Conditions for the Existence of Two Limit Cycles in a System with Hysteresis Nonlinearity

This work deals with a two-dimensional automatic control system containing a single nonlinear hysteretic element in the general form. The conditions sufficient for the existence of at least two limit cycles in the system are presented. To prove the existence of cycles, three closed contours embedded into each other are constructed on the phase manifold by “sewing” together pieces of the level lines of various Lyapunov functions. System trajectories cross the inner contour “from outside inwards” and the middle contour “from inside outwards.” The outer contour is crossed by system trajectories “from outside inwards.” The existence of these contours proves the presence of at least two limit cycles in the system. This paper is a continuation of our earlier published work “Conditions for the Global Stability of a Single System with Hysteresis Nonlinearity,” in which the conditions of global stability in this system are formulated.     

具脉冲预防接种的SIRS传染病模型中地方病周期解的存在性

对具脉冲预防接种的SIRS传染病模型进行分析,利用分支理论得到了系统中地方病周期解的存在性,并利用数值模拟的方法验证了所得结论的正确性,完善了对该系统的讨论结果     

多元秩-序模型MLE的存在性

本文对多元秩 序模型极大似然估计的存在性进行了研究,在对模型协方差阵Ω的一些约束下,文中给出了其参数极大似然估计存在的一些充分必要条件.     

Linearized Models with Constraints of Type I

In nonlinear regression models with constraints a linearization of the model leads to a bias in estimators of parameters of the mean value of the observation vector. Some criteria how to recognize whether a linearization is possible is developed. In the case that they are not satisfied, it is necessary to decide whether some quadratic corrections can make the estimator better. The aim of the paper is to contribute to the solution of the problem.     

Hysteresis and Stick-Slip Motion of Phase Boundaries in Dynamic Models of Phase Transitions

Summary. We investigate hysteretic behavior in two dynamic models for solid-solid phase transitions. An elastic bar with a nonconvex double-well elastic energy density is subjected to time-dependent displacement boundary conditions. Both models include inertia and a viscous stress term that provides energy dissipation. The first model involves a strain-gradient term that models interfacial energy. In the second model this term is omitted. Numerical simulations combined with analytical results predict hysteretic behavior in the overall end-load versus end-displacement diagram for both models. The hysteresis is largely due to metastability and nucleation; it persists even for very slow loading when viscous dissipation is quite small. In the model with interfacial energy, phase interfaces move smoothly. When this term is omitted, hysteresis is much more pronounced. In addition, phase boundaries move in an irregular, stick-slip fashion. The corresponding load-elongation curve exhibits serrations, in qualitative agreement with certain experimental observations in shape-memory alloys. Received August 4, 1998; revised December 11, 1998     

两类教育最优投资模型等价性及其相应最优投资准则

本研究了两类教育最优投资模型等价性，并且给出了相应的最优投资准则。     

Existence of Bayesian Estimates for the Polychotomous Quantal Response Models

This paper investigates the existence of Bayesian estimates for polychotomous quantal response models using a uniform improper prior distribution on the regression parameters. Necessary and sufficient conditions for the propriety of the posterior distribution with a general link function are established. In addition, the sufficient conditions for the existence of the posterior moments and the posterior moment generating function are obtained. It is also found that the propriety guarantees the existence of the maximum likelihood estimate.     

最优数学模型筛选法确定流量系数的经验公式

应用简单的最小二乘回归分析原理对多个数学模型进行分析,得到了水利工程中有坎宽顶堰流量系数的经验公式,并对其精度进行了讨论.对指导实际工程意义重大.     

A Posterior Estimate of the Particle Method Error for Shallow Water Models

The article examines the application of the particle method to numerical solution of the Cauchy problem for a quasi-linear system of first-order partial differential equations with discontinuous piecewise-constant initial conditions. A posterior estimate of the particle method error is derived for some shallow-water models.     

KKM Type Theorems and Coincidence Theorems with Applications to the Existence of Equilibria

In this paper, we obtain some coincidence theorems and some KKM-type theorems. We apply these results to establish the existence of the solution to generalized vector equilibrium problems, where a bimap f : X × Y 2^Z is involved and some sufficient conditions are imposed on f.     

Existence of Positive Solutions for Kirchhoff Type Problems with Critical Exponent

In this paper,we consider the following Kirchhoff type problemwith critical exponent $-(a+b∫_Ω|∇u|^2dx)Δu=λu^q+u^5, in\ Ω, u=0, on\ ∂Ω$, where $Ω⊂R^3$ is a bounded smooth domain, $0< q < 1$ and the parameters $a,b,λ > 0$. We show that there exists a positive constant $T_4(a)$ depending only on a, such that for each $a > 0$ and $0 < λ < T_4(a)$, the above problem has at least one positive solution. The method we used here is based on the Nehari manifold, Ekeland's variational principle and the concentration compactness principle.     

Semilinear Integrodifferential Equations of Hyperbolic Type: Existence in the Large

The main object of this work is the existence of global solutions to semilinear integrodifferential equations in Hilbert spaces for absolutely continuous convolution kernels, where the nonlinear term is the gradient of a functional having superlinear growth at infinity. An application to the theory of viscoelasticity concludes the paper providing motivations for the abstract theory.     

YoshiZawa型周期解定理和Massera型周期解定理研究进展简介

微分方程解的有界性和周期解的存在性是檄分方程理论研究中的两个重要课题，二者之间有着紧密的联系．在解的有界性与周期解的存在性的研究中，Yoshizawa周期解定理和Massera周期解定理是非常重要的结果，具有重要的理论意义和应用价值．本文以Yoshizawa型周期解定理和Massera型周期解定理的研究为主，简要介绍泛函微分方程周期解理论研究方面的一些新进展。     

广义Kuramoto－Sivashinsky型方程惯性流形的存在性

本文对一类广义Ｋｕｒａｍｏｔｏ－Ｓｉｖａｓｈｉｎｓｋｙ型方程证明了惯性流形的存在性，并对其维数作了估计同时研究了该方程的不变雄性质和轨线的强挤压性．     

非均匀介质GL型热弹性问题解的存在唯一性

We study a new model named the Green-Lindsay type therm-elastic model for nonhomogeneous media that consists of a system of dynamic thermoelasticity equations of displacement and dynamic heat conduction equation. We construct the model based on the classical GL-model for homogeneous material. This system is coupled dynamic problem and the displacement field and heat field must be solved at the same time. By using Fadeo-Galerkin method, we proved that the problem we proposed exist unique weak solution under some regular assumption.     

一类具有扩散的三种群生态模型正解的存在性

应用Dancer不动点指数理论,通过对一类具有扩散的三种群生态模型的研究,给出了讨论具有扩散的三种群相互作用模型正解存在性问题的一般方法．