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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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Some Characterizations of Left Weakly Regular Ordered Semigroups 被引量:1
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作者 TANG JIAN XIE XIANG-YUN 《Communications in Mathematical Research》 CSCD 2011年第3期253-267,共15页
In this paper, the notion of left weakly regular ordered semigroups is introduced. Furthermore, left weakly regular ordered semigroups are characterized by the properties of their left ideals, right ideals and (gener... In this paper, the notion of left weakly regular ordered semigroups is introduced. Furthermore, left weakly regular ordered semigroups are characterized by the properties of their left ideals, right ideals and (generalized) bi-ideals, and also by the properties of their fuzzy left ideals, fuzzy right ideals and fuzzy (generalized) bi-ideals. 展开更多
关键词 left weakly regular ordered semigroup generalized bi-ideal fuzzy left ideal fuzzy right ideal fuzzy bi-ideal fuzzy generalized bi-ideal
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Some Characterizations of Strongly Semisimple Ordered Semigroups
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作者 Tang Jian Xie Xiang-yun Du Xian-kun 《Communications in Mathematical Research》 CSCD 2013年第2期155-166,共12页
In this paper, the concept of quasi-prime fuzzy left ideals of an ordered semigroup S is introduced. Some characterizations of strongly semisimple ordered semigroups are given by quasi-prime fuzzy left ideals of S. In... In this paper, the concept of quasi-prime fuzzy left ideals of an ordered semigroup S is introduced. Some characterizations of strongly semisimple ordered semigroups are given by quasi-prime fuzzy left ideals of S. In particular, we prove that S is strongly semisimple if and only if each fuzzy left ideal of S is the intersection of all quasi-prime fuzzy left ideals of S containing it. 展开更多
关键词 ordered semigroup ordered fuzzy point quasi-prime fuzzy left ideal strongly semisimple ordered semigroup
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A CLASS OF NATURALLY ORDERED ABUNDANT SEMIGROUPS WITH A GREATESTIDEMPOTENT
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作者 曾祥金 景奉杰 《Acta Mathematica Scientia》 SCIE CSCD 1997年第2期198-204,共7页
On the base of the construction of abundant semigroups with a normal medial idempotent [14], in this paper we consider a class of naturally ordered abundant semigroups which satisfies the regularity condition and cont... On the base of the construction of abundant semigroups with a normal medial idempotent [14], in this paper we consider a class of naturally ordered abundant semigroups which satisfies the regularity condition and contains a greatest idempotent. Furthermore, we give a completely description of the overall structure of such ordered semigroups via the algebraic structure of them, which generalizes known result obtained by Blyth and McFadden[3]. 展开更多
关键词 abundant semigroups natural order greatest idempotents
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On the Fractional Extensions in Commutative Ordered Semigroups
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作者 LUO Cong-wen 《Chinese Quarterly Journal of Mathematics》 CSCD 北大核心 2008年第3期442-445,共4页
In this paper we extend the construction of the field of rational numbers from the ring of integers to an arbitrary commutative ordered semigroup. We first construct a fractional ordered semigroup and a homomorphism ... In this paper we extend the construction of the field of rational numbers from the ring of integers to an arbitrary commutative ordered semigroup. We first construct a fractional ordered semigroup and a homomorphism φs : R → S^-1 R. Secondly, we characterize the commutative ordered semigroup so constructed by a universal mapping property. 展开更多
关键词 ordered semigroup fractional extension HOMOMORPHISM
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Fuzzy Ordered Filters in Implicative Semigroups
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作者 库热西 黄文平 《Chinese Quarterly Journal of Mathematics》 CSCD 1998年第2期53-57, ,共5页
We fuzzify the concept of ordered filter in implicative negatively partially ordered semigroups and study its properties.
关键词 implicative) negatively partially ordered semigroup ordered filter fuzzy ordered filter level ordered filter
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Neutrosophicκ-Structures in Ordered Semigroups
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作者 G.Muhiuddin K.Porselvi +1 位作者 B.Elavarasan D.Al-Kadi 《Computer Modeling in Engineering & Sciences》 SCIE EI 2022年第5期979-999,共21页
In general,ordered algebraic structures,particularly ordered semigroups,play an important role in fuzzification in many applied areas,such as computer science,formal languages,coding theory,error correction,etc.Nowada... In general,ordered algebraic structures,particularly ordered semigroups,play an important role in fuzzification in many applied areas,such as computer science,formal languages,coding theory,error correction,etc.Nowadays,the concept of ambiguity is important in dealing with a variety of issues related to engineering modeling problems,network theory,decision-making problems in real-life situations,and so on.Several theories have been developed by various researchers to overcome the difficulties that arise from uncertainty,including fuzzy sets,intuitionistic fuzzy sets,probability,softsets,neutrosophic sets,andmanymore.Inthispaper,we focus solelyonneutrosophic set theory.In ordered semigroups,we define and investigate the properties of neutrosophicκ-ideals and neutrosophicκ-interior ideals.We also use neutrosophicκ-ideals and neutrosophicκ-interior ideals to characterize ordered semigroups. 展开更多
关键词 ordered semigroup IDEALS neutrosophicκ-structures neutrosophicκ-ideals neutrosophicκ-interior ideals
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Ordered Semigroups Characterized by Their Intuitionistic Fuzzy Generalized Bi-ideals
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作者 Muhammad Shabir Asghar Khan 《模糊系统与数学》 CSCD 北大核心 2009年第5期56-64,共9页
In this paper,we define intuitionistic fuzzy generalized bi-ideals in ordered semigroups and characterize regular and left weakly regular ordered semigroups in terms of intuitionistic fuzzy generalized bi-ideals.
关键词 模糊数学 模糊系统 系统论 理论
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N-fuzzy Filters in Ordered Semigroups
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作者 Asghar Khan Young Bae Jun Muhammad Shabir 《模糊系统与数学》 CSCD 北大核心 2010年第2期28-32,共5页
In this paper we define N-fuzzy filters,N-fuzzy bi-ideal subsets and N-fuzzy bi-filters of ordered semigroups and characterize ordered semigroups in terms of N-fuzzy filters,N-fuzzy bi-ideal subsets and N-fuzzy bi-fil... In this paper we define N-fuzzy filters,N-fuzzy bi-ideal subsets and N-fuzzy bi-filters of ordered semigroups and characterize ordered semigroups in terms of N-fuzzy filters,N-fuzzy bi-ideal subsets and N-fuzzy bi-filters.We establish relationship of N-fuzzy filters and prime N-fuzzy ideals of ordered semigroups. Also we discuss the relationship of N-fuzzy bi-filters and prime N-fuzzy bi-ideal subsets of ordered semigroups. 展开更多
关键词 模糊系统 计算方法 智能系统 自动化
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BOUNDEDNESS OF VARIATION OPERATORS ASSOCIATED WITH THE HEAT SEMIGROUP GENERATED BY HIGH ORDER SCHRODINGER TYPE OPERATORS 被引量:3
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作者 Suying LIU Chao ZHANG 《Acta Mathematica Scientia》 SCIE CSCD 2020年第5期1215-1228,共14页
In this article,we derive the Lp-boundedness of the variation operators associated with the heat semigroup which is generated by the high order Schrodinger type operator(—Δ)^2+V%2 in R%n(n≥5)with V being a nonnegat... In this article,we derive the Lp-boundedness of the variation operators associated with the heat semigroup which is generated by the high order Schrodinger type operator(—Δ)^2+V%2 in R%n(n≥5)with V being a nonnegative potential satisfying the reverse Holder inequality.Furt her more,we prove the boundedness of the variation operators on associated Morrey spaces.In the proof of the main results,we always make use of the variation inequalities associated with the hea t semigroup genera ted by the biharmonic operator(-Δ)2. 展开更多
关键词 Variation operators high order Schrodinger type operators heat semigroup
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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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CHARACTERISTIC CONDITIONS FOR THECOMPLETE INFINITESIMAL GENERATORS OFANALYTIC SEMIGROUPS OF GROWTH ORDER α
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作者 张显文 《Acta Mathematica Scientia》 SCIE CSCD 2000年第1期97-103,共7页
This paper obtains a group of necessary and sufficient conditions which guarantee a closed linear operator A to be the complete infinitesimal generator of an analytic semigroup of growth order α.
关键词 semigroup of growth order α ANALYTICITY GENERATOR
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Partial Orders on Right Inverse Semigroups
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作者 SHAO Yong ZHAO Xian-zhong 《Chinese Quarterly Journal of Mathematics》 CSCD 2009年第2期194-199,共6页
It is well known that there exists the smallest inverse semigroup congruence on an orthodox semigroup. We denote by Y the smallest inverse semigroup congruence on an orthodox semigroup. Let S be a right inverse semigr... It is well known that there exists the smallest inverse semigroup congruence on an orthodox semigroup. We denote by Y the smallest inverse semigroup congruence on an orthodox semigroup. Let S be a right inverse semigroup. We construct partial orders on S by some kind of its subsemigroups and uncover that partial orders on S have close contact with partial orders on S/Y. 展开更多
关键词 right inverse semigroup partial order q-subsemigroup inverse semigroup
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偏序半群的商序同态研究
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作者 邵海琴 梁茂林 +1 位作者 董芳芳 李长涛 《咸阳师范学院学报》 2024年第4期6-9,共4页
通过偏序半群的商半拟序、商半拟链和正则同余,研究了偏序半群的商序同态,给出了偏序半群的商序同态基本定理。同时,讨论了偏序半群的商半拟序与商序同态之间的关系,给出了由偏序半群S到T的商序同态φ构造S的商半拟序ρ_φ的方法以及S... 通过偏序半群的商半拟序、商半拟链和正则同余,研究了偏序半群的商序同态,给出了偏序半群的商序同态基本定理。同时,讨论了偏序半群的商半拟序与商序同态之间的关系,给出了由偏序半群S到T的商序同态φ构造S的商半拟序ρ_φ的方法以及S的一个商半拟序ρ?ρ_φ的充分必要条件,并得到了一些重要结论。 展开更多
关键词 偏序半群 商半拟序 商半拟链 正则同余 商序同态
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指数有界双连续n阶α次积分C半群与高阶抽象Cauchy问题研究
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作者 葛国菊 《佳木斯大学学报(自然科学版)》 CAS 2024年第4期173-176,92,共5页
算子半群理论在求解Cauchy问题等领域具有很大的应用价值,并且其在泛函分析理论等各方面的研究中同样有着重要意义。此次研究在Banach空间上,基于泛函分析、算子半群理论对柯西问题进行探讨。并基于n阶α次积分C半群的生成定理,对指数... 算子半群理论在求解Cauchy问题等领域具有很大的应用价值,并且其在泛函分析理论等各方面的研究中同样有着重要意义。此次研究在Banach空间上,基于泛函分析、算子半群理论对柯西问题进行探讨。并基于n阶α次积分C半群的生成定理,对指数有界双连续n阶α次积分C半群的生成定理与其Laplace逆变换表达式进行推算。由结果可知,L∞范数误差在分数阶n为1.47时达到最低值,为0.04,这表明其与实际值极为接近。在T=0.2,0.5两种时刻下,中精确解和正则解的变化趋势基本一致,并且二者的误差在x∈0.1,0.9区间内接近于0。研究有效验证了指数有界双连续n阶α次积分C半群解决高阶抽象Cauchy问题具有适用性与可靠性。 展开更多
关键词 高阶抽象Cauchy问题 适定性 指数有界 双连续 n阶α次积分C半群
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具有中间幂等元的r-宽大半群
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作者 白雪娜 宫春梅 《云南大学学报(自然科学版)》 CAS CSCD 北大核心 2024年第1期1-7,共7页
讨论了r-宽大半群上的中间幂等元及其相关幂等元的性质.借此,证明了具有弱型A可乘中间幂等元u的r-宽大半群是自然序r-宽大半群,其中u是最大幂等元.
关键词 r-宽大半群 中间幂等元 自然序 弱型A半群
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有限递减变换半群的商半群的一个注记
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作者 钱承镠 杨秀良 《杭州师范大学学报(自然科学版)》 CAS 2024年第1期106-112,共7页
令Sing n为X n={1,2,…,n}上的奇异变换半群,令S-n={α∈Sing n|xα≤x,x∈X n},这里1<2<…<n.本文得到富足半群S-n的一类同余ρ,其商半群S-n/ρ非正则且既不左富足也不右富足.
关键词 递减全变换半群 同余 正则半群 富足半群
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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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Approximate Controllability of Second-Order Neutral Stochastic Differential Equations with Infinite Delay and Poisson Jumps 被引量:4
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作者 PALANISAMY Muthukumar CHINNATHAMBI Rajivganthi 《Journal of Systems Engineering and Electronics》 SCIE EI CSCD 2015年第5期1033-1048,共16页
The modelling of risky asset by stochastic processes with continuous paths, based on Brow- nian motions, suffers from several defects. First, the path continuity assumption does not seem reason- able in view of the po... The modelling of risky asset by stochastic processes with continuous paths, based on Brow- nian motions, suffers from several defects. First, the path continuity assumption does not seem reason- able in view of the possibility of sudden price variations (jumps) resulting of market crashes. A solution is to use stochastic processes with jumps, that will account for sudden variations of the asset prices. On the other hand, such jump models are generally based on the Poisson random measure. Many popular economic and financial models described by stochastic differential equations with Poisson jumps. This paper deals with the approximate controllability of a class of second-order neutral stochastic differential equations with infinite delay and Poisson jumps. By using the cosine family of operators, stochastic analysis techniques, a new set of sufficient conditions are derived for the approximate controllability of the above control system. An example is provided to illustrate the obtained theory. 展开更多
关键词 Approximate controllability Hilbert space Poisson jumps second-order neutral stochas-tic differential equations semigroup theory.
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滤子软偏序半群研究 被引量:1
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作者 邵海琴 梁茂林 何建伟 《浙江大学学报(理学版)》 CAS CSCD 北大核心 2023年第5期521-526,共6页
将软集合理论应用于偏序半群。首先,引入偏序半群S上的左(右)滤子软偏序半群、滤子软偏序半群、完全左(右)滤子软偏序半群、完全滤子软偏序半群、素左(右)理想软偏序半群和素理想软偏序半群概念。其次,利用素左(右)理想软偏序半群和素... 将软集合理论应用于偏序半群。首先,引入偏序半群S上的左(右)滤子软偏序半群、滤子软偏序半群、完全左(右)滤子软偏序半群、完全滤子软偏序半群、素左(右)理想软偏序半群和素理想软偏序半群概念。其次,利用素左(右)理想软偏序半群和素理想软偏序半群,分别给出了S上的一个非空软集合是右(左)滤子软偏序半群和滤子软偏序半群的充分必要条件。最后,研究了S上的左(右)滤子软偏序半群、滤子软偏序半群、完全左(右)滤子软偏序半群和完全滤子软偏序半群的商序同态像和在偏序同态映射下的逆像,得到了一些相关结论。 展开更多
关键词 偏序半群 滤子软偏序半群 完全滤子软偏序半群 素理想软偏序半群 偏序同态 商序同态
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