Canonical form of a nonlinear monetary system

This paper addresses an autonomous system of quadratic ordinary differential equations, which describes a monetary system involving interest rate, investment demand and price index. The canonical form of this system is derived, which is dependent on a single parameter. On this basis, it is proved that this system is not smoothly equivalent to the generalized Lorenz canonical form.     

Optimal bounds and extremal trajectories for time averages in nonlinear dynamical systems

For any quantity of interest in a system governed by ordinary differential equations, it is natural to seek the largest (or smallest) long-time average among solution trajectories, as well as the extremal trajectories themselves. Upper bounds on time averages can be proved a priori using auxiliary functions, the optimal choice of which is a convex optimization problem. We prove that the problems of finding maximal trajectories and minimal auxiliary functions are strongly dual. Thus, auxiliary functions provide arbitrarily sharp upper bounds on time averages. Moreover, any nearly minimal auxiliary function provides phase space volumes in which all nearly maximal trajectories are guaranteed to lie. For polynomial equations, auxiliary functions can be constructed by semidefinite programming, which we illustrate using the Lorenz system.     

非扩散洛伦兹系统的周期轨道

混沌系统的奇怪吸引子是由无数条周期轨道稠密覆盖构成的,周期轨道是非线性动力系统中除不动点之外最简单的不变集,它不仅能够体现出混沌运动的所有特征,而且和系统振荡的产生与变化密切相关,因此分析复杂系统的动力学行为时获取周期轨道具有重要意义.本文系统地研究了非扩散洛伦兹系统一定拓扑长度以内的周期轨道,提出一种基于轨道的拓扑结构来建立一维符号动力学的新方法,通过变分法数值计算轨道显得很稳定.寻找轨道初始化时,两条轨道片段能够被用作基本的组成单元,基于整条轨道的结构进行拓扑分类的方式显得很有效.此外,讨论了周期轨道随着参数变化时的形变情况,为研究轨道的周期演化规律提供了新途径.本研究可为在其他类似的混沌体系中找到并且系统分类周期轨道提供一种可借鉴的方法.     

Lorenz混沌系统的分析与电路实现

利用Matlab的数值计算和Multisim的电路模型分析和实现著名的Lorenz混沌系统,观察Lorenz混沌吸引子,加深对混沌现象的认识,可将混沌理论与实验引入到大学物理实验教学项目中。     

Latest achievements in generalized Lorenz‐Mie theories: A commented reference database

Generalized Lorenz‐Mie theories form a set of analytical approaches dealing with the interaction between electromagnetic arbitrary shaped beams and a class of particles possessing enough symmetries to allow one to use the method of separation of variables. This paper provides a commented reference database concerning generalized Lorenz‐Mie theories for the period 2009‐2013.     

The pairwise egalitarian solution for the assignment game

In this note we consider the pairwise egalitarian solution (Sánchez-Soriano, 2003) on the domain of assignment games and study its relation with the core. Strengthening the dominant diagonal condition (Solymosi and Raghavan, 2001), we introduce k-dominant diagonal assignment games (k≥1), analyzing for which values of k the pairwise egalitarian solution fulfills the standards of fairness represented by the Lorenz domination and the kernel. We also characterize the Thompson’s fair division point (Thompson, 1981) for arbitrary assignment games.     

广义洛伦兹磁力的定义及证明

给出了广义洛伦兹磁力的定义和证明,论证指出电场既不是动磁场直接产生的更不是变磁场产生的;先有感应电流I,后有电压Uab和电场Eab。解决了愣茨与法拉第之间的原因与结果的哲学争议问题;在当时没有发现电子的情况下,法拉第的漩涡电场及其电动势都是虚构的;完整洛伦兹磁力是电磁感应的物理本质。     

Excess permittivity and excess conductivity of binary fluid mixture isobutyric acid – water along the coexistence curve

Excess permittivity and excess conductivity of the binary fluid mixture isobutyric acid–water (I–W) have been computed at three temperatures and along the coexistence curve, on the basis of refractive index and electrical conductivity data of the mixture. The other related properties, molar volume, molar refraction and polarisablities have also been reported. The temperature dependence of the molar refraction was also examined. The results have been interpreted in terms of the nature of specific intermolecular interactions between the components.