"What have you done since you got up this morning?" or "What have you been doing since you got up this morning?"
Dilemma: Present Perfect Or Perfect Continuous?
How do I clone a generic list in C#? Can you wait to add optional damage dice that apply on a hit (such as Divine Smite) until after seeing if the roll is a critical? I know this issue has been addressed before with different software, but how do I do it with Shapely?  I have a polygon with a very small gap on the interior of the shape:    Here is a close up:    The polygon is valid so I can't use the buffer trick, and simplifying the polygon also doesn't work. Multiple monitors, multiple workspaces? I connected my laptop to my LCD. Using the laptop display hotkey I can switch between different modes - only laptop monitor on, only LCD monitor on, both on and display the same view, both on and the desktop is stretched (divided).  But, I'm looking for something else - I would like to have two workspaces, one visible on the laptop monitor and the other on the LCD.  Is that possible? Google App Engine: Is it possible to do a Gql LIKE query? Homotopy equivalence of universal cover As part of am exam question (Q21F ), I'm trying to prove that if $X$ and $Y$ are path-connected, locally path-connected spaces with universal covers $\widetilde{X}$ and $\widetilde{Y}$, respectively, then if $X \simeq Y$ then $\widetilde{X} \simeq \widetilde{Y}$.  My attempt might be correct, but it seems too complicated and amongst the jumble I may have made some incorrect assumptions. So what I'm looking for is (a) verification or correction; and (b) ideas as to how I could simplify my argument.    My argument:  Let $p:\widetilde{X} \to X$ and $q:\widetilde{Y} \to Y$ be the covering maps, and let $X \overset{f}{\underset{g}{\leftrightarrows}} Y$ be a homotopy equivalence.  Fix a point $\widetilde{x} \in \widetilde{X}$, let $x=p(x) \in X$ and $y=f(x) \in Y$, and fix $\widetilde{y} \in q^{-1}(\{y\}) \subseteq \widetilde{Y}$. Also let $x' = g(y) \in X$ and fix $\widetilde{x'} \in p^{-1}(\{x'\}) \subseteq \widetilde{X}$.  Define a map $\widetilde{f} : \widetilde{X} \to \widetilde{Y}$ as follows. For $\widetilde{z} \in \widetilde{X}$ let $\widetilde{u}:[0,1] \to \widetilde{X}$ be a path from $\widetilde{x}$ to $\widetilde{z}$. Let $z=p(z)$ so that $u=p\widetilde{u}$ is a path in $X$ from $x$ to $z$. Let $v=fu$, so that $v$ is a path in $Y$ from $y$ to $f(z)$. Lift $v$ to a path $\widetilde{v}$ in $\widetilde{Y}$ with $\widetilde{v}(0) = \widetilde{y}$. Define $\widetilde{f}(\widetilde{z}) = \widetilde{v}(1)$.  Notice that $q\widetilde{v}=v$ so that $q\widetilde{f} = fp$.  Define $\widetilde{g}:Y \to X$ analogously: For $\widetilde{z} \in \widetilde{Y}$ let $\widetilde{a}:[0,1] \to \widetilde{Y}$ be a path from $\widetilde{y}$ to $\widetilde{z}$. Let $z=q(z)$ so that $a=q\widetilde{a}$ is a path in $Y$ from $y$ to $z$. Let $b=fa$, so that $b$ is a path in $X$ from $x'$ to $g(z)$. Lift $b$ to a path $\widetilde{b}$ in $\widetilde{X}$ with $\widetilde{b}(0) = \widetilde{x'}$. Define $\widetilde{g}(\widetilde{z}) = \widetilde{b}(1)$.  Likewise, notice that $p\widetilde{g}=gq$.  Claim: $\widetilde{X} \overset{\widetilde{f}}{\underset{\widetilde{g}}{\leftrightarrows}} \widetilde{Y}$ is a homotopy equivalence.  We have $p\widetilde{g}\widetilde{f} = gq\widetilde{f}=gfp \simeq p$ and $q\widetilde{f}\widetilde{g} = fp\widetilde{g} = fgq \simeq q$.  This shows that $\widetilde{g}\widetilde{f}$ and $\widetilde{f}\widetilde{g}$ are covering translations (deck transformations) and are therefore homotopic to the respective identity maps. So we have a homotopy equivalence.    Any comments would be appreciated. 16.04 Japanese Text Input not working How do I delete a file whose name begins with "-" (hyphen a.k.a. dash or minus)? Name "Chapter" is not showed in the table of the content Been trying to this line to parse for a good 20mins, but all attempts have failed:  \beta = $-$0.84, t = $-$2.09, P = 0.04   Could anyone tell me why I'm getting a Missing $ inserted error here? Suspend process without killing it So I've got a persistent program running in the background. Killing it just causes it to restart with a different PID. I'd like to suspend it (put it to sleep without actually killing it). Does kill -9 do this? If not, how should this be done? Objective-C - When to use 'self' Passing HTML to template using Flask/Jinja2 Could someone help me prove that given a finite measure space $(X, \mathcal{M}, \sigma)$ and a measurable function $f:X\to\mathbb{R}$ in $L^\infty$ and some $L^q$, $\displaystyle\lim_{p\to\infty}\|f\|_p=\|f\|_\infty$?    I don't know where to start. About number truncation of ticks display in ListPlot Place each foot on a scale: can you add the two to find your weight? I frequent a blog from a British psychologist, and every Friday he likes to pose an interesting puzzle or riddle. The Monday after that he posts the answer. They're good fun, and IANAP but  made my it-might-not-be-quite-as-simple-as-that detector go off.  My question boils down to this: let's say I have two identical scales, and I stand on the scales with one foot on each scale. The scales read W1 and W2. Does my weight equal W1 + W2? EDIT:  My question was poorly worded.   I wasn't asking about showing $\ln(1+x) &gt; \frac{2x}{2+x}$ for $x&gt;0$.   What I wanted to know is why the lower bound provided by $ \frac{2x}{2+x}$ was so tight for small positive values of $x$. This is addressed in robjohn's answer. I have this weird object (vascular tree) which is empty inside, but closed from the top and the bottom:  However, it is empty inside, which makes me unable to use boolean on a bigger object (I want to make a hole in an object through which this object will go through). So I thought I should fill it and then try to boolean. But, how do I fill it?  Thank you sincerely. Converting GeoPDF to vector format like CAD or shapefile? I want to convert a GeoPDF that has vectors entity in it to a vector format and preserve the real coordinates of these vectors. The GeoPDF has been exported from ArcMap and has layers in it.  I have try GDAL, but it rasterize the PDF before exporting it. Which is not good for me. Also I don't want a solution that would convert this image back to vectors, too complicated for the data I have.  Is someone aware of any tool that can do that? The resulting format can be a CAD file or a shapefile or anything that is a vector format. If $A + A^t = 2I$ then $\det(A) \geq 1$