Using difference quotient instead of derivative, the paper presents the solution method and procedure of the nonlinear least square estimation containing different classes of measurements. In the meantime, the paper s...Using difference quotient instead of derivative, the paper presents the solution method and procedure of the nonlinear least square estimation containing different classes of measurements. In the meantime, the paper shows several practical cases, which indicate the method is very valid and reliable.展开更多
A mathematical model was developed for layout optimization of truss structures with discrete variables subjected to dynamic stress, dynamic displacement and dynamic stability constraints. By using the quasi-static met...A mathematical model was developed for layout optimization of truss structures with discrete variables subjected to dynamic stress, dynamic displacement and dynamic stability constraints. By using the quasi-static method, the mathematical model of structure optimization under dynamic stress, dynamic displacement and dynamic stability constraints were transformed into one subjected to static stress, displacement and stability constraints. The optimization procedures include two levels, i.e., the topology optimization and the shape optimization. In each level, the comprehensive algorithm was used and the relative difference quotients of two kinds of variables were used to search the optimum solution. A comparison between the optimum results of model with stability constraints and the optimum results of model without stability constraint was given. And that shows the stability constraints have a great effect on the optimum solutions.展开更多
Let r be a given positive number. Denote by D=D r the closed disc in the complex plane C whose center is the origin and radius is r. For any subset K of C and any integer m≥1, write A(D m,K)={f|f∶D m→K is a cont...Let r be a given positive number. Denote by D=D r the closed disc in the complex plane C whose center is the origin and radius is r. For any subset K of C and any integer m≥1, write A(D m,K)={f|f∶D m→K is a continuous map, and f|(D m)° is analytic}. For H∈ A(D m,C)(m≥2), f∈A(D,D) and z∈D, write Ψ H(f)(z)=H(z,f(z),...,f m-1(z)). Suppose F,G∈A(D 2n+1,C), and H k,K k∈A(D k,C), k=2,...,n. In this paper, the system of functional equations F(z,f(z),f 2(Ψ H 2(f)(z)),...,f n(Ψ H n(f)(z)),g(z),g 2(Ψ K 2(g)(z)),..., g n(Ψ K n(g)(z)))=0 G(z,f(z),f 2(Ψ H 2(f)(z)),...,f n(Ψ H n(f)(z)),g(z),g 2(Ψ K 2(g)(z)),..., g n(Ψ K n(g)(z)))=0(z∈D) is studied and some conditions for the system of equations to have a solution or a unique solution in A(D,D)×A(D,D) are given.展开更多
Let r be a given positive number. Denote by D=D r the closed disc in the complex plane C whose center is the origin and radius is r. Write A(D,D)={f: f is a continuous map from D into itself, and ...Let r be a given positive number. Denote by D=D r the closed disc in the complex plane C whose center is the origin and radius is r. Write A(D,D)={f: f is a continuous map from D into itself, and f|D ° is analytic}. Suppose G,H: D 2n+1 →C are continuous maps (n≥2), and G|(D 2n+1 ) °, H|(D 2n+1 ) ° are analytic. In this paper, we study the system of iterative functional equationsG(z,f(z),…,f n(z), g(z),…,g n(z))=0, H(z,f(z),…,f n(z), g(z),…,g n(z))=0, for any z∈D,and give some conditions for the system of equations to have a solution or a unique solution in A(D,D) ×A(D,D).展开更多
Data,including the spatial data and the non-spatial data,are the basis of all digital scientific engineering projects,such as the digital earth and the digital nation,the digital mine.The spatial data have the charact...Data,including the spatial data and the non-spatial data,are the basis of all digital scientific engineering projects,such as the digital earth and the digital nation,the digital mine.The spatial data have the characteristics of many sources,multi-dimension,multi-type,many time states and different accuracy.The spatial data firstly must be processed before using these data.The parameter estimation model to process the data is commonly the more complex nonlinear model including random parameters and non-random parameters.So a generalized nonlinear dynamic least squares method to process these data is put forward.According to the special structure of the generalized nonlinear dynamic least squares problem and the solution to the first order,a new solving model and a corresponding method to process the problem are put forward.The complex problem can be divided into two sub-problems so that the number of the unknown parameters is reduced largely.Therefore it reduces the computing difficulty and load.展开更多
The unequal meshsteps are unavoidable in general for scientific and engineering computations especially in large Scale computations. The analysis of difference schemes with nonuniform meshes is very rare even by use o...The unequal meshsteps are unavoidable in general for scientific and engineering computations especially in large Scale computations. The analysis of difference schemes with nonuniform meshes is very rare even by use of fully heuristic methods. For the purpose of the systematic and theoretical study of the finite difference method with nonuniform meshes for the problems of partial differential equations, the general interpolation formulas for the spaces of discrete functions of one index with unequal meshsteps are established in the present work. These formulas give the connected relationships among the norms of various types, such as' the sum of powers of discrete values, the discrete maximum modulo, the discrete Holder and Lipschitz coefficients.展开更多
文摘Using difference quotient instead of derivative, the paper presents the solution method and procedure of the nonlinear least square estimation containing different classes of measurements. In the meantime, the paper shows several practical cases, which indicate the method is very valid and reliable.
基金Project supported by the National Natural Science Foundation of China (Nos. 10002005 and 10421002)the Natural Science Foundation of Tianjin (No.02360081)the Education Committee Foundation of Tianjin (No.20022104)the Program for Changjiang Scholars and Innovative Research Team in University of China and the 211 Foundation of Dalian University of Technology
文摘A mathematical model was developed for layout optimization of truss structures with discrete variables subjected to dynamic stress, dynamic displacement and dynamic stability constraints. By using the quasi-static method, the mathematical model of structure optimization under dynamic stress, dynamic displacement and dynamic stability constraints were transformed into one subjected to static stress, displacement and stability constraints. The optimization procedures include two levels, i.e., the topology optimization and the shape optimization. In each level, the comprehensive algorithm was used and the relative difference quotients of two kinds of variables were used to search the optimum solution. A comparison between the optimum results of model with stability constraints and the optimum results of model without stability constraint was given. And that shows the stability constraints have a great effect on the optimum solutions.
基金Supported by the National Natural Science Foundation of China (1 0 2 2 6 0 1 4) ,Guangxi Science Foun-dation (0 2 2 90 0 1 )
文摘Let r be a given positive number. Denote by D=D r the closed disc in the complex plane C whose center is the origin and radius is r. For any subset K of C and any integer m≥1, write A(D m,K)={f|f∶D m→K is a continuous map, and f|(D m)° is analytic}. For H∈ A(D m,C)(m≥2), f∈A(D,D) and z∈D, write Ψ H(f)(z)=H(z,f(z),...,f m-1(z)). Suppose F,G∈A(D 2n+1,C), and H k,K k∈A(D k,C), k=2,...,n. In this paper, the system of functional equations F(z,f(z),f 2(Ψ H 2(f)(z)),...,f n(Ψ H n(f)(z)),g(z),g 2(Ψ K 2(g)(z)),..., g n(Ψ K n(g)(z)))=0 G(z,f(z),f 2(Ψ H 2(f)(z)),...,f n(Ψ H n(f)(z)),g(z),g 2(Ψ K 2(g)(z)),..., g n(Ψ K n(g)(z)))=0(z∈D) is studied and some conditions for the system of equations to have a solution or a unique solution in A(D,D)×A(D,D) are given.
文摘Let r be a given positive number. Denote by D=D r the closed disc in the complex plane C whose center is the origin and radius is r. Write A(D,D)={f: f is a continuous map from D into itself, and f|D ° is analytic}. Suppose G,H: D 2n+1 →C are continuous maps (n≥2), and G|(D 2n+1 ) °, H|(D 2n+1 ) ° are analytic. In this paper, we study the system of iterative functional equationsG(z,f(z),…,f n(z), g(z),…,g n(z))=0, H(z,f(z),…,f n(z), g(z),…,g n(z))=0, for any z∈D,and give some conditions for the system of equations to have a solution or a unique solution in A(D,D) ×A(D,D).
基金Project(40174003)supported by the National Natural Science Foundation of China
文摘Data,including the spatial data and the non-spatial data,are the basis of all digital scientific engineering projects,such as the digital earth and the digital nation,the digital mine.The spatial data have the characteristics of many sources,multi-dimension,multi-type,many time states and different accuracy.The spatial data firstly must be processed before using these data.The parameter estimation model to process the data is commonly the more complex nonlinear model including random parameters and non-random parameters.So a generalized nonlinear dynamic least squares method to process these data is put forward.According to the special structure of the generalized nonlinear dynamic least squares problem and the solution to the first order,a new solving model and a corresponding method to process the problem are put forward.The complex problem can be divided into two sub-problems so that the number of the unknown parameters is reduced largely.Therefore it reduces the computing difficulty and load.
文摘The unequal meshsteps are unavoidable in general for scientific and engineering computations especially in large Scale computations. The analysis of difference schemes with nonuniform meshes is very rare even by use of fully heuristic methods. For the purpose of the systematic and theoretical study of the finite difference method with nonuniform meshes for the problems of partial differential equations, the general interpolation formulas for the spaces of discrete functions of one index with unequal meshsteps are established in the present work. These formulas give the connected relationships among the norms of various types, such as' the sum of powers of discrete values, the discrete maximum modulo, the discrete Holder and Lipschitz coefficients.
