During the evolution from cognitive radio to cognitive networks,the environment cognition extended from wireless environments to network and user environments.To understand the basic theory of Local Multi-Domain Cogni...During the evolution from cognitive radio to cognitive networks,the environment cognition extended from wireless environments to network and user environments.To understand the basic theory of Local Multi-Domain Cognition(LMDC),and to provide a theoretical basis for further study in cooperative multi-domain cognition and initiative multi-domain cognition,the LMDC is investigated in this paper.A Local Single-Domain Cognitive(LSDC)approach is first proposed based on multidimensional edge detection theory.This approach can divide the parameter space that describes the single-domain environment into different areas,and can represent each area with an identifier.Using this as a foundation,the single-domain environment is extended to multi-domain environments,and an LMDC approach is presented to describe the LMDC environment.The paper concludes by introducing two examples and the corresponding analysis to illustrate the feasibility of the proposed LMDC approach.展开更多
In this paper we define the tensor products of spaces of exponential type vectors of closed unbounded operators in Banach spaces. Using the real method of interpolation （K-functional） we prove the interpolation theo...In this paper we define the tensor products of spaces of exponential type vectors of closed unbounded operators in Banach spaces. Using the real method of interpolation （K-functional） we prove the interpolation theorems that permit to characterize of tensor products of spaces of exponential type vectors, We show an application of abstract results to the theory of regular elliptic operators on bounded domains. For such operators the exponential type vectors are root vectors. Thus we describe the tensor products of root vectors of regular elliptic operators on bounded domains.展开更多
Given a real-valued separable M-type 2 Banach space X with the p-th power of the norm of C2-class, the almost sure asymptotic upper bounds of the solutions of the Ornstein-Uhlenbeck Processes described by the followin...Given a real-valued separable M-type 2 Banach space X with the p-th power of the norm of C2-class, the almost sure asymptotic upper bounds of the solutions of the Ornstein-Uhlenbeck Processes described by the following equations {dz（t）=A（t,z（t））dt＋σ（t,z（t））dW（t）,z（0）=z0∈X,are investigated. This study generalizes the corresponding well-known finite dimensional results of Lapeyre （1989） and Mao （1992）.展开更多
This paper aims to study the solvability of vector Ky Fan inequalities and the compactness of its solution sets.For vector-valued functions with the cone semicontinuity and the cone quasiconvexity in infinite dimensio...This paper aims to study the solvability of vector Ky Fan inequalities and the compactness of its solution sets.For vector-valued functions with the cone semicontinuity and the cone quasiconvexity in infinite dimensional spaces,the authors prove some existence results of the solutions and the compactness of the solution sets.Especially,some results for the vector Ky Fan inequalities on noncompact sets are built and the compactness of its solution sets are also discussed.As applications,some existence theorems of the solutions of vector variational inequalities are obtained.展开更多
Functional limit theorems for scaled occupation time fluctuations of a sequence of generalized branching particle systems in Rd with anisotropic space motions and strongly degenerated splitting abilities are studied i...Functional limit theorems for scaled occupation time fluctuations of a sequence of generalized branching particle systems in Rd with anisotropic space motions and strongly degenerated splitting abilities are studied in the cases of critical and intermediate dimensions. The results show that the limit processes are time-independent measure-valued Wiener processes with simple spatial structure.展开更多
基金supported in part by the State Key Program of National Natural Science Foundation of China under Grant No. 61231008the National Natural Science Foundation of China under Grant No. 61072068the program for Cheung Kong Scholars and Innovative Research Team in University under Grant IRT0852
文摘During the evolution from cognitive radio to cognitive networks,the environment cognition extended from wireless environments to network and user environments.To understand the basic theory of Local Multi-Domain Cognition(LMDC),and to provide a theoretical basis for further study in cooperative multi-domain cognition and initiative multi-domain cognition,the LMDC is investigated in this paper.A Local Single-Domain Cognitive(LSDC)approach is first proposed based on multidimensional edge detection theory.This approach can divide the parameter space that describes the single-domain environment into different areas,and can represent each area with an identifier.Using this as a foundation,the single-domain environment is extended to multi-domain environments,and an LMDC approach is presented to describe the LMDC environment.The paper concludes by introducing two examples and the corresponding analysis to illustrate the feasibility of the proposed LMDC approach.
文摘In this paper we define the tensor products of spaces of exponential type vectors of closed unbounded operators in Banach spaces. Using the real method of interpolation （K-functional） we prove the interpolation theorems that permit to characterize of tensor products of spaces of exponential type vectors, We show an application of abstract results to the theory of regular elliptic operators on bounded domains. For such operators the exponential type vectors are root vectors. Thus we describe the tensor products of root vectors of regular elliptic operators on bounded domains.
基金the National Natural Science Foundation of China under Grant No.50579022the Foundation of Pre-973 Program of China under Grant No.2004CCA02500+1 种基金the SRF for the ROCS,SEMthe Talent Recruitment Foundation of HUST
文摘Given a real-valued separable M-type 2 Banach space X with the p-th power of the norm of C2-class, the almost sure asymptotic upper bounds of the solutions of the Ornstein-Uhlenbeck Processes described by the following equations {dz（t）=A（t,z（t））dt＋σ（t,z（t））dW（t）,z（0）=z0∈X,are investigated. This study generalizes the corresponding well-known finite dimensional results of Lapeyre （1989） and Mao （1992）.
基金supported by the Science and Technology Foundation of Guizhou Province under Grant No.20102133
文摘This paper aims to study the solvability of vector Ky Fan inequalities and the compactness of its solution sets.For vector-valued functions with the cone semicontinuity and the cone quasiconvexity in infinite dimensional spaces,the authors prove some existence results of the solutions and the compactness of the solution sets.Especially,some results for the vector Ky Fan inequalities on noncompact sets are built and the compactness of its solution sets are also discussed.As applications,some existence theorems of the solutions of vector variational inequalities are obtained.
基金supported by National Natural Science Foundation of China (Grant No. 10901054)
文摘Functional limit theorems for scaled occupation time fluctuations of a sequence of generalized branching particle systems in Rd with anisotropic space motions and strongly degenerated splitting abilities are studied in the cases of critical and intermediate dimensions. The results show that the limit processes are time-independent measure-valued Wiener processes with simple spatial structure.
