应用数学

By analyzing theory foundation of mathematical morphology in the digital image processing, researching morphology arithmetic of the binary Image, discussing two basic forms for the least structure element: dilation and erosion.

通过分析数学形态学在图像中的理论基础，研究二值图像的形态分析算法，探讨最小结构元素的两种基本形态：膨胀和腐蚀；分析了数学形态学复杂算法的基本原理，把数学形态学的部分并行处理理念引入到家实际应用中。

The linear function applicable scope is broad, when the reservoir turnover water volume and the time, the student leaves the staircase mouth population and the time and the time and the motion communication speech spends the comparison and so on the relational question has the important application;The study linear function, may deepen in the life the linear question understanding and the understanding, is helpful in solves some simple function problem; The linear function some problem solving method has the universality in mathematics, the linear function related theory may use for to solve some other mathematics problem, For instance the dual linear equation group, a Yuan inequality, a Yuan quadratic equation most value question and some complex mathematics question, the light is studies the linear function the theory is insufficient, the key is can utilize actual the linear function goes is our final goal.

一次函数的适用范围广，在蓄水池的进出水量与时间、学生出楼梯口人数与时间与时间和移动通讯的话费比较等的关系问题时均有重要的应用；学习一次函数，可以加深生活中线性问题的认识与理解，有助于解决一些简单的函数问题；一次函数的一些解题方法在数学中具有普遍性，一次函数的有关理论可以用来解决一些其它的数学问题，比如二元一次方程组、一元一次不等式、一元二次方程的最值问题及一些复杂的数学问题，光是学习一次函数的理论是不够的，关键是能把一次函数运用到实际中去才是我们最终的目的。

IGMs are a kind of experimentally new-identified optical mode, standing with apparent potential in design and application. However, the mathematical expression of IGMs under Elliptic Cylindrical coordinates, preventing us from understanding IGMs instinctively, stands a formidable challenge in application. The pure mathematical expressions of IGMs are composed by a great deal of calculation, which also bids us no help in common use. I am, therefore, prompted to build an easier mathematical approach in this study.

Ince- Gaussian modes为在实验中可见的一种崭新型态的光学模态，对於我们在应用和设计上的实现，拥有许多潜力；然而，由於IGMs是在椭圆圆柱座标系下的数学来表示，造成了我们无法直觉的去了解，也成了我们在使用上的一大考验； IGMs的不易亲近，也让我们无从进一步去了解其物理特性，若纯粹以数学出发，又包含了庞大的运算，无法达到普遍的运用，是故我希望能在这篇论文使用简单的数学描述来达成对IGMs较平易近人的理解。

Main creative points of the thesis are as following:1. It is the first time to apply 2-D and 3-D turbulent model of the air-water two phases flow to the study on hydraulic properties of groyne. It makes description of the turbulent flow field to be possible precisely. This offers a more accurate method to determine the water surface in channel improvement.2. Based on the results of experiment and simulation for 3-D turbulent model of air-water two phases flow, a new formula to compute the height of damming is built.3. Based on the 2-D mode and the formula to compute the height of damming, the subdivision method of 2-D computation for water surface at upstream and downstream.

本文的创新工作主要是：首次将三维水气两相流紊流数学模型应用于丁坝水动力学特性研究，使丁坝附近流场和紊动场的精细描述成为可能，为航道整治中水面线确定提供了一个更为准确的方法；(2)基于水槽实验和三维水气两相流紊流数学模型数值模拟结果，建立了新的丁坝前奎水高度计算公式；(3)基于上述奎水高度计算公式和本文二维水面计算数学模型，首次提出了丁坝上下游二维水面分段计算方法。

Using differential calculus knowledge to testify inequality, Calculus of higher mathematics is the core and calculus method of higher mathematics is typical of the whole mathematical method, the method is introduced for calculus ideas to solve the problem of finding an inequation, to make way for obtaining inequalities can be simple, the application of differential mid-value theorem and Taylor formula illustrate some of the inequality proof method.

运用微分学知识证明不等式；微积分是高等数学的核心，微积分思想方法是高等数学乃至整个数学的典型方法，微积分思想方法的引入为解决不等式证明的难题找到了突破，用来解不等式可使解题思路变得简单，文章应用微分中值定理及泰勒公式举例说明了部分不等式的证明方法。

Under these cir-cumstances,we were organ ized to compile"Infinitesimal Calculus and the Basis of Applied Math-ematics",which is a new mathematics teac...

作为高等职业教育公共基础课的数学教材，该书采用模块式、手册型，突出高职教育的应用性，便于自学，达到大学专科水平，注重对学生进行数学素质教育，特别重视培养学生的计算能力和抽象类比能力。并探索了将数学建模和计算机应用引入课堂教学。

This course mainly contents real number muster and function, limit of number sequence, limit of function, continuity, derived number and differential, differential mean value theorem and its application, completeness of real number, integral, series(including positive series and Fourier series), multiple- differential, double integral, integral with parameter, curve integral, camber integral and so on.

理解和掌握《数学分析》的概念、理论和方法，对于学生加深理解数学的基本思想和方法，培养抽象思维能力和逻辑思维能力，提高数学素养具有重要的意义。主要内容包括：实数集和函数，数列极限，函数极限，连续性，导数和微分，微分中值定理及其应用，实数完备性，积分、级数(包括幂级数、Fourier级数)、多元微分学、重积分、含参变量积分、曲线积分、曲面积分等。

This paper extracted and analysed 11Math-Mophological Features such as Area, Perimeter, X-Length, Y-Length, Shape-Parameter, Lobation, Sphericity, Circularity, Roundness, Eccentricity and HoleNumber. Based on 40 species of insects which belonging to 8 Orders, 25 Families. And then ranks the accountability of 11 features each in insect identification while assessing their implication to insect taxonomy on levels of Order, Superfamily, Family and Species. More than those, also describes the kinship among the insects of various categories within the same level from the perspective of mathematical morphology through cluster analyses.

论文对隶属于8个目25科的40种昆虫利用计算机视觉技术进行了自动鉴别研究，从昆虫图像中提取和分析了这些昆虫的面积、周长、横轴长、纵轴长、形状参数、叶状性、球状性、圆形性、似圆度、偏心率、亮斑数等11项数学形态特征，并分别探讨了在目、总科、科及种分类阶元上这些数学特征在昆虫分类中的应用可能性和可靠性，利用聚类分析从数学形态学角度对所涉及到的同阶元昆虫类群的亲缘关系做了描述。

The methods quantitatively analyze the mathematical abstraction and can help revealing the inner construction of mathematical theory with rich connotation by means of the theory of partial order set and graph theory, and so on.

该方法给出了数学抽象的定量分析，主要是应用了偏序集理论和图论等一些数学方法，它有助于揭示具有丰富内涵的数学理论的内在结构。

The proposed Arithmetic Word Problem Grammar can facilitate the maintenance of arithmetic word problems and their evolutions including Self-Evolution and Collaborative-Evolution.

我们提出的数学应用问题文法可促进维护数学应用问题以及问题的演化，包含自我演化以及合作式演化。

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。