I'm wondering how I would go about changing the default logon screen (just the background) in Ubuntu 12.04. I can't seem to figure it out.
I would like to set the wallpaper in the login screen (Unity Greeter), how do I do that?
Are continuous self-bijections of connected spaces homeomorphisms? I hope this doesn't turn out to be a silly question.  There are lots of nice examples of continuous bijections $X\to Y$ between topological spaces that are not homeomorphisms.  But in the examples I know, either $X$ and $Y$ are not homeomorphic to one another, or they are (homeomorphic) disconnected spaces.    My Question: Is there a connected topological space $X$ and a continuous bijection $X\to X$ that is not a homeomorphism?    For the record, my example of a continuous bijection $X\to X$ that is not a homeomorphism is the following.  Roughly, the idea is to find an ordered family of topologies $\tau_i$ ( $i\in \mathbb Z$) on a set $S$ and use the shift map to create a continuous bijection from $\coprod_{i\in \mathbb Z} (S, \tau_i)$ to itself.  Let $S = \mathbb{Z} \coprod \mathbb Z$.  The topology $\tau_i$ is as follows: if $i&lt;0$, then the left-hand copy of $\mathbb Z$ is topologized as the disjoint union of the discrete topology on $[-n, n]$ and the indiscrete topology on its complement, while the right-hand copy of $\mathbb Z$ is indiscrete.  The space $(S, \tau_0)$ is then indiscrete.  For $i&gt;0$, the left-hand copy of $\mathbb Z$ is indiscrete, while the right-hand copy is the disjoint union of the indiscrete topology on $[-n, n]$ with the discrete topology on its complement.  Now the map $\coprod_{i\in \mathbb Z} (S, \tau_i)\to \coprod_{i\in \mathbb Z} (S, \tau_i)$ sending $(S, \tau_i) \to (S, \tau_{i+1})$ by the identity map of $S$ is a continuous bijection, but not a homeomorphism. I have to maintain a large number of classic ASP pages, many of which have tabular data with no sort capabilities at all. Whatever order the original developer used in the database query is what you're stuck with.  I want to to tack on some basic sorting to a bunch of these pages, and I'm doing it all client side with javascript. I already have the basic script done to sort a given table on a given column in a given direction, and it works well as long as the table is limited by certain conventions we follow here.    What I want to do for the UI is just indicate sort direction with the caret character ( ^ ) and ... what?  Is there a special character that is the direct opposite of a caret?  The letter v won't quite cut it.  Alternatively, is there another character pairing I can use? I have a Nexus 7 (2013) and a Moto X (2014) running Lollipop. On both of these, if I get a heads-up notification (i.e., those that show up on top of the screen when the device is unlocked) and swipe down on it with 2 fingers, it 'breaks' further heads-up notifications:   I can't tap on them to open the responsible app For, e.g., an incoming phone call with 'answer' and 'dismiss' buttons, tapping the buttons does nothing. I can't answer phone calls anymore!   I can still swipe to the side to dismiss the notifications, and they still disappear on their own after a few seconds. I haven't been able to find a way to get the correct behavior back aside from a restart.  Yeah, the obvious workaround is to not two-finger swipe on them, but it's second nature as that same gesture expands notifications in other contexts.  I'm guessing the problem is generic, but I've triggered it on Hangouts and Phone notifications.  Do others experience the same thing? Any known 'fixes' aside from restarting? Join matrix based on conditions I typically have two needs:  Scenario A. Change a single PDF page.  In this case I have a PDF but not the original source file used to create the PDF. I don't want to try to recreate the document from scratch. I'd like to open the PDF and change a few things. A good example of this scenario: I was responsible for planning a big event at a campground site, I had a PDF of the site. I wanted to start with that document, highlight some parts, add some labels, remove some parts that weren't relevant.   or   Scenario B. Combine PDFs or extract page(s) from a PDF  This scenario usually arises because I want a single PDF deliverable that is made up of parts that are best created in different programs. In this case I have the source files for all the documents but they don't play well enough together to easily create a single PDF deliverable. For part of it, I may want to use Libre Office Writer. For another page I may want to use Gimp. Still another page I may use Libre Office Calc. I could use Writer as the master document and embed images or the Calc object into that, but for ultimate control, you can't beat separate PDF documents that are then combined.  What are the best tools / processes for editing PDFs in Ubuntu? What should be in the sources.list for Kali Rolling Linux? This is exact content from my sources.list:  #  # deb cdrom:[Debian GNU/Linux 2016.1 _Kali-rolling_ - Official Snapshot amd64 LIVE/INSTALL Binary 20160830-11:29]/ kali-rolling contrib main non-free #deb cdrom:[Debian GNU/Linux 2016.1 _Kali-rolling_ - Official Snapshot amd64 LIVE/INSTALL Binary 20160830-11:29]/ kali-rolling contrib main non-free   I couldn't install the Synaptic package manager and was told to modify sources.list.  I googled a lot and added some repos into it and ran update and upgrade command only to see Kali crash... I had to recover it.  Please mention the exact content that should be there to ensure that Kali Linux works. Why is it difficult to differentiate between  and ? Is it because we don't clearly understand how both of these phenomenon takes place?   My thoughts: From an answer to one of my earlier question  I could understand that light waves behave differently when it strikes a slit which is of several times bigger than its wavelength and when it strikes a slit of size comparable to it its wavelength.In the former case the different points on the slit acts as wave-front sources producing circular wave fronts which interfere to form the diffraction pattern but in the later case plane wave-front striking a slit after passing through it forms circular wave-fronts and two such wave-fronts from two different slits interfere to form the interference pattern. But, I'm not satisfied by that because I don't get any intuition about points on the slit acting as wavefront sources. So, what is actually happening? Why do German umlauts and sharp s (ß) work without a package in LaTeX? I am used to the fact that LaTeX will only know letters like ä, ö, ü, or ß if I use packages like  \usepackage{ucs} \usepackage[utf8x]{inputenc} \usepackage[T1]{fontenc}   Today, I tried LaTeX on a Mac for the first time, using the MacTeX distribution and texmaker. Without writing down any packages, all umlauts and ß were accepted correctly from scratch. Why is that and will the usage of special letters without using the packages cause any problems? I want to know where the Metro applications (Mail, People, Messages, ...) executable file path is.  Also, how can I run Mail application when my PC starts? New passport and entrance Schengen I am from Brazil and travel a lot in Schengen countries. Under the rules of Schengen visa (3 months stay in a 6 months period). In my passport are the entrance and exit stamps, also to chec the days I stay in Schengen.  I need a new passport and will get this in Brazil. So in this new passport are NOT the stamps. Does this mean I start new with the Schengen visa rule? I seems like. The new passport is empty. Or do I miss something? It would be great because I am almost on my 90 days stay in the period of 180 days. What conditions need to be fulfilled to enter the Schengen zone visa free? To what extent are child actors exposed to the violent aspects of the movie they perform in? Exercise 12 from SEC. 82 of Finite-Dimensional Vector Spaces - 2nd Edition by Paul R. Halmos.  If $A$ and $B$ are linear transformations on a finite-dimensional inner product space, and if $\textbf{0} \le A \leq B$, then $\det A \leq \det B$.  Notation: $0 \le A$ means that $A$ is positive.  If $\det B = 0$, choose $x \in \ker B$, then $0 \le ((B-A)x,x) = (Bx, x) - (Ax, x) = -(Ax, x) \le 0$. Therefore $\ker B \subseteq \ker A$ and $0 = det A \le det B = 0$. How to prove for the case when $B$ is invertible? Intuitively, I feel that since both $A$ and $B$ are positive their proper values are also positive and $B$'s proper values should be greater the $A$'s and same for determinants. Use of substitution into the integral $\int_0^2 \frac{\arctan x}{x^2+2x+2}dx$ This question: got some attention, but I didn't understand anything of it. Now I looked at the solution of the book and there is given the hint to use the change of variable $$x=\frac{1-t}{1+2t}$$ Could you please explain how one could think of such substitution? Is there some intuition behind this? Also after I used the substitution I got: $$\int_{-1/5}^1\frac{3\arctan\left(\frac{1-t}{1+2t}\right)}{5t^2+8t+5}dt$$ How can I finish this using the hint from the book? Darth Vader threw Emperor Palpatine to a pit. Well, , but unlike other times, Palpatine wasn't injured or unconscious when he was thrown.  Why didn't he simply prevent his fall using his lightsaber (I have seen such action in Star Wars: The Clone Wars TV series lots of time) and make his way out? What prevents investors from buying high yield stocks and selling them as soon as their dividend is paid out? What prevents investors from buying high yield stocks and selling them as soon as their dividend is paid out?   I guess I am confused: If you know the yield and when the dividend will be paid out, why not buy a share an instant before the dividend is paid out and then sell it?  Do you have to have held the share for some amount of time to get the dividend? Is there too much volatility in the instant the dividend is paid out? What type of path in shebang is more preferable? In scripts, first line should specify the path to interpreter. But on different servers Linux, Unix, or BSD this path could be different.  What is more preferable?  #!/usr/bin/env bash    or  #!/bin/bash If a matrix has orthonormal columns, they must be linearly independent, so $A^+ = (A^T A)^{−1} A^T$ . Also, the fact that its columns are orthonormal gives $A^T A = I$. Therefore,  $$A^+ = (A^T A)^{−1} A^T = (I)^{-1}A^T = A^T$$  Thus, $A^+ = A^T$. Am I correct? Thank you. I am trying to prove the summation formula using induction:  $$\sum_{k=1}^n \frac{1}{k(k+1)} = 1-\frac{1}{n+1}$$  So far I have...  Base case:   Let n=1 and test   $\frac{1}{k(k+1)} = 1-\frac{1}{n+1}$  $\frac{1}{1(1+1)} = 1-\frac{1}{1+1}$    $\frac{1}{2} = \frac{1}{2}$   True for n=1   Induction Hypothesis:   Assume the statement is true for the n-th case   $\sum_{k=1}^n  \frac{1}{k(k+1)} = 1-\frac{1}{n+1}$  Inductive Step:   Prove, using the Inductive Hypothesis as a premise, that   $$\sum_{k=1}^{n+1}  \frac{1}{k(k+1)} = \sum_{k=1}^{n}  \frac{1}{k(k+1)} + \frac{1}{(n+1)(n+2)} = 1-\frac1{n+1} + \frac{1}{(n+1)(n+2)} = \frac{(n+1)(n+2)}{(n+1)(n+2)}+\frac{-2-n}{(n+1)(n+2)}+\frac{1}{(n+1)(n+2)} = \frac{(n+1)(n+2)-2-n+1)}{(n+1)(n+2)} = \frac{(n+1)(n+2)-n-1}{(n+1)(n+2)} = \frac{n^2+2n+1}{(n+1)(n+2)} = \frac{(n+1)(n+1)}{(n+1)(n+2)} = \frac{n+1}{n+2}$$  To prove $$ 1-\frac{1}{n+2} = \frac{n+1}{n+2} $$ Multiply both sides by $n+2$ to get an equivalent expression. $$ (1-\frac{1}{n+2}) * (n+2) = (\frac{n+1}{n+2}) * (n+2)  $$ $$ n+1=n+2−1 $$  Does this all make sense? How can this be improved upon? Let $X$ be an arbitrary random variable  takes values in $\{0,1,2,...,10\}$. What are the minimum and  maximum values of variance of random variable $X$?