∗∗ In the paper we will be concerned with the topological structure of the set of solutions of the initial value problem of a semilinear multi-valued system on a closed and convex set. Assuming that the linear part of the system generates a C0-semigroup we show the Rδ-structure of this set under certain natural boundary conditions. Using this result we obtain several criteria for the existence ...

This article is concerned with strong propagations of chaos properties in Moran’s type particle interpretations of continuous time Feynman-Kac formulae. These particle schemes can also be seen as approximating models of simple generalized spatially homogeneous Boltzmann equations. We provide a simple, and original semigroup analysis based on empirical tensor measures combinatorics properties, m...

By a dynamical system (X, T ) we mean the action of the semigroup (Z,+) on a metrizable topological space X induced by a continuous selfmap T : X → X. Let M(X) denote the set of all compatible metrics on the space X. Our main objective is to show that a selfmap T of a compact space X is a Banach contraction relative to some d1 ∈ M(X) if and only if there exists some d2 ∈ M(X) which, regarded as...

This study is originally motivated by the thermal balance equations for the gas and solid interphase heat-transfer for the fast-igniting catalytic converter of automobiles. Instead of solving this problem directly, we proved some results concerning the existence and uniqueness for abstract semilinear initial value problem by means of C0, 1 -semigroup theories on locally convex topological space...

This paper studies FA-presentable structures and gives a complete classification of the finitely generated FA-presentable cancellative semigroups. We show that a finitely generated cancellative semigroup is FA-presentable if and only if it is a subsemigroup of a virtually abelian group.

Let Λ be a sub-semigroup of the reals. We show that the Bass and topological stable ranks of the algebras APΛ = {f ∈ AP : σ(f) ⊆ Λ} of almost periodic functions on the real line and with Bohr spectrum in Λ are infinite whenever the algebraic dimension of the Q-vector space generated by Λ is infinite. This extends Suárez’s result for APR = AP. Also considered are general subalgebras of AP. Intro...

A poset is said to be ω-chain complete if every countable chain in it has a least upper bound. It is known that every partially ordered set has a natural ω-completion. In this paper we study the ω-completion of partially ordered semigroups, and the topological action of such a semigroup on its ω-completion. We show that, for partially ordered semigroups, ω-completion and quotient with respect t...

We show that the quantum family of all maps from a finite space to a finite dimensional compact quantum semigroup has a canonical quantum semigroup structure. Let X be a finite space and Y be a compact space. Then the space F (X,Y ) of all maps from X to Y , is a compact space with compact-open topology. The notion of quantum family of all maps, defined by Woronowicz [8] and Soltan [5], is a no...

In this paper we investigate algebraic and topological properties of McAlister semigroups. We show that for a non-zero cardinal ? the group automorphisms semigroup M? is isomorphic to direct product Sym(?)×Z2, where Sym(?) permutations ?. semigroups admit unique compact Hausdorff topology. Each element semitopological isolated. It follows free inverse over singleton admits only discrete shift-c...

Let X be a separable complete metric space. We characterize completely the innnitesimal generators of semigroups of linear transformations in C b (X), the bounded real-valued continuous functions on X, that are induced by strongly continuous semigroups of continuous transformations in X. In order to do this, C b (X) is equipped with a locally convex topology known as the strict topology. Introd...