In this paper, we investigate the existence of best approximation for perturbed distance function by Gateaux derivative, get a necessary and sufficient condition for the existence of best approximation for perturbed distance function.

A hyperbolic perturbation method was presented for determining the homoclinic and heteroclinic solutions of certain strongly nonlinear autonomous oscillators in the form+c_1x+c_3x~3=εf(μ,x,x), in which the hyperbolic functions can be employed instead of the usual periodic functions in the usual perturbation procedure.

Study of a new weight function in the meshless method and its application;

Analysis on the stress intensity factor(SIF) for mixed-mode crack at bottom base layer with weight functions expressed with matrix;

Calculation on the stress intensity factor for the bottom crack of asphalt layer in asphalt pavement considering partial constraint by weight function;