代数数

两类代数数域的化简

The reduction of two classes of algebraic number field

主要把欧拉函数推广到全矩阵环M（Ok，n）上，其中Ok为代数数域K的整数环。

The Euler function is generalized over the full matrix ring M ( Ok , n ), where Ok is the integral number ring of the algebraic number field K.

有理数域Q的有限次扩域K叫作代数数域，数域K的所有代数整数构成一个环，称为K的代数整数环，记作ZK。

The finite extension K of Q is called algebraic number field .

代数数域上多项式的一个性质和Heisenberg群上算子的局部可解性

A Property of Polynomials with Coefficients Being Algebraic Numbers and Its Application to Local Solvability on the Heisenberg Group

利用Sturm定理和二分法，给出一类代数数的快速展开计算密钥流的算法。

A rapid digits expansion algorithm of algebraic number was built to calculate stream cipher using Sturm 's tool and dichotomy .

我们研究了代数数系数的缺项级数的代数点上的值，推广了Mahler的一个定理。

We studied the values of the lacunary series with algebraic coefficients on the algebraic points , and got a theorem which generalized one of Mahler 's.

得出了代数数根界的一个基于结式的有效实现算法，并且已用计算机代数系统MAPLE在微机上实现。

In this paper , we have given a new effective algorithm for root bound of the algebraic expression based on the resultant of the algebraic polynomial , also , with MAPLE ′ s help , we have realized this new algorithm in our microcomputer .

嵌入定理与代数数域上的大筛法

Imbedding theorems and the large sieve method in algebraic number fields

用实数卷积计算代数数域上整数卷积

On the calculation of integer 's cyclic convolution over algebraic number fields

实代数数符号判定的一种新算法

A New Algorithm for Determining Sign of Real Algebraic Numbers

关于代数数域的扩张次数

On the Degree of Extensions of Algebraic Number Field

一类实代数数的简单连分数展开式的算法

Algorithm to Compute Ordinary Continued Fractions for a Kind of Real Algebraic Numbers

代数数域中的均值定理

The mean value theorem in algebraic number fields

代数数域上的指数和的估值

On exponential sums over an algebraic number field

一类代数数的连分数表示的一个算法

An algorithm for continued fractions of algebraic number

多项式与一类代数数域域元素的判别式的闭形式

Closed Form of Discriminants about Elements of Some Type of Algebra Fields and Polynomials

基于最大根方法的实代数数符号判定算法

Algorithm for Determining the Sign of Real Algebraic Numbers Based on the Maximum Root Method

并用结式的基本理论给出了求代数数根界的一个有效算法。

And also got a new constructive root-bound algorithm based on resultant for algebraic expression ;

还证明了很多有限次代数数域不与上述的超积初等等价。

Also , it is proved that many algebraic number fields of finite degree are not elementarily equivalent to the above-mentioned ultraproducts .

对一类特殊的实代数数：可以分成二部分之和，且其中一部分为它定义多项式的最大根，另一部分的相反数也是它定义多项式的最大根进行了研究。

We have proposed an algorithm for determining the sign of the real algebraic numbers , which can be divided into two parts . Both can be the maximum root of their definitional polynomials .

现以2+3这个四次实代数数为例，给出一类实代数数简单连分数展开式的算法。

In the paper , taking the degree 4 real algebraic number 2 + 3 as example , for a kind of real algebraic numbers , we give an algorithm to compute their ordinary continued fractions .

利用对代数数序列的极限超越性的分析，我们给出了Mabler关于缺项级数超越性定理的一个推广。

Using the analysis on the transcendency of the limit of a sequence of algebraic numbers , we gave a generalization of a theorem of Mahler on the transcendency of the value of a lacunary power series .

迁移理论中一类算子实本征值的代数重数

The Index of Real Eigenvalues to some Operators in the Transport Theory

初中代数有理数程序教学实验研究

An experimental research on programmed instruction of rational number

由于工具有普通代数中数1的性质，称它为幺矩阵。

Since I behaves like the number 1 in ordinary algebra it is called the identity matrix .

进一步分析系统算子和其生成半群的谱性质，可证得该半群是拟紧的，并且0是孤立的代数重数为1的简单特征值。

In terms of the spectral properties , the C0-semigroup can be proved to be quasi-compactness and 0 is an isolated eigenvalue with algebra multiplicity one .

到14世纪，中国数学家们在代数、数的方程解答和基础二项式定理方面都取得了重大发展。

And by the 14th century Chinese mathematicians had made significant advances in algebra , in the numerical solution of equations and in the rudiments of the binomial theorem .

第三节中研究对应于该排队模型主算子的谱特征，得到0是该主算子及其共轭算子几何重数与代数重数为1的特征值。

In Section 3 we will study spectral properties of the operator corresponding to the queueing model . We will obtain that 0 is an eigenvalue of the operator corresponding to the model with geometric and algebraic multiplicity one .

EI代数的阶数

Orders of the EI algebra

蓖麻油长期抗鼠生育效果明显，在210d（正常小鼠的妊娠期是21~23d）内有效降低小鼠生育代数与产仔数，生育抑制率达80%以上。

In the field of long-term antifertility , castor bean extract is of good effect which decreased mice 's production and generations within 210 d ( mice 's normal gestation period is 21 ~ 23d ) .