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Deeply study the relationship between the Riemannian metric and the adjoint operator Ad kk ?1 and present the objective map expressions.

对Riemannian流形中的度规与空间伴随算子的内在联系作了深入研究，并给出了具体的映射关系。

Micro flexible mechanical structure topology optimization homogenization theory adjoint operator sensitivity analysis

微小型柔性结构；拓扑优化；均匀化理论；伴随变量法；敏度分析

The influence of nonlinear gain (including five order nonlinear gain term) on the Gordon-Haus effect of soliton transmission system controlled by fixed central frequency filter is studied by using adjoint operator method for the first time.

运用绝热演化方法研究了滑频滤波控制孤子传输系统的稳定条件，并首次解析研究了滤波器三阶项对滑频滤波控制系统孤子定时抖动的影响。

The adjoint operator method and the theory of normal form are used to investigated the normal forms in the four dimensional nonlinear systems with cubic nonlinearities. We give two methods to compute the normal form for the four dimensional nonlinear systems. The corresponding Maple programs are also given in the appendix. The results obtained in this dissertation have a completely agreement with the results obtained in other papers.

利用共轭算子法和规范形理论研究了含有三次非线性项的四维系统的规范形，给出了计算四维非线性规范形的两种算法，给出了相应的Maple符号推导程序，所得到的结果与其它文献所得结果完全一致。

Thenwe use adjoint operator method to compute normal form of order 7 for averaged systemswith Z2—symmetry and obtain relations between the coefficients of normal forms andthe coefficients of averaged systems.

然后利用共轭算子法计算了具有Z2—对称性的平均系统的7阶规范形，得到了规范形的系数与平均系统的系数之间的关系式。

In the first part,two methods calculating the coefficients of nilpotentclass normal forms are proposed.one is the iteration search method based onrepresentation theory of Li-algebra,and another is a new matrixrepresentation method based on the adjoint operator concepts,both are ableto be used to analyse the normal form problems with high orders and largedimensions efficiently.

在第一部分工作中，对于幂零类规范形的系数计算，分别提出了基于李代数表示论的迭代搜索的理论和方法以及基于共轭算子概念的新的矩阵表示的理论和方法，从而有效地解决了维数和阶数较高时的计算问题。

In the first part,we use adjoint operator method and matrixrepresentation method to compute normal forms of higher order for nonlinear dynamicalsystems with Z2—symmetry and Z2—asymmetry.

在第二部分里，利用多尺度法、规范形理论、普适开折理论、Melnikov方法和Petrov方法分别研究了参数激励作用下非线性振子、参数激励与强迫激励联合作用下非线性振子的局部分岔、余维2退化分岔、余维3退化分岔和全局分岔。

Using the adjoint operator of PW, nine sites'PWs are successfully assimilated into the initial condition and altered the initial temperature, water vapor and wind field. The change varies with variable fields and pressure levels.

本文利用开发的用于同化可降水量和天顶延迟的模式，成功地将9个站点的大气可降水量的分布及变化信息同化到初始场中，从而使初始场在湿度场、温度场和风场方面较同化前得到改变，这种改变在不同变量场、各个层次上变化的大小和形势是不相同的。

We explain the basic conception of the Lie group, Lie algebra and Riemannian manifolds in detail, deeply analyze and research the Special Euclidean Group SE(3) and se(3) in the Lie group, Lie algebra. Establish the relation between the adjoint transformation Adg and the operatorφ(k + 1,k) under a particular condition , substitute the operatorφ(k + 1,k)with spatial adjoint operator Ad kk ?

在多体系统动力学理论体系中，详细阐述了Lie群、Lie代数和Riemannian几何的基本概念，对Lie群、Lie代数中的特殊Euclidean群SE(3)和se(3)作深入分析与研究，建立Lie括号下的伴随变换Adg在特定条件下与空间算子代数理论中的空间变换算子φ(k + 1，k)之间的相互关系，并将空间伴随算子Ad kk ？

The notion of the adjoint operator of amodule homomorph ism defined on a densely submodule of a comp lete random inner p roduct module is introduced and discussed, in particular the closedness of adjoint operators is p roved.

摘 要 对定义在完备随机内积模的稠子模上的模同态引入了共轭算子的概念并讨论其基本性质，尤其证明了共轭算子的闭性。

Many will continue to choose to live in duality and in conflict.

许多人将继续选择活在二元对立性和冲突中。

I find that students of the University of Physical Education all wear sportswear at first sight.

我发现：体育大学的学生乍一看，都是穿运动衣，大家都一样