体上代数矩阵的素有理标准形与特征值

本文应用最小中心多项式给出了体上代数矩阵的素有理标准形与初等因子组的构造，由此得到体上代数矩阵相似的充要条件以及相似于一个对角矩阵的充要条件．本文还讨论了体上矩阵的左、右特征值的构造与性质．     

关于体上分块矩阵的群逆

本文利用分块矩阵方法．研究了体上两个矩阵乘积的群逆的存在性及表示形式，给出了体上两个矩阵乘积群逆存在的充分必要条件和表示形式．并且在一定条件下．给出了体上分块矩阵的群逆存在性及表示形式．     

四元数体上矩阵的广义对角化

引入了复四元数环和四元数体上矩阵可 对角化的概念,研究了复四元数环上矩阵的性质,给出了四元数体上矩阵可 对角化的充分必要条件和求矩阵 对角化的方法。     

体上线性映射的子空间的维数及其应用

本文给出体上左向量空间的线性映射的某些子空间的维数恒等式,并讨论了它在体上矩阵秩的理论上的应用,其中一个有趣的应用是,由体上矩阵秩的恒等式来刻划体上某些矩阵的特征性质。 以下设Ω是一个体。对Ω上左向量空间V映入Ω上左向量空间V′的线性映射σ:V V~σ,记σ的核空间为:     

体上矩阵的广义逆

关于矩阵广义逆的研究,自 R.Penrose 的论文发表以来,目前巳进行得相当深入,域上,以至某些交换环上矩阵的广义逆也已相继进行.但是,由于一般体的非交换性限制,任意体上矩阵的广义逆尚未见过具体的论述。在这篇文章中,我们将对具有一个对合反自同构的体,阐述其上矩阵的广义逆,将域上矩阵的 Moore-Penrose 逆存在的一个充要条件作了相应的推广,并给出了体上矩阵的 Moore-Penrose 逆、(1,…,i)一逆、(2)-逆的显式;最后,我们利用[7]中的一个结果,得到了四元数矩阵的(3)-逆、(4)-逆的显式。     

体上特征矩阵的简化形式与法式存在定理

谢邦杰在文献[2]—[5]中,研究了体上特征矩阵的简化形式与法式。本文在文献[1]的基础上,采用不同于[2]的方法,定义体上特征矩阵的另一种简化形式。对于我们所定义的简化形式,得到体上特征矩阵具有绝对唯一的简化形式,即法式存在的充分必要条件是矩阵满足中心化条件,从而使更广的一类特征矩阵存在法式。此外,我们还将[5]中体上矩阵的Caylcy-Hamilton定理再一次推广。     

四元数矩阵的惯性定理与稳定性

本文给出了四元数矩阵惯性的定义,讨论了四元数体上Lyapunov矩阵方程的唯一解,推广了一般惯性定理、Lyapunov稳定性定理、Carlson-Schneider定理、Stein稳定性定理等一些重要的结果到四元数矩阵,同时得出了四元数体上稳定矩阵的一些判别条件.     

EP矩阵的Hartwig-Spindelbck 问题与ρ·M-P 逆的倒换顺序律

本文证明了体上矩阵的ρ·M-P 逆的倒换顺序律的十种刻划,给出了四元数矩阵 M-P 逆的倒换顺序律的一种新刻划,并在四元数体上解决了文献[1]中关于 EP 矩阵的两个未解问题.     

EP矩阵的Hartwig-Spindelbck 问题与ρ·M-P 逆的倒换顺序律

本文证明了体上矩阵的ρ·M-P 逆的倒换顺序律的十种刻划,给出了四元数矩阵 M-P 逆的倒换顺序律的一种新刻划,并在四元数体上解决了文献[1]中关于 EP 矩阵的两个未解问题.     

四元数体Q上的双曲矩阵空间中的若干积分

该文计算了四元数体上的矩阵空间中的一些典型积分.由这些积分,可以得到相应的四元数体上的双曲矩阵空间的体积,这对于相关核函数的计算是有帮助的.     

城市老旧居住小区交通环境评价指标与评价方法

定量的评判城市老旧居住小区整体交通环境质量并进而科学有效的提出老旧小区交通环境更新与改善措施,对城市老旧居住小区交通环境进行了调查,明确了老旧居住小区存在的突出交通问题,并提出了城市老旧居住小区交通环境评价的指标体系,包括行人跨路出行指数、无人行道路段长度占比、停车泊位供需比、路内非法停车占比、平均停车步行距离、泊位数量户数比、人均步行空间、无障碍通道、盲道设置比例、非机动车泊位供需比、地面停放车辆数小区面积比、外部穿行交通周转量小区面积比等。并给出了具体指标的计算方法与获得办法。以长沙市四个典型老旧居住小区为例,对评价方法进行了论证,并得到城市老旧居住小区存在的一般问题,包括人车混杂、人车交织现象严重,停车泊位短缺、车辆乱停乱放,交通设施、特别是弱势群体交通设施缺乏。给出的评价指标、评价方法与结论可为城市老旧小区改造更新,特别是其中很重要的交通环境更新提供决策依据。     

The generalized hierarchical product of graphs

A generalization of both the hierarchical product and the Cartesian product of graphs is introduced and some of its properties are studied. We call it the generalized hierarchical product. In fact, the obtained graphs turn out to be subgraphs of the Cartesian product of the corresponding factors. Thus, some well-known properties of this product, such as a good connectivity, reduced mean distance, radius and diameter, simple routing algorithms and some optimal communication protocols, are inherited by the generalized hierarchical product. Besides some of these properties, in this paper we study the spectrum, the existence of Hamiltonian cycles, the chromatic number and index, and the connectivity of the generalized hierarchical product.     

Analysis of the Stress State of the Surface Layer of a Polymeric Mass upon Filling of Bulky Compression Molds

The stress state of the surface layer of a polymeric mass during filling of bulky compression molds is analyzed. It is shown that, at particular rheological characteristics of the mass, temperature, and filling rates, cracking of the surface layer occurs, which leads to defects in the finished products. A physical analysis of this process makes it possible to conclude that the cracks arise due to the normal stresses operating in the front region of the moving polymeric mass. It is found that, under certain flow conditions, areas with a pressure lower than the atmospheric one appear on the surface of the polymer. If the tensile stresses arising in these local regions are higher than the tensile strength of the mass, the continuity of the composition is broken in the direction determined by the greatest rate of the normal deformation. To confirm the reliability of the crack-formation mechanism proposed, the distribution of the pressure and normal stresses over the free surface is calculated based on a numerical method. These calculations show that, by comparing the stress level achieved in the front region with the tensile-strength characteristics of the polymeric composition, it is possible to predict, with a sufficient accuracy, the possibility of crack formation in the surface layer of such a mass under given flow conditions and thus to solve the question on flawless manufacturing of products.     

Utilization and maintenance in a model with scrapping

We consider a productive asset, called equipment or capital good, and we examine the properties of, as well as the interactions between, the operating policies, which are determined by its optimal utilization and maintenance, and the capital policy of scrapping, which defines the optimal time when the productive asset is retired from its current use. Starting with an abstract model and using the approach of optimal control, initially we characterize the various types of equipment by assigning to them a single total profit index, which indicates how the above policies affect the flow of operating revenues plus capital gains or losses. This index is a function of market-determined prices. So using it we then investigate how the operating and capital policies are influenced by the rate of discount, the price of new equipment, and the rise or fall of the price of new equipment relative to the value of its output. Among other interesting results, we find that the effects of these prices on the nature and interactions of optimal policies depend crucially on whether the equipment is of the usual profit making type, where output is the main source of revenue, or of the antique type, where the main source of revenue is capital gains.     

Rolling-ball method for estimating the boundary of the support of a point-process intensity

We suggest a generalisation of the convex-hull method, or ‘DEA’ approach, for estimating the boundary or frontier of the support of a point cloud. Figuratively, our method involves rolling a ball around the cloud, and using the equilibrium positions of the ball to define an estimator of the envelope of the point cloud. Constructively, we use these ideas to remove lines from a triangulation of the points, and thereby compute a generalised form of a convex hull. The radius of the ball acts as a smoothing parameter, with the convex-hull estimator being obtained by taking the radius to be infinite. Unlike the convex-hull approach, however, our method applies to quite general frontiers, which may be neither convex nor concave. It brings to these contexts the attractive features of the convex hull: simplicity of concept, rotation-invariance, and ready extension to higher dimensions. It admits bias corrections, which we describe and illustrate through implementation.     

Quality rating of a metal matrix-diamondcomposite from its thermal conductivity and electric resistance

The efficiency of hot-pressed diamond-containing composite materials (DCM) for various tool applications is greatly affected by microdefects, namely, the residual porosity of the metal matrix, damaged diamond grains, and imperfect diamond-matrix interfaces. An instrumental evaluation of these microdefects, predetermining the quality of a tool equipped with DCM, is rather difficult due to the small size, the nonstandard shape, and the strong heterogeneity of specimens. Proposed here is an alternative, nondestructive technique of DCM quality rating, which includes the measurement of electric resistance and thermal conductivity of diamond-containing composites and processing the obtained data by the methods of composite mechanics. It exploits the fact that diamond, being a dielectric, possesses an extremely high thermal conductivity, which allows estimating the residual porosity of a sintered metal matrix from the ratio of specific electric resistances, one being measured and another predicted by a theory. These data, in turn, are utilized to predict the thermal conductivity ofDCMwith an imperfect matrix. Matching with experiments, after solving the inverse problem gives the thermal resistance of diamond-matrix interface, which, within the frame work of the given model, simulates the damage of both the diamond grains and their bonds with the matrix. Thus, the numerical rating of quality is given in terms of two dimensionless parameters. The first one, 0 < K < 1, reflects the quality of the sintered metal matrix, whereas the second one, 0 < R <1, is an aggregate measure of the integrity of diamond grains and the perfection degree of composite interfaces. The quite satisfactory agreement observed between the theory and experiment confirms the efficiency of the technique and the reliability of the data obtained. Russian translation published in Mekhanika Kompozitnykh Materialov, Vol. 42, No. 3, pp. 361–374, May–June, 2006.     

邻避冲突中的利益相关者演化博弈分析——以污染类邻避设施为例

工业化、城市化进程的加快在推进社会经济发展的同时,也催生了公民权利意识和环保意识的觉醒。在整体利益与局部利益、经济利益与环境利益等一系列矛盾交织的宏观背景下,继劳资纠纷、征地拆迁之后,污染类邻避设施成为诱发群体性事件的关键因子。因此,探究政府、邻避设施营建企业与周边民众三方间利益关系,理清相关主体的利益诉求对于邻避冲突的预防和处置具有重要实践意义。本文基于利益相关者理论,探究污染类邻避设施相关利益主体在冲突中所扮演的角色和发挥的作用,进而从博弈论视角出发构建政府、邻避设施营建企业和周边民众之间的三方演化博弈模型。在此基础上,通过对政府、营建企业和周边民众的稳定演化博弈策略选择分析,得出推动博弈三方向演化稳定策略点收敛的条件。利用Matlab对三方演化模型模拟仿真,结果表明政府采取不监管策略、营建企业采取合作策略及周边民众采取不抵抗策略是邻避冲突中三方利益相关者演化博弈的稳定策略点;高强度的政府奖励力度有利于促进营建企业采取合作策略,而抑制周边民众抵抗行为策略的选择;营建企业的经济补偿对于降低民众抵抗力度具有临界点,只有高额的经济补偿才会激励民众选择不抵抗的行为策略;而周边民众的抵抗力度对营建企业的策略选择无显著影响。本文研究结果对邻避冲突中相关利益主体起到一定启示作用:第一,政府作为邻避设施建设的监管者,应注重把握监管力度,完善公众参与渠道,降低个体风险感知;第二,营建企业作为邻避设施建设的实施者,应积极采用环保技术,构建科学利益补偿机制;第三,周边民众对于邻避设施的“落地”发挥关键作用,应加强自身公共理性,合理评估邻避风险,自觉维护社会公共利益。     

乡村绿色生态旅游适宜等级VIKOR评估方法

针对乡村绿色生态旅游特征,并考虑旅游者个体感受与群体效益,本文从乡村绿色生态旅游开发与适宜评级概念出发,提出乡村绿色生态旅游适宜等级VIKOR评估模型与方法。首先,从等级评估的概念与内涵出发,刻画乡村绿色生态旅游适宜评级问题,避免混淆旅游适宜评级和排序两个本质不同的问题。然后,构建乡村绿色生态旅游适宜等级评估指标及隶属函数,提出评估指标的熵权确定方法。其次,提出乡村绿色生态旅游适宜等级VIKOR评估模型与二元语义等级评估方法。最后,通过案例研究和比较分析,说明本文所提模型与方法的合理性、可行性与实用性。     

Moment information for probability distributions,without solving the moment problem,II: Main-mass,tails and shape approximation

How much information does a small number of moments carry about the unknown distribution function? Is it possible to explicitly obtain from these moments some useful information, e.g., about the support, the modality, the general shape, or the tails of a distribution, without going into a detailed numerical solution of the moment problem? In this, previous and subsequent papers, clear and easy to implement answers will be given to some questions of this type. First, the question of how to distinguish between the main-mass interval and the tail regions, in the case we know only a number of moments of the target distribution function, will be addressed. The answer to this question is based on a version of the Chebyshev–Stieltjes–Markov inequality, which provides us with upper and lower, moment-based, bounds for the target distribution. Then, exploiting existing asymptotic results in the main-mass region, an explicit, moment-based approximation of the target probability density function is provided. Although the latter cannot be considered, in general, as a satisfactory solution, it can always serve as an initial approximation in any iterative scheme for the numerical solution of the moment problem. Numerical results illustrating all the theoretical statements are also presented.     

Calculation of damage and of force relaxation in amorpho-crystalline polymers

The dynamics of damage and of the relaxing force in amorpho-crystalline polymers under constant strain are calculated using the formulas for the probability of rupture of a deformed polymer molecule and a model representation of amorphous interlayers. The main parameters of the model are the maximum and minimum possible deformations of molecular chains, the energy of rupture activation, the function of the chain length distribution, the temperature, the macroscopic strain, and the relative dimensions of the amorphous interlayer. The conformity of the theoretical model and the association of the relaxation spectrum with the internal molecular and structural characteristics of the material are established.Zhambyl Technical Institute of Light and Food Industry, Taraz, Kazakhstan. Translated from Mekhanika Kompozitnykh Materialov, Vol. 35, No. 4, pp. 499–508, July–August, 1999.