A hierarchy of segmentations(partitions) is a multiscale set representation of the image. This paper introduces a new set of scale space operators or transformations on the space of hierarchies of partitions. An ordering of hierarchies is proposed which is endowed by an ω-ordering based on a global energy over the classes of the hierarchy. A class of Matheron semigroups are shown to exists in t...

let s be a locally compact foundation semigroup with identity and                          be its semigroup algebra. let x be a weak*-closed left translation invariant subspace of    in this paper, we prove that  x  is invariantly  complemented in   if and  only if  the left ideal  of    has a bounded approximate identity. we also prove that a foundation semigroup with identity s is left amenab...

In this paper, a commutative semigroup will be written as a disjoint union of its cancellative subsemigroups. Based on this fact we will define the left regular representation of a commutative separative semigroup and show that this representation is faithful. Finally concrete examples of commutative separative semigroups, their decompositions and their left regular representations are given.

In this paper, we attempt to investigate the connection between various types of ideals (for examples $(m, n)$-ideal, bi-ideal, interior ideal, quasi ideal, prime ideal and maximal ideal) of an ordered semigroup $(S,cdot ,leq)$ and the correspond hyperideals of its EL-hyperstructure $(S,*)$ (if exists). Moreover, we construct the class of EL-$Gamma$-semihypergroup associated to a partially orde...

In this paper the concept of Q-fuzzification of ideals of Γ-semigroups has been introduced and some important properties have been investigated. A characterization of regular Γ-semigroup in terms of Q-fuzzy ideals has been obtained. Operator semigroups of a Γ-semigroup has been made to work by obtaining various relationships between Q-fuzzy ideals of a Γ-semigroup and that of its operator semig...

We begin with a definition Definition 1. A one-parameter family T (t) for 0 ≤ t < ∞ of bounded linear operators on a Banach space X is a C 0 (or strongly continuous) Semigroup on X if 1. T (0) = I (the identity on X). 2. T (t + s) = T (t)T (s) (semigroup property) 3. lim t↓0 T (t)v = v for all v ∈ X (This the Strong Continuity at t = 0, i.e., continuous at t = 0 in the strong operator topology)...

A controlled Markov process in a Hilbert space and an ergodic cost functional are given for a control problem that is solved where the process is a solution of a parameter-dependent semilinear stochastic differential equation and the control can occur only on the boundary or at discrete points in the domain. The linear term of the semilinear differential equation is the infinitesimal generator ...

The concept of an automatic structure has been generalized from groups [ECH+] to semigroups [CRRT]. Several authors [CRR, Hof, Kam] have asked the following question: Let S be a finitely generated semigroup embeddable in a group and let G be its universal group [CP, Chapter ]. If G is automatic, must S be automatic? Examples in favour of this implication include: free groups and s...

We consider pseudodifferential operators that have non-smooth negative definite symbols and develop a corresponding symbolic calculus. Combining this symbolic calculus with the use of non-smooth symbols that are asymptotically constant in the co-variable we succeed in finding a parametrix for a certain pseudodifferential equation. This in turn allows us to show that some pseudodifferential oper...

Clifford and Preston (1961) showed several important characterizations of right groups. It was shown in Roy and So (1998) that, among topological semigroups, compact right simple or left cancellative semigroups are in fact right groups, and the closure of a right simple subsemigroup of a compact semigroup is always a right subgroup. In this paper, it is shown that such results can be generalize...