变分问题

In chapter three, we prove that there exist solutions to the Ky Fan variation inequality, as the set-valued mappings are defined on spheres in infinite dimensional Banach spaces or odd dimensional Euclidean spaces, following from these theorems, we obtain some fixed point theorems for set-valued mappings defined on a sphere. When G is an approximate compact convex subset of E, or G is a almost quasi-convex set-valued mapping, we prove that there exist solutions to and type generalized Ky Fan variation inequality, following these theorems, we prove several best approximation theorems and coincidence theorems involving two set-valued mappings and two different spaces. In chapter four, we first present a new Simplicial algorithm for computing the Leray - Schauder fixed points, the algorithm can solve the set-valued nonlinear complementarily problem. We give a condition to guarantee the computation proceeding in a bounded region. We present integer-labeling algorithms for computing fixed points of some set-valued mappings, the best approximation points and solutions to a kind of set-valued variation inequalities.

第四章给出了计算定义在非凸集上的非自映射的Leray-Schauder不动点的算法，而现有的不动点算法都是计算凸集的上半连续集值自映射的不动点；给出了保证计算有界的一个充分条件，我们的条件大大弱于Mdrrill条件，我们的算法也可用来计算Eaves不动点；给出了集值非线性互补问题存在解的一个充分条件，此时可利用Leray-Schauder不动点算法来求解；向量标号算法以往是计算集值映射不动点的唯一有效算法，我们给出用整数标号算法计算一类集值映射的Kakutani 不动点的算法；定义在紧凸集上的连续映射不一定有不动点，但一定有最近点，最近点是不动点概念的推广，我们给出了计算最近点的算法；集值映射变分不等式尚无有效的求解算法，我们给出求解一类集值映射变分不等式的算法。

From the ergodicity and the regularity of chaotic behavior,it is conclude that the algorithm has the asymptotical convergence property.

基于变分不等式的等价形式，构造了一种混沌搜索算法来直接求解变分不等式问题，根据混沌行为的遍历性和规则性，可以得到算法的渐进收敛性。数值试验结果表明，该算法是一个有效的方法

We re-examine a problem about action principle which may be easily ignored in the end. After some detailed study, we find that it is correct to do variation of the action with respect to scale factors for Bianchi IX model up to some higher derivative Lagrangian corrections.

我们最后重新检验了在变分法里头容易被忽略的一个问题，最后我们发现，在Lagrangian放入一些高阶修正项的Bianchi II， VIII， IX模型都可以直接对尺度因子变分而得到正确的场方程式。

We also introduce and study a new system generalized nonlinear variational inclusions for fuzzy mappings in Hilbert space.

我们利用极大单调映象的预解算子技巧，建立了这类模糊映象的变分包含组与非线性集值映象的不动点问题之间的等价关系，再利用Nadler的不动点定理给出了这类变分包含组的解的存在性定理。

Using the generalized mixed variational principle of elastic mechanics, GMVP of Reissner plates is derived, and generalized mixed finite elements method of Reissner plates is established too.

用一般弹性体的广义混合变分原理，导出了适合 Reissner板弯曲问题的广义混合变分原理及其有限元广义混合法。

The problem is researched that under what conditions the - resolvent operator of - subdifferential mapping of a proper functional is aLipschitz continuous single-valued mapping on whole space.

利用冲一预解算子分析了有限维欧氏空间中的广义参数集值变分包含问题唯一解的灵敏性；利用预解算子分析了有限维欧氏空间中的一般参数集值变分包含问题解集的灵敏性。

The following are the major work in this thesis which has been studied and still needs to be studied further in the future: 1 An improved adjoint variational method is developed, thus it can be applied to the LAGFD-WAM Wave Numerical Model for data assimilation; 2 A linear evolution equation of spectral perturbation is derived in order to analyze its increasing or decreasing mechanism.

本论文主要完成了以下几个方面的研究： 1）建立了推广形式的共轭变分同化方法，使之能够应用于LAGFD-WAM海浪数值模式； 2）导出了扰动谱线性演化方程，分析了扰动谱增长、衰减机制，考察了涌浪情况下扰动谱的持续时效问题及风浪情况下扰动的演变过程； 3）利用波谱共轭方程初步分析了同化模型中距离泛函的敏感性及敏感区域空间分布； 4）将推广的共轭变分方法应用于海浪谱能量平衡方程，建立了连续形式的海浪同化模型，特别是严格导出了风输入、破碎、底摩擦、波波非线性相互作用和波流相互作用各源函数的共轭源函数表示式； 5）分别进行了波谱层次上和有效波高层次上的同化试验，并对数值结果进行了分析。

Based on variation principle, a free vibration variation-integration equation of cantilever curved pipe for conveying fluid is derived. This is a bending-torsion-fluid tree phase coupled dynamics problem. It is difficult to uncouple and to obtain bending and torsion analytic solution separately. We can only look for approximate solution or numeral results.

根据变分原理导出了悬臂输液曲管的变分－积分方程，这是弯曲－扭转－流体三相藕合的动力学问题，无法解藕而单独求出弯曲和扭转的解析解，只能作近似计算。

At each time step, the variational formulation of the semidiscrete problem is derived.

借助人工边界条件给出半离散化问题的变分形式，讨论了所得的变分问题解的存在性与唯一性。

Moreover, this paper makes an effort in incorporating theCosserat theory in the VCFEM for the elastic-plastic analysis of heterogeneous materialsbased on the PVP. The chapters are divided as follows: In Chapter 1, the author summarizes the study on the equivalent mechanics properties ofheterogeneous materials (including the development of the universal relationship which isirrelevant to the micro structure, the discussion of the limitations of the effective moduli, thecomputation of the effective properties of heterogeneous materials with the micromechanicsmethod and the FEM, and the equivalence of the heterogeneous micropolar materials) and thepresentation, the evolution, the corresponding numerical studies of the Cosserat model and itsapplications in engineering.

本文基于参数变分原理，构建了Cosserat体弹塑性有限元分析模型并用于求解应力集中和应变局部化问题；利用Voronoi有限元法提出了适用于非均质材料宏观弹塑性性能计算的参数二次规划算法；进一步将Cosserat模型应用到Voronoi有限元法中，提出了基于Cosserat理论的Voronoi杂交有限元法，并采用参数变分原理进行新模型的分析计算。

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。