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Search: All articles in the CJM digital archive with keyword stability

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1. CJM Online first

Ashraf, Samia; Azam, Haniya; Berceanu, Barbu
 Representation stability of power sets and square free polynomials The symmetric group $\mathcal{S}_n$ acts on the power set $\mathcal{P}(n)$ and also on the set of square free polynomials in $n$ variables. These two related representations are analyzed from the stability point of view. An application is given for the action of the symmetric group on the cohomology of the pure braid group. Keywords:symmetric group modules, square free polynomials, representation stability, Arnold algebraCategories:20C30, 13A50, 20F36, 55R80

2. CJM 2012 (vol 65 pp. 222)

Sauer, N. W.
 Distance Sets of Urysohn Metric Spaces A metric space $\mathrm{M}=(M;\operatorname{d})$ is {\em homogeneous} if for every isometry $f$ of a finite subspace of $\mathrm{M}$ to a subspace of $\mathrm{M}$ there exists an isometry of $\mathrm{M}$ onto $\mathrm{M}$ extending $f$. The space $\mathrm{M}$ is {\em universal} if it isometrically embeds every finite metric space $\mathrm{F}$ with $\operatorname{dist}(\mathrm{F})\subseteq \operatorname{dist}(\mathrm{M})$. (With $\operatorname{dist}(\mathrm{M})$ being the set of distances between points in $\mathrm{M}$.) A metric space $\boldsymbol{U}$ is an {\em Urysohn} metric space if it is homogeneous, universal, separable and complete. (It is not difficult to deduce that an Urysohn metric space $\boldsymbol{U}$ isometrically embeds every separable metric space $\mathrm{M}$ with $\operatorname{dist}(\mathrm{M})\subseteq \operatorname{dist}(\boldsymbol{U})$.) The main results are: (1) A characterization of the sets $\operatorname{dist}(\boldsymbol{U})$ for Urysohn metric spaces $\boldsymbol{U}$. (2) If $R$ is the distance set of an Urysohn metric space and $\mathrm{M}$ and $\mathrm{N}$ are two metric spaces, of any cardinality with distances in $R$, then they amalgamate disjointly to a metric space with distances in $R$. (3) The completion of every homogeneous, universal, separable metric space $\mathrm{M}$ is homogeneous. Keywords:partitions of metric spaces, Ramsey theory, metric geometry, Urysohn metric space, oscillation stabilityCategories:03E02, 22F05, 05C55, 05D10, 22A05, 51F99

3. CJM 2007 (vol 59 pp. 1245)

Chen, Qun; Zhou, Zhen-Rong
 On Gap Properties and Instabilities of $p$-Yang--Mills Fields We consider the $p$-Yang--Mills functional $(p\geq 2)$ defined as $\YM_p(\nabla):=\frac 1 p \int_M \|\rn\|^p$. We call critical points of $\YM_p(\cdot)$ the $p$-Yang--Mills connections, and the associated curvature $\rn$ the $p$-Yang--Mills fields. In this paper, we prove gap properties and instability theorems for $p$-Yang--Mills fields over submanifolds in $\mathbb{R}^{n+k}$ and $\mathbb{S}^{n+k}$. Keywords:$p$-Yang--Mills field, gap property, instability, submanifoldCategories:58E15, 53C05

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