This thesis discussed the financial index of “Petrochina” with the Dupont financial system, and assessed the inner value of “Petrochina” with P/E model, EBIT model and DD(dividend discount)model.

Methods We chose the active locations of MSM reasonably,and used capture-recapture method and multiplier method to estimate the size of MSM in a certain city of a province.

Methods Simplified multiplier method and capture-recapture method were adopted to estimate the population size of drug users.

Multiplier method was adopted to investigate the selected STD clinics and get the number of CSWs who attended these clinics in th.

Several electricity problems are analyzed by use of Lagrange multiplier method, and some meaningful results are obtained.

The Lagrange multiplier method is derived from the view of geometry.

The Lagrange multiplier method is one of the approaches for determining conditional extremum of function in Advanced Mathematics.

The dividing-multiplicator method can easily attain the model with intuitionistic results.

The dividing-multiplicator method stated in this paper is one of the effective methods to solve these problems.

A explaination of λ in Lagrange multipliers;

A learning algorithm of recurrent functional network is proposed,which adopted Lagrange multipliers as an auxiliary function and sums up the learning process of function parameters as solving a series of linear eguations.

This paper presented a new kind of functional network model which is based on orthogonal functions,a learning algorithm of orthogonal functional network was proposed,the learning of function parameters uses orthogonal function characteristic and Lagrange multipliers by means of auxiliary function and solving a system of linear equation obtains functions parameters.