Where does the dark energy of space expansion come from?
Energy conservation in General Relativity
How do I insert the total continuation count in the allowframbreaks frame title? I would like to change the numbering of allowframbreaks frame, for instance, from I II III to (1/3) (2/3) (3/3)， but fail to find out a command to get the total continuation count. Here is the MWE.  \documentclass[compress]{beamer} \usetheme{Warsaw}   %allowframebreaks numbering in the title \setbeamertemplate{frametitle continuation}{(\insertcontinuationcount/)} %\setbeamertemplate{frametitle continuation}{(\insertcontinuationcount/\inserttotalcontinuationcount)}  \title{title} \author{author}  %%%%% \begin{document}  \begin{frame}[allowframebreaks]{allowframebreaks title} frame 1 \framebreak  frame 2 \framebreak  frame 3 \framebreak \end{frame}  \end{document} How can I do case insensitive string comparison in Python?  I would like to encapsulate comparison of a regular strings to a repository string using in a very simple and Pythonic way. I also would like to have ability to look up values in a dict hashed by strings using regular python strings. Weak solutions to the Neumann's problem (Evans PDE) How prove this $\prod_{1\le i<j\le n}\frac{a_{j}-a_{i}}{j-i}$ is integer I recently setup a new computer for my parents with windows 10 home. I made two local accounts for them - no microsoft accounts. I also would like to keep them without a password. Problem is now that windows automatically signs in with the last used account. No lock/login screen.  I tried a number of answers from similar questions here but none worked. Since it's a home version there are no group policies and the method using task scheduler does not work because accounts with no password are not allowed to create such tasks.  Are there other options to force windows to show a user list on startup without setting passwords for the accounts? Roman numerals with over- and underline This question led to a new package:      (using a variation of egreg's code, and stating this in the manual; the package isn't really new now, sorry for the delayed announcement)  I have read about "How to get Roman numerals" but asked myself how to get Roman numerals formatted as in     i.e. with fitted over- and underline (without manually using boxes and such)? I'm curious for your answer(s)! In Revenge of the Sith, after first being Force-choked by Anakin and then given births to Luke and Leia, Padme Amidala eventually lost her life on Polis Massa. We later, however, see her in the funeral procession on Naboo. The question is, how did she get there?    I mean, whoever delivered her there must have faced a lot of difficult questions, not just from her family but also from both the people and the authorities, since she was the former queen of the planet. Whoever it was, he could not have been just somebody, because it most certainly must not have been an easy task. It most likely was not any of the Jedi, since the world was probably half full of Palpatine's collaborators who would have immediately given them away.  So, who was it? And how was it carried out, in practice? Execute sudo without Password? Inspired by this ....  I am the sole person using my system with 12.04. Every time I issue a sudo command; the system asks for the user password (which is good in its own way).  However I was thinking; without activating the root account; how can I execute the sudo commands which will not ask for user password to authenticate.  NOTE: I want to execute sudo command without authenticating via password; only when they are executed via terminal. I don't want to remove this extra layer of security from other functions such a while using 'Ubuntu software center' or executing a bash script by drag-drop something.sh file to the terminal. Flag Options Missing - Is this a bug? This is normally what I see when flagging a post:   Which then provides the following options:    I have come across this problem before. Where I have wanted to flag a question, as not belonging here, but only have limited options.    When this happens, I use a custom flag and write in the reason, but am not happy doing so.  Is this a bug?   What is the best thing to do? This morning, I had eggs for breakfast, and I was looking at the pieces of broken shells and thought "What is the surface area of this egg?" The problem is that I have no real idea about how to find the surface area.    I have learned formulas for circles, and I know the equation for an ellipse; however, I don't know how to apply that.   The only idea I can think of is to put an egg on a sheet of paper and trace it, and then measure the outline drawn, and then try to find an equation for that ellipse and rotate that about the $x$-axis.  Now, my problem is how I can find the equation of the ellipse from the graph, and will my tracing method really be the edge of the egg?  Also, can I use the ? Will I have to use some techniques to solve the integral that are not covered in the ?  There has to be a better method for finding the surface area. Please, help me understand how to find the surface area of an egg; i.e., how to use my mathematical knowledge for something other than passing exams. How to deal with high correlation among predictors in multiple regression? How can I remove these apps from my device? How to prove $\lim \limits_{n\to\infty}(n+1)\int_{0}^{1}x^nf(x)dx=f(1)$ I need help to prove this in real analysis. I think it uses IMVT, but not sure how to do it.     Let $f(x)$ be a real valued continuous function on $[0,1]$. Show that   $$ \lim \limits_{n\to\infty}(n+1)\int_{0}^{1}x^nf(x)dx=f(1) $$ Order of product of two elements in an abelian group node.js conflicts: /sbin/node vs /usr/bin/node I have two Ubuntu 12.10 machines: machine A is a VMWare VM and machine B is and old Acer laptop. On both machines, I installed node using apt-get. However machine A installs the main binary as /usr/bin/node and machine B as /usr/bin/nodejs. Here are some behaviors I observed:   Both machine returns /usr/bin/node in response to the which node command. However, there is no such file on machine B. Issuing the command node works for machine A, not B. On B, I have to use nodejs instead. On B, there is a binary called /sbin/node, A does not have it.   These behaviors causes inconsistency problem when developing on both machines. For now, I worked around by renaming the binaries on B as such:  sudo mv /sbin/node /sbin/node-sbin sudo ln -s /usr/bin/nodejs /usr/bin/node   Is there a way to really fix this, so that node will be installed as /usr/bin/node instead of /usr/bin/nodejs? How can I type accented characters like ë? Currently I use the character palette applet in gnome panel to put special characters into text.  This is okay, but I have to stop typing, select the character I want from the applet and then copy and paste.  Is there a way to simply type special characters with different key combinations? If so, how do I do it? Evaluating the limit of a sequence given by recurrence relation $a_1=\sqrt2$, $a_{n+1}=\sqrt{2+a_n}$. Is my solution correct? Problem  The sequence $(a_n)_{n=1}^\infty$ is given by recurrence relation:   $a_1=\sqrt2$, $a_{n+1}=\sqrt{2+a_n}$.   Evaluate the limit $\lim_{n\to\infty} a_n$.  Solution   Show that the sequence $(a_n)_{n=1}^\infty$ is monotonic. The statement $$V(n): a_n &lt; a_{n+1}$$ holds for $n = 1$, that is $\sqrt2 &lt; \sqrt{2+\sqrt2}$. Let us assume the statement holds for $n$ and show that $V(n) \implies V(n+1)$. We have that $$a_n &lt; a_{n+1}.$$ Adding 2 to both sides and taking square roots, we have that $$\sqrt{2+a_n} &lt; \sqrt{2+a_{n+1}},$$ that is $a_{n+1} &lt; a_{n+2}$ by definition. Find bounds for $a_n$. The statement $$W(n): 0 &lt; a_n &lt; 2$$ holds for $n=1$, that is $0 &lt; \sqrt2 &lt; 2$. Let us assume the statement holds for $n$ and show that $W(n) \implies W(n+1)$. We have that $$0 &lt; a_n &lt; 2.$$ Adding two and taking square roots, we have that $$0 &lt; \sqrt2 &lt; \sqrt{2+a_n} &lt; \sqrt4 = 2.$$ The limit $\lim_{n\to\infty} a_n$ exists, because $(a_n)_{n=1}^\infty$ is a bounded monotonic sequence. Let $A = \lim_{n\to\infty} a_n$. Therefore the limit $\lim_{n \to\infty} a_{n+1}$ exists as well and $\lim_{n \to\infty} a_{n+1} = A$. (For $(n_k)_{k=1}^\infty = (2,3,4, \dots)$, we have that $(a_{n_k})_{k=1}^\infty$ is a subsequence of $(a_n)_{n=1}^\infty$, from which the statement follows.) We have that $a_{n+1} = f(a_n)$. That means that $A = \lim_{n\to\infty} a_n = \lim_{n \to\infty} {f(a_n)} = f(\lim_{n \to\infty} a_n) = f(A) = \sqrt{2 + A}$. Solving the equation $A = \sqrt{2 + A}$, we get $A = -1 \lor A = 2$. Putting it all together, we get that $A = 2$, because the terms of the sequence are increasing and $a_1 &gt; 0$.   Is my solution correct? Is calling a linear-equation a linear-function, misnomer or completely wrong? From my college life, I remember many professors used to call a linear-equation a linear-function, however:  A standard definition of linear function (or linear map) is:  $$f(x+y)=f(x)+f(y),$$ $$f(\alpha x)=\alpha f(x).$$  Where as linear equation is defined as:  $$f(x)=mx+b.$$  So, linear-equation is NOT a linear-function, according to the definitions defined above.  Though, for $b=0$ the linear-equation becomes a linear-function, but it is not true in general.  Question: Is it misnomer to call a linear-equation a linear-function, or it is completely wrong to say that? And linear-equation must be considered strictly as an affine-mapping. I think the questions says it all! :)  By TeX, I mean any derivative of TeX as long as the code is clearly a derivative of TeX, i.e. that it could belong on TeX.SX (and not pure Lua for example).  I'll give two answers myself so you see what I mean. My 8 year old son won't fall asleep We put him to bed at 9pm and he stays up til 1am or later. When I go to check on him he is always playing with his hands and sometimes talking. I ask him why he is awake and not trying to sleep and he says it's because he just wants to play. He never comes to tell us that he is having a hard time sleeping or that there is anything wrong. The weird thing is that he used to be the first one to fall asleep out of 3 boys and the staying up started a few months ago. He does this every night and on top of keeping us awake, he is now waking up his brothers.   About a month or so ago, we decided to punish him by grounding him from video games. He doesn't want to be grounded, but he still keeps doing it. Nothing we do seems to be helping and it seems to be getting worse. I have talked to him about why it is so important to get enough sleep and why it's even more important for kids. He also gets plenty of exercise and time to play during the day.   I'm really starting to wonder if he is doing it just to be defiant. If anyone has any suggestions I would greatly appreciate it.  The problem is that he is being disruptive to everyone in the house and it has been EVERY night for the last 3 months.   He is tired and emotional during the day, and it is causing his brothers to be tired during the day while they are at school.   Because he is tired during the day he doesn't really want to be as active as he used to be. However, I do still encourage him to be active. We have always had a bedtime routine. We have asked him many different times if he is just having trouble sleeping, if he is uncomfortable, and if there is something wrong. He always tells us that he just wants to play.   At the beginning of all this he told me that he wants to be the one to decide when he goes to sleep and when he wakes up. Which is why I would even ask if it was out of defiance.   We really didn't want to get to the point of punishing him, but nothing else seemed to help and it was only after he started keeping his brothers awake.   It's not like we haven't asked him what he thinks would help or what would help him sleep better. He ALWAYS says that he just WANTS to stay up and play because it is fun. We know it is important for him to get enough sleep, and I'm worried because I don't think he is (and he's preventing the rest of us from getting enough, too).