代数化

The elastic wave scattering of a cylinder with inhomogeneous interface properties is studied by use of wave function expansion method.

该文研究了这一问题，通过沿周向的离散化将弹性波散射的边界条件归结为一个超定线性代数方程组。

Analysis for testability is widely used in DFT and test pattern generation, but most testability analysis algorithms have the shortcoming of either inaccuracy or being too complicated. A new method to calculate the signal probabilities of the nodes in IC is pre-sented in Chapter 7 of this dissertation. The signal probabilities by our method is more exact than by the previous ones. A symbol of the signal probability at the fan-out node is created and is propagated to the RFON (Reconvergent Fan-out Nodes). At the RFON, the expression containing the symbol is simplified using the rule which corresponds to the law of identity in Boolean algebra. After the expression is simplified, the symbol is substituted with its numeric value. Theoretical analysis shows that this method is concise and has a low computing complexity.

可测试性分析在可测试性设计和测试生成中都有着广泛的应用，然而大部分的可测性分析方法都存在不精确或者过于复杂的毛病，在第七章中作者提出了一种新的计算IC电路节点的信号概率值的符号算法，该算法得出的信号概率值比用以往的算法法得出的要更准确，也更简洁，针对电路中的扇出节点重汇聚现象，我们在每一个扇出节点定义了一个信号概率的符号，在以后的计算中一直使用该符号参与计算，直到该符号传播至重汇聚处，利用一定的规则把含符号的表达式化简，再将符号的真实值代入，在计算符号概率的过程中定义了一个和布尔代数中的同一律相对应的运算规则，通过该运算规则，使得信号概率的结果更加准确，符号算法具有简洁方便，计算复杂度小的特点 4。

As we know, the resulting algebraic equations are large systems of non-linear equations with the expanded mixed finite element method for the equation.

用扩张混合有限元方法对其进行离散是常用的方法，其离散化所获得的代数方程组是一很大的非线性方程组。

It includes the definition of two basic operations, logical functions expansion and matrix formulation in OR-Coincidence algebra system, and the introduction of map expression--dj map, the complete research of the relations among CRM expansion^ maxteim expansion and RM expansion, iiamely tie relations among dj map, K-map and bj map, also includes the minimization of CRM expansion in fixed and mixed polarities-Meanwhile this dissertation points out the form and properties of basic symmetric function, simple symmetric function and basic CRM symmetric function in OR-Coincidence algebra system, discusses the relations and transform methods among the coefficients of the three kinds of symmetric functions.

包括连和与加合两种基本运算的定义，逻辑函数在或、符合代数系统里的展开式及矩阵表示式，展开式图形表示--d_i图的引入，对CRM展开式和最大项展开式、RM展开式，d_i图和K图、b_i图之间的关系及转换方法进行了较为全面的研究，以及CRM展开式在固定极性和混合极性下的最小化问题。

Based on the Saint-venant equations describing the channel flow movement, the nonlinear algebraic equations derived by the use of Preissmann weighted implicit four-point scheme are solved with the Netwon-Raphson method. A combined Gauss main-element elimination method with compress-storage technique is proposed. The relaxation iterative method for solving branch river networks is extended, which can turn the problem of any complex river networks into the problem of a series of single rivers. The coupling of hydraulic model with water quality model is built up. The combined model was applied to a large complicated river networks with numerical hydraulic structure which influenced by strong tide, storm and heave rain. Visualization of computational results is realized by means of MapInfo, which displays the computational results in fast, convenient and accurate way.

水力模型以描述河道洪水波运动的Saint-Venant方程组为基础，用Newton-Raphson方法直接求解按Preissmann加权四点格式进行离散所得的非线性代数方程组，提出了压缩存贮形式的Gauss列主元消去法并对数值解的收敛性进行了讨论；将支流流量的松弛迭代方法从树状河系推广到了环状河网，使任意复杂河网水力计算的问题都可化为一系列的单一河道的水力计算问题；建立了水力模型与水质模型的联接，初步应用于既有洪水、暴雨、强潮等综合影响，又存在多种水工建筑物及水力调度问题的大型复杂河网中的非恒定流水力、水质计算问题；利用MapInfo对计算结果的可视化进行了研究，有利于决策者快速、方便、准确地作出决策。

The powerful function of a new computer language MATLAB, produced by the America Mathworks company, is the mathematical software system for the calculation in science engineering. It can efficiently solve problems in science and engineering such as numerical linear hypercomplex system, digital approximation, optimization, numerical quadrature etc. It also has characters of beautiful interface and convenience for users.

MATLAB是Mathworks公司推出的适用於科学和工程计算的数学软件系统，可高效地解决数值线性代数、微分方程数值解、数值逼近、最优化、数值积分等科学和工程问题，且具有可视化图形处理、使用方便、开放式多功能於一体的新一代计算机语言。

Using this method,we discussed for generalized Burger equation with variable coefficients and linear danping,obtained its symmetry group,simliar reduced equations,infinitesimal generator and Lie algebras;In chapter 6,using the Exp-function method,the generalized solutions of combined KdV-mKdV equation with variable coefficients are discussed.

首先介绍了Lie群分析法的基本思想，其次用Lie群分析法得到了带线性阻尼项的变系数广义Burgers方程的无穷小变换、无穷小算子的李代数结构，并具体求出了带线性阻尼项的变系数广义Burger方程的群不变解和约化方程。

Symmetric cone complementarity problem; Euclidean Jordan algebra; C-function; Merit function; Hybrid Newton method; Regularized-smoothing method

对称锥互补问题；欧几里得若当代数；互补函数；价值函数；混合牛顿算法；正则光滑化牛顿算法

This course mainly consists of 4 parts:1.Logical algebra and logical simplification, Karnaugh Map and Q-M approach.

本课程由4部分组成，分别是：逻辑代数与逻辑函数化简、组合逻辑分析与设计、同步时序逻辑分析与设计、可编程逻辑设计。

In this paper the Karnaugh map for simplifying logic functions is used in computing canonical covers based on the equivalence between the theory of functional dependencies and logic algebra.

本文依据函数依赖理论与逻辑代数对应部分的等价性，引入化简逻辑函数的卡诺图法求函数依赖集的规范覆盖。

In the negative and interrogative forms, of course, this is identical to the non-emphatic forms.

。但是，在否定句或疑问句里，这种带有"do"的方法表达的效果却没有什么强调的意思。

Go down on one's knees;kneel down

屈膝跪下。。。下跪祈祷