Which of these two phrases would be correct in a sentence:- 'To better share' or 'to share better'?
Mark's generosity in this crisis seems to more than make up for his earlier stinginess.   Should those sentences always be avoided, or are there cases where they are valid?
Why don't we include $\rho g h$ in a hydraulic jack below? Consider a hydraulic jack with massless pistons as follows.    The famous equation for this system is   $$ \frac{F_1}{A_1}=\frac{F_2}{A_2} $$  My question is why isn't the equation as follows?  $$ \frac{F_1}{A_1}=\frac{F_2}{A_2} + \rho g h $$  It is based on  my understanding that any points in the same horizontal line have the same pressure.  Could you spot my misconception? Debugging errors of SAGA interpolation algorithms in QGIS Processing? Embed vimeo video into the body field For most OpenID options, it doesn't much matter if you pick the "Sign up" versus the "Log in" tab on the sign in page.  Whether you have an account on the site or not, it just does the right thing. Not so if you are using the Stack Exchange OpenID service:    (Bonus bug: the reCAPTCHA box is a bit too wide for the expanded "Sign up using Stack Exchange" container.)  Since we already have collected an email and password (well, two copies of the password), could we not check to see if they match and automagically log the user into their SE OpenID?  If not, the error needs to be reworded somehow to explain that while the email might have been used to create a Stack Exchange OpenID, that doesn't mean they can't log in with that OpenID to create an account.  Counterintuitively, they need to use the  even if they've never had an account there before.  The  link adds to the confusion since it sends an email that leads off with:     Someone requested an account recovery on The Workplace Stack Exchange for jericson@stackexchange.com, but we don't have an account on this site that matches this email address.   (For people with accounts on other sites and/or Stack Exchange OpenIDs, this paragraph is followed by other instructions that would probably work if followed. By that time I imagine many users are at wit's end.)  To simplify: If a user already has a Stack Exchange OpenID (likely because they have an account on another site) they should be able to use the  to sign up for an account or there should be clear instructions on what to do next if they fail. The company I work for has asked me to attend a training class on the other side of the country.  However my situation is my drivers license expired a few days ago. I do however have a separate printed email stating that the license has been renewed.  This drivers license is my only ID that shows both my name &amp; photo.  Is it possible to be able to board a flight with the expired drivers license and the printed email showing that it was renewed? Is there a test to determine whether solder is leaded or lead-free? Perhaps conductivity/resistance? Existence of area-preserving diffeomorphism between two sets in $\mathbb{R}^2$ Suppose that we have open sets $A, B\subset \mathbb{R}^2$ such that $A$ and $B$ are simply connected and have smooth boundaries. Furthermore, let us assume that $m(A) = m(B) &gt; 0$, where $m$ is the Lebesgue measure on $\mathbb{R}^2$. My question is as follows: when does there exist an area-preserving diffeomorphism between $A$ and $B$? In this context, an area-preserving diffeomorphism between $A$ and $B$ is a is a $C^{\infty}$-diffeomorphism $\phi : A\to B$ such that $m(S) = m(\phi(S))$ for all measurable $S\subseteq A$. If an area-preserving diffeomorphism doesn't always exist between sets $A$ and $B$ as above, are there any extra conditions we can impose on $A$ and $B$ such that there does exist an area-preserving diffeomorphism?  My thoughts thus far are that we always have a $C^{\infty}$-diffeomorphism between $A$ and $B$: this is a consequence of the . It's also obvious to me that if we can deform $A$ linearly to get $B$, then that deformation will be area-preserving. Furthermore, it seems that aside from this case, there's no reason why an area-preserving diffeomorphism should exist. However, I'm having a hard time proving that there necessarily isn't an area-preserving diffeomorphism between $A$ and $B$ if $B$ is not a linear deformation of $A$. Does anybody have any ideas? How can I dual boot Windows and Ubuntu? Although we didn't do any changes, this new error appeared in the GSC Structured Data section:    I don't really get what it means. There are many fields for Schema.org, is homeLocation suddenly a required field? Does that make any sense? I need to calculate the following indefinite integral:  $$I=\int \frac{1}{\cos^3(x)}dx$$  I know what the result is (from Mathematica):  $$I=\tanh^{-1}(\tan(x/2))+(1/2)\sec(x)\tan(x)$$  but I don't know how to integrate it myself. I have been trying some substitutions to no avail.   Equivalently, I need to know how to compute:  $$I=\int \sqrt{1+z^2}dz$$  which follows after making the change of variables $z=\tan x$. Is there a Google Drive client available? Scale Insetted Characters to Plot I need to create file with name is the result of the command in Solaris I need to create only one file with name is the result of the command ls -l | head -2. I can't use environment variables. The filename must contain newline symbols.  I've tried to use touch 'ls -l | head -2', but it hasn't worked. The positive integer solutions for $2^a+3^b=5^c$ What are the positive integer solutions to  the equation     $$2^a + 3^b = 5^c$$    Of course $(1,\space 1, \space 1)$ is a solution. Disable browser 'Save Password' functionality One of the joys of working for a government healthcare agency is having to deal with all of the paranoia around dealing with PHI (Protected Health Information). Don't get me wrong, I'm all for doing everything possible to protect people's personal information (health, financial, surfing habits, etc.), but sometimes people get a little too jumpy.  Case in point: One of our state customers recently found out that the browser provides the handy feature to save your password. We all know that it has been there for a while and is completely optional and is up to the end user to decide whether or not it is a smart decision to use or not. However, there is a bit of an uproar at the moment and we are being demanded to find a way to disable that functionality for our site.  Question: Is there a way for a site to tell the browser not to offer to remember passwords? I've been around web development a long time but don't know that I have come across that before.  Any help is appreciated. How do I start Nautilus as root? I've got a problem with Nautilus in Ubuntu 12.04 LTS.  When I run the command gksu nautilus /, the password ask box appears and I type my super-user password, then the password box disappears and Nautilus is not opened.  When I try to open Nautilus as a normal user in with the command nautilus, the folder is opened.  When I try in terminal   $ sudo nautilus   I got the following error  $ sudo nautilus /  ** (nautilus:8523): WARNING **: Command line `dbus-launch --autolaunch=2c8ce9b7da2257c2609b749700000007 --binary-syntax --close-stderr' exited with non-zero exit status 1: Autolaunch error: X11 initialization failed.\n Could not parse arguments: Cannot open display:   How can I fix this error? I just got this error message for the first time (I was getting this as the response to any request on the SE network for about the last five minutes, until now):     We're sorry...      There are an unusual number of requests coming from this IP address.   To protect our users, we can't process any more requests from this IP   address right now. We'll restore access as quickly as possible, so try   again soon. If you believe you have reached this page in error,   contact us.   As far as I know, I was not spamming SE or participating in DOS attack, and I find it unlikely that any of my office coworkers who share my IP address were doing so either.  Granted, I was pressing F5 a lot. But I've always pressed F5 a lot on SE, and have never gotten this message before. So my question is: Is it possible to get this error message simply by refreshing too much or too often? Or is that message reserved for a truly massive number of requests that are unlikely to be caused by one person refreshing a lot? (In the former case, I can't explain why I've never gotten it before; in the latter case, I can't explain why I just got it now). Implicit Differentiation Help I have to use implicit differentiation to find $\frac{dy}{dx}$ given:  $$x^2 \cos(y) + \sin(2y) = xy$$  I don't even know where to begin, I missed the class where we went over implicit differentiation, and because of that, I am completely stuck.   Thank you everyone.  Edit: I don't know how to make the equation look all nice and whatnot, so sorry about that Is it (theoretically) physically possible to project an image into thin air? Subcaption defaulting to capital letter labels? I seem to be having a unique problem. There are many questions asking about how to change subcaption to a label with capital letters but for me my program is defaulting to capital letters when I would prefer lowercase.  My preamble  \documentclass[12pt,reqno]{amsart} \setlength\parindent{0pt} %no auto indentation for new paragraphs \usepackage{geometry}  \geometry{a4paper}  \usepackage{natbib}  \usepackage[latin1]{inputenc} \usepackage{amsmath, amsthm, amssymb, calc, dsfont}    \usepackage{enumerate} \usepackage{subcaption, caption, graphicx} %figure packages \usepackage{authblk} %author affiliations \usepackage{setspace, lineno} %double spaced etc. options, line numbering  \usepackage{tikz} \usetikzlibrary{shapes,arrows,chains,automata,positioning}   My figure  \begin{figure}[h!]   \centering   \begin{subfigure}[]{0.48\textwidth}           \includegraphics{Figure1.pdf}           \caption{}           \label{FigPractice}    \end{subfigure}    \begin{subfigure}[]{0.48\textwidth}           \includegraphics{Figure2.pdf}           \caption{}           \label{PracticeAge}   \end{subfigure}   \caption{a caption} \end{figure}   I've also tried \renewcommand{\thesubfigure}{\alph{subfigure}}