Bluetooth Stays On
How can I deactivate Bluetooth on system startup?
How to resolve the "GPT detected. Please create a BIOS-Boot partition" error when using boot-repair? After installing Ubuntu, Windows didn't boot so I installed boot repair to fix this problem. But I am getting the message displayed below.  I tried to make a new partition with unformatted file system but still receiving the same message.  How do I fix it? I came across this problem when I was at a book store inside of a book made to prepare Berkeley graduates to pass a mandatory exam. I wanted to buy the book, but, alas, I didn't have the money (forty bucks is a lot of money when you don't have a job). So I took my phone out and started taking as many pictures as I could. Unfortunately, I didn't take any pictures of the solutions!  Enough backstory. Time for math. The problem is as follows:  Prove that $\cos^p( \theta) \le \cos(p \theta)$ if $0\le\theta\le\frac\pi2$ and $0\le p\le 1$.  I tried using the series expansion for cosine, but that seemed to be a dead end. Then I tried using Euler's theorem, but I got stuck. Then I got distracted and started to think about other cosine identities. For example, $$\cos\left(\frac\theta2\right)=\pm\sqrt{\frac{1+\cos(\theta)}{2}}.$$ Then what is $\cos(\frac\theta3)$ equal to? I tried to figure it out then I realized that I needed to find the root of a cubic polynomial. Then I realized that I'm better at staying focused than finding the roots of cubic polynomials.  Anyways, a proof would be nice here. I really appreciate any hints or answers. I apologize for my digressions! Black screen after suspend-after moving to the nvidia official drivers (not priority) How to prove $\int_{-\infty}^{+\infty} f(x)dx = \int_{-\infty}^{+\infty} f\left(x - \frac{1}{x}\right)dx?$ If $f(x)$ is a continuous function on $(-\infty, +\infty)$ and $\int_{-\infty}^{+\infty} f(x) \, dx$ exists. How can I prove that $$\int_{-\infty}^{+\infty} f(x) \, dx = \int_{-\infty}^{+\infty} f\left( x - \frac{1}{x} \right) \, dx\text{ ?}$$ Why is "Nature" usually spelt with an initial capital letter in scientific journals? I am mainly referring to life science here, in case this matters.  I am not talking about the obvious cases, like capitalisation in titles, at the beginning of a sentence, etc., but when it appears mid-sentence, where one would normally expect it to be lowercase.  I've heard some explanation that it gives the impression of Nature as a goddess (see comments on this post ) - but this is probably the last thing I would have expected in a scientific article... Uniqueness in existence of a bilinear form Let $E$ be a finite dimensional vector space over field $\mathbb R$ with $E^*$ as the dual space of $E$.($\dim E=n$)   $\Omega^P(E):=\{ \alpha\colon \overbrace{E\times\cdots\times E}^{p- times}\rightarrow \mathbb R\  \ , \alpha \text{ is alternating multilinear map}\}$ $\Omega^P(E^*):=\{ u\colon \overbrace{E^*\times\cdots\times E^*}^{p- times}\rightarrow \mathbb R\  \ , u \text{ is alternating multilinear map}\}$  I wish to prove that there exist an $\textbf{unique}$ bilinear form $B\colon \Omega^p(E^*)\times\Omega^p(E)\rightarrow\mathbb R$   such that for all $ f_i\in E^* \ , u_j\in E^{**}\simeq E \qquad  i,j=1,\cdots,p$, it has the following rule:  $B(u_1\wedge\cdots\wedge u_p,f_1\wedge\cdots\wedge f_p)=\det[f_i(u_j)]$.  $\wedge$ is wedge product between alternating maps i.e. $\alpha\wedge\beta(v_1,\cdots,v_{p+p})=\dfrac{1}{p! p!}\displaystyle\sum_{\sigma\in S_{p+p}}sign(\sigma)\alpha(v_{\sigma(1)},\cdots,v_{\sigma(p)})\beta(v_{\sigma(p+1)},\cdots,v_{\sigma(p+p)})$  How can I do this? Is "Smaug" pronounced "Smog"? Did Tolkien the linguist intend for the name of the dragon Smaug to be pronounced "Smog" [IPA: /smɒɡ/ or /smɔːɡ/]? The trailer for the second installment of The Hobbit trilogy pronounces the word (pronounced 'sma-ow-g' [IPA: /smaʊɡ/]) entirely differently than the way I have been reading it for all these many years. It is my understanding that I can disable my touchscreen by adding Option "Ignore" "on" to this file                                /usr/share/X11/xorg.conf.d/10-evdev.conf   Section "InputClass"           Identifier "evdev touchscreen catchall"           MatchIsTouchscreen "on"           MatchDevicePath "/dev/input/event*"           Driver "evdev"           EndSection   so it would look like this   Section "InputClass"           Identifier "evdev touchscreen catchall"           MatchIsTouchscreen "on"           MatchDevicePath "/dev/input/event*"           Driver "evdev"           Option "Ignore" "on"           EndSection   What would happen if I simplied changed MatchIsTouchscreen to "off"?   Section "InputClass"           Identifier "evdev touchscreen catchall"           MatchIsTouchscreen "off"           MatchDevicePath "/dev/input/event*"           Driver "evdev"           EndSection   Would this disable my touchscreen? On the three Stack Overflow chat servers, the  page displays the following image:    Is it from an actual episode, or is it a 'shop? Is it possible to change he/she (he or she) in a sentence into one word? For instance: When a student comes in, ask him or her to... I'm including \usepackage{hyperref} so that each instance of \ref (as well as each page number in the index and the table of contents) automatically links to that page.  When I'm viewing the document (in ) and I click a link, I jump to the linked page.  Is there any easy way to go "back" to where I was before I clicked the link?  (And is the answer any different when using Adobe Acrobat reader?) I have to prove that this is a metric: $$d(x,y):=\sum_{i=0}^\infty \frac{|x_i -y_i|}{2^i (1+|x_i-y_i|)}$$  The only thing that I can't prove is the triangle inequality, it's really hard. I know that $|x_i -y_i|\le |x_i -z_i|+|z_i -y_i|$, and I want to get: $$\frac{1}{2^i (1+|x_i-y_i|)} \le \frac{1}{2^i (1+|x_i-z_i|)}+\frac{1}{2^i (1+|z_i-y_i|)}$$ (I think...) The closest thing I've got is: $2^i (1+|x_i-y_i|)\le 2^i (1+|x_i-z_i|)+2^i (1+|z_i-y_i|)$ but... that's not quite what i want. I don't know how to get this... I have a  beautiful  inequality, but I can only prove part of cases. Given any positive real numbers $a,b,c$, we have   $$(a^{2}+2)(b^{2}+2)(c^{2}+2)\geq 9(ab+bc+ca)$$  How can we prove this statement? Evaluating this integral : $ \int \frac {1-7\cos^2x} {\sin^7x \cos^2x} dx $ The question :  $$ \int \frac {1-7\cos^2x} {\sin^7x \cos^2x} dx $$  I tried dividing by $\cos^2 x$ and splitting the fraction.  That turned out to be complicated(Atleast for me!)  How do I proceed now? List of Figures + Beamer? I want to have a List of Figures in my Beamer presentation.  I spent some time searching the web for a solution and only found desperate people telling others that it's not possible, i.e.  or .  I also made some experiments on my own, i.e. "abuse" tocloft to do the job. However, even \usepackage{tocloft} causes pdflatex to fail with ! LaTeX Error: \l@section undefined. (and lying to tocloft by defining the command as empty beforehand doesn't to any good either).  I can't really see why it should be that difficult to make a List of Figures in beamer, since \tableofcontents works flawlessly.   I'm not afraid of doing some coding on my own, but I'm not deep enough into TeX to really understand the magic behind the "List of Figures", "Table of Contents" and alike.  Is anyone out there having suggestions or links that might help me figure this out?  \documentclass{beamer}  % uncomment the following line % to get the error message % `! LaTeX Error: \l@section undefined.`  %\usepackage{tocloft}   % uncomment the following lines INSTEAD % to lie to tocloft % and get the next error message  %\makeatletter %\newcommand\l@section{} %\makeatother %\usepackage{tocloft}  \begin{document}  \begin{frame}{A frame} \begin{figure} \mbox{A} \caption{An 'A'} \end{figure} \end{frame}  \begin{frame}{List of Figures} \listoffigures \end{frame}  \end{document}   EDIT: Solution  Starting from Marco Daniels answer to my question, I modified his code to reflect my needs. Here is what I came up with. Please feel free to comment, improve and reuse this.  \RequirePackage{ifthen}  \makeatletter  \AtEndDocument{%   \clearpage   \beamer@tempcount=\c@page\advance\beamer@tempcount by -1%   \if@filesw   \newwrite\tf@lof   \immediate\openout\tf@lof\jobname.lof\relax   \newwrite\tf@lot   \immediate\openout\tf@lot\jobname.lot\relax   \fi }  \long\def\beamer@makecaption#1#2#3#4{%   \def\insertcaptionname{\csname#1name\endcsname}%   \def\insertcaptionnumber{\csname the#1\endcsname}%   \edef\insertframenumber{\theframenumber}%   \ifthenelse{\equal{#3}{\empty}}{%       \def\insertlistcaption{#2}%   }{%     \def\insertlistcaption{#3}%   }   \def\insertsource{#4}%   \def\insertcaption{#2}%   \ifthenelse{\equal{#1}{figure}}{%       \addtocontents{lof}{\protect\listoffigureformat{\insertcaptionnumber}{\insertlistcaption}{\insertframenumber}{\insertsource}}{}{}%   }{}   \ifthenelse{\equal{#1}{table}}{%       \addtocontents{lot}{\protect\listoftableformat{\insertcaptionnumber}{\insertlistcaption}{\insertframenumber}}{}{}%   }{}   \nobreak\vskip\abovecaptionskip\nobreak   \sbox\@tempboxa{\usebeamertemplate**{caption}}%   \ifdim \wd\@tempboxa &gt;\hsize   \usebeamertemplate**{caption}\par   \else   \global \@minipagefalse   \hb@xt@\hsize{\hfil\box\@tempboxa\hfil}%   \fi   \nobreak\vskip\belowcaptionskip\nobreak% }  \def\listoffigureformat#1#2#3#4{%   \makebox[2ex][r]{#1}%   \hspace{1ex}%   {\usebeamercolor[fg]{bibliography entry author} #2}%   \ifthenelse{\equal{#4}{\empty}}{}{ -- #4}%   \dotfill%   \makebox[2ex][r]{#3}\par% } \def\listoffigures{%   \setlength{\leftskip}{3ex}   \setlength{\parindent}{-3ex}   \@starttoc{lof}% } \def\listoftableformat#1#2#3{\makebox[2ex][r]{#1}\hspace{1ex}#2\dotfill\makebox[2ex][r]{#3}\par} \def\listoftables{%   \setlength{\leftskip}{3ex}   \setlength{\parindent}{-3ex}   \@starttoc{lot}% }  \long\def\@caption#1[#2]#3{   \par\nobreak   \begingroup     \@parboxrestore     \if@minipage       \@setminipage     \fi     \beamer@makecaption{#1}{\ignorespaces #3}{\ignorespaces #3}{\ignorespaces #2}\par\nobreak     \endgroup}  \makeatother Start ubuntu without a desktop environment but start an X application I want to do a small computer just for internet browsing. I dont want to load a desktop environment to keep RAM, CPU and GPU ussage as low as possible. The computer is going to run on a ARM CPU. I dont care with Distro I use, I thought about good old plain Debian. Which words in a title should be capitalized? how is this picture made? Good day guys, i have to something like this, any idea how is this picture made ?  so it looks like negative i did invert it in photoshop but the bright side of his face was blue, so there been negative effect and smting been used to change his face to blue before nagative or smting that changed his face to normal skin color after negative ? what can it be ? what do you guys think ? THANKS ! for help. Atiyah Macdonald, Exercise 8.3. Let $k$ be a field and $A$ a finitely generated $k$-algebra. Prove that the following are equivalent:   (1) $A$ is Artinian.   (2) $A$ is a finite $k$-algebra.   I have a question in the proof of (1$\Rightarrow$2): By using the structure theorem, we may assume that $(A,m)$ is an Artin local ring. Then $A/m$ is a finite algebraic extension of $k$ by . Since $A$ is Artinian, $m$ is the nilradical of $A$ and thus $m^n=0$ for some $n$. Thus we have a chain $A \supseteq m \supseteq m^2 \supseteq \cdots \supseteq m^n=0$. Since $A$ is Noetherian, $m$ is finitely generated and hence each $m^i/m^{i+1}$ is a finite dimensional $A/m$-vector space, hence a finite dimensional $k$-vector space.  But now how can I deduce that $A$ is a finite dimensional $k$-vector space? If it was possible to dig a hole that went from one side of the Earth to the other... ...And you jumped in.  What would happen when you got to the middle of the Earth? Would you gradually slow down, until you got to the middle and once you were in middle would every direction feel like it was up?