实数域

当V是实数域上的有限维向量空间，g（x，y）是正定对称纯量积时，本文给出了用矩阵的初等变换得到笛卡尔基的方法。

When Visa finite dimensional vector space over the field of real numbers , g ( x , y ) is a positive definite symmetric scalar product , This article gives a method to get a Cartesian basis by the elementary transformations of matrices .

其发展经历了由线性到非线性，由各向同性到各向异性扩散，由实数域到复数域的发展。

Its development experiences liner to nonlinear stages , isotropic to anisotropy stages and real domain to complex domain stages .

关于超实数域R的基数的一些注记

Notes on cardinal number of the hyperreal number field R

从超实数域R到R内的函数的两种连续性

Two kinds of continuity of functions from hyperreal number field R into R

超实数域R的序型

Order types of hyperreal fields

设F是域，R为实数域，本文主要研究交错阵的两个线性保持问题。

Let F be a field , R be a real field , this paper mainly studys two linear preserver problems on alternate matrices .

在超实数域R~上对Abel第一定理的扩充

The extended Abel theorem I over the field of hyper-real numbers

在实数域上，构造了三个拓扑空间：左闭拓扑空间E、右闭拓扑空间G、无限拓扑空间F。

In the real line , three topological spaces , which are the left shut topological space , the right shut topological space and the limitless topological space , are constructed .

实验证明，新的绘制标准不仅可以产生经典的Julia集图案，而且还可在实数域上设计出了精美的计算机艺术图形。

The new method generates not only classical Julia sets but also many brand-new beautiful computer art graphics in the Real Field .

当然，若将此文的R2（复数域）限制为R1（实数域），则（特殊地）适于实变量正、余弦函数的讨论。

Yet if R2 in this paper is confined to R1 , special field can apply to ( co ) sine with real variables .

与Fourier变换相比，Hartley变换以其实值变换的特点，在实数域能够替代Fourier变换，进行信号和图像的处理。

Because of the real number transform characteristic of Hartley transform comparing with Fourier transform , the signals and images in the real number area can be processed using Hartley transform instead of Fourier transform .

本文发展了Cantor用基本列构造实数域的理论，提出超基本列的新概念；

This paper develops cantor 's theory of making real numbers field with cauchy sequence . It put forwards the new concept of hyper cau - chy sequence .

该方案将Chebyshev多项式的状态空间扩展到实数域，从而利用Chebyshev多项式的半群特性构成具有单向带陷门的公钥加密算法，同时又可以避免上述已知密文的攻击。

In the paper we extend the state space of Chebyshev polynomials to the real number domain , employ the semi-group property of Chebyshev polynomials to construct a one-way door-trap function , and avoid the attack .

通过研究我们知道，一个系统只要在结构上（多元有理函数域（F（z））上）是能控能观的，则意味着实数域上该系统实际上总是能控能观的。

And we know by study , so long as system is controllable and observable at the structure ( over the field F ( z ) of the rational functions in multi-parameters ), it is always controllable and observable over the field R of real numbers .

浅谈实数域上的拓扑空间

Simple Discussion on the Topological Space on the Real Number Field

三元数及其在实数域上三维代数

Tri-ary numbers and the tri-dimensional algebra in the real fields

广义实数域上间断函数的微商

The Derivative of Discontinuous Functions Defined on Generalized Number Domain

实数域上从正交群到一般线性群的同态

Homomorphisms from Orthogonal Groups to General Linear Groups over the Real Number Field

在超实数域上对自治系统全局渐近稳定性的扩充

The expansion of hyper-global asympotic stability of autonomous system in hyper-real number region

关于实数域上矩阵的相似标准形

On the canonical forms for matrices over real numbers

基于进化策略的实数域准零相关区序列生成算法

Algorithm for real number space quasi-zero correlation zone sequences based on evolution strategy

超实数域R~的性质

The Property of Hyper - Real Numbers R

发现在实数域范围内本文所研究的系统存在着分形和尺度变换特性，存在着整体或局部相似的菱形结构。

The fractal pictures show a global or local similar structure of diamond shape .

实数域内矩阵的特殊分解

The Special Decomposition of Matrix on Real Range

实数域上一类凸灰子集及其性质

A Class of Convex Gray Subset in the Real Number Field and Its Quality

在超实数域上对标准分析的级数判别法中不定型的区分

Specification of indefinite form about decicion method of series of standard analysis at field hyper-read numbers

实数域上有限可除代数矩阵空间保幂等的线性算子

Idempotent preserving linear maps of matrix spaces of finite dimensional division algebra over real number field

研究实数域上亏损矩阵的幂的算法。

In this paper , the power of a defective matrix in real number field is studied .

这里，本文将运用统一的方法对实数域和复数域上的多元三次多项式的分解问题加以讨论。

By using unified method , we investigate decomposability of real or complex cubic polynomials in several elements .

因此，我们在研究不相容问题[1]时首先考虑实数域上的关联函数。

When we study incompatible problems , the dependent function of the real number field must be considered first .