周期系数的高维Riccati方程的周期解

本文研究了周期系数的高维Riccati方程X’＝X·A（t）·X＋B（t）·X＋C（t）,其中X∈R(n×1)A（t）∈R(1×n),B（t）∈R(n×n),C（t）E∈R(n×1);A（t）,B（t）,C（t）均是以2π为周期的实连续矩阵或向量函数,建立了该方程存在广义周期解的一个充要条件和存在周期解的两个充分条件,推广了周期系数的Riccati方程存在周期解的一些结论．     

Contractibility of Hyperspaces Ck（X）

This paper proves the following results： let X be a continuum, let k, m ∈ N, and let B ∈ C m （X）, consider the continuous surjection f k ： C k （X） → C k （X）. We define the mapping B ： C k （X） → C k＋m （X）： by B （A） = f k （A） B. Then following assertions are equivalent： （1） The hyperspace C k （X） is g-contractible; （2） For each m ∈ N and for each B ∈ C m （X） the mapping B is a W -deformation in C k＋m （X）; （3） For each m ∈ N there exists B ∈ C m （X） such that the mapping B is a W -deformation in C k＋m （X）; （4） There exists m ∈ N such that for each B ∈ C m （X） the mapping B is a W -deformation in C k＋m （X）; （5） There exist m ∈ N and B ∈ C m （X） such that the mapping B is a W -deformation in C k＋m （X）.     

矩阵方程A1X1B1＋A2X2B2＋…＋AlXlBl=C的中心对称解及其最佳逼近

设矩阵X=(xij)∈R ,如果xij=xn+1-i,n+1-j(i,j=1,2,…,n),则称X是中心对称矩阵.该文构造了一种迭代法求矩阵方程A1X1B1+A2X2B2+…+AlXlBl=C的中心对称解组(其中[X1,X2,…,Xl]是实矩阵组).当矩阵方程相容时,对任意初始的中心对称矩阵组[X1(0),X2(0),…,Xl(0)],在没有舍入误差的情况下,经过有限步迭代,得到它的一个中心对称解组,并且,通过选择一种特殊的中心对称矩阵组,得到它的最小范数中心对称解组.另外,给定中心对称矩阵组[X1,X2,…,X1],通过求矩阵方程A1X1B1+A2X2B2+…+AlXlBl=C(其中G=C-A1X1B1-A2X2B2-…-AlXlBl)的中心对称解组,得到它的最佳逼近中心对称解组.实例表明这种方法是有效的.     

一类缺项算子矩阵的谱补问题

对于Hilbert空间上的2×2算子矩阵,其中A∈B（H）,C∈B（K,H）,D∈B（H,K）给定,当X取遍B（K）中算子时,我们给出所有Nx的谱之交集和并集的刻画．     

关于Fuzzy矩阵的广州逆

本文分别给出了Fuzzy矩阵存在广义{1，3}－逆、广义{1，4}－逆以及Mocre-Penrose广义逆Fuzzy矩阵的一些充要条件。又得到求上述广义逆Fuzzy矩阵的一些公式。主要的结果有：1．Fuzzy矩阵A的广义{1，3}－逆A^(1,3)（广义{1，4}－逆A^(1,4)的充要条件是Fuzzy关系方程X。A^T。A＝（A。A^T。Y＝A）有解。2．Fuzzy矩阵A的Mocre-Penrose广义逆A^＋存在的充要条件是Fuzzy关系方程X。A^T。A＝A，A。A^T。Y＝A均有解。3．如果B、C分别的Fuzzy关系方程X。A^T。A＝A，A。A^T。Y＝A的一个解，那么A^ ＝A^T。C。B＝C^T。AB^T＝C^T。B。A^T。     

对称广义中心对称半正定矩阵模型修正的矩阵逼近法及其应用

设X,B分别是实测的位移矩阵和载荷矩阵, C是有限元模型估计,找对称广义中心对称半正定矩阵(A)使‖C-(A)‖F=min(A:AX=B)‖C-A‖F.我们证明这样的(A)存在唯一,并应用它来修正动力模型.数值结果证明方法是行之有效的.     

对称广义中心对称矩阵模型修正的矩阵逼近法及其扰动性

X,B是实测的位移矩阵和载荷矩阵,C是有限元方法得到的估计矩阵,给出了AX=B的对称广义中心对称矩阵解集合ζ的表达式,对于逼近问题||C-A||F=min A∈ζ||C-A||F的解A,给出了它的表达式并分析了解A的扰动性,数值结果表明方法是行之有效的.     

线性矩阵哈密顿系统的振动性

研究了线性矩阵 Hamilton系统X′=A( t) X + B( t) YY′=C( t) X -A*( t) Y　　 t≥ 0的振动性 .其中 A( t) ,B( t) ,C( t) ,X,Y为实 n× n矩阵值函数 ,B,C为对称矩阵 ,B正定 .借助于正线性泛函 ,采用加权平均法 ,得到了该系统的非平凡预备解的振动性 .这些结果推广、改进了许多已知的结果     

高中数学“短平快”同步练(3)

【高一代数】映射与函数选择题1．将实数a分别对应于它的①相反数，②绝对值，③倒数，其中可称为映射的对应有（）．（A）1个（B）2个（C）3个（D）0个2．将非负实数X对应于它的平方根，此对应不能称作映射的原因是（）．（A）X不一定有平方根（B）不同的X有不同的平方根（C）X平方根不一定唯一（D）逆对应不存在3．从集合A=｛，。2，。3｝到集合B一｛hi，bZ｝建立映射，可得不同的映射数为（）．（A）8个（B）7个（C）6个（D）5个4．以下四映射中，原象不唯一的映射是（）．（A、l一（B、1一xZ（C）＿一一上7（D）X——X’5．…     

求解矩阵方程AXB+CXD=F参数迭代法的最优参数分析

本文针对求矩阵方程AXB+CXD=F唯一解的参数迭代法，分析当矩阵A，B，C，D均是Hermite正（负）定矩阵时，迭代矩阵的特征值表达式，给出了最优参数的确定方法，并提出了相应的加速算法.     

R3中相交直线偶的运动密度

本文利用活动标架法,得到了积分几何中至今还没有的R3中相交直线偶的运动密度公式,并根据此公式计算了相交直线偶的交点落入凸体K的运动测度.     

从积分几何的观点看几何不等式——纪念李国平院士吴新谋教授诞辰100周年

该文先介绍一些中国数学家在几何不等式方面的工作.作者用积分几何中著名的Poincarè公式及Blaschke公式估计一随机凸域包含另一域的包含测度, 得到了经典的等周不等式和Bonnesen -型不等式.还得到了一些诸如对称混合等周不等式、Minkowski -型和Bonnesen -型对称混合等似不等式在内的一些新的几何不等式.最后还研究了Gage -型等周不等式以及Ros -型等周不等式.     

Global entropy solutions to the compressible Euler equations in the isentropic nozzle flow for large data: Application of the generalized invariant regions and the modified Godunov scheme

We study the motion of isentropic gas in nozzles. This is a major subject in fluid dynamics. In fact, the nozzle is utilized to increase the thrust of rocket engines. Moreover, the nozzle flow is closely related to astrophysics. These phenomena are governed by the compressible Euler equations, which are one of crucial equations in inhomogeneous conservation laws.In this paper, we consider its unsteady flow and devote to proving the global existence and stability of solutions to the Cauchy problem for the general nozzle. The theorem has been proved in Tsuge (2013). However, this result is limited to small data. Our aim in the present paper is to remove this restriction, that is, we consider large data. Although the subject is important in Mathematics, Physics and engineering, it remained open for a long time. The problem seems to rely on a bounded estimate of approximate solutions, because we have only method to investigate the behavior with respect to the time variable. To solve this, we first introduce a generalized invariant region. Compared with the existing ones, its upper and lower bounds are extended constants to functions of the space variable. However, we cannot apply the new invariant region to the traditional difference method. Therefore, we invent the modified Godunov scheme. The approximate solutions consist of some functions corresponding to the upper and lower bounds of the invariant regions. These methods enable us to investigate the behavior of approximate solutions with respect to the space variable. The ideas are also applicable to other nonlinear problems involving similar difficulties.     

中立型线性控制系统的最优控制

本文将就形如　的中立型线性控制系统进行深入讨论，给出此类系统的最优控制的最大值原理，并举例说明这一重要结论在经济管理系统中的应用。     

Movement of hot spots on the exterior domain of a ball under the Neumann boundary condition

We consider the Cauchy-Neumann problem of the heat equation in the exterior domain of a ball in R^N, and study the movement of hot spots of the solution as t→∞.     

On synchronization of chaotic systems based on the Thau observer design

In this paper we revisit the Thau observer design and concern its application to the synchronization problem of two Lorenz name related systems in the master-slave formalism. The first one is the Lorenz-Stenflo system possessing a positively invariant ellipsoid while another one is the hyperchaotic Lorenz system possessing a positively invariant cylinder. Information about loci of these invariant domains is applied for the observer design. Further, we present one assertion related to one spectral inequality arisen in the process of assigning stable spectrum to the observer matrix and show its use in the observer design. We demonstrate the efficiency of synchronization schemes for the both of systems with help of numerical simulation.     

Continuous spectrum, point spectrum and residual spectrum of operator matrices

Let M_C denote a 2 × 2 upper triangular operator matrix of the form , which is acting on the sum of Banach spaces X⊕Y or Hilbert spaces H⊕K. In this paper, the sets and ?_C∈B(K,H)σ_r(M_C) are, respectively, characterized completely, where σ_c(·) denotes the continuous spectrum, σ_p(·) denotes the point spectrum and σ_r(·) denotes the residual spectrum. Moreover, some corresponding counterexamples are given.     

强不变原理与完全收敛性的统一形式

本文建立了强不变原理与完全收效性的统一形式，得到了用强不变原理研究完全收敛性的方法，前人许多关于强不交原理和完全收敛性的结论是本文的推论．     

The coincidences among the semicore and the dominance core

We propose the semicore and the dominance core, and provide the coincidences between the semicore and the dominance core.     

An intriguing hybrid synchronization phenomenon of two coupled complex networks

This paper investigates the hybrid synchronization problem of two coupled complex networks. Employing the linear feedback and the adaptive feedback control methods which are simple, efficient, and easy to implement in practical applications, we obtain some useful criteria of the hybrid synchronization of two coupled networks based on the Lyapunov stability theory and Lasalle’s invariance principle. It shows that under suitable conditions, two coupled complex networks can realize an intriguing hybrid synchronization: the outer anti-synchronization between the driving network and the response network, and the inner complete synchronization in the driving network and the response network, respectively. Numerical simulations demonstrate the effectiveness of the proposed hybrid synchronization scheme.