实数集

在实数集上构造具有紧支集的n阶可导函数

Construct n-order differentiable function with compact support in set of real numbers

混沌系统对初始值十分敏感，在实数集上有着遍历性且长期不可预测，因而混沌序列有着良好的密码学特性。将混沌序列与AES算法结合可以有效地弥补原始AES算法的不足。

Chaotic system is very sensitive to the initial value and ergodicity on the set of real numbers as well as long-term unpredictability , thus the chaotic sequence has good cryptographic properties .

实数集R上一类拓扑&数列拓扑及若干性质

A class of topology on real number set r-sequence topology and some properties

Ⅲ、本文证明了：1、标准实数集R的测度为0；

ⅲ 、 The paper proves : 1 . The measure of the standard real number set R is equal to 0 ;

本文主要给出实数集R上的一般Fuzzy集关于算子（·V）的四则运算的作图方法。

In this paper , a graphical method is proposed for realizing the four fuzzy fundamental operations of operator (· v ) in real number field R.

最后本文还给出一个如何判断定性推理系统与实数集R是否存在同态映射的充分条件。

Finally , a sufficient condition which can decide whether there exists a homomorphism between a qualitative reasoning system and R ( real number set ) is presented .

文章利用不等式方法证明了幂平均数M（K）关于K在整个实数集上是单调上升的，并在此基础上将统计平均数加以推广。

This paper shows that the power mean is ( monotonic ) increasing about K on the set of real number using the inequation . Based on this the authors expand the concept of average .

fuzzy数集中这一种度量结构除具有myope拓朴所保持的实数集的重要性质外，还真有其它好的性质。

Besides having some important properties of real number set , which myope topology possesses , in fuzzy number set , it has other good properties .

用实数集R+上一个含幺Abelian半群的性质来研究n/2/P/Cm浕x调度在一类过程摄动下的鲁棒性。

In this paper , the robustness of the n / 2 / P / C_ ( m ɑ x ) scheduling problem is studied by using a property of Abelian semi-group which containing identity element on the real number set R ~ + .

实数集上的一个变换群的结构

The Structure of a Transformation Group on the Set of Real Numbers

实数集的上确界公理用到了实数集的子集，这是一种二阶逻辑的陈述。

The supremum axiom of the reals refers to subsets of the reals and is therefore a second-order logical statement .

模糊变量是描述模糊现象的数学方法，它被定义为一个从可能性空间到实数集的函数。

Fuzzy variables are mathematical descriptions for fuzzy phenomena , and are de-fined as functions from a possibility space to the set of real numbers .

从实数集的完备性的公理出发到讲解“实数理论”的一系列定理及用这些定理证明的后继定理都应该突出“实数集的完备性”。

The Real Number Completeness should be highlighted from the completely recognized theory of the real number collection to the explanation of a series of definitions in the Real Number Theory .

同时，采用非负实数集作为时间域还使我们可以利用标准的存在量词来表示变量隐藏，并可用逻辑蕴涵来表示反应系统间的求精关系。

In addition , the use of non-negative real numbers as time domain enables us to express hiding of variables as standard existential quantification and express the relation of refinement between reactive systems as implications between logic formulas .

分别利用区间的中值和Hausdorff测度将基于记分函数的实数型Vague集的相似度方法扩展到i-vVague集上，比较各种方法的优缺点。

The paper developed similarity measure of real number vague sets based on score function to i-v Vague sets by using the mean of interval number and Hausdorff metric respectively , and compare the advantage and disadvantage of different methods .

广义模糊实数及其水平集

Generalized Fuzzy Real Number s and Level Sets

研究广义模糊实数及其水平集之间的关系。

The relationship between the generalized fuzzy real number and its level set is studied .

建立了广义模糊实数及其水平集之间的关系，证明了一些重要性质。

The relationship between the generalized fuzzy real number and its level set is established and some properties concerned are proved .

利用已有的模糊数的定义，引入广义模糊实数及其水平集的概念，定义了广义模糊实数的加、减、乘、除运算和序。

Based on the usual fuzzy real number s , the concept of generalized fuzzy real number and its level set is introduced . The partial order and the operations of these numbers such as sum , minus , product and division are also defined .

负实数阶广义J集的演化

The Evolution of the General Julia Sets for Negative Real Index Number

正实数阶广义J集的嵌套拓扑分布定理

The Overlapping Embedment Topology Distribution Theorem of the Generalized J Sets for Real Index Number

点集拓扑的实数背景在点集拓扑教学中的作用

The Role Played in Teaching by Real Number Background of Point Set Topology

将这两种方法进行了推广，给出了一系列正实数阶广义M集的内部结构图。

The internal structures images of the general Mandelbrot sets for positive integer index number are symmetry and fractal .

研究表明：（1）负实数阶广义M集的内部结构具有分形特征。

The researches showed the following results : ( 1 ) The internal structure images of the general Mandelbrot sets for negative real index number have the fractal feature .