We give a sufficiently detailed account on the construction of marked Gibbs measures in the high temperature and low fugacity regime. This is proved for a wide class of underlying spaces and potentials such that stability and integrability conditions are satisfied. That is, for state space we take a locally compact separable metric space X and a separable metric space S for the mark space. This...

The problems of minimal state-space realization for a three-dimensional (3-D) separable-denominator digital filter and analysis of l2-sensitivity for the realized 3-D state-space model are investigated. First, a 3-D transfer function with separable denominator is expressed as a cascade connection of three one-dimensional (1D) transfer functions by applying a minimal decomposition technique. Nex...

We will present the problem of the Central Limit Theorem for random upper semicontinuous functions. Let us begin by providing the context for that problem. We need to present the space in which we will work, and specify the notions of random element of that space, convergence and the operations used to average random elements. Then we will make some historical remarks on limit theorems in this ...

Let (A, α) and (B, β) be C*-dynamical systems and assume that A is a separable simple C*-algebra and that α and β are ∗-automorphisms. Then the semicrossed products A×αZ and B ×β Z are isometrically isomorphic if and only if the dynamical systems (A, α) and (B, β) are outer conjugate.

The well-known results about the existence of separable, measurable resp., modifications of stochastic processes (e.g., [4, 5]) are generalized to the case of real valued random fields indexed by a separable, separable and locally convex resp., metric space.

In this work, attempts are made to study the dispersion of Love waves in dry sandy layer sandwiched between fiber reinforced layer and inhomogeneous half space.Inhomogeneity in half space associated with density and rigidity and considered in exponential form. Displacement components for fiber reinforced layer, dry sandy layer and inhomogeneous half-space have been obtained by using method of s...

Let Z be a fixed separable operator space, X ⊂ Y general separable operator spaces, and T : X → Z a completely bounded map. Z is said to have the Complete Separable Extension Property (CSEP) if every such map admits a completely bounded extension to Y ; the Mixed Separable Extension Property (MSEP) if every such T admits a bounded extension to Y . Finally, Z is said to have the Complete Separab...

A space is called d-separable if it has a dense subset representable as the union of countably many discrete subsets. We answer several problems raised by V. V. Tkachuk by showing that (1) X is d-separable for every T1 space X; (2) if X is compact Hausdorff then X is d-separable; (3) there is a 0-dimensional T2 space X such that X2 is dseparable but X1 (and hence X) is not; (4) there is a 0-dim...

We show that any separable stable Banach space can be represented as a group of isometries on a separable reflexive Banach space, which extends a result of S. Guerre and M. Levy. As a consequence, we can then represent homeomorphically its space of types.