By analyzing the structure of the objective function based on error sum of squares and the information provided by the objective function, the essential problems in the current parameter estimation methods are summari...By analyzing the structure of the objective function based on error sum of squares and the information provided by the objective function, the essential problems in the current parameter estimation methods are summarized: (1) the information extracted from the objective function based on error sum of squares is unreasonable or even wrong for parameter estimation; and (2) the surface of the objective function based on error sum of squares is more complex than that of the parameter function, which indicates that the optimal parameter values should be searched on the surface of the parameter function instead of the objective function. This paper proposes the concept of sample intersection and demonstrates the uniqueness theorem of intersection point (namely the uniqueness of optimal parameter values). According to the characteristics of parameter function surface and Taylor series expansion, a parameter estimation method based on the sample intersection information extracted from parameter function surface (PFS method) was constructed. The results of theoretical analysis and practical application show that the proposed PFS method can avoid the problems in the current automatic parameter calibration, and has fast convergence rate and good performance in parameter calibration.展开更多
In this article,we consider the integral representation of harmonic functions.Using a property of the modified Poisson kernel in a half plane,we prove that a harmonic function u(z) in a half plane with its positive pa...In this article,we consider the integral representation of harmonic functions.Using a property of the modified Poisson kernel in a half plane,we prove that a harmonic function u(z) in a half plane with its positive part u+(z)=max{u(z),0} satisfying a slowly growing condition can be represented by its integral of a measure on the boundary of the half plan.展开更多
The purpose of this paper is to study the traveling wave solutions of a diffusive predator- prey model with predator saturation and competition functional response. The system admits three equilibria： a zero equilibr...The purpose of this paper is to study the traveling wave solutions of a diffusive predator- prey model with predator saturation and competition functional response. The system admits three equilibria： a zero equilibrium E0, a boundary equilibrium E1 and a posi- tive equilibrium E. under some conditions. We establish the existence of two types of traveling wave solutions which connect E0 and E. and E1 and E., respectively. Our main arguments are based on a simplified shooting method, a sandwich method and constructions of appropriate Lyapunov functions. Our particular interest is to investi- gate the oscillation of both types of traveling wave solutions when they approach the positive equilibrium.展开更多
基金supported by the National Natural Science Foundation of China (Grant No. 51279057)the Major Program of National Natural Science Foundation of China (Grant Nos. 51190090 and 51190091)+1 种基金the Ph.D. Programs Foundation of Ministry of Education of China (Grant No.20120094120018)the Fundamental Research Funds for the Central Universities of China (Grant No. 2012B00214)
文摘By analyzing the structure of the objective function based on error sum of squares and the information provided by the objective function, the essential problems in the current parameter estimation methods are summarized: (1) the information extracted from the objective function based on error sum of squares is unreasonable or even wrong for parameter estimation; and (2) the surface of the objective function based on error sum of squares is more complex than that of the parameter function, which indicates that the optimal parameter values should be searched on the surface of the parameter function instead of the objective function. This paper proposes the concept of sample intersection and demonstrates the uniqueness theorem of intersection point (namely the uniqueness of optimal parameter values). According to the characteristics of parameter function surface and Taylor series expansion, a parameter estimation method based on the sample intersection information extracted from parameter function surface (PFS method) was constructed. The results of theoretical analysis and practical application show that the proposed PFS method can avoid the problems in the current automatic parameter calibration, and has fast convergence rate and good performance in parameter calibration.
基金the National Natural Science Foundation of China(No.10671022)Research Foundation for Doctor Programme (No.20060027023)Henan Institute of Education Youth Scientific Research Fund (No.20070107)
文摘In this article,we consider the integral representation of harmonic functions.Using a property of the modified Poisson kernel in a half plane,we prove that a harmonic function u(z) in a half plane with its positive part u+(z)=max{u(z),0} satisfying a slowly growing condition can be represented by its integral of a measure on the boundary of the half plan.
文摘The purpose of this paper is to study the traveling wave solutions of a diffusive predator- prey model with predator saturation and competition functional response. The system admits three equilibria： a zero equilibrium E0, a boundary equilibrium E1 and a posi- tive equilibrium E. under some conditions. We establish the existence of two types of traveling wave solutions which connect E0 and E. and E1 and E., respectively. Our main arguments are based on a simplified shooting method, a sandwich method and constructions of appropriate Lyapunov functions. Our particular interest is to investi- gate the oscillation of both types of traveling wave solutions when they approach the positive equilibrium.
