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If we fix a finite group $ G$ , there are two different useful homotopy theories on the set of $ G$ -equivariant topological spaces (which are CW complexes, say). One, the “weak” homotopy theory, is given by inverting all maps of spaces $ X\to X’$ which are homotopy equivalences, and it produces a homotopyRead more

My question is to get an idea of state of art in bifurcation analysis for the following class of problems : Consider the following nonlinear coupled-ODE system over a time-interval $ [0,1]$ : $ \dot{x}=N_1(x,y;a)\ \dot{y}=N_2(x,y;a)\ (x,y)\in\mathbb{R}^{2N}$ , with boundary conditions given as $ x(t=0)=x0, y(t=1)=y0$ . The parameter that we vary (to explore bifurcations)Read more

I was going over P. Scholze’s paper on $ p$ -adic Hodge Theory for rigid analytic varieties. Corollary 6.13 says that the “$ B_{\rm dR}$ -version” of the Poincaré Lemma for de Rham-étale cohomology follows directly from Proposition 6.10, for smooth and proper rigid analytic varieties. Prop. 6.10 is a description of the sheaf $Read more

Is it somehow related to the unofficial social contract that mafia maintains? How is all of it related to the game theory’s payoffs matrix? How does that justify the existence of the syndicate from the scientific point of view?Read more

I am very new to bitcoin and I am trying to understand a bit about mining theory. I do not dispute the convention of using GPU based computation for bitcoin mining, but rather I’m curious about why they outperform co-processors like this for mining. Maybe a nuanced discussion of a few of the various trade-offsRead more

I thinks there is some problem related to the solution of a 2 order differential equation given by Sturm-Liouville system which is nontrivial. It is well-know that the power of Sturm-Liouville theory see wiki https://en.wikipedia.org/wiki/Sturm–Liouville_theory, is due to it is some kind of “spectral decomposition” in the solution space. Two kind of problem is interesting, one is theRead more

I would like to ask for the paper of Kato: A generalization of local class field theory by using K -groups I, J. Fac. Sci. Univ. Tokyo Sec. IA 26 No.2, 1979, 303–376. I could not find it. Could anyone help? Thanks.Read more

I am aware of the strict policy about offtopic and opinion-based questions here on MO. I am ok with being redirected towards academia, or another stackexchange, but please, notice that my question is likely to be properly answered by mathematicians only: I kindly ask you at least the time to collect a few answers. InRead more

I study some definitions of accessible category (see 1) and the applications of that notions; my question: exist a notion of accessible category in therm of enriched category theory? (in case of exist, what uses have?)Read more

I’d like to begin by noting that I’m a chemist by training, not a mathematician. I know as much applied math as a chemist needs to know (through basic calculus), and beyond that I have only bits and pieces as an interested layman. I’m trying to scratch a curiosity itch. I was thinking about aRead more