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 $$ u(x,t) = \int_{\mathbb R}\mathcal G(x,x')u(x',0)\,\mathbb d x' \tag 3 $$
How does ESPN calculate the probability of a team winning a game?
Aug 10, 2020 · In this basketball win probability prediction competition which was funded by Google, you can see how different people build different prediction models on the same data. By the way if you are able to come up with a good algorithm for even one sport, you can make millions in the sports betting industry. Here is a another practical working ...
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 ...
Difference between "≈", "≃", and "≅" - Mathematics Stack Exchange
In my work "=" is the identity of a number so it states an equivalence. 1=1, 2x=10 ie x =5. The approximation sign "≈" I use for decimal approximations with tilde "~" being a rougher approximation.
calculus - What's the formula to work out number of fixtures for …
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How to find a general sum formula for the series: …
Nov 17, 2014 · $5+55+555+5555+55555+\cdots n$ terms, Sum of finite seqence of this pattern can be obtained by re-arranging this into geometric sequence.
partial differential equations - Intuitive explanation of Duhamel's ...
Coming back to the physical interpretation: you see that Wikipedia is being a bit imprecise: it is not the adding up of solutions that matters really; what drives Duhamel's principle is the fact that you are adding only a limited number of solutions.
Smooth Urysohn lemma - Mathematics Stack Exchange
Apr 28, 2024 · From topology I know the Urysohn lemma. My question is if there is some sort of Urysohn lemma for smooth manifolds.
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.