数学

Applied Mathematics and the history of mathematics can be said that as long.

数学应用和数学的历史可说一样长。

During the process of research on applied mechanics, he can grasp the proficient mathematics and the physical nature of the problem, which is consistent with the spirit of engineering science and applied mathematics.

在研究应用力学的过程中，他将娴熟的数学技巧和对物理本质的准确把握有机地结合在一起，其研究方法与后人所提倡的技术科学和应用数学的学术思想是相通的。

LIU Hui's Cyclotomic Method is one of the greatest achievements of the history of mathematics in China, even in the world, in which the special approach to understand the infinity and the method to solve it are presented.

刘徽的"割圆术"是中国数学史上的重要成就之一，其中包含着中国数学家对无限问题的独特认识和致用的处理方式。很多高等数学教科书在讲述极限概念时大都提及，但所述，并未体现刘徽本意。

Homotopy perturbation method; MOL method; nonlinear partial differential equation; approximate solution

基础科学，数学，数学分析同伦摄动法；直线法；非线性偏微分方程；近似解

The mathematical model was verified in experiment with the method of indirect squeeze cast Archimedean spiral proof sample. And the experimental results show that the maximum deviation between the theoretical value and measured value is less than 8%. This model can be used for quantitative analysis and estimating effects of the craft factors on the filling ability, and can also predict the maximum filling length. It has the important reference value to design the semi-solid alloy rheoforming technology and mould.

采用间接挤压铸造阿基米德螺旋线试样的方法对该数学模型进行了实验验证，实验结果表明：理论计算值与实验测定值之间的最大偏差小于8%；该数学模型可以定量分析和估算工艺因素对充型能力的影响，并可预测充型极限长度，这对半固态合金流变成形工艺设计和模具设计都有参考价值。

Archimedean mathematical thought gives us the inspiration: the ingenious physical deduction is the important method of the scientific discovery; the strict mathematical deduction is the necessary step to confirm the result; the several basic principles to be selected act as foundation of deduction; devote oneself to the scientific truth and do not seek secular profit.

由Archimedes的数学思想得到的启示是：巧妙的物理论证是科学发现的重要方法；严格的数学论证是确立结论的必需步骤；要精选若干基本原理，作为论证的基础；要献身科学真理，不为俗世需求所动摇。

Caculation of principle error of involute profile processed by Archimedean hobbing cutter ;2. The equation of single hobbing cutter 's locomotion locus and the mathematical model of its instantaneous cutting area are established.

建立了单把滚刀旋切运动的轨迹方程和瞬时切削面积的数学模型，在此基础上对旋切面积的数学模型进行分析及简化，为旋切技术的实际应用提供了有力的依据。

The complicated curve parts of the neckline and armhole of the garment prototype for female bodies have been studied and the accurate mathematic models have been built.

对原型结构图中结构复杂的领口线、袖孔线等曲线段绘制的数学模型进行深入探讨，并给出科学精准的数学模型。

Experiments of flow conductivity closure stress of typical propping agent are done, propping agent short-term flow conductivity alteration index is defined, by this, the relation between fissure short-term flow conductivity and closure stress, it is close to exponential relation. 4. Establishing the mathematical simulator of hydraulic fractured well's production in a steady state, finding the relation curve between dimensionless flow conductivity and fracture penetration coefficient by means of calculation and analyses, it is the basis of hydraulic fracture. 5. Expatiating the importance of optimized hydraulic fracturing design in reservoir engineering, advancing the optimizing design method, fracture dimension can be calculated easily when the physical parameters are known. 6. Production rate decline standard curve of vertical fractured wells is achieved by mathematical simulation, when the flow pressure is certain , by asymptotic analyze, this decline curve is close to exponential relation.

完成了国内外典型支撑剂的导流能力闭合应力影响实验，在数据分析中定义了支撑剂短期导流能力变异系数，并由此发现裂缝短期导流能力随闭合应力变化的近似符合指数关系式； 4 建立了一种水力压裂井稳态产能的数学模拟器，计算分析找到了最优无量纲导流能力与裂缝穿透比之间的新型关系曲线，它是水力压裂优化设计的基础； 5 阐述了水力压裂油藏工程优化设计的重要性，提出了优化设计方法，在已知支撑剂物性参数条件下可简洁计算最优裂缝尺寸； 6 数学模拟给出了垂直裂缝井产量递减标准曲线，在井底定压条件下通过渐近分析表明，该递减曲线满足指数关系式。

Just as he used logic to describe the foundations of mathematics in Principia Mathematica , Russell would use logic to clarify philosophy, through his concept of logical atomism, and linguistics, through his theory of descriptions.

正如他所使用的逻辑描述的基础数学中的数学原理，罗素将使用的逻辑，以澄清理念，通过他的逻辑原子主义的概念，与语言学，通过他的理论说明。

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。