Let A be a bornological quantum group and R a bornological algebra. If R is an essential A-module, then there is a unique extension to M（A）-module with 1x = x. There is a one-to-one corresponding relationship betwee...Let A be a bornological quantum group and R a bornological algebra. If R is an essential A-module, then there is a unique extension to M（A）-module with 1x = x. There is a one-to-one corresponding relationship between the actions of A and the coactions of . If R is a Galois object for A, then there exists a faithful δ-invariant functional on R. Moreover,the Galois objects also have modular properties such as algebraic quantum groups. By constructing the comultiplication Δ,counit ε, antipode S and invariant functional φ onR×R, R×R can be considered as a bornological quantum group.展开更多
Up to now, there have been many methods for knowledge representation and reasoning in causal networks, but few of them include the research on the coactions of nodes. In practice, ignoring these coactions may influenc...Up to now, there have been many methods for knowledge representation and reasoning in causal networks, but few of them include the research on the coactions of nodes. In practice, ignoring these coactions may influence the accuracy of reasoning and even give rise to incorrect reasoning. In this paper, based on multilayer causal networks, the definitions on coaction nodes are given to construct a new causal network called Coaction Causal Network, which serves to construct a model of neural network for diagnosis followed by fuzzy reasoning, and then the activation rules are given and neural computing methods are used to finish the diagnostic rea soning. These methods are proved in theory and a method of computing the number of solutions for the diagnostic reasoning is given. Finally, the experiments and the conclusions are presellted.展开更多
In this paper,we generalize the Takesaki-Takai duality theorem in Hilbert C~*-modules; that is to say,if (H,V,U) is a Kac-system,where H is a Hilbert space,V is a multiplicative unitary operator on H(?)H and U is a un...In this paper,we generalize the Takesaki-Takai duality theorem in Hilbert C~*-modules; that is to say,if (H,V,U) is a Kac-system,where H is a Hilbert space,V is a multiplicative unitary operator on H(?)H and U is a unitary operator on H,and if E is an (?)-compatible Hilbert (?)-module, then E×(?)×(?)K(H),where K(H) is the set of all compact operators on H,and (?) and (?) are Hopf C~*-algebras corresponding to the Kac-system (H,V,U).展开更多
文摘Let A be a bornological quantum group and R a bornological algebra. If R is an essential A-module, then there is a unique extension to M（A）-module with 1x = x. There is a one-to-one corresponding relationship between the actions of A and the coactions of . If R is a Galois object for A, then there exists a faithful δ-invariant functional on R. Moreover,the Galois objects also have modular properties such as algebraic quantum groups. By constructing the comultiplication Δ,counit ε, antipode S and invariant functional φ onR×R, R×R can be considered as a bornological quantum group.
文摘Up to now, there have been many methods for knowledge representation and reasoning in causal networks, but few of them include the research on the coactions of nodes. In practice, ignoring these coactions may influence the accuracy of reasoning and even give rise to incorrect reasoning. In this paper, based on multilayer causal networks, the definitions on coaction nodes are given to construct a new causal network called Coaction Causal Network, which serves to construct a model of neural network for diagnosis followed by fuzzy reasoning, and then the activation rules are given and neural computing methods are used to finish the diagnostic rea soning. These methods are proved in theory and a method of computing the number of solutions for the diagnostic reasoning is given. Finally, the experiments and the conclusions are presellted.
基金Supported by NSF 10301004,NSF 10171098Yantai University PHD Foundation SX03B14
文摘In this paper,we generalize the Takesaki-Takai duality theorem in Hilbert C~*-modules; that is to say,if (H,V,U) is a Kac-system,where H is a Hilbert space,V is a multiplicative unitary operator on H(?)H and U is a unitary operator on H,and if E is an (?)-compatible Hilbert (?)-module, then E×(?)×(?)K(H),where K(H) is the set of all compact operators on H,and (?) and (?) are Hopf C~*-algebras corresponding to the Kac-system (H,V,U).
