Let $f(z)$ be a holomorphic function on the unit disk $\mathbb{D}$ such that $\lvert f(z)\rvert \leq \frac{1}{1-\lvert z\rvert}$ for all $z\in \mathbb{D}$. Show that $\lvert f'(z)\rvert \leq \frac{4}{(1-\lvert z\rvert)^2}$ for all $z\in \mathbb{D}$. The only inequality that I know that looks sort of like this is the Schwarz-Pick lemma, but we do not have that $f(z)$ has range contained in $\mathbb{D}$, so we can not use this as is. I have also tried using the Cauchy Integral formula to estimate \begin{equation}\lvert f'(z)\rvert =\lvert \frac{1}{2\pi}\int_{\lvert \zeta\rvert =r}\frac{f(\zeta)}{(\zeta-z)^2}d\zeta\rvert\end{equation} for $1>r>\lvert z\rvert$, but I ended up with something going to infinity on the RHS as I tried to take $r\to1$. At this point I'm sort of throwing ideas at a wall, so if someone could give me a small hint, that would be excellent.

$f$ is an analytical function on the unit disk $\mathbb{D}$ for which there is a $C > 0$ such that  $\forall z \in \mathbb{D} \colon |f(z)| \leq \dfrac{C}{1-|z|}$.  I know have to prove that    $\forall z \in \mathbb{D} \colon |f'(z)| \leq \dfrac{4C}{(1-|z|)^2}$.  I tried using the Cauchy integral formula but I can't find a fitting circle to get this result.


Any tips on creating a material that will be easily reconized as glass, without it showing anything behind it? (0 transparency). I'm making a vehicle that has glass windows, but I don't want to make the interior, so I need something glass like that will not show what is behind the glass.

I am modeling plane and I don't want to model a cockpit so I want to use black windows which will reflect a lot of light but you can't see thought.   Currently I just use Glossy BSDF (GGX) with almost black color (0.01, 0.01, 0.01) and Rougness 0.015 but it don't look quite right. It lacks glass shine and looks too matt.  Edit:  Here is my simplified blend file:    Also here is what i want. Glass on this tie fighter is blackish and it looks like glass. In my blend file it looks more like plastic.    One more thing i noticed is when light reflect from glass whole glass section reflect same amount of light. It can be seen on tie fighter example above.


Can you please advise what is the best application for email encryption using iPhones and iPads?

I've started taking security more seriously lately. (Why only now you may ask? Because I'm a trusting fool that's why.) I've now got emails signing automatically and encrypting where I have their key.   Previously I only did this when necessary, but I'm trying to breed a sense of change around me and taking my own medicine seems sensible. I have no issue with GPG in Thunderbird, Outlook, or on Android with K9 Mail & APG, but I have no idea how to handle GPG on IOS.   I can't accept there's no way, it seems ridiculous, or maybe I'm approaching the problem wrong and there is a more appropriate route than GPG that's better supported?


I bought a new Lenovo Legion Y520 and wiped Windows 10 Home because I don't like and need it. The notebook comes with a Nvidia GTX 1050 and I was wondering what's the proper way to set up the graphics for occasional playing. With a fresh ubuntu setup, default drivers and settings I tried playing "Cities Skylines" with a lot of graphical issues (texture glitches, intolerable freezes and so on) so I assume my graphics aren't set up well. I tried a few things like simply updating Nvidia driver to 390 without any changes and started it over. Do you have any advices for me how to go on from a fresh Ubuntu 17.10 installation? Hope you guys could help me out!

I've just installed Ubuntu and I need either video, wireless, or some sort of other manufacturer (non-opensource) driver. How can I run the tool that will fetch all of these for me? I'd like graphical instructions.  Related:


Let $\alpha = \frac{1+\sqrt{5}}{2} \hskip 20pt \beta = \frac{1-\sqrt{5}}{2}$  be the two real roots of the quadratic equation $x^2 - x - 1 = 0.$ Prove that $f_n = \frac{\alpha^n - \beta^n}{\alpha - \beta}$ for all $n \in \mathbb Z^+$.  I'm confused as to how this could be simplified after doing the induction step where you add 1 to all of the "n's" making it, $f_n = \frac{\alpha^{n+1} - \beta^{n+1}}{\alpha - \beta}$

This formula provides the $n$th term in the Fibonacci Sequence, and is defined using the recurrence formula: $u_n = u_{n − 1} + u_{n − 2}$, for $n > 1$,  where $u_0 = 0$ and $u_1 = 1$.   Show that     $$u_n = \frac{(1 + \sqrt{5})^n - (1 - \sqrt{5})^n}{2^n \sqrt{5}}.$$    Please help me with its proof. Thank you.


In CWM Mac Lane uses the term $\mathbf {ENS}$  for a category having as objects the subsets of a given set and as morphisms the functions from these sets to these sets. What is abbreviated by the letters ENS?

Earlier someone was asking about the category "Ens" described in Categories for the Working Mathematician. My question is more basic: What does Ens stand for?  Most of the categories have names that are self explanatory, and maybe this one does too.  But for the life of me I can't think of it, and a Google search was no help.


Which package has a similar looking fancy R or does anyone know how to make one? (Note: the line underneath the R is just the notebook paper... this is from a scanned set of notes).

I know what my symbol or character looks like, but I don't know what the command is or which math alphabet it came from. How do I go about finding this out?


By considering the function $$f(x)=\sin x - x$$ for $0<x<\frac{\pi}{2}$, show that $$\frac{2}{\pi}x<\sin x<x$$ for $0<x<\frac{\pi}{2}$  My first step was to differentiate $f(x)$, upon which I get $\cos x - 1$. However, I do not know how to procede from there.

I need to show that $\dfrac{2}{\pi}<\dfrac{\sin(x)}{x}<1$ for $0<x<\dfrac{\pi}{2}$.  I know I need to use the mean value theorem, would I just say that since $f$ is continuous in the interval (call it I).  We know $\exists c\in I$ such that $f'(c) = \dfrac{f\left(\dfrac{\pi}{2}\right)-f(0)}{\dfrac{\pi}{2}}$. I don't know where this is going though.  Also, would I need to show $\lim_{x \to 0}\dfrac{\sin(x)}{x} = 1$? Is there a way to do this without L'H Rule?


I need to trying to get the Facebook SDK for JavaScript code inserted just after the  tag.  What's the easiest way to do this?

I would like to inject some elements directly after the <body> tag.   Is that possible using only WordPress hooks?


Given $p: \mathbb{R} × \mathbb{R} \to [0,\infty)$ is defined as $$p(x,y) = \frac{|x-y|}{1+|x-y|},$$ I wish to show $p$ is a metric on $\mathbb{R}$ but I'm having difficulty proving the triangle inequality property for $p(x,y)$. So I want to show $p(x,y) \le p(x,z) + p(z,y)$. Do I make use of the standard bounded metric induced by the metric $p(x,y)=|x−y|$?

I am pretty sure that this is such a stupid, stupid question, but how do you prove that $d_2(x,y)={|x-y|\over {1+|x-y|}}$ satisfying the third condition to be a metric, which is the triangle inequality.   I know that I should really be able to do this, but I just can't, I keep seeing a contradiction. Please help me.


The code is as follows      \begin{figure}[h] \centering \includegraphics[width=0.5\linewidth]{figure} \caption{Comparison elements in a row of $A_1$ and $B_1$} \label{fig} \end{figure} The above Figure shows that ...   The above is what I usually do in Latex. But I found the text after an inserted figures always has a space at the front. Like in this case there is a white space before   The above Figure shows that ...   How to remove the white space? One solution I know is to insert "\\" ,after$\end{figure}$.

\section{last paragraph} Here are some words in the last paragraph. Now a figure is inserted below. \begin{figure}[H] \centering \includegraphics[width=5cm]{...jpg} \caption[Example .]{.,,} \label{...} \end{figure} Now I want to start a new line after this figure. But there is always indentation at the begining. How to delete this indentation?   Here is the complied result:   I add the usage exmaple:  \documentclass[a4paper,12pt]{article}  \usepackage[english]{babel} \usepackage{graphicx} \usepackage{float}  \begin{document} \section{Paragraph} Here are some words in the last paragraph. Now a figure is inserted below. \begin{figure}[H] \caption{A picture of a gull.} \centering \includegraphics[width=0.5\textwidth]{Penguins.jpg} \end{figure} Now I want to start a new line after this figure. But there is always indentation at the begining. How to delete this indentation? \end{document}   Here is the compiled result:


I was working on this with a group and the group came up with the following for a proof:  Suppose $c \in f^{-1}(f(C))$.  Then by definition of $f^{-1}$, $f(c) \in f(C)$.  Hence $c \in C$ and $f^{-1}(f(C)) \subseteq C$.  This doesn't seem correct as it doesn't assume the hypothesis.  i.e.  there is no assumption or use of $f : A \rightarrow B$ and $C \subseteq A$.  Is the proof the group came up with correct and if not any help on the proof would be nice.

Let $A$ be a subset of the domain of a function $f$. Why $f^{-1}(f(A)) \not= A$. I was not able to find a function $f$ which satisfies the above equation. Can you give an example or hint. I was asking for an example function which is not addressed


Since upgrading to Ubuntu 13.10 on my laptop (actually to Xubuntu as I switched to XFCE) I'm running into problems with LightDM:  I use two external displays (one 24" and one 22" display) connected to my laptop docking station. After installing the NVIDIA driver 319 I used nvidia-settings to configure both displays to use TwinView and the correct native resolutions. I also stored this configuration in /etc/X11/xorg.conf. Right now when I login my display setup is "loaded" correctly.  However, LightDM seems to ignore my setup: Each time the login screen is presented in clone mode instead of TwinView with a wrong-sized (too small) background image for the 24" display.  How can I fix this?    Update:  I just noticed that LightDM uses the wrong display setup (i.e. clone mode) only when the laptop lid is closed in the docking station. When I keep the laptop lid open (even with laptop display disabled) LightDM behaves correctly and uses the exact display setup as I configured for my X session.    Solutions for   which involve using xrandr in a script and running it with the option "display-setup-script" or similar in the /etc/lightdm/lightdm.conf don't work: My script (see below) is executed but the resolution won't change. When executed manually in an X session, the script works perfectly.  Probably something is being overridden/enforced by the NVIDIA driver here? I already tried NVIDIA drivers 304, 319 and 331 without success. With 13.04 the problem did not occur, I didn't even need a script for LightDM.    My current script (/usr/share/lightdmxrandr.sh):  #!/bin/bash extscreens=$(xrandr -q | grep -c "DP-[02] connected") if [[ $extscreens == 2 ]]; then     xrandr --output DP-2 --primary --mode 1920x1200 \            --output DP-0 --mode 1680x1050 --right-of DP-2 --output LVDS-0 --off else     xrandr --output LVDS-0 --mode 1280x800 --output DP-2 --off --output DP-2 --off fi exit 0   /etc/lightdm/lightdm.conf:  [SeatDefaults] greeter-session=unity-greeter user-session=ubuntu display-setup-script=/usr/share/lightdmxrandr.sh session-setup-script=/usr/share/lightdmxrandr.sh greeter-setup-script=/usr/share/lightdmxrandr.sh     Solution:  After switching from Unity to XFCE, the solution was the following:   Install the default LightDM greeter for XFCE:  apt-get install lightdm-gtk-greeter xubuntu-default-settings Change the corresponding line in /etc/lightdm/lightdm.conf:  Before:  [SeatDefaults] greeter-session=unity-greeter ...   After:  [SeatDefaults] greeter-session=lightdm-gtk-greeter ...    Now all displays are configured correctly at the LightDM login screen.

I'm using multiple monitors.  When logged in everything is fine: The left monitor is positioned to the left and the right monitor is positioned to the right, but before I log in, the login-screen positions them the other way around.  This is also the position presented by bios and then the grub menu.  I don't mind where the login is displayed, but when moving the mouse, the boundary is the wrong way around and that's annoying.


I'm using the above computer, and it still works reasonably well. There is one huge issue though - there seems to be some sort of current leak that prevents the trackpad from functioning correctly. To make it work properly, I have to 'ground' the chassis with one hand. When it's really bad, the whole computer 'hums' with current. Over time, the current seems to increase, leading to very little 'shocks' which feel like the hairs on my forearm are being pulled. It can be discharged by touching a conductive item, like my iPhone(!) or the radiator, but that really isn't ideal. I've put stacks of research into this, so I can tell you that I'm using the grounded (3 pin Uk) adaptor, both directly into the wall socket and/or into surge protector mains adapters, and both with the long lead and the plug that fits onto the line-lump - neither make a difference. It happens when I'm barefooted, when I have my trainers on, on wooden floors and carpeted floors. I've even tried placing both hands on the computer and jumping into the air so that there is no ground. There is no longer a battery attached - after the 2nd one expanded I decided not to buy another. I've read that prolonged use could lead to long-term health risks, but I can't afford to replace the computer, and besides, I've read that the issue is also common on newer Macs. Is there anything that can be done? All my research up to this point suggests that there isn't, but I'm hoping there's a Super User with a solution. Thanks for looking.

I recently purchased a Macbook Pro retina display. When I use the 2 pin charger, and I touch the surface of the laptop I can feel electricity passing - basically laptop is vibrating softly. When I charge it with 3 pin, it does not vibrate. I have been charging it with 2 pin for about 10 days when I was not aware of this issue, so would that have messed up my laptop by any chance? To me laptop works perfectly, but I was wondering some hardware internally got messed up.


I remember when I was young really enjoying a SciFi book that I found in a closet of a house that we moved into in the late 80s - early 90s.  What I remember is it being about a kid or person who finds a crash landed alien mech. I don't think it was a very long book so it may have been meant for tweens or just a short story.

I am looking for the author / title of a short illustrated story about a robot (humanoid form) that crash-landed on planet earth and a boy finds the wreck. He climbs into it and goes up to the head and meets with the alien kid. Shortly after, the "mother" robot finds and rescues the stranded robot and the story ends.  The robot's control station is the "head".  I remember the cover having a yellow border and depicting in a grey tones a forest. In the centre of the cover there is a golden humanoid robot wreck, mainly the "face" is shown.  The book should be of the mid-80s and no more that 25-75 pages with a couple of illustrations and in english language.


I've created a class called Human that works properly, it takes 2 arguments, age and name, to create a human.  To create a Human with command line arguments, I want to write      java Filename -H "Anna" 25   And it should create a Human with thatname="Anna", and thatage=25, where 25 is an int.  The code I've written is creating a list called Argument, and iterating through it to find -H. I need to do this because I'm going to be using this to create different classes later. I just need help with the syntax on the lines where I've written thename=, and theage=, because I don't know how to get the next item in list, and next-next item in list.  public static void main(String[] args) {     ArrayList<String> Argument = new ArrayList<String>();             for (String item: args) {         Argument.add(item);              }      for (String item2: Argument) {         if (item2 == "-H") {             thatname = Argument.get(item2+1)             thatage = Argument.get(item2+2)             Human person = new Human(thatname,thatage);             System.out.println(person);         }

I've been using the == operator in my program to compare all my strings so far. However, I ran into a bug, changed one of them into .equals() instead, and it fixed the bug.  Is == bad? When should it and should it not be used? What's the difference?


My old machine died. I installed the old disk as an extra disk in the new Windows 10 (old machine also was Windows 10). A lot of files I can' delete. I've tryied to take ownership of everything but some files fail. I don't need an unused windows installation in the disk. I've tried to take ownership, but it keeps asking me to that I need to be my user to delete the files. I managed to delete some dirs following , but there are still some dirs that I can't delete. How do I gain control of everything so I can clean the disk?

I have a hard drive which I need to recover specific files from but all the folders in the K:\ drive are denying me access even though I took owner ship of the full drive I.E      C:\Windows\System32>takeown /F K:\   This granted me access to the drive and see the folders but I can not access any of the folders after that.   Is there a way in which I can use Takeown to apply ownership to every directory on the drive>


I'm trying to run this code and be able to "save" an object inside the "memory" array to view the past properties that the same object had after it changes.  this is the class:  class Circle { radius; center = {}; memory = [];  constructor(radius, x, y) {     this.radius = radius;     this.center.x = x;     this.center.y = y;  moveX(steps) {     if (!isNaN(steps)) {         this.saveMemory(this);         this.center.x += steps;     }     return this.center.x; } saveMemory(circle) {     let temp = (({ memory, ...rest }) => rest)(circle);     this.memory.push(temp); }   when I view the memory array it shows the object after the x change.  var circle1 = new Circle(5, 1, 1); circle1.moveX(2); // memory = [{radius:5,center{x:3,y:1})   How can I save the object before the changes were made?  edit: I want to get:  circle1.moveX(2); // memory = [{radius:5,center{x:1,y:1})

What is the most efficient way to clone a JavaScript object? I've seen obj = eval(uneval(o)); being used, but . I've done things like obj = JSON.parse(JSON.stringify(o)); but question the efficiency.  I've also seen recursive copying functions with various flaws.  I'm surprised no canonical solution exists.


In ArcMap 10.8 I have two shapefiles, the yellow area and the green square. I am trying to create a shapefile that is the yellow area without the green square.  I want to clip the small square out of the large yellow area (so I get a shapefile with a yellow area with a missing square), however- no matter how I input the data onto the "Input" and "Clip" features, it only clips the yellow area out of the square, leaving me with the square which I am trying to get rid of. Here is the image pre-clip, and the post-clip below and when I clip it with the green box being clipped out of the yellow box, it just gives me the green box again because it's in the yellow area. The yellow area does not get clipped at all.

I am working on a project doing spatial analysis at a statewide level. I am looking at a form of transportation coverage in a state, and part of my analysis involves buffers and drive time polygons. I am using a geodatabase (therefore ArcGIS) for all my work, so new features will be exported as feature classes in feature datasets. To visualize: I have said state border, and some dissolved buffer rings around some points, and they cover parts of the state. I want to create a feature class for the parts of the state these buffer rings don't cover, AKA gap areas. Is there a tool I can use or create to do this? I know I could draw them in manually in editor, but I am unsure if that's the most precise way to generate these feature classes. To me, I am thinking this operation would be like an inverted "Clip" in that I take the two layers, and instead of pulling out the clipped area, it would take everything not in the clipped area. I am using a Desktop Basic license.


I'm working on a set of graphs that contain circles drawn at various locations. I'm using the circle command to draw the circles on the graphs, but I'm not able to set the circle radii such that they match the axes scales. That is to say, a circle with a radius of 1 does not have a radius of 1 with respect to the x or y axes.  To figure out my problem, I turned to the manual. Unfortunately I cannot even reproduce the basic circle plot shown in the manual. The code below taken directly from the manual (I had to add the document class) produces what looks like an ellipsis and not the circle shown in the manual.  % MWE from manual (Revision 1.16, page 355) \pgfplotsset{width=7cm,compat=1.16} \documentclass{article} \usepackage{pgfplots}  \pgfplotsset{width=7cm,compat=1.16} \begin{document} \begin{tikzpicture} \begin{axis}[tiny,enlargelimits,    axis equal,    xmin=-1,xmax=1,    ymin=-1,ymax=1,    xtick={-1,0,1},    ytick={-1,0,1},    grid=major, ]    \draw [blue] (0,0) circle [radius=1]; \end{axis} \end{tikzpicture} \end{document}     One of the other answers here said the proper syntax should have a radius with a unit. Adding cm to the radius parameter as shown below produces a circle at the origin with a radius that goes beyond the x=1 plane.     \draw [blue] (0,0) circle [radius=1cm];     Here is what I'm trying to reproduce from the Revision 1.16 manual. I am compiling using lualatex with MikTex 2.9 on Windows 10. Any thoughts on how I could reproduce the circle as shown in the manual would be appreciated.

With a fresh installation of TeX Live (updated just before writing this post), circles in axis environments are distorted. Consider the following MWE:  \documentclass{article} \usepackage{pgfplots} \pgfplotsset{compat=1.16}  \begin{document}  \begin{tikzpicture} \begin{axis}[   ymin=-3, ymax=3,   xmin=-3, xmax=3 ]  \draw (1,0) circle [radius=1.5]; \fill (1,0) circle [radius=1];  \end{axis} \end{tikzpicture}  \end{document}   The output looks like this:   Obviously, the circles aren't even circles. I haven't encountered this problem before. Did I do anything wrong while setting up my new system?  EDIT: It's not an issue of using axis equal or not since the axes are scaled more or less equally already. Instead, the circles appear as rotated ellipses that are strongly stretched out in one dimension.  EDIT 2: Here's the output of \listfiles:  article.cls    2019/12/20 v1.4l Standard LaTeX document class   size10.clo    2019/12/20 v1.4l Standard LaTeX file (size option) pgfplots.sty    2018/03/28 v1.16 Data Visualization (1.16) graphicx.sty    2019/11/30 v1.2a Enhanced LaTeX Graphics (DPC,SPQR)   keyval.sty    2014/10/28 v1.15 key=value parser (DPC) graphics.sty    2019/11/30 v1.4a Standard LaTeX Graphics (DPC,SPQR)     trig.sty    2016/01/03 v1.10 sin cos tan (DPC) graphics.cfg    2016/06/04 v1.11 sample graphics configuration   pdftex.def    2018/01/08 v1.0l Graphics/color driver for pdftex     tikz.sty    2020/01/08 v3.1.5b (3.1.5b)      pgf.sty    2020/01/08 v3.1.5b (3.1.5b)   pgfrcs.sty    2020/01/08 v3.1.5b (3.1.5b) everyshi.sty    2001/05/15 v3.00 EveryShipout Package (MS) pgfrcs.code.tex  pgfcore.sty    2020/01/08 v3.1.5b (3.1.5b)   pgfsys.sty    2020/01/08 v3.1.5b (3.1.5b) pgfsys.code.tex pgfsyssoftpath.code.tex    2020/01/08 v3.1.5b (3.1.5b) pgfsysprotocol.code.tex    2020/01/08 v3.1.5b (3.1.5b)   xcolor.sty    2016/05/11 v2.12 LaTeX color extensions (UK)    color.cfg    2016/01/02 v1.6 sample color configuration pgfcore.code.tex pgfcomp-version-0-65.sty    2020/01/08 v3.1.5b (3.1.5b) pgfcomp-version-1-18.sty    2020/01/08 v3.1.5b (3.1.5b)   pgffor.sty    2020/01/08 v3.1.5b (3.1.5b)  pgfkeys.sty pgfkeys.code.tex  pgfmath.sty     pgfmath.code.tex pgffor.code.tex tikz.code.tex l3backend-pdfmode.def    2020-02-03 L3 backend support: PDF mode supp-pdf.mkii epstopdf-base.sty    2020-01-24 v2.11 Base part for package epstopdf epstopdf-sys.cfg    2010/07/13 v1.3 Configuration of (r)epstopdf for TeX Live


I have a table that has gotten a little out of control. I am not a DBA per se but seem to recall that deleting a huge volume of rows in one shot can cause transaction log issues, hamper overall system performance during the delete, etc...  Is there an efficient way for me to create a job that deletes records in small batches to over hampering other access/performance and prevents problems with the transaction log?  This process can be quite slow is that makes a difference  For additional context, the delete criteria will be based on something like... where x like '%blah%'. Also, there is one clustered index and 5 non-clustered indexes.

Using SQL Server 2005.  I am performing a huge DELETE FROM  with no where clauses.  It's basically equivalent to a TRUNCATE TABLE statement - except I'm not allowed to use TRUNCATE.  The problem is the table is huge - 10 million rows, and it takes over an hour to complete.  Is there any way of making it faster without:   Using Truncate Disabling or dropping indexes?   The t-log is already on a separate disk.  Any suggestions welcome!


Is it possible in some settings to get a notification when a question is put on hold?  I normally don't look very often on SE even if I have posted a question. My questions normally don't get any answers, and I simply forget about these questions.  Now some of them are put on hold, and I don't even know it. I don't look at my questions daily, because I get notifications when I get a comment or an answer.  I also heard that if you don't improve on-hold-questions your account will be deleted some day or you can't ask any questions any more.  I know that there is a similar question, but it seems to me that the discussion of eight answers was ended about five years ago, so I don't know if this is up-to-date. And it doesn't provide any answer to me either.

I think it would really help if you get notified that a question of yours was closed.  Especially for the multi-site power user, usually (at least for me) a question is asked and then left alone for while. I rely on the network-wide inbox to tell me when someone has commented or answered, but if I don't receive any messages then I tend to assume that the question wasn't answered or even noticed. It's only when I check the question a day or two later to see what I can add do I find out it was closed.  This would be especially helpful for duplicates, where the answers you need are already there. A message to the effect of, "Closed as duplicate of question" is just like notifying me that a new answer has been added!  Unfortunately, question closures can remain unnoticed by their askers until months have passed. By then, the questions may either be too old to migrate to the correct site, or may , depending on the specific closing reason. We should notify users of these question closures so that they can improve them and learn from their mistakes.  Could closed questions get added to the inbox?


Some answers were provided in this question:     It is clear then, that one can make a custom "breve below" macro. However, is the best way, as of today? That is, are there packages that provide more versatile definitions?

Because the beginning of the letter is moved a bit to the left when in italics mode, the breve also needs to move to the left,otherwise it is no longer under the letter.  \documentclass{article} \usepackage{semtrans} \begin{document} Right position: \U{h}  Wrong position: \textit{\U{h}} \end{document}     Any ideas how to correctly use a breve with italics?


hi i am using the regex to validate the email but when i try to user underscore in email address than is giving me the error.  Following is regx which i am using.  ^[a-zA-Z0-9-'+~]+(.[a-zA-Z0-9-'+~]+)*@([a-zA-Z_0-9-]+.)+[a-zA-Z]{2,10}$  if (not isValid("regex", arguments.propertyValue,"^[a-zA-Z0-9-'\+~]+(\.[a-zA-Z0-9-'\+~]+)*@([a-zA-Z_0-9-]+\.)+[a-zA-Z]{2,10}$")) { }   can any one please let me know which regx should i use?

Is there a regular expression to validate an email address in JavaScript?


My question is when the Weasley parents were Hogwarts students. They appear to be younger than Voldemort, and Molly mentions Slughorn rejected Arthur for the Slug Club. Also, Bill is about 25 in the series, so he was born about 1970.  In GOF, Molly says that the gamekeeper Og caught her and Arthur out after dark, and gave them a beating. However, in COS Hagrid was gamekeeper since the 1940s.

In Goblet of Fire, when Molly and Billy Weasley come to visit Harry before the Third Task, Molly talks about Hagrid’s predecessor.  Mrs. Weasley was intrigued by the Whomping Willow, which had been planted after she had left school, and reminisced at length about the gamekeeper before Hagrid, a man called Ogg. — Goblet of Fire, chapter 31 (The Third Task)  But wouldn’t Hagrid have been gamekeeper when she was in school? Hagrid was kicked out at 13 around 1943 and began training as gamekeeper. Molly would have arrived at Hogwarts in the early 60s when Hagrid would have been 30. Even if he was still in training or assistant gamekeeper, he would definitely still be there with Ogg. And as Ogg is described as the gamekeeper before Hagrid, that seems to imply that they weren't there together in Molly's memory. How does that work?


I read this sentence in a novel     The horses of Saint Mark's.   Is the use of Apostrophe correct in this sentence?   Since the novel is of a good author, I suppose it wouldn't be a mistake.  Edit: For explaining the question more thoroughly, here are some examples in which double genitives are used:     He is a friend of Rahul's.      The trophy is of my Father's.    Is using an apostrophe in such cases right?

I have often heard people say "x of his" or "x of mine". But since his and mine point out ownership, isn't using "of" here doubles that ownership? Wouldn't it be more appropriate to say "x of him" or "x of them" etc.?  Example:     I was a good friend of your dad's. He told me all about you`


In a python script of qgis I load layers from different datasources using the QgsVectorLayer() and  the QgsRasterLayer() commands. The coordinate reference systems of the data sources differs. Since I have for some sources only the permission to read, I cannot transfrom the CRS of the datasource. Thus, i have to change the CRS from old CRS into new CRS in the in memory layer. What is the way to do it, e.g. to get an extent() in the new coordinates?

I need to transform QgsVectorLayers in python from one crs into another crs. By googling I found the following solution (), which works for points only:  crsSrc = QgsCoordinateReferenceSystem(4326)    # WGS 84 crsDest = QgsCoordinateReferenceSystem(32633)  # WGS 84 / UTM zone 33N xform = QgsCoordinateTransform(crsSrc, crsDest) pt1 = xform.transform(QgsPoint(18,5))   Is there a way to make a crs transformation of an entire layer?


I have ajax call to get data from database and show the table row after success response. Inside the table row I have checkbox on it. I want to get selected index after the checkbox checked. I faces some problem when I set event handling to get selected index. This is my scripts.     I don't have problem with the ajax, my problem just inside second script to get the selected index. The script seems not working without any error. Please anyone help me to solve this problem. Thanks.

I have a bit of code where I am looping through all the select boxes on a page and binding a .hover event to them to do a bit of twiddling with their width on mouse on/off.  This happens on page ready and works just fine.  The problem I have is that any select boxes I add via Ajax or DOM after the initial loop won't have the event bound.  I have found this plugin (), but before I add another 5k to my pages with a plugin, I want to see if anyone knows a way to do this, either with jQuery directly or by another option.


Where $x_n$ is the solution of $\tan(x)=x$ in the interval $(n\pi ,n\pi +\frac\pi2)$ , $n\ge0$.  Any hints on how to approach this problem with elementary methods in the first place? The answer should be $\frac1\pi$. $$\lim_{n\to\infty}n\biggl(n\pi+\frac\pi2-x_n\biggr)$$

An equation that seems to come up everywhere is the transcendental $\tan(x) = x$. Normally when it comes up you content yourself with a numerical solution usually using Newton's method. However, browsing today I found an asymptotic formula for the positive roots $x$:  $x = q - q^{-1} - \frac23 q^{-3} + \cdots$  with $q = (n + 1/2) \pi$ for positive integers $n$. For instance here: , and here:  found from a comment here: .  The Mathworld article says that you can derive this formula using series reversion, however I'm having difficulty figuring out exactly how to do it.  Any help with a derivation would be much appreciated.


Find the equation of $2$ lines through the origin which intersect the line $\displaystyle \frac{x-3}{2} = \frac{y-3}{1} = \frac{z}{1}$ at an angle of $\displaystyle \frac{\pi}{3}$  $\bf{My\; Try::}$ Let equation of line be $\displaystyle \frac{x-0}{a} = \frac{y-0}{b} = \frac{z-0}{c}$ Where $<a,b,c>$ be the direction cosine of line parallell to that line. and Given Line is $\displaystyle \frac{x-3}{2} = \frac{y-3}{1} = \frac{z}{1}$ Where $<2,1,1>$ be the direction cosine of line parallell to that line and Given $\displaystyle \frac{\pi}{3}$ be the angle between $<a,b,c>$ and $<2,1,1>$ So $\displaystyle \cos \frac{\pi}{3} = \frac{2a+b+c}{\sqrt{a^2+b^2+c^2}\cdot \sqrt{6}}\Rightarrow \frac{1}{2}=\frac{2a+b+c}{\sqrt{a^2+b^2+c^2}\cdot \sqrt{6}}$ Now how can i solve it, Help required, Thanks

Find the equations of the two lines through the origin which intersect the line $\frac{x-3}{2}=\frac{y-3}{1}=\frac{z}{1}$ at an angle of $\frac{\pi}{3}$.    Let the direction ratios of the two required lines be $(a_1,b_1,c_1)$ and $(a_2,b_2,c_2)$. Therefore the two equations are  $\frac{x-0}{a_1}=\frac{y-0}{b_1}=\frac{z-0}{c_1}$ and $\frac{x-0}{a_2}=\frac{y-0}{b_2}=\frac{z-0}{c_2}$ As these lines are making an angle of $\frac{\pi}{3}$ with $\frac{x-3}{2}=\frac{y-3}{1}=\frac{z}{1}$. So,$\cos\frac{\pi}{3}=\frac{2a_1+b_1+c_1}{\sqrt6\sqrt{a_1^2+b_1^2+c_1^2}}$ And $\cos\frac{\pi}{3}=\frac{2a_2+b_2+c_2}{\sqrt6\sqrt{a_2^2+b_2^2+c_2^2}}$ But i am stuck here.How i can solve three variables with one equation.The book gives answer as $\frac{x}{1}=\frac{y}{2}=\frac{z}{-1}$ and $\frac{x}{-1}=\frac{y}{1}=\frac{z}{-2}$ Please help me.


reminded me of a novel I read in my youth. It was about a future earth with a very organized power structure where people are ranked (I believe it was 1-100) by their power/wealth.  The protagonist is a nobody (rank 100?) who by sheer will and desire never to be controlled by anyone rises through the ranks, eventually making some kind of deal with aliens to take control of everything.

Novel written before 2000.  The story begins on a planet which has been so environmentally damaged that the atmosphere is too toxic to breathe, forcing the population to live in air-tight domes or modules connected by tunnels.  Near the beginning, the protagonist working as a low-ranking gang or mob member. He's assigned to either kill or collect money from someone; when he confronts them, they taunt him about how the floor is electrified, how their body weight is shifted forward so shooting them will cause them to fall against an alarm button, and various other reasons why he can't possibly do anything... they continue right up until they're blown apart by some kind of miniature rocket launched from the protagonist's shoe.     Afterwards, I believe, his superiors in the organisation attempt to kill him because they deem him as "too dangerous", which causes him to retaliate by blowing up one of the passages, suffocating the people who were threatening him. From this point, or shortly after, he begins his own organisation which quickly grows in power until he is virtual ruler of the planet; eventually he cleans up the planet's environment to the point where people can live outside, again. At some point he meets a woman, courts her, but ultimately leaves her abruptly, telling her he swore never to let anyone have power over him, and since he's starting to fall in love with her, she's starting to have too much influence over him.         The society in this universe has ranked legal and illegal citizenships, with either 50 or 100 being the lowest rank, and rank 1 being the highest... after the protagonists becomes a level 1 illegal citizen, he sets his sights on becoming a legal citizen, which requires him to (at least in appearance) divest himself of all his criminal ties and assets, which he does by creating a complex nested structure of ownership between himself and the illegal organisations he controls.         As his influence increases in the legal world, he begins doing business with an alien race who, in order to trust him, give him the chance to let them implant him with some kind of organism that will kill him if he even thinks about betraying them.         Near the end of the story there is a part where someone close to him is trying to figure out why he's amassing so much money and military power, when he's not intending on using it against the human race, and can't use it against the aliens.


Evaluate the integral $$\int_{0}^{\infty}\frac{e^{ax}-e^{bx}}{(1-e^{ax})(1-e^{bx})}dx$$ for constants $a,b$.  I tried separation by partial fractions, but couldn't do it.

Given the integral $\int_{0}^{\infty} \frac{e^{ax}-e^{bx}}{(1+e^{ax})(1+e^{bx})} dx$  How can I evaluate it? Thanks!


I need to display BNF grammars, but couldn't find any LaTeX package that does this.

I googled and found two packages:   mdwtools bnf   Unfortunately, both of them have extremely poor documentation. There are only one to two examples for each one, which makes it hard to follow. Furthermore, none of them shows how to indent the grammar properly, rather than just setting up the environment to have a nice look. I wonder is there a major package for writing BNF, or we can just manually use tabbing to handle the indentation? Thank you.


Let $X$ be a normed linear space and let $f:X\to \mathbb K$ be a nontrivial linear functional. I want to prove that $f$ is open. I tried as follows:  Let $E$ be an open set in $X$ and let $y\in f(E)$. Then there is $x\in E$ such that $y=f(x)$. Since $E$ is open there exists $r>0$ such that $B_r(x)\subset E$. Let $z\in B_1(0)$ such that $f(z)=\delta>0$. If I can show that $(-\delta,\delta)\subset f(B_1(0))$, then I am through. But I could not show this. Please help me  to resolve this.

In the middle of another proof (Theorem 3.4, p. 60) in his Functional Analysis book, Rudin says that  "every nonconstant linear functional on $X$ (topological vector space) is an open mapping."   Is this obvious? Could someone please show me how the proof goes?


I would like to ask if it is possible to set up in bash so that each command is executed from of the top of terminal window. In other words if it is possible to execute clear before each command.   Also I wonder if it is possible to do this without using preexec() hook since I have history disabled anyway in bash.

I would like to configure bash to execute clear command every time I type some command in the terminal (before executing my command). How can I do that?  I'm using Debian Linux.


Which is correct and why:   I'll be grateful if you give me some details: where can I find the library and if there will be any novels?     I'll be grateful if you give me some details: where can I find the library and if will there be any novels?

Which of these two sentences is correct? And why?     A) We can't play tennis if it will be rainy tomorrow.   B) We can't play tennis if it is rainy tomorrow.


I have this table:  id  |  Name  | Age ================== 1   | AAA    | 22 1   | AAA    | 22 2   | BBB    | 33 2   | BBB    | 33 2   | BBB    | 33 3   | CCC    | 44 4   | DDD    | 55   I need to delete from this table all the duplicate records and leave only one record.  The table will looks like this:  id  |  Name  | Age ================== 1   | AAA    | 22 2   | BBB    | 33 3   | CCC    | 44 4   | DDD    | 55   I work with SQL Server CE for Mobile  Thanks

What is the best way to remove duplicate rows from a fairly large SQL Server table (i.e. 300,000+ rows)?  The rows, of course, will not be perfect duplicates because of the existence of the RowID identity field.  MyTable  RowID int not null identity(1,1) primary key, Col1 varchar(20) not null, Col2 varchar(2048) not null, Col3 tinyint not null


i don't even understand how to do this, surely this function is continuous at $|x|<1$ and have real value on that given integral. and $$\int_{-1}^{1}\sqrt{1-x^4}dx$$ should doable .   but since there isn't any variable outside root, i can't make any substitution of it. i'm trying sought on integral calculator but it said there isn't any antiderivative of this function .  so assuming this question is valid is there any way to solve this? ( i'm currently on mid-end of calculus 1). by the way  the provided answer just attach half circular image that says "symmetry"  and state $1.748$ is the answer and it doesn't make much sense for me

I am asked to show $\int_0^1\sqrt{1-x^4}dx=\frac{\{\Gamma(1/4)\}^2}{6\sqrt{2\pi}}$. I know the gamma function is defined by $\Gamma(n)=\int_0^\infty x^{n-1}e^{-x}dx$. I tried to substituted $x^2=\sin(t)$ but couldn't go further. I am really questioned how a radical function can convert to an exponential one? :-0 Thank you.


I have installed  as well as  and my ultimate goal is to plug in my guitar to play along with some backing tracks, for example from youtube.  System Information: I am running a full Ubuntu 18.04.4 LTS system (no virtual box)  I am using the  as interface and so far I can get the sound from guitarix outputted to my headphones, as long as these are connected to the Jam+ interface. As I cannot get any sound from my computer (e.g. from Youtube) outputted into the headphones connected to the Jam+, I wanted to output the sounds from guitarix to the headphones connected to the computer (and not to the Jam+)  My QJackctl connection looks like so (note the difference between my connection and the one shown , though I don't think this makes such a great difference:    Below is a screenshot of the basic parameters:    And on the advanced parameters it is where I have to choose the output device, which for both Input and Output are hw:Plus (JAM Plus hw:1)    In order to get the sound outputted to the headphones when connected to the computer, I pretty much change all the possible values on Output device (screenshot above). Though I did not restart guitarix - I only stopped and started the JACK after changing the output device.  Finally, even though I don't think it might be related, below is a screenshot of the sound settings of my Ubuntu system itself    Has anyone successfully outputted the sound from guitarix into the headphones when connected to the computer (and not to the audio interface)?

Whenever I launch hydrogen it breaks my audio in all other applications which use Pulse, for example, I can no longer play videos in Chrome after having launched Hydrogen once, until I restart my PC or do sudo alsa force-reload. I have found people with similar issues, but no actual guide to fix this, often there are links to  (which has moved to  ) I am using Ubuntu Studio 14.04 64bit.  ALTERNATIVELY if this is truly impossible to achieve, can someone tell me how to use Jack on one soundcard and Pulse on another? This way I could plug in a USB sound card only when I need JACK.  Please don't make me use windows.


My laptop which ran Fedora 20 fine until this morning is now stuck in emergency mode. I have not set a root password and I cannot proceed beyond the initial prompt. Attempting to continue in default mode (ctrl d) just returns me to the emergency boot prompt. How can I resolve this?

If we don't know the root password and don't have root access to the machine, how can we change the root password?


I am trying to build a Palindrome finder class that uses an ArrayStack of characters to find palindromes in any word or phrase passed to it. However, when I pass a palindrome as a string to my code, it returns false.  I have debugged my code several times and even wrote the program over, but I cannot figure out why my code isn't working properly. I think it may be something simple that I am overlooking in the isPalindrome() method, the constructor or instance variables.  public class PalindromeFinder {     ArrayStack<Character> charStack = new ArrayStack<>();     String strVerify = "";     private String strCheck;      public PalindromeFinder(String strCheck) {         strCheck = strCheck.toLowerCase();         pushStr(strCheck);         strVerify = popStr();     }      public void pushStr(String strToPush) {         for (int chVal = 0; chVal <strToPush.length(); ++chVal) {             char ch = strToPush.charAt(chVal);             ch = Character.toLowerCase(ch);             if (Character.isAlphabetic(chVal)) {                 charStack.push(ch);             }         }     }      public String popStr() {         while (!charStack.empty()) {             strVerify += charStack.pop();         }         return strVerify;     }      public boolean isPalindrome() {         return strVerify == strCheck;     } }   The following lines of code return false in the main method of my program:  PalindromeFinder p = new PalindromeFinder("mom"); System.out.println(p.isPalindrome());  Any help or improvements on my code would be greatly appreciated.

I've been using the == operator in my program to compare all my strings so far. However, I ran into a bug, changed one of them into .equals() instead, and it fixed the bug.  Is == bad? When should it and should it not be used? What's the difference?


Why is there no SE site dedicated to questions about beauty, cosmetics, skin care and related questions and answers?  There’s millions of different beauty products, but almost all information you can find on the subjects are sales pitches from various companies. This seems like a perfect opportunity for SE to serve a massive market.  There is a  discussing alternative SE sites, but it doesn’t explain why there is no dedicated beauty Q&A site.

Is there a Stack Exchange site where users can ask questions about skin care, cosmetics and beauty tips for both sexes?


Let's say I have a 90mm and an 135mm lens, and Nikon's 24mp full frame and 24mp APS-C DSLR. Assume they are the same optically.  Now, based on what I understood, doing a DX-crop on the image taken by 90mm lens on full frame camera will give you exactly same view of an image taken by 135mm on full frame, with less pixel. But, 24mp when cropped, will still provide enough pixel for viewing on computers. So, in terms of sharpness and details (I don't know their difference), will it be the same with an image taken with 135mm lens? How about when viewing on 100% size?  I find this confusing because, when you shoot further away, you will lose some tiny details, vs if you just shoot it with a longer lens. But that will mean APS-C inherently takes in less details than full frame, which doesn't sounds right. Or does using APS-C gives more details than doing a DX-crop on a full frame body? Is it because it gives more pixel? I read that pixel got nothing to do with sharpness, but in this case?  Sorry for the messy questions, this is so confusing that I am unable to tidy it up in my mind. Thanks!

Take an FF body and a crop body, with similar MP rating - and the FF body will give a sharper image of the same object. At least, that seems to be the case - as here:    I assume a low ISO was used in both images.  Why does the FF body, with the same lens and almost the same MP, give an image that is so much sharper?   My best guess is that the diffraction / airy still play a role, and the larger pixels reduce effective overlap - thus increasing contrast/sharpness by displaying less of the neighboring diffraction, as below?


Let's suppose $X$ is $n \times m$ not full rank matrix (ie any column vector in $X$ can be expressed as linear combination of others column vectors). If $$B = X^TX$$ why $B$ is singular?   The question is inspired from the statistics, wherein, if vector of independent variable is linearly dependent, then it is assumed that $X^TX$ is also dependent (or singular). It is difficult to grasp if $X$ is dependent then how $X^TX$ is dependent?

If $X$ is a singular matrix, then is $X'X$ singular? And why?  (' means transpose)  Thanks in advance!


I am wondering if a single article can be used for two nouns.  I came across an article on , and encountered one single indefinite article used for two nouns.     Despite changing sexual mores, it's clear that many men and women still expect the man to pay, particularly on a first and second date. That seems to be especially true outside the Northeast, where sex roles remain more traditional.    One article for two nouns is possible? Why not writing it again for the second noun? Like - "....particularly on a first date and a second date. That seems..."  Based on this, I want to say     "A first and a second layer" or "a first layer and a second layer"   instead of...     "A first and second layer"   Is that okay?

[...] Leonardo da Vinci became renowned for his multiple talents: he was a painter, architect, engineer, mathematician and inventor.   In the above sentence, why has only one "a" been used, even for words that begin with a vowel?


Let's say I have two files, file1 and file2.  file1:  passd:xxx hopla:alli gnar:gungg araf:utap   file2:  alli utap   How can i check what lines/words from file2 match file? Indeed I could probably do it with comm -1 -2 file1 file2 but is it possible to do it with awk?


When I am thinking about the interference of two laser beams, a curious question often comes to my head: Take a Mach-Zehnder interferometer as example and suppose the frequency of the leaser beams is the same, namely they are all monochromatic plane wave.   As we know, if we measure the optical power in different positions in the propagation direction, an interference fringe will appear.   What puzzled me is that in the destructive interference position, the optical power is zero, however, if the power meter keep fixedly in this position, the power is zero all the time, but the laser is still working, and where has the energy gone?

What happens to the energy when waves perfectly cancel each other (destructive interference)? It appears that the energy "disappear" but the law of conservation of energy states that it can't be destructed. My guess is that the kinetic energy is transformed into potential energy. Or maybe it depends on the context of the waves where do the energy goes? Can someone elaborate on that or correct me if I'm wrong?


I remember there being two girls, in their early twenties, maybe. They are from Earth, but somehow (drawing a blank) end up in another world. In a Wizard of Oz style, they must reach the realm's giant castle, but it's possible even that won't get them home.  One of the girls is approached by a local woman who offers them a means to make money for their journey: become a painted lady. These are highly treasured (and legally protected) courtesans who are painted with intricate blue "tattoos" across the whole of their bodies. There is a small vial of potion offered which allows for complete conscious choice, but wipes several hours of memory. She's told if she takes this role, the vial will help both sides - many political/royal figures hire the courtesans and pour out whatever moral dilemma, (etc.) they are dealing with.  She takes the markings, goes off on her first job, and decides NOT to drink it, so she will be able to remember and decide if she's really okay with doing this. If I'm remembering correctly, the painted ladies wear a minimal amount of clothing, a sheer wrap/dress. The tattoo pattern was swirled, and I remember it being described as winding around her arm like ivy.   I think the cover of my edition had the two girls in "modern" clothes at the bottom/foreground, looking towards a distant castle in a mountainside. I don't think I ever finished the book (it was the 80's, I was a teen, and lived in walking distance of THREE used book stores, so… I tended to buy a lot of books.)

I was reading  and was strongly reminded of a series I remember reading in my teens.  This would have been a series of novels (possibly just one), published in English, and likely before 1980 - I read it in the 90s and it was fairly old, a used book.  I do not think it is the same as the linked question, which is why I'm asking this separately.  It was definitely a fantasy, not sci-fi.  Plot:  At least two girls (and possibly also some boys/other girls) are transported from modern Earth into a fantasy world.  I think they're a group of friends, possibly with some romantic pairings, and are in the 16-25 age range.  The first significant scene I remember is two of the girls ending up in a city, where they are taken in by an older female artist (might have been a different creative type, like a sculptor/actress).  She's lesbian/bisexual.  At some point she attempts to give one of the girls a love potion, but they reverse it on her, so instead the artist falls in love with the girl and accompanies her for the rest of the books.  Twist: It's later revealed that the artist's friends recognized the love potion and removed it.  She pretended to be in love and went along because she thought it would be interesting.  At some point at least one of the girls ends up basically being a magical sex slave/prostitute.  I remember her being tattooed or painted - I think in blue - and also possibly given some magical jewellery/piercings that ensure her obedience/love of her owner.  I do not remember much of the over-arching plot, just a few disjointed pieces:  The world has chaos/wild magic storms.  The books might have called them something else.  Anyone or anything caught by these storms is transformed into something else entirely, so different objects or species.  These show up throughout as minor plot encounters.  I think they can be defended against with a special material.  Near the very end, a large storm engulfs a major city, giving it entirely new architecture and transforming the inhabitants into green, hermaphrodites with a centaurish body structure.  I am not 100% sure this was the same novel, but I recall a secondary character with a secret - at night he turns into a woman (not just his body, but an entirely different person).  At some point it's revealed that the woman was his lover, and he saved her life by sharing his body with her - of course, now they can never meet/touch again.


Suppose $\mathrm{P}=\mathrm{NP}$ were proven and a practical low-degree (2 or 3) polynomial algorithm was found before widespread quantum key distribution was available. How would internet security work? Presumably, there would be eventually fewer bugs because of formal verification, but everyone would need to use one-time pads. Major platforms could mail USBs or hard drives with keys to everyone and people could be taught to use one-time pads to talk securely with friends and family or could an alternative system work? Would the internet would be down for several months while major security bugs were found and fixed and the one-time pad distribution system was set up? Wouldn't internet security would be a hassle for years afterward? Edit: I am specifically asking about practical policy implications. If we knew that all the major cryptographic primitives would be unsalvageably tomorrow (other than one-time pads), what would we need to do to get the internet working and what would be the future limitations we would have to live with.

I've recently heard some people claiming that if the fact that P = NP is proven, most (all?) the current cryptographic algorithm considered secure like RSA will be unusable in secure systems.  My question is :  1. If P = NP is proven TODAY, will a RSA key (let say 3072 bits) be still enough to ensure a certain amount of security.  2. If not, what could we do to have at least the same amount of security (take a larger key length? a stronger algorithm?)


I'm facing the following problem:  Let $ F $ be a field, and let $ F(x)  $ denote all rational functions over $ F $ (functions of form $\frac{P(x)}{Q(x)}$, where $ P,Q$ are polynomials over $ F $). Find the degree $$ \left[ F(x): F \left( x^2 + \frac{1}{x^2}\right)\right] $$  Actually it's a homework exercise and I'm not sure what $ F \left( x^2 + \frac{1}{x^2}\right) $ is supposed to mean. Is it the smallest field contained in $ F(x) $ containing $ F \cup \{x^2 + \frac{1}{x^2}\} $?   If so, how do I find the degree of the extension? I'm not even sure where to begin.

Let $y=\frac{x^4+1}{x^2} \in F(x)$. Then $g(x)=0$ for the polynomial $g(s) = (s^4+1)-ys^2$. How to show that it is the minimal polynomial over the field $F(y)$?


doing:  >>>'a'*20 is "aaaaaaaaaaaaaaaaaaaa"   gives  >>>True   while doing:  >>>'a'*21 is "aaaaaaaaaaaaaaaaaaaaa"   gives   >>>False   Whats going on here? Is this a bug?

My  has failed me.  In Python, are the following two tests for equality equivalent?  n = 5 # Test one. if n == 5:     print 'Yay!'  # Test two. if n is 5:     print 'Yay!'   Does this hold true for objects where you would be comparing instances (a list say)?  Okay, so this kind of answers my question:  L = [] L.append(1) if L == [1]:     print 'Yay!' # Holds true, but...  if L is [1]:     print 'Yay!' # Doesn't.   So == tests value where is tests to see if they are the same object?


I'd like to know how StackExchange works? Is it just one installation which is divided to different parts or they use a separated installation for each subject? Askubuntu.com, tex.stackexchange.com, superuser.com, etc are integrated and authenticated well. Do they use their software categorizing system for it, Just think: Category=Forum and in this case rewriting URLs for subdomains, Or each of  are based on themselves?

What tools and technologies are used to build the Stack Exchange Network?  See also:


I am unable to install git on my ubuntu 12.10 system. I followed-  sudo add-apt-repository ppa:git-core/ppa sudo apt-get update sudo apt-get install git-core   sudo apt-get update gives me the error-  Err http://security.ubuntu.com quantal-security/main amd64 Packages   404  Not Found Err http://security.ubuntu.com quantal-security/restricted amd64 Packages   404  Not Found Err http://security.ubuntu.com quantal-security/universe amd64 Packages   404  Not Found Err http://security.ubuntu.com quantal-security/multiverse amd64 Packages   404  Not Found  Err http://archive.ubuntu.com quantal-updates/main amd64 Packages   404  Not Found Err http://archive.ubuntu.com quantal-updates/restricted amd64 Packages   404  Not Found Err http://archive.ubuntu.com quantal-updates/universe amd64 Packages   404  Not Found Err http://archive.ubuntu.com quantal-updates/multiverse amd64 Packages   404  Not Found  Err http://archive.ubuntu.com quantal/main amd64 Packages   404  Not Found Err http://archive.ubuntu.com quantal/restricted amd64 Packages   404  Not Found Err http://archive.ubuntu.com quantal/universe amd64 Packages   404  Not Found Err http://archive.ubuntu.com quantal/multiverse amd64 Packages   404  Not Found   Then some failed to fetch errors and finally-  E: Some index files failed to download. They have been ignored, or old ones used instead.   When I run sudo apt-get install git, I get-  Building dependency tree        Reading state information... Done The following extra packages will be installed:   git-man liberror-perl Suggested packages:   git-daemon-run git-daemon-sysvinit git-doc git-el git-arch git-cvs git-svn   git-email git-gui gitk gitweb The following NEW packages will be installed:   git git-man liberror-perl 0 upgraded, 3 newly installed, 0 to remove and 0 not upgraded. Need to get 6,800 kB/6,824 kB of archives. After this operation, 15.3 MB of additional disk space will be used. Do you want to continue [Y/n]? y WARNING: The following packages cannot be authenticated!   liberror-perl git-man git Install these packages without verification [y/N]? y Err http://archive.ubuntu.com/ubuntu/ quantal/main git-man all 1:1.7.10.4-1ubuntu1   404  Not Found Err http://archive.ubuntu.com/ubuntu/ quantal/main git amd64 1:1.7.10.4-1ubuntu1   404  Not Found Failed to fetch http://archive.ubuntu.com/ubuntu/pool/main/g/git/git-man_1.7.10.4-1ubuntu1_all.deb  404  Not Found Failed to fetch http://archive.ubuntu.com/ubuntu/pool/main/g/git/git_1.7.10.4-1ubuntu1_amd64.deb  404  Not Found E: Unable to fetch some archives, maybe run apt-get update or try with --fix-missing?   I have just set up ubuntu and this is the first I tried installing. Please help.

Recently I have installed an older version of Ubuntu on my old machine. Whenever I try to install any software, I get an error saying it couldn't be found:  $ sudo apt-get install vlc Reading package lists... Done                Building dependency tree        Reading state information... Done     E: Couldn't find package vlc


I accidentally erased my 1.5 tb external hd and need to recover/restore or undo this mistake to save 1.3 tb worth of music mp3's, mp4's, pictures, and programs etc. I am getting a message saying that the disc needs to be formated! What should I do?

I had 500GB portable hard drive. it fell from the table and when i joined it was not showing any data and asked me to format it. i did format. Then again it was not functioning properly so i had to quick format it again.  Now i had lots of data in it. Is there any software which can recover my files and folders with same structure as original


The  $e^X$ of a square symmetric matrix $X$ , where $$ e^X = \sum_{k=0}^\infty \frac{1}{k!} X^k $$ Does the exponentiation of each element of the symmetric matrix $X$ (not to be confused with the matrix exponential above) also result in a positive-definite matrix? $$\begin{pmatrix} e^{x_1} & e^{x_{1,2}} & e^{x_{1,3}}\\ e^{x_{2,1}} & e^{x_2} & e^{x_{2,3}}\\ e^{x_{3,1}} & e^{x_{3,2}} & e^{x_3}  \end{pmatrix}\neq e^X$$ After experimentally running this new question (different than the original question that was closed) with toy data, I am seeing that the element-wise exponential  matrix is not always positive-definite like how the matrix exponential always is. but I could be wrong. How can we prove that the element-wise exponential matrix does not guarantee positive-definiteness? (please general mathematical proofs only, rather than a counter-example)

This is a homework problem, but I feel like I'm struggling with not knowing facts from linear algebra.  Apparently this is supposed to be an easy question but I hit a brick wall at the following point.  Can anyone give me a tip or tell me if I'm going down the wrong road?  My approach:  Let $A$ be a symmetric $n\times n$ matrix, and then suppose $x$ is a real-valued column vector of dimension $n$ with not all entries equal to $0$.  I need to show that $x^Te^{A}x> 0$.  (based on looking up the definition of positive definite on wikipedia)  Then   $\begin{eqnarray*} x^{T}(e^{A})x &=& x^{T}(\sum_{n=0}^{\infty}\frac{A^{n}}{n!})x\\ &=& \sum_{n=0}^{\infty}\frac{x^{T}A^{n}x}{n!}\\ &=& \sum_{n=0}^{\infty}\frac{x^{T}A^{n}x}{n!})\\ \end{eqnarray*}$  As noted below, from here on is incorrect:  $\begin{eqnarray*} &=& \sum_{n=0}^{\infty}\frac{(x^{T}Ax)^{n}}{n!\|x\|^{2(n-1)}})\\ &=& \sum_{n=0}^{\infty}\frac{(x^{T}A^{T}x)^{n}}{n!\|x\|^{2(n-1)}}\\ &=& \sum_{n=0}^{\infty}\frac{((Ax)^{T}x)^{n}}{n!\|x\|^{2(n-1)}}\\ &=& \sum_{n=0}^{\infty}\frac{((Ax)^{T}(x^{T})^{T})^{n}}{n!\|x\|^{2(n-1)}}\\ &=& \sum_{n=0}^{\infty}\frac{((x^{T}Ax)^{T})^{n}}{n!\|x\|^{2(n-1)}}\\ \end{eqnarray*}$  As you can see this brings me no closer to getting $x^Tx$ somewhere, which I may assume is greater than $0$.  So my conclusion is that using only the fact that $A$ is symmetric is not enough.  Is there some result about symmetric matrices that I should use?


I messed up and now terminal closing itself as soon as I open him. I wanted that terminal execute command when it's starts, but I haven't noticed "when command exits" was "close terminal". Now it's closing itself as soon as I open it. How to fix? Reset terminal settings?

I am using Gnome Terminal in Ubuntu 14.04 and I modified the profile preferences, setting it to start with a custom command instead of the default. I can't remember what that custom command was, but now when I launch the terminal, it instantly closes.   Is there any way to change the profile preferences in terminal without having it open?


I don't understand this really good and couldnt find anything helpful on internet. I only found in book the following: A is the matrix with reflection over line through the origin with direction vector $\left(\cos(\frac{\alpha }{2} ) , \sin(\frac{\alpha }{2} ) \right) ^{T}$ $A=\begin{pmatrix} \cos(\alpha ) & \sin(\alpha ) \\ \sin(\alpha )  & -\cos(\alpha )    \end{pmatrix}$ I'm not sure how to connect this from book to solve it, because there is another direction vector.

I should determine reflection matrix over a line through the origin with direction vector $\vec{v}=\left(a,b\right) ^{T}  $  I dont understand this really good and couldnt find anything helpful on internet. I only found in one book the following:  A is the matrix with reflection over a line through the origin with direction vector $\left(\cos(\frac{\alpha }{2} ) , \sin(\frac{\alpha }{2} ) \right) ^{T} $  $A=\begin{pmatrix} \cos(\alpha )  & \sin(\alpha ) \\ \sin(\alpha )  & -\cos(\alpha )    \end{pmatrix} $   I am not sure how to connect this from book to solve my example, because there is another direction vector. I would be thankful if someone  could give me some tips or something like that.


We let {$a_n$}$_{n\in N}$ be $a_n$=$\frac{f^{n}(0)}{n!}$. I have to show that if $f$ is an even function so is $a_{2n-1}$$=0$ for all n$\in$N. How can I show it? By induction maybe? Can anyone give a hint? If we try induction:  Induction start: n=1: $$f(x)=f(-x)$$ $$f'(x)=-f'(x)$$ $$x=0 ->2f'(0)=0->f'(0)=0$$  Induction assumption is then: $$f^{2n-1}(0)=0$$  But now I can't move on my own. What to do then?

Let $f$ be a $k$ times continuously differentiable function defined on a neighborhood of $0 \in \mathbb{R}$. Show that if $f(-x) = -f(x) \forall x \in \mathbb{R}^n$, then the coefficients of the taylor series expanded about $0$ has all even coefficients equal $0$.  So this is an odd function, it makes sense. let's write a $k$-degree taylor polynomial:  $$\sum\limits_{i=0}^k \frac{f^{i}(0)}{i!}x^i = f(0) + f'(0)x+\frac{f''(0)x^2}{2} + . . .$$  $f(0) = 0$ we can easily conclude since $f$ is odd, but how can we say anything about any other terms? (since they all involve derivatives)


When answering questions that are except duplicates of other questions i feel the site only gets more cluttered, especially when the answer also is a copy of an old answer. The last time the subject was brought up (in 2009*) there seemed to be a consensus that rep. gained from answering a question that is then getting marked as a duplicate should remove rep gained from that since you are not adding any value to the site. * I'd like to know if that has changed over the last years and if there is a need to do that. From my personal experience with SO i have found that answering trivial questions that have been asked a thousand is "rewarded" with lots of rep while searching for duplicates is not. Since i feel "getting rep" is what is used to guide users into the direction of what is "the right way to go about asking and answering questions on SO" maybe that should get changed? On the other hand maybe we should  and let that rest? While i'd rather like  (i hope i don't misquote there):  Don’t answer questions that have already been answered elsewhere. Yeah, you might earn a couple of points of reputation, but, because you are duplicating content, you are actually making the Internet worse. [...]  luckily what i think doesn't matter that much but instead there is meta. So let me know  For a proposal there is not much more to say than aggregating the old thread: On closing a question as duplicate:  Question asker loses all rep gains or losses Answers lose all rep gains or losses  On reopening a question that was previously closed as duplicate  Question asker has the rep reapplied Answers have rep reapplied.  The people that provided the duplicates show be rewarded when the question is closed as a dup. There should be an initial recalc when this feature gets accepted and implemented Another way could be not to remove the rep gained from dup. question but lower it to show that, while answering is valuable, it's not as useful for dups.

This is a two in one question:  Should the asker of a duplicate question gain reputation for asking the duplicate question?   Should the answerers of duplicate questions gain reputation for answering them?  By asking a duplicate question you are diluting the value of the site. It takes lots of TLC to find the dupe and merge it in, yet you are still rewarded for producing that work.  The answerers of the duplicate question are also diluting the value of the site, because good and valuable information becomes splintered and harder to find.


Is it possible to do something like this in Python?  class MyClass():     def __init__(self):         someValue = 42          str = 'a'         # self.a = someValue         str = 'xyz'         # self.xyz = someValue          Essentially what I want to achieve is by reading the value of str (say the value of str resolves to 'myValue'), the code adds an additional attribute (self.myValue) into the class.

Suppose I have a python object x and a string s, how do I set the attribute s on x? So:  >>> x = SomeObject() >>> attr = 'myAttr' >>> # magic goes here >>> x.myAttr 'magic'   What's the magic? The goal of this, incidentally, is to cache calls to x.__getattr__().


My son can’t remember his password on an old Dell that we want to recycle.  I can’t follow the directions provided elsewhere since I don’t have a password and it won’t let me proceed when I type sudo passwd at the terminal prompt with a guest logon.  I don’t need to reformat - just want to clear whatever he had on there before we donate/recycle.  Thanks for your help.

I'm planning on selling a USB external hard drive that currently contains an old Ubuntu installation with stored passwords and banking information.  How can I securely erase the drive before selling it?


regexp = re.compile('[A-Z]\\d{4}') prefix = regexp.match("\"O1533_FOO\" INTEGER NOT NULL ,")   Prefix is None, but I expected it to be "O1533".  When I use the web based tool  it works.    I tried to escape the \ with different numbers of \s, and I also tried delimiting /s. Could not get it to work.  Can some RegExp expert please fix my expression?

What is the difference between the search() and match() functions in the ?  I've read the  (), but I never seem to remember it.  I keep having to look it up and re-learn it.  I'm hoping that someone will answer it clearly with examples so that (perhaps) it will stick in my head.  Or at least I'll have a better place to return with my question and it will take less time to re-learn it.


I have to acknowledge being an old timer U*ix system administrator. Software to be used by everybody had two possible locations: /usr/bin /usr/local/bin The best example is gcc and family. Now I find myself in a new world. My node installation lives in: /home/david/.nvm/versions/node/v14.7.0/bin/node So I added the corresponding directory to my path. How/where should the node package be installed? It would be done and owned by root, of course.

I've found numerous installation instructions for Node.js but they all seem so complicated -- I'm not a super sys admin but I can get around. I have yum on the system, but I didn't find any node.js packages, and I'm not sure how to compile code on the server or where to put it.


Let $\mathcal{C}$ and $\mathcal{D}$ be categories and $\mathcal{F}:\mathcal{C}\longleftrightarrow\mathcal{D}:G$ functors such that $\mathcal{G}$ is right-adjoint to $\mathcal{F}$, ie. we have a natural isomorphism $\text{Hom}_{\mathcal{D}}(\mathcal{F}(X),Y)\cong \text{Hom}_{\mathcal{C}}(X,\mathcal{G}(Y))$ for all objects $X$ in $\mathcal{C}$ and $Y$ in $\mathcal{D}$. I have proven that right-adjoint functors are unique up to natural transformation and I have constructed the unit $\eta:\text{Id}_{\mathcal{C}}\longrightarrow G\circ F$ as well as the counit $\varepsilon:F\circ G\longrightarrow\text{Id}_{\mathcal{D}}$. But now I am stuck: How can I show that $\mathcal{F}$ (resp. $\mathcal{G}$) is fully faithful if and only if $\eta$ (resp. $\varepsilon$) is an isomorphism?

Let $C,D$ be categories and $F:C\to D,G:D\to C$ be such that $F$ is a left adjoint of $G$. Prove that $F$ is fully faithful iff the unit is an isomorphism.   (This is an exercise from the book by T. Leinster)   I think I can do one direction:  $\impliedby$: If we let $\eta$,$e$ be unit/counit then as $\eta:\text{id}_C \implies GF$ is an isomorphism, it follows that the composite  $$ \text{Hom}(x,y)\to\text{Hom}(F(x),F(y))\to\text{Hom}(GF(x),GF(y)) $$  for all $x,y\in C$ is an isomorphism, which implies that $F$ is faithful. But $F$ must be full since the composite  $$ G=G\circ \text{id}_D \implies GFG \implies G $$  is an identity transformation (I'm rather skeptical about this).  But I don't have any idea regarding reverse direction, in which I have to show that the arrow $x\to GF(x)$ has an inverse for all $x\in C$.


Define the following matrix norm: $$ ||A||=\frac{\max|\langle Ax,x\rangle|}{||x||_2^2} $$ The spectral radius of $A$ is: $$ \rho(A)=\max_i\{|\lambda_i|:Ax_i=\lambda_ix_i; x_i \neq 0\} $$ Can you provide me some hints to show that: $$ ||A||=\rho(A) \text{ when } AA^T=A^TA? $$

Let $H$ be a Hilbert space and $T$ be linear bounded operator in $H$.  Prove that if $T$ is normal then the spectral radius of $T$,    $$r(T)=\|T\|.$$  Is this TRUE?


I have a line segment made of two points p1 and p2, and a second line segment made up of points p3 and p4. I'm trying to figure out if they intersect, and so far, I have had no luck. This is my code so far:  public static double angle(Point p1, Point p2, Point p3) {     double AB = length(p2, p1);     double BC = length(p2, p3);     double AC = length(p3, p1);     return Math.acos((sqr(BC) + sqr(AB) - sqr(AC)) / (2 * BC * AB)) * (180 / Math.PI); }  public static boolean doIntersect(Point p1, Point p2, Point p3, Point p4) {     double a = angle(p4, p3, p2);     double b = angle(p3, p2, p1);     double c = 180 - b - a;      System.out.println("a: " + a + ", b: " + b + ", c:" + c);      if((length(p3, p2) * Math.sin(a)) / Math.sin(c) > length(p2, p1)) return false;     if((length(p3, p2) * Math.sin(b)) / Math.sin(c) > length(p3, p4)) return false;     return true; }  public static double length(Point point1, Point point2) {     return Math.sqrt(sqr(point1.x - point2.x) + sqr(point1.y - point2.y)); }  public static double sqr(double doub) {     return Math.pow(doub, 2); }   But this isn't working. Sometimes, the angle "c" even comes out as negative numbers.  Also, Point is a custom class with two parameters: x and y. Should be fairly self-explanatory.

For a game I am developing I need an algorithm that can calculate intersections. I have solved the problem, but the way I have done it is really nasty and I am hoping someone here might have a more elegant solution.  A pair of points represent the end points of a line drawn between them. Given two pairs of points, do the drawn lines intersect, and if so, at what point?   So for example call the lines (A.x, A.y)-(B.x, B.y) and (C.x, C.y)-(D.x, D.y)  Can anyone think of a solution? A solution in any language will do.  Edit: A point I should have made clearer, the algorithm must return false if the point of intersection is beyond the lengths of the line segments.


Im trying to get the URI for the captured image from camera I why am i getting the exception as java.lang.NullPointerException: uri ,  here is my code.  Uri selectedImage = data.getData();   file = new File(URI(selectedImage));   public String URI(Uri contentUri)  {         Cursor cursor = null;  try  {     String[] proj = {MediaStore.ACTION_IMAGE_CAPTURE};       cursor=getActivity().getContentResolver().query(contentUri,proj,null,null,null);       intcolumn_index=cursor.getColumnIndexOrThrow(MediaStore.ACTION_IMAGE_CAPTURE);             cursor.moveToFirst();             return cursor.getString(column_index);         } finally {             if (cursor != null) {                 cursor.close();             }         }     }

What are Null Pointer Exceptions (java.lang.NullPointerException) and what causes them?  What methods/tools can be used to determine the cause so that you stop the exception from causing the program to terminate prematurely?


If we define a curve as a continuos image of the (unit) interval then one can construct example of so called Peano curve which is the whole square. However if our curve is homeomorphic to the (unit) interval (let us call such a curve by arc) then such situation cannot occur-the dimension is the topological invariant. However recently I've heard that still one can construct arcs of positive measure. How those "big" arcs are constructed?

Let $\gamma : [0,1]\rightarrow\mathbb R^2$ be a continuous curve whose image has positive Lebesgue measure. Must $\gamma$ have self-intersections? Intuitively this seems like it should be true, but I could not find a proof. An equivalent question is whether there is a positive measure subset of $\mathbb R^2$ which is homeomorphic to $[0,1]$.   Note that it is shown here  that $\gamma$ must in fact have lots of intersections if the image of $\gamma$ is a rectangle. But, here I am not making any topological assumptions on the image of $\gamma$. The answer to the linked question does not work in this generality.


I'm having a little bit of trouble with this proof.  Use mathematical induction to show that $f_{n−1} \cdot f_{n+1} − f_{2 n} = (−1)^n$ for $n$ in the set of positive integers.  I know that in recursive functions, at least the first term is provided and then you could play around with it to come to a conclusion.  I was maybe thinking of using the Fibonacci numbers definition as a guide but I'm not really going forward.

By calculating for $n\in \{1,2,3,4,5,6,7\}$, I've formulated the rule  \begin{equation} F_{n+1} \cdot F_{n-1} = F_n^2 + (-1)^n, \end{equation}  where $F_n$ is the $n$th fibonacci number. I want to show that this is true for all $n \in \mathbb{N}$.   I tried using induction, with $n=1$ as the basis step, but didn't get very far:  For the induction step, we assume the formula holds for a $n = k$, and checks for $n=k+1$: \begin{align*} F_{k} \cdot F_{k+2} &= F_{k} \cdot (F_{k+1} + F_{k})  \\ &= F_k \cdot F_{k+1} + F_k^2 \\ \end{align*} If somehow $F_k \cdot F_{k+1} = (-1)^k$, then I would be done. But I don't see how that's possible.   Is there a better way of proving this, maybe without using induction? Or am I just going about it the wrong way?


I have the following array, which I would like to reindex so the keys are reversed (ideally starting at 1):  Current array (edit: the array actually looks like this):  Array (  [2] => Object     (         [title] => Section         [linked] => 1     )  [1] => Object     (         [title] => Sub-Section         [linked] => 1     )  [0] => Object     (         [title] => Sub-Sub-Section         [linked] =>      )  )   How it should be:  Array (  [1] => Object     (         [title] => Section         [linked] => 1     )  [2] => Object     (         [title] => Sub-Section         [linked] => 1     )  [3] => Object     (         [title] => Sub-Sub-Section         [linked] =>      )  )


I am working in sharepoint site. In this site there is a user requirment where user want see the version numbers maintain by sharepoint in its OOB versioning feature in a document itself.   SO as the document ge modified sharepoint maintains the version number for each updation. User want to see that vesion number in that document itself as a text.  Can anyOne tell me Is it possible in sharepoint..? If yes the what will be best approch ro do it..?   Can I use document parser in this case..?  Thansks in advance Sachin

I'm trying to work out a way to display the contents of the version column from SharePoint (i.e. the value that changes every time a file is checked in) as a field (or something similar) inside of a Word document.  Ideally, I'd like to know how to configure SharePoint so I could click something like "Insert > Quick Parts > Document Property > Version", and it would include the version in the document.  The goal is to make it easier for someone to correlate a printed version of a document with the version history of SharePoint.  I have been able to add editable text columns to the Document content-type and have them show up as document property quick parts.  I've also been able to add a calculated column which gets the version as a text string... however this calculated column isn't showing up in Word as a document property.  (Perhaps I'm missing a setting on the calculated column)


The first time, I was not entitled to disclose the purpose of the travel to anyone beyond the company, so I applied for a tourist visa.  It feels, er, not completely true, but I couldn't provide an invitation from the inviting company (we didn't even know if we will sign an agreement, and the deal was a top secret).  I was rejected with a reason like "not convincing".  Is it bad?  Now I'm applying for a business trip visa. update: for a different date, for 3 days. It is not the same trip, but happens within a month from 1st application.  Should I include an explanation letter to a visa officer? What should I write there to convince the officer?  Here's why I think I need to provide extra explanations (these are USA rules but still):

Schengen refusal formulae can be difficult to understand sometimes.  Sometimes an applicant receives a refusal with:       Justification for the purpose and conditions of the intended stay was not reliable.     often accompanied by:       Your intention to leave the territory of the Member States before the expiry of the visa applied for could not be ascertained.   What is meant by this refusal reason?  What are they trying to say?


I want to revive my old computer (late 2012) with linux and I have a mac. I want to put linux on a hard drive using my mac and then plug the hard drive onto the windows computer and install linux on it. How do i do this?

I would like to see a full how-to guide on how to install Ubuntu.


I installed  on   $ virtualbox -help Oracle VM VirtualBox Manager 5.1.22_Ubuntu   using:  $ lsb_release -a No LSB modules are available. Distributor ID: Ubuntu Description:    Ubuntu 17.04 Release:    17.04 Codename:   zesty   If I open Play Store app and select WhatsApp, there is no option to install it. Only the option "add to wishlist" appears.  Is it possible to install WhatsApp via Play Store app on Android x86 virtual machine?

I've just installed Android using Virtualbox on Ubuntu, and now I want to install WhatsApp on it.  When I visit Google Play and try to install WhatsApp, it tells me that I have to associate a device via my Gmail account. When I'm connected, it's saying that I have to choose another device (because I've already installed it on my Nexus) but it doesn't list me the Virtualbox install as an option.  What's causing this problem?


In American psycho the main character describes how he kills and what he does when he kills in so much detail.

There's a word I thought I knew at some point, but can no longer remember what it was.  I tried looking up various thesaurus websites to no avail.  Similar words to what I'm looking for, but not quite:   Elaborate: too neutral -- I'm looking for a more negative connotation. Elucidate: too positive a connotation. Ruminate: The direction is correct, but it is about "thinking about something in too much detail" vs actually describing it so. Describe ad nauseum: 3 words, and awkward sounding.   Example sentence: "He began to __ the topic"  To clarify, I'm looking for a verb.


$A(I-A) = 0\implies\operatorname{rank}(A) + \operatorname{rank}(I-A)\le n$.   I managed to get this but wasn't able to go further. Any help would be appreciated.

Let $A$ be a square matrix of order $n$. Prove that if $A^2=A$ then $\mathrm{rank}(A)+\mathrm{rank}(I-A)=n$.   I tried to bring the $A$ over to the left hand side and factorise it out, but do not know how to proceed. please help.


I just noticed that the shading in my solid view is really dark. I can't find how to change it back.

I recently changed the lighting in the viewport in the system preferences.    How can I rest the positions of the lights? The Reset to Default Value does not work. it simple sets them all to a top light.  How can I reset the direction of the lamps without restoring factory defaults?


Please guys how can I do refrences in my LaTex work, I have TexMaker, Texworks and didn't know how to deal with it. I found some videos on Youtube but they were using Bibdesk to run their bibliography and I do not seem to find this bibdesk app anywhere. a link to a Youtube video will do. Thanks in advance.

As you can see in  article on Wikipedia, there is a distinction made between notes, citations and references. I would like to have a section called citations at the end of my document which I can refer to like this[2]  [2] Lasker (1934), p. 73  which is to be found in my references under "Lasker, Emanuel (1934). Lasker's Chess Primer. London: Billings (1988 reprint). ISBN 0-7134-6241-8". Ideally, I would like this citation to contain a hyperlink to this reference (although this is not done in the document). Any good way to do this or something similar?


I would like to spread some text on the screen using OpenGL in C++. Is there any example source or method for reference?

How do I draw a text string onto the screen using GLUT / OpenGL drawing functions?


Hi Stackoverflow community  I have been trying to find a resource or reference that explains what the usage() method does. Unfortunately the word 'usage' is indexed so often in different contexts that I simply can't find a good resource. Would anybody be able to point me in the right direction?  public static void main(String[] args) {         if (args.length == 0) {             usage();          } else if ("parse".equals(args[0])) {             final String[] parseArgs = new String[args.length - 1];              etc ....   I know that in C getusage() is used to get memory and CPU usage statistics. Is this the same case in Java? Any pointers would be highly appreciated.  Mike

I need to check CPU and memory usage for the server in java, anyone know how it could be done?


What kind of number is $2^\sqrt{2}$ ? It is real and obviously is not integer nor rational. Is it real algebraic number?

Is $2^\sqrt{2}$ irrational? Is it transcendental?


I have this following code snippet       // List of persons with name and age     List<Person> persons = new ArrayList<>();             // Adding 10,000 objects     for(int i = 0 ; i < 10000 ; i ++) {         Person p = new Person();         p.setName("Person " + i);         p.setAge(i);         persons.add(p);     }      long time1 = System.nanoTime();     System.out.println("Time before steram.reduce()" + time1);     Optional<Person> o1 = Optional<Person> o1 = persons.stream().reduce(BinaryOperator.maxBy(Comparator.comparingInt(p -> p.getAge())));     long time2 = System.nanoTime();     System.out.println(o1.get() + "\nTime after stream.reduce() " + time2);     System.out.println("**** Rough execution time for stream.reduce() : " + (time2 - time1) + " nano secs");       long time3 = System.nanoTime();     System.out.println("Time before stream.max() " + time3);     Optional<Person> o2 = persons.stream().max((p01, p02) -> p01.getAge() - p02.getAge());     long time4 = System.nanoTime();     System.out.println(o2.get() + "\nTime after stream.max() " + time4);     System.out.println("**** Rough execution time for stream.max() : " + (time4 - time3) + " nano secs");   While this might not be the ideal way to figure out execution time, basically what I am trying to do here is find the oldest Person and print out the time it took to find it out using stream.reduce() vs stream.max().  Output  Time before steram.reduce()8834253431112 [ Person 9999, 9999] Time after stream.reduce() 8834346269743 **** Rough execution time for stream.reduce() : 92838631 nano secs Time before stream.max() 8834346687875 [ Person 9999, 9999] Time after stream.max() 8834350117000 **** Rough execution time for stream.max() : 3429125 nano secs   P.S. I have ran this code multiple times changing the order of stream.max() and stream.reduce() and found out that stream.reduce() takes significantly more time to produce the output than stream.max().  So is stream.max() always faster than stream.reduce()? If yes then, when should we use stream.reduce()?

How do you write (and run) a correct micro-benchmark in Java?  I'm looking for some code samples and comments illustrating various things to think about.  Example: Should the benchmark measure time/iteration or iterations/time, and why?  Related:


When you use some of the predefined shortcuts in texstudio on selected text, it wraps the text with the appropriate tags(is that the proper term?). For instance, suppose i highlight Hello Worldand press Ctrl+i it becomes \textit{Hello World}.  That is pretty handy as you dont't have to move the end tags around. I was wondering whether there a way to program macro to have similar behavior too. Many thanks in advanced.   [edit] found a similar answered question:

I have a Tex file that I need to edit while somehow keeping the original words and sentences highlighted. To do this, I am going to cross out the part of the original text that I replace with my own words. The command \st{TEXT} in the package soul seems to do the job. I'm looking for a way to define a macro in TeXstudio such that by selecting the text, the cross out command encapsulate the text, i.e. \st{THE_SELECTED_TEXT}. I am not familiar with macro programming in TeXstudio.


I have been a Linux (Ubuntu) user for over 5 years now, currently running Ubuntu 18.04 on my Acer laptop. I always put my laptop to sleep instead of shutting it down to resume from whatever I was doing quickly. Sometimes if I try restarting it, it boots to the advanced section saying some part of the disk is corrupt and requires I run fsck. I have never run into a major issue performing this operation until recently. After executing fsck on the /dev/sda4 (my main hard drive) I couldn't log in again . It became an infinite login loop. I tried every solution I found online but none worked. I created another user through tty and could successfully log into the new account, but not my own.  What else can I try?

My Ubuntu is stuck in a login loop when trying to enter my desktop. When I login, the screen gets black and soon after that the login screen comes back.   I've read that the problem might be caused by an error depending on the graphics, here's my graphics card: ATI Radeon 7670M


When I attempted to navigate within the 3D viewport by using the CTRL-numpad options, it didn't seem to work, and I noticed a message in the communication part of the main header that gave the usual warning sign (an exclamation point within a red edged yellow triangle), followed by the text "View offset is locked". The warning appeared and closed so quickly I was not able to obtain a screenshot.  I don't know what I did to cause this, and cannot find any information in the manual or other Blender documentation about this warning message. How do I unlock the "viewport offset"?

I am starting to learn using blender, and at some point I managed to do something to the 3D view camera.  Usually the camera orbits around an object, but now the rotation seems to happen (atleast very close to) around the "camera's origin". Neither the input setting in "User Preferences", the pivot point selection nor Ctrl-Alt-Shift-C (as suggested on some forum) do anything to the issue.


I'm playing on iOS, and I need some help with commands. I'm trying to give mobs that I spawn custom names. I have tried the following:   /summon villager ~ ~ ~ {CustomName:"Dr.Tray"}   The error message I got was "Invalid Command Syntax"  If you know the correct way to do this, Please do not hesitate to tell me!

This question was recently split into different questions for each workaround. See   meta posts for more information.   Can you use NBT tags in commands? I’ve tried commands that normally work in Java Edition like: give @s minecraft:planks 30 1 {display:{Lore:["Wooden planks"]}} give @s stone_pickaxe{Unbreakable:1b} give @s item_frame{EntityTag:{Invisible:1b}} summon villager ~ ~ ~ {Offers:{Recipes:[{buy:{id:"emerald",Count:5b},sell:{id:"diamond_sword"}}]}} summon tnt ~ ~ ~ {Fuse:20s}


I had a small question concerning something in Ubuntu. I noticed that whenever I cd to a two-word place, Ubuntu seems to go there. However, when I mention the file path to this place, Ubuntu splits up the text.    As seen, in the first picture, the system can go to the specified place. However, when I mention the file path to the two-word place, Ubuntu seems to split up the two words and search for either of them, which don't exist.   Can someone help?  Note: I have tried '' instead of "" around the file, but it still doesn't work. I am also using the Linux application on Windows (which, yes, I know is very dangerous).

I want to enter the following folder in the terminal:  Milano, Torino (Jan)-Compressed   How should I write the command cd to enter this directory?  Spaces and several other special characters like \, *, ), ( and ? cause problems when I try to use them in the command line or scripts, e.g.:    $ cd space dir bash: cd: space: No such file or directory  $ cat space file cat: space: No such file or directory cat: file: No such file or directory  $ cat ( bash: syntax error near unexpected token `newline'  $ echo content >\ > ^C  $ ls ? (  )  *  ?  \   How do I enter file or directory names that contain special characters in the terminal in general?


The  cantrip may be among the most versatile spells in the whole game, and the effects that can be created with it vary widely.  Since the spell requires verbal and somatic components, we should probably assume that this applies to all of these different effects. However, if for example you want to use it in order to fool somebody or create a distraction, the verbal component might completely ruin your plan.  Has there ever been any clarification about what the verbal component is, and how it might depend on the desired effect?

In a recent game the verbal component of 'Suggestion' came up. I had assumed that the verbal component was just me saying the words and was added to mechanically stop me from casting it in magical silence. This came up because I tried casting it on a PC while a another party member was near-by.  My questions are:   Did my character actually perform a chant before giving the suggestion? Would the victim's character notice on a successful saving throw? Would a bystander notice that a spell was being cast?


Let $G$ be a finite group and $Z(G):=\{x\in G : gx=xg \ \ \forall g\in G\}.$ Prove that $[G:Z(G)]$ is not a prime number. I think that I should use the Lagrange Theorem, i.e., If $Z(G)$ is a subgroup of a group $G$, $$|G|=[G:Z(G)]|Z(G)|$$ So that $\dfrac{|G|}{|Z(G)|}$ cannot be a prime number. Can I get some help?

The question is to prove index of $Z(G)$ in $G$ is not a prime number.    We know that $|G:Z(G)|=|G:C_G (x)||C_G (x):Z(G)|$ where $C_G (x)$ means centralizer of $x \in G$  I want to mention that we do not want to use $G⁄Z(G)$ theorem.   We may assume that $|G:Z(G)|=p$ where $p$ is a prime.


I need a search icon button icon in my compoonent. I have got the code as well. Below is the link from where i have referred the code.     The problem that i am facing is for the svg.  the error says "Failed to save AddressSearch.cmp: No COMPONENT named markup://svg found : [markup://c:AddressSearch]: Source"  If there is no svg. how i create one for this kind of button???   <button class="slds-button slds-button_icon slds-button_icon-brand" title="Search"> <svg class="slds-button__icon" aria-hidden="true"> <use xlink:href="/assets/icons/utility-sprite/svg/symbols.svg#search"></use> </svg> Search </button>

Followed the Trailhead tutorial and I still get the same error about svg.  The code I am using is taken from the Lightning Design System. I created the supporting files as specified in the tutorial. Here is a snippet of the Component code (just note not all the code is included since it came directly from the LDS. The error is (Failed to save undefined: No COMPONENT named markup://svg found : [markup://michelleemanuel:forecastPlanComponent]: Source). Some of the other responses I saw said to read the tutorial - I have gone down that path and it did not work. I am not invoking this from a Visualforce page but from a Component.            <table class="slds-table slds-table--bordered slds-max-medium-table--stacked-horizontal">                                                         select all                                Opportunity Name                                                       Sort          ....


Using Legendre's symbol, knowing that $41 \equiv 1 \pmod{4}$ we can solve said equation. Then, I looked at the residue classes and I just counted my way to the solution $x = 9$. Verifying, $9^2 = 81$ and $81 \equiv -1 \pmod{41} $. I was wondering if there was an actual way to solve the equation $$x^2+1 \equiv 0 \pmod{41}$$ using quadratic residue formulas or any other formula for that matter, instead of counting to get the solution.

In general, how do you solve $x^2$ is congruent to $-1 \bmod p$, where $p$ is an odd prime and $x$ is an integer.  Specifically, I need to solve $x^2\equiv-1 \pmod{29}$