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We develop his ideas by finding some algebraic invariants under the adjoint actions of the group in addition to the Killing form and give a rigorous proof of the optimality of the one-parameter systems for the symmetry group of the given equations.

本文系统地研究了1+2维非线性发展方程的对称代数，证明了该方程容许一个七维李点对称群，利用Olver提出的方法，详细地建构了1+2维非线性发展方程的一维最优系统，在此基础上我们发展了他的方法，发现了除Killing型之外的其它六个在群伴随作用下的代数不变量，利用这些不变量证明了该最优系统的最优性。

Based on two-dimensional elastic wave equation and adopts the well logs as constraint condition, a new imaging method of crosswell seismic data-elastic wave equation inversion and imaging with the well logs constraint is given by using adjoint theory of distribution-parameter control system.

基于二维弹性波动方程，利用分布参数控制系统的伴随理论，采用测井资料作为约束条件，本文给出了一种井间地震资料速度成像的新方法——井间测井约束弹性波动方程反演成像。

With economic development, the rock material is widely applied in the water conservation、 resources mining、 the civil construction 、 the railway and so on, a lot of problem about rocks urgently is demanded to solve, so there are very important theory and realistic meanings to thoroughly research its nature、 concerning and destroying mechanism,Due to natural function, massive joint and crack with rock, though the scale of these is small, it changes mechanics nature of rock greatly and reduces deforms mould and intensity parameter, and makes it presenting aeolotropy .

随着我国经济建设的发展，岩石材料被广泛应用于水利、资源开采、土木建筑、铁路等领域，与此同时出现许多岩石方面迫切需要解决的问题，所以对其性质、本构关系、破坏机理的深入研究有重要的理论意义和现实意义。由于天然作用，岩石内部存在大量的节理和裂隙，虽然这些裂隙的规模不大，但裂隙的存在大大地改变了岩体的力学性质，使其变形模量及强度参数降低，且使岩体的力学性质呈各向异性。

Using group theory, author researched the theoretical discriminating method of rock aeolotropy types from aeolotropy type of rock, elastic symmetrical direction and the number of independent elastic parameter of rock and established the aeolotropy discriminant criteria of transversely isotropic rock and orthotropic rock first time.

论文首次运用群论的方法，从岩石材料各向异性类别、岩石材料的弹性对称方向和独立弹性参数的个数三个方面入手，研究了岩石材料各向异性类别的理论判别方法，并建立了横观各向同性的各向异性体和正交类各向异性体的各向异性类别判别体系。

Land surface temperature is an important parameter of energy balance of land surface and plays an important role in the interaction between land surface and atmosphere, and has important significance for energy balance on land surface, widely applied in many fields especially aerography, geology,hydrology,ecology and so on.

地表温度是地表能量平衡中的一个重要参数，它在地表与大气相互作用过程中起着重要的作用，对地表能量平衡的研究有着重要的意义，特别在气象、地质、水文、生态等众多领域有着广泛的应用需要。

After extracting target image gradient,this mehtod can put image gradient into CPM,and then figure out the affine transform parameter of the precongnition model and target image.

最后采用模板图像轮廓线在电场化后的梯度图像中的最大能量熵值，利用遗传算法确定先验模板图像与目标图像之间的仿射变换参数，达到轮廓匹配的目的。

In order to reduce conservativity, use Lyapunov function affine to the uncertain parameter.

为减少保守性，采用了与参数相关的Lyapunov仿射函数。

Compared with the invariant features of single parameter group, entirely global affine invariant features are more applicable, and chapter 4 introduces a new global affine invariant feature extraction method called EC-ARC, which is based on the invariance in affine geometry.

然后，提出了扩展质心(Extended Centroid， EC)和仿射区域划分(Affine Region Cutting， ARC)的新概念，并在EC和ARC的基础上，结合仿射几何性质，提出了构造具有完全仿射不变性的特征提取方法EC-ARC。

In Chapter 2, we will use one-parameter subgroups of the Lie group to develop a version ofNewton\'s method on an arbitrary Lie group for maps from a Lie group to its correspondingLie algebra which is independent of affine connections on the Lie group and differs fromNewton\'s method for sections on Riemannian manifolds.

在第2章中，我们主要研究关于从李群到其李代数的映射f的Newton法的收敛性。利用李群的单参数子群来给出关于映射f的Newton迭代点列，此Newton迭代与李群上的联络无关，也与第1章中研究的Newton迭代不同。

Following the change of rotation,scale,will lead to the distortion of the template,which can keep optimizing affine sport parameter during tracking,so the steady tracking can be realized.

在跟踪过程中，随着目标的旋转、尺度等仿射变化，小波特征模板随之变形，优化了目标的仿射运动参数，实现了对目标的稳定跟踪。

For a big chunk of credit-card losses; the number of filings (and thus charge-off rates) would be rising again, whether

年美国个人破产法的一个改动使得破产登记急速下降，而后引起了信用卡大规模的亏损。

Eph. 4:23 And that you be renewed in the spirit of your mind

弗四23 而在你们心思的灵里得以更新