Within framework of zero curvature representation theory, a family of integrable rational semi-discrete systems is derived from a matrix spectral problem. The Hamiltonian forms of obtained semi-discrete systems are co...Within framework of zero curvature representation theory, a family of integrable rational semi-discrete systems is derived from a matrix spectral problem. The Hamiltonian forms of obtained semi-discrete systems are constructed by means of the discrete trace identity. The Liouville integrability for the obtained family is demonstrated. In the end, a reduced family of obtained semi-discrete systems and its Hamiltonian form are worked out.展开更多
With the aid of symbolic computation system Maple, some families of new rational variable separation solutions of the （2＋1）-dimensional dispersive long wave equations are constructed by means of a function transfor...With the aid of symbolic computation system Maple, some families of new rational variable separation solutions of the （2＋1）-dimensional dispersive long wave equations are constructed by means of a function transformation, improved mapping approach, and variable separation approach, among which there are rational solitary wave solutions, periodic wave solutions and rational wave solutions.展开更多
The notion of an ideal family of weighted subspaces of a discrete metric space X with bounded geometry is introduced. It is shown that, if X has Yu’s property A, the ideal structure of the Roe algebra of X with coeff...The notion of an ideal family of weighted subspaces of a discrete metric space X with bounded geometry is introduced. It is shown that, if X has Yu’s property A, the ideal structure of the Roe algebra of X with coefficients in B(H) is completely characterized by the ideal families of weighted subspaces of X, where B(H) denotes the C*-algebra of bounded linear operators on a separable Hilbert space H.展开更多
The authors define the equi-nuclearity of uniform Roe algebras of a family of metric spaces. For a discrete metric space X with bounded geometry which is covered by a family of subspaces {Xi}i=1^∞, if {C^＊（Xi）}i=1...The authors define the equi-nuclearity of uniform Roe algebras of a family of metric spaces. For a discrete metric space X with bounded geometry which is covered by a family of subspaces {Xi}i=1^∞, if {C^＊（Xi）}i=1^∞ are equi-nuclear and under some proper gluing conditions, it is proved that C＊（X） is nuclear. Furthermore, it is claimed that in general, the coarse Roe algebra C^＊ （X） is not nuclear.展开更多
基金Supported by the Science and Technology Plan Projects of the Educational Department of Shandong Province of China under Grant No. J08LI08
文摘Within framework of zero curvature representation theory, a family of integrable rational semi-discrete systems is derived from a matrix spectral problem. The Hamiltonian forms of obtained semi-discrete systems are constructed by means of the discrete trace identity. The Liouville integrability for the obtained family is demonstrated. In the end, a reduced family of obtained semi-discrete systems and its Hamiltonian form are worked out.
基金supported by the Scientific Research Foundation of Beijing Information Science and Technology UniversityScientific Creative Platform Foundation of Beijing Municipal Commission of Education
文摘With the aid of symbolic computation system Maple, some families of new rational variable separation solutions of the （2＋1）-dimensional dispersive long wave equations are constructed by means of a function transformation, improved mapping approach, and variable separation approach, among which there are rational solitary wave solutions, periodic wave solutions and rational wave solutions.
基金Project supported by the Foundation for the Author of National Excellent Doctoral Dissertation of China (No. 200416)the Program for New Century Excellent Talents in University of China (No. 06-0420)+2 种基金the Scientific Research Starting Foundation for the Returned Overseas Chinese Scholars (No.2008-890)the Dawn Light Project of Shanghai Municipal Education Commission (No. 07SG38)the Shanghai Pujiang Program (No. 08PJ14006).
文摘The notion of an ideal family of weighted subspaces of a discrete metric space X with bounded geometry is introduced. It is shown that, if X has Yu’s property A, the ideal structure of the Roe algebra of X with coefficients in B(H) is completely characterized by the ideal families of weighted subspaces of X, where B(H) denotes the C*-algebra of bounded linear operators on a separable Hilbert space H.
基金supported by the National Natural Science Foundation of China(Nos.10731020,10971023)the Shu Guang Project of Shanghai Municipal Education Commission and Shanghai Education DepartmentFoundation(No.07SG38)the Foundation of the Ministry of Education of China
文摘The authors define the equi-nuclearity of uniform Roe algebras of a family of metric spaces. For a discrete metric space X with bounded geometry which is covered by a family of subspaces {Xi}i=1^∞, if {C^＊（Xi）}i=1^∞ are equi-nuclear and under some proper gluing conditions, it is proved that C＊（X） is nuclear. Furthermore, it is claimed that in general, the coarse Roe algebra C^＊ （X） is not nuclear.
