A counterexample to the Sura-Bura Theorem for non separated compact spaces

Is there a $T_1$ compact space such that the class of quasi-components differs from the class of connected components?  By the Sura-Bura theorem, this is not possible for $T_2$ compact spaces.


Any English equivalent for Russian idiom "to write for the desk drawer"?

It means "to write literary works, knowing that they will not pass censorship and be published". I am looking for some English equivalents that can be used to describe not only writing but also doing different things like taking photos for example for oneself and refusing to publish them. Thank you very much in advance      Let's just find an equivalent for "doing things for yourself and not caring whether it will be published or not". A good example is Kafka most of whose books were published after his death


We know that the equation of motion of particle can be derived from the respective action. But in the book I am reading, the author is saying:     ... timelike worldline of a massive particle is parametrised by proper time, $x^a=x^a(\tau)$. The velocity (tangent) vector is $u^a \equiv \dot{x}^a(\tau)$. This is normalised as $u^au_a =-c^2$.   How can one derive e.o.m?


Is there a way to set math mode font non-italic?

I read many things about people wanting math mode in sans-serif font and doing crazy things with packages and options to get that, but I did not find anything that would simply make my math mode font non-italic.  Is there an (easy) way to set math mode font to be non-italic?  And is there a way to do that globally for the whole document?


I have .pages document which have been damaged. I tried different methods like  and  one on internet but no success. My last hope is to read data from .iwa files but I cannot find a way to decompress .iwa files in order to read contents. Is there any way to get my data back through these files?


Why did Obi-Wan wait years after his death to tell Luke to go to Dagobah to find Yoda?

While reading , it came to me that Obi-Wan waited far too long to tell Luke to go find Yoda. Obi-Wan Kenobi could have appeared to Luke minutes after Luke blasted the first Death Star to pieces. He could have told him right then and there that another Jedi Master still lived and could train him.     BEN: You must go to the Dagobah System ... There you will learn from   one who taught me: Yoda, the Jedi Master.   Instead he waited 3 years. Luke could have been killed during those 3 years by some wampa beast, frozen during an ice storm on Hoth, shot by Boba Fett, or hunted down by Darth Vader. Very risky to wait because Vader would known the best time to hunt down Luke was before Luke completed another day of training!  Waiting also meant a 3 year gap in his training.  Luke was safe right after he destroyed the Death Star. You'd think a wise old Jedi would have told him to seek out Yoda immediately. You'd also think Obi-Wan would have known Darth Vader survived the Battle of Yavin and would have immediately landed his TIE fighter on the moon and tracked down on rebel base to find whomever destroyed the technological terror.  Why did Obi-Wan wait 3 years to tell Luke?  (I am looking for an in-universe explanation. Not an out-of-universe explanation.)  Edit: This is not identical to the question I linked to. That question is more about why Obi-Wan chose to contact Luke during a snowstorm on Hoth right after Luke stumbled out of the wampa cave. This is about why wait 3 years at all. Nothing in the answers to that question address the 3 year time wait.  The answers there all don't make sense when compared to the simple fact that Kenobi successfully contacted Luke during the first movie. Here are the answers from that question and why they don't hold up.   Obi-Wan needed time to learn to be a Force-Ghost to contact Luke. We know he could speak to Luke during the Battle of Yavin, so he should have been able to contact Luke immediately. Luke was vulnerable and therefore more receptive. Luke was certainly receptive to hearing Kenobi's advice during the Battle of Yavin. Luke was collapsing from extreme cold and therefore willing to listen to a ghost. Same answer to this one as #2. Luke needed to learn how to use the Force first or to meditate to receive the message. We know that's not true, because Luke heard Kenobi's message during the Battle of Yavin and he wasn't meditating or using the Force during the battle when Kenobi spoke to him. The planet Hoth was a Force nexus. Was the planet Yavin also some Force nexus that allowed Kenobi to speak to Luke then?


I cant update msf console in kali linux,how can i fix that ? I used this command apt update; apt install metasploit-framework   and got this error #E: Could not open lock file /var/lib/apt/lists/lock - open (13: Permission denied)


The nuclear binding energy, is the energy that is needed to seperate the nucleons in a nucleus. And binding energy is also defined as the energy given out when a nucleus forms from nucleons.   Also the larger the nucleus is, the more energy is required to break it apart, so why doesn't that mean that larger nuclei are more stable? I mean Uranium has a lower binding energy per nucleon than Iron, but there are many many more nucleons in Uranium that Iron so the total binding energy is going to be much greater.   Basically I don't understand why whether an element gives out energy by fusion or fission (why the lighter element provide energy by fusion not fission and vice versa for heavy elements) depends on binding energy per nucleon and not "total" binding energy


I am trying to install Hadoop in Ubuntu 12.04 version. Following the instructions from  , I installed java-6-openjdk from Ubuntu software-center. I have set java_home in .bashrc. Also set java_home in Hadoop conf/env.sh. While formatting the namenode, I am getting the following error:  usr/lib/jvm/java-6-openjdk/bin/java no such file or directory.     Thank you. But it's a 64bit OS.


Additional horizontal space when the last line of an environment is full

I have created an environment env which just adds a \medskip and some text (say "Blablabla") after the text inside \begin{env} ... \end{env}. The problem is that if the last line is full, then I get an additional horizontal space between the text and "Blablabla".  Here is an MWE:  \documentclass{article} \newenvironment{env}{ ENVIRONMENT:\par }{ \medskip \par\noindent Blablabla }  \begin{document}  \section*{First case: the last line is not full}  \begin{env} Lorem ipsum dolor sit amet, consectetur adipiscing elit. Nulla malesuada porta tortor non vestibulum. Vivamus vel tincidunt purus. Curabitur quam arcu, suscipit sed diam sed, ornare efficitur felis. Duis at arcu iaculis, viverra ligula sit amet, hendrerit eros. Proin finibus venenatis sollicitudin. Nunc ullamcorper sem ut lacinia posuere. Integer pulvinar nulla lorem, ut pulvinar ipsum egestas at. Duis quam ipsum, posuere ac pulvinar vitae, auctor non leo. \end{env}  \section*{Seconde case: the last line is full}  \begin{env} Lorem ipsum dolor sit amet, consectetur adipiscing elit. Quisque suscipit vitae neque eu gravida. Quisque et enim quam. Integer elementum diam a ex laoreet, ac egestas lacus volutpat. Nunc ullamcorper non urna tincidunt ultrices. Etiam eu ultricies diam. Proin mollis, nunc sit amet volutpat varius, ipsum tellus bibendum nulla, in eleifend lacus felis pellentesque nisl. Phasellus laoreet, libero quis auctor congue, nulla nulla aliquam metus, in hendrerit arcu justo quis tortor. Nunc nec nisi euismod, consectetur tellus nec, suscipit libero.  \end{env}  \end{document}


Prove this equality using a complex polynomial lower bound

Using the fact that if $P(z)=a_nz^n +···+a_1z+a_0,$ is a polynomial of degree $n$ then there is $R_0 > 0$ such that for $|z| > R_0$ the polynomial can be bounded from below as $$|P(z)|>\frac{1}{2}|a_n||z|^n$$I need to show that if $P(z)$ is polynomial of degree $n ≥ 2$ and $C_R$ is the circle of radius $R$ centered at 0 then $$\lim_{R\rightarrow \infty} \int_{C_R} \frac{1}{P(z)}dz=0$$  Any hints or help would be appreciated


Mount NTFS partition at startup, with non-root user as owner

I'm currently mounting an NTFS partition at startup using the following line in /etc/fstab:  /dev/sda3        /media/data           ntfs      nls=iso8859-1,umask=000   To my Ubuntu 11.10 installation, it looks as if all files and folders are owned by root - and since NTFS doesn't really support the same rights management system anyway, there's no way I can change it after the mount is complete. No matter what I do, ls -l anywhere on the NTFS partition will list every file and folder as owned by root:root.  However, this causes some problems for me. Most notably, some applicaitons running under my account (called tomas) complain about access rights. Also, whenever I try to copy (cp) or move (mv) files from one of my ext3 partitions to the NTFS partition, I get error messages saying  mv: preserving times for `[path to new file]`: Operation not permitted   or, similarly  mv: preserving permissions for ...   Would mounting the partition in my name instead of root help? If so, how do I accomplish that in fstab?    Update:  I have now changed the options according to the suggestions, and arrived at this:  nls=iso8859-1,permissions,users,umask=000,uid=tomas,gid=tomas   ls -l now shows all files owned by me instead of by root, and it seems some of the problems I had before are solved. However, not all of them.  When I start Eclipse, I get an error that a file related to the android-sdk cannot be run: Permission denied. ls -l tells me the following about the file:  -rwxrwxrwx 1 tomas tomas 159620 2011-11-29 14:50 adb*   This looks the way I want it to. But if I try to run it (./adb in a terminal) I also get permission denied errors. But if I run it with sudo, it works (I believe - at least it doesn't give me an error message, but it doesn't give me any output at all, which I think it shouldn't...)  Why is the above file, with execute permissions for anyone, still not executable by anyone else than root? How do I change the way I mount the file system so it is?    Update 2:  OK, I've now come a little bit further. By mounting with these options  nls=iso8859-1,permissions,users,auto   I got all the permissions set the way I expect them to, and chown and chmod actually change settings on the files (at least according to ls -l) =D  BUT my system still behaves in a weird way. The permissions for the adb script file come up as above, but neither I nor Eclipse can run it without "Permission denied" errors. But as far as I can see the file has all the required flags set (o=rwx should be enough, right?). Why doesn't it work?    Update 3  OK, I got everything working on the Ubuntu side, with the following options:  nls=iso8859-1,permissions,users,auto,exec   However, when I try to access files on the partition from Windows, the security settings are all messed up. On all the files (of those few I've examined) a new account called Account Unknown(long GUID) has been added to the list of users, and has full rights. Rigths for most other users are decreased so that I don't have rights to do stuff I expect. Notably "Everyone" does no longer seem to have right to "Traverse folder / execute".  This might be solvable by just selecting the partition and allow Everyone to do anything on the root folder, and then tell it to do it recursively, but I'd rather not as I'm afraid it will take days to complete...


Using contour integration to solve this integral

We need to use contour integration to solve $$\int_{-\infty}^\infty {e^{ax}\over e^x+1}dx$$ given that $0<a<1$. My question is about what contour to use, knowing that the singularities are at $z=i(2n+1)\pi$. I tried the standard D-shaped contour in the upper half plane, but I'm not being able to show that the integral will vanish along the semi circular curve as R goes to infinity.


How can i find out what is taking space on my system

I am trying to find out what files/folders are using most space on the filesystem  df -h Filesystem      Size  Used Avail Use% Mounted on /dev/sda3        94G   85G  4.4G  96% / tmpfs            16G  7.9G  7.9G  50% /dev/shm /dev/sda1       477M   82M  370M  19% /boot   I install ncdu to see what is taking space but i still couldn't find out what takes most of the space  1.9 GiB [##        ] /var     1.2 GiB [#         ] /usr   372.8 MiB [          ] /lib   129.7 MiB [          ] /tmp    79.3 MiB [          ] /boot    74.8 MiB [          ] /root    28.6 MiB [          ] /etc    18.4 MiB [          ] /lib64    18.1 MiB [          ] /opt    10.8 MiB [          ] /sbin   Edit  I did delete some big log file before posting this thread.I found it strange that it was showing much difference on df -h .On @Pavel Šimerda suggestion i did a soft reboot and here is the output  Filesystem      Size  Used Avail Use% Mounted on /dev/sda3        94G  3.9G   85G   5% / tmpfs            16G  236M   16G   2% /dev/shm /dev/sda1       477M   86M  366M  20% /boot   Why was a reboot needed in this case ?


I have a web page that has the ngx-monaco-editor implemented in angular. But i am not able send any data to the editor using sendKeys() . I tried replacing textContent of the div element but it just displays the text in the editor  but the other components does not detect that the text was entered.   Is there a way to properly send input to the ngx-monaco-editor using selenium protractor?  An example website would be :    I am not able to send values to the editor  Code i tried:  await browser.get('https://stackblitz.com/edit/ngx-monaco-editor-example')     await browser.sleep(10000)  await element(by.xpath('(//*[@class="view-line"])[1]')).sendKeys('some test')   Error i get:  Element <div class="view-line"> is not reachable by keyboard


Downloading Latest Blender Version from PPA

For a few days I've been looking for a trusted source for the latest version of Blender. I found two commands to download Blender, but the Launchpad page was like this:  so I just want to know if there is currently available a good compiled Blender version (it is 2.68a at the moment).  It would be great if someone would help me to get the latest Blender version. Thanks in advance.


no suitable conversion function from "std::string" to "const char *" exists c++

It's a simple program for version numbers directories. It fails to compile with this error:  no suitable conversion function from "std::string" to "const char *" exists  #include <iostream> #include <stdio.h> #include <io.h>  using namespace std;  int main() {     int max = 10, daily_patch = 0, monthly_patch = 0, yearly_patch;      cout << " Enter the yearly_patch Number : ";     cin >> yearly_patch;      for (int i = yearly_patch; i <= yearly_patch; i++) {         for (int j = 0; j < max; j++) {             for (int k = 0; k < max; k++) {                 string str1 = to_string(i);                 string str2 = to_string(j);                 string str3 = to_string(k)                 string dot = ".";                 string dir = str1 + dot + str2 + dot + str3;                                  mkdir(dir);             }         }     } }


I'm running Ubuntu 16 and i want to install libsodium library.  here's what i have tried:  apt-get update apt-get install libsodium   but the libsodium they have is outdated when i do apt-get.  they have the latest libsodium here:   it is called "LATEST.tar.gz". sorry im new to this but how do i install libsodium from the new source rather than the old one from apt-get?


Material that shows up as alpha channel on render, but shows up in reflections

Another way to put it is that I want to create a material that will do the cropping for me.  If I apply this shader to a cube in the middle of the shot, then my render will have a cube-shaped block of transparency in the middle of the shot, even if there are objects behind the cube.  Can anyone provide me a pointer on this? I'm new to nodes.  Thank you thank you!  EDIT: I'm using Cycles.  EDIT EDIT: Thank you for your answer, Denis. I realized today that there's one thing missing from the solution you provided. I also need the object to cast shadows and show up in reflections. I can't quite get my head around to make that happen. Any help out there?  EDIT EDIT EDIT: Figured it out!


How to install D-link DWA-131 B1 on Ubuntu 14.04?

Recently I built new PC with Ubuntu OS 14.04 (64bit). I noticed the D-Link Wireless N Nano USB Adapter doesn't get detected and installed automatically. The device is properly detected (listed in lsusb) but does not work out of the box  Following are the adapter specifications: •Model No: DWA-131 •Hardware Version : B1  How to install this wireless adapter? Thanks


sudo apt-get upgrade (E : unmet dependencies error)

I'm completely new to linux. If someone could make out from the  whats wrong it would be really helpful. Also I'm getting that red icon on the top panel.  I tried running these code :-  sudo apt-get clean cd /var/lib/apt sudo mv lists lists.old sudo mkdir -p lists/partial sudo apt-get clean sudo apt-get update   The above code made that red icon go away after I rebooted but when I used the sudo apt-get upgrade after using sudo apt-get update command it popped up back again.  sudo apt-get -f install gives me  output error  Also I have referred to this thread (How do I resolve unmet dependencies after adding a PPA?) but to no avail.  After running the sudo dpkg -- configure -a it gives me following error.  instincts@Instincts:~$ sudo dpkg --configure -a [sudo] password for instincts:  dpkg: dependency problems prevent configuration of ppa-purge: ppa-purge depends on aptitude.  dpkg: error processing package ppa-purge (--configure): dependency problems - leaving unconfigured dpkg: dependency problems prevent configuration of aptitude:i386: aptitude:i386 depends on libapt-pkg4.12 (>= 0.8.16~exp12ubuntu6). aptitude:i386 depends on libboost-iostreams1.46.1 (>= 1.46.1-1). aptitude:i386 depends on libc6 (>= 2.4). aptitude:i386 depends on libcwidget3. aptitude:i386 depends on libept1.4.12. aptitude:i386 depends on libgcc1 (>= 1:4.1.1). aptitude:i386 depends on libncursesw5 (>= 5.6+20070908). aptitude:i386 depends on libsigc++-2.0-0c2a (>= 2.0.2). aptitude:i386 depends on libsqlite3-0 (>= 3.6.5). aptitude:i386 depends on libstdc++6 (>= 4.6). aptitude:i386 depends on libtinfo5. aptitude:i386 depends on libxapian22.  dpkg: error processing package aptitude:i386 (--configure): dependency problems - leaving unconfigured Errors were encountered while processing: ppa-purge aptitude:i386   Any help would be appreciated. Thank you.


Prove that for every positive integer, this polynomial is divisible by 24.

Prove that:   $$24\mid n^4 + 2n^3 - n^2 - 2n, \quad \forall n\in \mathbb{Z}^+$$   I tried to prove it, but had no luck.


Remap Super/Windows Start Button on Keyboard?

Is it possible to remap the Super (Windows Start) button to open All Applications instead of the Activities Overview?  I installed Tweaks to do a few other things but haven't seen anything about mapping the Super Key directly and was wondering how it is possible in GNOME and if there was a UI I'm overlooking or if I should be looking for a terminal command?


Which is the best usage? "To whom it may concern" or "To whomever it may concern"?


Second PhD in Astro after a PhD in CMT (Physics)

Okay here is the current situation. I am entering my second year in my PhD program and most of my options of joining the Theoretical astrophysics groups are closed ( no professors working in that field and two of them who were working are leaving the university). Right now the only open option for me is to work in computational condensed matter theory which I am not sure I am interested in (But I do know that given a option between this and theoretical astro I would choose the latter) ie.. interest in Astro theory >> Interest in CMT. okay given this background the questions are,  1) what are the cons of doing another PhD in astro after completing my PhD in CMT (let us say it would take me 5 years here to complete my PhD and if I am applying to an university in UK for my second PhD I would complete it in 3 years so in total i would have spent around 8 years with 2 PhD's in my hand) cons ?  2) I know most of you would ask me to just reapply to other schools, But I am not sure how certain I am in getting an admission again and I dont want this entire two years here to go waste ( just 3 of more years I would have my PhD). So my second question is it even possible to get a PhD position in Europe after having PhD in US ?  So basically my reason for second PhD is not for a better career path, but instead to shift to my area of interest but as well as to not let these 2 years of my life go waste. Is it a good choice to make ?  Edit 1- I did read all the answers for double PhD questions but all the questions were in the line of "I want a better job/career, should I do double PhD?" mine is, "Let us say I complete my current PhD, is there any disadvantage of doing another one just because I would love to work in that field?"  PS: Yes I am working in US university right now, and yup as I am in my second year I have completed few course work and started the project. Rather than saying I "have to complete this PhD", I would put it this way - "I don't hate the work I am doing here, it is just that I would like working in the other field much more than this"  Edit 2- Thanks for the helpful answers. Let me explain my personal bias towards astrophysics. I am a math person by nature, and previously had my undergraduate in engineering.I wanted to move to physics mainly because of the rigorous mathematical structure of it compared to engineering, I self studied several physics stuff and hence wanted to do theoretical physics. But later (now) my views about theoretical physics is changing. On the whole this is what I think is the timeline chart in theoretical physics area apart from Astro) -  Experimentalists collect data of physical world  Theorists build model to explain the data   The new theory might lead experimentalists to further prob the physical world to test the theory   If it does, verify that theory, if not inform the theorist   Theorist then builds a new (or modify the old model) to explain the existing results.    So at the end of the day theorists keep on modifying their model until it agrees with all the experiments. At the end of the day, this is just model building/modifying till my theory fits the data(this creates a bound purpose to building the theory unlike mathematics). But in Astro, since there are very few experiments to verify, the set of all possible theories is large and theorists in this field actually have the freedom to keep on building theories(or models) to explain. And it is this abstract nature of this field (which is analogous to mathematics) where one needs no reason to build theory other than building it just for the fun of it interests me. These are my personal thoughts about general theoretical physics and the reason I want to move to Astro.


Prove area of a quadrilateral is $\frac14[4m^2n^2-(b^2+d^2-a^2-c^2)^2]^{\frac12}$

Someone asked me this question which I am really stuck at, any help is appreciated.     If $a,b,c,d$ are the sides of a  quadrilateral and $m,n$ are diagonals of the quadrilateral, then prove that area of the quadrilateral is $$\frac14[4m^2n^2-(b^2+d^2-a^2-c^2)^2]^{\frac12}$$   I do not recall anything like this from my school days. I need some hints to get started on this, I do not remember high school geometry formulas, may be one of them could help here.  It works fine for squares and recatngles, so I assume it is a valid formula.


find the radius  of convergence  of the power series  $\sum_{n=0}^{\infty} z^{n!}$.  My attempt : $\sum_{n=0}^\infty z^{n!}$ is a power series of the form $\sum_{n=0}^\infty {c_n z^n}$ with $$ c_n=\begin{cases} 1 & \text{if $n=k!$ for some integer $k$,}\\ 0 & \text{else}. \end{cases} $$  Any hints/idea/solution will be appreciated  thanks u


Why don't electrons return to their ground state immediately after photoexcitation?

In terms of photoluminescence, why don't the electrons, which have been excited by photons earlier, immediately fall down to their ground state and reemit a photon?   In other words, why does 'glow-in-the-dark' persist for a period of time? What causes the electrons to stay at a higher energy state and decay slowly?


Leading zeroes causing issue in Java code

Mathematically a leading zero does not have any effect on the number value i.e. 10 = 010 = 0...010. However my java code is unexpectedly giving strange result by decreasing the value of the number on putting any leading zero. package com.start;  public class Basics {          public static void main(String[] args) {         int a = 10;         int b = 010;         int c = 00000010;         System.out.println("a = "+a);         System.out.println("b = "+b);         System.out.println("c = "+c);     }  }


How do I create a system-wide autostart file?  This would be on a cloud server running the desktop version of Maverick.  I logged in as root and created an autostart file using System/Preferences/StartupApplications but it ended up in /root/.config/autostart and did not execute (as far as I can tell) upon rebooting.  The autostart file is to invoke a bash script that invokes the VNC server.    I copied the .desktop autostart file from /root/.config/autostart to /etc/xdg/autostart and rebooted.  This did not seem to make a difference.  Edit As mentioned in a comment, the objective is to run my bash script which starts the VNC server upon boot; not upon a login.


How javascript function with 'return as function' works

I am trying to understand how javascript function returns function handle and why following code prints '2' instead of '1'    var num = 01; function processAndIncrement() {   var process = function() {      console.log(num);    }   num++;   return process; } var proCall =  processAndIncrement(); proCall();


Lagrangian to Hamiltonian in Quantum Field Theory

While deriving Hamiltonian from Lagrangian density, we use the formula $$\mathcal{H} ~=~ \pi \dot{\phi} - \mathcal{L}.$$ But since we are considering space and time as parameters, why the formula  $$\mathcal{H} ~=~ \pi_{\mu}\partial^{\mu} \phi - \mathcal{L}$$ is not used? Is there any particular book/lecture notes dealing with these kind of issues in theoretical physics, I would love to know them?


Show $\lim\limits_{a \rightarrow + \infty} \int_0^{\infty} \frac{y}{1+y^2}e^{-ay} dy =0 $


How to make an event happen only at the first start of the game?

I want to know how to make something happen only once like a tutorial in a game which appears only when you first start your game and then when your game got saved to a further point it never appears again even when you close your game and start again.  I want to give players some amount of gold when they first got their hands on my game ... but I do not want to give them that again and again whenever they restart the game ...  So I want to know how to make something happen only once in a game application..  I hope you get my point ... thanks ..


Why does a variable not need a type inside a static block

A programming like this,  static {   a = 6; }   Why the element "a" does not need a type?


What does it mean to "interpret the sigmoid $\sigma(\theta^Tx)$ as a probability"?

In Goodfellow's Deep learning text, it is written    Is this way of defining a probability $p(y=1| x;\theta)$ even legal?  Recall the definition of a probability given a random variable     where $p_X$ is the probability mass function.  Is the logistic function $\sigma$ considered to be a probability mass function?   If so, what plausible process is responsible for generating this probability mass function? (i.e., a process similar to how geometric or Bernoulli pmf are defined)


Tokina SZ-X SLR 28-200mm Lens to Nikon D3300

I'm sure these kinds of questions are asked all the time but is it possible to mount an old SLR lens like this on a newer DLSR camera? The Tokina lens is made for a Pentax K1000 and I have a Nikon D3300. I've also got a Canon FD 70-210mm zoom lens but I read online you can't use those with DSLR bodies. Does anybody know where I could find an adapter for these lenses, if they're even compatible? Any info would be appreciated.


Find the number of solutions of $a_0+a_1+a_2=17$ if $2\le a_0\le 5$,   $3\le a_1\le 6$, $4\le a_2\le 7$.   This is an exmaple given by my professor, and his solution is:       The number of solutions to this equation satisfying the given   constraints is equal to the coefficient of $x^{21}$ in the expression   $$\left(\sum_{n=2}^5x^n\right)\left(\sum_{n=3}^6x^n\right)\left(\sum_{n=4}^7x^n\right)=x^9\left(\sum_{n=0}^3x^n\right)\left(\sum_{n=0}^3x^n\right)\left(\sum_{n=0}^3x^n\right).$$   This must be 3, since the coefficient of $x^8$ in $(1+x+x^2+x^3)^3$ is   3.   I understand actually nothing here. The expression of summation just pops up, and then comes the answer. What I only know that the idea of generating function is used here. Can someone help explain how the steps in the solution come?


If I have an ESTA approved for transit, can I visit a second time as a tourist?

I go to México in some time, and my fly tickets first I go from Peru to the US, because of that I require a visa to enter US.  In my country I can apply for VWP, but I'm a little scared of getting denied, while I'm in México it is possible that I would make a short tourism travel to US but in the ESTA form there is the following question.     Indicate whether your travel to the US is occurring in transit to   another country by selecting yes or no. Answering this question is   required to complete your application.   If I choose yes, definitely I can not enter US?  What scare me a little is, if I select no and then my request is denied, getting the visa would be a little complicated.


Rogue assassin, potential for double crit?

Let's assume a rogue assassin level 5 with the 5thE Assassinate. When an enemy hasn’t taken a turn yet, you get advantage and, if they are surprised, any hit is critical.   I am wondering if you roll a natural 20 in this situation where any hit is considered critical already, will it be a "double critical" or give you any type of bonus for rolling 20? I am assuming no but wanted to check!


Six days ago I put a +50 bounty on  which wasn't asked by me, but to which I'd previously posted a pretty decent answer. Since then I've earned 130 reputation from upvotes on my answer, netting me +80 reputation and a bronze badge from no work.  It seems possible to slowly generate free reputation by "investing" in your answers like this. I expect I could repeat this perpetually and continue to profit from it.  This strikes me as an abuse of the bounty system. Should anything be done to prevent it?  EDIT: For more concrete questions:   If I put another bounty on this question after this one expired, would that be considered abuse? What if I did it several times? ( the answer was  "yes", but the author was doing so to promote his own project.) What if I didn't do it to the same question, but was constantly promoting questions I'd answered, in order to promote my answers?


Group of even order contains an element of order 2

I am working on the following problem from group theory:     If $G$ is a group of order $2n$, show that the number of elements of $G$ of order $2$ is odd.   That is, for some integer $k$, there are $2k+1$ elements $a$ such that $a \in G,\;\; a*a = e$, where $e$ is the identity element of $G$.


Sum of counters at the beginning of file

New to this forum, but long time TeX and LaTeX user. I've had this problem recently, for which I couldn't find a solution:  I'd like to print out the total possible score at a test at the top of the test. This is of course the total sum of scores of the different questions. I've thus thought of creating a counter  \newcounter{total} \setcounter{total}{0}   at the beginning of the file, and at each question, I've used the command  \addtocounter{total}{ <the score at this question> }   But then, of course, the total score is effectively computed at the end of the document. How can I manage to print this score at the top of the document? Perhaps with a temporary external file, but I haven't looked into this...  All help is greatly appreciated! Thanks a lot in advance!


Much Less ≈ Still Less : How do the 2 words in each compound to mean 'let alone'?

For brevity, I symbolise (imperfect) synonymity with ≈ :  X ≈ Y  means  X and Y are synonyms.  From :  to say nothing of = let alone   ≈ much less ≈ still less.  I already recognise, and ask not, about each's meaning. Instead, how do the 2 words in each phrase combine ?


If $f\in \mathbb{R}[X]$, then do only real numbers count as roots of $f$?

I had an argument with a friend about this and I would like to know what you think. If we are given a polynomial $f\in \mathbb{R}[X]$, then do only real numbers count as roots of $f$? Let me give you an example. Let's say we are given the polynomial $f=X^2+1 \in \mathbb{R}[X]$. It is obvious that $f(i)=f(-i)=0$, but are $i$ and $-i$ considered to be roots of $f$ since they are not in $\mathbb{R}$? I think that they are not and they would be only if we were told that $f\in \mathbb{C}[X]$. EDIT: After the discussion in the comments, I came to the conclusion that a polynomial whose coefficients are in a field can also have roots in another field. Can you give me some examples of this occuring in polynomials which are not in $\mathbb{Z}[X],\mathbb{Q}[X],\mathbb{R}[X]$?


How create circle node in Tikz with T from lines inside? T made split node to 3 sectors

I woud like create 3 sector circle node. See the following figure    sectors are bounded by lines


QGIS 2.99 "qgis._core import error: DLL load failed"

I am trying to run a standalone application. However, it does not run the program because of mentioned error in title. Here is my code:  from qgis.core import * from qgis.gui import * from qgis.utils import * from PyQt5.QtCore import * from PyQt5.QtGui import *  app = QgsApplication([], True) path = "C:/OSGeo4W64/apps/qgis-dev" app.setPrefixPath(path, True) app.initQgis()  canvas = QgsMapCanvas() title = "PyQGIS Standalone Application Example" canvas.setWindowTitle(title) canvas.setCanvasColor(Qt.white)  layer_info = 'LineString?crs=epsg:4326' layer = QgsVectorLayer(layer_info, 'MyLine', "memory") pr = layer.dataProvider() linstr = QgsFeature() wkt = "LINESTRING (1 1, 10 15, 40 35)" geom = QgsGeometry.fromWkt(wkt) linstr.setGeometry(geom) pr.addFeatures([linstr]) layer.updateExtents() QgsProject.instance().addMapLayer(layer)  canvas.setExtent(layer.extent()) canvas.setLayers([layer]) canvas.zoomToFullExtent() exitcode = app.exec_() QgsApplication.exitQgis() sys.exit(exitcode)   When I run it, I get this error:  Traceback (most recent call last):   File "C:/Users/DELL/Desktop/MyMap/myMap.py", line 1, in <module>     from qgis.core import *   File "C:\OSGeo4W64\apps\qgis-dev\python\qgis\__init__.py", line 72, in <module>     from qgis.core import QgsFeature, QgsGeometry   File "C:\OSGeo4W64\apps\qgis-dev\python\qgis\core\__init__.py", line 34, in <module>     from qgis._core import *   ImportError: DLL load failed: The specified module could not be found.  Python version is: 3.6 PyQt   version is: PyQt5.9 Windows 10 - 64bit  I also add many path:  %SystemRoot%\system32 %SystemRoot% %SystemRoot%\System32\Wbem %SYSTEMROOT%\System32\WindowsPowerShell\v1.0\ C:\OSGeo4W64 C:\OSGeo4W64\apps C:\OSGeo4W64\apps\gdal-dev C:\OSGeo4W64\apps\gdal-dev\bin C:\OSGeo4W64\apps\gdal-dev\pymod3\Lib\site-packages C:\OSGeo4W64\apps\grass\grass-7.2.2\bin C:\OSGeo4W64\apps\Python36 C:\OSGeo4W64\apps\Python36\Scripts C:\OSGeo4W64\apps\Python36\DLLs C:\OSGeo4W64\apps\Python36\lib\site-packages C:\OSGeo4W64\apps\qgis-dev C:\OSGeo4W64\apps\qgis-dev\bin C:\OSGeo4W64\apps\qgis-dev\lib C:\OSGeo4W64\apps\qgis-dev\python C:\OSGeo4W64\apps\qgis-dev\python\qgis C:\OSGeo4W64\apps\Qt5 C:\OSGeo4W64\apps\Qt5\lib C:\OSGeo4W64\bin C:\OSGeo4W64\apps\qgis-dev\python C:\OSGeo4W64\apps\Python36\lib C:\OSGeo4W64\include C:\Users\Mustafa Uçar\AppData\Roaming\QGIS\QGIS3\profiles\default C:\Users\Mustafa Uçar\AppData\Roaming\QGIS\QGIS3\profiles\default\QGIS   How can I fix this error?


Voldemort is the only one to make seven, but surely at some point, other dark wizards would have tried/succeeded in making horcruxes. Are there any other wizards that have created Horcruxes?


How to use wildcards for characters inside the name

I have shapefiles in that form  RCs4s3s2c10_S2C10 RCs4s3s2c20_S2C20 RCs4s3s2c30_S2C30 RCs4s3s2c40_S2C40 RCs4s3s2c50_S2C50 RCs4s3s2c60_S2C60 RCs4s3s2cb_S2CB RCs4s3s2c10_1_S2C10 RCs4s3s2c20_1_S2C20 RCs4s3s2c30_1_S2C30 RCs4s3s2c40_1_S2C40 RCs4s3s2c50_1_S2C50 RCs4s3s2c60_1_S2C60 RCs4s3s2cb_1_S2CB RCs4s3s2c10_2_S2C10 RCs4s3s2c10_2_S2C10 RCs4s3s2c20_2_S2C20 RCs4s3s2c30_2_S2C30 RCs4s3s2c40_2_S2C40 RCs4s3s2c50_2_S2C50 RCs4s3s2c60_2_S2C60 RCs4s3s2c10_2_S2C10 RCs4s3s2cb_2_S2CB   How can i use a second wildcard parameter in my code for the first group of fc which don't have a number between _ cause with the following code  featureclasses = arcpy.ListFeatureClasses("RCs*", "Polyline", "")     for fc in featureclasses:           ....   i get everything but i want only the first group of feature classes


Linq to SQL and Codepages in generated SQL

We have a poorly-performing query in L2S.  The actual query looks something like this:  SELECT * FROM Table WHERE      ([ColA] IN (@p0) AND ColB = @p1)      OR ColB IN (@p2, @p3, @p4, @p5) -- @p0: Input Int (Size = 0; Prec = 0; Scale = 0) [220] -- @p1: Input VarChar (Size = 14; Prec = 0; Scale = 0) [CountryDefault] -- @p2: Input NVarChar (Size = 0; Prec = 0; Scale = 0) [] -- @p3: Input NVarChar (Size = 0; Prec = 0; Scale = 0) [] -- @p4: Input NVarChar (Size = 7; Prec = 0; Scale = 0) [WF1 1XU] -- @p5: Input NVarChar (Size = 3; Prec = 0; Scale = 0) [WF1] -- Context: ProfiledSqlProvider(Sql2008) Model: AttributedMetaModel Build: 3.5.30729.1   One problem is a merge-sort as a result of the OR, but we're looking into that.  The other problem is more interesting.  One of our DBAs pointed out there's quite a performance hit in the codepage conversion between the NVarChar parameters and the column they're being compare with VarChar.  The weird thing is how L2S chose for some of those parameters to be NVarChar, and the p1 parameter to be VarChar.  In the code they are all strings, although p1 is a string literal while the others are variables.  Notice they're all being compared to the same column (ColB) so it's nothing to do with the column datatype.  How does L2s decide what datatype to use when generating the query, based on the values passed-in?  If possible, how do I control that?


Is there a possibility to make reference to the line in the lstlisting environment?

I was wondering if it is possible to refer to the lines of the code enclosed in lstlisting environment rather than just manually write a number of the line I want to describe. I have never met with this feature, is this available?


How to make active application float to the top of the launcher

How would one make icons on the launcher jump to the top of the launcher when switching to a window using Alt+Tab  or by clicking that window's icon on the launcher ?


I have a question about a sentence.   When writing for mass media, success goes to he or she who puts their most important info at the top of the story.   Should it be he or she paired with their?


TikZ: Precisely controlling arrow tip position

Usually, when drawing a path with an arrow tip in TikZ, we want the tip to end precisely at the last point of the path, and this is what TikZ does by default. However, with some specific arrow tips, one may wish to control a little more precisely the position of the arrow tip: for instance you may want the base of the arrow to be positioned at the last point of the past instead of the tip.   Here is an example drawing an interval on the real line:  \documentclass{article} \usepackage{tikz,amssymb} \usetikzlibrary{arrows}  \begin{document} \begin{tikzpicture} \draw (-3,0) -- (3,0) node[anchor=south] {$\mathbb{R}$}; \foreach \x in {-1,0,1} \draw (\x,2pt) -- (\x, -2pt) node[anchor=north] {$\x$}; \draw[thick,blue,[-[] (-1,0) -- (1,0); \end{tikzpicture} \end{document}     Is it possible to make sure that the closing square bracket [ is positioned on the tick corresponding to x=1? Of course, it is possible to adjust it manually but this does not seem to be a satisfactory solution.


Copy site with content to another site collection

Are there any SharePoint tools out there that copy all of the content from one site collection to another?  We need to get one site from our site collection and all of the lists and libraries and all of the items on those lists to an entirely new site collection. Are there any good tools out there for this? We also thought a PowerShell script could be viable, does that seem like it may work?  Thank you for your help.


Do mature Stack Exchange sites ever close?

Communities need to pass some critical mass and quality criteria in order to come out of Area51 into StackExchange proper, and be "born". But do sites ever "die" ?   Put another way - is the number of StackExchange sites over time strictly a monotonically increasing function ?   A simple "yes/no" answer would be fantastic, but if this generates discussion, I'm all the happier.   Note : I'm explicitly referring to sites that have already exited Area51 and public beta.   does not seem to answer my question.


I am looking to dual boot Ubuntu alongside Windows 8. While installing Ubuntu from Live CD, I see the whole hard disk as free space even though Windows 8 is already installed and there are 3 partitions.  Could someone guide me on how to install Ubuntu?


For what reasons a bank deny basic saving account

I applied to open a basic saving account with Citibank few days back in Malaysia (I'm not a Malaysian citizen, nor I am an American). I work in Malaysia, and one of the strict conditions of the bank to open account, is to have a work permit valid for 12 months at least. My work permit is valid for 13 months when I applied, and my employment letter (I attached) states I'm a permanent employee. However, two days later, the bank called me to inform me my application was not approved. When I asked what is the reason, she said it is management decision and they cannot disclose it.   I'm baffled as what could be the reason. I read this thread , I could not use the advised website as it seems it only applies to American citizens with social security number (I wonder if there is any equivalent website for none Americans). My salary is higher than the average in this country for my position, and in fact I never had a credit card, never took a loan (I always preferred to pay cash). I've been living in Malaysia for four years, and never had any banking trouble with other local bank.  Is there any way to find out the reason.


Compute $\lim\limits_{x \to 0} \frac{e^x-1}{x}$ without using derivatives

How to compute $\lim\limits_{x \to 0} \frac{e^x-1}{x}$ without using derivatives? Every method I can think of gives me some indeterminate form.


How to make radius of one edge bigger than of a rest

I have a round cube 100x150x100mm with radius 2mm (standard mesh shape). I want to make one edge more rounded than the rest - with radius 10mm. How can I do this?


NullPointerException when insert app: layout _ behavior

I'm working on a app in Android Studio. When i create a new blank activity, by default there is this line in the content_main.xml  app:layout_behavior="@string/appbar_scrolling_view_behavior"   This line destroys me Layout Preview. Happened after updaten from 1.2 to 1.4 To run the app on a device or emulator works just fine.  And i'll get this NullPointerException in the Event log  null java.lang.NullPointerException     at com.intellij.android.designer.designSurface.AndroidDesignerEditorPanel.hasAlphaChannel(AndroidDesignerEditorPanel.java:1386)     at com.android.tools.idea.rendering.multi.RenderPreview.createErrorThumbnail(RenderPreview.java:769)     at com.android.tools.idea.rendering.multi.RenderPreview.tryRenderSync(RenderPreview.java:606)     at com.android.tools.idea.rendering.multi.RenderPreview.renderSync(RenderPreview.java:531)     at com.android.tools.idea.rendering.multi.RenderPreviewManager$3.run(RenderPreviewManager.java:1382)     at com.intellij.util.concurrency.QueueProcessor.runSafely(QueueProcessor.java:238)     at com.intellij.util.Alarm$Request$1.run(Alarm.java:351)     at java.util.concurrent.Executors$RunnableAdapter.call(Executors.java:511)     at java.util.concurrent.FutureTask.run(FutureTask.java:266)     at com.intellij.util.concurrency.QueueProcessor$RunnableConsumer.consume(QueueProcessor.java:298)     at com.intellij.util.concurrency.QueueProcessor$RunnableConsumer.consume(QueueProcessor.java:295)     at com.intellij.util.concurrency.QueueProcessor$2$1.run(QueueProcessor.java:110)     at com.intellij.util.concurrency.QueueProcessor.runSafely(QueueProcessor.java:238)     at com.intellij.util.concurrency.QueueProcessor$2.consume(QueueProcessor.java:107)     at com.intellij.util.concurrency.QueueProcessor$2.consume(QueueProcessor.java:104)     at com.intellij.util.concurrency.QueueProcessor$3$1.run(QueueProcessor.java:215)     at com.intellij.util.concurrency.QueueProcessor.runSafely(QueueProcessor.java:238)     at com.intellij.util.concurrency.QueueProcessor$3.run(QueueProcessor.java:212)     at com.intellij.openapi.application.impl.ApplicationImpl$8.run(ApplicationImpl.java:400)     at java.util.concurrent.Executors$RunnableAdapter.call(Executors.java:511)     at java.util.concurrent.FutureTask.run(FutureTask.java:266)     at java.util.concurrent.ThreadPoolExecutor.runWorker(ThreadPoolExecutor.java:1142)     at java.util.concurrent.ThreadPoolExecutor$Worker.run(ThreadPoolExecutor.java:617)     at java.lang.Thread.run(Thread.java:745)     at org.jetbrains.ide.PooledThreadExecutor$1$1.run(PooledThreadExecutor.java:56)   Also i get in the Preview the following Error Message, on API 19, not on API 22.  Rendering Problems The graphics preview in the layout editor may not be accurate:  - PorterDuff Color Filters are not supported.   I cleaned and rebuild the Project, also reinstalled the SDK  What impact has this line of code in the xml file?


Algebraic independence over $\overline{\mathbb Q}$ and over $\mathbb Q$

Is it true that if $x_1, \dots, x_n \in \Bbb C$ are algebraically independent over $\mathbb Q$, then they are algebraically independent over $\overline{\mathbb Q}$?  I know how to prove it for $n=1$, by the contrapositive. If $P(x)=0$ and $P \neq 0$ has coefficients $a_0,...,a_n$ in $\overline{\mathbb Q}$, then $x$ is algebraic over $\mathbb Q(a_0,...,a_n)$ which is itself algebraic over $\mathbb Q$, therefore $x$ is algebraic over $\mathbb Q$, so it satisfies some relation $Q(x)=0$ where $Q \neq 0$ is a polynomial with rational coefficients.  For $n \geq 2$, I tried induction, but I was not sure how to proceed.  Thank you for your help!


I have several applications and scripts that I want to redirect the output to custom files.  I launch those applications using   command | logger -t TAG   I would like to filter these messages based on their tags and redirect them to different files. I don't want to use bash redirection as those applications are mainly long running process and need proper log rotation.  I have tried to add a custom filter in /etc/rsyslog.d/60-myfilter.conf ;  if $syslogtag == 'giomanager' then /var/log/giomanager.log   What am I doing wrong ?  What is the proper way to filter based on the tag or is there a better option to have similar result?


What does it mean to Fourier transform a ladder operator (in the input-output formalism)?

I am currently trying to get my head around the input-output formalism.  In describing the input-output formalism  , Gardiner and Collett take ladder operators in the Heisenberg picture and apply the Fourier transform to define the input operator.   Specifically, they start with ladder operator $ b(\omega)$, for a mode of frequency $\omega$  which takes the value $b_0(\omega)$ at time $t_0$ and then define the input field $b_{in}(t)$ as (for $t_0 <t$):  $$b_{in}(t) = \frac{1}{\sqrt{2 \pi}} \int_{-\infty}^\infty d\omega e^{-i\omega(t-t_0)}b_0(\omega) \, .$$  I am confused as to how to interpret this. What frequency does the mode now correspond to if frequency has been 'integrated out'? Also is the operator $b_0(\omega)$ not already in the time domain, since it is specified at $t_0$? Could we not write $b$ as a function of $t$ and $\omega$ eg. as $b(t, \omega) = b_0(\omega)$ for $t=0$?  I would appreciate if anyone could clear this up. I suppose my specific questions would be:   How do we interpret the Fourier transform of an operator? Why do we do this in the case of the input-output formalism? What does $b_{in}(t) $ correspond to physically? Any other hints/tips for thinking about this kind of problem.


So I recently lost an iPhone 6s Plus, and ordered a new iPhone 7 plus through the insurance, once the 7 arrived, I restored it via iTunes from a previous backup, now here's the issue. It is logged into my current Apple ID and iCloud accounts, and it is asking me to sign into the accounts to confirm, but they have a two way authentication that sends a 6 digit code to your main device, so essentially it should be getting sent to the new 7, but I receive no message


How can I show a supremum of a set is also its limit point?

It just seems like I can't wrap my head around this. For a set $A$ how can I show that the supremum of that set $\sup(A)$ is also a limit point of said set? Can I just set $$a=\sup(A)$$ $$b\le a \: \:  \forall \: b \in A$$ and then show that there's a point different from $a$ in any $\epsilon$-neighbourhood for any $\epsilon>0$? Or should I use a completely different approach?


From Orwell's essay:  "But apart from these, there are two well-known types of pest by whom every second-hand bookshop is haunted. "  Why is the singular used here? Why not the plural?


What is the word that describes the absence of bureaucracy?

What is the word which describes the absence of formless, of long procedure with bureaucrats? I was thinking about formsless but it sounds weird...


how to write a batch file that takes an arguement from rightClk-> SendTo folder

I have a command from ImageMagick magick '*.jpg' -resize 120x120 thumbnail%03d.jpg  that resizes all jpeg files in a path.  I want to right click on an image and resize it. how do I edit the ImageMagick code so that it accepts this input.  sorry for the obscure question. is it something like '@' or '$1'? I think bash would be something like magick $1 -resize 120x120 $1


I have a directory with a very large number of subdirectories (~800) that were generated programmatically. I want to get a count of the number of files in each of these subdirectories to check for anomalies (if the code broke on a run then some of the files will be missing). What's a quick way to do this? The sort of output I'm looking for is:    Name_of_Folder_1 [# of files in Folder 1]    Name_of_Folder_2 [# of files in Folder 2] ...


Is there a way that I can pipe the output of this command (assuming there is only one file found) to vi.  I want to find this command, and then call it up in vi.  Thanks.  find . -name 'id.properties'


Show the existence of a certain subgroup of F2

This is a homework question: I need to find three subgroups of the free group with two generators, $F_2$, with certain properties. I have found the other two by constructing covering spaces of $S^1 \vee S^1$ and using fundamental groups; I don't think that this approach works here:     Show that $F_2$ has an infinite index, free subgroup of rank two.   If anyone could nudge me in the right direction I'd be very grateful!


How to optimize performace by parallel files acess

There is an application that reads files content of a certain folder and visualizes results in parallel . In case of parallel file access on HDD it works really good, but when I am doing the same things on DVD Rom it works awfull long. When I am wrap the file IO in a lock granting that it only single file read possible) I suisfied with DVD performance, but lacking performance on HDD.  Currently thinking of a mechanism of recognition of a storage performance by given folder path, and then, having some metric I would like to load balance parallel file reading.  How can I get such a metrics? (or if there is a way to get just slow devices like DVD, USB2?)  Is there better solution rather the one I am thinking of?


I've a regex pattern to get some HTML tags in my code. The problem is that the pattern is getting more than just a tag, bringing all the part of code between the first match and the lastest match.  Here is my regex tests:   This is how my current regex looks:  <option_(.*)_[0-9]>   And in the following text and need two different matches (<option_teste_2>,<option_teste_1>):

<option_teste_2>

<input_nome_funcionario>

	<option_teste_1>

   Thanks.


Post notice for posts migrated to per-site Meta gives wrongly worded reasoning again

On the  announcement, :      The wording on the migration banner is kind of awkward when a question is migrated to a Meta site. :   This question was migrated to  because it can be answered by professional and enthusiast programmers.  But it was asked on the site for “professional and enthusiast programmers”. An idea for a better wording:  This question was migrated to  because it’s a question about the site for professional and enthusiast programmers.   It was marked  and Yaakov Ellis has  on 2019-12-23:  The language of the migration notice from main sites to meta sites has been updated to This question was migrated to [$toSiteName$]($destinationUrl$), our site for discussion, support, and feature requests for this site.  If you look at , you’ll still see the old wording:  The other example question from the older report also has the old wording, currently. If this has previously been fixed around the end of last year, it seems that this bug has reappeared. Since the announcement is locked, I can’t ping Yaakov there. Unless I missed something, this needs to be fixed (again).


How do I split template defintion and instantiation into hpp and ipp files

I want to split my template classes into 2 files like how normal classes function with a .hpp where the declaration is and an .ipp where the implementation lives.   I have got this working with normal methods. But with methods that are themselves templates I am facing some issues.  Using the following structure:  #ifndef MATRIX_HPP #define MATRIX_HPP  #include <array> #include <type_traits>  template<typename t,          std::size_t m,          std::size_t n> class Matrix {  static_assert(std::is_arithmetic<t>::value,                   "Matrix can only be declared with a type where std::is_arithmetic is true."); public:     Matrix();      template<std::size_t y, std::size_t x, std::size_t p, std::size_t q>     Matrix<t, p, q> slice() const;  private:     std::array<std::array<t, n>, m> data{}; };  #include "Matrix.ipp"  #endif   Matrix.ipp:  #include "Matrix.hpp"  template<typename t, std::size_t m, std::size_t n> Matrix<t, m, n>::Matrix() {}  template<typename t,          std::size_t m,          std::size_t n,          std::size_t y,          std::size_t x,          std::size_t p,          std::size_t q> Matrix<t, p, q> Matrix<t, m, n>::slice() const {     auto mat = Matrix<t, p, q>();      for (std::size_t i = y; i < m; i++)     {         for (std::size_t j = x; j < n; j++)         {             mat[i - y][j - x] = (*this)[i][j];         }     }      return mat; }   main.cpp  #include "Matrix.hpp"  int main() {     auto m = Matrix<3, 3, int>();     auto sliced = m.template slice<1, 1, 2, 2>();      return 0; }   Now when I compile this it fails with the following message:  ../Matrix.ipp:14:17: error: prototype for ‘Matrix<t, p, q> Matrix<t, m, n>::slice() const’ does not match any in class ‘Matrix<t, m, n>’  Matrix<t, p, q> Matrix<t, m, n>::slice() const                  ^~~~~~~~~~~~~~~ In file included from ../main.cpp:0:0: ../Matrix.hpp:20:18: error: candidate is: template<class t, long unsigned int m, long unsigned int n> template<long unsigned int y, long unsigned int x, long unsigned int p, long unsigned int q> Matrix<t, p, q> Matrix<t, m, n>::slice() const   Matrix<t, p, q> slice() const;   I am not sure how to handle this since the compiler won't recognize it. Is there a way to fix this?  I hope somebody can help me. Thanks!


Redirecting passed arguments to a windows batch file

I would like to call a jar file from a windows batch file. One requirement is to be able to pass all the batch file arguments as-is to the jar file invocation. For example,  Required Command line:  foo.bat --flag1=x --flag2=y --flag3=z   The batch file foo.bat should invoke foo.jar like follows:  java -jar foo.jar --flag1=x --flag2=y --flag3=z   How do I make the batch file do this?  I can do some batch variable magic with % to do this, but is there a simpler way to do this?


What did Logan try to say at this event?

I couldn't make out what the exact words were in the following scene from Logan and would like to ask if anybody can explain it to me.      After burying Professor Xavier, Logan tries to deliver a eulogy but chokes up with emotion/grief.   Was it intended that the audience can't tell what exactly he's trying to say?


What is the correct usage of the word "both" in this example?

I have been provided with the following sentence by a native English speaker  Successful coalitions carefully choose the brands that they think are the best fit for their programme both in terms of value and benefit to their customers.  I am not a native English speaker so a bit hesitant to point out that the correct placement of the word "both" should be as below. Am I right?  Successful coalitions carefully choose the brands that they think are the best fit for their programme in terms of both value and benefit to their customers.


How to find $m$ if $(x^2 + x + 1) | ((x + 1)^m - x^m - 1)$ I tryed to use eyler theorem, but nothing happens. Sorry for bad english.


My professor said me that algebraic topology is an interesting subject.So I decided to study.Sir gave me a book of FRED H Croom.But when I read it I feel it's more difficult to understand. Please help me to give a basic text to understand this topic from it's base.


Show that axiom of replacement implies from the Axiom of Specification [Proof Verification]

Axiom $3.6$ (Replacement). Let $A$ be a set. For any object $x \in  A$ and any   object $y$, suppose we have a statement $P(x, y)$ pertaining to $x$ and $y$,   such that for each $x\in A$ there is at most  one $y$ for which $P(x,y)$ is   true. Then there exists a set $\{y: P(x, y) \text{ is true for some } x \in A\}$    such that for апy object $z$,  $$ z\in \{y : P(x, y)\text{ is true for some } x \in A\}  \iff  P(x,z)\text{ is true for some } x \in A.$$      Axiom $3.5$ (Specification). Let $A$ be a set, and for each  x$\in$  $A$, let $P(x)$ be a property pertaining to $x$ (i.e., $P(x)$ is either  a   true statement or a false statement). Then there exists a set,  called   $\{x \in A : P(x) \text{ is true}\}$ (or simply $\{x \in A : P(x) \text{ for short}\}$),  whose elements are precisely the elements $x$ in $A$ for which $P(x)$  is true. In other words, for any object $y$,  $$у \in \{x \in A: P(x)\text{ is true}\} \iff (y \in A \text{ and } P(y)\text{ is true}).$$   I have to show that $3.6\implies 3.5.$  Proof: By $(3.6)$ we can assume the following set $$\{x:P(x,x)\text{ is true for some }x\in A\}.$$ Let $Q(x)=P(x,x)$ then we get the set $$\{x\in A:Q(x) \text{ is true for some }x\},$$ which is what $(3.5)$ wants. Is this proof correct?  PS. I have read other answers to this question on MSE, but none of them use this formulation of the axiom and I guess use more formal notation. I am learning from Tao's Analysis book and so I've not been introduced to such notation.


Limit the amount of posts for Newsfeed (Site)

Newsfeed (within a site, as a microfeed) works really nicely on Sharepoint, except for the fact that I can't limit the Newsfeed webpart to a certain height (or number of posts). It looks like it is stuck at 10 and there's no way to change this from the interface/webpart editor. In some instances, the webpart can be so tall and not very wieldly.  So, granted there's no way to tweak it from the Sharepoint UI, is there a way to do it using another tool/via programming method, so we can set the initial post number to, say, 5 posts only?  Many thanks!


Play store won't let me download any apps

My internal storage is about 50MB and my SD Card is about 300 MB. When I want to download an app that only need 20 something MB, it says insufficient storage. Even though I delet most of my apps and make my internal storage to about 100MB, it still says insufficient storage when I want to download an app that need 20MB. Please help me to solve this problem as soon as possible.


I'm Unable to Boot into Mac OS Partition, partition type FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF

I've seen similar answered questions like this.  I'm unable to boot into my MacOS partition.  Long story short, I had Windows BootCamp, removed it and then later installed Ubuntu Linux, then tried to delete the Linux partition and I think I ended up deleting the Boot recovery partition. And then tried to run repair, and now my main mac partition now shows FFFFFFF something.  My Macbook is this one   I'm guessing my Macbook got updated to Mojave 10.14 before this happened but I'm not 100% sure of it, it may be on High Sierra but I'm guessing.  I'm booting into Internet Recovery and this is what I've pulled up in the pictures below.  I would like to be able to boot into my regular Mac OS partition.   I'm unable to figure out if the partition is a OS X Standard Partition or CoreStorage or APFS or etc. Is my recovery boot system too old if I need to use gpt to set it to an APFS argument? Should I check if the EFI partition and the Recovery HD partition are corrupted Would the 650 MB boot/recovery partion always be the last 650 MB of the disk Does the partition table contains an MBR instead of an PMBR and would the MBR need to be replaced by a PMBR? Previously the main MacOS partition was resized by me, how and when would be the best time and way for me to resize it to occupy the entire free space like stock?   Please Help.  It default boots into this.  If type exit, I get this.  Holding Option on boot shows   This is rest of the stuff I pulled from internet recovery        Please Help!


How can I find a Douglas-Peucker algorithm for simplification?

I want to understand simplification methods in GIS. I searched the Internet and found that the best simplification method is the . I could not find any information about the algorithm and how the algorithm works. Is there a resource detailing the methodology behind the algorithm?


In simple terms, is the permittivity of free space the polarizability of a vacuum?

I'm having a hard time understanding the permittivity of free space in my own words. Wikipedia defines the permittivity of free space as "the value of the absolute dielectric permittivity of classical vacuum." and it defines the absolute dielectric permittivity as "a measure of the electric polarizability of a dielectric". So would that mean that the permittivity of free space is the polarizability  of a vacuum? If not, could someone please explain it in simple terms. (I need to give a simple definition in a lab report and I want to understand it fully in my own words to avoid any possible plagarism.)


Intuitive (combinatorial) proof of $2^n=\sum_{k=0}^n {n\choose k}$

Why should we expect that $$2^n=\sum_{k=0}^n {n\choose k}$$   It is easily seen to be true, by the binomial theorem:  just set $x=y=1$ in $(x+y)^n$.  But what is an intuitive reason why it is true (in terms of subsets)?


What is the value of $\sum\limits_{i=1}^\infty\frac{1}{p_{p_i}}$ where $p_{i}$ is the $i$th prime?

What is the value of $\sum\limits_{i=1}^\infty\dfrac{1}{p_{p_i}}$ where $p_n$ is the nth prime (and so $p_{p_n}$ is the $k$th prime, where $k$ is the $n$th prime) ?  Thus $\frac{1}{3}+\frac{1}{5}+\frac{1}{11}+...=$ ??  How do I efficiently decide if $\sum_{i=1}^\infty\dfrac{1}{p_{p_i}}\gt1$ is true without using a computer ?  I assume this infinite sum is an irrational number. Has this already been proven ?


Normalize .ogg audio files with the command line

I'm trying to normalize (and or compress) around 100 .ogg files which have audio level really too low.  I know that by hand I can use Audacity ... but that will be too much clicks! Instead I was looking for a tool which can be used in a small script (or with --recursive).  Just tried to look in man oggenc, man ffmpeg, with no success yet...  Thanks!


I really want to fight Plantera, because I have all the gear and stuff. But there's one problem; I don't know how to summon it. What do I have to do to summon Plantera?


i bought Dell Vostro 2520 in which Ubuntu was already installed. i want to uninstall Ubuntu and install win7 on that machine. For that i used Gparted on Ubuntu and had eraseed partiion of Ubuntu. And for install win7 i used win7 DVD from Boot optionn, But laptop not getting boot via DVD. even i tried bootable Pan drive of Win7 but had same problem.  i have Ubuntu live cd.  is there any solution for this problem? plz show me step by step.


Why is Nearly-Headless Nick a ghost, and Harry's parents aren't?

In Harry Potter and the Sorcerer's Stone, Nearly-Headless Nick and some other ghosts can visit the Hogwarts students, but why can't other deceased people - such as Harry's parents?


How to change browser page title dynamically to match it with  title in javascript or jQuery?

I would like to change my page title dynamically so that it will match with the value of 'h1' heading element.  Need to write a global javascript, which I can use throughout the application for every page. Kindly advice.  Thanks in advance


Objective-C: Any TreeSet or TreeDictionary?

Is there any analog in Objective-C to the TreeSet or TreeDictionary in Java. Basically, either a Set or Dictionary data structure that's implemented via a tree (sorted) versus a hash table (un-sorted).   Thanks!


When I use Windows I currently use AutoHotKey to re-map keys (I swapped keyboards on my laptop).  Is there any way I can do this in Ubuntu via a script which I can just double-click from the desktop? Or can AutoHotKey/anything similar be used on Ubuntu?  Any example is most welcome- say remap the insert key to the home key?


How do I privately tell the mods that I think a user is using a bot-net to gain points? Is there a way to do this privately?


Completely unable to acess admin password due to reset

I accidentally removed Admin permissions from my main account. For whatever reason, there is a secondary "Administrator" account that I am completely unable to login to. It also says "Password must be changed to use" so I cannot access the "forgot password" prompt. My computer is essentially useless now, and about two hours of searching for similar issues yielded no luck. My computer is windows 10.


If $a^6 \mid b^6$, where $a,b\in \mathbb{Z^{+}}$, then does $a\mid b$?    I was thinking of using the Fundamental Theorem of Arithmetic to show that $$a^6=\prod_{i}p_{i}^{6k_i}\quad\text{and}\quad b^6=\prod_{i}p_{i}^{6q_i}$$ And, since $6k_i\leq 6q_i$, $\forall i$, $k_i \leq q_i$ which implies $a\mid b$.   Is this correct?


Karlov attacking together with a lifelink creature

If I attack with  and another creature with lifelink, is Karlov getting 2 counters before he deals his damage this turn? Or are both damages dealt at the same time?


A list of topics well-suited for self-answered questions

The idea of self-answers seem to be slightly against the primary purpose of this site. This site doesn't want to accumulate the kind of junk other sites tend to (I think). Also, this site wants to become an encyclopedia of non-trivial, useful information in the form of questions and answers.  But if self-answers are allowed, then the question-answers (might be) more inclined towards being trivial or not useful for a lot of people.   My question is: What kind of self-answered questions must be promoted to be more suitable for this site. What kind of topics? etc.


returning float with all the numbers after period

Wanted to ask, why  5 / 100  returns 0 , but it works with  5 * 0.01 , even though arithmetically both should return the same value?  even float(5 / 100) returns 0.0


Why does my badges page have fewer badges than my usercard says I have?

If you check  you will see there's a problem with my badges.  There where it shows the Gravatar and reputation, it says I have 15 badges. But  where it shows what badges I have it only says I have 14. How many do I really have? Why does it show two different counts?


How do I change the equation numbering to appear in the right, instead of the left default side in Lyx?


I'm trying to setup OpenVPN using NetworkManager. The GUI seems buggy and unresponsive. Are there any other tools for setting up a VPN client?


WIll partitioning an SSD make it slower?

Having read a number of SSD reviews, in particular, of those made by Crucial (a.k.a Micron), I've come to the conclusion that partitioning an SSD is going to make it slower. Here is the logic:  Those reviews explained that (at least the Crucial SSD's based on Marvel controllers) are essentially a RAID array of memory chips soldered to the board, invisible to the end-user as separate entities. I recall one or more of the reviews explicitly stated that the smaller capacity drive sequential access speeds were lacking because it had only half the number of chips of the larger drive. The slowdown was almost linear according to their testing. Thus, I conclude that when I partition such a drive, only a part of the chips are going to be in the partition, thus I'm going to suffer from the said linear slowdown.  Is the above true for Marvell based Crucials? For other drives such as Samsung-controller based, Sandforce-based, others? I'm particularly interested in the Crucial drives, them being the best bang for the buck right now. I'd be happy to also RAID a couple of those on an X79, but totally unsure about partitioning that either. However, that would be a separate question, and not a part of this one, so I'd like to first firgure out partitioning a single SSD drive.


Remove write protect from Sandisk Cruzer blade 16 GB?

1 Month Old Sandisk Cruzer Blade 16 GB. Became write protect while trying to copy 13 GB data from a friend's computer using Windows 7. Suddenly transfer stopped because of write protect. Did scan for malicious viruses in my computer running on Windows 10. Windows Defender finds worms and Trojan win32 and destroys it. But its back. Not able to format the usb because of write protect. Did  1. Quick format 2. in regedit added value of WriteProtect in StorageDevicePolicies to 0 3. There is no way for gpedit.msc since my system is running on Windows 10 Home edition 3. In disk part, able to make attributes as readonly but not able to clean because of write protect 4. in Disk management no option to format at all  5. Tried using third party softwares like usbfixer, HDD low level format tool and HD Tune Nothing worked because of write protect.  How to remove write protect?


Looking for a novel about a dystopian future where the resistance operates a help line

I read this while up at my grandparents somewhere around 1990ish. Given how many books they had from when my dad was growing up, there's a decent chance that it's older. It was a novel where the government kept pretty strict control of society. They had some sort of mass entertainment covered because I remember a reference to the government giving the citizens "their bread and circuses" as a reference to the Roman practices. The biggish twist is that the resistance isn't so much actively fighting the government as that they're producing a pressure valve by using their hackers to set up telephone relays which act as support lines. Anyone can call and talk about their troubles. The telephone technology was relatively old — I think I remember them talking about mechanical relays — and they advertised the changing numbers (they had to keep going to new ones as the government shut down the old ones) on flyers that they posted all over the place.  The one bit of imagery that really stuck out to me was where a female member of the resistance was explaining to the male protagonist that, no matter how bad things got, they had to stay on the line, and she recounted one of her first calls involving a mother who'd locked her baby into a high-chair and was flinging spoonfuls of vitriol (acid, but they specifically used the word "vitriol") at the baby as she talked.  I don't think I ever got to finish the book, so I have no idea how it ended.


Improving "This question belongs on another site in the Stack Exchange network"

On closing panel in stackoverflow there is the following form:    Sometimes I find questions, that are more suitable for  or , but I can't vote for migration there, using this panel. So I have to raise a flag: "it needs ♦ moderator attention", and write: "belongs to codereview.stackexchange.com".  Is it possible to allow voting for migration to the other sites of stackexchange network?


How to delete a command that was made while typing

-So I mistyped \newline and a new command was made like \newlithen and now every time I type \new, the wrong command prompts up first and it is really starting to annoy me, anyone know how to delete a command. Thanks


Greatest common divisor / euclidean algorithm linear combination proof

Consider integers $m$ and $n$, not both 0. Show that gcd$(m,n)$ is the smallest positive integer that can be written as $am + bn$ for integers $a$ and $b$.  I'm confused on what exactly to do--I'm having trouble wrapping my head around the question. I know that using the euclidean algorithm backwards will provide me with an $a$ and a $b$ such that $am + bn = gcd(m,n)$. But I'm not sure how to prove that it is the smallest positive integer.


I have been going through String class in Java in depth.         String in Java is backed by character array.  To create strings that have initial values, we call the constructor as:       /* String creation */          String s = new String("example");   The constructor code in the String class is:          public String(String original) {             this.value = original.value;         }   Can some one please explain me the logic of "original.value". From the source code, I understand it returns character array. But how java generates it?


Is it dangerous to keep my phone plugged in indefinitely?

I just recently got a new phone, so my old one has been sitting in a drawer for the last month. However, a friend recently suggested the Sleep Cycle alarm to me, and I'd like to try it out, but I'm not willing to put my nice new phone under my bed every night and run the risk of it overheating or breaking.  However, my old phone, a ZTE Valet (Incredibly cheap, all-around low quality phone), I couldn't care less about. So my plan is to plug that in next to the wall, and use it exclusively for the alarm. I go to bed, I set the alarm, I wake up, I turn it off. It never leaves the wall.  However, I'm concerned about safety. It'll be in airplane mode and I'll disable other background apps that I can (probably just factory reset it before doing this), but is it dangerous to keep my phone constantly plugged into a wall on top of bedsheets? I know this might be bad for the batter (don't really care, I'm not doing anything else with the phone anyway), but I'm much more worried about any potential overheating problems that could burn me or start a fire. Should I be?  EDIT: I don't think this is a duplicate. I really couldn't care less if the phone is harmed by the constant charging, I just want to know if it's dangerous.


How do I recover my Google account (or Gmail) password or username?

I have forgotten the password or username for my Google account, or I'm unable to access my account for other reasons.  How can I recover my account?  (This Q&A is meant as a general description for all Google and Gmail username/password questions. See: )


Character array passed in double quotes to a function

What happens behind the scene when a string in double quotes is passed as an argument to a function? Where is memory allocated for that string?  If I do memcpy(ptr, "SINGH", strlen("SINGH")+1);, output is SINGH only. From where is the extra byte copied from?  For below program:  void func(char *ptr) {     memcpy(ptr, "SINGH", strlen("SINGH"));     cout << ptr << endl; /* Output is SINGHHELLO */     /* If I do memcpy(ptr, "SINGH", strlen("SINGH")+1); Output is SINGH only. From where does extra byte is copied from? */ }  int main() {     char str[11] = "HELLOHELLO";     char str2[10] = "ABC";     memcpy(str, "HELLO", strlen("HELLO")); /* Where is memory allocated for string 'HELLO' ? */     cout << str << endl << str2 << endl;     func(str);     return 0; }


Why does dust form islands on top of water?

When you pour sand into water, first the dust particles that are floating on the surface, are separately all over.    Then as the water flows, the dust particles should just randomly move around staying mostly separately, but for some reason, all the dust particles are moving together and sticking together into islands, just like planets are formed from dust in the solar systems.    It is like there was some force that is pulling these dust particles together, and keeping them in these islands. Is this the same Van der Waals force that keeps the water molecules together?    Question:   Why are dust particles moving together into these islands on top of the water?


How can I delete Time Machine backups, moved into trash?

I was going to delete the Time Machine backups. I made a mistake and instead of deleting them using Time Machine, I just moved the Backups.backupdb folder to the trash. Now, if I try to empty the trash, Finder attempts to count the number of files that will be deleted, and this process is incredibly time-consuming, because the Finder tries to count each file in each backup. The same thing happens if I try to move the Backups.backupdb folder from the trash back on my hard drive where it was before.  What can I do in this situation? How can I delete the backups?


Why? My website is not showing "cache option" in search result

Plz guide me. Why? my website is not showing "cache option" in search result.  when I check Ex- (Cache:  ) then it shows -  "404. That’s an error."  URLs are indexed & no any issues in search console.   We dropped my ranking due to it. so plz


why math.round(1.755,2) result is 1.75 not 1.76 but round(1.7555,3) is 1.756


Hypernym for "audio podcast", "radio drama", and "audiobook"

I'm setting up my media library to contain music, movies, shows, audio podcasts, radio dramas, and audiobooks.  I would like audio podcasts, radio dramas, and audiobooks to be in the same category, but I can't think of any term that includes all three. (The closest I can think of is Non-Music Audio.)  Is there any good collective term for audio podcasts, radio dramas, and audiobooks?


Reversing a string in C without using library functions

I am trying to write a code in C, to reverse a string. Needless to say that using library functions is not an option as I am trying to build a little bit of logic. I am getting a read access violation at line 22. I tried doing this using character arrays as well as string pointer, but both give the same "access violation" result. Can somebody clear the concepts regarding the string access rules using this example? #include<stdio.h> #include<stdlib.h>  int main() {     char reversed_string[21], input[21];// *temp;     printf("Please enter the string(max 20 characters) : ");     gets_s(input, 20);     unsigned short int i, j,length;      i = j=length = 0;     while (input[i] != '\0')     {         length++;         i = i + 1;     }     i = length - 1;      while (i >= 0)     {         reversed_string[j] = input[i];         i = i - 1;         j = j + 1;     }     reversed_string[j] = '\0';          printf("\n The reversed string is : %s.\n\n", reversed_string);          system("pause");     return 0; }


Would equations for a spinning top be an (x,y,z) vector

I am following the equations on , and for torque it is $mgr\sin\theta$, but I am curious about $r$.  I am working on a game and I want to correctly model the top, and am curious if $r$ should be the distance from the tip of the top to the center of mass as an $(x,y,z)$ vector, or should it just be the scalar version?


I understand 'when' we right censore a survival time. But why do we do so? And how does it affect analysis in survival context. I would appreciate it anyone could recommend some reference.


Proof by contradiction, why does it work?

I'm reading learning to reason by Nancy Rodgers, and in her textbook she says: (we have to derive $r$)  "To justify the validity of a proof by contradiction, we can argue as follows. When we assume $∼r$ is true and derive c and -c, we have proved the following implication: $$∼r⇒(c∧∼c)$$ Next we translate the above implication as an or-sentence. $$r∨(c∧∼c)$$ since $(c∧∼c)$ is false, $r$ must be true."  I dont really get this, "assume $∼r$ is true" blah blah.. "so $r$ must be true" how can $∼r$ and $r$ both be true?  One more doubt, I know she used this equivalence: $(p∨q)⇔ (∼p⇒q)$, but I dont get this either:  "it's blue or it's red $⇔$ if it's not blue then it's red" what if it's yellow though? both sentences would be false (correct since they're equivalent) but I can't say that since "it's not blue" it's red, because it's yellow! This is what the the textbooks seem to say: "since $(c∧∼c)$ is false, $r$ must be true." but how? what if it's another thing? I'm so confused, can you guys help me please?


Why has a circle when the point light through my glass？

I found there is a circle when the point light through my glass material using the circle render.  How could I solve it?


Hints for showing that if $x,y \geq 0$, then $(x+y)^k \geq x^k + y^k$ for all $k \geq 1$

I'm trying to show the following:          If $x,y \geq 0$, then $(x+y)^k \geq x^k + y^k$ for all $k \in \mathbb{R_{\geq 1}}$      So, far I've tried a few things, but nothing seems to stick. Clearly $x \leq x+ y$ and since both sides of the inequality are positive, the inequality $x^k \leq (x + y)^k$ will hold for $k \geq 1$. Similarly, $y^k \leq (x+y)^k$. Adding both inequalities together, we obtain: $x^k + y^k \leq 2(x+y)^k$. While this is close, of course, it is not what we want to show.  Alternatively, I was thinking that if we fix $x,y \geq 0$, let $f(k) = (x+y)^k$, and let $g(k) = x^k + y^k$, we can show using the binomial theorem that $(x+y)^r \geq x^r + y^r$ for all $r \in \mathbb{Z^+}$. Then, if we can show both $f$ and $g$ intersect only when $k =1 $, we might have better luck proving the statement since then we would have $(x+y)^r > x^r + y^r$ for all positive integers $r \geq 2$. A real number $m \notin \mathbb{Z}$ with the property that $f(m) = g(m)$ could not then exist since then that would violate the fact that $k=1$ is the only intersection. We could then invoke the continuity of $f$ and $g$ together with the fact that $(x+y)^r > x^r + y^r$ for all positive integers $r \geq 2$ to obtain our result. Of course, all of this is dependent on rigorously showing that $f$ and $g$ intersect only when $k=1$.  Otherwise, I'm running low on ideas. Any hints would be greatly appreciated.


How to make Windows login automatically to a user if there are more than one users?

The system is Windows7 64-bit Integral Edition. There are two administrator users : Ambre-68 and postgres. When I start my computer then there is the screen showing the choice of users. I want Windows to login automatically to the user AMbre-68. How to do that ?


Under what circumstances can the word "be" be used directly without any change?

Possible Duplicate:          2 examples first:  1.It is announced that the accounting class of the 3rd and 4th hours on the morning of this Wednesday be cancelled  2.It is expected that everybody and each household be on guard  Someone told me this kind of examples above appears in the textbook as strict sentences to be taught in the classroom, so is that right for the usage of be  Meantime I looked up the word be at thefreedictionary.com and found one piece of interpretation says :      Archaic Used with the past participle of certain intransitive verbs to   form the perfect tense: "Where be those roses gone which sweetened so   our eyes?" (Philip Sidney).   So is there any connection between the archaic usage & the examples above? BTW, how to understand the short phrase "the 3rd and 4th hours". Many thanks!


How do you "OR" criteria together when using a criteria query with hibernate?

I'm trying to do a basic "OR" on three fields using a hibernate criteria query.  Example  class Whatever{  string name;  string address;  string phoneNumber; }   I'd like to build a criteria query where my search string could match "name" or "address" or "phoneNumber".


How do I recalculate normals for all objects in the scene? Normally, I select an object at a time, press Tab, press a to select all vertices/faces and press Ctrl-n. If I have 20+ objects in the scene, can do it in one hit combo?


Connected CPU to PCI-E connector. Did I fry something?

I just bought an AMD motherboard and CPU and a modular PSU.  The PSU came with a cable with 2 8-PIN connectors, one RED and one BLACK.  I haven't been  careful enough and I connected the motherboard's 12v 8-PIN CPU connector (BLACK) using the BLACK-RED cable to the RED connector on the PSU.  The computer did not start and the PSU was making a lot of hissing noise. Even the CPU fan was not running. I disconnected everything.  Subsequently, I re-checked the connections and realised I connected the 12V 8-PIN CPU connector to the PCI-E connector of the PSU.  I amended the connection and when I press the power button the fan now spins up but the computer still doesn't start.  Did I fry something? What may I have fried?


Intuitive interface for Composing Boolean Logic?

I'm interested to know how people have, or would construct an interface which simplifies constructing logical boolean conditions? (Yes, it's a database query builder) In my mind a bad interface has them typing lots of AND, NOT IN, OR keywords etc. Or else has a million combo boxes.  I'm wondering if anyone has a good example I could glean ideas from? Or some suggestions?  At the moment I'm considering a split screen with a grid for composing the query and a canvas to display a visual representation of the sets of conditions and how they overlap etc. Like a Venn Diagram. This still gives me a problem with the usability/intuitiveness of the controls on the grid.  EDIT:  I'm very interested in ideas which simplify it for less technical users. However, ideas for a version of the UI for advanced users are very helpful as well.


A complete picture of the lattice of subfields for a cyclotomic extension over $\mathbb{Q}$.

Is there a good general purpose algorithm (batch of theorems) allowing one to determine the intermediate fields between $\mathbb{Q}(\zeta)$ and $\mathbb{Q}$, where $\zeta$ is some primitive root of unity?  Let $p$ be a prime. Consider the case where $\zeta=\zeta_{p}$ is a primitive $p$-th root of unity. Then the Galois extension is cyclic of order $p-1$ and $1,\zeta,\dots,\zeta^{p-1}$ is a $\mathbb{Q}$-basis for the extension. In this case for any subgroup $H$ of $G=\mathbb{Z}/(p-1)$, by considering the sum $$\alpha_H=\sum_{\sigma\in H}\sigma\zeta,$$ we can observe that $\alpha_H$ lies in the fixed field for $H$, and any automorphism $\tau$ not in $H$ (note automorphisms are identified with subgroups of $\mathbb{Z}/(p-1)$ in the natural way), $\tau$ does not fix $\alpha_H$. Therefore we can conclude that $\mathbb{Q}(\alpha_H)$ is the fixed field of $H$.  In this way we can get all of the intermediate fields of $\zeta_p$ for all odd primes $p$.  We also have a theorem that says if we have $n=p^sq^t$, then $$\text{Gal}(\mathbb{Q}(\zeta_n)/\mathbb{Q})\simeq \text{Gal}(\mathbb{Q}(\zeta_{p^s})/\mathbb{Q})\times\text{Gal}(\mathbb{Q}(\zeta_{q^t})/\mathbb{Q}).$$  So what I have yet to understand is  How can one generally find the intermediate fields between $\mathbb{Q}(\zeta_{p^s})$ and $\mathbb{Q}$ for $s\ge 1$? I would like to also understand the case where $p=2, s>1$ though this might turn out to be a separate case.  EDIT: Even the case $n=pq$ is a little murky to me. Even given the isomorphism given by the Chinese Remainder Theorem I don't see a priori how to get all the "product" subfields. My idea is that you can consider the separate subfields under $\text{Gal}(\mathbb{Q}(\zeta_{p})/\mathbb{Q})$ and $\text{Gal}(\mathbb{Q}(\zeta_{q})/\mathbb{Q})$ separately and then consider the pairwise product of the generators of various subfields to see if you get anything new, but my idea is too inchoate.


$f:X\longrightarrow\mathbb{R}$ is continuous iff $\{x\in X:f(x)\geq\alpha\}$ and $\{x\in X:f(x)\leq\alpha\}$ are closed $\forall\alpha\in\mathbb{R}$

I'm trying to prove that $f:X\longrightarrow\mathbb{R}$ is continuous if, and only if, the sets $$\{x\in X:f(x)\geq\alpha\} \text{ and } \{x\in X:f(x)\leq\alpha\}$$ are closed $\forall\alpha\in\mathbb{R}$, where $X$ is a metric space.  I've managed to prove the $\left(\Rightarrow\right)$ direction:  I'm using the negative, that is, supposing that one of the sets are not closed and showing that $f$ won't be continuous. Suppose $A\equiv\{x\in X:f(x)\geq\alpha\}$ is not closed, then there's a limit point $y\notin \{x\in X:f(x)\geq\alpha\}$ and a sequence $y_n\longrightarrow y$. Without loss of generality, let $y_n\in A,\forall n\in\mathbb{N}$, then $f(y_n)\geq\alpha$, but $f(y)<\alpha$.  Therefore, $|f(y)-f(y_n)|\geq\varepsilon >0,\forall n\in\mathbb{N}$, where $\varepsilon = \alpha - f(y)>0$. $\Box$  However, I'm having some trouble with the $\left(\Leftarrow\right)$. Can anyone give me some tips?  Thanks for helping! :D


Will a Codon result in same amino acid across organisms

Will all organisms with the same 3 nucleotide sequence in the codon produce the same exact same amino acid. I read that the three nucleotide sequence will code for a particular amino acid. I did not understand if that is the case across organisms. Can someone explain this in simple terms.


Estimate the number of trials needed to observe all the possible outcomes of an experiment

I am stuck with the following problem: Each package of Pokemon cards contains 1 of N possible legendary Pokemon. How many packs do you expect to buy to get all N? We assume all N legendary cards are equally likely with each purchase.  Here it is my trial of incomplete solution.  I model the problem as follows: I have an unrn containing $N$ different objects labeled from 1 to $N$.  I am performing draws with replacement from this urn. I report the results of my experiment into an $N$ component vector, $\vec{k_n}=(k_1^n,\dots, k_N^n)$ where $k_i^n$ is the number of times that event $i$ has occurred out of $n$ trials. Clearly $\Sigma_{i=1}^{N}k_i^n=n$.  Therefore the probability of observing a given vector of outcomes $\vec{k}$ out of a number of $n$ drawings is $$ p(\vec{k_n}=(\tilde{k_1}, ...,\tilde{k_N})|n\text{ trials})=\frac{n!}{\tilde{k_1}!\dots\tilde{k_N}!}p_1^{\tilde{k_1}}\dots p_N^\tilde{k_N} $$ since all the legendary cards are equally probable we have that $$ p_1=p_2=\dots=p_N=\frac{1}{N} $$ and remembering that  $$ \Sigma_{i=1}^{N}\tilde{k_i}=n $$ We get $$ p(\vec{k_n}=(\tilde{k_1}, ...,\tilde{k_N})|n\text{ trials})=\frac{n!}{N^n}\frac{1}{\tilde{k_1}!\dots\tilde{k_N}!} $$  Arrived at this point I have no a precise idea on how to continue (maybe using bayesian inference?) and need an help...


I'm trying to dual-boot Win10 and Ubuntu 18.04 LTS, if that matters. I have made a partition for Ubuntu, changed my SSD from RAID to ACHI mode, and disabled fast-boot. I have a Nvidia GTX1060.  I've been trying to install Ubuntu on my XPS 8900, and I noticed that my computer is not compatible with Ubuntu. When running the installer, the kernel gives me the error:   kernel: tpm_crb MSFT0101:00: [Firmware Bug]: ACPI region does not cover the entire command/response buffer. [mem 0xfed40000-0xfed4087f flags 0x201] vs fed40080 f80   kernel: tpm_crb MSFT0101:00: [Firmware Bug]: ACPI region does not cover the entire command/response buffer. [mem 0xfed40000-0xfed4087f flags 0x201] vs fed40080 f80   Also, the installer hangs when it gets to creating partitions. I've heard that you can fix this by editing the grub command line to boot the kernel with the following line of code:   pcie_aspm=off   So, how do I fix the first error, edit the grub code, make my system compatible, and do anything else I need to do to install correctly?


Can anyone please explain how air suspension lockout works? I mean physically what happens inside the shock?  There are also multiple setting in lockout, how are they implemted?


I have been solving problems using a "Potentially Helpful Formulas" sheet from my esteemed math professor. i want to solve for:   $\sum_{n=1}^{\infty} \dfrac{1}{n^4} =$ ?  On my formula sheet i have:  $\sum_{n=1}^{\infty} \dfrac{1}{n^2} = \dfrac{\pi^2}{6}$  Which looks similar to what i want, but not quite. Might someone guide me towards the solution (or provide the solution with explanation?


What is the value of $\operatorname{Arg}(\frac{z}{\bar{z}})$?

As part of an exercise, I was asked to plot this condition on the complex plane:  $$-\frac{\pi}{2} \leq \operatorname{Arg}\left(\frac{z}{\bar{z}}\right) \leq\frac{\pi}{2}$$  My question is:      What is the value of $\displaystyle\operatorname{Arg}\left(\frac{z}{\bar{z}}\right)$?


What is $\lim_{x \to 1} \sin(\frac{1}{x-1}) ?$  I have attempted this question by substituting 1 into the equation however I know I am not allowed to divide by zero, how would I attain a limit (I have not learnt any rules such as l'hopital's rule.  Thank you


How to check what application is requesting port?

Is it possible to check which application is requesting specific port in a debian server? I'm getting a ton of these in iptraf:     x x UDP (77 bytes) from 172.16.0.2:25748 to 212.59.1.1:53 on eth0   x x UDP (105 bytes) from 212.59.1.1:53 to 172.16.0.2:25748 on eth0   x x UDP (77 bytes) from 172.16.0.2:15956 to 212.59.1.1:53 on eth0   x x UDP (93 bytes) from 212.59.1.1:53 to 172.16.0.2:15956 on eth0   x x UDP (77 bytes) from 172.16.0.2:64869 to 212.59.1.1:53 on eth0   x x UDP (105 bytes) from 212.59.1.1:53 to 172.16.0.2:64869 on eth0   x x UDP (77 bytes) from 172.16.0.2:27489 to 212.59.1.1:53 on eth0   x x UDP (93 bytes) from 212.59.1.1:53 to 172.16.0.2:27489 on eth0   x x UDP (77 bytes) from 172.16.0.2:32834 to 212.59.1.1:53 on eth0   x x UDP (105 bytes) from 212.59.1.1:53 to 172.16.0.2:32834 on eth0   x x UDP (77 bytes) from 172.16.0.2:31633 to 212.59.1.1:53 on eth0   x x UDP (93 bytes) from 212.59.1.1:53 to 172.16.0.2:31633 on eth0   x x UDP (55 bytes) from 172.16.0.2:31892 to 212.59.1.1:53 on eth0   x x UDP (83 bytes) from 212.59.1.1:53 to 172.16.0.2:31892 on eth0   172.16.0.2 is the internal IP (using dummy package) of virtual machine inside xen (which I'm monitoring right now - this snippet is from 172.16.0.2 machine), 212.59.1.1 is my ISP DNS server.  Is it possible to see which application/PID is making these requests? Or is this a normal behaviour? Investigating this because I might be flooding myself by those request, even losing my network connectivity.


Allow flagging a comment after upvoting it

It's sad to upvote a comment on a post that's subsequently updated in a way that renders the comment obsolete and not be able flag it afterwards.  There may well be other cases where one would want to flag an upvoted comment too.  Related:     From November '09:  Note that this was before comment votes could be undone, so one slip and you were stuck.  The suggested solution there is to flag the post instead with a note about which comment to look at which is inelegant and potentially a problem as flagging a post can have repercussions beyond just bringing it to the mods' attention. From June '10:  Also pre-, which is presumed to address the problem, except that it doesn't in this case.     So here it is nearly three years later and this question lingers unresolved.  It's been positively received (no downvotes yet!), but hasn't gotten any developer response.  The problem that this change would address is still a problem.  The UI as implemented is still confusing: flags are generally orthogonal to votes on questions and answers, so why do comments take an either/or approach?  Comments are purposely second-class citizens, but this seems like privileging them--protection for comments that should be removed!


Convert pressure cooker recipes for 8 psi

I have a new electric multi cooker, it works at 8PSI and I am having difficulty at finding out how to convert stove top pressure cooker times at 15PSI down to 8PSI, hoping for your help. Regards Joan


C# process.start() pausing the execution - BEGINNER

I have a C# forms application, and it has few buttons on it. I have used Process.start to execute a .exe program (this hapens as soon as the program is launched (onload())). Now what i need to do is, when a user clicks on a particular button on the form, i need to pause the execution of the .exe file and when they click on another button  i need to resume execution.  How should i do this ?  Help appreciated.


Are salesforce record ids generated lexicographically ?

I am planning to store the records in a particular object in an HBase table. I want to know if a new record Id is created lexicographically.


With the phone ringing: "I don't know who it is" or "I don't know who they are"?

Your phone is ringing and your daughter picked up the phone but she hasn't answered the call. Then do you ask her:     Who is it?   or      Who are they?   And when she tells you, would she say:     I don't know who it is"   or     I don't know who they are?   If none of the above isn't natural, then what is it?


I recently started watching Ghost Adventures and they seem real to me. But then I checked it on the web and found that it is a fake show. Some say it is fake, while others say it is real.   Still, I decided to check Wikipedia. I found that the show has "script" written by some crew member.  So, is this TV Series real or fake? If this is real, why it has "script"?