时标上指数函数运算规律的应用

Application of Law of Calculation of Exponential Function on Time Scale

时标上动力系统理论是把连续型和离散型动力系统理论统一起来的理论.时标上的动力系统广泛应用于生物数学模型、热传导模型和传染病模型等的研究.时标上的指数函数理论可以用来研究时标上的动力系统.本文利用时标上圈加和圈减定义及运算法则,利用时标上的指数函数的运算规律,证明了一个关于化简指数函数的命题和一个关于指数函数积分的命题.

The dynamical system theory on time scales unifies the continuous and discrete dynamical system theory.Dynamic system on time scales has been widely used in study of biological mathematical model,heat conduction model and infectious disease model.The exponential function theory on time scales can be used to study the dynamic system on time scales.In this paper,using the definition and operation laws of circle addition and circle subtraction,using the operation law of the exponential function on the time scale,a propositional proposition about the simplification of exponential function and a propositional proposition about the integral of exponential function are proved.