Zobrazeno 1 - 10
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pro vyhledávání: '"Crabb, M."'
Autor:
Crabb, M. C.
We give a direct proof of a result due to Karasev (2008), Karasev-Matschke (2014) and Schnider-Sober\'on (2023). Given $m+1$ Borel probability measures on the space of affine hyperplanes in a real vector space $V$ of dimension $m+1$, there exist a li
Externí odkaz:
http://arxiv.org/abs/2403.08794
Autor:
Crabb, M. C.
Suppose that $f_1,\ldots ,f_m : S(V)\to R$ are $m$ ($\geq 1$) continuous functions defined on the unit sphere in a Euclidean vector space $V$ of dimension $m+1$ satisfying $f_i(-v)=-f_i(v)$ for all $v\in S(V)$. The classical Borsuk-Ulam theorem asser
Externí odkaz:
http://arxiv.org/abs/2401.02209
Autor:
Crabb, M. C.
We establish a stable homotopy-theoretic version of a recent result of Farber and Weinberger on the fibrewise topological complexity of sphere bundles and prove, by closely parallel methods, a similar result for real, complex and quaternionic project
Externí odkaz:
http://arxiv.org/abs/2305.12836
Autor:
Crabb, M. C.
An elementary result in point-set topology is used, with knowledge of the mod $2$ cohomology of real projective spaces, to establish classical results of Lebesgue and Knaster-Kuratowski-Mazurkiewicz, as well as the topological central point theorem o
Externí odkaz:
http://arxiv.org/abs/2302.14492
Autor:
Crabb, M. C.
We describe a connective $K$-theory Borsuk--Ulam/Bourgin--Yang theorem for cyclic groups of order a power of a prime $p$. Consider two finite dimensional complex representations $U$ and $V$ of the cyclic group $Z /p^{k+1}$ of order $p^{k+1}$, where $
Externí odkaz:
http://arxiv.org/abs/2211.08087
Autor:
Crabb, M. C.
Let $G$ be a finite group and $V$ a finite dimensional (non-zero) orthogonal $G$-module such that, for each prime $p$ dividing the order of $G$, the subspace of $V$ fixed by a Sylow $p$-subgroup of $G$ is non-zero and, if the dimension of $V$ is odd,
Externí odkaz:
http://arxiv.org/abs/2208.09637
Autor:
Crabb, M. C.
Let $f: R^{m+1}\to R^{m+2^r}$, where $2^{r-1}\leq m+1 <2^r$, be a continuous map. Improving a recent result of Frick and Harrison, we show that there are $4$ points $x_0,\, x_1,\, y_0,\, y_1$ in $R^m$, which are distinct if $m+1\not=2^{r-1}$, and sat
Externí odkaz:
http://arxiv.org/abs/2207.03131
Autor:
Crabb, M. C.
Let $G$ be a compact Lie group and let $U$ and $V$ be finite-dimensional real $G$-modules with $V^G=0$. A theorem of Marzantowicz, de Mattos and dos Santos estimates the covering dimension of the zero-set of a $G$-map from the unit sphere in $U$ to $
Externí odkaz:
http://arxiv.org/abs/2201.09564
Autor:
Crabb, M. C.
The Intermediate Value Theorem is used to give an elementary proof of a Borsuk-Ulam theorem of Adams, Bush and Frick that, if $f: S^1\to R^{2k+1}$ is a continuous function on the unit circle $S^1$ in $C$ such that $f(-z)=-f(z)$ for all $z\in S^1$, th
Externí odkaz:
http://arxiv.org/abs/2108.10705
For many inverse parameter problems for partial differential equations in which the domain contains only well-separated objects, an asymptotic solution to the forward problem involving 'polarization tensors' exists. These are functions of the size an
Externí odkaz:
http://arxiv.org/abs/2104.08870