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Q&A for professional mathematicians
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I hope everyone is doing well. Let $K \subset \mathbb{R}^n$ be a centrally symmetric convex body $(K = -K)$. Denote by $K \mid H$ the orthogonal projection of $K$ onto $H$, where $H$ is an $n - 1$
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0 days
Possible contradiction between Federer (1956) and Hansen (1983) on $\pi_1(M_0(S^...
I am trying to understand an apparent contradiction in the literature about degree-zero component $M_0(T_1,S^2)$ of the space of free maps from the torus $S^1\times S^1$ to the sphere $S^2$.
In Herbert Federer's 1956 paper "A Study of Function Spaces by Spectral Sequences" (top of page 358), he states that $\pi_1((S^2)^{S^1\times S^1}),w)$ is non-abelian, where $w$ is a constant map. Hansen also appears to be aware of this result: in his... -
0 days
Proving there is no entire $f:\mathbb{C}→\mathbb{C}$ with $\text{Re}(f(z))\text{...
To show that there is no entire function $f:\mathbb{C}\to\mathbb{C}$ such that $\text{Re}(f(z))\text{Re}(f(w))<0$ or $\text{Im}(f(z))\text{Im}(f(w))<0$ whenever $|z-w|=1$, one can use the fact that $\chi(\mathbb{R}^2)>4$ (see here).
Is there a complex analytic proof of this fact?... -
0 days
Integration Over Feynman Parameters Arising from an Expectation of a Rational Fu...
Let $\mathbf a,\mathbf b\in\mathbb R^{n}$ be generic vectors, and $(s,t)\in\left[0,1\right]^2$. Define
$$A=|\mathbf a-\mathbf b|^{2},\qquad B(s)=|s\mathbf a+(1-s)\mathbf b|^{2},\qquad C=\sqrt{\|\mathbf{a}\|^2\|\mathbf{b}\|^2-(\mathbf{a}\cdot\mathbf{b})^2},$$... -
6 months
Additively idempotent semirings that are not lattices
I am looking for examples of additively idempotent semirings (which are always join semilattices) that do not have an underlying lattice structure, i.e. either meets do not exist or exist outside the semiring considered. It is certain that any such example...
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