既约

在古埃及数学中，通常将一个既约分数mn分拆成若干个单位分数之和。

In ancient Egyptian mathematics , the irreducible fraction mn was usually partitioned become a sum of unit fractions .

关于亚直既约环的一些有限条件

Subdirectly Irreducible Rings Where Some Finite Conditions are Satisfied

连续并既约元及其在刻画Fuzzy关系方程解集中的应用复制与拼贴&当今中国油画一瞥

Continuous Join-Irreducible Elements and Their Applications to Describing the Solution Set of Fuzzy Relational Equations Reproduction and Join - Sticking

Gauss整数的既约分解

The irreducible decomposition of Gauss integral number

本文利用既约子环套给出了Fuzzy子环的Fuzzy商环，Fuzzy子环的直和及和Fuzzy子环等概念。

In this paper , the irreducible nested subring is introduced to express the fuzzy quotient ring of the fuzzy subrings , direct summation of fuzzy subring and sum fuzzy subrings .

明确地构造了量子代数Uq（Sl（2））当q＝i和z中心扩张时的两维循环表示，此表示是既约的；

We give explicitly the 2-dimensional cyclic representations of quantum algebra Uq ( sl ( 2 )) with central extension .

第二种通过右互质既约分解，给出了通解关于一组自由参量和矩阵J的特征值的显式表达式。

By utilizing some right coprime fractions , the second solution is given in an explicit form with respect to the free parameter vectors and the eigenvalues of the matrix J.

最佳纠突发错误既约Goppa码的存在性与渐近性

Existence and Asymptote on the Optimum Burst-Error-Correcting Irreducible Goppa Codes

提出一种二块校正既约Hessian方法的非单调信赖域回代算法来解决约束优化问题。

We propose a two-piece update of projected Hessian algorithm with trust region method for solving nonlinear equality constrained optimization problems .

使用广义既约梯度法（GRG法）解非线性规划问题并进行了灵敏度分析。

A sensitivity analysis for nonlinear programming using generalized reduced gradient method ( GRG ) is made .

本文通过讨论除环D上的n次多项式f（x）的既约分解，证明了f（x）的所有左、右零点至多分布于D内n个共轭类中。

In this paper , we discuss the irreducible factorizations of the polynomia f ( x ) of degree n over a division ring D and prove that all the left and right zeros of f ( x ) belong to at most distribution n conjugacy classes of D.

在合理的条件下，算法具有整体收敛性且两块校正的双边既约Hessian投影法将保持超线性收敛速率。

The global convergence results of the proposed algorithm are proved while maintaining fast local superlinear convergence rate is established by performing a two-piece update of two-side projected reduced Hessian .

针对高速公路动态OD矩阵估计问题的特点，建立了两个不同情况下的模型，并设计出基于既约梯度投影混沌的快速算法。

For the characteristics of dynamic OD matrix estimation of freeway , models under two different situations are put forward . A high-speed algorithm based on the Method of Reduced Gradient Projection chaos optimization algorithm is designed .

为求解大规模问题，采用等式约束的Jacobian矩阵的QR分解和两块校正的双边既约Hessian矩阵投影，将问题分解成零空间和值空间两个信赖域子问题。

In order to deal with large problems , QR decomposition of the Jacobian for equality constraint and a two-piece update of two-side projected reduced Hessian are performed into a pair of trust region sub-problems in horizontal and vertical subspaces .

本文提出了解等式约束优化的一个信赖域方法，该方法以既约Hessian逐步二次规划为基础，它享有信赖域方法与既约Hessian方法的优点。

This paper presents a trust region method for solving equality constrained optimization problem . The method is based on the reduced Hessian successive quadratic programming method . The new method shares advantages of trust region methods and reduced Hessian method .

网络既约梯度法在水电系统经济调度中的应用

Application on Network Gradient Method in Economic Dispatch of Hydroelectric Systems

基于广义既约梯度法的航空发动机性能寻优控制

Based on generalized reduced gradient method for aero-engine performance seeking control

有理既约真分式化为部分分式的又一方法

Another Method for Transforming Rational reduced True Fraction into Partial Fraction

广义既约梯度法解非线性规划问题的灵敏度分析

Sensitivity analysis for nonlinear programming using generalized reduced gradient method

线性约束规划拓广的既约梯度法及其收敛性

An extension of reduced gradient method for linearly constrained Programmings

非线性规划的一个既约梯度法

A reduced gradient algorithm for nonlinear progamming with linear or nonlinear constraints

关于广义既约梯度法假设条件的注记

A Note About the Nondegenerate Condition in the GRG Method

一个新的广义既约梯度法及其收敛性

A new general reduced gradient method and its global convergence

既约剩余系的一个性质及其推论

One Property and a Corollary for Reduced Residue System

线性约束不可微凸规划的既约次梯度法

A Method of Reduced . Subgradient for Nondifferentiable Convex Programming uuder Linear Constraints

在既约梯度法中有限性转轴的简化

Simplified finite pivoting processes in the reduced gradient algorithm

不用特殊转轴的既约梯度方法

A convergent reduced gradient method without using special pivot

关于亚直既约环确定的结构空间

On the Structure Spaces Determined by Subdirectory Irreducible Rings

既约剩余系中同阶元的对称函数（Ⅰ）

Symmetric Functions of Elements of the Same Order in Reduced Residue System (ⅰ)

在分子格范畴中乘积的既约性

Irreducibility of Products in Category of Molecular Lattices