代数学的

In recent years, derived categories and derived equivalences have been adapted extensively to a number of subjects beyond algebraic geometry, and have become one of the dominant subjects.

由Grothendieck-Verdier在上个世纪60年代提出的导出范畴的概念和建立的理论体系，标志着代数学发展的一个新的里程碑，它架设了代数与几何联系的一座桥梁。

We describe the algebraic characteristic of the public-key cryptosystems based on algebraic structures such as elliptic curves,bilinear pairings,as well as braid group s,with the emphasis on the difficulties of constructing public-key cryptosystems based on non-commutative algebraic structures.

通过分析基于椭圆曲线、双线性对以及基于辫子群的公钥密码体制的代数学特征，着重讨论了构建基于非交换代数的公钥密码体制所面临的困难。

The proof of fundamental theorem of algebra involves much algebra knowledge which is difficult to understand.

代数学基本定理的经典证明用到较多的代数知识，且难以理解，文章探讨用数学分析的方法予以证明。

Providing new insights into classical results and opening avenues for further applications, the book then uses representation-theoretic techniques-especially induction theory-to examine equivariant higher algebraic K-theory, their relative generalizations, and equivariant homology theories for discrete group actions.

提供更进一步的应用的新对古典结果和开的大街了解，书然后使用代表理论技术特别是就职理论检查equivariant高代数学K 理论，他们有关概括，和equivariant 相同理论适合分离的组行动。

Using the theories of probability, algebra, cryptography, Information theory and "Hybrid technique" and "Reduction theory" as tools, and basing on the notion of computational indistinguishability, properties and constructions of DES-model permutations are studied in this dissertation and some useful conclusions are given.

本文综合运用概率论、代数学、密码学、信息论等相关学科的知识及"混合技巧"和"归约论证"思想，以计算不可分辨性为基础，研究了DES型置换的性质和构造，得到较为实用的结果。

The course is a comprehensive introduction to the theory, algorithms and applications of integer optimization and is organized in four parts: formulations and relaxations, algebra and geometry of integer optimization, algorithms for integer optimization, and extensions of integer optimization.

本课程对整数最优化的理论、算法和应用做了全面的介绍。课程分为四部分：公式和松弛、整数最优化的代数学和几何学、整数最优化的算法，以及整数最优化的拓展。

Moreover, by discussing the role of geometrical proof in Ars Magna and Cardano's attitude on irrational number, negative number and imaginary number, the paper points out that the role of geometry in Renaissance algebra had been tending weaker.

同时，通过考察几何证明在《大术》中所起的作用以及卡尔达诺对无理数、负数和虚数的处理，指出在文艺复兴时几何在代数学中的作用己逐渐减弱。

There is reason coefficient polynomial in there is reason few area top can't invite of judge axioms is algebra learned of important problem.

翻译一段数学上的东西，高手帮忙下'''有理系数多项式在有理数域上不可约的判定定理是代数学中的重要问题。

No prior preparation in probability and statistics is required, but familiarity with basic algebra and calculus is assumed.

初次学习本课程的学生不需要具备任何概率与统计学的基础，但要求学生熟悉基本的代数学和微积分知识。

In Chapter Seven, This chapter established on the comparison of the Fibonacci's Liber Abaci, al-Khwārizmī'algebra and al-Karajī's al-Fakhrī.

本章建立在对斐波那契《计算之书》、花拉子米《代数》、以及凯拉吉的《奇妙之事》中代数学比较研究基础之上，分析他们在代数技巧、代数方法有效性的证明方法、未知数设定、二次方程分类、算题选择和设置形式等方面的异同。

I'm strongly against the death penalty — it's an eye for an eye.

我不赞成死刑——这是以牙还牙的报复行为。

And to get you the support you need, we're enlisting all elements of our national power: our diplomacy and development, our economic might and our moral suasion, so that you and the rest of our military do not bear the burden of our security alone.

并给你们所须的支援，我们正徵召国家所有各种的力量：我们的外交及发展，我们的经济力量与道德劝说，所以你们与其他军人不须要孤独地负起国家安全的责任。