Restore the "Downloads" folder in "Places"
How do I restore a Places folder I accidentally deleted in Nautilus?
Downloading large files reliably in PHP How do I clear Bash's cache of paths to executables? What's the frequency of filesystem check on boot? What is the maximum number of times the root filesystem on this computer can be mounted before it is automatically checked? An example of a norm which can't be generated by an inner product I realize that every inner product defined on a vector space can give rise to a norm on that space.  The converse, apparently is not true.  I'd like an example of a norm which no inner product can generate. The square roots of different primes are linearly independent over the field of rationals Prove that for every $a\in A$ $\exists$ $q\in M,s\in A$ s.t. $a=sba+qa$ where $M$ is maximal ideal in $A$. Let A be a commutative ring with unity ring, M be a maximal ideal and $b\notin M$ . Show that there exists $q \in M, s\in A$ such that for every $a \in A$ we have $a=sba+qa$. Show that this is true only when $M$ is a maximal ideal.   Suppose if we take $A=2\mathbb Z$ and $M=4\mathbb Z$, $a=6.$ Then by the given statement $\exists$ $s\in A$, $q\in M$ s.t. $6=6(2s+q)$ $\implies$$s=\frac{1-q}{2}\implies q \text { is odd}$. But $q \in 4\mathbb Z.$  Please someone give some hints. how can solve this.  Thank you.. In the simple linear regression model, $\hat{\beta}$ is the sum of independent normally distributed random variables.  Is it false because in linear regression there is $\beta$ and not $\hat{\beta}$? How do I make protocol foo hostname-aware? This is a  about hostname-awareness and proxying.   I know that some protocols are hostname-aware; that is, when I connect to the HTTP server at www.example.com it knows I want www.example.com's HTTP service, not www.example.net's, even though they are on the same IP address.  How can I do this for protocol foo?  (Temporary note: this question appears pursuant to .) Explanation that air drag is proportional to speed or square speed? A falling object with no initial velocity with mass $m$ is influenced by a gravitational force $g$ and the  (air resistance) which is proportional to the object's speed. By Newton´s laws this can be written as:   $mg-kv=ma$ (for low speeds)  $mg-kv^2=ma$ (for high speeds).    I assume that $k$ is a positive constant that depends on the geometry of the object and the viscosity. But how can one explain that the air resistance is proportional to the velocity? And to the velocity squared in the second equation? How do I execute PHP that is stored in a MySQL database? I'm trying to write a page that calls PHP that's stored in a MySQL database. The page that is stored in the MySQL database contains PHP (and HTML) code which I want to run on page load.  How could I go about doing this? Prerequisites for Algebraic Geometry Is it possible to get into algebraic geometry by just knowing calculus and linear algebra or is this too far of a stretch?  If not could anyone give me a list of book/lecture notes recommendations in chronological order to dive into algebraic geometry with my state of knowledge?  Thanks Is GNU's Java Compiler (GCJ) dead? How do I find a command if I don't know its name? As a Unix beginner, I often find myself wanting to know the name of the command that achieves a particular function I'm after. How can I go about finding out the name of the command, given a description of what it does? I am trying to adjust spacing between entries in LoF and LoT. My code is  \documentclass[11pt,a4paper]{book} \usepackage[english,greek]{babel} \setcounter{secnumdepth}{3} \usepackage[iso-8859-7]{inputenc} \usepackage{kerkis} \usepackage[pdftex]{graphicx} \usepackage[margin=2.8cm]{geometry} \usepackage[Glenn]{fncychap} \usepackage{fancyhdr} %!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! \usepackage{tocloft} \setlength\cftparskip{-15pt}%For ToC works great \setlength\cftbeforesecskip{-8pt}%For ToC works great \setlength\cftbeforesubsecskip{-5pt}%For ToC works great \setlength\cftbeforechapskip{-1pt}%For ToC works great \setlength\cftaftertoctitleskip{-50pt}%For ToC works great  % I also tried \renewcommand instead of \setlength \setlength\cftbeforeloftitleskip{-2cm}%It has no effect in LoF \setlength\cftbeforelottitleskip{-5cm}%It has no effect inLoT  \makeatletter \newcommand*{\tocwithouttitle}{\@starttoc{toc}} \makeatother %-------------------------------------------------------------------------------- \makeatletter \newcommand*{\lofwithouttitle}{\@starttoc{lof}} \makeatother %-------------------------------------------------------------------------------- \makeatletter \newcommand*{\lotwithouttitle}{\@starttoc{lot}} \makeatother %-------------------------------------------------------------------------------- %!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! \renewcommand{\cftsecleader}{\cftdotfill{\cftdotsep}}  \begin{document}  %~~~~~~~~~~~~~~~~~~~~~~~Front-Page~~~~~~~~~~~~~~~~~~~~~~~~~~ \begin{titlepage} Εξώφυλλο \end{titlepage}  \chapter*{\contentsname} \markboth{\MakeUppercase{\contentsname}}{\MakeUppercase{\contentsname}} \tocwithouttitle \addcontentsline{toc}{chapter}{Πειρεχόμενα}  %LoF \chapter*{Κατάλογος σχημάτων}%List of Figures \markboth{\MakeUppercase{Κατάλογος Σχημάτων}}{\MakeUppercase{Κατάλογος Σχημάτων}} %\renewcommand\cftbeforeloftitleskip{5pt} %\renewcommand\cftbeforelottitleskip{5pt} \lofwithouttitle %\setlength\cftbeforefigskip{0pt} \addcontentsline{toc}{chapter}{Κατάλογος Σχημάτων}  %LoT \newpage  \chapter*{Κατάλογος Πινάκων} \markboth{\MakeUppercase{Κατάλογος Πινάκων}}{\MakeUppercase{Κατάλογος Πινάκων}} \lotwithouttitle %\renewcommand\cftbeforeloftitleskip{5pt} %\renewcommand\cftbeforelottitleskip{5pt} \addcontentsline{toc}{chapter}{Κατάλογος Πινάκων}  \newpage \end{document}   While some code is working on ToC(See comments in Preamble) I cannot adjust spacing in LoF/LoT. How can this be achieved? Removing text between two specific strings Prove $ \sin(A+B)\sin(A-B)=\sin^2A-\sin^2B $ How would I verify the following double angle identity. $$ \sin(A+B)\sin(A-B)=\sin^2A-\sin^2B $$ So far I have done this. $$ (\sin A\cos B+\cos A\sin B)(\sin A\cos B-\cos A\sin B)  $$But I am not sure how to proceed. $(z_{2n})_{n\in \mathbb{N}}$ and $(z_{2n+1})_{n\in \mathbb{N}}$ converges to same limit. Show $(z_n)_{n\in \mathbb{N}}$ converges to the same limit. $(z_n)_{n\in \mathbb{N}}$ is a complex valued sequence such that subsequences $(z_{2n})_{n\in \mathbb{N}}$ and $(z_{2n+1})_{n\in \mathbb{N}}$ converges to same limit.  How could I show that the sequence $(z_n)_{n\in \mathbb{N}}$ converges to the same limit using $\epsilon$, $N$ definition?    For every $\epsilon &gt;0$,  $|z_{2n}-l|&lt;\epsilon$ whenever $n&gt;N_1$, and   $|z_{2n+1}-l|&lt;\epsilon$ whenever $n&gt;N_2$.  We want to show that for every $\epsilon &gt;0$, there exists $N$ such that $|z_{n}-l|&lt;\epsilon$ whenever $n&gt;N$. I tried something like  $|z_{n}-l|\le|z_n-z_{2n}|+|z_{2n}-l|$ but wasn't sure what to do next Did Sam's memories transfer to the displacee when he leaped? In the TV show Quantum Leap Sam Beckett would travel history and "right" wrongs, temporarily displacing someone native to that timeline in the process. Would the memories of what Sam did transfer to the person he displaced upon his leaping out, or would they wind up with amnesia for the time Sam was there? How to show that the determinant of the following $(n\times n)$ matrix  $$\begin{pmatrix} 5 &amp; 2 &amp; 0 &amp; 0 &amp; 0 &amp; \cdots &amp; 0 \\ 2 &amp; 5 &amp; 2 &amp; 0 &amp; 0 &amp; \cdots &amp; 0 \\ 0 &amp; 2 &amp; 5 &amp; 2 &amp; 0 &amp; \cdots &amp; 0 \\ \vdots &amp; \vdots&amp; \vdots&amp; \vdots &amp; \vdots &amp; \vdots &amp; \vdots \\ 0 &amp; \cdots &amp; \cdots &amp; 0 &amp; 2 &amp; 5 &amp; 2 \\ 0 &amp; \cdots &amp; \cdots &amp; \cdots &amp; \cdots &amp; 2 &amp; 5 \end{pmatrix}$$  is equal to $\frac13(4^{n+1}-1)$?    More generally:     How does one compute the determinant of the following  (where the three diagonals are constant)?      $$M_n(a,b,c) = \begin{pmatrix} a &amp; b &amp; 0 &amp; 0 &amp; 0 &amp; \cdots &amp; 0 \\ c &amp; a &amp; b &amp; 0 &amp; 0 &amp; \cdots &amp; 0 \\ 0 &amp; c &amp; a &amp; b &amp; 0 &amp; \cdots &amp; 0 \\ \vdots &amp; \vdots&amp; \vdots&amp; \vdots &amp; \vdots&amp; \vdots &amp; \vdots \\ 0 &amp; \cdots &amp; \cdots &amp; 0 &amp; c &amp; a &amp; b \\ 0 &amp; \cdots &amp; \cdots &amp; \cdots &amp; \cdots &amp; c &amp; a \end{pmatrix}$$      Here $a,b,c$ can be taken to be real numbers, or complex numbers.   In other words, the matrix $M_n(a,b,c) = (m_{ij})_{1 \le i,j \le n}$ is such that $$m_{ij} = \begin{cases} a &amp; i = j, \\ b &amp; i = j - 1, \\ c &amp; i = j + 1, \\ 0 &amp; \text{otherwise.} \end{cases}$$  There does not seem to be an easy pattern to use induction: the matrix is not a diagonal  of the type $M = \bigl(\begin{smallmatrix} A &amp; C \\ 0 &amp; B \end{smallmatrix}\bigr)$ (where we could use $\det(M) = \det(A) \det(B)$ for the induction step), and there are no lines or columns with only one nonzero entry, so  gets complicated quickly.  Is there a general pattern that one could use? Or is the answer only known on a case-by-case basis? It's possible to compute the determinant by hand for small $n$:  $$\begin{align} \det(M_1(a,b,c)) &amp; = \begin{vmatrix} a \end{vmatrix} = a  \\ \det(M_2(a,b,c)) &amp; = \begin{vmatrix} a &amp; b \\ c &amp; a \end{vmatrix} = a^2 - bc \\ \det(M_3(a,b,c)) &amp; = \begin{vmatrix} a &amp; b &amp; 0 \\ c &amp; a &amp; b \\ 0 &amp; c &amp; a \end{vmatrix} = a^3 - 2abc \end{align}$$  But there is no readily apparent pattern and the computation becomes very difficult when $n$ gets large. The cow in the field problem (intersecting circular areas) What length of rope should be used to tie a cow to an exterior fence post of a circular field so that the cow can only graze half of the grass within that field?  updated: To be clear: the cow should be tied to a post on the exterior of the field, not a post at the center of the field.