上解

所得的迭代序列为上解序列和下解序列，它们均单调收敛于问题的准确解，本文建立了这些算法的比较定理。

Any iterative sequence generated by the algorithms is a upper solution or a lower solution sequence , which converges monotonically to the solution of the problem .

极小时间函数是下半连续的且是相依Hamilton-Jacobi方程的粘性上解。

The minimum time function is lower semicontinuous and it is a viscosity supersolution to the contingent Hamilton-Jacobi equation .

他从脖子上解下围巾。

He unwound his scarf from his neck .

Banach空间微分方程在闭集上解的存在性

Thee existence of the solution of differntial equation on the closed set in Banach space

强非退化型在Z／p￣nZ上解的个数公式

A formula for the numbers of solutions of the strongly nondegenerate forms over z / p ￣ nz

提出了一种非结构网格上解HamiltonJacobi方程的自适应局部加密方法。

An adaptive method for Hamilton-Jacobi equations on unstructured meshes is given , the paper presents the key ingredient to choose smooth indicator .

第四章研究了在非结构网格上解Hamilton-Jacobi方程的自适应局部加密方法。

In chapter 4 , we present an adaptive method for Hamilton-Jacobi equations on unstructured meshes .

利用Sobolev插值不等式以及关于时间t的先验估计证明了该方程在无界域上解的存在性；

The Sobolev interpolation inequality and prior estimate on time are applied to show the existence of solution in unbounded domain .

该方法是在粗网格有限元空间■上解一个小的非线性问题，同时在细网格有限元空间■（h■H）上解一个线性问题。

The advantage of this method is that we only need solve a small nonlinear problem on a coarse mesh finite element space ■, and solve a linear problem on a fine mesh finite element space ■( h ■ H ) .

第三章研究非结构网格上解二维Hamilton-Jacobi方程的有限元方法。

In chapter 3 , we study the finite element methods for the Hamilton-Jacobi equations on the unstructured meshes .

给出了种群个体的序和密度定义，在此定义下又给出目标空间中Pareto界面上解的质量度量函数和均匀性度量函数。

The rank and density of the population were firstly defined , and a quality measuring function of solutions and a uniformity measuring function of solutions in objective space were clearly given .

O-code可在物理机上解译（为VM），或从O-code编译为主机的本机语言。

The O-code could be interpreted on a physical machine ( as a VM ) or compiled from O-code to the native machine language of the host .

本文主要讨论了非结构网格上解Hamilton-Jacobi方程的无振荡有限体积方法和局部自适应加密方法。

This thesis is concerned with the non-oscillatory numerical method for Hamilton-Jacobi equations on unstructured meshes . Finite volume schemes and the local adaptive refinement method are included in this thesis .

本文对一类非线性算子的障碍问题提出了几个Schwarz算法，所得迭代序列为上解序列或下解序列，它们单调收敛于问题的准确解。

In this paper , we propose several Schwarz algorithms for obstacle problems with a type of nolinear operators . Any iterative sequence generated by the algorithms is a super-solution or a lower-solution sequence , which converges monotonically to the problem .

借助于前一章的非结构网格上解Hamilton-Jacobi方程的ENO思想，构造结构网格上的无振荡数值格式，并研究与这种格式相匹配的自适应局部加密方法。

By using the ENO philosophy on unstructured meshes in chapter 4 , we construct the non-oscillatory numerical schemes with high order accuracy on structured meshes . The local adaptive refinement method is developed for local regions where the solutions of the Hamilton-Jacobi equations vary sharply .

利用不动点定理得到了带脉冲的奇异边值问题的上解和下解方法，并且给出了带脉冲的Emden-Fowler方程奇异边值问题正解存在的充分必要条件。

We obtain the method of lower and upper solutions to the impulsive singular boundary value problems using the fixed point theorem and give necessary and suffcient condition for the existence of positive solutions to the impulsive singular boundary value problems of Emden-Fowler equations .

任意四边形网格上解辐射输运方程的一种数值方法

A Numerical Method for Solving Radiation Transport Equation on Lagrangian Mesh

于是猎人又花了一天时间把网从锐利的荆棘上解下来。

So he spent a secondday unhooking his net from sharp thorns .

他从脖子上解下围巾。

He unwound the scarf from his neck .

我从表链上解下手表。

I detached my watch from the chain .

他从绳子上解下捅，把钩子系到绳子上。

He untied the bucket from the rope and tied the hook to the rope .

她从头上解下那条褐色纱巾，把它围在他的脖子上。

She unwound the brown veil from her head and tied it about his throat .

我说着从身上解下救生带，递给了她。

While I spoke I had pulled off the life-belt and held it out to her .

本文提出在玻尔兹曼网络上解旅行商问题的一种有效方法。

An efficient method for Solving Travelling Salesman Problems ( TSP ) on Boltzmann machine is presented .

本文研究了稀疏矩阵技术在微型机上解电力网络的节点方程组。

The node equation set of the electric network is solved on a microcomputer with sparse matrix technique .

工程师把电线从线圈上解下来。议事日程上的下一个项目是妇女解放。

The engineer wound the wires off . The next item on the agenda is women 's liberation .

人们利用相关的技术手段，可以从遥感影像上解译出丰富的大量信息。

A wealth and rich of information can been interpreted from remote sensing images used some technical means .

我从那孩子的肩上解下书包。这个问题得放到下次会上解决。

I unburdened the boy of his satchel . We have to spread the issue over next meeting .

定义并研究了加权形式的A调和方程的很弱解，很弱上解和很弱下解。

Define and consider very weak solutions , very weak supersolutions and very weak subsolutions for weighted A-harmonic equations .

中央本级收入32671.99亿元，地方上解收入939.93亿元。

This consists of3.267199 trillion yuan directly collected by the central government and93.993 billion yuan turnedover by local governments .