条件方程

Criterions of partial stable matrix and normal form of partial positive definete matrix are given, some conditions of solvability and uniqueness of Lyapunov matrix equation are discussed.

给出了部分稳定矩阵的几种判据与部分位正定矩阵的标准型，研究了矩阵方程可解性、唯一性的几种条件，提出一些可供进一步研究的问题。

In Chapter 3,a hybrid adaptive CGNR algorithm based on the normal equationand polynomial preconditioning is derived.

第三章提出了一个基于法方程和多项式预条件的自适应混合CGNR算法。

By introducing the general notion of nonwandering operator semigroup T and utilizing a basic result in normed linear space,the nonwandering property of T=e~ is investigated with the constructive method.

通过给出一般算子半群T的非游荡性概念，利用赋范空间的一个基本结果和直接的构造法证明了具有变系数的线性发展方程的强连续解半群T=etA在适当的条件下是非游荡的；另外，通过对C-半群T概念的引进，定义了一个无界算子半群etA，进一步证明了这二者关于非游荡性的联系；最后给出了一个无界算子半群etP关于非游荡性理论的刻画，其中P是微分多项式。

A general Godunov finite difference schemes-WENO schemes which had fifth-order accuracy was used to make a numerical calculation for 2-dimensional axis symmetrical laser-supported plasma flow field under laser ablated solid target and laser ablated propulsion efficiency parameters(mechanical coupling coefficient etc.) was obtained by the simulation.The models of the calculation of ionization degree of plasma and the interaction between laser beam and plasma and the simplified eos of plasma were considered in the simulation.

采用针对高温气体电离度的一种近似计算方法，以及具有五阶精度的广义Godunov差分格式-加权本质无振荡格式WENO(weighted essentially non-oscillatory schemes)，给出了高温气体状态方程的简便描述，并考虑激光与等离子体的相互作用，模拟了强激光与固体靶相互作用时激光支持靶面等离子体流场的动态物理过程，并给出了不同参数条件下激光烧蚀固体靶的推进效应参数。

The numerical solutions for different coefficient and different boundary conditions are obtained for two models of radon field which have respectively source in the side and inside of collapse column.

根据流体场的扩散理论和对流理论，建立了扩散系数与对流速度为常量或变量情况下的氡气场三维状态方程；对于陷落柱柱体侧面有源氡气场和柱体体内有源氡气场两种理论模型，给出了不同系数和边界条件下的数值解的形式。

In this paper, we discuss the numerical solutions of the Helmholtz equation with damping boundary conditions:Where G ?

本文主要讨论由时间调和声波产生的具有阻尼边界条件的Helmholtz方程的数值解：其中？

The main results can beexpressed as follows:(1)Based on πtheory, some affected factors about wave forces are given, and therelation between affected factors and wave forces is analysised by experimentalresults.(2) The distribution of wave press at representative time and reflection nature aregiven and their variety charactes are discussed by experimental results.(3)By comparing the wave forces of quarter-circular breakwater and semi-circularbreakwater under the same wave conditions,some approximately wave forcesexpressions of quarter-circular breakwater are given.(4)Based on VOF method to trace water free surface,solve numerical value ofRANS equation,and get the distributions of flow field and wave press ofquarter-circular breakwater at the same time during one period,the mechanism ofwave force is also discussed elementarily.(5) Based on the result that RANS equation of numerical simulation agree wellwith experimental results,a new approach to study hydraulic natures of quarter-circular breakwater is provided.

其主要结论如下：一、通过π定理，确定影响波浪力的无因次参变量，根据试验结果对其影响因素进行分析；二、基于模型试验，给出典型时刻圆弧面防波堤的同步波压分布和反射特性，讨论它们的变化特点；三、通过相同条件下圆弧面防波堤与半圆型防波堤两种堤型试验波浪力的比较，给出了圆弧面防波堤波浪力的近似方法；四、利用VOF法追踪自由水面，数值求解RANS方程，得到圆弧堤堤体周围的流场和压力场，初步分析了速度涡流与压力场的相互影响；五、对比数值分析与试验结果，探讨数值方法研究圆弧面防波堤水力特性的可行性，提供新的研究途径

Stability is one of the most important conditions in which we numerically solve the wave equations.

稳定性是数值计算波动方程的最重要条件之一。

Keywords: Banach space;operator;equation;boundary condition;perturbation.

中文关键词：巴拿赫空间；算子；方程；边界条件；扰动

Numerical simulation example shows that, under satisfying constraint conditions of equation of state, it is feasible to obtain the optimal trajectory by optimal control and genetic algorithm.

数值仿真算例表明，在满足状态方程约束条件下，通过最优控制解法和遗传算法求取最优弹道方法可行。

But we don't care about Battlegrounds.

但我们并不在乎沙场中的显露。

Ah! don't mention it, the butcher's shop is a horror.

啊！不用提了。提到肉，真是糟透了。