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MathOverflow : Recent Questions and Answers (Page 42)

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Can a fixed finite-length straightedge and finite-size compass still construct all constructible points in the plane?

I am hoping that the brilliant MathOverflow geometers can help me out. Question 1. Suppose that I have a fixed finite-length straightedge and fixed finite-size compass. Can I still construct...

Asked on 11/17/2020 by Joel David Hamkins

2 answer

Genus $0$ algebraic curves integral points decidable?

It is known there is an explicit algebraic variety in $mathbb Z[x_1,dots,x_t]$ a bounded $t>2$ whose integral zero-set is non-empty is undecidable.If the variety has genus $0$...

Asked on 11/14/2020 by 1..

0 answer

Interlocking (weak) factorization systems

I'm interested in instances of the following data:$C$ is a (possibly higher) category;$(L,M)$ is a weak factorization system (wfs) on $C$;$(M,R)$ is a...

Asked on 11/09/2020 by Tim Campion

0 answer

Monte Carlo simulations

I was wondering what were the models of statistical physics that are still considered difficult/slow to simulate (exactly, or approximately) with the current technology of Monte Carlo approaches. I can...

Asked on 11/07/2020 by Alekk

3 answer

Measurable total order

Under what conditions on a metric space $X$, equipped with the Borel $sigma$-algebra, does there exist a measurable total ordering of the elements of $X$? By "measurable...

Asked on 11/05/2020 by Aryeh Kontorovich

1 answer

Recover approximate monotonicity of induced norms

Let $A$ some square matrix with real entries.Take any norm $|cdot|$ consistent with a vector norm. Gelfand's formula tells us that $rho(A) = lim_{n rightarrow infty}...

Asked on 11/03/2020 by ippiki-ookami

1 answer

Geodesics and potential function

I try to assemble concepts of differential geometry for my own comprehension of the subject. I understand a manifold is a higher dimensional surface. It has a metric which perform...

Asked on 10/29/2020 by Bruno Peixoto

0 answer

Independent increments for the Brownian motion on a Riemannian manifold

In am not a probabilist, but I must do some stochastic-flavoured work on a connected Riemannian manifold $M$. A nice thing about the Brownian motion on $mathbb R^n$...

Asked on 10/26/2020 by Alex M.

0 answer

Multivariate monotonic function

Let $f(x_1, dots, x_n)$ be a real function on the $n$-dimensional unit cube (that is, mapping $[0,1]^n mapsto mathbb{R}$). Assume furthermore that $f$ is monotonic in every coordinate, and that...

Asked on 10/25/2020 by Kurisuto Asutora

2 answer

adding one point from the Stone-Cech compactification

Let $X$ be any non-compact Tychonoff space and $beta X$ be its Stone-Čech compactification.The following fact is known: any point $p$ from the reminder $beta...

Asked on 10/18/2020 by Arkady

0 answer

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