关于矩阵方程X+A*X-1A=P的解及其扰动分析

考虑非线性矩阵方程X＋A^＊（X^-1）A=P其中A是n阶非奇异复矩阵,P是n阶Hermite正定矩阵．本文给出了Hermite正定解和最大解的存在性以及获得最大解的一阶扰动界,改进了文[5,6]中的部分结论．     

Nonlinear Evolution Related to Invariant Functionals and the SUSY Transformations

A supersymmetrized formalism of the nonlinear evolution equations and the relation to the invariant functional are discussed.     

The Hamiltonian structures of 3D ODE with time-independent invariants

We have proved that any 3-dimensional dynamical system of ordinary differential equations (in short, 3D ODE) with time-independent invariants can be rewritten as Hamiltonian systems with respect to generalized Poisson brackets and the Hamiltonians are these invariants. As an example, we discuss the Kermack-Mckendrick model for epidemics in detail. The results we obtained are generalization of those obtained by Y. Nutku. First Received Nov. 22, 1993     

Topological Invariants of Vapor–Liquid,Vapor–Liquid–Liquid and Liquid–Liquid Phase Diagrams

The study of topological invariants of phase diagrams allows for the development of a qualitative theory of the processes being researched. Studies of the properties of objects in the same equivalence class may be carried out with the aim of predicting the properties of unexplored objects from this class, or predicting the behavior of a whole system. This paper describes a number of topological invariants in vapor–liquid, vapor–liquid–liquid and liquid–liquid equilibrium diagrams. The properties of some invariants are studied and illustrated. It is shown that the invariant of a diagram with a miscibility gap can be used to distinguish equivalence classes of phase diagrams, and that the balance equation of the singular-point indices, based on the Euler characteristic, may be used to analyze the binodal-surface structure of a quaternary system.     

Bifurcations of Nonlinear Normal Modes of Linear Oscillator with Strongly Nonlinear Damped Attachment

Linear oscillator coupled to damped strongly nonlinear attachment with small mass is considered as a model design for nonlinear energy sink (NES). Damped nonlinear normal modes of the system are considered for the case of 1:1 resonance by combining the invariant manifold approach and multiple scales expansion. Special asymptotical structure of the model allows a clear distinction between three time scales. These time scales correspond to fast vibrations, evolution of the system toward the nonlinear normal mode and time evolution of the invariant manifold, respectively. Time evolution of the invariant manifold may be accompanied by bifurcations, depending on the exact potential of the nonlinear spring and value of the damping coefficient. Passage of the invariant manifold through bifurcations may bring about destruction of the resonance regime and essential gain in the energy dissipation rate.     

Banach空间上泛函微分方程的渐近性

§ 1　IntroductionIn the last few years,invariant sets and attractors of (functional) differentialequations have been extensively discussed and various interesting results on the invariantsets and attractors,and estimates on the basin of attraction have been reported(see,forinstance,[1 ,2 ,4,6,1 0 ,1 3 ,1 5,1 8] ) .However,not much hasbeen developed in the directionof giving criteria on the existence of invariant sets and attractors for the functionaldifferential equations even though there ar…     

基于LVQ神经网络的目标识别技术

通过对目标特征的分析比较,选取不变矩作为识别特征.为了达到很好的识别效果,对不变矩做了优化处理.采用LVQ神经网络技术建立了识别模型,提高了识别速度.运用有限的样本对目标识别技术进行了测试,结果表明采用此技术后的识别成功率较高,平均约为98%,识别速度快,每幅二值目标图像的识别时间约为16 ms.     

Algebraic traveling waves for the generalized Newell–Whitehead–Segel equation

In this paper we provide the only possible algebraic traveling wave solutions for the celebrated general Newell–Whitehead–Segel equation.     

《APPLIED MATHEMATICS–A JOURNAL OF CHINESE UNIVERSITIES》 Volume 29, Series B, 2014

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