同余的

Rough ideals been first introduced by Kuroki N. Under the condition of the congruence relation, a rough set of a subsemigroup was proved to be its subsemigroup, while that of a leftideal was also proved to be its leftideal.

Kuroki N研究了半群中的粗理想，首次提出了粗子半群和粗理想的概念，证明了在同余关系下，半群的粗糙集是半群，左理想的粗糙集是左理想。

Kuroki N firstly put forward the notion of rough subsets and rough ideals in semigroups, testifying that Under the condition of the congruence relation, a rough set of a subsemigroup was proved to be its subsemigroup, while that of a leftideal was also proved to be its leftideal.

Kuroki N首先研究了半群中的粗理想，首次提出了粗子半群和粗理想的概念，证明了在同余关系下，半群的粗糙集是半群，左理想的粗糙集是左理想。

Owing to the importance of Disquisitiones Arithmeticae in histoiy of number theory and the core position of the congruent theory in elementary number theory, this paper is to focus on the following two topics: the origin and development of Fermats little theorem and the quadratic reciprocity law which was hailed as golden by Gauss.

鉴于《算术研究》在数论发展史上的重要性以及同余理论在初等数论中的核心地位，本文重点研究费马小定理和被高斯誉为"黄金定律"的二次互反律的起源和发展。

N[1] and[2], the classification theory of indices set of irreducible nonnegative matrices isstudied,according to that theory . An algorithm for the period and the classification of indices setof irreducible nonnegative matrices are given. Using this algorithm.

文［1］和［2］讨论了不可约非负矩阵指标集的分类理论，在此基础上，本文给出了不可约非负矩阵的周期与指标集的分类算法，这一算法能同时求出周期与同余类，当矩阵的阶不大时，该算法容易在图上实现。

It deserves to be mentioned that the Modulo Construction algorithm we proposed has a sufficiently large approximation ratio with a low time complexity.

值得一提的是，我们提出的同余构造算法在时间复杂度较低的情况下，具有很高的近似比。

In addition, new proofs are presented for two symmetric difference identities, as well as Ramanujans congruence modulo 11 on the partition function.

此外，作者重新证明其中另外两个对称差恒等式，并利用Chan的_∞~(10)的二重级数表示公式重新确认Ramanujan的关于分拆函数的模11同余性质。

aim: to generate random sequences that can fit the anticipated probability distribution based on the thinking of mc, methods: we establish a method in the ide of visual studio by the way of linear congruential method to generate random sequences.we also test the homogeneity and independence by the chi-sqare goodness of fit test and self-correlation test.

v+\$oXb；L^7h_0 目的：基于mc法生成符合预期概率分布的随机序列，以便应用在以后的仿真系统中。方法：应用线性同余法在visual studio环境中建立随机模型模拟随机序列生成。并采用χ2拟合优度检验法和自相关检验法检验生成的随机序列的均匀性、独立性。

Pastijn left the question open whether is a congruence on the free idempotent semiring generated by two free generators. In this paper, the open question will be solved.

从而，提出了一个公开问题：是否为由两个自由生成元生成的幂等元半环上的同余，本文给出了这个问题的一个肯定的回答。

We investigate this kind of numbers in Chapter 4 and give the following results:(1) By generating functions theory, we have established a number of identities involving the powers of generalized Fibonacci and Lucas numbers. From these identities, we can obtain some new congruences.

第四章：利用发生函数理论以及一些运算技巧，讨论与广义Fi-bonacci，Lucas数有关的问题：(1)利用发生函数原理，建立了一系列涉及广义Fibonacci，Lucas数的幂的恒等式，并由这些恒等式得到了新的同余关系。

In this paper, we discuss some recurrence relations and congruence properties of Bell polynomial, and give a class of recurrence relations satisfied by GSN pairs. Furthermore, we givethe definition of extended GSN pairs Gand G, so we unify the binomial coefficients, Gaussian coefficients, and Stirling numbers. We provide urn ,models for G(n,k|w,0) andG(n,k|0,w).

在这篇论文中，我们讨论了Bell多项式中的递归关系和同余问题，给出了广义Stirling数对的一类递归关系式，提出了扩展的GSN对G和G的概念，统一了二项式系数、高斯系数和Stirling数，并利用模型对G和G进行了组合解释。

It seems likely that Kraft will return with a better offer.

看起来卡夫要重新考虑一个更好的出价了。

But he'd rather burn off my feelers and watch me squirm.

可他却放任那个家伙对我为所欲为！