二次域

费尔玛下降法在一实二次域中的应用

An Application of Fermat 's Method of Descent to a Real Quadratic Field

给出了实二次域Q（p）当类数等于1时，除去有限个以外，素数p≡1（mod4）的一般表达式。

Except for a few prime numbers , this paper presents a general expression for primes satisfying p ≡ 1 ( mod 4 ) on condition that class number of the real quadratic field Q ( p ) equals to 1 .

关于虚二次域Tame核计算的一个注记

A Remark on Computing the Tame Kernel of Quadratic Imaginary Fields

实二次域上的一个Diophantine方程

A Diophantine equation over real quadratic fields

本文运用Baker方法讨论了一类虚二次域类数的可除性。

In this paper , with the Baker method , we discuss the divisibility of class numbers for a class of imaginary quadratic fields .

给出了实二次域Q（8k+1）~（1/2）上的正定幺模格种类及其邻格关系和邻格链个数。

The positive definite unimodular lattices , the adjacent lattice relations and the number of adjacent lattice chains of the positive unimodular lattices over Q ( 8k + 1 ) ~ ( 1 / 2 ) are given .

一类有关虚二次域理想类群的指数丢番图方程

An Exponential Diophantine equation concerning ideal class groups of imaginary quadratic fields

类数为1的二次域上线性分组码的构造

Codes from Quadratic Number Fields of Class Number One

一类虚二次域类数的可除性和一类著名结果统一的新证明

A new and brief proof of the divisibility result of class number of a kind of imaginary quadratic fields

椭圆曲线与实二次函数域的DLP等价

The Equivalence of Discrete Logarithms between Elliptic Curve and Real Quadratic Function Field

对有限域Eq上某些函数域K（包括全实函数域和二次函数域）给出Minkowski常数Mk。使K的每个分式理想类包含次数≤Mk整理想AOk。

We give a ( Minkowski ) constant MK for several kinds of function field K over Fq ( including totally real function fields and quadratic function fields ) such that each fractional ideal class of the ring Ok of integers contains an integral ideal with degree ≤ Mk.

理想类群指数≤2的虚二次函数域

On imaginary quadratic function fields with ideal class group of exponent < 2

Huber利用二次分圆域的代数整数环构作了面向二维信号且具有代数译码算法的纠错码。

H μ ber use the algebraic integer ring of quadratic cyclotomic field to construct block codes for coding two dimensional signals which are able to correct some error patterns .

将新算法与二次模型信赖域算法、传统锥模型信赖域算法比较得到了较好的数值结果，并证明了新算法的全局收敛性和超线性收敛性。

Compared with them , the new conic model has been relatively good numerical results . And the global convergence and superlinear convergence are proved .

近年来，锥模型信赖域算法的研究引起了专家们的普遍关注，弥补了二次模型信赖域算法的缺陷。

In recent years , the conic model for the study of trust region algorithm has aroused wide spread concern , made up for the deficiencies of quadratic model trust region algorithm .

一个关于二次规划问题信赖域中可行下降算法

A Feasible Descent Direction Algorithm in Trust Region for Quadratic Programming

最后，介绍了序列二次规划和信赖域算法等约束优化方法。

Finally , the sequential quadratic programming and trust region method for constrained optimization are described .

该类算法的基本思想是通过求解一系列二次函数在信赖域中的极小值点逼近最优化问题的解。

The basic idea of these methods is to approximate the optimization problem by a sequence of quadratic minimization problems subject to some trust region .

新生儿暂时性呼吸急促与上皮细胞钠离子通道编码基因多态性之间是否存在相关性：对α亚单位二次跨膜结构域的研究

Is transient tachypnoea of the newborn associated with polymorphisms in the epithelial sodium channel encoding gene ? Investigation of the second transmembrane spanning domain of the α subunit

提出一种基于齐次模型的信赖域算法，传统的基于二次模型的信赖域算法只是它的一个特例。

This paper presents a trust region algorithm based upon the homogeneous model . The traditional trust region algorithm based on the quadratic model is one of its special cases .

在这种算法中，每迭代一次需要计算两次投影：第一次为到可行域上的投影，第二次为到可行域或可行域与一超平面的交上的投影。

Two projections are needed at each iteration with this method . One is onto the domain , the other is either onto the domain or the intersection of the domain with a hyperplane .

然而，对于非二次性态强、曲率变化比较剧烈的函数，二次模型信赖域算法显得力不从心。

But for strong non-quadratic form and the sharp change in curvature function , the quadratic model seems to unable to solve it .