算术

As an example we will write a small program to read and evaluate arithmetic expressions consisting of floating point numbers, parentheses and the usual operators for addition, subtraction, and so on.

例如我们要写一个计算由浮点数、圆括号及一些常用的加、减等算术符号组成的算术表达式的程序。

The definition and properties of line segment arithmetic are given,which is a special situation of point set arithmetic,but easily calculated.

文章给出了线段算术的定义和性质，它是点集算术的特殊情况，但更便于计算；提出了线段Bézier曲线的概念，就是把区间Bézier曲线中的长方形换成满足一定条件的线段，这里的线段是指该线段上所有点的集合；给出了线段Bézier曲线的性质及其细分算法。

In describing the arithmetic unit, it is seen that various sequences of operations are required in the arithmetic unit.

改译：在描述算术逻辑部件时，我们看到在算术逻辑部件中要进行各种操作序列。

On putting forward a research method of the history of mathematical economics by synthesizing the intrinsic and extrinsic historical factors, the author examines some problems in the early development of mathematical economics in the light of arithmetization of analysis.

提出研究数理经济学史内、外史结合的一种方法，并用该方法以 1 9世纪分析算术化为背景，考察了数理经济学早期发展的若干问题，指出数学基础问题是 1 870年前在经济学中应用数学方法的主要障碍，以分析算术化为代表的数学基础重建则是此后数理经济学迅猛兴起的重要条件。

By putting forward a research method on the history of mathematical economics through the synthesis of the intrinsic and extrinsic historical factors , the author examines some issues in the early devel-opment of mathematical economics in the light of arithmetization of analysis.

提出研究数理经济学史的内、外史相结合的方法，并以十九世纪分析算术化为背景，用该方法探讨了数理经济学早期发展的若干问题，指出数学基础尚未完善的问题是1870年前在经济研究中应用数学方法的主要障碍，而以分析算术化为代表的数学基础重建则是此后数理经济学迅猛兴起的重要原因。

In the geometry of matrices, the points of the associated space are a certain kind of matrices, there is an arithmetic distance of two points in this space, and there is a transformation group acting on this space. Two distinct points is said to be adjacent if their arithmetic distance is one or minimal.

在矩阵几何中，空间中的点是某一类矩阵，两点间存在一种算术距离，还有一个变换群作用在这个空间上，两个不同的点间的算术距离为1或最小时称这两点是粘切的。

In this paper we considered three problems on Asian options pricing: The valuation of geometric average Asian options with stochastic averaging period, the valuation of Asian options with fixed strike price and floating strike price in the case of arithmetic average.

本文考虑了三个关于亚式期权的定价问题：平均周期是随机的几何平均亚式期权的定价；具有固定执行价格的算术平均亚式期权的定价和具有浮动执行价格的算术平均亚式期权的定价。

4Based on a fact that the price formula of Asian options can be transformed into that of vanilla European option when the time to maturity is less than or equal to the length of average, we skillfully obtain the analytical price formula for the option on the minimum or the maximum of two geometric average prices and generalize it to obtain the price formula of several average prices for the first time. We also apply the method of [121], which approximates the arithmetic average by the geometric average, to the pricing of opitons on the minimum or the maximum of two arithmetic average prices to obtain Its approximated price formula. Numerical results show that the approximated price is relatively accurate when the riskless interest rate is large or the option is in the money and the volatility of two underlying assets are high and its accuracy is a little reduced but still good when the dividends are considered. However, it is hardly affected by the sampling number.

我们基于观察到的一个事实即当离到期时间小于或等于平均期间时亚洲期权的价格可变换成普通的欧式期权的价格，从而巧妙地得到了两个几何平均价格的最小或最大值期权价格的解析公式，通过简单地推广，首次得到了多个几何平均时的价格公式；将[121]用于算术平均亚洲期权的定价方法推广到两个算术平均价格的最小或最大值期权，从而得到它的渐进公式，数值结果表明：渐进价格的准确性在无风险利率较大或期权为实值且两标的资产的波动率较小时较好，抽样的个数对它没有影响，但考虑红利时它稍有下降但仍较好。

Del incompleteness theorem is based on some interpretation of first order arithmetic.

本文首先从形式主义的角度介绍了哥德尔不完全性定理，提出"哥德尔不完备性定理"的说法是容易混淆的，说明一阶算术有非标准模型，哥德尔的证明是基于标准模型的，可以推出一阶算术在标准模型上的不完备。

Persecution is used in t h eology, not in arit h metic, because in arit h metic t h ere is knowledge, but in t h eology t h ere is only opinion.

迫害仪发生于神学领域，而不见于算术领域，因为在算术中有知识，而在神学中仅有观点。

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。