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However, in the algebraic representation of this theory, it is difficult to understand the essence of rough set theory, and efficient algorithm of knowledge reduction has not been found.

该文首先建立了知识与信息之间的关系；然后，在此基础上给出了粗糙集理论中概念与运算的信息表示；最后，证明了知识约简在信息和代数两种不同表示下是等价的。这些结论有助于人们深刻理解粗糙集理论的本质，同时，为寻找高效的知识约简算法奠定了基础

In order to study the numerical method to solve the viscous incompressible flow with free surface, the 3-D mathematical model for steady and unsteady hydrodynamic problem had been established and closed by k-εbuoyant turbulence model. The algebraic coordinate transformation method was used to fit the free surface, the Runge-Kutta method of three step and second precision was devised to simulate the time step. A high precision up-winding compact scheme was studied for the convection term, and the generalized conjugate residual method was set to solve the Poisson equation.

为了研究粘性不可压缩三维问题的数值求解方法，本文从基本的Navier-Stokes方程出发，采用代数拟合方法处理自由表面，用三级二阶Runge-Kutta方法对时间步进过程进行了模拟，并且对对流项的高精度迎风格式进行了研究，给出了求解压力Poisson方程的广义共轭剩余法，从而建立了能够模拟有自由表面的粘性不可压缩问题的定常、非定常三维水动力学模型，并采用k—ε浮湍流模型对其进行封闭。

An algebraic construction method for LDPC codes with 8-girth is proposed based on complete residue system.

最后，在分析、研究现有构造方法的基础上，基于代数中的完全剩余系，作者提出了一种代数构造方法，使得LDPC码对应因子图上的围长为8，并采用计算机对其性能进行了仿真，结果表明该码能够取得比较理想的译码性能。

The Riemann- Jacobi inversion is discussed to yield the final expression of explicit solution by means of the Riemann theta function, which is directly related to algebraic geometry.

为了最终生成由θ函数所给出的显式解，我们讨论了Riemann-Jacobi反演，这一过程直接关系到代数几何。

It introduces partial fractions of meromorphic functions, product developments of entire functions, Hadamard's theorem, Riemann Zeta functions, Poisson-Jensen's formula; elliptic functions, including simply periodic functions and doubly periodic functions; algebraic functions and algebroid functions, Riemann surface, Nevanlinna theory, including characteristic functions, the first and second fundamental theorems, growth orders, etc; complex differential equations and complex functional equations, etc.

具体为：亚纯函数的部分分式、整函数的无穷乘积展开、Hadamard定理、Riemann Zeta函数、Poisson-Jensen公式；椭圆函数，包括单周期函数、双周期函数；代数函数和代数体函数、Riemann曲面简介；Nevanlinna理论简介，包括特征函数、第一和第二基本定理、增长级等；复微分方程和复函数方程，等等。在教学内容上充分体现基础性、新颖性。

Maximal Z-order ; relative K_1 group; excision; ring of algebraic integers.

基础科学，数学，代数、数论、组合理论极大z-序；相对K_1群；切割；代数整数环

To solve the problem of robust stability test of the systems, we develop a 2-D algebraic test for stability of time-delay systems with an edge test set based on Kharitonov vertex polynomials.

为解决这一类系统的鲁棒稳定性问题，我们提出时滞系统棱边鲁棒稳定性的2-D代数检验，该检验基于由Kharitonov端点集合构造的棱边集合。

Since the Schr〓dinger equation is very difficult to be solved for the moleculescontained relatively more atomes, the algebraic approach is more efficient.

由于对原子数较多的分子，其薛定谔方程的求解非常困难，因此处理这一问题的比较有效的方法是代数方法。

In the secondary modeling,"Hidden Euler" approach is applied to solve the nonlinear simultaneous differential equations, and the discrete nonlinear algebraic equations are calculated by "Newton-Raphson" numerical approach.

二次建模时，采用隐式欧拉法求解常微分方程组，离散后形成的非线性代数方程组采用牛顿-辛普生方法进行计算。

A set of simultaneous, linear algebraic equations results for the entire structure, in which the structural displacements are unknowns.

阿的同时，线性代数方程的整体结构，在这种结构位移未知结果集。

Chrysanthemum of 10 thousand birthday is lax to edaphic requirement, with the arenaceous qualitative loam with fecund, good drainage had better.

万寿菊对土壤要求不严，以肥沃。排水良好的砂质壤土为好。

He unstepped the mast and furled the sail and tied it.

他拔下桅杆，把帆卷起，系住。