PHP - removing invisible characters pre-MySQL insert
UTF-8 all the way through
In the US, it is common to use the idiomatic expression "knock on wood" to keep "a good thing going."  Is it the same in the UK, or do they use a different idiomatic expression? is it possible to skip immediately preceding time points? So that, if, for example, you are using model order 2, that is, two time points, but not the two immediately previous time points, but rather, say for example, skipping 2 points, and then using those two points.  So, e.g., it would be y=x(t-3) + x(t-4). How to prove that $A_5$ has no subgroup of order 30? I would like to create a md5 checksum list for all files in a directory.  I want to cat filename | md5sum &gt; ouptput.txt. I want to do this in 1 step for all files in my directory.   Any assistance would be great. \documentclass[]{phstyle} \usepackage{latexsym,amsfonts,amssymb, undertilde} \usepackage[fleqn]{amsmath} \usepackage{makeidx}  %Preamble  \numberwithin{equation}{chapter} %\renewcommand{\theequation}{\thesection.\arabic{equation}}  \begin{document}  %\include{chapI}   these 2 lines are because the chapters are different tex files  %\include{chap1}  \renewcommand{\thechapter}{\Roman{chapter}}  %\setcounter{chapter}{0} %\renewcommand{\theequation}{\thechapter.\arabic{equation}}  \chapter{Introduction}  \section{Chap I Section1}  \begin{equation} this is equation I.1 \end{equation}  \begin{equation} this is equation I.2 \end{equation}  \section{Chap I Section2}  \begin{equation} this is equation I.3 \end{equation}  \chapter{Chapter 1}  \section{Chap 1 Section 1}  \begin{equation} this is equation 1.1.1 \end{equation}  \begin{equation} this is equation 1.1.2 \end{equation}  \end{document}     I have been typing Chapters 1-5 that contain sections and subsections and equations. The equations were numbered globally, i.e. if I had 3 equations in section 1 of Chap 1, they were numbered 1.1.1, 1.1.2, 1.1.3 and for Section 2, the equations were 1.2.4, 1.2.5, etc.  Recently I had to change Chap 1 and everything in it to Chapter I (roman number) and Chap 2 were renumbered to Chap 1, etc.  My problem is that LaTeX started numbering the equations in Chap I (the other chapters did not have this problem) according to the sections and not globally anymore. That is, the 3 equations in Chap I were I.1, I.2, I.3, and the equations in the second section of Chap I became I.1, I.2, etc instead of I.4, I.5, etc  I needed the prefix to be the chapter and not the sections. I don't understand why there is a change. I have never used \numberwithin in my book  Here are some of my codes  \documentclass[]{phstyle} \usepackage{latexsym,amsfonts,amssymb, undertilde} \usepackage[fleqn]{amsmath}   for the equation numbering in Chap I  \renewcommand{\thechapter}{\Roman{chapter}} \renewcommand{\theequation}{\thechapter.\arabic{equation}} **   Previously when Chap I was Chap 1, ** was  \renewcommand{\theequation}{\thesection.\arabic{equation}}   I have also tried the line below but it didn't work  \renewcommand{\theequation}{I.\arabic{equation}}   Thank you in advance Is there an idiom for someone who gets what he deserved? Like someone receiving punishment for his evil deeds or someone getting awarded for his good deeds? Word/phrase for the activity of hiding mistakes What word/phrase can I use to describe the activity of hiding a stupid mistake/incident, such as quickly cleaning up tea spilled by accident before anyone could notice? Newline in a WPF-label? How can I add a newline in the text of a label in WPF such as the following?  &lt;Label&gt;Lorem    ipsum&lt;/Label&gt; How variance is defined? The variance of a random variable $X$ is defined as $E[(x-\mu )^2]$. Why can't it be defined as $E[|x-\mu |]$. i.e., What is the basic idea behind this definition. Thank you. Random matrix theory impact on covariance matrix analysis Forcing series convergence Unsealed meat in freezer Below is my situation:  Is completely (vacuum) sealing leftover meat in the freezer absolutely necessary? I would always just use a plastic bag to cover the meat and fold it around couple of times so it's almost as good as sealed (usually grocery plastic bag is much bigger than the piece of meat) and have never had a problem with it last a decade or so I have been cooking.  But recently I got this new roommate who insists on me using special small plastic bags with sealers to use and he is being very paranoid, obsessive about it.  So my question is: Is he right? Is my Geoserver "Direct WMS Integration" working? Command with percent symbols not running in crontab The following crontab does not work:  # TEST LINE DOES DOT RUN */1 * * * * /bin/echo 'test '`/bin/date +%Y-%m-%d` &gt;&gt; /tmp/test   I also tried starting it with:  SHELL=/bin/bash   Update: I thought the backtick characters ` were the villains, but as the answer below clarifies the percentage % was the culprit! On finding polynomials that approximate a function and its derivative (extensions of Stone-Weierstrass?) The Stone-Weierstrass Theorem tells us that we can approximate any continuous $f:\mathbb{R}^n\to\mathbb{R}$ arbitrary well on a compact subset of $\mathbb{R}^n$ by some polynomial. Suppose that $f$ is continuously differentiable, under what conditions can we guarantee we can find a polynomial $p$ such that $p$ approximates arbitrarily well $f$ and the partial derivatives approximate of $p$ arbitrarily well those of $f$ (on a compact subset of $\mathbb{R}^n$)? References are welcome. See below for my (probably naive) approach to the question.    It is straightforward to find conditions if $n=1$: Let $K:=[a,b]\subseteq\mathbb{R}$ and let $K_+$ denote some open cover of $K$. Suppose that $f:K_+\to\mathbb{R}$ is continuously differentiable and let $f'$ denote its derivative. Then, by Weierstrass's approximation Theorem we have that there exists a polynomial $q$ such that   $$||f'(x)-q(x)||\leq \varepsilon$$  for all $x\in K$. Choose some $y\in K$. For any $x\in K$ define  $$p(x):=f(y)+\int_y^xq(t)dt.\quad\quad(*)$$  By the Fundamental Theorem of calculus we have that $p'=q$. So for any $x\in K$  $$||f(x)-p(x)||=\left|\left|\int_y^x (f'(t)-q(t))dt\right|\right|\leq \int_y^x ||f'(t)-q(t)||dt\leq \varepsilon||x-y||\leq \varepsilon (a-b).$$  However, the above argument doesn't work in higher dimensions because the analogue of $(*)$ does not imply that $\nabla p = q$ (since not every vector of polynomials spans a gradient field). Can anyone suggest a way around this? That is, a way to to show that for continuously differentiable $f:\mathbb{R}^n\to\mathbb{R}$ and for any $\varepsilon&gt;0$, we can always find a polynomial $p$ such that   $$||f(x)-p(x)||+||\nabla f(x)-\nabla p(x)||\leq \varepsilon$$  for all $x$ in some compact set $K$? Feel free to add extra conditions on $K$, if it makes life easier. Is it possible to check out subdirectories of a repository in Git?  Imagine I am setting up a new WordPress installation. I will create two new directories for my plugin and theme customization:   wordpress/wp-content/plugins/myplugins/  wordpress/wp-content/themes/mytheme/   I want to maintain these directories via Git. In Subversion, I would accomplish this by having trunk/myplugins/ and trunk/mytheme/ directories and checking out subdirectories. Does Git have a way to accomplish the same task using a single repository?  I could just be missing the boat on some Git paradigm, as a long time SVN user with little exposure to Git.  Edit:  storing different content is an interesting way to handle this. How to sample a function non-uniformly? See this example code:  \documentclass{article}  \usepackage{pgfplots} \pgfplotsset{compat=1.10} \begin{document}   \begin{tikzpicture}     \begin{axis}[                  xmin=-0.1,                  xmax=1.1,                  ymin=-1.1,                  ymax=1.1,                  domain=0:1,                  samples=30                 ]       \addplot[blue] {sqrt(x)};       \addplot[purple] {-sqrt(x)};     \end{axis}   \end{tikzpicture} \end{document}   The result appears acceptable far from zero, but near zero it's too much undersampled:    Increasing samples value makes the plot nice, but it considerably slows down processing. As a workaround I could just plot the inverse in a parametric plot (i.e. (y^2,y)), but in my actual code it'd require quite a bit of additional work.  Is there a way to provide a custom sampling function or specify different density of samples in different parts of the domain? How far does a rogue move when dashing twice using Cunning Action? A rogue receives a bonus Cunning Action, and one option is to Dash. My understanding is a Dash allows a player to move up to twice his speed for his turn.  If a rogue is using a regular action to Dash (hence, is already dashing) can he also use his cunning action as a bonus to Dash again — effectively moving 4 times normal speed in a turn? I look today on a few fresh question, and the view count was 0. Even after I refreshed the page a few time. This is definitely a bug, since the question isn't mine.  Also I don't think the all page was cached, since that the DateTime mark was change every reload.  But maybe the SQL result is cached. Find $a$ such that $(x+a)(x+1991)+1=(x+b)(x+c)$ with $a,b,c\in\Bbb Z$ Find all integer values of $a$ such that the quadratic expression $(x+a)(x+1991)+1$ can be factored as a product $(x+b)(x+c)$ where b and c are integers.   I tried to do it by comparing the two expressions but I can't proceed.