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Throughout his life Euler was much absorbed by problems dealing with the theory of numbers , which treats of the properties and relationships of integers, or whole numbers 0,±1,±2, etc.

没有一个人能像他那样多产和那样高超地掌握数学的技巧，在数学的许多分支中都有以他命名的公式、常数等等。

In addition, by utilizing Jacobi two square numbers theorem and Lagrange four square numbers theorem and some theta function identities, we also prove the known results of number theory: two triangular number theorem, four triangular number theorem, and the number of representations of a positive integer by various quadratic forms in terms of divisor functions

包括Jacobi二平方数定理，Lagrange四平方数定理等，然后利用这些结果结合几个theta函数恒等式，我们获得了把任意一个正整数表示成两个三角数或四个三角数的和以及其他的二次形式的方法数，这些方法数都是用因子函数来表示的。

Under the condition of the following factors concerning the optimization models:the investment cost, operating cost, unfair cost, payment evade cost, drivers' extra cost and environmental pollution cost, this paper raises the optimized models of multi-modes payment of toll collection system and its algorithm is proposed by SAGA hybrid optimization strategy, which can simultaneously optimize the following results: the optimum locations of toll stations, numbers of toll stations, the numbers of different tolling modes' tollgates of every toll station, ETC users' discount rate, and can estimate the installation rate of TAG of every toll station, the actual traffic flow capacity of different tollgate, can obtain the best toll collection system under the different simulated decision conditions.

本文充分考虑了驾驶员缴费技术选择与缴费车道选择的特性，提出了驾驶员缴费方式随机选择模型；在考虑了收费系统的投资成本、营运成本、不公平成本、漏收成本、驾驶员的额外成本和环境污染成本等因素的基础上，提出了多收费方式收费系统的优化模型，提出采用模拟退火遗传算法进行收费系统寻优的算法，可同时优化出一个收费系统的收费站位置与数量、不同收费站不同收费方式的收费车道数和ETC用户的折扣率等参数，可估算不同收费站TAG的安装率、不同收费车道实际使用量，可模拟不同决策情境下的最佳系统资源配置方案。

The total cell numbers and differential cell numbers in BALF were counted.

哮喘组BALF中PMN和嗜酸性粒细胞计数显著高于对照组(P.01)。

The tractarian state of electron is discontiguous, so the finding result of four quantum numbers is discontiguous, the logical combination of four quantum numbers are corresponding to the suitable energy state of electron.

既然电子的运动状态是不连续的，因此四个量子数的取值也是不连续的，四个量子数的合理的组合对应着电子的一种能量状态：。我翻译如下，请高手指正，急用，请高手快点。

Consideration of the natural numbers also leads to the transfinite numbers , which formalize the concept of counting to infinity .

考虑自然数也引起了超越数，超越数形式化计数到无限的概念。

Fuzzy constraints based triangular fuzzy numbers and the fuzzy cost based trapeze fuzzy numbers are discussed in this paper.

本文讨论了基于三角形模糊数的模糊约束条件和基于梯形模糊数的模糊费用。

According to the experiential data of the DRASTIC index, the standard values of 10 classes for 7 indexes are proposed in the form of triangular fuzzy numbers, and similarly the weights of indexes are expressed in the form of triangular fuzzy numbers.

参照DRASTIC方法的经验性数据，给出了10个级别7项指标以三角模糊数表示的标准特征值，给出了三角模糊数表示的指标权重。

With regard to the fuzzy multi attribute decision making problems, in which the information about attribute weights are unknown completely and the attribute values are in the form triangular fuzzy numbers, a method based on the linear programming model and projection of fuzzy numbers vectors is proposed.

针对属性权重完全未知且属性值为三角模糊数的模糊多属性决策问题，提出了一种基于线性规划和模糊向量投影的决策方法。

A register pair is needed because a multiplication of two 32 bit numbers results in a 64 bit result, just like 9*9=81 - two one digit numbers result in a two digit result.

寄存器对必须的因为乘法是两个32位整数结果存在一个64位结果中。例如9*9=81 两个一位数结果在一个两位结果中。

Pachomius manual labour was organized as an essential part of the monastic life; and since it is a principle of the monks as distinguished from the mendicants, that the body shall be self-supporting, external work of one sort or another has been an inevitable part of the life ever since.

根据圣pachomius体力劳动组织作为一个重要组成部分寺院生活；以来，这是一个原则的和尚，作为有别于乞丐，该机构应自支撑，对外工作的这种或那种已一个必然的一部分，生活至今。

In order to study the effects of parametrical rolling on the ship movement and tilts, in allusion to ship's navigating in regular following waves, the equation of ship rolling motion is transformed into normal Mathieu equation by proper variable replacement when strong parametrical excitation in restoring moment varied according to sine or cosine wave.

为研究参数横摇对船舶运动和倾覆的影响，通过对船在规则波上随浪航行时，恢复力矩中出现的1个以正余弦规律变化的强参数激励项进行适当的变量置换，将船舶的横摇运动方程转换成标准形式的Mathieu方程。