具有内部构造安全保障体系的冗余机器系统的特征值的问题

对具有内部构造安全保障体系的冗余机器系统中的特征值的存在性进行了分析求解,给出了实例,并对该系统的特征值进行了一个特征值对应一个特征向量的求征.     

具有四个状态的系统特征值的存在性

针对具有四个状态的系统所建立的模型,得出了系统算子一个特征值对应一个特征向量的结论,并证明了除0特征外还存在另外非零实特征值.     

一个Bargmann系统与一个Neumann系统

本文引入一个特征值问题导出一类非线性演化方程,在位势与特征函数之间的两种不同的约束下,此特征值问题被非线性化为一个以为Hamiltonian函数的完全可积的Bargmann系统和一个以为Hamiltonian函数的完全可积的O.Neumann系统。     

一类Dirac方程特征值问题的迹恒等式

讨论了带有非局部边界条件的一维Dirac方程BdY/dx+P(x)Y=λY的特征值问题,其中首先建立了问题的特征值集合与一个整函数u(λ)零点集合的对应,并对Dirac算子的特征值进行了估计,然后借助于一个积分恒等式,采用留数方法,得到了该问题的特征值的迹恒等式.     

线性离散事件动态系统的辨识

本文讨论利用输出数据来估计或确定系统矩阵特征值和特征向量问题.首先我们给出了特征值的一个估计,然后证明在一定条件下可以确定系统矩阵的特征值和特征向量,或用极限来表征它们,最后指出了所得到的结果在离散事件动态系统分析和控制中的意义.     

求解陀螺系统特征值问题的收缩二阶Lanczos方法

本文研究陀螺系统特征值问题的数值解法,利用反对称矩阵Lanczos算法,提出了求解陀螺系统特征值问题的二阶Lanczos方法.基于提出的陀螺系统特征值问题的非等价低秩收缩技术,给出了计算陀螺系统极端特征值的收缩二阶Lanczos方法.数值结果说明了算法的有效性.     

一个新的Liouville可积系统及其Lax表示，Bi—Hamilton结构

从一个特征值问题出发,首先推导一族非线性发展方程,其中包括著名MKdV方程做为特殊约化,进一步证明这族方程在Liounille意义下可积并具有Bi-Hamilton结构,而在位执函数和特征函数之间的一定约束下,特征值问题被非线性化为一完全可积的有限维Hamilton系统。     

基于矩阵幂运算的重特征值存在性定理

对于判断矩阵重特征值的存在性问题,运用“若λ是矩阵A的特征值,则入“是Ak的特征值”这一性质,通过矩阵的迹与特征值的关系,得到了实数域上矩阵重特征值的存在性定理并给出了证明．定理实现了“由矩阵幂运算来判断矩阵重特征值的存在性”这样一个计算过程,对讨论矩阵特征值问题具有一定的启示意义．     

高阶张量Pareto-特征值的若干性质（英文）

考虑高阶张量特征值互补问题,由于求解张量的最大Pareto-特征值是一个NP难问题,关注于Pareto-特征值的估计,并给出若干关于Z-张量和M-张量的Pareto-特征值的性质.     

高阶张量Pareto-特征值的若干性质

考虑高阶张量特征值互补问题,由于求解张量的最大Pareto-特征值是一个NP难问题,关注于Pareto-特征值的估计,并给出若干关于Z-张量和M-张量的Pareto-特征值的性质.     

宏观因素影响下的系统中元件重要性研究

为研究复杂系统在工作环境中其组成元件对系统安全运行的重要性,将汪培庄先生的因素空间理论与笔者提出的空间事故树理论相结合,构造了一套元件重要性研究方法.构建系统T={U,C,D},将元件作为研究对象集合U,系统工作的宏观环境作为因素集C,元件重要性排序集作为D.对宏观环境中的工作时间a1和温度a_2进行划分形成不同的状态区域S_q,计算在S_q中元件xj的失效权重γ(AS_q(x_j))和在S_q中系统T的失效权重δ(AS_q(T))),从而得到x_j在S状态下的等效失效权重Z(AS_q(x_j)),研究状态S_q下的原件重要性排序D_η,及元件x_j失效性对a_1及a_2的敏感性.使用一个实际的电气系统维修情况统计资料,使用上述方法进行了研究,结果表明:不同工作环境下元件对系统的重要程度是不同的.元件对温度和使用时间是敏感的,并得到了在10³0°且5030°且50⁷5d环境下工作系统可靠性是最高的结论.在给定工作环境下,重要性大的元件多储备,重要性小的元件少储备,以满足系统维修需要,并指导实际工程.     

On the Properties of the Nonlinear Ship Equations of Motion

Nonlinear ship control systems can be designed by exploiting system properties like passivity and dissipativeness in nonlinear system. The nonlinear ship model is written in a vectorial setting with emphasis placed on matrix properties like positiveness, symmetry and skew-symmetry. As a result of energy conservation the ship dynamics can be considered as two interconnected systems. The first system describes the dissipative motion of the rigid-body (ship) while the second system represents the forces due to potential theory generated by the ambient water particles. It is shown that for a stable ship, both subsystems are passive as well as the interconnected system. For an unstable ship, the ambient water system is input feedforward passive with shortage of passivity and therefore the ship must be stabilized by positive feedback. The structural properties of the nonlinear equations of motion are exploited in the Lyapunov analysis when designing ship control systems.     

A new method for solving the eikonal equation in the spherical computing domain

In order to overcome the problem of singularities and nonuniform grids arising when solving eikonal equation in spherical coordinate systems, a spherical Cartesian coordinate system is defined and the Hamiltonian form of the eikonal equation according to this coordinate system is given. A modified velocity function that can transform spherical coordinate system–based eikonal equation into ones based on a spherical Cartesian coordinate system is deduced by using a differential geometric method where a layered distribution of the velocity function is assumed. After comparing the results of using this approach with the traditional method of solving eikonal equation based on a spherical coordinate system, the viability of the transformation to a spherical Cartesian coordinate system based on a modified velocity function is proven. Despite the assumption of a layered distribution of the velocity function, it is also proven that the method will hold for a velocity function under any three-dimensional distribution. The new method overcomes problems present in traditional approaches and opens up a new way of solving eikonal equation in a spherical computational domain.     

考虑废旧品质量的闭环供应链混合回收渠道选择研究

为确定最优的回收渠道,对由单个制造商、零售商和第三方组成的闭环供应链系统进行研究。在该系统中,可能存在制造商和零售商、制造商和第三方、零售商和第三方以及制造商、零售商和第三方同时回收的四种渠道,并根据质量差异对废旧品进行翻新或再制造。在分散决策下建立了四种回收渠道模型。比较发现:站在制造商和系统收益最大化及社会效益角度,三渠道是最佳选择,此时得到的废旧品最多;制造商不进行回收时获利最低,且不利于提高废旧品的获取量。最后,通过算例剖析了废旧品再制造率对四种混合回收渠道下成员及系统利润的影响。结果表明:制造商应尽量将废旧品用于再制造。     

On the spectrum for the artificial compressible system

Stability of stationary solutions of the incompressible Navier–Stokes system and the corresponding artificial compressible system is considered. Both systems have the same sets of stationary solutions and the incompressible system is obtained from the artificial compressible one in the zero limit of the artificial Mach number ? which is a singular limit. It is proved that if a stationary solution of the incompressible system is asymptotically stable and the velocity field of the stationary solution satisfies an energy-type stability criterion by variational method with admissible functions being only potential flow parts of velocity fields, then it is also stable as a solution of the artificial compressible one for sufficiently small ?. The result is applied to the Taylor problem.     

On the better behaved version of the GKZ hypergeometric system

We consider a version of the generalized hypergeometric system introduced by Gelfand, Kapranov and Zelevinsky (GKZ) suited for the case when the underlying lattice is replaced by a finitely generated abelian group. In contrast to the usual GKZ hypergeometric system, the rank of the better behaved GKZ hypergeometric system is always the expected one. We give largely self-contained proofs of many properties of this system. The discussion is intimately related to the study of the variations of Hodge structures of hypersurfaces in algebraic tori.     

一个供应链系统的可靠性模型的适定性分析

供应链系统是一个复杂的动态系统,许多影响因素的存在,使得供应链系统具有强烈的随机性,从而直接影响供应链系统的可靠性,我们通过分析供应链系统的状态之间的转移关系,引入增补变量法,用偏微分方程组建立了供应链系统的可靠性模型,并对该模型系统解的存在唯一性进行了讨论和证明.     

On the chaotic behavior of the non-ideal vibrating systems

The paper discusses the chaotic behavior of a vibrating structure coupled to an energy source. The structural response of this system may act like energy sink under certain conditions so that a part of the energy supplied by the source is spend to vibrate the structure rather than increasing the drive speed, according to the Sommerfeld effect [1]. The energy source is influenced by the response of the system and consequently, the system exhibits jumps at critical values of the energy source. The system mimics a disappearance of the energy in the resonance regions which can affect the stability of the system, sending it to chaos [2-4]. (© 2015 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

On the dimension of the subspace of Liouvillian solutions of a Fuchsian system

The effect of small constantly acting random perturbations of white noise type on a dynamical system with locally stable fixed point is studied. The perturbed system is considered in the form of Itô stochastic differential equations, and it is assumed that the perturbation does not vanish at a fixed point. In this case, the trajectories of the stochastic system issuing from points near the stable fixed point exit from the neighborhood of equilibrium with probability 1. Classes of perturbations such that the equilibrium of a deterministic system is stable in probability on an asymptotically large time interval are described.     

我国社会诚信建设的博弈分析

社会诚信体系是建设社会主义市场经济的必要条件也是构建社会主义和谐社会的根本要求.社会诚信体系由个人诚信体系、企业诚信体系和政府诚信体系构成,利用博弈分析方法,分析个人诚信、企业诚信和政府诚信间的博弈问题,根据博弈结果提出我国社会诚信建设的相应对策.