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
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
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.
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
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
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
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
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
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
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
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
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.
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
Adjoint semigroups of BCI algebras were introduced by Huang [1] and some of its important properties were obtained. In this paper,some characterizations of positive implicative BCK algebras are given by discussing the...Adjoint semigroups of BCI algebras were introduced by Huang [1] and some of its important properties were obtained. In this paper,some characterizations of positive implicative BCK algebras are given by discussing the adjoint semigroups. Moreover,the semigroup differences between positive BCK algebras and implicative BCK algebras are discussed,and some semigroup characterizations of implicative BCK algebras are given.展开更多
In this article, we propose a generalized exp(-Φ(ξ))-expansion method and successfully implement it to find exact traveling wave solutions to the fifth order standard Sawada-Kotera (SK) equation. The exact traveling...In this article, we propose a generalized exp(-Φ(ξ))-expansion method and successfully implement it to find exact traveling wave solutions to the fifth order standard Sawada-Kotera (SK) equation. The exact traveling wave solutions are established in the form of trigonometric, hyperbolic, exponential and rational functions with some free parameters. It is shown that this method is standard, effective and easily applicable mathematical tool for solving nonlinear partial differential equations arises in the field of mathematical physics and engineering.展开更多
Based on semi - order fuzzy supermaringales andsubmartingales, the semi- order fuzzy supermartingaleand submartingale theory is developed. The main resultis to generalize the Doob decomposition and the Riesz de-compos...Based on semi - order fuzzy supermaringales andsubmartingales, the semi- order fuzzy supermartingaleand submartingale theory is developed. The main resultis to generalize the Doob decomposition and the Riesz de-composition theorems of standard martingale theory tosemi - order fuzzy supermaringales and submartingales.The structure of semi - order fuzzy supermaringales andsubmartingales and the conditions of that they has Doobdecomposition (resp. Riesz decomposition) are discussedin detail.展开更多
This article explores the O(t^(-β))synchronization and asymptotic synchronization for fractional order BAM neural networks(FBAMNNs)with discrete delays,distributed delays and non-identical perturbations.By designing ...This article explores the O(t^(-β))synchronization and asymptotic synchronization for fractional order BAM neural networks(FBAMNNs)with discrete delays,distributed delays and non-identical perturbations.By designing a state feedback control law and a new kind of fractional order Lyapunov functional,a new set of algebraic sufficient conditions are derived to guarantee the O(t^(-β))Synchronization and asymptotic synchronization of the considered FBAMNNs model;this can easily be evaluated without using a MATLAB LMI control toolbox.Finally,two numerical examples,along with the simulation results,illustrate the correctness and viability of the exhibited synchronization results.展开更多
文摘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).
基金The authors are grateful to the anonymous referees for careful checking of the details and for helpful comments that improved this paper.This work was supported by the Taif University Researchers Supporting Project(TURSP-2020/246),Taif University,Taif,Saudi Arabia.
文摘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.
文摘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.
基金supported by the Higher Education Commission of Pakistan under Grant No.I-8/HEC/HRD/2007/182
文摘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.
基金The NSF(10961014) of Chinathe NSF(0501332) of Guangdong Province+1 种基金the Excellent Youth Talent Foundation(2009SQRZ149) of Anhui Provincethe Fuyang Normal College Youth Foundation (2008LQ11)
文摘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.
基金The NSF (10961014) of Chinathe NSF (S2011010003681) of Guangdong Province+3 种基金the Science and Technology Projects (2010B010600039) of Guangdong Provincethe Excellent Youth Talent Foundation (2012SQRL115ZD) of Anhui Provincethe University Natural Science Project (KJ2012B133) of Anhui Provincethe NSF (2007LZ01) of Fuyang Normal College
文摘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.
文摘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].
基金Supported by the Natural Science Foundation of Hubei Province in China（2004D006）
文摘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.
基金supported by the National Natural Science Foundation of China(11701453)Fundamental Research Funds for the Central Universities(31020180QD05)+2 种基金The second author was supported by the National Natural Science Foundation of China(11971431,11401525)the Natural Science Foundation of Zhejiang Province(LY18A010006)and the first Class Discipline of Zhejiang-A(Zhejiang Gongshang University-Statistics).
文摘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.
基金Supported by the NNSF of China(10961014)Supported by the NSF of Jiangxi Province(2008GZ048)Supported by the SF of Education Department of Jiangxi Province(GJJZ[2007]134)
文摘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.
基金supported by the National Board for Higher Mathematics,Mumbai,India under Grant No.2/48(5)/2013/NBHM(R.P.)/RD-II/688 dt 16.01.2014
文摘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.
文摘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.
基金Foundation item： Supported by NSF of China（10471112） Supported by Shaanxi Provincial Natural Science Foundation（2005A15） Acknowledgement The authors express their gratitude to the referees for very helpful and detailed comments.
文摘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.
文摘Adjoint semigroups of BCI algebras were introduced by Huang [1] and some of its important properties were obtained. In this paper,some characterizations of positive implicative BCK algebras are given by discussing the adjoint semigroups. Moreover,the semigroup differences between positive BCK algebras and implicative BCK algebras are discussed,and some semigroup characterizations of implicative BCK algebras are given.
文摘In this article, we propose a generalized exp(-Φ(ξ))-expansion method and successfully implement it to find exact traveling wave solutions to the fifth order standard Sawada-Kotera (SK) equation. The exact traveling wave solutions are established in the form of trigonometric, hyperbolic, exponential and rational functions with some free parameters. It is shown that this method is standard, effective and easily applicable mathematical tool for solving nonlinear partial differential equations arises in the field of mathematical physics and engineering.
文摘Based on semi - order fuzzy supermaringales andsubmartingales, the semi- order fuzzy supermartingaleand submartingale theory is developed. The main resultis to generalize the Doob decomposition and the Riesz de-composition theorems of standard martingale theory tosemi - order fuzzy supermaringales and submartingales.The structure of semi - order fuzzy supermaringales andsubmartingales and the conditions of that they has Doobdecomposition (resp. Riesz decomposition) are discussedin detail.
基金joint financial support of Thailand Research Fund RSA 6280004,RUSA-Phase 2.0 Grant No.F 24-51/2014-UPolicy(TN Multi-Gen),Dept.of Edn.Govt.of India,UGC-SAP(DRS-I)Grant No.F.510/8/DRS-I/2016(SAP-I)+1 种基金DST(FIST-level I)657876570 Grant No.SR/FIST/MS-I/2018/17Prince Sultan University for funding this work through research group Nonlinear Analysis Methods in Applied Mathematics(NAMAM)group number RG-DES-2017-01-17。
文摘This article explores the O(t^(-β))synchronization and asymptotic synchronization for fractional order BAM neural networks(FBAMNNs)with discrete delays,distributed delays and non-identical perturbations.By designing a state feedback control law and a new kind of fractional order Lyapunov functional,a new set of algebraic sufficient conditions are derived to guarantee the O(t^(-β))Synchronization and asymptotic synchronization of the considered FBAMNNs model;this can easily be evaluated without using a MATLAB LMI control toolbox.Finally,two numerical examples,along with the simulation results,illustrate the correctness and viability of the exhibited synchronization results.
