具有左R-模结构的类型及其范畴逻辑模型

以范畴逻辑与类型论为基础,引入类型中的交换群理论、环理论以及左R-模理论.证明了类型中的交换群理论在满足分配律的范畴中的模型是交换群对象,环理论的模型是环对象,左R-模理论的模型是左R-模对象,并给出左R-模理论在集合范畴和层范畴等几个具体范畴中的模型.     

关于波莱尔的积分思想研究

波莱尔在测度理论方面的工作奠定了现代测度理论和积分理论发展的基础,对勒贝格的积分工作有重要影响.他利用零测集理论和构造性方法给出了与勒贝格不同的积分理论,这一点目前很少有相关文章和著作进行介绍.本文基于原始文献,利用历史分析和比较的方法对波莱尔的积分理论进行探讨,对理解积分理论的历史发展有重要意义.     

从Riemann积分的定义看推广变量收敛理论的必要性

指出了R iem ann积分定义中积分和的极限已超出了数学分析中变量极限理论的范围,由此看出推广变量极限理论是必要的;简要地介绍了更一般的收敛理论,即网的Moore-Sm ith收敛理论,并通过这种收敛理论给出了定积分的严格定义.     

微极连续统的耦合场理论的再研究(Ⅱ)──微极热压电弹性理论和电磁热弹性理论

W.Nowacki曾建立起系统的微极热压电弹性理论和电磁热弹性理论。戴天民对W.Nowacki建立的微极热压电弹性理论和电磁热弹性理论进行了再研究,对这些理论局限于线性情形的原因和它们的不完整处进行了分析。针对这些理论中所存在的问题,建立起微极热压电弹性理论和电磁热弹性理论的更普遍的能量守恒原理和局部能量方程以及Hamilton原理。从戴天民所建立的更普遍能量守恒原理和Hamilton原理很自然地推导出局部和非局部微极热压电和电磁热弹性理论的完整的运动方程和边界条件以及能率均衡方程。通过引入两个新泛函和全变分还可另外得到位移、微转动、电势和温度边界条件。     

横观各向同性体滑移线场理论

本文系统推演了横观各向同性体滑移线场理论.为解决地球动力学与岩土力学问题,考虑到成层地质体横观各向同性与非均匀温度场作用,本文选择了Gol'denblat-Kopnov破坏准则.并使物性参数随温度变化,建立了复杂介质的强度准则.通过关联流动法则,导出了塑性流动基本方程.应用特征线理论,导出了滑移线斜率公式、应力沿滑移线微分公式和速度沿滑移线微分公式.应用本文理论计算了基础承压问题.本文理论将许多着名的经典理论如Mises理论,Hill理论、Coulomb理论概括为特例.这一综合理论可应用于岩土工程、地质构造、石油、采矿等许多领域.     

形式演绎系统L~*中封闭理论的性质及其应用

本文在模糊命题演算的形式演绎系统L~*中引入了封闭理论的概念,讨论了封闭理论的基本性质,并利用封闭理论给出了形式演绎系统L~*的基于公式集的完备性的证明.首先,在形式演绎系统L~*中引入了封闭理论的概念,给出了理论封闭化扩张的方法;其次,在形式演绎系统L~*中引入了完全封闭理论的概念,证明了满足相关条件的完全封闭理论的存在性;第三,对形式演绎系统L~*中的封闭理论确定的同余关系性质进行了讨论,在公式集中引入了强同余关系的概念,给出了封闭理论和强同余关系相互决定的方法;第四,在形式演绎系统L~*中证明了封闭理论型L~*-Lindenbaum代数是R_0代数,并且封闭理论型L~*-Lindenbaum代数是全序的当且仅当封闭理论是完全的;最后,利用完全封闭理论型L~*-Lindenbaum代数完成了形式系统L~*完备性的证明,并改进了原有的结果.     

浅海声传播的波束位移射线简正波理论 *

适用于一般分层浅海的波束位移射线简正波 (BDRM)理论 ,该理论的特点是将边界对声场的影响通过等效边界反射系数来表示 ,因而容易推广到具有切变弹性的海底 .对浅海声场的理论计算表明 ,BDRM理论具有计算精度较高、计算速度较快等优点 .利用BDRM理论计算了浅海中脉冲波形传播 ,理论与实验数据符合比较好 .     

扭转映射的Aubry－Mather理论及其应用

本文介绍Ａｕｂｒｙ－Ｍａｔｈｅｒ理论近年来的发展情况，文章讨论了该理论与ＫＡＭ理论、保面积映射不动点理论的联系，并简单地介绍了它的一些推广。作为该理论的应用，对平面Ｈａｍｉｌ－ｔｏｎ系统Ｍａｔｈｅｒ集的存在性给出了一些结果．     

变异理论下解题思维模式的探究及应用

变异理论作为一种重要的教育理论,在国内外数学教学中应用广泛.本文尝试用变异理论指导函数构造解题,探究该理论下解题的思维模式并选取一道典型的高考题进行应用.1变异理论变异理论(Variation Theory)是由瑞典哥德堡大学马飞龙教授所创立的一种学习理论.其基本观点是:学习是培养学生对事物看法的一种方式,对事物本质特征的鉴别区分以及对这些特征的同时关注,是建立这种方式的基础,而对本质特征的辨别依靠这个特征在某一维度上的变化.变异理论是对传统迁移理论的超越,该理论强调对于学习内容的共同性和差异性的研究,确定关键属性,通过“审辨”和“变异”促进学生学习.     

犹豫模糊集在决策理论上的研究综述

文章介绍了犹豫模糊集的含义及起源,分别对犹豫模糊集的测度理论、属性权重分配理论、信息融合理论以及决策方法进行了概述,展望了犹豫模糊集决策理论未来的研究方向.     

四元数体上任意矩阵的UR分解

根据体上(半)正定矩阵的理论,探讨四元数体上任意矩阵的UR分解,并通过构造性证明,给出一种有实用价值的分解法.     

Note on roots location of a symmetric polynomial with respect to the imaginary axis

In the theory of the separation of roots of algebraic equations, the well-known Routh–Hurwitz–Fujiwara theorem enables us to separate the complex roots of a polynomial with complex coefficients in terms of the inertia of a related Hermitian matrix. Unfortunately, it fails if the polynomial has a nontrivial factor which is symmetric with respect to the imaginary axis. In this article, we present a method to overcome the fault and formulate the inertia of a scalar polynomial with complex coefficients in terms of the inertia of several Hermitian matrices based on a factorization of a monic symmetric polynomial into products of monic symmetric polynomials with only simple roots in the complex plane and on computing the inertia of each factor by means of a subtle perturbation.     

Analysis of marginal and conditional density functions for separate inference

Summary This paper discusses, with measure-theoretical rigor, some basic aspects of the theory of separate inference. To analyze densities of marginal and conditional submodels, certain operators are introduced. First a general concept of decomposition of a model is proposed, and the corresponding factorization of densities of the model is established. Next it is shown that the property of smoothness of a family of densities is retained in the operation of conditioning, and therefore it yields the differentiability of the conditional expectation of a real-valued statistic in a certain sense. On the basis of this result, two measures of the effectiveness of a submodel in separate inference are investigated. The Institute of Statistical Mathematics     

Factoring matrices into the product of two matrices

Linear algebra of factoring a matrix into the product of two matrices with special properties is developed. This is accomplished in terms of the so-called inverse of a matrix subspace which yields an extended notion for the invertibility of a matrix. The product of two matrix subspaces gives rise to a natural generalization of the concept of matrix subspace. Extensions of these ideas are outlined. Several examples on factoring are presented. AMS subject classification (2000)  15A23, 65F30     

On tridiagonal conjugate-normal matrices

Conjugate-normal matrices play the same role in the theory of unitary congruences as conventional normal matrices do with respect to unitary similarities. Naturally, the properties of both matrix classes are fairly similar up to the distinction between the congruence and similarity. However, in certain respects, conjugate-normal matrices differ substantially from normal ones. Our goal in this paper is to indicate one of such distinctions. It is shown that none of the familiar characterizations of normal matrices having the irreducible tridiagonal form has a natural counterpart in the case of conjugate-normal matrices.     

Some explicit formulas for the polynomial decomposition of the matrix exponential and applications

This paper is devoted to the study of some formulas for polynomial decomposition of the exponential of a square matrix A. More precisely, we suppose that the minimal polynomial M_A(X) of A is known and has degree m. Therefore, e^tA is given in terms of P₀(A),…,P_m−1(A), where the P_j(A) are polynomials in A of degree less than m, and some explicit analytic functions. Examples and applications are given. In particular, the two cases m=5 and m=6 are considered.     

模糊矩阵三种广义逆的判定定理

给出模糊矩阵存在广义{1,3}逆,广义{1,4}逆和Moore-Penrose广义逆的判定定理.     

任意除环上一矩阵方程组的一般解与中心和反中心对称解

Necessary and sufficient conditions are given for the existence of the general solution, the centrosymmetric solution, and the centroskewsymmetric solution to a system of linear matrix equations over an arbitrary skew field. The representations of such the solutions of the system are also derived.     

二阶矩阵的n次方和n次方根

利用Chebyshev多项式讨论了二阶矩阵的n次方的各元素的表达式和其n次方根的存在条件.     

关于正交矩阵特征值与行列式的两个定理

以两种证明思路给出了正交矩阵特征值与行列式关系的定理,并在此基础之上提出了对称正交矩阵行列式的迹定理.