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Riemannian geometry structure 黎曼几何结构
Riemannian Geometry and Geometric Analysis 3rd ed. 黎曼几何与几何分析第3版。
AN INTRODUCTION TO DIFFERENTIABLE MANIFOLDS AND RIEMANNIAN GEOMETRY, REVISED. 微分流形与黎曼几何概论。
General Riemannian geometry falls outside the boundaries of the program. 一般的黎曼几何在这个纲领所能包括的边界之外。
The text however develops basic Riemannian Geometry, Complex Manifolds, as well as a detailed theory of Semisimple Lie Groups and Symmetric Spaces. 然而课程还将简单介绍了基本的黎曼几何和复流形的知识，并会详细讨论半单李群和对称空间的理论。
W . M . Boothby: An Introduction to Differentiable Manifolds and Riemannian Geometry . Academic press , INC. 陈维桓：微分流形初步，高等教育出版社.
It can be excluded with data dependent way based on Riemannian geometry for improved SVM. 基于黎曼几何的SVM数据依赖性改进方法能够剔除支持向量携带的冗余信息,改进SVM的性能。
Furthermore,this course is benefitial to study differential topology, Riemannian Geometry, Lie group and Nonlinear Analysis etc. 为进一步学习微分几何、微分拓扑、几何分析、黎曼几何、李群、低维拓扑和非线性分析等相关课程奠定良好的基础，并为阅读当代数学文献创造条件。
At the same time, other treatments of Riemannian geometry are available at varying levels and interests,so I need not introduce everything. 而中方记载，因多为防御战和溃败，资料极其匮乏，尤其是日方损失和战斗细节，不是编造就是阙如，日方资料正可丰富这方面的记载。
These results are in agreement with those obtained by general relativity expressed in Riemannian geometry and that from practical observations. 结果与用黎曼几何表述的广义相对论和实际观测相符。
But it has some limitations of geometry structure, so scaling up the draft tube spouted bed is an urgent task. 但是导向管喷动床的几何结构也有一定的限制。
The algorithm introduces twice training of Riemannian geometry’s modifying the kernel function as well as a forgetting factor to decrease the the number of support vectors. 考虑到简化算法模型和降低计算复杂度，该算法引入遗忘因子和使用黎曼几何修改核函数的二次训练方法减少了算法的支持向量数目。
The basic geometry structure, the vibration spectra and molecular orbital density of the C20 fullerene molecule have been studied. 利用密度泛函方法研究了富勒烯分子的结构、光谱和分子轨道分布特性。
I have, therefore, attempted a viable introduction to Riemannian geometry for a very broad group of students, with emphases and developments in areas not covered by other books. 千年虽逝，但那个追求率性、珍惜自我、强调精神自由的时代却久久地为后人所怀念。
To consider the geometry structure information of data set, new clustering validity functions are defined by modify possibilistic partition coefficient. 该文考虑到数据集的几何结构信息,对可能性划分系数进行改进,提出了新的聚类有效性标准。
In this paper,an ant algorithm based on a geometry structure of TSP is presented to solve these shortcomings,constructing candidate list by quadrant neighbor list and initializing pheromone table by dual quadrant neighbor method. 本文提出了一种基于旅行商问题(TSP)几何结构的蚁群算法,利用象限邻居表构造候选集和对偶限象邻居的方法初始化信息素,用以克服上述缺陷。
The preconditioner is generated from the target’s "geometry structure " and not from the "matrix element", which assured the computational complexity for generating the preconditioner is only O(N). 在构造预条件因子时,采用从目标的"几何结构剖分"出发,而不是从"矩阵元素"出发确定"基权函数之间的作用量关系",这样保证了构造预条件矩阵的计算复杂度仅为O(N)。
Applications of riemannian geometry on parallel mechanisms dynamics 黎曼几何在并联机构动力学中的应用
The geometry structures of undoped,charge doped,and heteroatom(B and P) doped oligosilanes(containing 21 Si atoms) are optimized using density functional theory(DFT) at the B3LYP/6-31G(d) level as implemented in GAUSSIAN 03 program. 本文利用GAUSSIAN 03程序包中的密度泛函理论;在B3LYP/6-31G(d)水平下;对聚21硅烷、电荷掺杂的聚21硅烷以及杂原子(硼和磷)掺杂的聚21硅烷进行几何全优化;并对它们的几何结构和自旋密度进行了比较性理论研究.
Abstract: The geometry structures, net charge, frequency and combination energy of alkylamine chloride ionic liquids were calculated successfully by density function theory （DFT）. 文章摘要: 采用密度泛函方法计算了氯化烷基季铵盐离子液体中阴阳离子的几何构型、净电荷、振动频率和结合能等。