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【期刊论文】Shape reconstruction by genetic algorithms and artificial neural networks
刘希玉, Liu Xiyu, Tang Mingxi and John Hamilton Frazer
Engineering Computations Vol. 20, No. 2, 2003, pp. 129-151,-0001,():
-1年11月30日
This paper presents a new surface reconstruction method based on complex form functions, genetic algorithms and neural networks. Surfaces can be reconstructed in an analytical representation format. This representation is optimal in the sense of least-square fitting by predefined subsets of data points. The surface representations are achieved by evolution via repetitive application of crossover and mutation operations together with a back-propagation algorithm until a termination condition is met. The expression is finally classified into specific combinations of basic functions. The proposed method can be used for CAD model reconstruction of 3D objects and free smooth shape modelling. We have implemented the system demonstration with Visual C++ and MatLab to enable real time surface visualisation in the process of design.
Neural networks,, Genetic algorithms,, Model,, Design
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【期刊论文】Solutions of Impulsive Boundary Value Problems on the Half-Line
刘希玉, Xiyu Liu
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS 222, 411-430 (1998),-0001,():
-1年11月30日
This paper presents some existence results for a class of impulsive boundary value problems with nonhomogeneous boundary data on the half-line. By applying fixed-point theorems on cones, we obtain the existence of positive bounded and unbounded solutions. Our methods are integral equations, approximate solutions, a priori bounds and modified Arzela techniques.
Existence, impulsive boundary value problems, singular, cone
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【期刊论文】Visualization and Genetic Algorithms in Minimax Theory for Nonlinear Functionals
刘希玉, Xiyu Liu, John Frazer, and Ming Xi Tang
,-0001,():
-1年11月30日
In this paper, evolution and visualization of the existence of saddle points of nonlinear functionals or multi-variable functions in finite dimensional spaces are presented. New algorithms are developed based on the mountain pass lemma and link thery in nonlinear analysis. Further more, a simple comparison of the steepest descent algorithm and the genetic algorithm is given. The process of the saddle point finding is visualised in an inteactive graphical interface.
Visualization, genetic algorithm, minimax theory, nonlinear.,
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【期刊论文】BOUNDARY-IRREGULAR SOLUTIONS TO SINGULAR BOUNDARY VALUE PROBLEMS
刘希玉, LIU XIYU and YAN BAOQIANG
Nonlinear Analysis. Theory. Methods & Applications, Vol. 32, No. 5, pp. 633-646, 1998,-0001,():
-1年11月30日
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【期刊论文】Bifurcation of Nonlinear Problems Modeling Flows Through Porous Media
刘希玉, Liu Xiyu
Acta. Mathematica Sinica, New Series 1998, January, Vol. 14, No. 1, pp. 125-134,-0001,():
-1年11月30日
This paper desla with a class of nonlinear boundary value problems which appears in the study of models of flows through porous media. Existence results of asymptotic bifureation and continua are reported both for operator equations and for boundary value problems
Bifurcation, Continua, Operater theory, Flow through porous media
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