The algebraic structure ([0,∞), +, ≤), together with Lebesgue measure (and the usual topology), is the standard representation of time for a variety of probabilistic models. These include reliability theory and the aging of lifetime distributions, renewal processes, and Markov processes, to name just a few. The purpose of this monograph is to study probability models in which the standard repre...

LetP be a semigroup that admits an embedding into a groupG.Assume that the embedding satisfies the Toeplitz condition recently introduced by the third named author and that the Baum–Connes conjecture holds for G. We prove a formula describing the K-theory of the reduced crossed product A α,r P by any automorphic action of P . This formula is obtained as a consequence of a result on the K-theory...

We investigate the results of a partially ordered ternary semigroup containing right bases and characterize when non-empty subset is base. Moreover, we give characterization base to be subsemigroup show that have same cardinality. Finally, complement union all maximal proper left ideal.

Let X be an infinite linearly ordered set and let Y a nonempty subset of X. We calculate the relative rank semigroup OP(X,Y) all orientation-preserving transformations on with restricted range modulo O(X,Y) order-preserving Y. For = X, we characterize generating sets minimal size.