算术

About this, Pierre de Fermat wrote in 1637 in his copy of Diophantus's Arithmetica,"I have discovered a truly remarkable proof but this margin is too small to contain it."

G.Bachet所翻译的丢番图《算术》中写道︰「我已发现了一个真正不凡的证明，但页边太小，写不下。

Its actual birth isusually credited to Diophantus of Alexandria, who wrote "Arithmetica" in Greekduring the third century.

而它真正的诞生通常归功于公元三世纪的希腊人丢番图，他著有《算术》一书。

The Greek mathematician Diophantus of Alexandria\'s Arithmetica, which dealing with problems in indeterminate analysis, is systematically studied in this doctoral dissertation.

丢番图《算术》的重要性一直为西方科学史家所关注，很早就开展了这方面的研究工作。

Combining Inclusion-Exclusion principle with Disjoint Sum of products formula,the new formula contains terms which correpond one by one to a class of special subnetworks. For a given newtork,terms of new formula are fewer than those of corresponding stryanarayna formula. Finally,an example illustrates our conclusion.

该公式本质上是将容斥原理公式和不交和公式融合在一起，公式中各项和网络的一类特殊子网络一一对应，与相应的Satyanarayanna公式比较，该公式包含更少的项和更少的算术运算，并给出一个算例验证上述这个结论。

The first few chapters, covering divisibility, prime numbers and modular arithmetic, assume only basic school algebra, and are therefore suitable for first or second year students as an introduction to the methods of pure mathematics.

最初的几个章节，涉及分割，素数的和模块化的算术，只承担基础学校代数，因此，作为一个纯数学的方法引入第一或第二年的学生更合适。

Software Description: XCCalc is a Floating-Point calculator program with the following features:- Can calculate with complex numbers like z = x + i*y - Extra precision to millions of decimal places - Uses Fast Hartley Transform to speed-up long multiplies - Separate input and output notation, base 2 to base 36 - Efficient Transcendental functions - Hyperbolic functions - Greatest Common Divisor function.

XCCalc XPCalc 是一款带有下列功能的浮点计算器软件：可以计算诸如 z = x + i*y 这样的复杂算术公式；带有数百万小数位的额外精度；使用 Fast Hartley Transform 以加速长乘法计算；基于2到36个单独的输入和输出表记法；高效的验算函数；双曲线函数；最大公约数函数。

The main reason for using float is to save storage in large arrays, or, less often, to save time on machines where double-precision arithmetic is particularly expensive.

使用float类型主要是为了在使用较大的数组时节省存储空间，有时也为了节省机器执行时间(双精度算术运算特别费时)。

This paper is concerned with the RS encoder over a dual basis, and RS encoder in DVB-C system was implemented as a example.

在有限域的各种算术运算中，乘法是研究较多的，其中Berlekamp比特串行乘法器的硬件较为简单[1]，适合用于RS码编码器。

In the improved algorithm, two matrices describing the relation between transfer stations of all levels with angular points of grids and the relation between two adjacent levels transfer stations were established to delete constraints and compress greatly variables of the model; an evolutionary algorithm based on evolutionary similarity was applied to mix the basic properties of global and local search; the selfadaptive delta variation operator, dual arithmetic crossover operator, peakjump operator were used to improve the behaviors of artificial fishswarm algorithm.

在算法中建立了各级中转站与网格点关系矩阵和相邻两级中转站间的关系矩阵来消除约束条件和压缩变量数；使用了基于相似性的演化算法来融合全局搜索和局部搜索；使用了自适应delta变异算子、双算术交叉算子、峰跳操作算子等多种算子改进人工鱼的各种行为。

In the improved algorithm, two matrices describing the relation between transfer stations of all levels with angular points of grids and the relation between two adjacent levels' transfer stations were established to delete constraints and compress greatly variables of the model; an evolutionary algorithm based on evolutionary similarity was applied to mix the basic properties of global and local search; the self-adaptive delta variation operator, dual arithmetic crossover operator, peak-jump operator were used to improve the behaviors of artificial fish-swarm algorithm.

在算法中建立了各级中转站与网格点关系矩阵和相邻两级中转站间的关系矩阵来消除约束条件和压缩变量数；使用了基于相似性的演化算法来融合全局搜索和局部搜索；使用了自适应delta变异算子、双算术交叉算子、峰跳操作算子等多种算子改进人工鱼的各种行为。

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。