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Unitariness in Ordered Semigroups
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作者 Michael Tsingelis 《Applied Mathematics》 2023年第8期531-543,共13页
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... 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 ≤ e<sup>2</sup> 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, S<sup>e</sup>:= S ∪ {e} and U<sup>e</sup>:= U ∪ {e}, we give conditions that an (“extension” of S) ordered semigroup and the subset U<sup>e</sup> of S<sup>e</sup> 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). 展开更多
关键词 Left (Right) Translation of an Ordered semigroup Bitranslation of an Ordered semigroup Translational Hull of an Ordered semigroup Unitary Subset of an Ordered semigroup Almost Unitary Subset of an Ordered semigroup Strongly almost Unitary Subset of an Ordered semigroup
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Generating Sets of the Complete Semigroup of Binary Relations Defined by Semilattices of the Class Σ8(X, 5)
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作者 Nino Tsinaridze 《Applied Mathematics》 2024年第2期169-197,共29页
In this article, we study generating sets of the complete semigroups of binary relations defined by X-semilattices of unions of the class Σ<sub>8</sub>(X, 5). Found uniquely irreducible generating set for... In this article, we study generating sets of the complete semigroups of binary relations defined by X-semilattices of unions of the class Σ<sub>8</sub>(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. 展开更多
关键词 semigroup SEMILATTICE Binary Relation
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Boundedness Types of Perturbations on the Growth of Semigroups
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作者 Zuheir Khidir Ahmed Abdelgader Nariman Khider Ahmed Abdalgadir +1 位作者 Entisar Bakhit Bashir Elshikh Abualez Alamin Ahmed Ali 《Advances in Pure Mathematics》 2023年第1期1-10,共10页
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 gener... 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 &#981;<sup>j</sup>-bounded strongly continuous semigroups. Furthermore, these results are used to investigate the effect of the Perturbation on the type of the growth of sequences. 展开更多
关键词 Cesáro Average C0-semigroups BOUNDEDNESS Perturbation Stability Hille-Yosida Growth of Sequences
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DIFFERENTIABILITY OF C_0-SEMIGROUPS WITH APPLICATION
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作者 金振东 喻文焕 +1 位作者 靳展 王辅敏 《Transactions of Tianjin University》 EI CAS 1999年第2期25-29,共5页
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 ... 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. 展开更多
关键词 C 0 semigroup infinitesimal generator generalized continuity strongly Frechet differential dalay equation
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关于Semigroups of Linear Operators and Applications to Partial Differential Equations的两个注解
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作者 乔花玲 窦丽娜 +1 位作者 赵华新 李顺琴 《延安大学学报(自然科学版)》 2003年第1期24-25,共2页
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。
关键词 CO半群 无穷小生成元 可微半群 抽象柯西问题
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The Spectrum of High Rank Differential Operators of the C_0 Semigroups 被引量:1
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作者 杨茂 《Chinese Quarterly Journal of Mathematics》 CSCD 2000年第2期76-79,共4页
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 relat... 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) . 展开更多
关键词 C 0 semigroup n rank differential opetator spectral point.
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Topological inverse semigroups 被引量:6
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作者 ZHUYongwen 《Journal of Chongqing University》 CAS 2004年第1期82-85,共4页
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 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. 展开更多
关键词 topological inverse semigroup COMPACT projective limit injective limit
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α-Times Integrated C-Semigroups 被引量:2
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作者 Man Liu Da-Qing Liao +1 位作者 Qian-Qian Zhu Fu-Hong Wang 《Advances in Pure Mathematics》 2012年第3期211-215,共5页
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.
关键词 α-Times INTEGRATED C semigroups LAPLACE Inverse Transformation Pseudo-Resolvent IDENTITY
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Inverse wpp Semigroups 被引量:1
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作者 胡志斌 郭小江 《Chinese Quarterly Journal of Mathematics》 CSCD 2011年第4期521-525,共5页
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.
关键词 wpp semigroup inverse wpp semigroup C-wrpp semigroups
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OSCILLATION AND VARIATION OF THE LAGUERRE HEAT AND POISSON SEMIGROUPS AND RIESZ TRANSFORMS 被引量:1
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作者 J.J.Betancor R.Crescimbeni J.L.Torrea 《Acta Mathematica Scientia》 SCIE CSCD 2012年第3期907-928,共22页
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 as... 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. 展开更多
关键词 OSCILLATION VARIATION heat Laguerre semigroup Riesz transforms
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A Note on C-wrpp Semigroups 被引量:2
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作者 唐向东 《Northeastern Mathematical Journal》 CSCD 2001年第1期71-74,共4页
In this paper, we give equivalent characterizations of C wrpp semigroups.
关键词 C wrpp semigroup construction of axiomatic partial order Clifford semigroup SEMILATTICE
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Trotter-kato Theorems for an α-times Integrated Semigroups 被引量:4
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作者 郎开禄 杨光俊 《Chinese Quarterly Journal of Mathematics》 CSCD 1999年第3期11-16, ,共6页
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.
关键词 times integrated semigroups CONVERGENCE appoximation
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ASYMPTOTIC BEHAVIOR FOR COMMUTATIVE SEMIGROUPS OF ALMOST ASYMPTOTICALLY NONEXPANSIVE TYPE MAPPINGS 被引量:1
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作者 曾六川 《Acta Mathematica Scientia》 SCIE CSCD 2006年第2期246-254,共9页
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 conver... 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. 展开更多
关键词 Semitopological semigroup almost asymptotically nonexpansive type mapping almost orbit asymptotic behavior
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A Class of Regular Simple ω2-semigroups-Ⅱ 被引量:1
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作者 Shang Yu Wang Li-min +1 位作者 Feng Ying-ying Du Xian-kun 《Communications in Mathematical Research》 CSCD 2013年第4期351-362,共12页
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.
关键词 regular semigroup simple ω2-semigroup generalized Bruck-Reilly ex-tension
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The Lawson Partial Order on Wrpp Semigroups 被引量:1
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作者 LIU Hai-jun GUO Xiao-jiang 《Chinese Quarterly Journal of Mathematics》 CSCD 2012年第1期139-144,共6页
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 ... 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. 展开更多
关键词 wrpp semigroup partial order compatibility
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(Generalized)Green's Relations of GV-Semigroups 被引量:1
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作者 张建刚 申冉 《Journal of Donghua University(English Edition)》 EI CAS 2012年第2期175-177,共3页
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 semigrou... 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. 展开更多
关键词 GV-semigroup GV-inverse semigroup Green’s relations
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SOME REMARKS ON (L)-GREEN’S RELATIONS AND STRONGLY RPP SEMIGROUPS 被引量:1
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作者 杜兰 郭聿琦 K.P. Shum 《Acta Mathematica Scientia》 SCIE CSCD 2011年第4期1591-1599,共9页
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.
关键词 (l)-Green’s relations strongly rpp semigroups semilattice congruences Dprimitive idempotents
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Regular Elements of the Complete Semigroups <i>B<sub>X</sub>(D)</i>of Binary Relations of the Class &sum;<sub>2</sub>(<i>X</i>,8) 被引量:1
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作者 Nino Tsinaridze Shota Makharadze 《Applied Mathematics》 2015年第3期447-455,共9页
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) ... 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 . 展开更多
关键词 SEMILATTICE semigroup Binary Relation
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The Structure of NBe-rpp Semigroups 被引量:1
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作者 郭小江 《Northeastern Mathematical Journal》 CSCD 2000年第4期398-404,共7页
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 semigrou... 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. 展开更多
关键词 strongly rpp semigroup NBe rpp semigroup C rpp semigroup normal band
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Right pp Semigroups with Multiplicative Right Adequate Transversals 被引量:1
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作者 HU Yao-hua GUO Xiao-jiang 《Chinese Quarterly Journal of Mathematics》 CSCD 2011年第3期366-371,共6页
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 ... 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. 展开更多
关键词 rpp semigroup right adequate transversal right normal band
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