Unitariness in Ordered Semigroups

We introduce the concepts of unitary, almost unitary and strongly almost unitary subset of an ordered semigroup. For the notions of almost unitary and strongly almost unitary subset of an ordered semigroup, we use the notion of translational hull of an ordered semigroup. If (S,⋅,≤) is an ordered semigroup having an element e such that e ≤ e2 and U is a nonempty subset of S such that u ≤ eu, u ≤ ue for all u ∈ U, we show that U is almost unitary in S if and only if U is unitary in . Also if (S,⋅,≤) is an ordered semigroup, e ∉ S, U is a nonempty subset of S, Se:= S ∪ {e} and Ue:= U ∪ {e}, we give conditions that an (“extension” of S) ordered semigroup and the subset Ue of Se must satisfy in order for U to be almost unitary or strongly almost unitary in S (in case U is strongly almost unitary in S, then the given conditions are equivalent).

Generating Sets of the Complete Semigroup of Binary Relations Defined by Semilattices of the Class Σ8(X, 5)

In this article, we study generating sets of the complete semigroups of binary relations defined by X-semilattices of unions of the class Σ8(X, 5). Found uniquely irreducible generating set for the given semigroups and when X is finite set formulas for calculating the number of elements in generating sets are derived.

Boundedness Types of Perturbations on the Growth of Semigroups

We study types of boundedness of a semigroup on a Banach space in terms of the Cesáro-average and the behavior of the resolvent at the origin and also exhibit a characterization of type Hille-Yosida for the generators of ϕj-bounded strongly continuous semigroups. Furthermore, these results are used to investigate the effect of the Perturbation on the type of the growth of sequences.

DIFFERENTIABILITY OF C_0-SEMIGROUPS WITH APPLICATION

This paper considers the differentiability of C 0 semigroups with respect to (w.r.t.) parameters contained in their infinitesimal generators.It is proved that the generalized continuity and strong differentiability of their infinitesimal generators w.r.t.parameters imply the differentiability of the C 0 semigroups.The results are applied to the differentiability of the solution of a linear delay differential equation w.r.t.its delays.

关于Semigroups of Linear Operators and Applications to Partial Differential Equations的两个注解

指出文献[1]关于C0半群可微性的定理2.4.11的证明过程中一处错误,及关于柯西问题解的指数衰变的定理4.4.1的证明过程中的不妥之处,并给出新的证明。

The Spectrum of High Rank Differential Operators of the C_0 Semigroups

In this paper,the author study the spectrum of high rank differential operators T (n) (t) of C 0 Semigroup T(t) ,given an approach to construct the spectral set opetator T (n) (t) ,and discussed the relation between the spectral points of both T (n) (t) and infinitesimal generator A of T(t) .

Topological inverse semigroups

That the projective limit of any projective system of compact inverse semigroups is also a compact inverse semigroup, the injective limit of any injective system of inverse semigroups is also an inverse semigroup, and that a compact inverse semigroup is topologically isomorphic to a strict projective limit of compact metric inverse semigroups are proved. It is also demonstrated that Hom (S,T) is a topological inverse semigroup provided that S or T is a topological inverse semigroup with some other conditions. Being proved by means of the combination of topological semigroup theory with inverse semigroup theory, all these results generalize the corresponding ones related to topological semigroups or topological groups.

α-Times Integrated C-Semigroups

The α-times integrated C semigroups, α > 0, are introduced and analyzed. The Laplace inverse transformation for α-times integrated C semigroups is obtained, some known results are generalized.

Inverse wpp Semigroups

It is dedicated to the study of inverse wrpp semigroup, we obtain some charac- terizations of inverse wpp semigroup. In particular, we establish some charactizations for C-wrpp semigroup.

OSCILLATION AND VARIATION OF THE LAGUERRE HEAT AND POISSON SEMIGROUPS AND RIESZ TRANSFORMS

In this article, we study LP-boundedness properties of the oscillation and vari- ation operators for the heat and Poissson semigroup and Riesz transforms in the Laguerre settings. Also, we characterize Hardy spaces associated to Laguerre operators by using the variation operator of the heat semigroup.

A Note on C-wrpp Semigroups

In this paper, we give equivalent characterizations of C wrpp semigroups.

Trotter-kato Theorems for an α-times Integrated Semigroups

In this paper,we discuss on the convergence and approximation of an α times integrated semigroups. The Trotter kato theorems for an α times integrated semigroups are obtained.

ASYMPTOTIC BEHAVIOR FOR COMMUTATIVE SEMIGROUPS OF ALMOST ASYMPTOTICALLY NONEXPANSIVE TYPE MAPPINGS

This article introduces the concept of commutative semigroups of almost asymptotically nonexpansive-type mappings in a Banach space X which has the Opial property and whose norm is UKK, and establishes the weak convergence theorems for almostorbits of this class of commutative semigroups. The author improves, extends and develops some recent and earlier results.

A Class of Regular Simple ω2-semigroups-Ⅱ

In this paper, we study regular simple ω2-semigroups in which D｜Es = Wd by the generalized Bruck-Reilly extension and obtain its structure theorem.

The Lawson Partial Order on Wrpp Semigroups

In this paper,we introduce Lawson partial order ≤ w on wrpp semigroups.After obtaining some properties of ≤ w,we determine when ≤ w is(left;right) compatible with the multiplication.These results extend and enrich the related results of Lawson and GuoLuo on abundant semigroups,of Guo-Shum on rpp semigroups and of Liu-Guo on wrpp semigroups.

(Generalized)Green's Relations of GV-Semigroups

Green's relations and generalized Green's relations play a fundamental role in the study of semigroups.GV-semigroups are the generalizations of completely regular semigroups in the range of π-regular semigroups.In this paper,Green's relations and generalized Green's relations on GV-semigroups are considered by the structure of GV-semigroups.D=j and D C D* on GV-semigroups will be proved.

SOME REMARKS ON (L)-GREEN’S RELATIONS AND STRONGLY RPP SEMIGROUPS

In order to study rpp semigroups, in particular, some special cases, several facts on （l）-Green’s relations and strongly rpp semigroups are given as some remarks.

Regular Elements of the Complete Semigroups <i>B_X(D)</i>of Binary Relations of the Class &sum;₂(<i>X</i>,8)

As we know if D is a complete X-semilattice of unions then semigroup Bx(D) possesses a right unit iff D is an XI-semilattice of unions. The investigation of those a-idempotent and regular elements of semigroups Bx(D) requires an investigation of XI-subsemilattices of semilattice D for which V(D,a)=Q∈∑2(X,8) . Because the semilattice Q of the class ∑2(X,8) are not always XI -semilattices, there is a need of full description for those idempotent and regular elements when V(D,a)=Q . For the case where X is a finite set we derive formulas by calculating the numbers of such regular elements and right units for which V(D,a)=Q .

The Structure of NBe-rpp Semigroups

The aim of this paper is to study a class of strongly rpp semigroups with normal idempotent bands, so called NBe rpp semigroups. The structure of such semigroups is established in terms of C rpp semigroups and normal bands.

Right pp Semigroups with Multiplicative Right Adequate Transversals

In this paper,the concept of right adequate transversals of rpp semigroups is introduced.We establish the structure of rpp semigroups with multiplicative right adequate transversals in terms of right normal bands and right adequate semigroups.In particular, some special cases are considered.