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By replacing pseudo-Mersenne numbers with generalized Mersenne numbers, we propose a new notion-Generalized Optimal Extension Fields, and study the fast arithmetic about multiplication and modular arithmetic in GOEFs.

利用广义Mersenne数代替伪Mersenne数，提出了广义最优扩域的概念，并研究其上的快速乘法运算和取模运算，为乘法运算给出了通用的复杂度公式，为取模运算给出了具体的运算公式，推广了Bailey，Mihailescu和Woodbury等在最优扩域上的相应结果。

To the moduli with special forms (such as Mersenne numbers, pseudo-Mersenne numbers, generalized Mersenne numbers), we analysis and study modular arithmetic laws, and obtain the conclusions as follows: for Mersenne numbers and pseudo-Mersenne numbers, we get modular arithmetic formulas, and determine exact expressions of the number of modular addition to generalized Mersenne numbers generated by irreducible monic trinomials and pentanomials.

针对具有特殊形式的模数(如Mersenne数，伪Mersenne数，广义Mersenne数等)，深入分析了其取模运算规律，得到如下结果：对Mersenne数和伪Mersenne数，给出了取模运算转换为模加或模减运算的公式；对模数为任意首一三项式和五项式产生的广义Mersenne数，推导了相应取模运算的复杂度计算解析表达式。

The two fuzzy neural network models are constructed respectively for generalized modus ponens and modus tollens. The paper gives the properties, learning algorithms and inference instances of the two neural networks. And the paper also compares this generalized method with the other inference methods.

传统的区间值模糊集的相容性则度由于结构复杂，从而掩盖了它的一些本质，而且与人的某些直觉不符，为此本文另外提出了一个"相合度"概念，并将两者进行了比较，分别给出了相容度和相合度为1的充分必要条件和直观解释，并首次讨论了模糊推理对相容度和相合度的传播问题。

Firstly the fuzzy entropy in quadratic form is modified by substituting standard negative operator of Zadeh with generalized negative operator of Sugeno, and the generalized fuzzy entropy formula is obtained.

首先将Sugeno广义否定算子替代二次型模糊熵公式的Zadeh标准否定算子，得到了参数型的广义模糊熵表达式；其次，将其应用于构造图像阈值化分割的准则函数；最后，给出了图像阈值化分割新算法中的广义模糊熵参数自动选取方法。

The circulation problem and the generalized circulation problem cover the whole field of the flow analysis about the generalized network flow problem.

环流问题和一般环流问题构成了一般网络流量分析问题。

Based on a new distance, Dave's generalized noise clustering algorithm is extended to non-Euclidean generalized noise clustering model.

利用一种新的距离测度将Dave的广义噪声聚类扩展成非欧氏距离的广义噪声聚类。

The Generalized Kolmogorov Probability generalized the 1st Kolmogorov's axiom and allows the probability values to be within the whole open real interval of (-infinite,+infinite).

广义的柯尔莫果洛夫概率(Generalized Kolmogorov Probability)推广了柯尔莫果洛夫概率三公理的第一公理：概率可在开区间范围内取值。

A systematic study is made on the technology of conflict detection and negotiation in collaborative design from the viewpoint of generalized design constraint network in the dissertation. The main results and originative work are as follows: Research on the model of generalized design constraint network.

本论文从广义约束网络的角度出发，对协同设计中的冲突检测与协商技术进行了系统深入的研究，主要工作和研究成果如下：广义设计约束网络模型的研究。

In this paper, we introduce the concepts of generalized Schur complement and generalized Perron complement, and obtain many important inequalties involing them.

在已有文献的基础上，本文引入并研究了矩阵广义Schur补，广义Perron补，得到了一系列与其有关的重要不等式。

In order to change the situation, this article is to give the definition of an axiomatic generalized real positive definite matrices and make analysis into some of the quality of generalized positive definite matrix under the new definition.

为改变这种现状，本文给出一种公理性的广义正定矩阵的定义，并对新意义下广义正定矩阵的若干性质进行了分析和研究。

Warden: That's a beautiful dog, but don't bring her again.

那是条漂亮的狗，但是不要再把她带来了。

You get up in the morning – no hangover!

你第二天早上起来的时候—不会宿醉！