单位根在解一类非线性方程组中的应用

利用单位根在多项式整除性研究中的应用引伸到解决一类非线性方程组中，使这一类对称方程组的问题得到较为满意的结果。     

瞬态温度场有限元微分方程组求解的一个新方法

汽轮机组子寿命管理研究的一个重要内容是转子瞬态湿度场的计算，本文给出了求解有限元微分方程组的新方法－双重预估校正法成功地消除了差分法的缺陷，大大提高了计算结果的精度和可靠性，从而为瞬态浊度场的计算提供了一个有力手段。     

Numerical algorithm of distributed TOPKAPI model and its application

The TOPKAPI （TOPographic Kinematic APproximation and Integration） model is a physically based rainfall-runoff model derived from the integration in space of the kinematic wave model. In the TOPKAPI model, rainfall-runoff and runoff routing processes are described by three nonlinear reservoir differential equations that are structurally similar and describe different hydrological and hydraulic processes. Equations are integrated over grid cells that describe the geometry of the catchment, leading to a cascade of nonlinear reservoir equations. For the sake of improving the model＇s computation precision, this paper provides the general form of these equations and describes the solution by means of a numerical algorithm, the variable-step fourth-order Runge-Kutta algorithm. For the purpose of assessing the quality of the comprehensive numerical algorithm, this paper presents a case study application to the Buliu River Basin, which has an area of 3 310 km^2, using a DEM （digital elevation model） grid with a resolution of 1 km. The results show that the variable-step fourth-order Runge-Kutta algorithm for nonlinear reservoir equations is a good approximation of subsurface flow in the soil matrix, overland flow over the slopes, and surface flow in the channel network, allowing us to retain the physical properties of the original equations at scales ranging from a few meters to 1 km.     

有关方程组的几个问题

通过对线性代数教学中经常遇到4个问题的解答，指出了在已知方程组的基础解系的条件下，求解该方程组的方法，得出用初等变换互变的二个线性方程组同解的二个持征。     

(2+1)维Burgers方程组的周期孤立波解

给出一种新的辅助函数法,并给出该辅助函数的一些新解。作为例子,求解(2+1)维Burgers方程组。显然,该辅助函数法也可以解其他类型的非线性发展方程。