Differentiable conjugacy of the Poincaré type vector fields on

We prove that on , except for those germs of vector fields whose linear parts are conjugated to , any two Poincaré type vector fields are at least conjugated to each other provided their linear approximations have the same eigenvalues and the nonlinear parts are generic.

     

On the Nature of Buffering

We state a theorem on the instability of self-similar cycles and tori of a certain type in a system which is a quasinormal form of a boundary-value problem for a nonlinear wave equation in the square.     

Nonlinear Filtering for Diffusions in Random Environments

Suppose that the signal X to be estimated is a diffusion process in a random medium W and the signal is correlated with the observation noise. We study the historical filtering problem concerned with estimating the signal path up until the current time based upon the back observations. Using Dirichlet form theory, we introduce a filtering model for general rough signal X ^W and establish a multiple Wiener integrals representation for the unnormalized pathspace filtering process. Then, we construct a precise nonlinear filtering model for the process X itself and give the corresponding Wiener chaos decomposition.     

On the Ulam stability of Jensen and Jensen type mappings on restricted domains

In 1941 Hyers solved the well-known Ulam stability problem for linear mappings. In 1951 Bourgin was the second author to treat this problem for additive mappings. In 1982-1998 Rassias established the Hyers-Ulam stability of linear and nonlinear mappings. In 1983 Skof was the first author to solve the same problem on a restricted domain. In 1998 Jung investigated the Hyers-Ulam stability of more general mappings on restricted domains. In this paper we introduce additive mappings of two forms: of “Jensen” and “Jensen type,” and achieve the Ulam stability of these mappings on restricted domains. Finally, we apply our results to the asymptotic behavior of the functional equations of these types.     

Optimizing matrix stability

Given an affine subspace of square matrices, we consider the problem of minimizing the spectral abscissa (the largest real part of an eigenvalue). We give an example whose optimal solution has Jordan form consisting of a single Jordan block, and we show, using nonlipschitz variational analysis, that this behaviour persists under arbitrary small perturbations to the example. Thus although matrices with nontrivial Jordan structure are rare in the space of all matrices, they appear naturally in spectral abscissa minimization.

     

水下任意刚性散射体对Bessel波的散射特性分析

本文利用Bessel波的谐波展开式, 采用T矩阵方法的推导思路, 建立了水下任意刚性散射体在Bessel波照射下的声散射场计算公式. 以水下刚性椭球体和两端附连半球的刚性圆柱体为例, 计算了在不同波锥角β 下的反向散射形态函数, 同时, 依据镜反射波和绕行波的干涉物理模型, 给出了预报Bessel波照射下的反向散射形态函数峰峰间隔值的计算模型. 仿真结果表明本文提出的Bessel波照射下反向散射形态函数峰峰间隔值预报方法是准确有效的, 同时也说明, 本文建立的基于T矩阵法计算水下任意刚性散射体在Bessel波束下的声散射场方法是有效的, 这拓展了T矩阵法的应用领域.     

Caractérisation spectrale de la forme de Jordan

Soit , où désigne l'ensemble des matrices n×n à coefficients complexes. Nous montrons qu'on peut complètement caractériser la forme de Jordan de A en examinant le polynôme caractéristique de tA+X pour tous les tC et tous les . Ceci nous permet de donner une démonstration plus élémentaire d'un théorème de Baribeau et Ransford sur les transformations holomorphes de qui préservent le spectre.

Denote by the set of complex n×n matrices, and let . We give a variational, purely spectral characterization of the Jordan form of A by examining the characteristic polynomial of the perturbed matrices tA+X for tC and . This allows us to give a more elementary proof of a theorem of Baribeau and Ransford on spectrum-preserving holomorphic maps on .     

Jordan标准形定理的初等变换证明

本文对 Jordan标准形定理给出了一种使用初等变换的证明 ,直观意义明显、易于理解 ,可用于线性代数教学 .     

Stability problem of a circular sandwich ring under uniform external pressure

The solution of the stability problem of a circular sandwich ring under uniform external pressure is given in a refined statement. The need to determinate the precritical stresses in load-bearing layers in the refined statement with regard to the transverse compression of the core is established, which is the basis for the detection of the mixed flexural buckling forms (BFs) with more than two half-waves along the circumferential coordinate (n>2). It is found that sandwich structures with a determining parameter of transverse compression corresponding to the limit of transition from the mixed BFs to synphasic ones are the most efficient from the weight viewpoint. Translated from Mekhanika Kompozitnykh Materialov, Vol. 36, No. 3, pp. 317–328, May–June, 2000.     

Hermite and Smith normal form algorithms over Dedekind domains

We show how the usual algorithms valid over Euclidean domains, such as the Hermite Normal Form, the modular Hermite Normal Form and the Smith Normal Form can be extended to Dedekind rings. In a sequel to this paper, we will explain the use of these algorithms for computing in relative extensions of number fields.