The Optimality of Combining Ridge adn Principal Components Estimate in the class of Reduced-dimension Estimators;

Here we obtain the best approximation property of spline wavelets interpolation in researching the spline wavelets to approximating the functions in Sobolev Spaces.

With the view of the optimal approximation for the formed beams, the radiation pattern and the field distribution in the focus zone of Fresnel zone plate antenna approximation with the fields of the linear array have been studied based on the methods of weighted residue and Prony,which suit for the approximation for the real patterns of various Fresnel zone focusing configuration.

Based on the representation of interval rational Bezier curves and surfaces and by a serial of mathematical transformation, the degree reductions of them are converted to those of polynomials with upper bounds, then several algorithms are presented, with linear programming and optimal approximation methods.

We not only prove that the new operator converges to arbitrary continuous functions with period 2π uniformly on the whole axis,but also obtain the best approximation order simultaneously.

A two-dimensional strip-packing problem is formulated as a nonlinear programming(NLP) model and the notion of tangent cones in variational analysis is employed to establish the first-order optimality conditions for the NLP problem.

Based on some new characterizations of the Clarke derivative and Clarke subdifferential of the objective function,we develop the first-order optimality conditions for(GSMMP)in terms of second-order multipliers.