In this paper we study the relationships existing between total measurability in variation and Gould type fuzzy integrability (introduced and studied in [21]), giving a special interest on their behaviour on atoms and on finite unions of disjoint atoms. We also establish that any continuous real valued function defined on a compact metric space is totally measurable in the variation of a regula...

in [1,2,3], a. c. baker and j.w. baker studied the subspace ma(s) of the convolution measure algebra m, (s) of a locally compact semigroup. h. dzinotyiweyi in [5,7] considers an analogous measure space on a large class of c-distinguished topological semigroups containing all completely regular topological semigroups. in this paper, we extend the definitions to study the weighted semigroup algeb...

Motivated by call centers, we study large-scale service systems with multiple customer classes and multiple agent pools, each with many agents. We propose a family of routing rules called Queue-and-Idleness-Ratio (QIR) rules. A newly available agent next serves the customer from the head of the queue of the class (from among those he is eligible to serve) whose queue length most exceeds a speci...

in this paper by use of mathematical modeling of an observer [14,15] the notion of relative information functional for relative dynamical systemson compact metric spaces is presented. we extract the information function ofan ergodic dynamical system (x,t) from the relative information of t fromthe view point of observer χx, where x denotes the base space of the system.we also generalize the inv...

It is shown that for an SDE in a Hilbert space, eventual compactness of the driving semigroup together with compact perturbations can be used to establish the existence of an invariant measure. The result is applied to stochastic functional differential equations and the heat equation perturbed by delay and noise, which are both shown to be driven by an eventually compact semigroup.

It is well known that the semi-Riemannian (pseudo-Riemannian) manifolds (M,g) of Lorentzian signature play a special role in geometry and physics, and that they are models of space time of general relativity. Let Mn+1 p (c) be an (n+1)-dimensional complete connected semi-Riemannian manifold with constant sectional curvature c and index p (see [13, page 227]). It is called an indefinite space fo...

It is well known that no infinite homogeneous space is both compact and extremally disconnected. (Since there are infinite compact homogeneous spaces and infinite extremally disconnected homogeneous spaces, it is the combination of compactness and extremal disconnectedness that brings about this result.) The following question then arises naturally: How “close to compact” can a homogeneous, ext...

A separated cell A of a topological space X is a family of pairwise disjoint open sets with the property that, for any partition A= A1 ∪ A2 of A, ⋃ A1 and ⋃ A2 are completely separated. The separated cellularity sc(X) of X is the supremum of all cardinals of separated cells. A space X has finite separation if it has no infinite separated cells. With X compact, every separated cell of X has size...

We prove that for any separable Banach space X, there exists a compact metric space which is homeomorphic to the Cantor space and whose Lipschitz-free space contains a complemented subspace isomorphic to X. As a consequence we give an example of a compact metric space which is homeomorphic to the Cantor space and whose Lipschitz-free space fails the approximation property and we prove that ther...