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In this note, we prove a congruence relation on real quadratic fields which relates class number and certain character sum.

本文证明了关于实二次域的类数和某类特征和的同余式，同时给出某类实二次域的类数可除性的一个判别法则。

Owing to the importance of Disquisitiones Arithmeticae in histoiy of number theory and the core position of the congruent theory in elementary number theory, this paper is to focus on the following two topics: the origin and development of Fermats little theorem and the quadratic reciprocity law which was hailed as golden by Gauss.

鉴于《算术研究》在数论发展史上的重要性以及同余理论在初等数论中的核心地位，本文重点研究费马小定理和被高斯誉为"黄金定律"的二次互反律的起源和发展。

The first chapter introduces the trust region method , quadratic model and conic model.

第一章主要简介了信赖域方法的基本思想、二次模型和锥模型的研究状况。

In terms of the minimum question of a positive definite quadratic function,a set of Newton directions in minimum points derived with an accurate single dimensional search are used to produce a set of conjugate direction ,and a proof of convergence is presented.

对正定二次函数极小问题，利用精确一维搜索所得极小点处的牛顿方向来生成一组共轭方向，并给出收敛性证明

The path is defined as linear combination of a sequence of conjugate directions whichare obtained by applying standard conjugate direction method to approximate quadratic functionof unconstrained optimization.

Bulteau和Vial在[7]中构造了无约束最优化问题的共轭梯度路径，其基本思想是将标准共轭方向法应用于无约束优化目标函数f的局部二次近似函数，得到一组共轭方向序列。

If the method is applied to a convex quadratic function, conjugate directions are chosen with the goal of accelerating convergence.

直接目标是保证该方法应用于凸二次函数，选择共厄方向来加速收敛。

The decreasing conditions of an energy function are investigated by the use of convex function. By utilization of the primal convex function, the conditions are analyzed under which its conjugate function minus a quadratic function is also convex.

利用凸函数的定义研究了能量函数下降的条件，根据凸函数的性质分析它的共轭函数减去二次函数之差仍为凸函数的条件。

The equation of conservation of momentum is changed into a quadratic equation of a certain physical quantity.

将动量守恒方程变成一个物理变量的二次方程。

Based on the study of the relationship between the bit rate for video coding and the content complexity, this paper presents a new quadratic rate distortion model for video coding, which retains the constant term in Taylor series.

摘要基于对视频编码比特率与内容复杂度之间关系的研究，该文提出了一种新的视频编码二次率失真模型。

This function is a kind of orthonormal function, and it can approximate almost any curve in quadratic continuous integral space, thus it enhances the generalization ability of the SVM.

该核函数不仅具有平移正交性，而且可以以其正交性逼近二次可积空间上的任意曲线，从而提升了支持向量机的泛化性能。

Lugalbanda was a god and shepherd king of Uruk where he was worshipped for over a thousand years.

Lugalbanda 是神和被崇拜了一千年多 Uruk古埃及喜克索王朝国王。

I am coming just now,' and went on perfuming himself with Hunut, then he came and sat.

我来只是现在，'歼灭战perfuming自己与胡努特，那麼，他来到和SAT 。