关于乘法逆特征值问题有解的充分条件

1．引言本文讨论如下乘法逆特征值问题[1]有解的充分条件．问题MR．给定nxn实矩阵A—（a＊和n个实数人l，…，An，求实对角矩阵X一山x以xl，…，1＊使得＊A的特征值为人，…，入．关于此问题可解的充分条件，deOliveira［2］，何旭初和戴华［31等给出过一些结果，但由于都是把此问题作为一般代数特征值反问题的特例来处理，没有注意到乘法问题的独特性，因而得到的可解条件比较强．本文根据乘法问题的特点，运用［31，［4］中的技术及拓扑度理论给出一些新的条件，这些条件大大改进了［2，3，5］中的结果．2．主要结果首先弓l进几个记号…     

一类特殊矩阵的广义特征值反问题

在给定部分特征值及部分特征向量的情况下讨论了一类特殊矩阵的议特征值反问题，给出了问题可解的条件及相应的算法和算例。     

一类亚半正定矩阵的左右逆特征值问题

1．引言在工程技术中常常遇到这样一类逆特征值问题：要求在一个矩阵集合S中，找具有给定的部分右特征对（特征值及相应的特征向量）和给定的部分左特征对（特征值及相应的特征向量）的矩阵．文［2］，［3］讨论了S为。x。实矩阵集合的情形．文［4］－［7］对S为nxn实对称矩阵．对称正定矩阵，对称半正定矩阵集合的情形进行了讨论．文【川讨论了S为亚正定阵集合的情形．并提到了对于亚半正定矩阵的情形目下无人涉及，有待进一步研究．本文将对S为nxn亚半正定矩阵集合的情形进行讨论．给出了亚半正定矩阵的左右逆特征值问题有解的充要条件…     

由主特征对构造对称三对角矩阵

本文讨论了由给定的两个特征对(λ1，x^(1))和(λ2，x^(2))来重构一个对称三对角矩阵的问题．给出了保证λ1为Tn的最大特征值的条件．     

具有正Ricci曲率紧Riemann流形上的第一特征值估计

M为紧致n维Riemann流形，Ricci曲率具有正下界n-1，d是M的直径，本文证明了其Laplace算子的第一特征值λ1≥π^2/d^2 n-1/2。     

斜对称双对角矩阵特征值反问题

讨论了关于斜对称双对角矩阵的特征值反问题．即：已知一个n阶斜对称双对角矩阵的特征值和两个n-1阶子矩阵的部分特征值，则可求得该矩阵．最后给出了数值例子．     

求解实对称三对角矩阵特征值的二分法

本文利用2×2阶实对称矩阵特征值的计算，并以秩—1修正为基础，通过建立一种二分模式，得到了计算n除实对称三对角矩阵所有特征值的新方法．结果表明，当要求所有特征值时，本文方法优于QR方法。由于算法过程中数据的不相关性，本文方法具有很好的并行性，尤其适合于MIMD并行实现。     

一类高阶微分方程第二特征值的上界

本文考虑形如（－１）ｔＤｔ（ｐ（ｘ）Ｄｔｙ）＝λ（－Ｄ２）ｒｙ，ｘ∈（ａ，ｂ），Ｄｋｙ（ａ）＝Ｄｋｙ（ｂ）＝０，ｋ＝０，１，２，…，ｔ－１｛的第二特征值λ２的上界问题，得到了定理１和定理２，其中定理１的估计系数与［ａ，ｂ］无关，定理２的结果在一定条件下比定理１的好．     

解大型非对称特征问题的精化块不完全正交化算法

0引言 块Arnoldi方法~[5]是解大型非对称特征值问题的正交投影方法，然而Jia~[3]的分析表     

图的特征多项式的若干性质

图的特征多项式有许多性质，本文给出了特征多项式的指数表达式，特征多项式的导数的几个不同表达式以及高阶导数的图论意义。     

A study of design velocity field computation for shape optimal design

Design velocity field computation is an important step in computing shape design sensitivity coefficients and updating a finite element mesh in the shape design optimization process. Applying an inappropriate design velocity field for shape design sensitivity analysis and optimization will yield inaccurate sensitivity results or a distorted finite element mesh, and thus fail in achieving an optimal solution. In this paper, theoretical regularity and practical requirements of the design velocity field are discussed. The crucial step of using the design velocity field to update the finite element mesh in the design optimization process is emphasized. Available design velocity field computation methods in the literature are summarized and their applicability for shape design sensitivity analysis and optimization is discussed. Five examples are employed to discuss applicability of these methods. It was found that a combination of isoparametric mapping and boundary displacement methods is ideal for the design velocity field computation.     

Bifurcation-free design method of pulse energy converter controllers

In this paper, a design method of pulse energy converter (PEC) controllers is proposed. This method develops a classical frequency domain design, based on the small signal modeling, by means of an addition of a nonlinear dynamics analysis stage. The main idea of the proposed method consists in fact that the PEC controller, designed with an application of the small signal modeling, is tuned after with taking into the consideration an essentially nonlinear nature of the PEC that makes it possible to avoid bifurcation phenomena in the PEC dynamics at the design stage (bifurcation-free design). Also application of the proposed method allows an improvement of the designed controller performance. The application of this bifurcation-free design method is demonstrated on an example of the controller design of direct current–direct current (DC–DC) buck converter with an input electromagnetic interference filter.     

LMI Optimization Approach to Observer-Based Controller Design of Uncertain Time-Delay Systems via Delayed Feedback

In this paper, we propose a design method of an observer-based controller for uncertain time-delay systems by delayed feedback. Based on the Lyapunov method, an LMI (linear matrix inequality) criterion is derived to design an observer-based controller which makes the system stable. A numerical example is included to illustrate the design procedure.     

关于试验设计的效率及有关问题

效率是试验设计的根本出发点和追求目标,但实际上它是一个抽象和模糊的概念,容易误解和产生偏颇,至今还很少有文献对它专门进行过很好的阐述和研究。常见的各种试验设计方法所追求的效率一般都是单一地在某种数学模型及相应的数学准则下要求实现最优而已。本文将探讨试验设计的基本原理,解释和研究到底什么是试验设计的效率?应该怎样来追求试验设计的效率?并指出现有试验设计学科的一些不足和问题,提出一个改进的试验设计框架和学说。     

Some results on resolvable incomplete block designs

This paper is concerned with the uniformity of a certain kind of resolvable incomplete block (RIB for simplicity) design which is called the PRIB design here. A sufficient and necessary condition is obtained, under which a PRIB design is the most uniform in the sense of a discrete discrepancy measure, and the uniform PRIB design is shown to be connected. A construction method for such designs via a kind of U-type designs is proposed, and an existence result of these designs is given. This method sets up an important bridge between PRIB designs and U-type designs.     

Optimum design in the presence of parametric uncertainty

A new class of optimal design problems that incorporates environmental uncertainty is formulated and related to worst-case design, minimax objective design, and game theory. A numerical solution technique is developed and applied to a weapon allocation problem, a structural design problem with an infinite family of load conditions, and a vibration isolator design problem with a band of excitation frequencies.     

无穷方差厚尾过程变点的小波估计

研究随机设计下噪声为厚尾随机变量时非参数函数中的变点估计问题.首先,通过设计变换将随机设计转化为等间距固定设计,进而利用小波方法估计变换后的变点的位置,再利用逆设计变换求得随机设计下变点位置的估计,并给出估计的收敛速度.模拟研究结果说明对于无穷方差厚尾过程中的变点估计问题小波方法是有效的.     

An adaptive design to assess the reliability of the pyrotechnic control subsystem in opening the solar array

The pyrotechnic control subsystem plays an important role in opening the solar array of a satellite. Assessing the reliability of the subsystem requires determining the level of a control factor that is needed to cause the desired response and energy output with high probability. A two-phase adaptive design to estimate the level of interest is proposed and studied. The convergence of the design is obtained. A simulation study shows that the estimate is very close to its population value and is robust to the initial guess of the design. As an application, the design is used to assess the reliability of a real pyrotechnic control subsystem.