对称的广义中心对称矩阵逆特征问题的最佳逼近

在结构设计中,矩阵逼近问题通常用来校正刚度矩阵或质量矩阵,使得它们具有给定谱约束条件.本文基于逆特征值理论讨论了线性流形上的一类对称的广义中心对称矩阵逼近问题,给出了它们的最小二乘解的显示表达式及其最佳逼近,提供了一个数值方法并给出了数值例子.     

线性约束下反Hermitian广义反Hamiltonian矩阵的最佳逼近问题

讨论了线性约束下反Hermitian广义反Hamiltonian矩阵的最佳逼近问题。提出并征明了约束矩阵集合SA非空的充分必要条件,给出了集合SA中元素的一般表达式。对于任意一个复矩阵,得到了它在SA中的最佳逼近矩阵A的表达式。     

线性矩阵方程AXB=C的中心对称解及其最佳逼近

利用矩阵的广义异值分解，得到了线性矩阵方程AXB=C有中心对称解的充分必要条件，且有解时，给出了其解的一般表达式。另外，给出了在矩阵方程的解集合中与给定矩阵的最佳逼近解的表达式。     

子矩阵约束下矩阵方程ATXA=B的实矩阵解及其最佳逼近

本文讨论了子矩阵约束下一类矩阵方程的实矩阵解问题。基于矩阵的奇异值分解和广义奇异值分解方法,给出了该问题有解的充要条件和解的一般表达式。并证明了对任一给定的实矩阵,在上述解集合中必存在唯一的最佳逼近解,给出了最佳逼近解的形式。     

线性流形上广义次对称矩阵的最佳逼近

讨论了线性流形上广义次对称矩阵的最小二乘解,得到了解的一般表达式,对于任意给定的实对称矩阵A,在最小二乘解集中得到了A的最佳逼近解。     

一类一阶耦合广义系统的极点配置问题

讨论了Hilbert空间中广义分布参数系统与广义集中参数系统所构成的一类一阶耦合广义系统的无限多极点配置问题,应用有界线性算子的广义逆给出了问题的解及解的构造性表达式。     

矩阵和关于广义逆的混合第二吸收律

本文研究了广义逆运算理论,定义了两个矩阵和关于广义逆的混合第一和第二吸收律的概念,利用矩阵的广义Schur补概念与秩方法,对于混合第二吸收律有关的矩阵表达式的极秩进行了研究,推导了这些矩阵表达式的极大秩与极小秩公式,并利用这组公式建立了两个矩阵和关于｛1｝-逆与{1,3｝-逆、{1｝-逆与{1,4}-逆的混合第二吸收律...     

自反矩阵和反自反矩阵反问题的最小二乘解

研究了自反矩阵和反自反矩阵反问题的最小二乘解及最佳逼近,给出了最小二乘解和最佳逼近解,并得到丁反问题有解的充要条件及解的表达式。     

线性流形上复对称矩阵的最小二乘问题

本文主要讨论了线性流形上复对称矩阵的最小二乘问题。在推导出所给线性流形中任意矩阵的显式表达的基础上,利用奇异值分解和Frobenius范数的酉不变性得到了该最小二乘问题通解的一般表达式。此外,文章还考虑了任一给定矩阵对此最小二乘问题解集合的最佳逼近问题,证明了该最佳逼近问题存在唯一解,并利用酉矩阵的性质得到了最佳逼近解的表达式。     

一类二阶耦合广义系统的极点配置问题

应用算子的广义逆讨论了一类二阶耦合广义系统的极点配置问题 ,给出了解法及解的构造性表达式     

Generalized Rayleigh-Lamb equation

The dynamics of the vapor-liquid interface when a solid particle heated to a high temperature comes into contact with a cold liquid is analyzed. The generalized Rayleigh-Lamb equation taking into account temperature changes in the liquid and the vapor, the saturation vapor pressure change associated with it, and the emergence of the mass flux due to liquid evaporation at the interface is deduced. At medium parameters far from the critical point, the generalized Rayleigh-Lamb equation reduces to its well-known form. Around the critical point, the difference between the obtained equation and arising modes of changes of the vapor-liquid interface can be rather considerable. Unlike the well-known Stefan problem, far from the critical liquid temperature, the phase transition temperature and, respectively, the saturation vapor pressure change with the vapor-liquid interface movement, which yields various modes of dynamics of the vapor cavity. In the special case of small variations from the stationary mode, an analytical solution for the problem on a small change in the vapor cavity radius with time was developed.     

Generalized Bezout Identity

We describe a new approach of the generalized Bezout identity for linear time-varying ordinary differential control systems. We also explain when and how it can be extended to linear partial differential control systems. We show that it only depends on the algebraic nature of the differential module determined by the equations of the system. This formulation shows that the generalized Bezout identity is equivalent to the splitting of an exact differential sequence formed by the control system and its parametrization. This point of view gives a new algebraic and geometric interpretation of the entries of the generalized Bezout identity. Received: June 6, 1997; revised version: December 10, 1997     

广义距离回归

实际工作中涉及的两个测得量的回归极为有用.从一个量有不确定度的一般回归讨论到两个量有不确定度的正交回归,最后讨论到普遍的广义距离回归,并以实例说明.     

Generalized fracture mechanics

The application of generalized fracture mechanics to ductile materials is considered. The deformations leading to crack propagation in SEN specimens of a copper-beryllium alloy in two conditions were established experimentally and can be described in terms of the generalized theory. In particular, it was possible to define and measure a surface work for fracture propagation in specimens subject to general yielding. The values of surface work obtained were 7.5×10⁸ mJ m^–2 for the alloy in a low yield stress (235 MPa) condition and 1.2×10⁸ mJ m^–2 for the high yield-stress (725 MPa) condition.On secondment from RARDE (Ministry of Defence) Fort Halstead, Sevenoakes, Kent.     

广义波导不变量

海洋波导中声场在空间-频率域形成明暗相间的干涉条纹,Chuprov根据距离-频率(r-ω)域干涉条纹定义了波导不变量。一直以来,科研工作者探讨波导不变量定义式均未考虑声源-接收器方位角对波导不变量β值的影响,传统的声场干涉研究也忽略方位角变化对干涉条纹的影响。通过实验和仿真发现,对于我国近海大陆架常见的水平缓变楔形波导,方位角变化对干涉条纹的影响显著,因此将Chuprov给出的仅考虑传播距离变化对干涉条纹影响的波导不变量定义式推广为同时考虑方位角变化对干涉条纹影响的波导不变量定义式,并将之称为广义波导不变量。通过理论推导、数值仿真及海上实验数据分析发现,在水平缓变楔形波导环境下,传统波导不变量定义式无法解释干涉现象时,广义波导不变量可很好地解释数值仿真及海上实验声场干涉现象。     

Generalized CAZA sequences

ABSTRACT

Constant amplitude zero auto-correlation (CAZA) sequences and periodic sequences have been widely used as preambles for synchronization and channel estimation in the literature. In this paper, we first construct generalized CAZA (GCAZA) sequences in the time domain. Then, their Cramer-Rao bounds containing no matrix inversion for the purpose of joint carrier frequency offset and channel impulse response estimation are derived. The properties of auto-correlation and the discrete Fourier transform of a GCAZA are then presented analytically. The latter also explains the relationship between the conventional frequency-domain CAZA and the proposed time-domain GCAZA. Finally, we conduct numerical simulations and compare the results with existing sequences in the literature for fading channels.     

Generalized copula-graphic estimator

In this paper, a copula-graphic estimator is proposed for censored survival data. It is assumed that there is some dependent censoring acting on the variable of interest that may come from an existing competing risk. Furthermore, the full process is independently censored by some administrative censoring time. The dependent censoring is modeled through an Archimedean copula function, which is supposed to be known. An asymptotic representation of the estimator as a sum of independent and identically distributed random variables is obtained, and, consequently, a central limit theorem is established. We investigate the finite sample performance of the estimator through simulations. A real data illustration is included.