The purpose of this paper is to add some complements to the general theory of higher-order types of asymptotic variation developed in two previous papers so as to complete our elementary (but not too much!) theory in ...The purpose of this paper is to add some complements to the general theory of higher-order types of asymptotic variation developed in two previous papers so as to complete our elementary (but not too much!) theory in view of applications to the theory of finite asymptotic expansions in the real domain, the asymptotic study of ordinary differential equations and the like. The main results concern: 1) a detailed study of the types of asymptotic variation of an infinite series so extending the results known for the sole power series;2) the type of asymptotic variation of a Wronskian completing the many already-published results on the asymptotic behaviors of Wronskians;3) a comparison between the two main standard approaches to the concept of “type of asymptotic variation”: via an asymptotic differential equation or an asymptotic functional equation;4) a discussion about the simple concept of logarithmic variation making explicit and completing the results which, in the literature, are hidden in a quite-complicated general theory.展开更多
A micro-extended-analog-computer （uEAC） is developed on the basis of Rubel＇ s extended analog computer（EAC） model. Through the uEAC mathematical model, the resistance properties of the conductive sheet, several f...A micro-extended-analog-computer （uEAC） is developed on the basis of Rubel＇ s extended analog computer（EAC） model. Through the uEAC mathematical model, the resistance properties of the conductive sheet, several feedback uEAC models, and a more flexible uEAC cell structure with a multi-level hierarchy are discussed. Futhermore, for the dynamic uEAC array with a linear Lukasiewicz function, a nonlinear differential equation description is presented, and then a sufficient global asymptotic stability condition is derived by utilizing a Lyapunov function and a Lipchitz function. Finally, comparative simulations for a cam servo mechanism system are conducted to verify the capability of the uEAC array as an adaptive controller.展开更多
文摘The purpose of this paper is to add some complements to the general theory of higher-order types of asymptotic variation developed in two previous papers so as to complete our elementary (but not too much!) theory in view of applications to the theory of finite asymptotic expansions in the real domain, the asymptotic study of ordinary differential equations and the like. The main results concern: 1) a detailed study of the types of asymptotic variation of an infinite series so extending the results known for the sole power series;2) the type of asymptotic variation of a Wronskian completing the many already-published results on the asymptotic behaviors of Wronskians;3) a comparison between the two main standard approaches to the concept of “type of asymptotic variation”: via an asymptotic differential equation or an asymptotic functional equation;4) a discussion about the simple concept of logarithmic variation making explicit and completing the results which, in the literature, are hidden in a quite-complicated general theory.
基金Supported by the National Natural Science Foundation of China(61433003,61273150)Beijing Higher Education Young Elite Teacher Project
文摘A micro-extended-analog-computer （uEAC） is developed on the basis of Rubel＇ s extended analog computer（EAC） model. Through the uEAC mathematical model, the resistance properties of the conductive sheet, several feedback uEAC models, and a more flexible uEAC cell structure with a multi-level hierarchy are discussed. Futhermore, for the dynamic uEAC array with a linear Lukasiewicz function, a nonlinear differential equation description is presented, and then a sufficient global asymptotic stability condition is derived by utilizing a Lyapunov function and a Lipchitz function. Finally, comparative simulations for a cam servo mechanism system are conducted to verify the capability of the uEAC array as an adaptive controller.
基金The National Natural Science Foundations(11201362)the Science Foundation of the Education Department of Shaanxi Province(14JK1305)the Natural Science Foundations of Shaanxi Province(2016JM1009)
