In this paper, we discussed about the optimal investment decisions and given the optimal mathematical models for different investment decisions.

As to the continuous time portfolios model,a question on optimal investment and consumption whichis affected by inflation is researched with dividend payment and stochastic income in incomplete markets under the assumption that securities processes are jump-diffusion processes.

A conclusion can be drawn through a constructed case study that the improved model is meaningful and with it investors could make an optimal investment portfolio decision in realworld application.

For the difficulty of determining the reliability of each sensor and low precision of observed data,a new fusion method based on supporting matrix and optimal weight is presented.

Through training and simulating,by means of MATLAB and compared with optimal weight filter method,BP neural network provides better accuracy in retraining white noise.

Through training and simulating,by means of MATLAB and compared with optimal weight filter method,BP neural network provides better accuracy in restraining white noise.

This paper brings forward combining these 3 prediction methods after best weighting method,forming a combination prediction method which has the respective advantage of the 3 methods.

onsidering the overall situation of the water producing system, a mathematical model of the optimum chemicals-feeding quantity and its solution for water treatment plants have been put forward.

The main contribution includes:(1) Proving optimal projection line theoremand projection neighbor theorem;(2) Proposing an optimal projection line and .