history with the arrow keys and hit (for example) the following string:  git clone hgit clone https://github.com/electron/electron-quick-start   In the next line of history I get something like this:  git clone hls   Where ls is the command from history and git clone h is my unwanted artifact.  The following lines from .bashrc are suspect:  PROMPT_DIRTRIM=2 YELLOW="\[\033[0;33m\]" RED="\[\033[0;31m\]" GREEN="\[\033[0;32m\]" ORANGE="\033[38;5;208m" PROMPT_COMMAND='echo -ne "\033]0; ${USER}@${HOST}\007"' PS1="${YELLOW}\u@\h:${ORANGE}\w ${GREEN}\$ "


Is a single photon emitted as a spherical EM wavefront?

If yes, could the same photon hit multiple targets as it expands? If not, how does the photon acquire the wave-ness if it is not born as a spherical wave? Also, in second case, how can multiple photons synchronize to make up a single wave front?