查询词典 variational method

The variational problem of semi-discrete problem is given, the well-posedness of the variational problem is proved, and some error estimates are presented.

给出半离散化问题的变分问题，证明了变分问题的适定性，并给出了误差估计。

In this paper,we first establish an equivalence between a vector variational inequality problem and a generalized variational inequality problem.

文章首先建立了向量变分不等式与广义变分不等式之间的等价关系，然后利用这个结论，建立了向量变分不等式的Levitin-Polyak适定性与广义变分不等式的Levitin- Polyak适定性之间的等价关系。

The thesis consists of three parts:The first part deals with optimal Sobolev inequalities on compact Riemannian manifolds;the second part is concerned with some variational models in image processing,and we propose variational models as well as experimental results for detection,denoising and mosaicking;the last part deals with inverse differential geometry in 3-D non-local image restoration.

本论文由三个部分组成。第一部分是流形上的非线性分析：第二部分是基于能量极小化方法的图像处理；第三部分是三维非局部图像重建及逆向微分几何。在第一部分中，我们研究了紧致流形上的最优Sobolev不等式，证明了某些不等式虽然就整体而言是不成立的，但总是局部成立的。

The variational form of the governing equations is given on the basis of the extended Hu-Washizu three-field variational principle.

基于胡海昌-Washizu三变量广义变分原理结合特征线法给出了控制方程的单元弱形式。

Firstly, this paper investigated roundly the basic theory of the ambient vibration method, analyzed systematically the main methods of ambient vibration identification, and discussed their advantages and disadvantages. Then we established the finite element model of structural dynamics and test model and analyzed their mutual relation, improved MUSIC method and correlation function method in the harmonic identification, and gave the subspace method and correlation function method based on continuous model, which is multi-harmonic retrieve technique. And then, this paper also puts forward least-squares method to estimate directly structural physical and modal parameters; this approach replaced the derivative operator in the continuous time model with an equivalent approximation, and estimated the physical parameters of structures by the least-squares method. And then, we discussed the approximation methods of derivative and their convergence. Finally, this paper researched the modal parameters of a frame structure by the simulation and test. The results demonstrated that subspace method, correlation function method and the least-squares method are effective and stable respectively.

全面地研究环境振动识别方法的基本理论，系统地分析环境振动识别方法的主要方法，讨论它们的优点和不足；建立结(来源：6666AB44C论文网www.abclunwen.com)构动力学的有限元模型和试验模型，分析有限元模型与试验模型之间的相互关系；改进谐波识别中的MUSIC识别方法和相关函数识别方法，给出大型结构模态识别的连续型的子空间分解识别方法和相关函数识别方法，这个方法是多元谐波识别方法；提出直接识别结构的物理参数和模态参数的最小二乘方法，这个方法利用导数的近似值代替导数值，并运用最小二乘方法识别结构的物理参数，讨论导数近似值的选择方法，分析算法的收敛性；通过仿真计算和模型实验，研究高层框架结构的模态参数识别，验证子空间分解识别方法、相关函数识别方法和最小二乘识别方法的有效性，算法的稳定性；从理论和试验两个方面分析和研究噪声对识别精度的影响，影响识别精度的因素，以及部分模态成分的模态参数不能够被识别的原因。

The revised Hargraves formula has the best result compared with Penman-Monteith formula, the average relative error is 6%, moreover, Hargaves method requiring the least data in calculating ETo, so this method has the high actual application value; The following are Radiation method and Blaney-Criddle method ; The worst is the Pan method, even after revised, the highest and average relative error is 36% and 10%, respectively. So, in this study, Penman-Monteith method, Radiation method, Blaney-Criddle method and Hargraves method are used except Pan method.

在这四种方法中，修正后的Hargraves方法与彭曼—蒙特斯方法的计算结果符合最好，其平均相对误差为6％，而Hargraves方法需要的气象数据只有计算时段的最高、最低温度，该方法具有较高的实际应用价值；辐射方法和布兰尼—克里德尔方法次之；蒸发皿方法最差，即使在修正后，E601型蒸发皿的最大误差也高达36％，平均为10％，所以在预报系统的研究设计中采用了除蒸发皿方法之外的四种方法。

The primary studying works and characteristics:1 To summarize reinforcing theory of cement mixing pile composite foundation2 To analyze the primary mechanics characters and changing rules of cement mixing pile, based on analysis of test data both indoor and outdoor.3 To discuss siding frictional resistance, ending resistance, ultimate bearing capacity of simple mixing pile and effectiveness factor of grouped piles, loading ratio of soil between piles under cushion cap of grouped piles and stress ratio of pile and soil and so on, and use many computation method and experimentation method to ensure bearing capacity of mixing piles composite foundation.4 To point out and analyze eight sides flaws and problems of the bearing capacity calculation method of mixing pile compositefoundation which ensured by national and normative method/ formula.5 To apply test results of loading tests and a few settlement observation data, use gray theory to predicate ultimate bearing capacity of deep mixing piles, actual example demonstrate engaging between theoretical predicted value and actual value.6 To apply groovy layerwise summation method to discuss entity piles method, double foundation method, equivalent layerwise summation method and consolidation theoretical method and so on, especially by combination of engineering example, use FEM to calculate or discuss the settlement and changing rules of composite foundation.7 To discuss problems of critical length of composite foundation by combination of engineering example and numerical analysis method, and analyze the contrast of critical length between simple pile load and most area load of composite foundation, not only critical length of composite foundation is relative to modulus ratio between piles and soil, but also upside load distribution area of composite foundation.

主要的研究工作与特色为：(1)总结了水泥搅拌桩复合地基的加固原理；(2)在对室内外试验资料进行统计分析的基础上，系统分析了搅拌桩水泥土的主要力学特性及其变化规律；(3)探讨了搅拌单桩的侧摩阻力、端阻力、极限承载力及群桩效率系数、群桩承台下桩间土荷载分担比及桩土应力比等，提出用多种计算方法并结合试验方法来综合确定搅拌桩复合地基的承载力；(4)明确指出和分析了按国家有关规范的方法确定搅拌桩复合地基承载力所存在的八个方面的缺陷与问题；(5)利用过去没有加载至破坏阶段的载荷试验成果和较少的沉降观测数据，尝试了用灰色理论预测深层搅拌桩的极限承载力，实例表明理论预测值与实测值吻合较好；(6)在常规分层总和法的基础上，探讨了复合地基沉降计算的实体墩基法、双层地基法、等效作用分层总和法、固结理论法等，特别是结合工程实例，用有限元数值计算等方法计算和讨论了搅拌桩复合地基的沉降及其变化规律；(7)结合工程实例，用数值分析方法探讨了复合地基临界桩长的问题，指出和分析了单桩荷载下的临界桩长与复合地基大面积荷载下的临界桩长存在很大的差别，复合地基的临界桩长不仅与桩土模量比有关，而且与复合地基上部荷载分布面积有关。

This method is variational method, which will be much faster and more efficiency than other method.Firstly we use gauss integral method to disperse the least potential energy of barrette pile group, with the help of vertical settlement finite series and Mindlins equation, we derived vertical load-settlement solution of barrette pile group.

另外，目前有关壁板桩群桩水平承载特性的研究也比较少，因此，为了加深对壁板桩群桩承载特性的理解，本文利用变分法对壁板桩群桩竖直或水平受荷情况下的承载特性进行了初步的研究，通过变分法直接得出荷载位移显式方程，较之以往方法更加快捷。

The first section introduces some basic concepts[9].The second section introduces Schmidt"s method of proving isoperimetric inequality [2].The third section introduces Hurwitz"s method [9].The fourth section takes from my tutors lecture notes.The method is due to REILLY [10].Finally,I make use of variational method to prove the circle among the curves of length L encloses the biggest area on the plane.

首先介绍了平面上的一些基本概念[9]，其次介绍了文献[2]中Schmidt证明等周不等式的方法，再次介绍了文献[9]中Hurwitz证明等周不等式的方法，然后介绍了导师吴发恩整理的文献[8]中REILLY的方法证明平面上的等周不等式[10]，最后我利用变分的方法证明了平面上等长的曲线围成的面积最大时为圆。

It provides an effect theoretical tool for studying many nonlinear problems, mainly including topological degree method , variational method , partial ordering method and analytic method and so on.

它为解决各种各样的非线性问题提供了一个富有成效的理论工具。利用非线性泛函分析研究问题的主要方法有：拓扑度理论、临界点理论、半序方法以及分析方法等。

New Zealand is a big safari park which has a variety of wild animals.

新西兰是一个巨大的野生动物园，这里有着种类繁多的野生动物。

Henry's hat-trick helped the champion triumph over the chal—lengers.

亨利的帽子戏法帮助冠军对战胜了挑战者。