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For the first patern, elastic dynamics is adopted to study the steady state rolling contact, elastic dynamics incorporating with rigid dynamics is adopted to study the non-steady state. For the steady state, the analytical solution is obtained, and for the non-steady state, the variational formulation to solve the problem numerically is derived For the later patern, the function type friction coefficient is introduced. On the basis of the quasi-stastic theories of constant friction coefficients, both the exact theory and the simplified theory of the function type friction coefficient are established, the computer programms for both the theories are also made out. Using the function type friction coefficient, Shen-Hedrick-Elkins theory's application range is extended to large creepage .

对于速度对接触体力学特性的影响，本文采用弹性动力学方法和弹性动力学与刚体动力学相结合的方法分别对稳态和非稳态两种情况进行了研究，得到了稳态情况的解析解，给出了对非稳态情况进行数值求解的变分公式；对于速度对相关物理量的影响，本文主要讨论了速度对摩擦系数的影响，在滚动接触准静态理论的基础上引进了函数型摩擦系数，建立了函数型摩擦系数的滚动接触准静态精确理论和简化理论，并分别编制了相关的计算程序，还用函数型摩擦系数将简便的Shen-Hedrick-Elkins理论的适用范围扩展到大蠕滑区。

The long-term seepage control effects of the surrounding rocks of the underground powerhouse are performed by a stationary seepage analysis method combining the variational inequality formulation of Signorini's type with an adaptive penalty Heaviside function to guarantee the numerical stability and convergence. Meanwhile, the difficulty in finite element mesh generation is reduced and the calculation time and modeling accuracy are balanced with a global model of equivalent modeling and a submodel of accurate modeling for drainage hole array.

为确保数值计算的稳定性和收敛性，采用Signorini型变分不等式和自适应罚函数相结合的稳定渗流分析方法，对厂房围岩的长期渗控效应进行计算分析；同时，采用基于等效模拟的整体模型分析和基于精细模拟的子模型分析相结合的方法，以减小有限元建模难度并协调计算量和计算精度之间的矛盾。

In this paper, an united variational inequality model of instantaneous dynamic user optimal problem is proposed.

本文建立了瞬时动态用户最优配流问题的变分不等式模型。

We give a modified algorithm to solve a kind of variational inequality.

4我们给出一个改进的算法求解一类变分不等式。

Hence, it is necessary to study the well-posedness for variational inequality to judge the stability of the sequence of solution.

因此有必要研究变分不等式的适定性来判断序列解的稳定性。

As special cases,some existence results of solutions to implicit vector variational inequality are presented.

作为特殊情况，给出了隐式向量变分不等式解的存在性结论。

The neural networks of the linear variational inequality are studied.

给出了一个解线性变分不等式问题的神经网络。

At last,we conclude the essay and put forward to some new questions and ways by which may be solved(variational inequality and functional analysis).

在文章的最后，对本文进行了总结，并且提出了一些新的问题以及可能解决的方法(变分不等式结合泛函分析的方法)。

In this dissertation, two problems in the variational inequality theory are mainly considered: the existence of solutions and the approximation schemes.

本文主要讨论了变分不等式理论中的两个方面的问题：解的存在性问题以及解的逼近问题。

Chapter 1 is the introduction of this dissertation, which introduces the variational inequality problem and the complementarity problem, the context of this dissertation and the main results obtained in this dissertation.

第一章是绪论部分，简单介绍了变分不等式与互补问题，本文所研究的内容，以及本文的主要工作。

The split between the two groups can hardly be papered over.

这两个团体间的分歧难以掩饰。

This approach not only encourages a greater number of responses, but minimizes the likelihood of stale groupthink.

这种做法不仅鼓励了更多的反应，而且减少跟风的可能性。