数学

Translation; mathematical commentary; methods of Diophantus; general methods of resolution; constructible problems

基础科学，数学，数学概论翻译；评注；丢番图的方法；解法的一般性；可构成性问题

Further, it explores and analyses the reasonable theoretical bases of HPM are genetic approach and constructionism.

2具体探讨了数学史与数学教育为何得以整合的各个层面。

In this paper, we are discussing the concept of intuitionism, and their logic ,and their constructive mathematics.

本文主要讨论直觉主义派的数学观、无穷观、逻辑规则和构造性数学，同时还概述了人们对直觉主义派的一般评论。

Peter Borwein is Professor of Mathematics at Simon Fraser University and the Associate Director of the Centre for Experimental and Constructive Mathematics.

彼得Borwein在西蒙·弗雷泽大学和实验和有建设性数学的中心的副主管是数学的教授。

Furthermore,we obtain a sufficient and necessary condition about continuity of functional series and integral with parameter,and show the sufficient condition about differential .

将数学分析中一致收敛性的概念加以推广，分别对函数项级数和含参量积分引入次一致收敛的概念，证明了函数项级数、含参量非正常积分连续性的充要条件和可微性的充分条件，推广了数学分析中的相应结

In this paper, we discuss two math problems:On the continuity of function which displays 0/0 type on certain point If China mathmaticiam Hua Luogeng did the work on the nonstandard number.

关于两个数学问题ⅰ呈0/0型函数的连续性问题；中国数学家在非标准数学方面是否有过工作的问题；对前者给出探讨性结论，对后者给出考证。

The paper uses precise step to produce the continuity function of water hammer mathematic model, not only gains more precise water hammer pressure function and water hammer wave speed functionbut also founds correct water hammer mathematic modelContinuity EquationMovement EquationAfter ignoring subordinate facts, function (1) and (2) translate into the current applied water hammer pressure function and water hammer wave speed function.

本论文对水击数学模型中的连续性方程重新进行了严谨的推导，不仅得到了更加准确的水击压强和水击波速的计算公式也建立了正确的水击数学模型连续性方程运动方程当忽略次要因素以后，公式(1)和(2)即可转化为当前应用的水击压强计算公式和水击波速计算公式。

HJB equation; quasivariational inequality; domain decomposition; convergence; iterative algorithm; relaxation algorithm; existence; multigrid method

基础科学，数学，数学分析HJB方程；拟变分不等式；区域分解；收敛性；迭代法；松弛算法；存在性；多重网格法

The core problem of load forecasting is technical matters or the mathematical model. Conventional model is described by clear mathematic representation, which has the advantages of little calculation and high speed, but which has lots of limitations such as non-self learning, and non-self adapting at the same time.

传统的数学模型是用显示的数学表达式加以描述，具有计算量小、速度快的优点，但同时也存在很多的缺陷和局限性，比如不具备自学习、自适应能力、预测系统的鲁棒性没有保障等。

Uncertainty theory is a branch of mathematics based on normality, monotonicity, self-duality, countable subadditivity, and product measure axioms.

不确定理论是基于规范性、单调性、自对偶性、可列次可加性和乘积测度公理的数学系统，是研究不确定现象的数学分支。

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。