Hans Lundmark
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 5h revised Solution for this question (Precalc) edited tags 1d comment Use the persistence theory to find a set of sufficient conditions for two species competitive ODE system Sufficient for what...? 1d answered An example of non euclidean inner product 2d revised Theory of 4 colors edited tags 2d comment How can I integrate $\sqrt{1-x^2/a^2-y^2/b^2} dx dy$ in the ellipse? Let $u=x/a$ and $v=y/b$, then change to polar coordinates. 2d revised Is CHESS a-game of courtroom interest or conflict technique? edited tags 2d comment Idea behind Lyapunov functions? Did you try reading the proof of Lyapunov's theorem somewhere? (That should answer your question, since the proof is precisely what explains how the conclusions follow from the hypotheses.) If so, was there anything particular that you got stuck on? As it stands, this question is rather vague and difficult to answer... 2d comment What it means for a Jacobian determinant to be zero in the context of PDEs and their solution? What book? Solution of which equation? There's not enough context in this question. Apr23 comment Interval arithmetic - faster version You're welcome! (Note that in interval computations it might be more common to use closed intervals $[a,b]$ where the endpoints are included: $a \le x \le b$. And the two sign cases should perhaps be nonnegative/negative rather than positive/negative, so that you also take into account that one or both of the endpoints can be zero.) Apr23 comment Interval arithmetic - faster version An interval $(a,b)$ is a set of the form $a < x < b$, so you need to have \$a