With the aid of MATHEMATICA, the direct reduction method was extended and applied in 2+1_dimensional variable coefficient generalized Kadomtsev_Petviashvili equation(VCGKPE).

First, with the help of Mathematica,three kinds of reductions of MDWW equations areobtained by using direct reduction method.

In this artical, we utilize the extended direct method to sove shallow water wave equations based on physics, and obtain several new similarity solutions of them.

The direct constraint procedure,a new and steady solution to the contact problem,was applied to analyzed the collector head and the contact,and optimization techniques were developed to analyze the contact of the pantograph-catenary and to evaluate the key parameters of the spring system.

A direct constraint procedure was used to model the discontinuous mechanical behavior(such as sliding and disjointing) of faults and weak interlays in steep slopes to evaluate the safety of such slopes.

The study on the interaction of gravity dam and plant of the Shuikou Hydropower Station under the action of upstream and downstream water pressures was made, based on a novel contact calculation method named direct constraint procedure.

Study on contact characteristics between seal and door based on direct restriction;

Five long-chain saturated alkanoyl-6O-D-isoascorbates(alkanoyl=decanoyl,lauroyl,myristoyl,palmitoyl and stearoyl) were synthesized by esterification(or transesterification) of D-isoascorbic acid with alkanoic acids using concentrated H_2SO_4 as a medium and a catalyst at room temperature.

There are two methods for synthesis of the fluoroporphyrins: direct and indirect fluorination.