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These issues are mostly difficult to solve according to the general study of mathematical models, but the Monte-carlo method is very convenient for calculating Multiple Integral of low dimension in regular domain of integration or complex range or even non-connected region.

这类问题绝大多数按数学的研究处理模式出发，都是难以解决的，而蒙特卡罗方法对计算高维空间中维数不很高且积分区域是规则的积分、以及复杂区间甚至不连通的区域上的积分都却是很方便的。

A biological recognition method by feature detection of human body on the move was presented, and the mathematical model of Doppler shift was established.

根据生物的生命体行为特征，提出一种新的生物识别方法，并建立了多普勒频移数学模型。

In mathematical terms, the Facing Ratio is the Dot Product of the angle rather than the angle itself.

在数学术语上，Facing Ratio是角度的数量积相当于角度本身。

The dozer operating course is summarized with using fuzzy control theory, and the fuzzy mathematical model and the control algorithm of the dozer implement are designed.

应用模糊控制理论，总结推土机的操纵过程，建立了推土机工作装置的模糊数学模型及其控制算法。

This paper analysed the kinematic properties of ball joint hi nged on the piston rod and steering drag link of a separated assistant steering m echanism, and the equations of the path and mathematical model of pressure angle were established.

文摘：分析了分置式转向助力机构的液压缸活塞杆与转向直拉杆相铰接的球头销的运动特性，建立了其轨迹方程及压力角的数学模型。

Based on the systematic analyses of the applications and developments of step motor, the driving technique of step motor are analyzed in this paper, and upon these statements, a mathematical model of VR step motor is built. With this model, the coil current of step motor with chopping driver and the non-loaded starting frequency are simulated for the base of designing of step motor servo system.

本文在系统分析了步进电机应用和发展的基础上，对步进电机的驱动技术作了详尽的论述，建立了三相反应式步进电动机的数学模型，并利用该模型对斩波驱动的步进电机绕组电流及空载运行的启动频率等进行了仿真，为步进电机驱动系统的设计提供了依据。

What this paper finished mainly work as follows: Five-phase hybrid step motor driver system with fixed-chopping frequency and constant total current driving is fully described. Mathematical model of the system, included the current control circuit, power driving circuit and five-phase hybrid stepping motor is established. The steady modeling of the system is established and studied. Based on the steady modeling of the system, dynamic modeling of the system is studied and single step response characteristic is constructed with MATLAB/Simulink. The simulation results, which is certified by the theory analysis, coincide with the theory analysis.

本文主要完成的工作包括几个方面：对五相混合式步进电动机恒频斩波恒总流驱动系统进行了完整的描述；建立了包括电流控制电路、功率驱动电路以及五相混合式步进电动机在内的恒频斩波恒总流驱动系统的完整的数学模型；基于MATLAB/Simulink建立了恒频斩波恒总流驱动系统稳态仿真模型，并进行了仿真；在建立其稳态仿真模型的基础上，对动态模型进行研究，并借助于MATLAB/Simulink工具建立了恒频斩波恒总流驱动系统单步响应特性的仿真模型并对其单步响应特性进行了仿真研究，仿真结果与理论分析相符。

In this paper, we focus on such aspect as mathematic expression in DNA and protein sequences, similarity analysis and phylogenetic tree structure. Mainly include:After summarization mathematical methods of DNA and protein sequences in detail, the paper presents a 2D graphical representation of DNA sequences based on dual nucleotide, and graphical representation of the distribution curve of sequences with nucleotide sequences of the classification.

论文在DNA和蛋白质序列的数学表示、相似性分析和进化树的构造等方面进行研究，主要工作包括：在对DNA和蛋白质序列的数学表示方法进行较为详细的综述后，提出了一种基于双核苷酸的DNA序列2D图形表示方法，利用核苷酸的分类给出了序列的分布曲线图形表示。

Although I am not stupid, the mathematical side of my brain is like dumb notes upon a damaged piano.

"教学生思考、观察、推理、发现，才是学数学真正的价值"上帝一定是个几何学家！

This treatment of competition, first published in Researches into the Mathematical Principles of Wealth , is referred to as Cournot duopoly .

这种待遇的竞争，首次公布的研究数学原理的财富，被称为古诺双寡头。

I can still vividly recall the impressive scenes you gave. You were among my friends and relatives who accompanied me from my house to the seaport and when the porters were slow to show up, you obligingly carried my suitcase for me.

你对我的种种感人情意，使我记忆犹新，那天你随着我的亲友从家里送我上轮船，搬运工迟迟不来，你毅然替我提着皮箱上船。

St. Nicholas became the patron saint of Russia, where he was famous for his red cape, flowing white beard, and bishop's mitre.

圣尼古拉成了俄罗斯人的守护神，在那里，他以身披红斗篷，留着飘逸的白胡须，戴着主教法冠而闻名。