查询词典 submanifold

For the equivariance of the momentum mapping, we consider the Poisson reduction on some submanifold of the Poisson manifold T*M×g*, and get the reduction phase space.

由于矩映射的等变性，就可以考虑在乘积Poisson流形T*M×g*的某些子流形上做Poisson约化，并得到约化相空间。

Part of the Republic of China portrait painting smaller works, while the majority of thick glass, portrait oil painting works of rough, especially the characters open face is not very sophisticated, by Shi oil painting uneven, and often do not paint Shi submanifold, so save up to now a lot of injuries Cai , complete less.

民国时期的油画一部分画工较细，而大部分玻璃较厚，画工粗，尤其是人物的开脸不是很精细，所施油彩薄厚不均，常常油彩不施地子，所以保存到现在伤彩的很多，完整的较少。

By constructing different quotient spaces,using the method of symplectic geometry,the self-adjoint extensions of symmetric differential operators in the direct sum spaces for the different deficiency indices at(2,2)singular points was discussed. The classification and description of complete Lagrangian submanifold that correspond with self-adjoint domains of second order differential operators were given.

由于对称微分算子在端点处的亏指数取值情况不同，当微分算子在端点处的亏指数均取(2， 2)时，通过构造商空间，应用辛几何的方法讨论了直和空间的对称微分算子的自共轭扩张问题，并给出了与二阶微分算子自共轭域相对应的完全Lagrangian子流型的分类与描述。

In this framework, image frame, audio and text are represented, which are the three modalities in video shots as data points by the 3rd-order tensor. Then a subspace embedding and dimension reduction method is proposed, which explicitly considers the manifold structure of the tensor space from temporal-sequenced associated co-occurring multimodal media data in video. It is called TensorShot approach. Transductive learning uses a large amount of unlabeled data together with the labeled data to build better classifiers. A transductive support tensor machines algorithm is proposed to train effective classifier. This algorithm preserves the intrinsic structure of the submanifold where tensorshots are sampled, and is also able to map out-of-sample data points directly. Moreover, the utilization of unlabeled data improves classification ability.

在此框架中，视频镜头首先被表示成由视频中所包含的文本、视觉和听觉等多模态数据构成的三阶张量；其次，基于此三阶张量表达及视频的时序关联共生特性设计了一种子空间嵌入降维方法，称为张量镜头；由于直推式学习从已知样本出发能对特定的未知样本进行学习和识别，最后在这个框架中提出了一种基于张量镜头的直推式支持张量机算法，它不仅保持了张量镜头所在的流形空间的本征结构，而且能够将训练集合外数据直接映射到流形子空间，同时充分利用未标记样本改善分类器的学习性能。

Keywords: Calabi-Yau manifold; special Lagrangian fibration; stable vector bundle; special Lagrangian submanifold; mirror symmetry.

中文关键词：卡拉比-丘流形；特殊拉格朗日纤维化；稳定向量丛；特殊拉格朗日子流形；镜对称

I didn't watch TV last night, because it .

昨晚我没有看电视，因为电视机坏了。

Since this year, in a lot of villages of Beijing, TV of elevator liquid crystal was removed.

今年以来，在北京的很多小区里，电梯液晶电视被撤了下来。