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Landau-Lifshitz-Bio ch equation on Riemannian manifold
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作者 Zonglin JIA Boling GUO 《中国数学前沿:英文版》 SCIE CSCD 2019年第1期45-76,共32页
We bring in Landau-Lifshitz-Bloch equation on m-dimensional closed Riemannian manifold and prove that it admits a unique local solution. When m ≥ 3 and the initial data in L^∞-norm is sufficiently small, the solutio... We bring in Landau-Lifshitz-Bloch equation on m-dimensional closed Riemannian manifold and prove that it admits a unique local solution. When m ≥ 3 and the initial data in L^∞-norm is sufficiently small, the solution can be extended globally. Moreover, for m = 2, we can prove that the unique solution is global without assuming small initial data. 展开更多
关键词 Orientable VECTOR BUNDLE RIEMANNIAN curvature tensor on VECTOR BUNDLE SOBOLEV space on VECTOR BUNDLE
Invariant Einstein metrics on generalized Wallach spaces
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作者 Zhiqi Chen Yurii Gennadievich Nikonorov 《中国科学:数学英文版》 SCIE CSCD 2019年第3期569-584,共16页
Invariant Einstein metrics on generalized Wallach spaces have been classified except SO(k + l+ m)/SO(k) × SO(l) × SO(m). In this paper, we first give a survey on the study of invariant Einstein metrics on ge... Invariant Einstein metrics on generalized Wallach spaces have been classified except SO(k + l+ m)/SO(k) × SO(l) × SO(m). In this paper, we first give a survey on the study of invariant Einstein metrics on generalized Wallach spaces, and prove that there are infinitely many spaces of the type SO(k + l + m)/SO(k)× SO(l) × SO(m) admitting exactly two, three, or four invariant Einstein metrics up to a homothety. 展开更多
关键词 compact HOMOGENEOUS SPACE generalized Wallach SPACE symmetric SPACE HOMOGENEOUS RIEMANNIAN METRIC EINSTEIN METRIC RICCI flow
Image-based 3D model retrieval using manifold learning
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作者 Pan-pan MU San-yuan ZHANG +2 位作者 Yin ZHANG Xiu-zi YE Xiang PAN 《信息与电子工程前沿:英文版》 SCIE EI CSCD 2018年第11期1397-1408,共12页
We propose a new framework for image-based three-dimensional(3D) model retrieval. We first model the query image as a Euclidean point. Then we model all projected views of a 3D model as a symmetric positive definite(S... We propose a new framework for image-based three-dimensional(3D) model retrieval. We first model the query image as a Euclidean point. Then we model all projected views of a 3D model as a symmetric positive definite(SPD) matrix, which is a point on a Riemannian manifold. Thus, the image-based 3D model retrieval is reduced to a problem of Euclid-to-Riemann metric learning. To solve this heterogeneous matching problem, we map the Euclidean space and SPD Riemannian manifold to the same high-dimensional Hilbert space, thus shrinking the great gap between them. Finally, we design an optimization algorithm to learn a metric in this Hilbert space using a kernel trick. Any new image descriptors, such as the features from deep learning, can be easily embedded in our framework. Experimental results show the advantages of our approach over the state-of-the-art methods for image-based 3D model retrieval. 展开更多
关键词 Model RETRIEVAL Euclidean SPACE RIEMANNIAN MANIFOLD HILBERT SPACE Metric learning
“新里曼”理论导论:一次调查与一次历史的纵览
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作者 理查德·科恩 唐小波 高拂晓 《中央音乐学院学报》 CSSCI 北大核心 2017年第1期125-135,共11页
译者前言:《音乐理论杂志》(Journal of Music Theory)1998年第2期集中发表了关于“新里曼”理论最新研究的11篇文章。理查德·科恩(Richard Cohn)的这篇《新里曼理论导论:一次调查与一次历史的纵览》(Introduction to Neo-R... 译者前言:《音乐理论杂志》(Journal of Music Theory)1998年第2期集中发表了关于“新里曼”理论最新研究的11篇文章。理查德·科恩(Richard Cohn)的这篇《新里曼理论导论:一次调查与一次历史的纵览》(Introduction to Neo-Riemannian Theory:a Survey and a Historical Perspective)是为这11篇论文写的一篇“序言”,但这篇论文的本身已超出“序”的意义,对“新里曼”理论形成的来龙去脉进行了概述。 展开更多
关键词 新里 RIEMANNIAN 音乐理论 转换形式 音级 无调性音乐 平均律 五度 和声功能 列文
FINITE ELEMENT EXTERIOR CALCULUS FOR EVOLUTION PROBLEMS
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作者 Andrew Gillette Michael Hoist Yunrong Zhu 《计算数学:英文版》 SCIE CSCD 2017年第2期187-212,共26页
阿诺德, Falk,和 Winther
关键词 有限元素方法 演算 部分微分方程 RIEMANNIAN manifolds SEMILINEAR 椭圆形的方程 近似理论
本刊英文版Vol.30(2014),No.12论文摘要(英文)
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《数学学报》 SCIE CSCD 北大核心 2015年第1期181-184,共4页
Regularity of the Inverse of a Homeomorphism with Finite Inner Distortion Chang Yu GUO Abstract Let f:Ω→f(Ω)R<sup>n</sup> be a W<sup>1,1</sup>-homeomorphism with L<sup>1</sup&g... Regularity of the Inverse of a Homeomorphism with Finite Inner Distortion Chang Yu GUO Abstract Let f:Ω→f(Ω)R<sup>n</sup> be a W<sup>1,1</sup>-homeomorphism with L<sup>1</sup>-integrable inner distortion.We show that finiteness of min{lip<sub>f</sub>(x),k<sub>f</sub>(x)},for every x∈Ω\E,implies that f<sup>-1</sup>∈W<sup>1,n</sup>and has finite distortion,provided that the exceptional set E hasσ-finite H<sup>1</sup>-measure.Moreover,f has finite distortion,differentiable a.e.and the Jacobian J<sub>f</sub>】0 a.e. 展开更多
关键词 DIFFERENTIABLE INTEGRABLE implies distortion exceptional No.12 Vol.30 manifold satisfying RIEMANNIAN
数据处理、信息处理
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《电子科技文摘》 2002年第1期142-145,共4页
【正】 Y2001-62772-13 0201563群集基于模型的距离=A model-based distance for clus-tering[会,英]/Rattray,M.//2000 IEEE InternationalJoint Conference on Neural Networks,Vol.4.—13~16(HC)定义了 Riemannian 距离、适应于群... 【正】 Y2001-62772-13 0201563群集基于模型的距离=A model-based distance for clus-tering[会,英]/Rattray,M.//2000 IEEE InternationalJoint Conference on Neural Networks,Vol.4.—13~16(HC)定义了 Riemannian 距离、适应于群集多变量数据,这种距离要求数据与允许定义适当 Riemannian 测度的可微分密度模型首先拟合,然后对高斯矩阵模型研究了易处理的近似,用仿真数据测试此距离,证明了处理不同长度标刻和线性不可分数据群集的能力,要求进一步研究大数据集的性能。参4 展开更多
关键词 大数据集 仿真数据 RIEMANNIAN 密度模型 距离要求 边缘检测方法 矩阵模型 图象分割 纹理分割 虚拟现实技术
A BRIEF INTRODUCTION TO THE MEMBERS (MATHEMATICS) OF ACADEMIA SINICA NEWLY ELECTED IN 1991 预览
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作者 TANG, TY 《数学物理学报:B辑英文版》 SCIE CSCD 1993年第2期121-133,共13页
Ding Xiaxi, research professor of Wuhan Institute of Mathematical Sciences, Academia Sinica, was born in Yiyang, Hunan Province, in May 1928. After graduation in 1951 from the Department of Mathematics, Wuhan
关键词 Wuhan PROFESSOR HUNAN gauge RIEMANNIAN engaged Shandong udent ENGINEER jointly
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ON THE NON-EXISTENCE OF L~2-EIGENVALUES OF MANIFOLDS OF COLUM TYPE 预览
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作者 陈杰诚 《分析理论与应用:英文刊》 1992年第4期58-60,共3页
In[4],Li proved that Yau’s conjecture“For non-compact connected completeRiemannian manifold M.M has no L~2-eigenvalues if its sectional curvature K_m≥0”holds if M can be represented as a Riemannian product M=R~1... In[4],Li proved that Yau’s conjecture“For non-compact connected completeRiemannian manifold M.M has no L~2-eigenvalues if its sectional curvature K_m≥0”holds if M can be represented as a Riemannian product M=R~1×N.Acturally,heproved(without the restriction K_m≥0) 展开更多
关键词 RIEMANNIAN curvature MANIFOLD CONJECTURE connected holds sectional Laplace dense shorter
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REGULARITY OF HARMONIC MAPS INTO POSITIVELY CURVED MANIFOLDS
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作者 忻元龙 《数学年刊:B辑英文版》 SCIE CSCD 1992年第4期385-395,共11页
Let M be a compact Riemannian manifold of dimension m, N a complete Amply connected δ-pinched Riemannian manifold of dimension n. There exists a constant d(n). It is proved that if m≤d(n), then every minimizing ma... Let M be a compact Riemannian manifold of dimension m, N a complete Amply connected δ-pinched Riemannian manifold of dimension n. There exists a constant d(n). It is proved that if m≤d(n), then every minimizing map from M into N is smooth in the interior of M. If m=d(n)+1, such a map has at most diserete singular set and in general the Hausdorff dimension of the singular set is at most m-d(n)-1. 展开更多
关键词 RIEMANNIAN MANIFOLD singular minimizing HAUSDORFF BUNDLE connected interior REGULARITY ordinary
WEAK TYPE(1,1)BOUNDEDNESS OF RIESZ TRANSFORM ON POSITIVELY CURVED MANIFOLDS
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作者 陈杰诚 《数学年刊:B辑英文版》 SCIE CSCD 1992年第1期1-5,共5页
For complete Riemannian manifold M,it is proved that▽(-△)<sup>-1/2</sup> is boundedfrom L<sup>2</sup>(M)to weak-L<sup>1</sup>(M)if Ric(M)≥0.
关键词 RIEMANNIAN manifold BOUNDEDNESS kernel COMMUTATIVE 云一 EARLIER RIESZ 一灯 Transformation
COMPARISON BETWEEN MAXIMAL AND SQUARE FUNCTIONS OF 1-FORMS AND ITS APPLICATIONS
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作者 陈杰诚 《数学年刊:B辑英文版》 SCIE CSCD 1992年第3期374-383,共10页
A norm relation between nontangential square function and nontangential maximalfunction of 1-forms is obtained.As applications,the author gets L~p-boundedness ofLittlewood-Paley-Stein g-function operator on 1-forms,... A norm relation between nontangential square function and nontangential maximalfunction of 1-forms is obtained.As applications,the author gets L~p-boundedness ofLittlewood-Paley-Stein g-function operator on 1-forms,and gives an analytic proof ofL~p-boundedness of Riesz transform,where 1【p【∞. 展开更多
关键词 BOUNDEDNESS proof RIESZ ANALYTIC RIEMANNIAN kernel DISJOINT mutually Polarization 动句
WEYL TRANSFORMATIONS ON MANIFOLDS Ⅱ. Generalized Trace and Inverse Mapping Formula
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作者 钱敏 许连超 《应用数学学报:英文版》 SCIE CSCD 1992年第4期289-297,共9页
IN this paper, we give an extended definition of trace which is called the generalited traceand expose a relation between the generalized trace and the Weyl transformation. We also providea formula for computing the... IN this paper, we give an extended definition of trace which is called the generalited traceand expose a relation between the generalized trace and the Weyl transformation. We also providea formula for computing the trace of G△. 展开更多
关键词 Mapping inverse MANIFOLD satis RIEMANNIAN SUPPOSE kernel arbitrary INEQUALITY OPERA
THE ORBIT SHIFT TOPOLOGICAL STABILITY OF ANOSOV MAPS
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作者 孙文祥 《应用数学学报:英文版》 SCIE CSCD 1992年第3期259-263,共5页
It is shown that Anosov maps are orbit shift topologically stable.
关键词 ORBIT RIEMANNIAN SPANNING implies NEIGHBORHOOD proof smallest appearing UNSTABLE MANIFOLD
A CHARACTERISTIC OF RIEMANNIAN SPACES ADMITTING QUASI-CONCIRCULAR TRANSFORMATION 预览
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作者 李中林 《数学物理学报:B辑英文版》 SCIE CSCD 1991年第1期56-64,共9页
In this paper, we have considered some properties of quasi-umbilical hypersurfaces of a Riemannian space and obtained a characteristic of Riemannian spaces admitting quasi-concircular transformation.
关键词 RIEMANNIAN UMBILICAL QUASI DIVISOR 临公 七无 万加 readily 立入 主一
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Mathema tica Acta ycientia GENERAL CONTENTS 预览
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《数学物理学报:B辑英文版》 SCIE CSCD 1991年第4期477-479,共3页
关键词 周爱辉 郭柏灵 李开泰 RIEMANNIAN EIGENVALUE 赵树松 周笠 illation SOLITON 陆启铿
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ESTIMATE ON LOWER BOUND OF THE FIRST EIGENVALUE OF A COMPACT RIEMANNIAN MANIFOLD 被引量:1
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作者 蔡开仁 《数学年刊:B辑英文版》 SCIE CSCD 1991年第3期267-271,共5页
The author gives an optimum estimate of the first eigenvalue of a compact Riemannian manifold. It is shown that let M be a compact Riemannian manifold, then the first eigenvalue λ<sub>1</sub> of the Lap... The author gives an optimum estimate of the first eigenvalue of a compact Riemannian manifold. It is shown that let M be a compact Riemannian manifold, then the first eigenvalue λ<sub>1</sub> of the Laplace operator of M satisfies α<sub>1</sub>+max{0,-(n-1)K}≥π<sup>2</sup>/d<sup>2</sup> where d is the diameter of M and (n-1)K is the negative lower bound of the Ricci curvature of M. 展开更多
关键词 RIEMANNIAN EIGENVALUE RICCI MANIFOLD curvature Laplace FIRST 二军 proof apply
HODGE DECOMPOSITION THEOREM ON THE NONORIENTABLE COMPACT C~∞ RIEMANNIAN MANIFOLD
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作者 周坚 徐森林 《中国科学通报:英文版》 SCIE 1991年第5期432-433,共2页
Let M be an n-dimensional C~∞ manifold, (π)an orientation cover. It is not difficult to proveLemma 1. is orientable. When M is compact, is compact too.
关键词 MANIFOLD RIEMANNIAN 士一 江月 司词
THE CHARACTERISTIC VALUES OF LAPLACIAN △ ON THE NONORIENTABLE COMPACT C~∞ RIEMANNIAN MANIFOLDS
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作者 徐森林 周坚 《中国科学通报:英文版》 SCIE 1991年第5期433-435,共3页
Let (M, g)=(M, 【,】) be an orientable compact C~∞ Riemannian manifold, ∧~kM a set of all C~∞ k-forms on M. Set
关键词 RIEMANNIAN MANIFOLD 州台 脚口 士一
A CLASS OF QUASILINEAR ELLIPTIC SYSTEMS WITH NATURAL GROWTH CONDITION 预览
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作者 沈尧天 郭信康 《数学物理学报:B辑英文版》 SCIE CSCD 1991年第2期121-127,共7页
Let Ω be a bounded domain in R~n with smooth boundary (?)Ω. In this paper we shall study the Dirichlet problem for the following quasilinear elliptic system:
关键词 DIRICHLET ELLIPTIC CLASS BOUNDEDNESS RIEMANNIAN holds familiar 神川 合喻 varia
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