两相同部件冷贮备可修系统解的定性分析

用强连续算子半群理论给出了两相同部件冷贮备可修系统动态非负解的唯一性证明，并证明了0是系统主算子的本征值，给出了0本征值对应的本征向量。     

k/N:G冗余表决系统的渐近稳定性

分析了带有修理设备和多重致命及非致命操作故障的k／N(G)冗余表决系统的渐近稳定性．用该系统算子生成的正定C-半群证明了系统非负时间依赖解的存在唯一性．同时通过对系统算子谱点分布的分析，证明了本征值0对应的本征向量恰好是系统的静态解，并且，0是虚轴上系统算子唯一的谱点，从而证明了系统的渐近稳定性．     

在常规故障条件下具有易损坏储备部件可修复系统的稳定性分析

讨论了在常规故障条件下具有易损坏储备部件可修复系统的渐进稳定性;证明了系统非负稳定解恰是系统算子0本征值对应的本征向量;系统算子的谱点均位于复平面的左半平面,且在虚轴上除0外无谱点;此外,证明了0的代数重数为1和求解了系统算子的共轭算子.     

一类冷贮备可修系统的指数稳定性

研究了修理工可延误休假的冷贮备可修系统.通过选取空间及定义算子,将模型方程转化成Banach空间中抽象的Cauchy问题,运用预解正算子和C_0半群理论证明了系统动态解的存在唯一性,并通过分析系统算子的谱分布,得出系统算子的严格占优本征值及近似本征值,进而得到系统的指数稳定性.     

人口算子的谱特性与人口半群的渐近性质

本文讨论人口算子的谱特性,证明了人口算子只有一个实本征值γ_0,γ_0是实部最大的本征值,找到了妇女临界生育率βcr与γ_0的对应关系。本文还论述了人口系统半群的存在性和渐近特性,由此给出了人口系统稳定性问题的结论,从理论上证明了,在临界生育率条件下存在稳态人口状态。这些都是定量人口理论的新结果。 *)三个单位同志同时得出本文主要结论,因此联名发表。     

两部件并联维修系统算子的性质

研究了两部件并联维修系统算子的性质,通过选取空间和定义算子将模型方程转化成了抽象柯西问题,证明了系统算子是定义域稠的预解正算子,0是系统算子的几何重数为1的本征值.讨论了系统算子的共轭算子及其定义域,证明了0是共轭算子的代数重数为1的特征值.     

可修复人机储备系统解的渐近稳定性及可靠性分析

讨论了可修复人机储备系统解的渐近稳定性及可靠性分析.证明了系统算子在Banach空间中生成正压缩C0半群,系统的非负稳定解恰是系统算子0本征值对应的本征向量,系统算子的谱点均位于复平面的左半平面且在虚轴上除0外无谱.此外,证明了系统解在特例情况下的可靠性,即瞬态可靠度大于等于其牢固可靠度.     

有两种修复方法的复杂可修复系统解的渐近稳定性

讨论了两种修复方法的系统解的渐近稳定性.证明了系统在Banach空间中生成正压缩c0半群,系统的非负稳定解恰是系统算子0本征值对应的本征向量,系统算子的谱点均位于复平面的左半平面且在虚轴上除0外无谱.     

可修复系统解的渐近稳定性及最优检测时间

应用C0半群理论,证明了服从一般分布的可修复系统的唯一非负时间依赖解的存在性,并指出该解恰是系统算子的0本征值对应的规范化后的本征向量.然后基于系统静态可用度,给出了系统检测时间和系统静态可用度之间的关系表达式,并分析了系统最优检测时间的存在性.     

具有边界控制的线性Timoshenko型系统的指数稳定性

研究多孔弹性材料在实际应用中的稳定性问题.多孔物体的动力学行为由线性Timoshenko型方程描述,这样的系统一般只是渐近稳定但不指数稳定,假定系统在一端简单支撑,另一端自由,在自由端对系统施加边界反馈控制,讨论闭环系统的适定性和指数稳定性.首先,证明了由闭环系统决定的算子A是预解紧的耗散算子、生成C0压缩半群,从而得到了系统的适定性.进一步通过对系统算子A的本征值的渐近值估计,得到算子谱分布在一个带域,相互分离的,模充分大的本征值都是A的简单本征值.通过引入一个辅助算子A0,利用算子A0的谱性质以及算子A与A0之间的关系,得到了A的广义本征向量的完整性以及Riesz基性质.最后利用Riesz基性质和谱分布得到闭环系统的指数稳定性.     

Riesz Bases in Subspaces of L2 (R+ )

In a recent investigation [8] concerning the asymptotic behavior of Gram—Schmidt orthonormalization procedure applied to the nonnegative integer shifts of a given function, the problem of determining whether or not such functions form a Riesz system in arose. In this paper, we provide a sufficient condition to determine whether the nonnegative translates form a Riesz system on . This result is applied to identify a large class of functions for which very general translates enjoy the Riesz basis property in . August 5, 1998. Date revised: August 25, 1999. Date accepted: January 11, 2000.     

The critical exponent conjecture for powers of doubly nonnegative matrices

Doubly nonnegative matrices arise naturally in many setting including Markov random fields (positively banded graphical models) and in the convergence analysis of Markov chains. In this short note, we settle a recent conjecture by C.R. Johnson et al. [Charles R. Johnson, Brian Lins, Olivia Walch, The critical exponent for continuous conventional powers of doubly nonnegative matrices, Linear Algebra Appl. 435 (9) (2011) 2175–2182] by proving that the critical exponent beyond which all continuous conventional powers of n-by-n   doubly nonnegative matrices are doubly nonnegative is exactly n−2$n-2$. We show that the conjecture follows immediately by applying a general characterization from the literature. We prove a stronger form of the conjecture by classifying all powers preserving doubly nonnegative matrices, and proceed to generalize the conjecture for broad classes of functions. We also provide different approaches for settling the original conjecture.     

Nonnegative Rank Factorization of a Nonnegative Matrix A with A A ≥0

In this article we obtain a nonnegative rank factorization of nonnegative matrices A satisfying one or both of the following conditions: (i) AA ? ? 0 (ii) A ? A ? 0, thus providing a new set of conditions that guarantee the existence of a nonnegative least-squares solution of a linear system. Indeed, the characterization of such matrices improves some of the previous known conditions for the existence of a nonnegative least-squares solution of a linear system.     

A uniqueness result for a semilinear parabolic system

We prove that for nonnegative, continuous, bounded and nonzero initial data we have a unique solution of the reaction-diffusion system described by three differential equations with non-Lipschitz nonlinearity. We also find the set of all nonnegative solutions of the system when the initial data is zero and in the last section we briefly discuss a generalization of the theorem to a system of n equations.     

Nonnegative Rank Factorization of a Nonnegative Matrix A with A A ≥0

In this article we obtain a nonnegative rank factorization of nonnegative matrices A satisfying one or both of the following conditions: (i) AA † ≥0 (ii) A † A ≥0, thus providing a new set of conditions that guarantee the existence of a nonnegative least-squares solution of a linear system. Indeed, the characterization of such matrices improves some of the previous known conditions for the existence of a nonnegative least-squares solution of a linear system.     

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??In this paper, precise large deviations of nonnegative, non-identical distributions and negatively associated random variables are investigated. Under certain conditions, the lower bound of the precise large deviations for the non-random sum is solved and the uniformly asymptotic results for the corresponding random sum are obtained. At the same time, we deeply discussed the compound renewal risk model, in which we found that the compound renewal risk model can be equivalent to renewal risk model under certain conditions. The relative research results of precise large deviations are applied to the more practical compound renewal risk model, and the theoretical and practical values are verified. In addition, this paper also shows that the impact of this dependency relationship between random variables to precise large deviations of the final result is not significant.     

[a,b]-因子包含给定圈的充分条件

设G是一个图且a,b是非负整数,a≤b.图G的一个[a,b]-因子是图G的一个支撑子图H且满足对所有的x∈V(G),a≤dH(x)≤b都成立.给出了图中[a,b]-因子包含给定圈的一个充分条件.     

l k,s -Singular values and spectral radius of rectangular tensors

The real rectangular tensors arise from the strong ellipticity condition problem in solid mechanics and the entanglement problem in quantum physics. In this paper, we study the singular values/vectors problem of real nonnegative partially symmetric rectangular tensors. We first introduce the concepts of l ^k,s -singular values/vectors of real partially symmetric rectangular tensors. Then, based upon the presented properties of l ^k,s -singular values /vectors, some properties of the related l ^k,s -spectral radius are discussed. Furthermore, we prove two analogs of Perron-Frobenius theorem and weak Perron-Frobenius theorem for real nonnegative partially symmetric rectangular tensors.