Styan不等式的推广

设ｘ为ｎ×１单位向量，Ａ为ｎ×ｎ正交阵，Ｓｔｙａｎ［１］证明了这里λ１和λｎ为Ａ的最大和最小特征值。本文的目的是将上式的ｘ推广为ｎ×ｐ矩阵Ｘ，即证明了，对一切满足Ｘ′Ｘ＝Ｉｐ的矩阵ｘ和正定阵Ａ这里ｎ＞２ｐ，λ１≥…≥λｎ为Ａ的特征值，ｔｒ（Ａ）表示方阵Ａ的迹。     

一类二阶线性Gronwall不等式及其应用

给出了一类二阶线性Gronwall不等式的初等证明，并应用到非线性Newton运动方程的初、边值问题中，通过具体的例子说明了它在误差估计方面的作用。     

有关幂等矩阵的Bellman不等式的一些结果

给出了幂等矩阵在一定条件下的Bellman不等式。     

精确华宁不等式与最佳 Hermite 插值结点组

利用Hermite插值误差的余项估计式,在最大框架下确定了Sobolev空间在最大和平均范数下逼近问题的最优Hermite插值结点组,并对在Hermite插值结点组上Hermite数据为零的函数给出了计算华宁不等式最佳常数的方法。先利用构造辅助函数的方法给出了Hermite插值误差的一种估计式,在此基础上把华宁不等式最佳常数的计算转化为一个显式积分表达式,并用两个例子来说明结果。同时在最大框架下给出了Sobolev空间利用Hermite插值逼近误差的准确值,并找出了当Hermite插值结点个数固定时的最优Hermite插值结点组。对一些特殊情形,给出了最优插值结点组的显式表达式;对于一般情形,把最优插值结点组的计算归结为求一些具体函数的最小值点。利用Mathematical计算了华宁不等式最优系数的一些具体值。     

缺项算子矩阵的二阶代数补Ⅱ

对于任意给定的二阶多项式p(t)以及缺项算子矩阵（AC?B)，本文给出存在补矩阵T＝（^AC XB)使得p(T)=0的充分必要条件，而且给出这种二阶代数补的完全刻画。     

基于Riccati不等式的微动隔振平台鲁棒性能控制器设计

针对辨识参数存在摄动的精密隔振平台系统的鲁棒性能控制器设计问题,基于参数摄动系统的鲁棒性能与Riccati不等式解之间的关系,推导出了一类参数摄动系统的输出反馈鲁棒性能控制器设计方法,将鲁棒性能控制器设计转化为参数确定的辅助系统的一般输出反馈鲁棒控制器求解,计算较方便.通过对单自由度微动隔振平台的仿真分析表明,空气弹簧支撑隔振平台虽能隔离地基的高频成分,但对低频成分以及台面直接干扰的隔振效果不好;采用所设计的鲁棒性能控制器,闭环系统能够在不确定参数较大的摄动范围内有效隔离地基的低频振动,而且对台面直接干扰和量测噪声也具有很好的鲁棒性.     

二次损失下带线性等式约束的多元线性模型中线性预测的可容许性

本文在二次损失下研究了带线性等式约束条件的多元线性模型中条件线性可预测变量的可容许线性预测,并分别在齐次线性预测和非齐次线性预测类中得到了条件线性可预测变量的一个线性预测是可容线性预测的若干充要条件.     

楔形上Altman不等式的推广

本文给出Bnnach空间中楔形上半紧1-集压缩映象A的方程Az=ux解的某些结果。其次,还扩充和改进几个具Altman型行列式的不等式的不动点定理。     

具有非线性扰动的线性多时变时滞系统的有记忆状态反馈控制

本文探讨一类非线性扰动满足范数有界的线性多时变时滞系统的有记忆状态反馈控制,通过构造恰当的Lyapunov泛涵,利用Jensen不等式来处理泛涵导数中的交叉项,应用线性矩阵不等式技术和Schur补引理,我们得到了系统镇定的时滞相关的充分条件,并给出了有记忆状态反馈控制器的设计方法.最后,数值例子验证了文中所得的结论的保守性更低及求解方法的有效性.     

基于Hilbert振动分解和高阶能量算子的行星齿轮箱故障诊断研究

行星齿轮箱广泛应用于各种机械设备中,其故障诊断问题是近年来的研究热点之一。提出了基于Hilbert振动分解和高阶微分能量算子的故障诊断方法。Hilbert振动分解计算复杂性低,能够将复杂信号分解为单分量,应用该方法对信号进行分解,满足高阶微分能量算子的要求。高阶微分能量算子的时间分辨率高,对信号的瞬态变化具有良好的自适应性,应用该方法检测故障引起的瞬态冲击,估计信号的幅值包络和瞬时频率。对高阶微分能量算子输出以及幅值包络和瞬时频率进行Fourier变换,通过频谱识别特征频率,从而诊断行星齿轮箱故障。分析了行星齿轮箱的仿真信号和实验信号,准确地诊断了太阳轮、行星轮和齿圈的故障,验证了该方法的有效性。     

关于一类积分不等式的推广及其应用

本文讨论了一类新的关于两个无关变元积分不等式,所得结论是Pachpatte型的积分不等式的自然推广,并把主要结果应用于偏微分方程的定性理论中。     

鲁棒线性最优化的若干扩展

本文基于凸锥理论对鲁棒线性最优化作了若干拓展。本文的拓展分为三部分。首先我们放松了对不确定集的限制,把鲁棒线性最优化拓展到凸锥和子空间平移的交的不确定集的情形。其次我们考虑了由凸不等式定义的不确定集的鲁棒线性最优化。再次,我们把鲁棒线性最优化拓展到了包含系数不确定性和解的实现误差的情形。对某些特殊的情形,我们导出了鲁棒线性最优化的确定性等价问题。     

Bending analysis of thick laminated plates using extended Kantorovich method

This study is concerned with bending of moderately thick rectangular laminated plates with clamped edges. The governing equations, based on Reissner first-order shear deformation plate theory; in terms of deflection and rotations of the plate include a system of three second-order, partial differential equations (PDEs). Application of extended Kantorovich method (EKM) to the system of partial differential equations reduces the governing equations to a double set of three second-order ordinary differential equations in the variables x and y. These sets of equations were then solved in an iterative manner until convergence was achieved. Normally three to four iterations are enough to get the final results with desired accuracy. It is demonstrated that, unlike other weighted residual methods, in the extended Kantorovich method initial guesses to start iterations are arbitrary and not even necessary to satisfy the boundary conditions. Results of this study also reveal that the convergence of the EKM is rapid and the method is an efficient way to solve system of PDEs of the same type. To compare the results of this study, the problem was also analyzed using commercial finite element software, ANSYS. Results show reasonably good agreement with the finite element analysis.     

The Kantorovich method applied to bending,buckling, vibration,and 3D stress analyses of plates: A literature review

This study presents a thorough review of the applications of the Kantorovich method to several plate problems. The main objective of this review is to compile an up-to-date list of studies that employ the Kantorovich method, which is a semi-analytical numerical method, to bending, buckling, vibration, and three-dimensional elasticity problems of plates. The reviews highlight the derivations of the governing equations, which are written in form of ordinary differential equations, and the solution methods used to solve those equations. This review should be helpful for researchers and engineers to quickly gain an overview of the application of the method to thin-walled structures.     

关于 Bernstein 算子， Kantorovich 算子的逼近问题

本文建立了Ｂｅｒｎｓｔｅｉｎ多项式和Ｋａｎｔｏｒｏｖｉｃｈ多项式的Ｐ阶导数对函数的Ｐ阶导数逼近的渐近度开式。     

The Smallest Correction of an Inconsistent System of Linear Inequalities

The problem of calculating a point x that satisfies a given system of linear inequalities, A x #x2265; b, arises in many applications. Yet often the system to be solved turns out to be inconsistent due to measurement errors in the data vector, b. In such a case it is useful to find the smallest perturbation of b that recovers feasibility. This motivates our interest in the least correction problem and its properties.Let A x #x2265; b be an inconsistent system of linear inequalities. Then it is always possible to find a correction vector y such that the modified system A x #x2265; b #x2212; y is solvable. The smallest correction vector of this type is obtained by solving the least correction problem Let denote the convex cone which consists of all the points for which the system A x #x2265; u is solvable. Let denote the polar cone of . It is shown that the least correction problem has a simple geometric interpretation which is based on the polar decomposition of into and . A further insight into the least correction concept is gained by exploring the duality relations that characterize such problems.     

Banach格上算子范数的若干反例

本文对Banach格上几种常见的算子范数的等价问题给出了若干反例,这一些例子回答了与之相关的问题。     

线性空间中有限维与无限维之差异

通过例举7条差异给出了线性空间中无限与有限的区别.     

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。     

Implementation of a generalized exponential basis functions method for linear and non‐linear problems

In this paper, we address shortcomings of the method of exponential basis functions by extending it to general linear and non‐linear problems. In linear problems, the solution is approximated using a linear combination of exponential functions. The coefficients are calculated such that the homogenous form of equation is satisfied on some grid. To solve non‐linear problems, they are converted to into a succession of linear ones using a Newton–Kantorovich approach. The generalized exponential basis functions (GEBF) method developed can be implemented with greater ease compared with exponential basis functions, as all calculations can be performed using real numbers and no characteristic equation is needed. The details of an optimized implementation are described. We compare GEBF on some benchmark problems with methods in the literature, such as variants of the boundary element method, where GEBF shows a good performance. Also, in a 3D problem, we report the run time of the proposed method compared with that of Kratos, a parallel, highly optimized finite element code. The results show that in this example, to obtain the same level of error, much less computational effort is needed in the proposed method. Practical limitations might be encountered, however, for large problems because of dense matrix operations involved. Copyright © 2015 John Wiley & Sons, Ltd.