parametric - Curve on a basketball - Mathematics Stack Exchange
Apr 19, 2014 · The sewing pattern on a basketball is composed of two great circles and a single curve that intersects each great circle twice. Does this curve have a name? Are there any parametric descriptions of the curve? The same question can apply to the sewing pattern on a tennis ball. Answers about why this sewing pattern came to be used are also welcome.
Heat equation $u_t=u_{xx},u_x(t,0)=0,u(0,x)=e^{-x^2}$
Aug 28, 2018 · This solution requires you to know the Green's function on the standard heat equation $$ u_t = Du_{xx} $$ which is $$ \mathcal G(x,x') = \frac{1}{\sqrt{4\pi D t}}e^{-\frac{(x-x')^2}{4Dt}} \tag 2 $$ From this you can easily find the solution by integration $$ u(x,t) = \int_{\mathbb R}\mathcal G(x,x')u(x',0)\,\mathbb d x' \tag 3 $$
The backwards heat equation is not well posed
Please see the following papers where (easy to check) necessary and sufficient conditions for the solvability of the Cauchy problem of the backward heat equation are found. Similar condition also works in case of bounded domains with Dirichlet boundary condition. arXiv:1905.05845; A note on time analyticity for ancient solutions of the heat ...
heat equation - Ill-posedness and well-posedness - Mathematics …
Feb 28, 2016 · The backwards heat equation does posses a unique solution for a common set up of boundary and initial conditions. It can however be shown that the solution, which eventually explodes, does not depend on the initial conditions anymore. For further detail you can check the ill-posedness of the backward heat equation.
16 teams enter a competition - Mathematics Stack Exchange
Sep 13, 2015 · 16 teams enter a competition. They are divided into four pools (A, B, C and D) of four teams each. Every team plays one match against the other teams in its pool.
Backwards Heat Equation $ u_{t} = -\\lambda^2 u_{xx}$
May 16, 2015 · I am pretty sure that for backwards heat equation the uniqueness of solution holds, but the stability fails. $\endgroup$ – Vlad Commented May 16, 2015 at 1:14
general topology - Are hereditarily connected spaces and …
Nov 19, 2024 · $\begingroup$ I found a counterexample for ultraconnected spaces. It ended up being a quite long proof, and I've already nearly finished typing it up before my browser suddenly crashed...
Percentages, discrete or continuous? - Mathematics Stack Exchange
May 7, 2016 · I have this question I can't figure out. A basketball player starts a game. During the first period of the game, the success rate of his shots is less than $80$%. At the end of the game, his success rate is over $80$%. Is it certain, that at some point during the game, his success rate was exactly $80$% ?
Why is gradient the direction of steepest ascent?
Other answers are correct in using the directional derivative to show that the gradient is the direction of steepest ascent/descent.
Why is $111111111 \\times 111111111 = 12345678987654321$
Feb 16, 2018 · I was looking around on the internet until I stumbled upon this equation. $$111111111\\times111111111 = 12345678987654321$$ How does this actually work? It is quite amazing how the number ascend and