We introduce the notion of the contraction integrated semigroups and give the Lumber-Phillips characterization of the generator, and also the charaterazied generators of isometric integrated semigroups. For their appl...We introduce the notion of the contraction integrated semigroups and give the Lumber-Phillips characterization of the generator, and also the charaterazied generators of isometric integrated semigroups. For their application, a necessary and sufficient condition for q-matrices Q generating a contraction integrated semigroup is given, and a necessary and sufficient condition for a transition function to be a Feller-Reuter-Riley transition function is also given in terms of its q-matrix.展开更多
A structure theorem for superabundant semigroups in terms of semilattices of normalized Rees matrix semigroups over some cancellative monoids is obtained. This result not only provides a construction method for supera...A structure theorem for superabundant semigroups in terms of semilattices of normalized Rees matrix semigroups over some cancellative monoids is obtained. This result not only provides a construction method for superabundant semigroups but also generalizes the well-known result of Petrich on completely regular semigroups. Some results obtained by Fountain on abundant semigroups are also extended and strengthened.展开更多
SEMIGROUP S is said to be rpp (dually, lpp) if every principal right ideal aS^1(S^1a) of S, re-garded as a right (left)S^1-system, is projective. The semigroup which is both rpp and lpp is said to be abundant. These k...SEMIGROUP S is said to be rpp (dually, lpp) if every principal right ideal aS^1(S^1a) of S, re-garded as a right (left)S^1-system, is projective. The semigroup which is both rpp and lpp is said to be abundant. These kinds of generalized regular semigroups have aroused wideattention. The Green’s,relations (~*-Green’s relations introduced by Pastijn) have formed avery useful tool in study on regular (abundant) semigroups. In order to develop the study onrpp semigroups a step further, we introduced the so-called (1)-Green’s,relation which展开更多
For injective, bounded operator C on a Banach space X , the author defines the C -dissipative operator, and then gives Lumer-Phillips characterizations of the generators of quasi-contractive C -semigro...For injective, bounded operator C on a Banach space X , the author defines the C -dissipative operator, and then gives Lumer-Phillips characterizations of the generators of quasi-contractive C -semigroups, where a C -semigroup T(·) is quasi-contractive if ‖T(t)x‖‖Cx‖ for all t0 and x∈X . This kind of generators guarantee that the associate abstract Cauchy problem u′(t,x)=Au(t,x) has a unique nonincreasing solution when the initial data is in C(D(A)) (here D(A) is the domain of A ). Also, the generators of quasi isometric C -semigroups are characterized.展开更多
In this article, we consider a stochastic SIR model and show that the distributions of the solutions of the system are absolutely continuous. Furthermore, we analyze long-time behaviour of densities of the distributio...In this article, we consider a stochastic SIR model and show that the distributions of the solutions of the system are absolutely continuous. Furthermore, we analyze long-time behaviour of densities of the distributions of the solution. We prove that the densities can converge in L1 to an invariant density.展开更多
A U-abundant semigroup S in which every H-class of S contains an element in the set of projections U of S is said to be a U-superabundant semigroup.This is an analogue of regular semigroups which are unions of groups ...A U-abundant semigroup S in which every H-class of S contains an element in the set of projections U of S is said to be a U-superabundant semigroup.This is an analogue of regular semigroups which are unions of groups and an analogue of abundant semigroups which are superabundant.In 1941,Clifford proved that a semigroup is a union of groups if and only if it is a semilattice of completely simple semigroups.Several years later,Fountain generalized this result to the class of superabundant semigroups.In this paper,we extend their work to U-superabundant semigroups.展开更多
The concepts of L*-inverse semigroups and left wreath products of semigroups are introduced. It is shown that the L*-inverse semigroup can be described as the left wreath product of a type A semigroupΓand a left regu...The concepts of L*-inverse semigroups and left wreath products of semigroups are introduced. It is shown that the L*-inverse semigroup can be described as the left wreath product of a type A semigroupΓand a left regular band B together with a mapping which maps the semigroupΓinto the endomorphism semigroup End(B). This result generalizes the structure theorem of Yamada for the left inverse semigroups in the class of regular semigroups. We shall also provide a constructed example for the L*-inverse semigroups by using the left wreath products.展开更多
As a generalization of an orthodox semigroup in the class of regular semigroups, a type W semigroup was first investigated by El-Qallali and Fountain. As an analogy of the type W semigroups in the class of abundant se...As a generalization of an orthodox semigroup in the class of regular semigroups, a type W semigroup was first investigated by El-Qallali and Fountain. As an analogy of the type W semigroups in the class of abundant semigroups, we introduce the U-orthodox semigroups. It is shown that the maximum congruence μ contained in on U-orthodox semigroups can be determined. As a consequence, we show that a U-orthodox semigroup S can be expressed by the spined product of a Hall semigroup W U and a V-ample semigroup (T,V). This theorem not only generalizes a known result of Hall-Yamada for orthodox semigroups but also generalizes another known result of El-Qallali and Fountain for type W semigroups.展开更多
We investigate the dynamical behavior of quantum steering (QS), Bell nonlocality, and entanglement in open quantum systems. We focus on a two-qubit system evolving within the framework of Kossakowski-type quantum dyna...We investigate the dynamical behavior of quantum steering (QS), Bell nonlocality, and entanglement in open quantum systems. We focus on a two-qubit system evolving within the framework of Kossakowski-type quantum dynamical semigroups. Our findings reveal that the measures of quantumness for the asymptotic states rely on the primary parameter of the quantum model. Furthermore, control over these measures can be achieved through a careful selection of these parameters. Our analysis encompasses various cases, including Bell states, Werner states, and Horodecki states, demonstrating that the asymptotic states can exhibit steering, entanglement, and Bell nonlocality. Additionally, we find that these three quantum measures of correlations can withstand the influence of the environment, maintaining their properties even over extended periods.展开更多
In this work, we prove the existence and uniqueness of the solution of the generalized Schrödinger equation in the periodic distributional space P’. Furthermore, we prove that the solution depends continuously r...In this work, we prove the existence and uniqueness of the solution of the generalized Schrödinger equation in the periodic distributional space P’. Furthermore, we prove that the solution depends continuously respect to the initial data in P’. Introducing a family of weakly continuous operators, we prove that this family is a semigroup of operators in P’. Then, with this family of operators, we get a fine version of the existence and dependency continuous theorem obtained. Finally, we provide some consequences of this study.展开更多
In this paper, we study the class of ortho-u-monoids which are generalized orthogroups within the class of E（S）-semiabundant semigroups. After introducing the concept of （-）-Green＇s relations, and obtaining some ...In this paper, we study the class of ortho-u-monoids which are generalized orthogroups within the class of E（S）-semiabundant semigroups. After introducing the concept of （-）-Green＇s relations, and obtaining some important properties of （-）-Green＇s relations and super E（S）-semiabundant semigroups, we have given the semilattice decomposition of ortho-u-monoids and a structure theorem for regular ortho-u-monoids. The main techniques that we used in the study are the （-）-Green＇s relations, and the semi-spined product of semigroups.展开更多
The boundary stabilization problem of a Timoshenko beam attached with a mass at one end is studied. First, with linear boundary force feedback and moment control simultaneously at the end attached with the load, the e...The boundary stabilization problem of a Timoshenko beam attached with a mass at one end is studied. First, with linear boundary force feedback and moment control simultaneously at the end attached with the load, the energy corresponding to the closed loop system is proven to be exponentially convergent to zero as time t →∞. Then, some counterexamples are given to show that, in other casest the corresponding closed loop system is, in general, not stable asymtotically, let alone exponentially.展开更多
Let （X, d, μ） be a metric measure space endowed with a distance d and a nonnegative Borel doubling measure μ. Let L be a second order self-adjoint positive operator on L^2（X）. Assume that the semigroup e-^tL gen...Let （X, d, μ） be a metric measure space endowed with a distance d and a nonnegative Borel doubling measure μ. Let L be a second order self-adjoint positive operator on L^2（X）. Assume that the semigroup e-^tL generated by -L satisfies the Gaussian upper bounds on L2（X）. In this article we study a local version of Hardy space hi （X） associated with L in terms of the area function characterization, and prove their atomic characters. Furthermore, we introduce a Moser type local boundedness condition for L, and then we apply this condition to show that the space hzL（X） can be characterized in terms of the Littlewood-Paley function. Finally, a broad class of applications of these results is described.展开更多
The author gives a characterization of the Fourier transforms of bounded bilinear forms on C＊（S1）×C＊（S2） of two foundation semigroups S1 and S2 in terms of Jordan ＊-representations, hemimogeneous random fi...The author gives a characterization of the Fourier transforms of bounded bilinear forms on C＊（S1）×C＊（S2） of two foundation semigroups S1 and S2 in terms of Jordan ＊-representations, hemimogeneous random fields, and as well as weakly harmonizable random fields of S1 and S2 into Hilbert spaces.展开更多
文摘We introduce the notion of the contraction integrated semigroups and give the Lumber-Phillips characterization of the generator, and also the charaterazied generators of isometric integrated semigroups. For their application, a necessary and sufficient condition for q-matrices Q generating a contraction integrated semigroup is given, and a necessary and sufficient condition for a transition function to be a Feller-Reuter-Riley transition function is also given in terms of its q-matrix.
文摘A structure theorem for superabundant semigroups in terms of semilattices of normalized Rees matrix semigroups over some cancellative monoids is obtained. This result not only provides a construction method for superabundant semigroups but also generalizes the well-known result of Petrich on completely regular semigroups. Some results obtained by Fountain on abundant semigroups are also extended and strengthened.
文摘SEMIGROUP S is said to be rpp (dually, lpp) if every principal right ideal aS^1(S^1a) of S, re-garded as a right (left)S^1-system, is projective. The semigroup which is both rpp and lpp is said to be abundant. These kinds of generalized regular semigroups have aroused wideattention. The Green’s,relations (~*-Green’s relations introduced by Pastijn) have formed avery useful tool in study on regular (abundant) semigroups. In order to develop the study onrpp semigroups a step further, we introduced the so-called (1)-Green’s,relation which
文摘For injective, bounded operator C on a Banach space X , the author defines the C -dissipative operator, and then gives Lumer-Phillips characterizations of the generators of quasi-contractive C -semigroups, where a C -semigroup T(·) is quasi-contractive if ‖T(t)x‖‖Cx‖ for all t0 and x∈X . This kind of generators guarantee that the associate abstract Cauchy problem u′(t,x)=Au(t,x) has a unique nonincreasing solution when the initial data is in C(D(A)) (here D(A) is the domain of A ). Also, the generators of quasi isometric C -semigroups are characterized.
基金supported by Program for Changjiang Scholars and Innovative Research Team in University,NSFC of China(11371085 and 11201008)the Ph.D.Programs Foundation of Ministry of China(200918)
文摘In this article, we consider a stochastic SIR model and show that the distributions of the solutions of the system are absolutely continuous. Furthermore, we analyze long-time behaviour of densities of the distributions of the solution. We prove that the densities can converge in L1 to an invariant density.
基金supported by National Natural Science Foundation of China (Grant Nos.10671151,10971160,10871161)Natural Science Foundation of of Shaanxi Province (Grant No.SJ08A06)a grant of Wu Jiehyee Charitable Foundation,Hong Kong 2007/09
文摘A U-abundant semigroup S in which every H-class of S contains an element in the set of projections U of S is said to be a U-superabundant semigroup.This is an analogue of regular semigroups which are unions of groups and an analogue of abundant semigroups which are superabundant.In 1941,Clifford proved that a semigroup is a union of groups if and only if it is a semilattice of completely simple semigroups.Several years later,Fountain generalized this result to the class of superabundant semigroups.In this paper,we extend their work to U-superabundant semigroups.
文摘The concepts of L*-inverse semigroups and left wreath products of semigroups are introduced. It is shown that the L*-inverse semigroup can be described as the left wreath product of a type A semigroupΓand a left regular band B together with a mapping which maps the semigroupΓinto the endomorphism semigroup End(B). This result generalizes the structure theorem of Yamada for the left inverse semigroups in the class of regular semigroups. We shall also provide a constructed example for the L*-inverse semigroups by using the left wreath products.
基金supported by National Natural Science Foundation of China (Grant No. 10671151)Natural Science Foundation of Shaanxi Province (Grant No. SJ08A06)partially by UGC (HK) (Grant No. 2160123)
文摘As a generalization of an orthodox semigroup in the class of regular semigroups, a type W semigroup was first investigated by El-Qallali and Fountain. As an analogy of the type W semigroups in the class of abundant semigroups, we introduce the U-orthodox semigroups. It is shown that the maximum congruence μ contained in on U-orthodox semigroups can be determined. As a consequence, we show that a U-orthodox semigroup S can be expressed by the spined product of a Hall semigroup W U and a V-ample semigroup (T,V). This theorem not only generalizes a known result of Hall-Yamada for orthodox semigroups but also generalizes another known result of El-Qallali and Fountain for type W semigroups.
文摘We investigate the dynamical behavior of quantum steering (QS), Bell nonlocality, and entanglement in open quantum systems. We focus on a two-qubit system evolving within the framework of Kossakowski-type quantum dynamical semigroups. Our findings reveal that the measures of quantumness for the asymptotic states rely on the primary parameter of the quantum model. Furthermore, control over these measures can be achieved through a careful selection of these parameters. Our analysis encompasses various cases, including Bell states, Werner states, and Horodecki states, demonstrating that the asymptotic states can exhibit steering, entanglement, and Bell nonlocality. Additionally, we find that these three quantum measures of correlations can withstand the influence of the environment, maintaining their properties even over extended periods.
文摘In this work, we prove the existence and uniqueness of the solution of the generalized Schrödinger equation in the periodic distributional space P’. Furthermore, we prove that the solution depends continuously respect to the initial data in P’. Introducing a family of weakly continuous operators, we prove that this family is a semigroup of operators in P’. Then, with this family of operators, we get a fine version of the existence and dependency continuous theorem obtained. Finally, we provide some consequences of this study.
基金Supported by National Natural Science Foundation of China （Grant Nos. 10871161, 10926031）, Natural Science Foundation Project of CQ CSTC2009BB2291, the Young Science and Technology Fund of Xi＇an University of Architecture and Technology （Grant No. QN0829）
文摘In this paper, we study the class of ortho-u-monoids which are generalized orthogroups within the class of E（S）-semiabundant semigroups. After introducing the concept of （-）-Green＇s relations, and obtaining some important properties of （-）-Green＇s relations and super E（S）-semiabundant semigroups, we have given the semilattice decomposition of ortho-u-monoids and a structure theorem for regular ortho-u-monoids. The main techniques that we used in the study are the （-）-Green＇s relations, and the semi-spined product of semigroups.
基金Project supported by the the National Key Project of China.
文摘The boundary stabilization problem of a Timoshenko beam attached with a mass at one end is studied. First, with linear boundary force feedback and moment control simultaneously at the end attached with the load, the energy corresponding to the closed loop system is proven to be exponentially convergent to zero as time t →∞. Then, some counterexamples are given to show that, in other casest the corresponding closed loop system is, in general, not stable asymtotically, let alone exponentially.
基金supported by China Postdoctoral Science Foundation funded project(Grant No.201104383)the Fundamental Research Funds for the Central Universities(Grant No.11lGPY56)+1 种基金National Natural Science Foundation of China(Grant No.10925106)Guangdong Province Key Laboratory of Computational Science and Grant for Senior Scholars from the Association of Colleges and Universities of Guangdong
文摘Let （X, d, μ） be a metric measure space endowed with a distance d and a nonnegative Borel doubling measure μ. Let L be a second order self-adjoint positive operator on L^2（X）. Assume that the semigroup e-^tL generated by -L satisfies the Gaussian upper bounds on L2（X）. In this article we study a local version of Hardy space hi （X） associated with L in terms of the area function characterization, and prove their atomic characters. Furthermore, we introduce a Moser type local boundedness condition for L, and then we apply this condition to show that the space hzL（X） can be characterized in terms of the Littlewood-Paley function. Finally, a broad class of applications of these results is described.
基金the Research Project No. 830104the Center of Excellence for Mathematics of the University of Isfahan for their financial supports
文摘The author gives a characterization of the Fourier transforms of bounded bilinear forms on C＊（S1）×C＊（S2） of two foundation semigroups S1 and S2 in terms of Jordan ＊-representations, hemimogeneous random fields, and as well as weakly harmonizable random fields of S1 and S2 into Hilbert spaces.
