Banach空间中线性系统精确零可控性

本文研究了状态空间为一般 Banach空间的线性系统的精确零可控性问题 .首先建立了一个同对偶半群有关的映射的可测性 .然后利用此可测性和 Banach空间中闭凸集的强分离定理导出了精确零可控性的充分必要条件     

A new approach in modelling groundwater pollution under uncertainty

This article presents a new methodology to model the time and space evolution of a contaminant in a system of aquifers when certain components of the model, such as the geohydrologic information, the boundary conditions, the magnitude and variability of the sources or physical parameters are uncertain and defined in stochastic terms. The method is based on applications of modern mathematics to the solution of the resulting stochastic transport equations. This procedure exhibits considerable advantages over the existing stochastic modelling techniques. In particular, the semigroup solutions are not restricted to small variances in the stochastic elements (perturbation techniques), unsteady dynamic conditions are specifically considered, time and space randomness may be considered in the sources, the boundary conditions or the parameters, and the methodology reflects a well-posed functional-analytic theory. Several basic example problems are presented in order to illustrate the application of the methodology to the modelling of complex spatially and temporally distributed sources of interest in engineering hydrology today. Further potential applications of the method are very promising.