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Software reliability is one of the most important quality characteristics. The definition of software assessment is discussed, the mechanism of software failures is described, 2 software reliability assessment methods based on triangular fuzzy number arithmetic operations and trapezoid fuzzy number arithmetic operations respectively are proposed, and some examples to use these methods are given.

软件可靠性是航天型号软件的重要质量特性之一，本文阐述了软件可靠性评估的定义，讨论了软件的失效机理，提出了基于三角形模糊数算术运算和基于梯形模糊数算术运算的软件可靠性评估方法，并给出了使用这些方法的示例。

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。

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。

Acquired conclusion was that the sample mean value submitted to normal distribution, and the sample variance was composed of a number of linear sum of random variable submitted to Chi-Squared distr.

得出的结论是：样本均值服从正态分布，样本方差由若干个服从卡方分布的随机变量的线性之和组成；样本均值的期望等于各管落点期望的算术平均值，方差为各管方差的算术平均值；样本方差是各管落点总体平均方差的无偏估计，方差与各管落点散布的差异相关；样本均值与方差相互独立的充要条件是：各管落点属于独立同分布样本。

In addition, deterministic calculations were carried out using (1) arithmetic mean values of untransformed hydraulic parameters,(2) arithmetic mean values obtained after backtransformation of Gaussian distributed parameters, and (3)alternatively using a set of mean bimodal retention and conductivity curves. Predictions obtained with the two stochastic methods and the deterministic cases are compared with measured cumulative outflow and moisture content profiles from fifteen 1 m long undisturbed soil columns collected along the same transect.

此外，决定论计算被实行使用改变与水有关的参数的(1)算术平均价值观，在 backtransformation 以后为得到高斯的(2)算术平均价值观的散布参数和(3)另一种选择使用一套卑鄙双峰的保留和传导性弯曲。，用二有可能的方法和决定论情况为得到的预言被把和仔细斟酌累积的流出比较和从十五1 m 长不受干扰土壤柱，沿着把同样的 transect。

Since that time, Boole's original conception has been extensively developed and refined by algebraists and logicians.

由于布尔代数，最初的概念逻辑学和二进制算术之间的内在联系，数，逻辑学和二进制算术之间的内在联系，使得布尔代数的理论在电子计算机的发展中起到举足轻重的作用。

Basic numeracy skills, such as the ability to tell the time, count money and carry out simple arithmetic , became essential in this new urban lifestyle.

基本算术技能，如能告诉的时间，金钱和伯爵进行简单的算术，成为必不可少的这个新的城市生活方式。

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。