Topologically Associating Domains: An invariant framework

Topologically Left Invariant Mean on Dual Semigroup Algebras

TOPOLOGICALLY STATIONARY LOCALLY COMPACT SEMIGROUP AND AMENABILITY

In this paper, we investigate the concept of topological stationary for locally compact semigroups. In [4], T. Mitchell proved that a semigroup S is right stationary if and only if m(S) has a left Invariant mean. In this case, the set of values ?(f) where ? runs over all left invariant means on m(S) coincides with the set of constants in the weak* closed convex hull of right translates of f. Th...

Rapidly evolving in humans topologically associating domains

Rapidly evolving in humans topologically associating domains Gennadi V. Glinsky 2 1 Institute of Engineering in Medicine University of California, San Diego 9500 Gilman Dr. MC 0435 La Jolla, CA 92093-0435, USA Correspondence: [email protected] Web: http://iem.ucsd.edu/people/profiles/guennadi-v-glinskii.html The Stanford University School of Medicine, Medical School Lab Surge Bldg., Room P214,...

Characterizations of amenable hypergroups

Let $K$ be a locally compact hypergroup with left Haar measure and let $L^1(K)$ be the complex Lebesgue space associated with it. Let $L^infty(K)$ be the dual of $L^1(K)$. The purpose of this paper is to present some necessary and sufficient conditions for $L^infty(K)^*$ to have a topologically left invariant mean. Some characterizations of amenable hypergroups are given.

The three-dimensional genome: principles and roles of long-distance interactions.

The linear sequence of eukaryotic genomes is arranged in a specific manner within the three-dimensional nuclear space. Interactions between distant sites partition the genome into domains of highly associating chromatin. Interaction domains are found in many organisms, but their properties and the principles governing their establishment vary between different species. Topologically associating...