Jtdylktuy

up vote 0 down vote favorite I want to show that $displaystyle frac{1}{2pi r}int_{partial B(x,r)}u(y),mathrm{d}s(y)=frac{1}{|S^1|}int_{S^1}u(x+rtheta),mathrm{d}s(theta)$ This is essentially a shift and dilation from (or) to the unit sphere. I defined a diffeomorphism $Phicolon S^1rightarrowpartial B(x,r)subsetmathbb{R}^2\ thetamapsto x+rtheta$ where $theta$ is a point on $S^1$ . It follows that $|det(DPhi(S^1))|= r$ and therefore $displaystyle frac{1}{2pi r}int_{partial B(x,r)}u(y),mathrm{d}s(y)=frac{1}{2pi r}int_{S^1}u(Phi(S^1))r,mathrm{d}s(theta)=frac{1}{2pi(=|S^1|)}int_{S^1}u(x+rtheta),mathrm{d}s(theta)$ Is this correct? If yes, I appreciate to have a look at solutions using a different approach. integration lebesgue-integral integral-transforms ...

up vote 0 down vote favorite Is it possible to set up a window (Usually games) to run in full screen, without always being on top? My end goal is I want to be able to have a specific window painted over the game, but the task bars get in the way, unless the game is always above. If the game is always above, and has focus, then it draws over the overlay. kde kde-plasma-5 share | improve this question asked Nov 21 at 12:16 Ryan The Leach 110 6 ...