On the Stability of Periodic Mercury-type Rotations

We consider the stability of planar periodic Mercury-type rotations of a rigid body around its center of mass in an elliptical orbit in a central Newtonian field of forces. Mercurytype rotations mean that the body makes 3 turns around its center of mass during 2 revolutions of the center of mass in its orbit (resonance 3:2). These rotations can be 1) symmetrical 2π- periodic, 2) symmetrical 4π-periodic and 3) asymmetrical 4π-periodic. The stability of rotations of type 1) was investigated by A.P.Markeev. In our paper we present a nonlinear stability analysis for some rotations of types 2) and 3) in 3rd- and 4th-order resonant cases, in the nonresonant case and at the boundaries of regions of linear stability.     

Ergodicity of a Class of Cocycles Over Irrational Rotations

It is proved that if is irrational and L²(S¹) with o(l/n)then for each mZ\{0} the corresponding skew product is ergodic. The rigidity of specialflows over irrational rotations with roof functions whose Fouriercoefficients are in o(l/n) is also shown.     

一类随机微分方程的稳定性

本文用Rn中一类半线性椭圆方程正解结果讨论了随机微分方程的随机稳定性.     

关于一类多项式族的鲁棒稳定性研究

本文对包括区间多项式族和菱形多项式族的一类多项式族的鲁棒稳定性进行了研究.我们给出并证明了其中几个可用有限检验来判断的多项式族的Hurwitz稳定的实例;同时举例说明了有限检验对所有这一类多项式族并不总是可行的.     

一类间接控制系统的绝对稳定性问题

利用厄米特二次型和若当标准形理论研究了一般间接控制系统的绝对稳定性问题,给出了绝对稳定性的代数形式的判别准则。所得到的结果是新的和有用的。     

一类生态系统的周期解的全局渐近稳定性

本文研究了有三个种群相互作用的数学模式: 我们分别建立了系统(*)和(**)存在唯一的大范围渐近稳定的正周期解的充分条件.     

The Best Bound on the Rotations in the Stability of Periodic Solutions of a Newtonian Equation

In most cases, the third order approximation of a scalar Newtonianequation can lead to the Lyapunov stability of a periodic solutionthrough the obtaining of a nonzero twist coefficient. Recently,Ortega obtained the twist property of a periodic solution whenthe second order coefficient does not change sign and the thirdone is negative under a crucial limitation to the rotation ofthe linearization equation. The paper finds that the best boundon the limitation of the rotations is .     

一类离散动力系统的稳定性

研究一类作 为基因选择模 型的离散动力系 统ｙ ｎ ＋ １ ＝ ｙｎ ｅｂ（ １ － ２ ｙ ｎ － ｋ ）１－ ｙｎ ＋ ｙｎ ｅｂ（ １ － ２ ｙ ｎ － ｋ ） ,　ｎ ＝ ０,１,… ,的稳定性 ,其中 ｂ∈（０,∞）, Ｋ∈ ｛１,２,…｝     

On the Stability of Sizing Optimization Problems for a Class of Nonlinearly Elastic Materials

In this work we deal with a stability aspect of sizing optimization problems for a class of nonlinearly elastic materials, where the underlying state problem is nonlinear in both the displacements and the stresses. In [14] it is shown under which conditions there exists a unique solution of discrete design problems for a body made of the considered nonlinear material, if the nonlinear state problem is solved exactly. In numerical examples the nonlinear state problem has to be solved iteratively, and therefore it can be solved only up to some small error \eps . The question of interest is how this affects the optimal solution, respectively the set of solutions, of the design problem. We show with the theory of point-to-set mappings that if the material is not too nonlinear, then the optimal design depends continuously on the error \eps . Accepted 15 March 2001. Online publication 14 August 2001.     

一类抛物型偏微分方程反问题的稳定性

本文讨论一类抛物型偏微分方程反问题，研究测量值在特定边界上给定时源项确定的稳定性，在合理的假设下证明了该反问题具有按Ｌｉｐｓｃｈｉｔｚ型连续依赖于测量值的稳定性，推广了Ｙａｍａｍｏｔｏ的结果．     

一类二阶非线性微分方程零解的全局渐近稳定性

本文研究二阶非线性微分方程■零解的全局渐近稳定性,其中各函数是实数上的连续函数．我们得到了零解全局渐近稳定的一些充分必要条件和充分条件．推广和改进了文献中的一些结论．     

On Rotations and the Generation of Binary Trees

The rotation graph, G_n, has vertex set consisting of all binary trees with n nodes. Two vertices are connected by an edge if a single rotation will transform one tree into the other. We provide a simpler proof of a result of Lucas that G_n, contains a Hamilton path. Our proof deals directly with the pointer representation of the binary tree. This proof provides the basis of an algorithm for generating all binary trees that can be implemented to run on a pointer machine and to use only constant time between the output of successive trees. Ranking and unranking algorithms are developed for the ordering of binary trees implied by the generation algorithm. These algorithms have time complexity O(n²) (arithmetic operations). We also show strong relationships amongst various representations of binary trees and amongst binary tree generation algorithms that have recently appeared in the literature.     

一类循环序列的稳定性

讨论了循环序列x_(n+1)=(α-βx_n)/(γ+x_(n-1)),n=0,1,2,….解的整体渐近稳定性,用系数α,β,γ给出了其正的平衡点是全局吸引的充分条件及全局吸引域.其中α,β,γ为正实数.     

一类超线性不对称Duffing方程的Aubry-Mather集

通过引进合适的作用-角变量变换,并运用新的估计方法,对超线性不对称Duffing方程的Poincaré映射,应用推广的Aubry-Mather定理,证明了一类超线性不对称Duffing方程的Aubry-Mather集的存在性.     

一类(0,1)-矩阵的最大积和式

本文给出了每条线恰有n-2个1的n阶(0.1)-矩阵的最大积和式的组合表达式.     

一类差分方程的渐近性

本文对高维非自治差分方程x(τ+1)=f(τ,x)+g(τ,y);y(τ+1)=k(τ,x,y) (1)得到了保证其平凡解渐近稳定,一致渐近稳定的判别准则,而对V逐数的差分不要求负定性,推广了文[1]中相应的结果.