推广数学命题的几种思考方法

推广数学命题 ,是一项综合性很强 ,难度较大的创造性工作 .它需要付出类比、联想、猜测、归纳等富有探讨性、技巧性的劳动 .其关键在于抓住原命题的本质特征 ,从中挖掘和发现隐晦的信息 ,善于从一类对象或情境转换成另一类与之相关联的对象或情境 ,通过尝试实验、摸索规律、提出假设和新的构想 ,从而产生新的更广义、更一般、更深刻的数学命题 .本文仅就自己的体会 ,谈谈推广数学命题的几种思考方法 .1　由数字型向字母型推广不少数学命题是由数字与运算符号构成 ,在挖掘命题中的隐含条件 ,找出数量间的关系和规律之后 ,用字母代替这些数字 …     

Gauss整环上不可分解的Hermite型

本文给出了构作虚二次域Ｑ（－ｍ）的整数环上不可分解的正定整Ｈｅｒ ｍｉｔｅ型的方法．     

二阶差分方程为极限圆型的判定

本文找到了方程属极限圆的用系数表示的充要条件 ,并给出了比较容易验证的充分条件 ,改进了已有的结果 .     

基于微分博弈的区域经济合作行为分析

针对区域经济合作行为问题,构建微分博弈模型,将区域合作情况分为弱弱型拮抗博弈、强弱型主从博弈、强强型协同博弈三类,并考察其最优努力策略、最优收益与联盟总体收益变化.研究结果显示:①地区间经济合作努力程度随着合作成本系数、产出漏损系数的上升而下降,随着边际努力产出系数、边际努力收益系数、产出影响系数的上升而上升;②"激励因子"作为一种激励机制,可提高地区间合作努力度、最优收益及联盟整体收益;③三种类型中,强强性协同博弈最优策略及整体最优收益均严格优于其他两种情形.但这种协同合作需要确定联盟整体收益分配系数的取值范围.     

一类交替型脉冲微分系统的解

主要讨论一类超前型与滞后型交替的脉冲微分系统.首先给出具常系数的脉冲微分系统解存在的充分条件以及解唯一的表达形式;对于变系数的微分系统也作了相应的讨论.     

Herz型Hardy空间上乘子算子的Jackson型和 Bernstein型不等式

在Herz型Hardy
空间上对乘子算子建立了Jackson型和Bernstein型不等式.
这些不等式可以应用于Fourier分析中的一些重要算子,
如大于临界阶的Bochner-Riesz算子,
广义Bochner-Riesz平均和广义Abel-Poission算子.     

p-凸函数与几类不等式

研究p-凸函数的一些新的性质及判别准则,并建立p-凸函数的Jensen型、Rado型及Hadamard型不等式.     

某类系统广义指数型E稳定性(英文)

研究某类系统广义指数型 E稳定性 ,推广了文献 [1 ],[2 ]的某些结果 .     

中立双曲型时滞偏微分方程解振动的充要条件

本文讨论一类线性中立双曲型时滞微分方程解的振动性质，获得了其一切解振动的充要条件．     

二型模糊系统研究与应用

简单介绍模糊系统和二型模糊系统发展，概述二型模糊系统的应用范围、条件和组成，比较详细的介绍了二型模糊集合基础理论，按照二型模糊系统的组成模块描述模糊器，规则库，推理引擎，降型器，精确器的表达式和推导过程，最后还总结了二型模糊系统现阶段存在的不足和可能发展方向。     

Fekete and Szegö problem for a subclass of quasi-convex mappings in several complex variables

Let K be the familiar class of normalized convex functions in the unit disk. Keogh and Merkes proved the well-known result that max?f∈K|a3−λa22|≤max?{1/3,|λ−1|},λ∈?, and the estimate is sharp for each λ. We investigate the corresponding problem for a subclass of quasi-convex mappings of type B defined on the unit ball in a complex Banach space or on the unit polydisk in ?n. The proofs of these results use some restrictive assumptions, which in the case of one complex variable are automatically satisfied.     

Heisenberg型群上的不存在性定理

本文建立了Heisenberg型群G上的一些积分恒等式 ,得到了G上半线性次Laplace方程非负解的一个不存在性定理     

Decay estimates for the wave equation of p‐Laplacian type with dissipation of m‐Laplacian type

In this paper, we study decay properties of solutions to the wave equation of p‐Laplacian type with a weak dissipation of m‐Laplacian type. Copyright © 2006 John Wiley & Sons, Ltd.     

Global and local behavior of zeros of nonpositive type

A generalized Nevanlinna function Q(z)$Q(z)$ with one negative square has precisely one generalized zero of nonpositive type in the closed extended upper halfplane. The fractional linear transformation defined by _Qτ(z)=(Q(z)−τ)/(1+τQ(z))$Q_{\tau }(z)=(Q(z)-\tau )/(1+\tau Q(z))$, τ∈R∪{∞}$\tau \in \mathbb{R}\cup \{\infty \}$, is a generalized Nevanlinna function with one negative square. Its generalized zero of nonpositive type α(τ)$\alpha (\tau )$ as a function of τ is being studied. In particular, it is shown that it is continuous and its behavior in the points where the function extends through the real line is investigated.     

Extension of the Leray-Schauder degree for abstract Hammerstein type mappings

We introduce a new extension of the classical Leray-Schauder topological degree in a real separable reflexive Banach space. The new class of mappings for which the degree will be constructed is obtained essentially by replacing the compact perturbation by a composition of mappings of monotone type. It turns out that the class contains the Leray-Schauder type maps as a proper subclass. The new class is not convex thus preventing the free application of affine homotopies. However, there exists a large class of admissible homotopies including subclass of affine ones so that the degree can be effectively used. We shall construct the degree and prove that it is unique. We shall generalize the Borsuk theorem of the degree for odd mappings and show that the ‘principle of omitted rays’ remains valid. To illuminate the use of the new degree we shall briefly consider the solvability of abstract Hammerstein type equations and variational inequalities.     

On a Maximum Principle and Uniqueness Theorems for a System of First Order Equations of Mixed Type

A maximum principle for a system of first order equations of mixed type is established. The uniqueness theorems of solutions t.o the generalized Tricomi type problem and to the Frankl's problem are proved by the method of auxiliary functions.     

The Sharp Estimates of all Homogeneous Expansions for a Class of Quasi-convex Mappings on the Unit Polydisk in Cn

In this paper,the sharp estimates of all homogeneous expansions for f are established,where f(z)=(f1(z),f2(z),…,fn(z))'is a k-fold symmetric quasi-convex mapping defined on the unit polydisk in Cn and theorem for a k-fold symmetric quasi-convex mapping are established as well.These results show that in the case of quasi-convex mappings,Bieberbach conjecture in several complex variables is partly proved,and many known results are generalized.     

Quasi-convex Mappings on the Unit Polydisk in $\mathbb{C}^{n}$

In this paper, the sharp estimates of all homogeneous expansions for f are established, where f(z) = (f ₁(z), f ₂(z), …, f _n (z))′ is a k-fold symmetric quasi-convex mapping defined on the unit polydisk in ℂ ⁿ and