This paper deals with periodic solutions of impulsive second order boundary value problems with parameter, Existence results are presented for nonlinearity with mixed sublinear and superlinear term at λ-0 and (or) λ≠0. Continua of the solution set are obtained. The main technique is fixed point argument of expansion and compression type.

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.

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.

In this paper, we study properties of the eigenfunctions of singular boundary value problems. The main results show that for a class of singular boundary value problems, the Sturmian oscillation theorem holds. It is a generalization of the standard case to the singular case.

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.