A generalized Mehler semigroup (Ornstein-Uhlenbeck semigroup) associated with some strongly continuous semigroup of linear operators on a real separable Hilbert space may be defined by using a skew convolution semigroup. Under a mild moment assumption, it is proved that the characteristic functional of any centered skew convolution semigroup is absolutely continuous and characterizations are gi...

In this paper, we study the Casimir effect of a scalar field with Dirichlet boundary condition in some certain topologies. By numerical analysis we show that Casimir energy is a shape-dependent quantity. We also obtain the phase transition in different topologies in which the Casimir force changes from attractive to repulsive or vice versa.  eararqr

We present a decentralized VPN service that can be built over generalized mobile ad-hoc networks (Generalized MANETs), in which topologies can be represented as a time-varying directed multigraph. We address wireless ad-hoc networks and overlay ad-hoc networks as instances of Generalized MANETs. We first propose an architecture to operate on various kinds of networks through a single set of ope...

In this paper we attempt to find and investigate the most general class of posets which satisfy a properly generalized version of the Hofmann-Mislove theorem. For that purpose, we generalize and study some notions (like compactness, the Scott topology, Scott open filters, prime elements, the spectrum etc.), and adjust them for use in general posets. Then we characterize the posets satisfying th...

In this paper, several optimum structures of a cascaded multilevel inverter is proposed. This optimization is based on generation a constant number of output voltage levels by using minimum number of power switches or dc voltage sources or minimum amount of blocked voltage by power switches. In addition, the optimum structure for a constant number of dc voltage sources by using minimum number o...

A non-contradictible axiomatic theory is constructed under the local reversibility of the metric triangle inequality. The obtained notion includes the metric spaces as particular cases and the generated metric topology is T$_{1}$-separated and generally, non-Hausdorff.

The first dual-port server-centric datacenter network, FiConn, was introduced in 2009 and there are several others now in existence; however, the pool of topologies to choose from remains small. We propose a new generic construction, the stellar transformation, that dramatically increases the size of this pool by facilitating the transformation of well-studied topologies from interconnection ne...

Recent work in the ideal theory of commutative rings and that of C*-algebra is unified and generalized by first noting that these spaces are Lawson-closed subspaces of continuous lattices, equipped with the restriction of the lower topology. These topologies were first studied by Nachbin in the late 1940’s (in [32]), as the topologies of those open sets in a compact Hausdorff space which are up...