The neural network partial least square (NNPLS) method was used to establish a robust reaction model for a multi-component catalyst of methane oxidative coupling. The details, including the learning algorithm, the num...The neural network partial least square (NNPLS) method was used to establish a robust reaction model for a multi-component catalyst of methane oxidative coupling. The details, including the learning algorithm, the number of hidden units of the inner network, activation function, initialization of the network weights and the principal components, are discussed. The results show that the structural organizations of inner neural network are 1-10-5-1, 1-8-4-1, 1-8-5-1, 1-7-4-1, 1-8-4-1, 1-8-6-1, respectively. The Levenberg-Marquardt method was used in the learning algorithm, and the central sigmoidal function is the activation function. Calculation results show that four principal components are convenient in the use of the multi-component catalyst modeling of methane oxidative coupling. Therefore a robust reaction model expressed by NNPLS succeeds in correlating the relations between elements in catalyst and catalytic reaction results. Compared with the direct network modeling, NNPLS model can be adjusted by experimental data and the calculation of the model is simpler and faster than that of the direct network model.展开更多
A genetic algorithm(GA)-based approach is proposed to evaluate the straightness error of spatial lines. According to the mathematical definition of spatial straightness, a verification model is established for straigh...A genetic algorithm(GA)-based approach is proposed to evaluate the straightness error of spatial lines. According to the mathematical definition of spatial straightness, a verification model is established for straightness error, and the fitness function of GA is then given and the implementation techniques of the proposed algorithm is discussed in detail. The implementation techniques include real number encoding,adaptive variable range choosing, roulette wheel and elitist combination selection strategies,heuristic crossover and single point mutation schemes etc.An applicatin example is quoted to validate the proposed algorithm. The computation result shows that the GA-based approach is a superior nonlinear parallel optimization method. The performance of the evolution population can be improved through genetic operations such as reproduction,crossover and mutation until the optimum goal of the minimum zone solution is obtained. The quality of the solution is better and the efficiency of computation is higher than other methods.展开更多
Two properties are given in this paper about the scaling function: suppose Vj; j ∈ Z is a multiresolution analysis with a continuous scaling function φ which have compact support set and that φ the Fourier transfor...Two properties are given in this paper about the scaling function: suppose Vj; j ∈ Z is a multiresolution analysis with a continuous scaling function φ which have compact support set and that φ the Fourier transform of φ is a continuous real function, compactly supported, then φ(0) ≠ 0 and when supp φ = [a1,b1]∪[a2,b2](b1 < a2,0 < a2), then we havea1 ≤ 0, 0 < b1, a1 < b2/2 ≤ b1, 2π < b2 - a1 ≤ 8π.展开更多
In the present study we have formulated a Minimum Cross Fuzzy Entropy Problem （Minx（F）EntP） and proposed sufficient conditions for existence of its solution. Mentioned problem can be formulated as follows. In the ...In the present study we have formulated a Minimum Cross Fuzzy Entropy Problem （Minx（F）EntP） and proposed sufficient conditions for existence of its solution. Mentioned problem can be formulated as follows. In the set of membership functions satisfying the given moment constraints generated by given moment functions it is required to choose the membership function that is closest to a priori membership function in the sense of cross fuzzy entropy measure. The existence of solution of formulated problem is proved by virtue of concavity property of cross fuzzy entropy measure, the implicit function theorem and Lagrange multipliers method. Moreover, Generalized Cross Fuzzy Entropy Optimization Methods in the form of MinMinx（F）EntM and MaxMinx（F）EntM are suggested on the basis of primary phase of minimizing cross fuzzy entropy measure for fixed moment vector function and on the definition of the special functional with Minx（F）Ent values of cross fuzzy entropy measure. Next phase for obtaining mentioned distributions consists of optimization of defined functional with respect to moment vector functions. Distributions obtained by mentioned methods are defined as （MinMinx（F）Ent）m and （MaxMinx（F）Ent）m distributions.展开更多
This paper proposes a novel intelligent estimation algorithm in Wireless Sensor Network nodes location based on Free Search,which converts parameter estimation to on-line optimization of nonlinear function and estimat...This paper proposes a novel intelligent estimation algorithm in Wireless Sensor Network nodes location based on Free Search,which converts parameter estimation to on-line optimization of nonlinear function and estimates the coordinates of senor nodes using the Free Search optimization.Compared to the least-squares estimation algorithms,the localization accuracy has been increased significantly,which has been verified by the simulation results.展开更多
In this paper,we characterize the multipliers of generalized Bergman spaces A^p，q，α with 0＜p≤1, 0＜q, α<∞into some analytic function spaces and into sequence spaces,and show that the multipliers of A^p，q，...In this paper,we characterize the multipliers of generalized Bergman spaces A^p，q，α with 0＜p≤1, 0＜q, α<∞into some analytic function spaces and into sequence spaces,and show that the multipliers of A^p，q，α(0<p≤1,0<q, α<∞) into a given space are the same as those of A^p，α(0<p≤1, α>0) in almost every case considered. The corollaries on multipliers of the spaces A^p，q，α extend some related results.展开更多
This paper generalizes the basic principle of multiplier-enlargement approach to approximating any nonbounded continuous functions with positive linear operators, and as an example, Bernstein polynomial operators are ...This paper generalizes the basic principle of multiplier-enlargement approach to approximating any nonbounded continuous functions with positive linear operators, and as an example, Bernstein polynomial operators are analysed and studied. This paper gives a certain theorem as a general rule to approximate any nonbounded continuous functions.展开更多
文摘The neural network partial least square (NNPLS) method was used to establish a robust reaction model for a multi-component catalyst of methane oxidative coupling. The details, including the learning algorithm, the number of hidden units of the inner network, activation function, initialization of the network weights and the principal components, are discussed. The results show that the structural organizations of inner neural network are 1-10-5-1, 1-8-4-1, 1-8-5-1, 1-7-4-1, 1-8-4-1, 1-8-6-1, respectively. The Levenberg-Marquardt method was used in the learning algorithm, and the central sigmoidal function is the activation function. Calculation results show that four principal components are convenient in the use of the multi-component catalyst modeling of methane oxidative coupling. Therefore a robust reaction model expressed by NNPLS succeeds in correlating the relations between elements in catalyst and catalytic reaction results. Compared with the direct network modeling, NNPLS model can be adjusted by experimental data and the calculation of the model is simpler and faster than that of the direct network model.
文摘A genetic algorithm(GA)-based approach is proposed to evaluate the straightness error of spatial lines. According to the mathematical definition of spatial straightness, a verification model is established for straightness error, and the fitness function of GA is then given and the implementation techniques of the proposed algorithm is discussed in detail. The implementation techniques include real number encoding,adaptive variable range choosing, roulette wheel and elitist combination selection strategies,heuristic crossover and single point mutation schemes etc.An applicatin example is quoted to validate the proposed algorithm. The computation result shows that the GA-based approach is a superior nonlinear parallel optimization method. The performance of the evolution population can be improved through genetic operations such as reproduction,crossover and mutation until the optimum goal of the minimum zone solution is obtained. The quality of the solution is better and the efficiency of computation is higher than other methods.
文摘Two properties are given in this paper about the scaling function: suppose Vj; j ∈ Z is a multiresolution analysis with a continuous scaling function φ which have compact support set and that φ the Fourier transform of φ is a continuous real function, compactly supported, then φ(0) ≠ 0 and when supp φ = [a1,b1]∪[a2,b2](b1 < a2,0 < a2), then we havea1 ≤ 0, 0 < b1, a1 < b2/2 ≤ b1, 2π < b2 - a1 ≤ 8π.
文摘In the present study we have formulated a Minimum Cross Fuzzy Entropy Problem （Minx（F）EntP） and proposed sufficient conditions for existence of its solution. Mentioned problem can be formulated as follows. In the set of membership functions satisfying the given moment constraints generated by given moment functions it is required to choose the membership function that is closest to a priori membership function in the sense of cross fuzzy entropy measure. The existence of solution of formulated problem is proved by virtue of concavity property of cross fuzzy entropy measure, the implicit function theorem and Lagrange multipliers method. Moreover, Generalized Cross Fuzzy Entropy Optimization Methods in the form of MinMinx（F）EntM and MaxMinx（F）EntM are suggested on the basis of primary phase of minimizing cross fuzzy entropy measure for fixed moment vector function and on the definition of the special functional with Minx（F）Ent values of cross fuzzy entropy measure. Next phase for obtaining mentioned distributions consists of optimization of defined functional with respect to moment vector functions. Distributions obtained by mentioned methods are defined as （MinMinx（F）Ent）m and （MaxMinx（F）Ent）m distributions.
基金National Research Foundation for the Doctoral Program of Higher Education of China(No.20060266006)the High-school Natural Science Research Foundation of Jiangsu Province(No.07KJB510095)
文摘This paper proposes a novel intelligent estimation algorithm in Wireless Sensor Network nodes location based on Free Search,which converts parameter estimation to on-line optimization of nonlinear function and estimates the coordinates of senor nodes using the Free Search optimization.Compared to the least-squares estimation algorithms,the localization accuracy has been increased significantly,which has been verified by the simulation results.
文摘In this paper,we characterize the multipliers of generalized Bergman spaces A^p，q，α with 0＜p≤1, 0＜q, α<∞into some analytic function spaces and into sequence spaces,and show that the multipliers of A^p，q，α(0<p≤1,0<q, α<∞) into a given space are the same as those of A^p，α(0<p≤1, α>0) in almost every case considered. The corollaries on multipliers of the spaces A^p，q，α extend some related results.
文摘This paper generalizes the basic principle of multiplier-enlargement approach to approximating any nonbounded continuous functions with positive linear operators, and as an example, Bernstein polynomial operators are analysed and studied. This paper gives a certain theorem as a general rule to approximate any nonbounded continuous functions.
