局部凸空间的正规性

本文建立局部凸拓扑向量空间的正规性、完全正规性和单调正规性的等价条件．作为这些结果的应用，研究了函数空间的单调正规性和可度量性．     

序列位差空间的拓扑性质

利用拓扑学的一般理论,研究了序列位差空间的连通性,给出了序列位差空间为可分空间、紧致空间的充分必要条件.     

由给定的子空间构造新的子空间

本给出并证明了若干个子空间的并以及两个子空间的基构成子空间的充要条件，从而本质地揭示了除子空间的交与和是构造新的予空间的方法外，集合的其它运算不能构造新的子空间，最后分析了子空间直和的两种不同定义的优缺点，指出了张禾瑞教材中子空间直和定义推广时应注意的一个问题。     

核局部凸空间的一个新特征

Ａ．Ｐｉｅｔｓｃｈ＾［１］在讨论核局部凸空间时给出了两类矢值序列空间ｌ１［Ｘ］和ｌ１｛Ｘ｝。本文建立了矢值序列空间ｌ１［Ｘ］及ｌ１｛Ｘ｝和连续线性算子空间Ｌ（ｃ０，Ｘ）及绝对可和算子空间ＡＳ（ｃ０，Ｘ）之间的拓扑同胚关系。通过ｃ０上的矢值算子类Ｌ（ｃ０，Ｘ）和ＡＳ（ｃ０，Ｘ）及其上的拓扑等价关系，对局部凸空间Ｘ是核空间给出了一个新的特征刻划。     

Radon空间的非标准表示

证明了在扩大的非标准模型中S-空间可完全表示Radon空间并讨论了S-空间的若干性质.还给出一个有限Borel测度空间为Radon空间的充要条件.最后证明了Radon空间的一个＊-有限表示定理.     

关于GB型空间的若干结果

本文对GB型空间进行了若干讨论,得到了一些结果。 设X为Banach空间,X为X的共轭空间,B(X,X)为X到X的所有有界线性算子组成的空间。如果X中的弱收敛序列为弱收敛序列,则称X为GB型空间。Grothendieck.A于1953年证明了l~∞是GB型空间。显然自反空间是GB型空间。     

序列型空间的一个特征刻划

本文证明了拓扑向量空间E是序列型空间的一个特征为：（1）E的每个序列开集都是开集；（2）取值于E中的任意无穷矩阵（xij）i,j,若对每个j均有limxij=xj，并且limxj=x,则一定存在严格递增序列（ik）和（jk）使得limxikjk=x.作为应用证明了序列型A-空间必是k-空间．     

关于Lasnev空间的超空间

讨论了Ｌａｓｎｅｖ空间的超空间的某些性质．文中构造一反例，证明存在可数Ｌａｓｎｅｖ空间，其紧子集超空间不是层型空间．并指出文［６］中关于上述结果的证明中有一关键性失误，故［６］中的反例尚不能说明上述结论成立．本文还对具有σ－ＣＦ拟基的ｋ′空间给出一个刻画定理     

三种类型汽车的能耗和使用成本的建模研究

本文对电动,传统,混合动力三种类型汽车的能耗和使用成本问题进行了建模、求解及分析．首先定义了电动汽车的能量利用率ηE。根据能量守恒将所有电量转换成汽油消耗量,而传统车型则直接反映到汽油的消耗上,混合动力汽车则综合电动汽车和传统汽车的能耗模型,从而统一能耗水平评价标准．这样,我们就得到了三种不同类型车的能耗模型再进行模型求解以此来分析比较三种类型车哪一种节能效果好．对电动汽车来说,使用成本主要包括驾驶维护成本、报废处理成本,而对传统汽车来说,使用成本主要包括驾驶维护成本、报废处理成本、环境成本和其他成本,混合动力汽车则结合二者使用成本．因此,根据不同车型使用成本类型建立相应的数学模型,按照建立的公式,可以得到电动汽车的使用成本LCC1、传统汽车的使用成本LCC2和混合动力汽车的使用成本LCC3,从而进行模型求解．     

In Defense of Logical Universalism: Taking Issue with Jean van Heijenoort

Van Heijenoort??s main contribution to history and philosophy of modern logic was his distinction between two basic views of logic, first, the absolutist, or universalist, view of the founding fathers, Frege, Peano, and Russell, which dominated the first, classical period of history of modern logic, and, second, the relativist, or model-theoretic, view, inherited from Boole, Schr?der, and L?wenheim, which has dominated the second, contemporary period of that history. In my paper, I present the man Jean van Heijenoort (Sect. 1); then I describe his way of arguing for the second view (Sect. 2); and finally I come down in favor of the first view (Sect. 3). There, I specify the version of universalism for which I am prepared to argue (Sect. 3, introduction). Choosing ZFC to play the part of universal, logical (in a nowadays forgotten sense) system, I show, through an example, how the usual model theory can be naturally given its proper place, from the universalist point of view, in the logical framework of ZFC; I outline another, not rival but complementary, semantics for admissible extensions of ZFC in the very same logical framework; I propose a way to get universalism out of the predicaments in which universalists themselves believed it to be (Sect. 3.1). Thus, if universalists of the classical period did not, in fact, construct these semantics, it was not that their universalism forbade them, in principle, to do so. The historical defeat of universalism was not technical in character. Neither was it philosophical. Indeed, it was hardly more than the victory of technicism over the very possibility of a philosophical dispute (Sect. 3.2).     

The three-dimensional motion of optimalpyramidal bodies

The three-dimensional inertial motion of pyramidal bodies, optimal in their depth of penetration, formed from parts of planes tangential to a circular cone and having a base in the form of a rhombus or a star, consisting of four symmetrical cycles, is investigated using the numerical solution of the Cauchy problem of the complete system of equations of motion of a body. It is assumed that the force action of the medium on the body can be described within the framework of a local model, when the pressure on the body surface can be represented by a two-term formula, quadratic in the velocity, and the friction is constant. It is shown that the stability criterion, obtained previously for the rectilinear motion of a pyramidal body on the assumption that the perturbed motion of the body is planar, also enables one, in the case of an arbitrary specification of the small perturbations of the parameters leading to the tree-dimensional motion of the body, to determine the nature of development of these perturbations. It is shown that if the rectilinear motion of the body is stable, its perturbed three-dimensional motion can be represented in the form of the superposition of plane motions, and when investigating each of them, the analytical solution of the plane problem obtained earlier can be used.     

一個多元函數的內插公式

本文介绍一个新型多元函数结构.它在一定条件下: 1)可根据一定的已知数值决定函数的其他近似值, 2)可作为构成经验公式的骨架.     

Impressions of the early days of programming

The paper describes the author's experience of working with the Edsac, Cambridge, England, in 1951 and 1953. The author's background in astronomical calculations using hand methods and his plans for spending a year in Cambridge are first described. This is followed by impressions of the Mathematical Laboratory, Cambridge, its staff, the external characteristics of the Edsac, the library of subroutines, documentation for programmers, machine language, paper tape preparation equipment, and organization of the use of the Edsac. The second major part of the paper describes the steps leading to an Edsac-program for calculating the motion of a minor planet by step-by-step integration of the equations of motion, with special attention to the preparation and check of large amounts of input to the program.     

基于储量结构变化的油田开发指标预测与优化数学模型研究

大型油田开发过程中,随着不同类型新储量的不断投入,地质储量结构发生变化,表征油田整体开发技术与经济效果的关键性指标,如产量、可采储量、采收率、储采比、开发成本与操作成本等等也随之改变,其变化规律可用一套数学模型来描述。在开发指标预测基础上,运用多属性决策方法如TOPSIS,可以实现新投产区块组合方案的优选。应用实例表明,本文方法实用、操作性强,可以为油区开发决策提供重要方法与手段。     

中国能源强度与经济结构变化特征研究

中国经济持续增长伴随着能源强度下降的特征引起部分学者对中国经济增长和能源消费数据真实性的怀疑,因此,对中国能源强度变化特征进行研究具有重要的现实意义。迄今为止,对中国经济结构变动如何影响能源强度变化仍然缺少定量研究。本文分析了中国能源强度的变化趋势,说明其前后趋势基本上是一致、合理的。以此为基础,将能源强度变化分解为结构份额和效率份额,提出了结构份额和效率份额的计算方法,对我国能源强度变化中的结构份额和效率份额进行了定量分析,结构表明:1998-2000年间,我国能源强度下降的主要动力来自于各产业能源利用效率的提高,其中工业能源强度下降是总体能源强度下降的主要原因。     

细观等效理论预测再生混凝土宏观力学参数北大核心CSCD

预测分析再生混凝土各组分对再生混凝土宏观力学参数的影响是开展再生混凝土基本力学性能的一种方式.为了分析再生混凝土各组分对再生混凝土宏观力学参数的影响,根据再生混凝土的细观结构组成,建立了细观等效模型,利用扭转变形、细观夹杂理论、弹性等效思想和M-T模型方法,推导了由原生骨料、老界面层、老水泥砂浆、新界面层和新水泥砂浆等组成的再生混凝土的宏观力学参数预测模型.预测结果表明,随着再生骨料的取代率增加,水泥砂浆的含量不断增加,再生混凝土孔隙率也随之增大,导致再生混凝土的Poisson比随之增大,弹性模量、剪切模量和体积模量不断降低.模型的预测结果较好地反映了再生混凝土宏观力学参数随再生骨料取代率的增加不断变化的这一趋势,也为再生混凝土宏观力学参数的预测提供了一条简单实用的新方法,有利于再生混凝土基本力学性能的研究分析.     

公平偏好下基于批发价契约的供应链 协调研究

文中基于Nash讨价还价博弈思想建立公平偏好框架,构建公平偏好效用体系,以此为基础对采用批发价契约的报童模型展开行为研究,采用数理模型和数值分析方法分析了零售商和供应商的公平偏好行为对零售商和供应链系统最优订货量的影响,即零售商和供应商同时关注公平时,零售商和供应链系统的最优订货量趋于保守;并发现零售商和供应链系统的最优订货量随零售商的公平偏好程度增加而递减,但随着供应商公平偏好程度增加而递增,且供应链系统最优订货量变化趋势比零售商明显．然后,在此基础上分析比较得到,无论供应商和零售商是否偏好公平,批发价契约都不能实现供应链协调．最后,对批发价、零售价、供应商生产成本、零售商缺货成本和供应商缺货成本进行敏感度分析．     

On lattices of varieties of restriction semigroups

The left restriction semigroups have arisen in a number of contexts, one being as the abstract characterization of semigroups of partial maps, another as the ‘weakly left E-ample’ semigroups of the ‘York school’, and, more recently as a variety of unary semigroups defined by a set of simple identities. We initiate a study of the lattice of varieties of such semigroups and, in parallel, of their two-sided versions, the restriction semigroups. Although at the very bottom of the respective lattices the behaviour is akin to that of varieties of inverse semigroups, more interesting features are soon found in the minimal varieties that do not consist of semilattices of monoids, associated with certain ‘forbidden’ semigroups. There are two such in the one-sided case, three in the two-sided case. Also of interest in the one-sided case are the varieties consisting of unions of monoids, far indeed from any analogue for inverse semigroups. In a sequel, the author will show, in the two-sided case, that some rather surprising behavior is observed at the next ‘level’ of the lattice of varieties.