In order to help user doing ooa & ood and strengehen his comprehension of object and its usage , we view class of object - oriented as a set , view object of a class as an element of the set and then express them in mathematical formulas 为了协助用户进行面向对象分析和设计，加强对象的理解和使用，本文试图从数学的角度来分析面向对象的概念。首先把面向对象中的类看作集合，类的对象看成集合中的元素，并用数学公式来表示。
Varley and her colleagues found that although the subjects could no longer grasp grammatical distinctions between , say , “ the dog bit the boy ” and “ the boy bit the dog , ” they could interpret mathematical formulas incorporating equivalent structures , such as “ 59 ? 13 ” and “ 13 ? 59 瓦尔利和同事发现，虽然受试者已经无法了解语法差异，比方狗咬男孩与男孩咬狗，却可以了解结构相同的数学算式，如59 ? 13与13 ? 59的区别。
The mathematical formula about the dynamic object standard device used for measurement tracking precision in the factory is thorough researched in this paper , too . the entirety example calculate method used for define the parameter of the complex maths model about the dyamic object standard device is described 本论文还对跟踪精度室内检测装置- - - -动靶标标准装置的数学模型进行了较深入的研究，并将穷举法用于确定具有复杂数学模型的动靶标标准装置基本参数。
Plant endemism is the key problem in floristic study . analysis of endemism in a flora has significant implications in demonstrating floristic richness and diversity , the relationship between plants and their environment , and also in conserving biodiversity of the flora . in view of the situation that most of the past studies on endemism were qualitative , this study is the first tentative approach to the introduction of quantitative indices to the analysis of floristic endemism , with an purpose to push the study of endemism from qualitative to quantitative . four quantitative indices are introduced , i . e . level of endemism ( l ) , coefficient of endemism ( c ) , degree of endemism ( d ) and general index of endemism ( a ) . mathematical formulae have been given to each of the above indices and explanations for them have been presented , and the scope of their use in floristic studies has been delimited and exemplified in this paper . the result shows that they are of good applicability . the proposed indices embody full information of plant systematics and plant geography . with the aid of qualitative analysis , the application of the proposed indices will improve the comparability and precision of endemism study in floristics 过去有关特有现象的研究主要限于定性的分析，可比性和精确性较差.该文尝试引入特有现象的定量化指标，以推动特有现象的分析研究从定性水平向定量水平迈进.所引入的4种定量化指标分别是：特有水平、特有系数、特有度以及特有综合指数.对每种量化指标都给出了数学表达式，说明了其区系学意义，例证和界定了这些指标在植物区系分析中的应用，结果表明，它们有良好的适用性.这些指标充分地包含了植物系统学和植物区系学的信息.结合定性分析，这些指标的应用将增强植物区系研究的可比性，使植物区系特有现象的分析达到更精确的水平
Geometrical and physical meanings of difference surface are presented , and the parameters of tooth surface topographic deviations are derived . in addition , the complete mathematical formulae of the 0th , the 1st , 2nd order form deviations is proposed , and diagnostic parameters of each order form deviation is gotten by the least square method , which lead to evaluate the tooth surface topographic deviation quantificationally 系统地给出了差曲面的几何意义和物理意义,提取了齿面拓扑误差参数;给出了零阶误差、一阶误差、二阶误差的完整数学公式,并且用最小二乘法得到了各阶误差的特征参数值,实现了对齿面拓扑误差的定量评定。
In the finite element method analysis , the constitutional relationships of steel and three - dimension compressed concrete were conducted by using increment plastic theory . in the paper a serious of joint models were analyzed by using the program ansys and the mathematical formulas for determination of load - carrying capacity of shearing and bending in the joint region were also given . at last the influence of many parameters to the load - carrying capacity in the joint region was analyzed and some suggestions were given for the design in the practical projects 在有限元分析中，用增量塑性理论推导出钢材以及三维受压混凝土的本构关系，重点是三维受压混凝土的本构关系，建立了模型的单元刚度矩阵，给出了程序中非线性方程的求解方法，并用ansys软件计算了一系列节点模型，得出了节点域的抗剪、抗弯承载力及各参数对节点域承载力的影响情况，并用试验结果和计算公式验证了有限元计算结果。
By means of comprehensive study of the whole process to derive the calculation of relative gain variation , a mathematical formula how to make a well - founded understanding and correct use of the differential calculation method when making every efforts to accurately calculate the relative variation of the closed - loop gain of an amplifier was advanced based on another accurate calculation method given 因此，本文通过全面考察推导增益相对变化量的计算全过程，根据所给出的另一种准确计算方法，重点提出了在要求准确地计算放大器闭环增益的相对变化量时，怎样正确理解和运用微分计算方法的数学表达式。
The mechanical impedance analyzing method utilized , the mathematical formula for the input impedance and transformer ratio of ultrasonic horn are built up , some vibration performance of ultrasonic horns are discussed under different load impedance , the relationship and applicational conditions between the transformer ratio of ultrasonic horn and the radiational impedance are analyzed 采用机械阻抗分析方法，建立了超声变幅器的输入阻抗和变幅比的数学表达式，讨论了不同负载阻抗下超声变幅器的振动性能，分析了超声变幅器的变幅比与换能器辐射阻抗之间的关系及应用条件。
Based on these mathematical formulas , we describe and deduce a series of axioms , theorems , formulas , algorithms and design principles , which can be used not only as theory knowledge for studying object - oriented analysis and design but also as a tool and guiding principle for object - oriented database design , object - oriented formalization analysis and design , the automatization of test and evaluation 然后以此为基础来描述、推导或证明面向对象分析和设计中的一系列公理、定理、公式、算法和设计原则。这些公理、定理、公式、算法、设计原则既可作为学习面向对象设计的理论知识，又可作为进行面向对象分析和设计的工具和指导原则。
By the preceding analysis , the author revises the pricing model , that is , the whole value of target firm is supposed to plus the net implied returns of target firm on the basis of rappaport or weston model . the mathematical formula is as follow : value of target firm = basic value + net implied returns of target firm 通过上述分析，笔者提出修正的目标企业定价模型， gf目标企业的整体价值应在运用rappaport模型或weston模型得出基本价值的基础上，加上目标企业隐含的净收益。用数学公式表达如下： ? 、目标企业价值二基本价值目标企业净收益其中：目标企业净收益一目标企业隐含收益一隐含咸本5
