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.
本文讨论了三角函数在有理度数上的取值的代数性质，得出其取值均为代数数。
This paper discusses an algebraic property of values of rational degrees of triangle functions. We obtain that they are all algebraic Numbers.
类似于代数数据类型理论，本文提出了对象、对象类型及抽象对象类型的代数模型。
In analogy to algebraic data type theory, this paper proposed the mathematical model of objects, object types and abstract object types.
十九世纪的代数学知识体系庞大，它包含置换群、矩阵、代数数论、代数几何等多个分支。
In the nineteenth century, the system of algebraic knowledge is enormous, which contains the permutation group, matrix, algebraic number theory, algebraic geometry and other branches.
然后着重在代数范围内进行讨论，得到下列的结果：每个有限次实代数数域都不是归纳域；
Then he considers the case of algebraic numbers and obtains some results like the following: Every real algebraic number field of finite degree is non-inductive;
丢番图方程是数论中一个十分重要的研究课题，与代数数论、组合数学、代数几何等有密切联系。
Diophantine equation is an important subject in number theory and closely connected with algebraic number theory, combinatorics, algebraic geometry and computer science etc.
去年冬天，达蒙在人民杂志中谈到和道格拉斯扮演情侣时，“这有点让我回想起我的高中代数数代。”
Damon spoke this past winter about playing lover to Douglas, telling People Magazine, "I kind of think of it in algebra terms, back to my high-school days."
这是一个科学计算库，支持多维数组和线性代数数，在某些计算概率、标记、聚类和分类任务中用到。
This is a scientific computing library with support for multidimensional arrays and linear algebra, required for certain probability, tagging, clustering, and classification tasks.
崔国华(通讯作者)，男，1947年生，教授，博士生导师。主要研究方向：访问控制，密码体制的安全性分析，代数数论。
Cui Guohua, Male, born in 1947, Professor, Supervisor of PhD Candidates. Main research: access control, the security analysis of cryptosystem, algebra number theory.
自相似测度的研究可以追溯到上个世纪30年代，随着研究的深入，人们逐渐发现它与调和分析、代数数论、动力系统及维数的估计都有密切的联系。
The self-similar measure has been studied since 1930's, revealing connections with harmonic analysis, the theory of algebraic numbers, dynamical systems and Hausdorff dimension estimation.
自相似测度的研究可以追溯到上个世纪30年代，随着研究的深入，人们逐渐发现它与调和分析、代数数论、动力系统及维数的估计都有密切的联系。
The self-similar measure has been studied since 1930's, revealing connections with harmonic analysis, the theory of algebraic numbers, dynamical systems and Hausdorff dimension estimation.
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