It is well-known that the finite-gap solutions of the KdV equation can be generated by its recursion operator. We generalize the result to a special form of Lax pair,from which a method to constrain the integrable sys...It is well-known that the finite-gap solutions of the KdV equation can be generated by its recursion operator. We generalize the result to a special form of Lax pair,from which a method to constrain the integrable system to a lower-dimensional or fewer variable integrable system is proposed.A direct result is that the n-soliton solutions of the KdV hierarchy can be completely depicted by a series of ordinary differential equations(ODEs),which may be gotten by a simple but unfamiliar Lax pair.Furthermore the AKNS hierarchy is constrained to a series of univariate integrable hierarchies.The key is a special form of Lax pair for the AKNS hierarchy.It is proved that under the constraints all equations of the AKNS hierarchy are linearizable.展开更多
An explicit Bargmann symmetry constraint is computed and its associated binary nonlinearization of Lax pairs is carried out for the super NLS-MKdV hierarchy. Under the obtained symmetry constraint, the n-th flow of th...An explicit Bargmann symmetry constraint is computed and its associated binary nonlinearization of Lax pairs is carried out for the super NLS-MKdV hierarchy. Under the obtained symmetry constraint, the n-th flow of the super NLS-MKdV hierarchy is decomposed into two super finite-dimensional integrable Hamiltonian systems, defined over the super-symmetry manifold R4N|2N with the corresponding dynamical variables x and tn. The integrals of motion required for Liouville integrability are explicitly given.展开更多
A 3 × 3 matrix spectral problem and a Liouville integrable hierarchy are constructed by designing a new subalgebra of loop algebra A^-2. Furthermore, high-order binary symmetry constraints of the corresponding hi...A 3 × 3 matrix spectral problem and a Liouville integrable hierarchy are constructed by designing a new subalgebra of loop algebra A^-2. Furthermore, high-order binary symmetry constraints of the corresponding hierarchy are obtained by using the binary nonlinearization method. Finally, according to another new subalgebra of loop algebra A^-2, its integrable couplings are established.展开更多
The symmetry constraint and binary nonlinearization of Lax pairs for the super classical-Boussinesq hierarchy is obtained. Under the obtained symmetry constraint, the n-th flow of the super classical-Boussinesq hierar...The symmetry constraint and binary nonlinearization of Lax pairs for the super classical-Boussinesq hierarchy is obtained. Under the obtained symmetry constraint, the n-th flow of the super classical-Boussinesq hierarchy is decomposed into two super finite-dimensional integrable Hamiltonian systems, defined over the super-symmetry manifold with the corresponding dynamical variables x and tn. The integrals of motion required for Liouville integrability are explicitly given.展开更多
The constraints and the operations play an important role in database generalization.They guide and govern database generalization.The constraints are translation of the required conditions that should take into accou...The constraints and the operations play an important role in database generalization.They guide and govern database generalization.The constraints are translation of the required conditions that should take into account not only the objects and relationships among objects but also spatial data schema (classification and aggregation hierarchy) associated with the final existing database.The operations perform the actions of generalization in support of data reduction in the database.The constraints in database generalization are still lack of research.There is still the lack of frameworks to express the constraints and the operations on the basis of object_oriented data structure in database generalization.This paper focuses on the frameworks for generalization operations and constraints on the basis of object_oriented data structure in database generalization.The constraints as the attributes of the object and the operations as the methods of the object can be encapsulated in classes.They have the inheritance and polymorphism property.So the framework of the constraints and the operations which are based on object_oriented data structure can be easily understood and implemented.The constraint and the operations based on object_oriented database are proposed based on object_oriented database.The frameworks for generalization operations,constraints and relations among objects based on object_oriented data structure in database generalization are designed.The categorical database generalization is concentrated on in this paper.展开更多
By introducing a SchrSdinger type spectral problem with four potentials, we derive a new hierarchy nonlinear evolution equations. Through the nonlinearization of eigenvalue problems, we get a new finite-dimensional Ha...By introducing a SchrSdinger type spectral problem with four potentials, we derive a new hierarchy nonlinear evolution equations. Through the nonlinearization of eigenvalue problems, we get a new finite-dimensional Hamiltonian system, which is completely integrable in the Liouville sense.展开更多
Role based access control (RBAC)was proposed in 70's, and prevailed in 90's, and then Sandhu etc pro-posed formal RBAC model. Now RBAC is attracting increasing attention, and many governmental and commercial o...Role based access control (RBAC)was proposed in 70's, and prevailed in 90's, and then Sandhu etc pro-posed formal RBAC model. Now RBAC is attracting increasing attention, and many governmental and commercial or-ganizations have adopted it, its importance is more and more apparent. In this paper we illuminates the distinctionsand similarities of role and user groups, and based the model that was proposed by Sandhu, we examine the relation-ship of role hierarchies and role constraints and formally describes that, and explain the most important part of roleconstraints ,which is separation of duties.展开更多
基金Supported by National Natural Science Foundation of China under Grant No.10735030Natural Science Foundation of Zhejiang Province under Grant Nos.R609077,Y6090592National Science Foundation of Ningbo City under Grant Nos.2009B21003,2010A610103, 2010A610095
文摘It is well-known that the finite-gap solutions of the KdV equation can be generated by its recursion operator. We generalize the result to a special form of Lax pair,from which a method to constrain the integrable system to a lower-dimensional or fewer variable integrable system is proposed.A direct result is that the n-soliton solutions of the KdV hierarchy can be completely depicted by a series of ordinary differential equations(ODEs),which may be gotten by a simple but unfamiliar Lax pair.Furthermore the AKNS hierarchy is constrained to a series of univariate integrable hierarchies.The key is a special form of Lax pair for the AKNS hierarchy.It is proved that under the constraints all equations of the AKNS hierarchy are linearizable.
文摘An explicit Bargmann symmetry constraint is computed and its associated binary nonlinearization of Lax pairs is carried out for the super NLS-MKdV hierarchy. Under the obtained symmetry constraint, the n-th flow of the super NLS-MKdV hierarchy is decomposed into two super finite-dimensional integrable Hamiltonian systems, defined over the super-symmetry manifold R4N|2N with the corresponding dynamical variables x and tn. The integrals of motion required for Liouville integrability are explicitly given.
基金supported by China Postdoctoral Science Foundation and National Natural Science Foundation of China under Grant No.10471139
文摘A 3 × 3 matrix spectral problem and a Liouville integrable hierarchy are constructed by designing a new subalgebra of loop algebra A^-2. Furthermore, high-order binary symmetry constraints of the corresponding hierarchy are obtained by using the binary nonlinearization method. Finally, according to another new subalgebra of loop algebra A^-2, its integrable couplings are established.
基金Project supported by the National Natural Science Foundation of China (Grant Nos.61072147 and 11071159)the Natural Science Foundation of Shanghai,China (Grant No.09ZR1410800)+2 种基金the Science Foundation of the Key Laboratory of Mathematics Mechanization,China (Grant No.KLMM0806)the Shanghai Leading Academic Discipline Project,China (Grant No.J50101)the Key Disciplines of Shanghai Municipality of China (Grant No.S30104)
文摘The symmetry constraint and binary nonlinearization of Lax pairs for the super classical-Boussinesq hierarchy is obtained. Under the obtained symmetry constraint, the n-th flow of the super classical-Boussinesq hierarchy is decomposed into two super finite-dimensional integrable Hamiltonian systems, defined over the super-symmetry manifold with the corresponding dynamical variables x and tn. The integrals of motion required for Liouville integrability are explicitly given.
文摘The constraints and the operations play an important role in database generalization.They guide and govern database generalization.The constraints are translation of the required conditions that should take into account not only the objects and relationships among objects but also spatial data schema (classification and aggregation hierarchy) associated with the final existing database.The operations perform the actions of generalization in support of data reduction in the database.The constraints in database generalization are still lack of research.There is still the lack of frameworks to express the constraints and the operations on the basis of object_oriented data structure in database generalization.This paper focuses on the frameworks for generalization operations and constraints on the basis of object_oriented data structure in database generalization.The constraints as the attributes of the object and the operations as the methods of the object can be encapsulated in classes.They have the inheritance and polymorphism property.So the framework of the constraints and the operations which are based on object_oriented data structure can be easily understood and implemented.The constraint and the operations based on object_oriented database are proposed based on object_oriented database.The frameworks for generalization operations,constraints and relations among objects based on object_oriented data structure in database generalization are designed.The categorical database generalization is concentrated on in this paper.
文摘By introducing a SchrSdinger type spectral problem with four potentials, we derive a new hierarchy nonlinear evolution equations. Through the nonlinearization of eigenvalue problems, we get a new finite-dimensional Hamiltonian system, which is completely integrable in the Liouville sense.
文摘Role based access control (RBAC)was proposed in 70's, and prevailed in 90's, and then Sandhu etc pro-posed formal RBAC model. Now RBAC is attracting increasing attention, and many governmental and commercial or-ganizations have adopted it, its importance is more and more apparent. In this paper we illuminates the distinctionsand similarities of role and user groups, and based the model that was proposed by Sandhu, we examine the relation-ship of role hierarchies and role constraints and formally describes that, and explain the most important part of roleconstraints ,which is separation of duties.
