We discuss the quantum Lax-Phillips theory of scattering and unstable systems. In this framework, the decay of an unstable system is described by a semigroup. The spectrum of the generator of the semigroup corresponds to the singularities of the Lax-Phillips S-matrix. In the case of discrete (complex) spectrum of the generator of the semigroup, associated with resonances, the decay law is exact...

the weighted semigroup algebra mb (s, w) is studied via its identification with mb (s) together with a weighted algebra product *w so that (mb (s, w), *) is isometrically isomorphic to (mb (s), *w). this identification enables us to study the relation between regularity and amenability of mb (s, w) and mb (s), and improve some old results from discrete to general case.

Different structures of master-equation used for the description of decoherence of a microsystem interacting through collisions with a surrounding environment are considered and compared. These results are connected to the general expression of the generator of a quantum dynamical semigroup in presence of translation invariance recently found by Holevo.

Different structures of master-equation used for the description of decoherence of a microsystem interacting through collisions with a surrounding environment are considered and compared. These results are connected to the general expression of the generator of a quantum dynamical semigroup in presence of translation invariance recently found by Holevo.

— In these notes we study combinatorial and algebraic properties of affine semigroups and their algebras: (1) the existence of unimodular Hilbert triangulations and covers for normal affine semigroups, (2) the Cohen–Macaulay property and number of generators of divisorial ideals over normal semigroup algebras, and (3) graded automorphisms, retractions and homomorphisms of polytopal semigroup al...

Central subsets of a discrete semigroup S have very strong combinatorial properties which are a consequence of the Central Sets Theorem. Call a set a C-set if it satisfies the conclusion of the Central Sets Theorem. We obtain here a reasonably simple characterization of C-sets in an arbitrary discrete semigroup.

Various semigroups can be associated with graphs and hypergraphs. Mainly, these have been endomorphism monoids. However, other types of semigroups (e.g. restrictive semigroups of partial extensive transformations of graphs) have been considered. A good survey of semigroups connected with graphs is given in [5]. In this paper, a new type of semigroups connected with hypergraphs is considered. We...