应用数学

And many kinds of ways that any summable functions expande to FOURIER progression in symmetrical and dissymmetrical area that was defined , and

以及定义在对称和非对称区域上的任意可积函数展开成FOURIER级数的各种方法，并以典型算例说明其在数学中的应用。

Actuarial Studies involves the study of mathematics, statistics, accounting, economics, finance and their application to financial management in life insurance, general insurance, health insurance, superannuation, funds management and banking and finance.

精算研究涉及的研究数学，统计，会计，经济，金融和他们的应用财务管理的人寿保险，一般保险，健康保险，养老金，基金管理和银行业和金融业。

As a kind of method based on symbolic logic, Formal method has gained more and more attention because of its preciseness. It has been applied broadly in systems in which the security and reliability are the key issues. For example, protocol security analysis, operating system security model, software development.

作为一种以数学逻辑为基础的方法，形式化方法以其严密性越来越受到众多领域的重视，尤其是在安全性和可靠性作为关键问题的系统，如协议安全性分析、操作系统安全模型、软件开发等方面得到了较为广泛的应用。

The basic theories of mathematical morphology for binary image are stated, and the most simple structure elements of morphologic transformation for binary images are proposed and proved. The geodetic morphologic transformation models are also developed. For the purpose of improving the speed of transformation in computer, the"set symmetric difference"is introduced to adapt each model. Some new morphologic filtering models and quantitative evaluating model of filtering effects in image processing are proposed, under the applied condition. The morphologic thinning methods are studied, and two new morphologic thinning models are developed. On the basis of analyzing the characteristics of mining maps, the image vectorizing tactics and a series of algorithms are proposed, including dynamic adaptive image thresholding using two thresholds, graphic and text separation, noise removal, and multi elements extracting models with mathematical morphology. Accuracy preserving compressed vectorizing model for image vectorization is put forward to generate vector data in multi layer.

论文对二值图象形态学的基础理论进行了较系统的阐述，提出并证明了二值图象处理中形态变换的最简单结构元素，并发展了测地形态变换模型；为了提高形态变换的计算机实现速度，引入了集合论中"对称差"的概念对各形态变换模型进行了改化；针对数学形态学在图象处理中的实际应用，提出了新的形态滤波模型及滤波效果的度量评价模型；研究了形态细化方法，提出了快速形态细化和保形快速形态细化算法；在研究矿图基本特征基础上，提出了人机协同矿图扫描图象矢量化处理策略及一系列扫描图象处理算法模型，包括双阈值动态自适应图象二值化、图文分离、噪声去除、图面多种要素提取形态变换模型等；在图象栅格—矢量转换中，提出了保精度压缩矢量化模型，以生成分层要素矢量数据。

Linear time-invariant state space symmetric system, model reduction, stability, nondegenerate matrix, gradient flow, optimization

湖南第一师范学校；香港理工大学应用数学系长沙410002；铜罗湾；香港重庆师范大学数学与计算机科学系；重庆400047线对称性时不变系统；梯度流；稳定性；优化

The characteristics of postures, crown form, branch appearance and the leaf shape of Syringa oblata were analyzed by practical measurement of individual plant Mathematic method and model were adopted to analyze the sample data and deeply explore the vegetation quantity of Syringa oblata in Harbin. A quantitative method was put forward for vegetation quantity of Syringa oblata distributed in Harbin and the information management system of vegetation quantity of Syringa oblata for Harbin has been established.

本项研究选取了哈尔滨市园林绿化上数量最多、应用最广的木犀科丁香属植物中的紫丁香为研究对象，立足于哈尔滨市的环境特点，采用逐株实测的方法，具体分析紫丁香姿态、冠形、枝形、叶形的特点，采用数学方法和模型研究对紫丁香样本数据进行分析，并深入研究紫丁香"绿量"的内涵，探索出了哈尔滨市紫丁香"绿量"的量化方法，建立了哈尔滨市紫丁香绿量信息管理系统。

Taylor formula has many important applications to mathematical analysis and study.

泰勒公式在分析和研究数学问题方面，有着重要的应用。

Several important nonlinear equations of mathematical physics such as φ4 equation, Klein-Gordon equation, the approximate equations of sine-Gordon equation and sinhGordon equation, Landau-Ginzburg-Higgs equation, Duffing equation, nonlinear telegraph equation are the special cases of the nonlinear wave equation presented in this paper.

几个有重要应用的非线性数学物理方程，如矿方程，Klein-Gordon方程，Sine-Gordon方程，及Sinh-Gordon方程的近似，Landau-Ginzburg-Higgs方程，Duffing方程，非线性电报方程等都可作为该方程的特殊情形得到相应的显式精确解，这里方法也可推广到n+1维空间情形。

The tensor quality of energy density function, which contains coordinate vector, is mathematically proofed.

考虑到模型中能量密度函数含有坐标轴方向向量一项，该文对能量密度函数的张量性进行了严格的数学证明，并将VMIB模型初步应用到脆性材料的单轴受压破坏。

Contains more engineering and physics applications, and more mathematical proofs and theory of partial differential equations, than the first edition.

本书在第1版的基础上增加了偏微分方程在工程和物理学方面的应用，并且提供了更多数学证明和偏微分方程的原理。

We have no common name for a mime of Sophron or Xenarchus and a Socratic Conversation; and we should still be without one even if the imitation in the two instances were in trimeters or elegiacs or some other kind of verse--though it is the way with people to tack on 'poet' to the name of a metre, and talk of elegiac-poets and epic-poets, thinking that they call them poets not by reason of the imitative nature of their work, but indiscriminately by reason of the metre they write in.

索夫农 、森那库斯和苏格拉底式的对话采用的模仿没有一个公共的名称；三音步诗、挽歌体或其他类型的诗的模仿也没有——人们把&诗人&这一名词和格律名称结合到一起，称之为挽歌体诗人或者史诗诗人，他们被称为诗人，似乎只是因为遵守格律写作，而非他们作品的模仿本质。

The relationship between communicative competence and grammar teaching should be that of the ends and the means.

交际能力和语法的关系应该是目标与途径的关系。