It is known that a left C-wrpp semigroup can be described as curler structure of a left band and a C-wrpp semigroup. In this paper, we introduce the class of weakly left C-wrpp semigroups which includes the class of weakly left C-rpp semigroups as a subclass. We shall particularly show that the spined product of a left C-wrpp semigroup and a right normal band is a weakly left C-wrpp semifroup. ...

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 characterize when a Cayley automaton semigroup is a group, is trivial, is finite, is free, is a left zero semigroup, or is a right zero semigroup.

In this paper we combine results from [1] and [3] in order to determine the relationship between the deficiency of a group G and the deficiency of a Rees matrix semigroup S over G; in particular, we investigate how the efficiency of S depends on the efficiency of G. We start by defining semigroup and group presentations. Let A be an alphabet. We denote by A the free semigroup on A consisting of...

That is, W0 is the set of all finite products of the generators, allowing repetitions. Let W signify the larger multiplicative semigroup generated by W0 together with {1/2}. We call W the wild semigroup and W0 the Wooley semigroup. The question we consider is: Which integers belong to these semigroups? The sets of integer elements W(Z) := W ∩ Z and W0(Z) := W0 ∩ Z themselves form multiplicative...

Polyacrylic acid/ octavinyl polyhedral oligomeric silsesquioxane, nanocomposite hydrogel with 3-D network was synthesized via radical polymerization. Octavinyl polyhedral oligomeric silsesquioxane was used as crosslinker and nanofiller simultaneously in the preparation of the hydrogel. Hydrogel adsorption performance was determined by adsorption of methylene blue. The adsorption capacity was ev...

We introduce the notion of ideals in implicative semigroups, and then state the characterizations of the ideals. 2000 Mathematics Subject Classification. 20M12, 06F05, 06A06, 06A12.

A k-trestle of a graph G is a 2-connected spanning subgraph of G of maximum degree at most k. We show that a polyhedral graph G has a 3-trestle, if the separator-hypergraph of G contains no two different cycles joined by a path of 3-separators of length ≥ 0. There are graphs not satisfying this condition that have no 3-trestles. Further, for each integer k every graph with toughness smaller tha...

In this paper we describe the modulus semigroup of the C0-semigroup associated with the linear differential equation with delay { u1ptq Auptq Lut (t ¥ 0), up0q x∈X, u0 f ∈Lpp h, 0;Xq, in the Banach lattice X Lpp h, 0;Xq, where X is a Banach lattice with order continuous norm. The progress with respect to previous papers is that A may be an unbounded generator of a C0-semigroup possessing a modu...

Rauzy graphs of subshifts are endowed with an automaton structure. For Sturmian subshifts, it is shown that its transition semigroup is the syntactic semigroup of the language recognized by the automaton. A projective limit of the partial semigroups of nonzero regular elements of their transition semigroups is described. If the subshift is minimal, then this projective limit is isomorphic, as a...