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In this paper, we mainly study representations of strong semisimple n-Lie algebras, prove that a representation of a strong semisimple n-Lie algebra is a representation of the reductive Lie algebra LP, and the relative properties.

本文主要研究了强半单的n-李代数的表示，证明了强半单的n-李代数的表示可转化为一个约化李代数Lρ的表示，并证明了不变线性形等其它相关性质。

This result is a generalization of the Chevalley basis in case a simply-laced complex simple Lie algebra. Meanwhile, it generalizes also the corresponding Chevalley forms in case affine Lie algebras and 2- extended affine Lie algebras.

该结果是simply-laced复半单李代数情形下Chevalley基的推广，同时也是仿射李代数和2-扩大仿射李代数的相应Chevalley结构形式的推广。

After giving the concept and some elementary properties of subideals of Lie triple system,the author shows that every subalgebra of a nilpotent Lie triple systems is a subideal and a Lie triple system is solvable if every subalgebra is a subideal.

证明了幂零李三系的子系数都是次理想；当李三系的所有子系数都是次理想时，该李三系是可解的。

Lie group method ; Lie theory ; Matrix exponentiaE Symmetric space ; Lie triple system

非线性度李群方法；李理论；矩阵指数；对称空间；李三系

Firstly the Lie group description and method of seismic wave propagation in phase space is proposed, which is, in other words, symplectic group description and method for seismic wave propagation, since symplectic group is a Lie subgroup and symplectic method is a special Lie group method.

文中首先给出相空间中地震波的李群表述和算法，也即地震波的辛群表述和辛算法，辛群是李群的子群，辛算法是特殊的李群算法。

In the fifth chapter,we study dipolarizations in some quadratic Lie algebras.Inthe first section,we obtain some results on the classification of dipolarizations in gen-eral quadratic Lie algebras,and prove that there exist dipolarizations in the solvablequadratic Lie algebras whose Cartan subalgebras consist of semisimple elements.

第五章讨论了某些二次李代数的双极化，在第一节中，我们给出了二次李代数的双极化的一些分类结果；特别证明Cartan子代数是由半单元组成的二次李代数上存在双极化，第二节确定了四维扩张Heisenberg代数的所有双极化，在第三节中，我们构造了2n+2维扩张Heisenberg代数的六类双极化，我们发现两个不同于半单李代数情形的有趣事实：（1）在扩张Heisenberg代数上同时存在对称和非对称双极化；（2）对应于扩张Heisenberg代数的双极化的特征元有的是半单的有的是幂零的。

Whispering Steppe Love is dear, love is rare Love is never where your eyes would stare Unexpectedly, even blindingly Love will show its face to you, no lie Fears 3subside, clearly why Time has come for me to stand aside 4Unencumberedly, though 5reluctantly Upon the 6whispering 7steppes I lie with pride It was the 8cradle of my hopes now lies my resting grave The warmth of life has left me half-embraced For those who 9rendered fears and pain I will surely pay with a smile you can't escape Free at last, from the past Time has come for me to greet the vast Unencumberedly, though reluctantly Upon the whispering steppes I lie

细语吟咽的草原爱之珍，爱之罕爱令双目不可逼视就那么出人意料，甚至茫然无绪地爱呈现出至真性情，没有谎言湮灭了惧栗，也明白了时空于我就这样静止的缘由无所畏惧，却又犹豫迟疑地我走上这为之骄傲的细语吟咽的草原这里，过去是我希望的摇篮，如今是我安息之地对那些在幸福生活中抛弃过我的令我忧虑痛苦的人而今我要报以一个你们怎也躲不掉的笑容自由了，终于脱离过去的阴影自由了广阔天地在我面前展现无所畏惧，却又犹豫迟疑地我走上这为之骄傲的细语吟咽的草原注释： 1 The room is turning slowly away from the moon。

The life lies in its intensity but not to lie in its length, the life significance lies in climbs unceasingly and closely examines but does not lie in sits idle and enjoys the fruits, the life value will lie in surmounted unceasingly but models shape tomorrow a newly ego.

生命在于它的强度而不在于它的长度，生命的意义在于不断地攀登和追问而不在于坐享其成，生命的价值在于不断地超越而塑形明日的新我。

Assume a Lie algebra g has a form B which has all the useful properties of Killingform:bilinearity nondegeneracy,symmetry and invariance.Note that for such a Liealgebra the adjoint representation is equivalent to the coadjoint representation.We callit a symmetric self-dual Lie algebra and the form B an invariant scalar product.

在第一部分的最后一节，我们引进了拟Heisenberg代数的概念，证明了这些李代数均为具有非极大秩的CN李代数，进一步我们还证明了这些CN李代数构成的集合与极大秩幂零李代数构成的集合之间存在着1-1对应关系。

Thismethod adopted affine transformation model and a Lie derivative-based analytical algorithm.We introduced the process and characters in extracting information of biological visionsystem, studied the feasibility of the generalized Gabor function used as receptive fieldfunction in extracting information and analyzed affine transformation group and Liederivatives. Finally, we deduced the mathematical denotation for Lie derivatives, i.e. theinfinitesimal generator of the geometric distortion in affine transformation.

对生物视觉信息提取的过程及特点进行了介绍，其中主要研究了广义Gabor函数作为感受野函数提取初级视觉信息的可行性；对仿射变换作为外界图像信息在视觉成像系统上的投影模型的原理进行了初步讨论；对Lie变换群微分算子用于提取仿射变换不变量的分析方法作了剖析，并推导了该方法中关键部分——仿射变换Lie微分算子的具体表达式，也就是几何变形无限小微分算子的计算表达式，使下一步编程实现该方法成为可能。

You can snipe the second and third union leaders from this position.

您可以鹬第二和第三工会领袖从这一立场出发。

Aiming at the currently shortage of XML streams quality detecting, this paper proposes a new forecasting method of XML streams quality by least squares support vector machines, which is used the method of XML keys' vector matrix as windows, and vector product wavelet transform to multilevel decompose and refactor the XML streams series, that can fulfill real-time checking demand of XML quality, and ensure constraint, consist- ency and integrality. For even more adapting net load, it proposes a control strategy by weight and adaptive adjustment to ensure XML streams quality.

针对当前XML数据流质量检测存在的不足，提出构建XML键的矢量矩阵作为窗口，利用矢量积小波变换多级分解与重构XML数据流，再结合最小二乘支持向量机对XML数据流质量进行预测的一种方法，满足XML数据流质量重构时实时检测的要求，保证XML数据的约束性、一致性与完整性；为了更好的适应网络负载，采取加权与自适应窗口调整等调度策略充分保证XML数据流的质量检测。