I am trying to install devstack on Ubuntu server 14.04.  I had a few problems before with HOST_IP, GIT_BASE and some updates... I fixed all of them, but now I am stuck on this one. I tried apt-get update and apt-get install libsystemd-dev, and I get  E: unable to locate package libsystemd-dev


We have an industrial program. For a device that is running 24 hours a day. The database is constantly used. What I noticed today after 4 months: The database log file size was 80 Gig !  Query execution speeds were slower. Shrink did not reduce the volume of logs. With my search I set the Recovery Model to Simple, and then I did the Shrink . Logs volume reduced to 1 MB !  Recovery model set to Full.  But why did this happen? And how can I stop it?  If you need more info tell me to add it


Moment of inertia of a cylinder about its base

I've tried to find the moment of inertia of a cylinder rotating about an axis parallel to its base (i.e about the 'End diameter') as one can see  . But when I checked my results with different references ,I've found that it's incorrect!.I need a help to figure out where I did it wrong. since $$I=\int\limits x^2.dm$$ $$dm = \rho.dv$$ where $$dv= r.d\theta . dr .dh$$ & $$\rho=\frac{M}{\pi R^2 H}$$ $M$:cylinder total mass. $H$:total height of cylinder. $R$:the radius of the cylinder. The distance of each infinitesimal element from the axis of rotation would be : $$\sqrt{r^2+h^2}$$ Therfore, $$I= \frac{2M}{ R^2 H}\int\limits_{0}^{R} \int\limits_{0}^{H}\, r(r^2+h^2)dh\,dr$$ and this gives a result of : $$\frac{M~H^2}{3}+\frac{M~R^2}{2}$$ Which is obviously wrong since the second term should be multiplied by a factor of $1/2$.


I just booted 1st time into Ubuntu Server 14.04.1 LTS (no GUI), enabled UFW, went to update with sudo apt-get update and the results showed this:  Ign cdrom://Ubuntu-Server 14.04.1 LTS _Trusty Tahr_ - Release amd64    (20140722.3) Trusty InRelease Ign cdrom://Ubuntu-Server 14.04.1 LTS _Trusty Tahr_ - Release amd64 (20140722.3) Trusty/main Translation-en_CA Ign cdrom://Ubuntu-Server 14.04.1 LTS _Trusty Tahr_ - Release amd64 (20140722.3) Trusty/main Translation-en Ign cdrom://Ubuntu-Server 14.04.1 LTS _Trusty Tahr_ - Release amd64 (20140722.3) Trusty/restricted Translation-en_CA Ign cdrom://Ubuntu-Server 14.04.1 LTS _Trusty Tahr_ - Release amd64 (20140722.3) Trusty/restricted Translation-en Reading package lists... Done   This is not what I expected to see. In my current desktop environment there is a long list that scrolls past in the terminal.  I assume that there are no repositories listed in the /etc/apt/source.list (haven't figured out how to read contents of that file yet)  What should I do?


I am doing a Master in Physics. My area of research is experimental particle physics. During the literature review, I have read this statement many times, this happens because of the Cronin effect, then I started to understand what is Cronin effect, but unfortunately did not found any source. Please explain clearly and in easy wording about the .


Say I have x = 'abcde'. If I write x[::] I get 'abcde', If I write x[::2] I get 'ace'. So the spaces between the colons implies for the first space, "the start of the list" and for the second space "the end of the list". It's as if you were writing x[0:len(x)] right?   Okay, so when I write x[::-1] I get the list completely in reverse, i.e. 'edcba'. So what are the equivalent values I could substitute in?  x[len(x)-1:0:-1] won't work because the second space is not including that number, so I would get 'edcb' and if I went x[len(x)-1:-1:-1] it would simply do nothing because x[len(x)-1] == x[-1].   Yes, it will always work if I leave the colons in, my confusion comes is what does just having x[::] actually doing, what values is it actually substituting? Because if it were always just "the start of the list and the end of the list" then there's no way it would work for x[::-1], it would simply print nothing, and if it somehow knows to reverse it, then what values is it putting because even if we didn't have the problem of not being able to terminate at the right place (i.e. can't put 0 in the middle space because that wouldn't be include but can't put -1 because that's the end of the list) we have the problem that it should still start at 0, i.e. we should have  aedcb instead?   Can anyone shed light on the behind the scenes magic here?   Thank-you.  (Yes I googled for this, and tried to look it up in the docs and could find no explanation to this specific question)  edit: The answer to my question can be found in the non accepted answer of , namely, .   Thanks guys


What is the best way to step my signal from 5V to 3V3?

I have some analogue signals between 0 and 5 Volts being fed from a multiplexer into another board that only accepts signals up to 3v3.     What is the best way to step down the voltage?  The signal doesn't need to be very precise (It is going to be used to select one of 32 options depending on which range of values it falls under and will be a fixed value)  and doesn't need to be updated often (User is only likely to change the value two or three times during operation)   I was thinking of just using a 3K3 Ohm x 2K2 Ohm voltage divider with precise tolerances but I wonder if anyone can foresee any problems with this or can recommend a better method?    How should I link my analogue reference? am I going to run into problems if I just use another identical divider to jump the 5V rail down?


I'm trying to create a toc in a large Latex document which uses the KOMA script.  In the toc I would like to center the parts and remove all other components (pagenumber, partnumber). I use tocloft (a hard requirement for other reasons).  While I managed to remove the pagenumber, the partnumber is still there and the parts are very much on the right site instead of being centered.  A simplified example is:  \documentclass{scrbook} \usepackage[ngerman]{babel}  \usepackage{lipsum}  \usepackage{tocloft} \renewcommand{\cftpartfont}{\hfill\Large\bfseries} \renewcommand{\cftpartaftersnum}{\hfill} \addtocontents{toc}{\cftpagenumbersoff{part}}  \begin{document} \tableofcontents \part{A} \section{a} \lipsum \part{B} \section{b} \lipsum  \end{document}   I have adapted the commands for the centering from an example of the tocloft manual, where      \renewcommand{\cftZtitlefont}{\hfill\Large\bfseries} together with   \renewcommand{\cftafterZtitle}{\hfill} will give a centered Large   bold title.   was used to center the title (instead of the parts).   So my question, how can I center the parts and remove the partnumber?


What could the following line possibly mean?  my $x = shift;


I have a Nikon d3400 with kit lens 18-55 mm af-p DX. What is the right camera settings for northern lights photography?


The Dirac-delta function as an initial state for the quantum free particle

I want to ask if it is reasonable that I use the Dirac-Delta function as an initial state ($\Psi (x,0) $) for the free particle wavefunction and interpret it such that I say that the particle is exactly at x=0 during time t=0? If I use this initial state, can I also use it to predict how the wavefunction should evolve in time? That is, if $\Psi (x,0) = \delta(x) $, then, $$ \phi(k) = \frac{1}{\sqrt{2 \pi}} \int_{-\infty}^{\infty} \delta(x)e^{-ikx} dx=\frac{1}{\sqrt{2 \pi}} $$ then, $$ \Psi(x,t)= \frac{1}{\sqrt{2 \pi}} \int_{-\infty}^{\infty} \phi(k)e^{i(kx-\omega t)} dk $$ or, $$ \Psi(x,t)= \frac{1}{2 \pi} \int_{-\infty}^{\infty}e^{i(kx-\omega t)} dk. $$  Is the above wavefunction a valid expression to see how a particle that is initially localized in the origin evolves in time?


I just visited , and Stack Exchange offered to log me in, so I did so (refreshing the page in the process). The page then told me that I should upvote the question and answers if I found them useful. I can't upvote them, because the question is locked. Since I can't actually vote, I shouldn't have been prompted.


I’m trying to use CSS to make all my buttons this style:  button {   background-color: #4CAF50;   border: none;   color: black;   padding: 15px 32px;   text-align: center;   text-decoration: none;   display: inline-block;   font-size: 16px;  }   But now, I have a different type of button where it is <input type=“button>. I tried changing the CSS to make it include buttons AND inputs like this:  button, input {   background-color: #4CAF50;   border: none;   color: black;   padding: 15px 32px;   text-align: center;   text-decoration: none;   display: inline-block;   font-size: 16px; }   The problem with that, it makes ALL inputs, like text fields green. So is there any way that I can make my inputs, ONLY ones that have the button type be styled?


Cauchy Problem for inviscid Burgers' equation

Consider the Cauchy Problem of finding $u(x,t)$ such that    $$\frac{\partial u}{\partial t}+u\frac{\partial u}{\partial x}=0,x\in\mathbb{R},t>0$$ $$u(x,0) = u_0(x), x\in\mathbb{R}$$ Which choices of the following functions for   $u_{0}$ yield a $C^{1}$ solution $u(x,t)$ for all   $x\in\mathbb{R},t>0$         $u_{0}(x)=\frac{1}{1+x^{2}}$   $u_{0}(x)=x$   $u_{0}(x)=1+x^{2}$   $u_{0}(x)=1+2x$.      If I use the existence and uniqueness theorem for Cauchy problem i get the corresponding determinant is non zero so all are true according to me. But in answer key only option 2nd and 4th is given. Please help me to solve the problem. Thanks a lot.


I have the following problem: Let $|x_{n+1} - x_n| < 1/3^n$. Show that $(x_n)$ is a Cauchy sequence.

We have that $(x_n)$ is a sequence of real numbers. And the relation on the title: $$ |x_{n+1} - x_n| < \frac{1}{3^n}. $$ We must prove that this is a Cauchy sequence. I know that an Cauchy sequence follows the definition: given $\epsilon>0$, exists $n_0 > 0$, such that $m,n > n_o \Rightarrow |x_m - x_n|< \epsilon$ But I don't know how to use both informations to prove the exercise. If someone please may help me, I'd be very thankful.


Easiest way to open CSV with commas in Excel

CSV files are automatically associated with Excel but when I open them, all the rows are basically in the first column, like this:    It's probably because when Excel thinks "comma-separated values", it actually searches for some other delimiter (I think it's semicolon but it's not important).  Now when I have already opened this file in Excel, is there a button or something to tell it "reopen this file and use comma as a delimiter"?  I know I can import the data into a new worksheet etc. but I'm asking specifically for a help with situation where I already have a CSV file with commas in it and I want to open it in Excel without creating new workbook or transforming the original file.


What is the theory behind a simple pattern involving binomial coefficients?

These binomial equations are all true.  $\binom{7}{4} = \binom{4}{4} + 3[ \binom{4}{3} +  \binom{4}{2}] +  \binom{4}{1}$  $\binom{8}{4} = \binom{5}{4} + 3[ \binom{5}{3} +  \binom{5}{2}] +  \binom{5}{1}$  $\binom{9}{4} = \binom{6}{4} + 3[ \binom{6}{3} +  \binom{6}{2}] +  \binom{6}{1}$  $\dots$     Is this the result of some general binomial identity or theory?   My work  I stumbled upon this while working with a recurrence relation in $(m,n)$ with $m,n \in \Bbb Z^+$ that I was trying to put into closed form.


How do I delete an entity from the Minecraft world folder?

Basically, I acidentally spawned too many ArmorStands due to a wrong code writing , resulting in the game crashing, and wanted to know how to delete those armorstands from the World save folder. They hava names and I belive they also have a scoreboard set, if that helps.   I have already tried to open the world but it crashes, I tried to open a server (Since it worked the last time I tried it) and killing it all from the console but, different from the last time, it crashed before killing them and now I just tried MCedit but it crashes as well.


Find all primes $p$ such that $\phi(x)=x^{13}$ is a homomorphism $\Bbb Z/p\Bbb Z \rightarrow \Bbb Z/p\Bbb Z$.

The Question:  Find all primes $p$ such that $\phi(x)=x^{13}$ is a homomorphism $\Bbb Z/p\Bbb Z \rightarrow \Bbb Z/p\Bbb Z$    My Thoughts:  So from what I understand  \begin{align} \ & \phi:\Bbb Z/p\Bbb Z \rightarrow \Bbb Z/p\Bbb Z \quad\text{is a homomorphism} \\ \ \iff & \phi(xy) \equiv \phi(x)\phi(y) \pmod p \quad \forall \; x,y\\ \ \iff & (xy)^{13}\equiv x^{13}y^{13} \pmod p\quad \forall \; x,y \end{align}  But isn't $(xy)^{13}\equiv x^{13}y^{13} \pmod p\quad \forall \; x,y$ always true, regardless of $p$?  Or is there something I am not understanding?


The ordinary differential equation $\frac{d^2y}{dx^2}-q(x)y = 0$ , $0≤x<∞$ , $y(0)=1 $, $y'(0)=1$ multiple choice question

I am stuck on the following question:     Assuming $$\frac{d^2y}{dx^2}-q(x)y = 0,\;\; 0 \le x \lt \infty ,\;\;y(0)=1,\;\;y'(0)=1$$ wherein $q(x)$ is monotonically increasing continuous function,then which one of the following is true.        (a) $y(x) \to \infty$ as $x \to \infty$         (b) $\frac{dy}{dx}\to \infty$ as $x \to \infty$         (c) $y(x)$ has finitely many zeros in $[0,\infty)$         (d) $y(x)$ has infinitely many zeros in $[0,\infty)$       I am completely stuck on it.can anyone help me please.


Is there a way to use the limit definition to prove that the limit as $x$ approaches 0 of $\dfrac{\sin x} x = 1$? I get the definition (sort of), but it doesn't seem to have any practical applications in terms of extension of knowledge, just raw verification and mathematical rigor.   Thanks.  EDIT: John: it was a typo. Sorry for the confusion, the limit of sin(x)/x as x approaches infinity seems much more obvious. I am more interested as x approaches 0. My question really comes down to a much simpler concept: it seems like proofs often reveal to us new information through a series of logically consequent statements. However, I can't tell what the new information gained by epsilon delta proofs are, and I was wondering if there was some new mathematical idea that was revealed by this method.


Automatically use specific language in Notepad++ for files with no extension

Specifically, I want NPP to remember to use Ruby syntax highlighting whenever I open a Vagrantfile. These don't have an extension, and I tried adding "Vagrantfile" to the user extensions in the style configurator, but it did not work.  Anyone get this working?


I deleted the linux partition from a dual boot configuration and now it boots into grub prompt

I deleted the linux partitions from a dual boot configuration and extended the unallocated space back to my main C drive. Now when I boot back into my PC it automatically boots into the grub prompt. What should I do? I already tried many of the solutions on this site. I can boot into windows using the chainloader command but I would like the prompt to disappear entirely


"But is referred to by another package." - Finding that package

It is not unusual for an Ubuntu (or other distro with apt package management) user to encounter the error: user@box ~ $ sudo apt install x [sudo] password for user:  Reading package lists... Done Building dependency tree        Reading state information... Done Package x is not available, but is referred to by another package. This may mean that the package is missing, has been obsoleted, or is only available from another source  E: Package 'x' has no installation candidate  There have been several questions asked concerning this on various StackExchange sites,for example  on AskUbuntu, but these are generally about how to obtain the specific package despite the error. I have found no package that is not found simply (though not always easily) by determining if it is still distributed, and under which repository if so, and ensuring that repository is in apt.sources, or the worst comes to the worst downloading a .deb or source to compile. So my question is more general, and although I am guessing it has a rather simple and therefore non-exciting answer I cannot think how to find it by conventional search engine methods, so I turn to AskUbuntu: Is there a command or option I can use to determine what package / which packages reference the missing package?


Applying scale on the armature messes up whole animation, How to apply scale on Armature correctly?

I imported a mixamo character in blender 2.83. Its armature scale is set to 0.01.I want to apply this scale (Ctrl+A).  But whenever I apply the scale, the armature and mesh changes it location and the animation becomes all messed up.


How to make some value sliders of a node in a node group display on the group node

I made my first node group , now i want the node group to display some fields inside it on the node itself , how do i do that.


Why is 'Where's it' Grammatically incorrect?

I want to explain to the Spanish developers of a website why this text label sounds wrong:     If your column isn't country data, where's it?   IMHO, you have to say "Where is it?" - but I don't know why.  EDIT  For context, the meaning of "where's it" here is "in which country are the regions represented by the data in your column?"  And to be clearer, I'm not asking about when it's ok to use contractions in semi-formal English. To my (native Australian) ear, "Where's it?" sounds wrong in any context. Not "informal", but wrong.   EDIT 2  There is a near-duplicate question . I think the difference between "what" and "where" is significant enough to not want to merge the two.


Why am I being prompted for a sudo password when I specified "NOPASSWD" in my /etc/sudoers file?

I’m using Ubuntu 14.04.  I have this in my /etc/sudoers file  Defaults        env_reset Defaults        mail_badpass Defaults        secure_path="/usr/local/sbin:/usr/local/bin:/usr/sbin:/usr/bin:/sbin:/bin"  # Host alias specification  # User alias specification  # Cmnd alias specification  # User privilege specification root    ALL=(ALL:ALL) ALL  # Members of the admin group may gain root privileges %admin ALL=(ALL) ALL %deployers ALL=(ALL) ALL  rails ALL = NOPASSWD: /usr/local/rvm/gems/ruby-2.3.0/bin/bundle, /usr/local/rvm/rubies/ruby-2.3.0/bin/ruby, /usr/local/rvm/gems/ruby-2.3.0/bin/rake, /usr/bin/service, /sbin/   restart  # Allow members of group sudo to execute any command %sudo   ALL=(ALL:ALL) ALL   I thought including the above command (the one with “NOPASSWD”) would prevent getting prompted for a password, but after I reboot my system and login as my “rails” user, note I’m still getting asked for a password when running sudo …  rails@mymachine:~$ sudo rake db:migrate [sudo] password for rails:  rails@mymachine:~$ which rake /usr/local/rvm/gems/ruby-2.3.0/bin/rake   What do I need to do so I’m not prompted for a password when running the “rake” command (and other commands I listed)?


How can I tell if my computer went to sleep?

I'm trying to work out if my computer has actually fallen asleep, I have set it to fall asleep, but it restarts so quickly, I cannot tell if it was actually having zzzzs or not.  What logs are there to tell me when and if my PC fell asleep?


How to get rid of (base) inside terminal app in 10.14.6?

when I get a fresh terminal, my prompt says   (base) ~>    The (base) part is something that seems new. Was this added during a recent update? How do I get rid of it? There is one piece of customization in my dot .profile, namely  export PS1="\[\e[32;1m\]\w> \[\e[0m\]"   I also installed Conda recently, which might be related to that.  How do I remove  (base) ?


Export each feature to a new geojson individually

I have a shp file in qgis. I would like to export that shp file into geojson. I have seen the save as option. But, my point is to create individual files for each individual shape in the gis project. Is that possible?


Comparing numbers between (0 and 2) and (0 and 1).

I read that between any two number , there are infinite numbers. And that infinities are equal (number of numbers between 0 and 1 is equal to number of numbers between 0 and 2). Let the numbers be 0 and 1, 0 and 2 . Let the numbers between 0 and 1 be "x". Let's take any  number between 0 and 1, "0.pqrst", there cannot be "1.pqrst" between them. But between 0 and 2, it exists. So it implies for every number between 0 and 1 ie '0.something' there will be '0.something' and '1.something' between 0 and 2. Doesn't it imply that the number of numbers between 0 and 2 is double the number of numbers between 0 and 1?   Please explain if I have any conceptual blunder or anything like that.....


MicroSD (Secure Digital Storage Device) is not formattable, deletable or reusable

My question detected as a similar question, and the similar answer is to throw your SD in the garbage! I want to update my question by asking, what happens technically when a microSD card happens to act like that? It is totally readable, but not changeable, either delectable or formattable. It turned to a stone slab with carved data on it. I recently trying to format and reuse a microSD card, which turned to "Secure Digital Storage Device" by an android phone 7.1 version. The data on the card is available and totally accessible but every moment I want to delete a folder it is automatically recovered. Even when I used it on the desktop, I did not insert it into the phone. Every possible solution in links like below turned out to not work.  I used many ways to solve this issue, which provided with other websites, they all failed to work: Diskpart Format, Use the Registry. Please note that I don't want to use third-party software. please do not post solutions like that. I am curious how this card is so undeletable, I can use it for other purposes, and this discussion open for your explanation. but for now, I want a method to simply reuse my micro sd as an ordinary sd card


Any reservations about the potential of this (given in the link below/title above)? Does it seem like a helpless attempt or something which might have the potential of developing into something real?


What is the cause of gravitional force of attraction?

Ok,this is a silly question. But for quite long I have been thinking about this. What is gravitation all about?? My book directly writes since force of gravitation is directly proportional to the masses and inversly proportional to the square of the distance ie. $$F = G\frac{M_1 . M_2}{r^2}$$ . So is this gravitation all about? What is the cause of it? The book then says     We are not in the scope in classical approach so as to discuss the cause of this. However,as a matter of fact that if there are more than one mass,then there is gravitation as it is their fundamental property.( Cause of gravitation can be attributed to exchange of non-classical particles between the masses) .    Then it ended the talkings. What are those non-classical particles? Why and how are they exchanged? So far I have studied physics , I never found such weird phenomenon like this. I want to know what is the cause of gravitation and what is the cause of exchange of those so-called non-classical particles? And how do they do it?


Least Squares Estimation of Poisson Parameter

"Assume independent random variables $Y_i$~$Poisson(λx_i)$. Supposing that $x_i$ are given, fixed constants, obtain the least squares estimator of $λ$ and compute its variance."  This kind of a problem is the first one faced by me. The first things that are coming to my mind are regression equation of the form $log(Y)=a+bx$ and then trying the least square algorithm by minimizing $∑(log(y)-a-bx)^2$. From this I will be getting the least squares estimates of $a,b$ but how do I get $λ$?  As I said, this is the first time I am facing such a question. I know point estimation in terms of MLE and moment-equality. I need help and resources (i.e. more knowledge) about solving this kind of a question. Can you kindly supply me with the answer and the explanation along with maybe links to some pdf's? Google is not helping me. Thanks in advance.  (EDIT:) While I was waiting for any response to this question, I looked up deeper and found that I did not know one information. That is, the least square estimator for a parameter $θ$ is obtained by minimising $∑(Y_i-E(Y_i|x_i,θ))^2$. So I tried to work on this using my new knowledge.  I get the LSE of $λ$ as $\dfrac{∑x_iY_i}{∑(x_i)^2}$. Please tell me if this is correct.  Then the variance of this LSE is $\dfrac{λ∑(x_i)^3}{(∑(x_i)^2)^2}$.   Is this right? Thanks for your time.


How to add current date to cell if the rest of the cells (or some cells) in that row are edited, but only the first time?

I have a column A4:A (heading = Date), and other columns after it B4:O.  I want column A to fill in today's date automatically when I fill in any other columns (some of these B4:O maybe empty, but most will be filled) in that row. But I only want that to happen the first time I edit any other columns within that row.  What I've tried:  A7: =IF(B7 > 0,TODAY(),)


How long do I have to stay outside of the Schengen Area?

I was in Germany and Switzerland for 90 days in total. I'm a US citizen just traveling and looking to pick up work and perhaps, find real employment. How long must I wait before I can legally re-enter into the Schengen countries?


I'm trying to make a text based game but my If statement won't print. Whats wrong?     System.out.print("What path do you choose?: ");    String pathChoice= kb.nextLine();    System.out.println(" ");    System.out.println(" ");    System.out.println(" ");    if (pathChoice==("North") || pathChoice==("north")){        System.out.println("You begin walking north and encounter an ogre of significant size.");        System.out.println("You draw your crude sword. How will you attack? ");


The power of an EM wave is proportional to the amplitude (squared). But also the frequency?

The power of an electromagnetic wave is proportional to its amplitude squared. (Watts, usually)  But, it is also proportional to its frequency, correct?  The higher the frequency, the greater? ( measured in eV).  Is the TOTAL strength of the wave it's watts and electron-volts combined?  So, what is the difference between a laser, say, with a large number of infrared photons versus an x-ray laser with fewer photons, but higher frequency?  They have the same total energy, but do they cut the same?  Can a low-frequency laser beam, if intense enough, ionized atoms and molecules like individual photons of x-rays do?


Is this a correct bijection between $(0,1]$ and $[0,1]$?

I need to give an explicit bijection between $(0, 1]$ and $[0,1]$ and I'm wondering if my bijection/proof is correct. Using the hint that was given, I constructed the following function $f: (0, 1] \to [0,1]$: $$ x \mapsto \left\{ \begin{array}{ll} 2 - 2^{-i} - 2^{-i-1} - x & \text{if } x \in (1-2^{-i}, 1-2^{-i-1}]\text{ for an } i \in \mathbb{N}_0 \\ 1 & \text{if } x = 1 \end{array}\right. $$  It's easy to see that for every $x \in (0, 1)$, there exists such an $i$.  Now define $\tilde{f}: [0,1] \mapsto (0,1]$ with  $$ x \mapsto \left\{ \begin{array}{ll} 2 - 2^{-i} - 2^{-i-1} - x & \text{if } x \in [1-2^{-i}, 1-2^{-i-1})\text{ for an } i \in \mathbb{N}_0 \\ 1 & \text{if } x = 1 \end{array}\right. $$  I want to prove that $\tilde{f}(f(x)) = f(\tilde{f}(x)) =  x$, so it has an inverse and therefore is a bijection. The case $x=1$ is trivial, so assume that $x \in (0,1)$ with $x \in (1-2^{-i}, 1-2^{-i-1}]$ for some $i \in \mathbb{N}_0$. This interval has length $1-2^{-i-1} - (1-2^{-i}) = 2^{-i-1}$, so we can write $x = 1-2^{-i} + \epsilon\cdot 2^{-i-1}$ for some $\epsilon \in (0, 1]$. We now calculate $f(x)$: \begin{align*} f(x) &= 2 - 2^{-i} - 2^{-i-1} - x\\ &= 2 - 2^{-i} - 2^{-i-1} - (1-2^{-i} + \epsilon\cdot 2^{-i-1})\\ &= 1 - 2^{-i-1}(1+\epsilon). \end{align*} We conclude that $f(x) \in [1-2^{-i}, 1-2^{-i-1})$. We now use the definition of $\tilde{f}$, so if we calculate $\tilde{f}(f(x))$, we get \begin{align*} \tilde{f}(f(x))  &= 2 - 2^{-i} - 2^{-i-1} - f(x) \\ &= 2 - 2^{-i} - 2^{-i-1} - (2-2^{-i} - 2^{-i-1} - x) \\ &= x. \end{align*}  We conclude that $f$ has an inverse. Using exactly the same reasoning, we get that $f(\tilde{f}(x)) = x$ for all $x \in [0,1]$. Therefore it's inverse exists and it has to be a bijection.  I know there are less cumbersome methods of proving this fact, but as of now this is the only thing I can come up with.


Was Kylo Ren's Blaster Bolt Freezing Really Force Telekinesis?

In this questions answer its stated that Kylo Ren freezes the blaster bolt in midair with telekinesis:       Because he is extremely skilled in Force telekinesis, Kylo Ren is able   to freeze not just objects but even blaster bolts in midair.   But as a commenter already pointed out, this seems nonsense (even in star wars force physics). The blaster bolt is, as far as I know, a cloud of plasma. If it is stopped by telekinesis, why should it continue its old path with its old speed after it is released? Wasn't it more a completely new force ablility like "time freeze"? While I admit in a case of time freeze the bolt should not have flickered all the time. Also the plasma should have expanded and vanished or simply cooled down releasing its energy to the surrounding air.  So when it was force telekinesis Kylo must have done the following:   Stop every atom in the plasma cloud Keep the cloud compressed and in form and shape. Isolate it to prevent the heat flow or keep it on temperature (is this still telekinesis?) Not just releasing it but accelerate it again exactly on its old path and speed.   This would be indeed a greate never seen mastery of telekinesis. And very ineffective. And if he wanted to be cool, wouldn't it be even cooler to change the path after the "release" so that it hits one of his enemies?  So what was going on there? Pure telekinesis or something else? Did the writers intend this? Or did they just not thinking it to the end?


Expression doesn't match double quoted strings

I'm learning about regular expressions and trying to make an expression that will match only those strings which are written in double quotes and for that my expression is : "\S*" and target string is <aname="Name4"text="Super"> but the expression is matching whole string after first double quoted string is found. I'm using this  for testing an expression


Why is bubble sort time complexity referred to as n squared?

There have been other questions about bubble sort time complexity, but this question is different. Everyone says that bubble sort worst case is O(n^2). In the bubble sort after i iterations of the list, the last i elements of the list are in order and don't need to be ever touched or compared again. The time complexity would only be O(n^2) if you needlessly ran over the final elements again and again.   Given that a major feature of the bubble sort is that the elements after (input size minus iteration) never need to be compared again, because it's in its correct place, why is bubble sort time complexity said to be that for something that to me I didn't think was bubble sort? Even in Wikipedia it says the time complexity is O(n^2), and then only halfway into the article it mentions that it can be "optimised" to take only about 50% of the time by not unnecessarily comparing the last i elements.  I was reminded of this because I was making a loop which checked collisions of all my objects in the world, and the pattern was that I checked:  for (int i = 0; i < numberofobjects - 1; i++) {    {       for (int iplusone = i + 1; iplusone < numberofobjects; iplusone++)         // check collision between i and iplusone    } }   With 400 objects a time complexity of O(n^2) would be 400 * 400 = 160,000. However it only did 79,800 comparisons, roughly 50%, which is exactly what Wikipedia said. This reminded me of the bubble sort so when I checked I was surprised to see everyone saying it was O(n^2).  Does this mean that whenever someone refers to the bubble sort they're referring to the version that needlessly reiterates over the final elements that have already been sorted? Also when different algorithms are compared bubble sort always fares the worse, but is the writer referring to the obviously  bad n^2 version?


Where is the mistake in proving 1+2+3+4+… = -1/12?

As I watched the video on YouTube of proving sum of $$1+2+3+4+\cdots= \frac{-1}{12}$$  Even we know that the series does not converge.  First I still can't prove what wrong in infinite sum of $$1-1+1-1+1+\cdots= \frac{1}{2}$$  and I want to know more about of what mistake did they make in the video.  I did research on our forum about this topic. But still not clearly understand about of that proving.  Thank you. (Sorry about my bad English )


I am building a site for a women's accessories brand.  The site has a Homepage, a Store page (where all accessories are displayed), a page for each of the accessories description, an about page and a contact page. There is also a whole set up for shopping cart and checkout (irrelevant to this question).  My issue is the SEO. Where can I put the keywords? The home page has only the menu and some photos. The store page displays the items and its titles. Then the specific item's page has a description of the item (pulled from the database), category and price. However, I feel like this is not enough for SEO for google ranking.  Where could I add tags in this type of site?


What does 2>&1 means in crontab commands?

I've seen many crontab commands written this way:  */5 * * * * ~/script.sh >/dev/null 2>&1   Can someone explain what is the exact meaning of 2>&1?


Which terminal should I connect it to for a "C" wire when none are labeled "C"?

I am looking to replace my old battery operated thermostat with a new wifi model. There is no "C" common wire connected to my old thermostat. There is a blue wire that is at the thermostat but cut short with no copper exposed. I went up to the attic and took a look at the A/C unit. There was also a wiring diagram that was available. There is no "C" terminal on the unit but there is a "B" terminal which I assume is the right one I should use. I tested the voltage from "R" to "B" and it was about 26.5 Volts (The new thermostat requires 24 volts). There is a wire connected to the the "B" and "Y1" terminal it seems like its the wiring that goes to the outside Unit. Its the other Red wire and white wire. (See photo below.)  I have attached pictures of the wire terminal on the A/C unit in the attic as well as the Wiring diagrams. In the wire terminal picture you will see the extra blue wire wrapped around the main wire and is not used. I would like to use that wire as my "C" common wire. Is it safe to connect the Blue wire to the "B" terminal? Im worried because another cable is already connected to it and its reading 26.5 volts...       Click for full size  Update 1  First off, big thank you for the help and responses! I really appreciate it!  I went back up and opened the unit. This is what I saw inside. The two wires coming out of the transform have a voltage of about 26.5 volts. I could not find 24 volts anywhere. The transformer says its a 24VAC transformer. Looking at this picture, where do I connect the C wire to? Which wire coming out of the transformer?


Extend Schengen visa to go to the UK for a short stay

I am Jamaican and I am currently in Europe on a Schengen visa. I have been invited to the UK next month for 2 weeks. How much will it cost to extend my schengen visa? I am a musician and may play percussions on two shows while I am in the UK. What is the cost variation?


Expected number of variables that are at least n

I wasn't sure what to title this.  We have n objects distributed uniformly and independently at random among n people. Calculate the expected number of people that receive at least 5 objects.  I know how to calculate the probability that one person receives at least 5 objects, but I do not know to calculate the expected number, as it seems that the probability of the second person receiving 5 objects depends on the first, and so on. Is this just using an indicator variable for each person or is there more involved?


After running postqueue -p i sometimes finds misspelled email-adresses, is there a way to change the reception adress (envelop to adress) of the messages, so it can be delivered.  exemple:  postqueue -p -Queue ID- --Size-- ----Arrival Time---- -Sender/Recipient------- A78C42189B1     2523 Thu Jul 25 14:53:57  xxxx@xxxx.se                 (connect to tellia.com[141.8.224.25]:25: Connection timed out)                                          yyyyy@tellia.com -- 2 Kbytes in 1 Request.   I want to pick upp A78C42189B1, and change the adress yyyyy@tellia.com to yyyyy@telia.com


Can I have a logical explanation for why this number is so ridiculously close to a whole number?

$$e^ {\pi\sqrt{163}}=262537412640768743.9999999999992\cdots$$  Why does this number run so incredibly close to a whole number? Can I have a logical explanation for why this finding? I know how to calculate it, but I want an answer that would explain it to me by intuition only. Thank you very much for any help. It is not the same as the other similar problem because I am looking for a logical reason and the other is wondering whether or not it is concidence.


What is so special about $\alpha=-1$ in the integral of $x^\alpha$?

Of course, it is easy to see, that the integral (or the antiderivative) of $f(x) = 1/x$ is $\log(|x|)$ and of course for $\alpha\neq - 1$ the antiderivative of $f(x) = x^\alpha$ is $x^{\alpha+1}/(\alpha+1)$.  I was wondering if there is an intuitive (probably geometric) explanation why the case $\alpha=-1$ is so different and why the logarithm appears?  Some answers which I thought of but which are not convincing:   Taking the limit $\alpha=-1$ either from above or below lead to diverging functions. Some speciality of the case $\alpha=-1$ are that both asymptotes are non-integrable. However, the antidrivative is a local thing, and hence, shouldn't care about the behavior at infinity.


how to create new event in SharePoint calendar list with JavaScript?

i want to create new event in SharePoint calendar list in which I have some custom columns,i tried below code but it is not working      function bookingRoomForMeeting() {         var ctx = new SP.ClientContext(appWebUrl);//Get the SharePoint Context object based upon the URL           var list = ctx.get_web().get_lists().getByTitle("MyCalendarList"); //Get the List based upon the Title         var listCreationInformation = new SP.ListItemCreationInformation(); //Object for creating Item in the List         listItem = list.addItem(listCreationInformation);         listItem.set_item('Title', $("#txt_Title").val());         var date = $("#txt_startTime").val();         var dateTime = moment(date, 'DD/MM/YYYY HH:mm a').format("MM/DD/YYYY HH:mm a");         listItem.set_item('EventDate', dateTime);         var enddate = $("#txt_endTime").val();         var enddateTime = moment(enddate, 'DD/MM/YYYY HH:mm a').format("MM/DD/YYYY HH:mm a");         listItem.set_item('EndDate', enddateTime);         listItem.set_item('EmailId1', $("#txt_EmailId1").val());         listItem.set_item('EmailId2', $("#txt_EmailId2").val());         listItem.update();         ctx.load(listItem);         ctx.executeQueryAsync(             Function.createDelegate(this, success),             Function.createDelegate(this, fail)            );     } function success() {     alert("Completed"); } function fail() {     alert("operation failed"); }   list am using is SharePoint hosted app list,can any one tell me where am going wrong?


Why do I have different IP addresses on different websites?

My wireless router shows the IP address is 113.46.75.*, which some websites like ip138.com, www.ip.cn show as my IP.   But other websites, like googling for "what is my ip", www.whatismyip.com, www.whatsmyip.org, show that my IP is 121.18.126.*.   I am very curious why this happens and how is it possible.   So, why do different websites show that I have different IPs?  Thanks all!  Plus: I changed my IP address several times (restarting the modem) and all addresses is like 113.46.*.*, but my IP address does not change when googling for "what is my ip".  My ISP is a small company, so I think it is true that when visiting some websites, I am NATted or proxied to some IP addresses which have access to those websites -- not to avoid firewall though, since I am still blocked from some websites.  But I still want some more information or resources to support our guess. Thank you!


If $A,B$ are commuting diagonalizable complex matrices , then $A,B$ have a common eigen-basis ?

If $A,B$ are diagonalizable complex matrices of size $n$ such that $AB=BA$ , then is there a common eigen-basis of $A$ and $B$ ?


- java.lang.NullPointerException - setText on null object reference

This is what I'm trying to do for several hours: I've got a MainActivity.java file (listing below) and a fragment_start.xml file with a start button. Tapping the start-button should display the activity_main.xml file with points-/round- and countdown-Textviews. It doesn't work and this is what is happening:  The logcat tells me: PID: 1240 java.lang.NullPointerException: Attempt to invoke virtual method 'void android.widget.TextView.setText(java.lang.CharSequence)' on a null object reference  The emulator displays: Unfortunately, GAME has stopped.  Necessary to mention that I'm rather new in programming?  Thanks for any advice!  import android.app.Activity; import android.os.Bundle; import android.view.View; import android.view.ViewGroup; import android.widget.TextView;   public class MainActivity extends Activity implements View.OnClickListener {  private int points; private int round; private int countdown;  @Override protected void onCreate(Bundle savedInstanceState) {     super.onCreate(savedInstanceState);     setContentView(R.layout.activity_main);     showStartFragment(); }  private void newGame () {     points=0;     round=1;     initRound(); }  private void initRound() {     countdown = 10;     update(); }  private void update () {     fillTextView(R.id.points, Integer.toString(points));     fillTextView(R.id.round, Integer.toString(round));     fillTextView(R.id.countdown, Integer.toString(countdown * 1000)); }  private void fillTextView (int id, String text) {     TextView tv = (TextView) findViewById(id);     tv.setText(text); }  private void showStartFragment() {     ViewGroup container = (ViewGroup) findViewById(R.id.container);     container.removeAllViews();     container.addView(             getLayoutInflater().inflate(R.layout.fragment_start, null) );     container.findViewById(R.id.start).setOnClickListener(this); }  @Override public void onClick(View view) {     if(view.getId() == R.id.start) {         startGame();     } }  public void startGame() {     newGame(); } }


How to force bash star * wildcard expanding in ascending order for numerical values?

Please assume that we are now within a directory containing 13 files that were named as follows:  p1 p2 p3 ... p11 p12 p13   Through bash, when we execute the following command:  for i in p*; do echo $i; done   The star * wildcard seems to be expanded without an ascending order:  p1 p10 p11 ... p7 p8 p9   Yet for example, the following piece of commands expand the numerical values in an ascending order:  for i in p{1..13}; do echo $i; done   Is there any bash settings to alter this default star * wildcard behaviour?  If not, could you please tell us what is the motivation behind this preference for such an expansion?  PS: For a similar question, please refer to: . Yet herein I wonder if we can change the default behaviour of bash, and if so, how?


How to continue on proving that rank (A+B) ≤ Rank A + Rank B?

Theorem: $rank(A+B) \leq rank (A) + rank(B)$.  Proof: Let $U = Im(A)$ and  $W = Im(B)$. By dimension theorem, we know that:        $Dim(U+W) = Dim(U) + Dim(W) - Dim (U \cap W)$. By substituting $U$ and $W$ we get:        $Dim(Im(A)+Im(B))= Dim(Im(A)) + Dim(Im(B)) - Dim(Im(A) \cap Im(B))$.  I am stuck here. I know that $dim(Im) = Rank$ but I cannot continue from here. Please can someone help me? Thank-you:)


Finding perfect squares in a quadratic equation

Well, I have a number $\text{p}$ that is given by:  $$\text{p}=9+108x^2(1+x)\tag1$$  I want to find $x\in\mathbb{Z}$ such that $\text{p}$ is a perfect square.     I found no solutions. Is there a way to prove that there aren't any solutions? Except for the obvious ones: $x=0$ and $x=\pm1$.     My work  Since $\text{p}$ must be a perfect square we can write:  $$\text{p}^2=9+108x^2(1+x)\tag2$$  Now, because $\text{p}^2\ge0$ we need:  $$9+108x^2(1+x)\ge0\space\Longleftrightarrow\space x\ge-\frac{1}{3}\left(1+2^\frac{2}{3}+2^{-\frac{2}{3}}\right)\approx-1.07245\tag3$$


Please add support for tables in answers and questions

I would like to use tables in answers and questions. Without such support, I find myself using ASCII art tables with the code-text tool, but that takes too long, and isn't really maintainable.  This could be used to illustrate memory cells, and of course to create "real tables" with information contained.    It looks like HTML tables using
 are not going to be supported. I would like to ask for a feature in the editor that allows and supports creating tables using ASCII art (so the nasty manual managing with spaces will go away), at the very least (no CSS guy - but could imagine there are other styling techniques too).     As a workaround, google chart supports the creation of graphviz diagrams, which is also able to render some limited HTML for creating tables. So the following URL:  chart.apis.google.com/chart?cht=gv&chl=digraph html{abc [shape=none,margin=0,label=<

Algorithm	Example

First Row 1	Second Row 2

Last Row 1	Last Row 2

>]; Funny -> abc:tryp:ne;}  Gives when properly encoded this picture


Is the following use of "in case" natural in American English?     In case you can't find my house, just call me.   I'd appreciate your help.


Python allows creation of objects without specifying the essential argument

I am new to Python OOP.  Consider this code snippet below:  class LinearTopo(Topo):      def __init__(self, k=2, **opts):         Topo.__init__(self, **opts)         ...         ...   LinearTopo(k=4) # Not passing the **opts argument   I believe, **opts is an essential argument which is needed for creating an object of class LinearTopo. However, Python allows to create objects of class LinearTopo without this argument. Could someone explain, how it is possible ?


Is "_NOUN_ who each _VERB_" grammatically correct?

I just came across the following sentence;     A company with 1,000 employees who each send eight e-mail messages per workday would produce two million messages per year.   where who each send sounds incorrect.  (used in Google-Books)  After I tried to  on Google-Ngrams, no ngram was found for the first one. So, is it grammatical?


How would I attempt to brute force a RSA encrypted message with a 64bit computer if it the memory can't put up with calculations bigger than 64bit? Without going that far to attempting to crack it, how does my computer encrypt a message with a public key that's bigger than 64bit (e.g 2048)?


Can I add extension methods to an existing static class?

I'm a fan of extension methods in C#, but haven't had any success adding an extension method to a static class, such as Console.  For example, if I want to add an extension to Console, called 'WriteBlueLine', so that I can go:  Console.WriteBlueLine("This text is blue");   I tried this by adding a local, public static method, with Console as a 'this' parameter... but no dice!      public static class Helpers {     public static void WriteBlueLine(this Console c, string text)     {         Console.ForegroundColor = ConsoleColor.Blue;         Console.WriteLine(text);         Console.ResetColor();     } }   This didn't add a 'WriteBlueLine' method to Console... am I doing it wrong? Or asking for the impossible?


How to solve $a^{b^2} = b^a$ in positive integers

I have this exercise:  $a,b$ are positive integers. Get all $a,b$ numbers that satisfies $a^{b^2} = b^a$  Is hard to me, but I have these advances:  $a,b$ must be both even or both odd, since $a, b$ are the base.  Besides, if $a > b$, the exponent and the exponent of $a$ is $b^2$ and the exponent of $b$ is $a$, therefore $a > b^2$  So far I have managed to develop the exercise, what can I do? How do you work with these types of mathematical problems? Thanks in advance


Existences and uniqueness theorem, finding a unique solution of a first order ODE

Consider the initial value problem  $$y′=3x(y−1)^{1/3},y(x_{0})=y_{0}$$  Using the existness and uniqueness theorem, for what points ($x_{0}$,$y_{0}$) imply that the above IVP  has a unique solution on some open interval that contains $x_{0}$?  What i tried  Using the seperable equation method,  I got  a solution of $$y=1+(x^{2}+c)^{1.5}$$  Im unsure of how to find the value of $c$ given the inital conditions and whether is it necessary to find the value of $c$ for this problem. While using the  existence and uniqueness theorem, $y_{0}$ must not be equal to $1$ in order for a unique solution to exist. But from here im unsure of how to find the points  ($x_{0}$,$y_{0}$), I was thinking that since i already know that $y_{0}$ does not equals to $1$, i must combine this result with the above solution that i got  in order to get $x_{0}$ and hence the point ($x_{0}$,$y_{0}$) but im unsure how to do so, especially when there is a $c$ involved. Could anyone explain. Thanks


How to create a sphere with an outer layer of removable pieces?

I'm creating a video game which requires an inner sphere ("the core") and an outer sphere. The core is a solid icosphere, but the outer core must be made of individual triangular prisms that fit tightly to the core and each other. During the course of gameplay, the pieces of the outer core are removed one by one until the core is revealed. After making my core, I tried to make a single triangular prism piece and to use it to construct my outer sphere, but I can't get the pieces to fit together right (see below).  I came to realize that the triangles are not all the same, so I've gone back to blender and extruded and then push/pulled all of my vertices to start an outer layer.  My question is: how can I easily connect all of these dots, create faces for each individual triangular prism (such that the normals are facing outward for each individual prism), and break them apart into individual objects so that I can save an outer sphere and import it into my game? And how can I do this with as little headache as possible?


How do I get detailed SMART disk information on OS X (Mavericks or later)

I'm trying to get a detailed SMART status report on the drives in my Mac. I'm not talking about "Verified," I'm talking about the detailed report that's about 100 lines long listing all the vital statistics of the drive.  Anyone know how to do this with diskutil? If diskutil can't do it is there a different free tool I can use?


Why do some people pronounce "cotton" as codden and "satin" as saddin and Russian leader "Putin" as pudin?    These pronunciations are made even by professional news people on national television.


Make multiple edits with a single call to sed

I'm trying to use sed to edit a config file. There are a few lines I'd like to change. I know that under Linux sed -i allows for in place edits but it requires you save to a backup file. However I would like to avoid having multiple backup files and make all my in place changes at once.  Is there a way to do so with sed -i or is there a better alternative?


Algorithm for rating books: Relative perception

So I am developing this application for rating books (think like IMDB for books) using relational database.   Problem statement :  Let's say book "A" deserves  8.5 in absolute sense. In case if A is the best book I have ever seen, I'll most probably rate it > 9.5 whereas for someone else, it might be just an average book, so he/they will rate it less (say around 8). Let's assume 4 such guys rate it 8.  If there are 10 guys who are like me (who haven't ever read great literature) and they all rate it 9.5-10. This will effectively make it's cumulative rating greater than 9  (9.5*10 + 8*4) / 14 = 9.1  whereas we needed the result to be 8.5 ... How can I take care of(normalize) this bias due to incorrect perception of individuals.  MyProposedSolution :  Here's one of the ways how I think it could be solved. We can have a variable Lit_coefficient which tells us how much knowledge a user has about literature. If I rate "A"(the book) 9.5 and person "X" rates it 8, then he must have read books much better than "A" and thus his Lit_coefficient should be higher. And then we can normalize the ratings according to the Lit_coefficient of user. Could there be a better algorithm/solution for the same?


I am typesetting a book, which has got more number of plants. While entering the text, I have to record the total number of plants recorded in my book.   In fact, I have created an index of all these plants, but the question is should I count manually, or LaTeX can count itself.  Here is my simple  document.  \documentclass[a4paper,10pt]{article}  %For multiple index \usepackage{imakeidx} \makeindex  \makeindex[name=ch, title=Chemical index] \makeindex[name=pl,title=Plant Index]  \begin{document}  This is my test docment. It contains total 5 plants. Plant 1\index[pl]{plant 1}  has                 chemicals 1\index[ch]{chemical 1} and 2\index[ch]{chemical 2}. Another plant\index[pl] {plant 2} continas the chemicals 2\index[ch]{chemical 2} and 3\index[ch]{chemical 3}.  List of plants: Plant 3\index[pl]{plant 3} plant 4\index[pl]{plant 4} plant 5\index[pl]{plant 5}  \printindex \indexprologue{\small Index of plants} \printindex[pl]  \indexprologue{\small Index of chemicals} \printindex[ch]  \end{document}


Prove that for all $a,b \in\mathbb{R}$, $a·b=0$ if and only if $a=0$ or $b=0$. Using these field axioms:  (A1) Addition is commutative (A2) Addition is associative (A3) Addition has a neutral element $0$ (A4) Any element has an additive inverse (A5) Multiplication is commutative (A6) Multiplication is associative (A7) Multiplication has a neutral element $1$ (A8) Any non-zero element has a multiplicative inverse (A9) Multiplication distributes over addition   My answer: Suppose $𝑎𝑏=0$ and by (A6) $𝑏=1⋅𝑏=(𝑎^{−1}⋅𝑎)⋅𝑏=𝑎^{−1}⋅(𝑎⋅𝑏)$. Either $𝑎=0$ or it is not. If a does not equal $0$,then by (A8),there is a unique element $𝑎^{−1}=(1/𝑎)∈ℝ$ such that $𝑎^{−1}⋅(𝑎⋅𝑏)=𝑎^{−1}⋅0=0$ thus $b=0$


Looking for a short story about "zombies" (artificial humans") and a space war

over on "World Building" reminded me of a short story I read a long time ago.  I would have read it in the mid 1990s or earlier.  The story itself would have been much older. In the story, humans are involved in a space war.  It seems things aren't going so well, so they've started building "zombie crewmen" out of the bits of biological debris left over from their dead crewmen.  We're not talking reanimation here.  Think "scrape the dead dudes off the walls and use them as raw material." There is mention of deliveries of "material" as "bales." Like the  that comes out of a car crusher, but made of bits and pieces of multiple dead crewmen. The story itself is about a naturally born, newly promoted commander of a small ship (scout or some such that only needs a few crewmen.) He is sent to the "factory" where they produce the "zombies" to pick up the crew for his new ship. Part of the story involves reminiscences about when the zombies were first produced - slow, stupid, suitable only for menial tasks.  There's specifically mention of having to remember to "turn off" a zombie crewman.  Rather, remember to tell them to stop.  The example was that if you told one to polish the bulkhead, it'd keep on polishing the bulkhead until it had worn through the wall. The newer zombies were better.  As good as naturally born human beings in almost all ways. The new crew was not pleased to meet their new commander.  They had been exposed to a lot of prejudice during their training, and were resentful of their treatment.  That, and the one thing that zombies couldn't do - father children. The commander talks to the crewman to find out why they resent him on first sight - the prejudices of the trainers comes out, as well as the reproduction issue. They assume that the reproductive ability has been held back to differentiate between zombies and humans. The commander knows different.  If the medical folks could give the zombies reproductive powers, then they'd also be able to fix sterility in humans - and the commander is sterile due to a near hit on his previous ship with some kind of radioactive weapon. In the end, the commander and the crew bond over their common disability, with the implication that they are going to go out and be heroes so that they'll at least be remembered for their actions.  The humans call the zombies more nasty things than just "zombies." They also call them "blobs."  There are probably more that I don't remember. The zombies in turn have their own words for naturally born humans.  The commander invites his crew to use them all on him and get it out their systems.  He specifically mentions being called "eutie" and "wombat" because he thought words were cute when used in that context.


An automorphism of the field of $p$-adic numbers

Is an automorphism of the field $\mathbb{Q}_p$ of $p$-adic numbers the identity map? If yes, how can we prove it?  Note:We don't assume an automorphism of $\mathbb{Q}_p$ is continuous.


What is difference between Standard Normal Distribution and Mean Normalization approaches to feature-scaling?

The tag feature-scaling seems to convey that one of the scaling methods is Standard Normal Distribution. Further, I read an Answer on this site saying that Mean Normalization is a form of feature scaling. What is the difference between two approaches to scaling? Note: I think that statistics and mathematics of normalization do differ.


How can i get my community Base URL in apex

I am using  Salesforce Community and I have network Id of the community but I don't know how can I get Base URL of my community. Any one know how can I get my community base URL using its id in apex as a internal user.  Is there any other way in which salesforce internal user can get the base URL of all his community in the apex also i don't find any object in which Community Base URL is stored. I checked network sObject but it only store community path prefix not the complete URL so how can i get the base URL for my community?


Some friends and I bought the Humble Bundle with Sims 3 (and expansions).  And we want to know if possible to play in a "cooperative mode". I mean, share the same neighbourhood, to interact between our sims...  Is this possible?  How would we do this?


What is the best betting strategy to maximize probability of winning?

The question appeared in one of the assignments I am using to self study Probability and Statistics:     I begin turning a deck of cards one at a time. At some point (before I have turned over all $52$ cards) you can bet the next card is red to   receive one dollar; otherwise you receive nothing. Design   a strategy to maximize the probability that you will receive the dollar.   When should you bet?   $E_k$ is the event that bet is placed on card number $k$ and that it is red. Obviously, $E_1=E_2=\frac{1}{2}$ which led me to believe it is immaterial when one bets on the cards. I tried to derive the same using a case for  $E_{k} \text{ when }k-1$ cards have already been drawn.    $P(E_k)=\frac{26}{52-(k-1)}\frac{26\choose{k-1}}{52\choose{k-1}}+\frac{26-1}{52-(k-1)}\frac{{26\choose{k-2}}{26\choose{1}}}{52\choose{k-1}}...\frac{26-(k-1)}{52-(k-1)}\frac{{26\choose{0}}{26\choose{k-1}}}{52\choose{k-1}}$ $P(E_k)=\frac{1}{(53-k){52\choose{k-1}}}\sum_{i=0}^{i=k-1}(26-i){26\choose{k-1-i}}{26\choose{i}}$  How do I evaluate this value? Also I realize for my particular solution, $k\le 26$. What would be a more general solution?


If capital letters are supposed to be sets, why is $N$ used as a number? For example, in this definition of a Cauchy Sequence it says:      A sequence ${p_n}$ in a metric space $X$ is said to be a Cauchy sequence if for every $\epsilon\gt 0$ there is an integer $N$ such that $d(p_n,p_m)\lt \epsilon$ if $n\ge N$ and $m\ge N$.   Is this saying that for an arbitrarily large $n$ and $m$ this is true? I'm confused on why it uses $N$ when I've been told that capital letters are supposed to be sets.


What evidence is there that 'to' belongs to any particular part of speech?

Reopen note:  There is a quite finite and modest amount of evidence in the literature about this issue, which members can record here as they see fit. Less than there is for example about what a noun is or what a verb is, or how to tell what the Subject of a sentence is. It's a simple question, that people need to be able to get answered on a site such as this. It is of continuing interest as more recent questions such as  attest to. The fact that people disagree about the outcome of the evidence does not mean that there is too much evidence to be documented. Quite the reverse. They disagree because there is relatively little evidence altogether. However, it is seriously interesting evidence.   The question   What part of speech is to as in:   I need to know. To err is human, to forgive divine. What am I to do?   This question is not really about the difference in meaning between the examples. It is a question about what grammatical or syntactic reasons we have to classify this item as a particular part of speech. If arguing that it is 'its own part of speech', I'd like to know what grammatical - but not historical - reasons you have for your claim.   Just to clarify, I'm not asking about what assignment any particular authority or publication gives it. I'm interested to know the reasons why. Your own personal insights are also very welcome.  If you're a grammar anorak - like me - then you may want a list of the contenders out there from other grammarians. In no particular order:   preposition subordinator non-finite auxiliary verb modal verb inflectional element   Can you help?


I remember back in 2012, when I tried to upgrade to Oneric using Software Updater, I got something called a partial upgrade and it was a mess to deal with.  Is there any way to avoid that from happening now that I want to upgrade to Bionic?  I have safety measures such as having backups, and separate home partition.


A question from my homework I'm having trouble understanding. We are given:  $A(1) = \{\varnothing\}$, $A(n+1) = A(n)\cup (A(n)\times A(n))$  $A=A(1)\cup A(2)\cup A(3)\cup \cdots \cup A(n)\cup A(n+1) \cup \cdots$ to infinity  The questions are:  1) show that $A\times A \subseteq A$  2) Is $A \times A = A$?  Thank you for your help.  I've tried writing $A(2)$ but it gets really complicated and I'm having trouble understanding what the sets are. Let alone solve the question.


$X,Y$ are independent random variables, normal distribution, $XY$ has normal distribution

$X,Y$ are random independent variables with normal distribution. Can we conclude that $XY$ has also normal distribution ?     I know definition of normal distributio, however I have a problem with it. Can you explain it ?


i would like a picture on a canvas print 40inch x 22inch. The picture is 96dpi. Will this be okay to get a good clear picture, if not what would be?? many thanks


Can't finish registration in Stackoverflow.ru

I have an account on Stack Overflow and also on Russian Stack Overflow. I can ask questions on Russian Stack Overflow, but it always displays the phrase "Finish registration". I have tried logging in by different methods — Facebook, Google, etc. — but it still says that my registration is not finished. Can someone help me with it? or explain what I should do there to finish the registration?  P.S: I can't write questions in Meta Russian Stack Overflow because it says that my registration is not finished.  P.S.S: I have already tried "Click the "register" link at the top of the page." it brings to the login page with the phrase "Finish signing up by using any of the following options:". I have already tried all options there. I also can't merge them because they already linked.


UTF-8 encoding problem upon retrieving arabic letters from database after switching from mysql to mysqli php

Our project (coded in mysql) is working for a hotel since long time and storing names of arabic letters in database and it was to retrieve the data correctly from the database but after recoding the project in mysqli we found that we are not able to retrieve the old data correctly as they display in strange characters but there is no problem for the new inserted data. I've searched a lot everywhere and I never found a solution. Can we find some way to resolve this problem as there are more than 10000 records which could be lost in this way. Here Below are 2 images for what I am talking about    The first row of the table above was inserted after using Mysqli code while the rest was insert in the old code of mysql    This is how the database looks like, the same like the table above. By the table in using utf8_general-ci Collation  Many thanks in advance


Let $R$ be the relation on $N\times (N\setminus\{0\})$ defined by $((a, b),(c, d)) \in R$ if $ad = bc$. Prove that $R$ is an equivalence relation.  I'm pretty confused with this problem, mainly because I don't understand the significance of $(N\setminus\{0\})$. Any ideas on how to solve this?


Are two variables that are dependent also correlated? / Can two dependent variables not be correlated?

I cannot find the answer to my question anywhere, I hope someone can help.   I did a Chi-Square test with several variables to see if they were dependent or independent. The result showed that they were dependent.   After that I did a Spearman´s rho test to see if they were correlated or not (looking at the P-value). All of them were correlated except one. Can this be correct?   Can two dependent variables not be correlated?


Show you have flagged a post in the flag dialogue window

When I vote to close a question and I open back up the dialogue window it will say      You voted to close this question {time} ago   which is fair enough.    However, if I flag a post I will get told      You have already flagged this post for moderator attention    only after I try and submit a second flag. I think it would be helpful to display      You flagged this post as {reason}, {time} ago   if I open the dialogue box again.


I tried to find bounds for the sum using regular techniques, but couldn't get any result nor contradiction.


It seems to be the  that tables should not be used for layout in HTML.   Why?  I have never (or rarely to be honest) seen good arguments for this. The usual answers are:   It's good to But this is a fallacious argument; . I guess it's true that using the table element for layout has little to do with tabular data. So what? Does my boss care? Do my users care?Perhaps me or my fellow developers who have to maintain a web page care... Is a table less maintainable? I think using a table is  than using divs and CSS.By the way... why is using a div or a span good separation of content from layout and a table not? Getting a good layout with only divs often requires a lot of nested divs. Readability of the codeI think it's the other way around. Most people understand HTML, few understand CSS. It's better for SEO not to use tablesWhy? Can anybody show some evidence that it is? Or a statement from Google that tables are discouraged from an SEO perspective? Tables are slower.An extra tbody element has to be inserted. This is peanuts for modern web browsers. Show me some benchmarks where the use of a table significantly slows down a page. A layout overhaul is easier without tables, see .Most web sites that need an upgrade need new content (HTML) as well. Scenarios where a new version of a web site only needs a new CSS file are not very likely. Zen Garden is a nice web site, but a bit theoretical. Not to mention its  of CSS.   I am really interested in good arguments to use divs + CSS instead of tables.


I'm completely confused when it comes to the combinations with over / down / out:     Thank you for coming over / - coming down / - coming out.      Come over here / - down here / - out here.      Over there / Down there / Out there.   How do I decide which one and when to use?


I do PCA manually with numpy in the same method as Scikit Learn and getting same values but different signs


Would an Imp be resistant to the bludgeoning damage from a Mace of Warning?

The Damage Resistances for a 5E Imp are:  Cold; Bludgeoning, Piercing, and Slashing from Nonmagical Attacks that aren't Silvered  Would this Imp be resistant to damage from a Mace of Warning?  You could argue "Yes" because any Weapon of Warning should be considered a magical weapon, and therefore the damage it deals is considered magical. You could argue "No", with a liberal interpretation of the resistances, because the mace is not silvered.


A function $f: \mathbb R \rightarrow  \mathbb R$ is called proper if $f^{-1}(C)$ is compact for every compact set C. Prove or give a counterexample: If $f,g$ are continuous and proper, then the product $fg$ is proper.  My attempt: Let $h(x)=f(x)g(x)$ and product of two continuous function is continuous. This implies $h(x)$ is continuous.   Now, I claim that $h(x)$ is proper by showing that $f^{-1}(C)$ has finite number of subcovers.  Is this idea is correct? If not can anyone suggest the contradict example?


Integral of $\log(\sin(x))$ using contour integrals

I know the integral is possible with a simple fourier series expansion of $-\log(\sin(x))$  But I am interested in complex analysis, so I want to try this.  $$I = \int_{0}^{\pi} \log(\sin(x)) dx$$  The substitution $x = \arcsin(t)$ first comes to mind.   But that substitution isnt valid as,   The upper and lower bounds would both be $0$ because $\sin(\pi) = \sin(0) = 0$  What is a workaround using inverse trig or some other way?  Inverse sine is good, because that gives us a denominator from which we will be able to find poles.  $$x = arctan(t)$$  Is also good, but it would hard to do.  Idea?


In my bachelor courses, we have defined the space $C^1(\mathbb{R})$ as $$C^1(\mathbb{R}) = \{f: \mathbb{R} \rightarrow \mathbb{R}~|~f \text{ is differentiable}~\land~f' \text{ is continuous}\}.$$ However, I really do not understand why it is required that $f'$ must be continuous. Indeed, if $f$ is differentiable at $a \in \mathbb{R}$, then the limit $$\lim_{x \rightarrow a} \frac{f(x) - f(a)}{x - a}$$ does exist. Isn't it equivalent to the fact that our function $f'$ is continuous in $a$ ? I asked my teacher for an example of a function that would be differentiable at a point but whose derivative would not be continuous at this point. He gave me the function $$f(x) = |x| \quad \text{at zero.}$$But I disagree with him, it's not that the derivative is not continuous in zero, it doesn't even exist because these two limits don't agree $$- 1 = \lim_{x \rightarrow 0^-} \frac{f(x) - f(0)}{x - 0} \neq \lim_{x \rightarrow 0^+} \frac{f(x) - f(0)}{x - 0} = 1.$$ Therefore, $f$ is not differentiable at $0$. Could someone explain to me the definition of $C^1(\mathbb{R})$? Is there an example of a differentiable function whose derivative is not continuous? Thank you very much!


I downloaded a blender file and opened it but UI did not match V2.80.  I guess that because the file have been made in old version its UI did not match V2.80. I want change UI as V2.80 easily.  Is there any way for me?


One day I needed paper and I turned all of my sugar cane into sugar.  So, I wondered do you find sugar cane near water?


How do I remove this Elder Scroll from my inventory?

In the quest  I received an Elder Scroll.  This is great and all, and who doesn't want to own an Elder Scroll, but the problem is that it weighs 20 (pounds? kilos? I'm not sure) and is marked as a quest item, causing me to be unable to store it in a chest etc.  Is there a way to make it unmarked as a quest item, giving me the ability to keep it but store it away? If not, is there a way to get rid of it without using the console (I'll use the console if I have to, but I'd rather not).


Firefox can do it, can Chrome?   Here's what I'm looking for:


Connect through Finder with server, save permissions?

I'm trying to access my FTP server through Finder, I can open the server and access the files. But when I try to change a .css file or something and save I then get an error stating that I don't have permission.  I tried this but this didn't work . On my server the permissions are correct.  I edit with brackets.  Someone know what I'm doing wrong?


How can an an ant lift 50 times its own weight and pull 30 times its weight?

According to many sites like , an ant can apparently  lift 50 times its own weight and pull 30 times its weight. Is it true?  Can it be proved using physics? Though most sites agree that an ant can lift many times its own weight, not all agree with exactly how many times its weight. The explanations provided if any are usually vague and do not use specific numbers. Can a specific numerical value be calculated?  Secondly, how is it possible for the ant to pull 30 times its weight? I find it unbelievable. Can anyone explain this?


cross references different from tableofcontents

I have a document divided into \part \chapter \section and \subsection. I have 3 parts and in each part I reset all the counters.  I want that, when I do a crossref to something that is in the 1st part, chapter 3 and section 5, that LaTeX prints something like I-3.5, but  I don't want that in the tableofcontents part that LaTeX prints the part number. For example, what I want is:     Part I      chapter 1 section 1.1 section 1.2      chapter 2   AND NOT     chapter I-1 section I-1.1 section I-1.2      chapter I-2   The command that I've tried   \renewcommand{\thechapter}{\thepart-\arabic{chapter}} \renewcommand{\thesection}{\thechapter.\arabic{section}}   does exactly what I've said  Can anyone help me?


Port selection not possible in Arduino IDE on Ubuntu 20.04

I have upgraded to 20.04. Arduino IDE loaded with: snap install arduino  as suggested (version 1.8.13). The port selection item cannot be selected. As suggested in other posts, I have done: sudo usermod -a -G dialout $USER  Actually, this added dialout in groups. I rebooted, dialout is still in groups, but still the port cannot be selected and, of course, I cannot upload anything on Arduino.


Too much width for long post title in profile page

When the post title is long enough then such string occupies too much space in profile page on the post section. For example in :        As you can see the “Q” icon is obscured by the post score indicator, and post date is wrapped to two lines.


How to find exactly how much memory a Java application uses from within the application

I am working on an application written solely in Java which will often be using very large amount of data (at most 500 GB). The program will be saving data not currently in use in a database.   However, I want to keep as much data as possible within the application since a lot of it is reused often. In order to not get any out-of-memory errors I want to be able to check how much memory the application as a whole is using at any one moment, so that I can store it when the application approaches a predefined limit.  Something like this;  long memoryUsage = SomeClass.getCurrentMemoryUsage();


We use multiplication for repeated addition, and in turn use exponents for repeated multiplication. What topic comes after this, for repeated exponentials? Is there something my teachers are hiding from me?


How to solve the following problem - A ∩ B ⊂ A ⊂ A ∪ B?

Prove that $$(A \cap B) \subset  A \subset  (A \cup B).$$  I understand $\cap$, $\subset $, $\cup$ concepts, but i wonder how to solve this problem.


Well this is my third uk visa refusal and although two times before the ECO said that there was no problem with my salary, yet this time this was his reply  Regarding the other reason, you tell me   And for those who will tell me to hire a lawyer, well i contacted alot even lawyers in UK yet they answer by that they don't deal with egyptian citizens or they don't deal with the ukvi at all


It is possible for the actions bar to span 2 lines.  It is particularly disorienting when the (1) and the action that it corresponds to are on different lines.  (in this case close)


How do I show that $\sum_{k = 0}^n \binom nk^2 = \binom {2n}n$?

$$\sum_{k = 0}^n \binom nk^2 = \binom {2n}n$$  I know how to "prove" it by interpretation (using the definition of binomial coefficients), but how do I actually prove it?


Any way to use function results for a countif conditional in Excel

For example I have a list of dates in A2 through A31 (1st April to 30th April) and want to count the number of weekdays.  In B2 to B31 I could use =WEEKDAY(A2,2)<6 to give true or false. Then separately  count the trues.  Is there anyway to do it all in 1 cell with something similar to =COUNTIF(A2:A31,WEEKDAY(A2,2)<6)?


I'm sorry if this is a duplicate, but I can't seem to find the answer to this.  If $Z_t$ is a white noise process and $X_t$ satisfies  $$ \phi(B) X_t = \theta(B) Z_t $$  (where $B$ is the lag operator), then when is $X_t$ stationary?  If $\theta(z)$ and $\phi(z)$ have no common roots and $\phi(z)$ has a root with $|z| = 1 $ then $X_t$ is necessarily non-stationary [Brockwell and Davis, Remark 3 in Chapter 3].  I also know that a moving average of a stationary process with absolutely summable coefficients is also stationary [Brockwell an Davis, Proposition 3.1.2]. So if $\phi(z)$ has no roots in with $|z| \leq 1$ then the Maclaurin series for $1/\phi(z)$ has radius of convergence greater than 1. Therefore $X_t$ is a moving average of $\theta(B) Z_t$ with absolutely summable coefficients, and hence stationary.  By stationarity, I mean weak (=second order) stationarity.  The lecturer has a habit of putting this on the final, so I'd like to know if there's a general theorem governing it.  From a past paper:


$\sum_i |a_i x_i|<\infty$ whenever $\sum_i |x_i|<\infty$, so ${a_i}$ is a bounded sequence.

My attempt:  $\lim_{n\to\infty}|a_n||x_n|=0$ , $\lim_{n\to\infty}|x_n|=0$ and so $\lim_{n\to\infty} |a_n|=0$. So $\lim_{n\to\infty} a_n = 0$. Hence the sequence {${a_n}$} is bounded.


I have a service similar to the URL shortening service bit.ly. The link generation method is similar but the site is not. A user uses my site just like the mentioned bit.ly, but I offer a different kind of service for which I want to rank (on Google) for.  If I were to generate links such as: mysite.com/my-keywords/1Asdf34 would it be considered spammy or black hat?  The same for bit.ly would be: bit.ly/url-shortening-services/3k1dS4sd For bit.ly it would defeat the purpose, but URL length in my case does not have to be short.


What are the answers for these basic quetions?

It has been a while I was away from maths, and I am doing a comeback.  I would highly appreciated if someone (in detail, and plain 6th grade English) can explain these to me.   B : {0, 1}d --> {0, 1}d A Є {0, 1}d uniform distribution vectors (I know they have more than a single characteristics, like direction and weight) but what doe they mean inside cryptography, for example, vectors of sub keys). differential (what does it mean in general? does it mean differences between numbers or so. An example would be appreciated. For example, what does Differential XOR mean)   Thanks :)


It installs fine but there is no GUI anywhere for it nor is it in the recommended open with programs. I'm guessing its a repository issue because in the software updater I get this error.   E:The repository 'https://dl.winehq.org/wine-builds/ubuntu bionic Release' does not have a Release file.  W:Updating from such a repository can't be done securely, and is therefore disabled by default.  W:See apt-secure(8) manpage for repository creation and user configuration details.  E:The repository 'http://ppa.launchpad.net/wine/wine-builds/ubuntu bionic Release' does not have a Release file.  W:Updating from such a repository can't be done securely, and is therefore disabled by default.  W:See apt-secure(8) manpage for repository creation and user configuration details.  W:GPG error: http://archive.canonical.com precise Release:   The following signatures couldn't be verified because the public key is not available: NO_PUBKEY 40976EAF437D05B5  E:The repository 'http://archive.canonical.com precise Release' is not signed.


So I get an error message saying "Keychain "login" cannot be found to store "551961960"" and when I get to keychain access and try to repair using the keychain first aid thing and I get "Keychain Access wants to use the "Local items" keychain" and asks for the password. I try my admin password and that doesn't help. I don't know the password. Help!


Isomorphism between $\Bbb R$ and $\Bbb R(X)$?

My questions are:     $1.$ Is there a field morphism $\Bbb R(X) \hookrightarrow \Bbb R$ ?      $2.$ If the answer to $1.$ is "yes", are $\Bbb R$ and $\Bbb R(X)$ isomorphic as fields?   $ $    $ $  For $1.$, here are some comments:   This is true for $\Bbb C$, see . The key point here is the fact that $\Bbb C$ is algebraically closed, of cardinality $2^{\aleph_0}$, and of characteristic $0$. The same argument doesn't work for $\Bbb R$. We can actually find a subfield $F$ of $\Bbb R$ such that $F \cong F(X) \cong F(X,Y) \cong \cdots$, see .  that $\Bbb Q(X)$ does not embed in $\Bbb Q$ (as a field).  This is equivalent to: Is there an injective ring morphism $\Bbb R[X] \hookrightarrow \Bbb R$ ? (By taking the fraction fields).   As for 2. :   They are isomorphic as abelian groups, and actually as $\Bbb Q$-vector spaces. They are not isomorphic as $\Bbb R$-algebras, because they haven't the same transcendence degree over $\Bbb R$. Let's try to see how to construct such a field isomorphism. We could try$^{[1]}$ to find a subset $B$ of $\Bbb R$ such that $\Bbb R = \Bbb Q(B)$ and $C \subsetneq B \implies \Bbb R \neq \Bbb Q(C)$.  The set $B$ must contain transcendental elements, pick such an $x_0 \in B$.  Then $\Bbb R = \Bbb Q(B) = \Bbb Q(B \setminus \{x_0\})(x_0)$ and we could try$^{[2]}$ to find a field isomorphism $\Bbb Q(B \setminus \{x_0\}) \cong \Bbb Q(B)$, so that $\Bbb Q(B \setminus \{x_0\})(x_0) \cong \Bbb Q(B)(x_0) \cong \Bbb R(X)$.  For ${[1]}$, I tried to use Zorn's lemma on $\mathscr B = \{B \subset \Bbb R \mid \Bbb R = \Bbb Q(B)\}$ and the partial order $B_1 ≤ B_2 \iff B_1 \supset B_2$. But this is not clear to me why this should be an inductive set.  For ${[2]}$, my idea was to define $f : \Bbb Q(B \setminus \{x_0\}) \cong \Bbb Q(B)$ by choosing a bijection $b : B \setminus \{x_0\} \to B$ (these sets should be uncountable), and then trying to extend $f\vert_{B \setminus \{x_0\}} = b$ to a field morphism.     Edit for $^{[1]}$: in  article (MINIMAL GENERATING SETS OF GROUPS, RINGS, AND FIELDS, by LORENZ HALBEISEN, MARTIN HAMILTON, AND PAVEL RUZICKA) the theorem 2.4. proves that $\Bbb R$ has no minimal generating set as field (or $\Bbb Q$-algebra, i.e. as ring). The argument uses Artin-Schreier theorem. Minimal generating sets of modules are   .  I think that $B$ is a minimal generating set of a subfield $K \subset \Bbb R$ over $\Bbb Q$ if and only if any element of $B$ cannot be written as a rational fraction of other elements of $B$. Under these conditions and using (transfinite) induction, we can probably prove (and this was my first idea) that any function $f: B \to \Bbb C$ such that $b$ and $f(b)$ are conjugate over $\Bbb Q$ (i.e. have the same minimal polynomial) extends to a (unique) field morphism $\sigma : K = \Bbb Q(B) \to \Bbb C$.  Actually, the collection $\mathscr B$ defined above doesn't have to be an inductive set, at least if we replace $\Bbb R$ by $K =\Bbb Q(\sqrt 2, \sqrt[4]{2},\sqrt[8]{2},\dots)$, because the descending chain $\left(E_n = \{\sqrt[2^m]{2} \mid m \geq n\}\right)_{n \geq 1}$ satisfy $K = \Bbb Q(E_n)$, but $K \neq \Bbb Q\left(\bigcap_{n≥1} E_n\right)=\Bbb Q$, so the chain has no upper bound w.r.t. $≤$ in $\mathscr B$.


I use overleaf while I am writing my thesis and I want the authors in each citation to appear in chronological order. I use biblatex: \usepackage[style=authoryear,sorting=nyt,dashed=false,uniquelist=false,maxnames=1,minnames=1,maxbibnames=99,backend=biber,sortcites=true]{biblatex}  An example from my text is the following: these paleolakes could have hosted habitable conditions and contributed organic material to sediments sinks at the landing site. There are many potential fluvial valleys and sediment fans in the study area  \parencite{molina2017coogoon,fawdon2018ancient,dickeson2020topographic}.  but when I recompile it appears like that:


Find the infinite sum: $\frac{1}{(1)(2)}+\frac{1}{(3)(4)}+\frac{1}{(5)(6)}+\cdots$.   I thought of expanding it as $\frac{1}{1}-\frac{1}{2}+\frac{1}{3}- \cdots$, but it would yield nothing useful as this runs into the non-convergence issue.


Sacrifice creature question (Magic the gathering)

Let's say my opponent plays  and I have to choose to sacrifice a creature.  I have  on the board, so can I choose to sacrifice it, and then play it's ability at the same time?   I know that if the opponents card had him choose a target, and that target had an sacrifice ability, I could use it and it would resolve first. But since here I have to choose the target myself, how does the stack work here?   The spell is already on the stack once my opponent plays it, so does me choosing a target to sacrifice resolve the spell, meaning I can't play any abilities in between, or does it stay on the stack still and let me play abilities in between?  Edit: Similarly, if an opponent would play an ability that said f.ex: "Opponent discards 2 cards from his hand" and I had a card in my hand that said something like "Discard this card, draw a card" and a card in play that said "Discard a card, this creature gains +1-+1". Could I choose to discard the draw card to trigger the effect and another card to trigger the creature effect at the same time the opponents spell resolves?


I am writing this java program to find all the prime numbers up to num using the Sieve of Eratosthenes, but when I try to compile, it says I can't use a long var as an array index, and it expects an int var in its place. But I'll be working with large numbers, so I can't use int. What can I do?  import java.util.*; import java.lang.*;  public class t3{     public static void main(String[] args){         long num = 100;          //declaring list and filling it with numbers         ArrayList<Long> numlist = new ArrayList<Long>();         for(long x=2 ; x<num ; x++){             numlist.add(new Long(x));         }          //sieve or eratosthenes         for(long x=0 ; x<Math.sqrt(num) ; x++){             for(long y=x+1 ; y<numlist.size() ; y++){                 if(numlist[y]%numlist[x] == 0){                     numlist.remove(y);                 }             }         }          //print list         for(Object item : numlist){             System.out.println((Long)item);         }     } }


Why are triangles drawn like so when working with gravity on an inclined plane?

This is my first year as a physics student, and I've never learned about vectors past a basic level, so this is confusing me. When we have gravity on an inclined plane, we separate it into two components, which I understand.  However, consider the image below, and there's a box at point A. When separating the gravity components, you draw a triangle AGC (sorry, the G and D are on top of each other and difficult to distinguish). AG becomes the force of gravity in the y-direction, and GC becomes the force of gravity in the x-direction. Then you do the trig functions from there. However, when I tried this myself, I drew triangle ADF instead and tried the trig functions from there. It didn't work. I'm having trouble understanding why you can't compute the trig functions from AGF. The only partial solution I came up with was that force of gravity in the y-direction can't be the hypotenuse, as the force of gravity in the y-direction is always less than the force of gravity. But I think I'm missing something more.


The "too short" comment error is absent on mobile web

When I'm in the full site and attempt to leave a comment containing fewer than N characters, I get an "N to go..." message.  On mobile web, the comment only fails to submit. No errors or any hints. I propose that the user be somehow alerted on mobile web when a comment is too short.


How to guarantee the footnote is at the bottom when there is a table setting with [b]

I have a footnote in the text. However, there is a table with \begin{table}[b]. The table appears below the footnote now. Like this:  How can I make sure that the footnote is at the bottom instead of the table?


Linux command line. Move all files and directories in directory, except some files and directories

I have a folder A which has files and directories, I want to move all those files and directories to another folder B, except file, file2, directory, and directory2.  How can this be done?


Someone else is booking international ticket for me using their credit or debit card. Do they need to be present physically at the time of check in?

If someone else is booking international ticket for me using his credit or debit card, does he need to be present physically at the time of check-in?   Suppose I am coming back from Singapore to my home country and my ticket is booked by my friend for me, who lives in my home country. Do airlines in Singapore ask for the person to be present physically to check in?


In-line long division symbol (French style)

I am looking for long division symbol for inline use. For US style there are .  For displayed long division, French style, there is .   I am looking for the inline version, French style, which, for $x \div y$,  would look something like an $x\ L y$ with $y$ inside $L$.


How can I set the TTY font size manually in Lubuntu?

I'm configuring some minimal Lubuntu installs, which will run within VMs. They do not have window managers, and I do not intend to install any. I would like to increase the TTY font size so that 4 of these VMs can be tiled on a single display, and yet still be usable, but I can't figure out how to do this.  I assume there's just a conf file somewhere (/etc/....?) where this can be set. If someone could point me at that, it would be much appreciated!


Do I need iptables or ufw if I have gufw?

On my Ubuntu computer I have Iptables,ufw and gufw installed on it but I am trying to figure out if I need to remove one so I did a experiment and removed iptables and I saw ufw and gufw was removed automatically with iptables I reintall iptables and it did not  automatically came with ufw or gufw I install gufw without installing ufw and ufw was install automatically with gufw It like there are all connected to function properly but that just a experiment I went a true answer?


If time-varying electric and magnetic fields originate each other, how come they are in phase?

As I have read that "time varying electric field is source of changing magnetic field and time varying magnetic field is source of changing electric field "  Hence, I have the following doubt : If time varying nature of one field originates other changing field. Then, why are they in phase?  One is changing and producing the second thing hence second must depend upon first's derivative, I. e. If one is sine then second will be cosine Hence a phase difference of pi/2 and not in phase. Where am I wrong?


Alice has a secret A, Bob has a secret B. They have a secure channel and a MAC. They each want to know the other's secret, but don't particularly want to give up their own. However, neither will not lie about the secret, but if possible, will stop communications once [s]he learns the other's secret.  How can such a protocol work, that if Alice or Bob doesn't correctly follow all steps in the protocol, neither person can gain any information about the other's secret.  You may not use a third party.


Why add a slash after each command on text as \latex?

On the question  I learned I need to add {} (may be also \relax) every time I use a text command like \latex to print the the word LaTeX nicely and keep the correct text hyphenation.   But while fixing my document template accordingly to the hyphenation rules, I found several commands appended with a single backslash as in:  criadas sequencialmente, o \abnTeX\ instrui o \LaTeX\ para que uma vírgula seja   Why they were appending a backslash on it? Can I still fix the hyphenation with \latex{}\ or I should use only \latex{} or perhaps \latex\relax


seems to be the opposite of . Back then,  included a nice analysis of what the effect would be when this change occurs.  I think it would be nice to have an impact analysis (something more substantial than the askers will gain more reputation which is quite obvious).  A particular point of this analysis would be the following case (questions):   score < 0 current reputation gained by user from the question < 0 new reputation gained by user from the question > 0   If there are many such cases, it would significantly encourage asking bad questions.  Question: Is there any impact analysis being done for the question reputation change similar to the one done in the past?


One way in which an object is affected by temperature rise is that the wavelength of the radiation it emits is gets smaller and smaller. Another way of looking at it is that as an object gets hotter, the electrons of the atoms orbit faster and faster. It seems that the maximum temperature and object could have is when:  A) The wavelength of the radiation reaches Planck length.   B) When the speed of the electrons nears the speed of light.  Do processes A and B occur at the same temperature? Is it possible to have a wavelength smaller than Planck length, but it would be immeasurable (Would that be in some sense "infinite" or "negative temperature")?  Please keep the answers in layman's terms.


I really don't understand why this code  #include <map>  template<typename T, typename U> std::ostream& operator<<(std::ostream& o,         const std::map<T,U>& input) {     for (std::map<typename T,typename U>::iterator it=input.begin(); it!=input.end(); ++it)     {         o << it->first << " => " << it->second << '\n';     }     return o; }   returns this compilation error:  error: wrong number of template arguments (1, should be 4) error: provided for ‘template<class _Key, class _Tp, class _Compare, class _Alloc> class std::map’   can anyone help me please??


How to handle lots of file downloads from my linux server

I have a file 50MB file hosted in my deticated linux server, each day there is almost 50K users that download this file (2.5GB a day).  There are lots of crashes and users reports that sometimes even the file can't be downloaded since the server is overload.  I wonder if someone can help me how do I calculate which server/bandwidth/anything I need to handle that?  Is there any solution where I can host the file and pay per download?  Is there any setting or anything that I can improve or do on my server that will help to fix this issue?  My current server specification is:  2 x Intel Xeon E5 2620V2 2 x (6 x 2.10 GHz) 128 GB REG ECC 256GB SSD HD 1 IP Address 1 Gbit/s port Shared Bandwidth   I'll appreciate any help from you guys.  Thank you very much.


How do you create a method for a custom object in JavaScript?

Is it like...  var obj = new Object();  obj.function1 = function(){     //code }   or something like that?


I have Solaris 8 OS installed in French.  Is it possible to switch from French to English without reinstalling the OS ? If yes how ?  When locale -a i have this :  POSIX common en_US.UTF-8 C iso_8859_1 en_CA en_CA.ISO8859-1 en_US en_US.ISO8859-1 en_US.ISO8859-15 en_US.ISO8859-15@euro fr_CA fr_CA.ISO8859-1 iso_8859_15 th th_TH th_TH.TIS620   Even when I try to edit /etc/default/init with :  LANG=en_US.ISO8859-15 LC_COLLATE=en_US.ISO8859-15 LC_CTYPE=en_US.ISO8859-15 LC_MESSAGES=en_US.ISO8859-15 LC_MONETARY=en_US.ISO8859-15 LC_NUMERIC=en_US.ISO8859-15 LC_TIME=en_US.ISO8859-15 LC_ALL=en_US.ISO8859-15   and reboot : nothing happens.  To verify the result i always use date and when i reboot : i also have the date in french.  P.S : I have to do this configuration in a computer which isn't here in my office, so i have to this manipulation in a an another computer here in my office and if it works, i'll do it to the other computer.  So the computer here is configured in English and i have to switch it to French. Here is the content of my ~./dt :  C                     errorlog              sessionlogs Desktop               errorlog.old          sessions Trash                 errorlog.older        simulateur.dtwmrc appconfig             help                  startlog appmanager            icons                 startlog.old asr.dtwmrc            outils.dtwmrc         startlog.older bin                   palettes              tmp bookmarks             sdtfonts              types dtwmrc                sdtpcaction.conf      wsmenu en_US.ISO8859-15      sdtpcaction.conf.bak   Thanks


Delete Ubuntu 18.04 with dual boot with linux mint on SSD

I have installed linux ubuntu but had some problem with the divers so i installed linux mint but now they are splitted in 2 halves on my SSD and want to delete ubuntu now. I am new to linux so i dont know how to do it and searching on google only gives me this situation but with windows instead. Can anyone help me?


Can you transfer between a Google and a Trainer Club account?

Can you transfer data from your Gmail to Pokemon Trainer Club, because I know you get rewards and I want to switch data so it won't get erased.


What are the generators of $\mathbb{Z}_9^*$?

I am to understand that $\mathbb{Z}_9^*$ is cyclic because $9=3^2$, where $3^2$ is of the form $p^{\alpha}$, with $p$ an odd prime... but I can't find any generators for the set...  $|\mathbb{Z}_9^*|=6$, and $\mathbb{Z}_9^*=\{\overline{1},\overline{2},\overline{4},\overline{5},\overline{7},\overline{8}\}$  Using a table:  \begin{array}{c|cccccc} \cdot & 1 & 2 & 4 & 5 & 7 & 8 \\\hline 1 & 1 & 1 & 1 & 1 & 1 & 1 \\ 2 & 2 & 4 & 7 & 5 & 2 & 4 \\ 4 & 4 & 7 & 4 & 7 & 4 & 7 \\ 5 & 5 & 7 & 4 & 2 & 1 & 5 \\ 7 & 7 & 4 & 7 & 4 & 7 & 4 \\ 8 & 8 & 1 & 8 & 1 & 8 & 1 \\ \end{array}  I'm not sure if I'm misunderstanding the definition of a generator, but since I'm assuming that $\mathbb{Z}_9^*$ is cyclic, it should have $\varphi(\varphi(9))=2$ generators... but I can't find a single one.


, is there a way to delete the Stack Exchange OpenID?