We present and explore a general method for deriving a Lie-Markov model from a finite semigroup. If the degree of the semigroup is k, the resulting model is a continuous-time Markov chain on k states and, as a consequence of the product rule in the semigroup, satisfies the property of multiplicative closure. This means that the product of any two probability substitution matrices taken from the...

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...

We establish a surprisingly close relationship between universal Horn classes of directed graphs and varieties generated by socalled adjacency semigroups which are Rees matrix semigroups over the trivial group with the unary operation of reversion. In particular, the lattice of subvarieties of the variety generated by adjacency semigroups that are regular unary semigroups is essentially the sam...

ABSTRACT. In this paper we study a singular perturbation of an asymptotically convergent operator C0-semigroup, and describe the spectral behaviour and a power series expansion of the perturbed semigroup. As an application of our results we obtain the description of the asymptotic behaviour of the solutions to a nonhomogeneous singularly perturbed differential equation in a Banach space, extend...

Suppose A 1 ; ; A s are (1;?1) matrices of order m satisfying (4) Call A 1 ; ;A s a regular s-set of matrices of order m if (1), (2), (3) are satissed and a regular s-set of regular matrices if (4) is also satissed, these matrices were rst discovered by J. Seberry and A. L. Whiteman in \New Hadamard matrices and conference matrices obtained via Mathon's construction", Graphs and Combinatorics, ...

In this paper, we introduce a new notion of strong pseudo-amenability for Banach algebras. We study some matrix Using tool, characterize [Formula: see text], provided that text] is uniformly locally finite inverse semigroup. As an application, show Brandt semigroup pseudo-amenable if and only amenable finite. give examples to the differences between other classical notions amenability.

Chain conditions, finiteness conditions, growth conditions, and other forms of finiteness, Noetherian rings and Artinian rings have been systematically studied for commutative rings and algebras since 1959. In pursuit of the deeper results of ideal theory in ordered groupoids (semigroups), it is necessary to study special classes of ordered groupoids (semigroups). Noetherian ordered groupoids (...

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...

We establish representation types (finite, tame or wild) of finite dimensional Munn algebras with semisimple bases. As an application, we Rees matrix semigroups, in particular, 0-simple and their mutually annihilating unions.