Hsiang, Wu Yi 1937
Overview
Works:  58 works in 173 publications in 5 languages and 4,279 library holdings 

Genres:  Conference papers and proceedings Biographies Biography History 
Roles:  Author, Editor 
Publication Timeline
.
Most widely held works by
Wu Yi Hsiang
Least action principle of crystal formation of dense packing type and Kepler's conjecture by
Wu Yi Hsiang(
)
9 editions published in 2001 in English and held by 1,522 WorldCat member libraries worldwide
The dense packing of microscopic spheres (i.e. atoms) is the basic geometric arrangement in crystals of monoatomic elements with weak covalent bonds, which achieves the optimal ""known density"" of p/v18. In 1611, Johannes Kepler had already ""conjectured"" that p/v18 should be the optimal ""density"" of sphere packings. Thus, the central problems in the study of sphere packings are the proof of Kepler's conjecture that p/v18 is the optimal density, and the establishing of the least action principle that the hexagonal dense packings in crystals are the geometric consequence of optimization of
9 editions published in 2001 in English and held by 1,522 WorldCat member libraries worldwide
The dense packing of microscopic spheres (i.e. atoms) is the basic geometric arrangement in crystals of monoatomic elements with weak covalent bonds, which achieves the optimal ""known density"" of p/v18. In 1611, Johannes Kepler had already ""conjectured"" that p/v18 should be the optimal ""density"" of sphere packings. Thus, the central problems in the study of sphere packings are the proof of Kepler's conjecture that p/v18 is the optimal density, and the establishing of the least action principle that the hexagonal dense packings in crystals are the geometric consequence of optimization of
Lectures on Lie groups by
Wu Yi Hsiang(
)
19 editions published between 1998 and 2017 in English and held by 1,371 WorldCat member libraries worldwide
"This volume consists of nine lectures on selected topics of Lie group theory. We provide the readers a concise introduction as well as a comprehensive "tour of revisiting" the remarkable achievements of S Lie, W Killing, É Cartan and H Weyl on structural and classification theory of semisimple Lie groups, Lie algebras and their representations; and also the wonderful duet of Cartan's theory on Lie groups and symmetric spaces. With the benefit of retrospective hindsight, mainly inspired by the outstanding contribution of H Weyl in the special case of compact connected Lie groups, we develop the above theory via a route quite different from the original methods engaged by most other books. We begin our revisiting with the compact theory which is much simpler than that of the general semisimple Lie theory; mainly due to the well fittings between the FrobeniusSchur character theory and the maximal tori theorem of É Cartan together with Weyl's reduction (cf. Lectures 14). It is a wonderful reality of the Lie theory that the clearcut orbital geometry of the adjoint action of compact Lie groups on themselves (i.e. the geometry of conjugacy classes) is not only the key to understand the compact theory, but it actually already constitutes the central core of the entire semisimple theory, as well as that of the symmetric spaces (cf. Lectures 59). This is the main reason that makes the succeeding generalizations to the semisimple Lie theory, and then further to the Cartan theory on Lie groups and symmetric spaces, conceptually quite natural, and technically rather straightforward."Publisher's website
19 editions published between 1998 and 2017 in English and held by 1,371 WorldCat member libraries worldwide
"This volume consists of nine lectures on selected topics of Lie group theory. We provide the readers a concise introduction as well as a comprehensive "tour of revisiting" the remarkable achievements of S Lie, W Killing, É Cartan and H Weyl on structural and classification theory of semisimple Lie groups, Lie algebras and their representations; and also the wonderful duet of Cartan's theory on Lie groups and symmetric spaces. With the benefit of retrospective hindsight, mainly inspired by the outstanding contribution of H Weyl in the special case of compact connected Lie groups, we develop the above theory via a route quite different from the original methods engaged by most other books. We begin our revisiting with the compact theory which is much simpler than that of the general semisimple Lie theory; mainly due to the well fittings between the FrobeniusSchur character theory and the maximal tori theorem of É Cartan together with Weyl's reduction (cf. Lectures 14). It is a wonderful reality of the Lie theory that the clearcut orbital geometry of the adjoint action of compact Lie groups on themselves (i.e. the geometry of conjugacy classes) is not only the key to understand the compact theory, but it actually already constitutes the central core of the entire semisimple theory, as well as that of the symmetric spaces (cf. Lectures 59). This is the main reason that makes the succeeding generalizations to the semisimple Lie theory, and then further to the Cartan theory on Lie groups and symmetric spaces, conceptually quite natural, and technically rather straightforward."Publisher's website
Cohomology theory of topological transformation groups by
Wu Yi Hsiang(
Book
)
25 editions published between 1975 and 2013 in 4 languages and held by 500 WorldCat member libraries worldwide
Historically, applications of algebraic topology to the study of topological transformation groups were originated in the work of L.E. 1. Brouwer on periodic transformations and, a little later, in the beautiful fixed point theorem ofP. A. Smith for prime periodic maps on homology spheres. Upon comparing the fixed point theorem of Smith with its predecessors, the fixed point theorems of Brouwer and Lefschetz, one finds that it is possible, at least for the case of homology spheres, to upgrade the conclusion of mere existence (or nonexistence) to the actual determination of the homology type of the fixed point set, if the map is assumed to be prime periodic. The pioneer result of P.A. Smith clearly suggests a fruitful general direction of studying topological transformation groups in the framework of algebraic topology. Naturally, the immediate problems following the Smith fixed point theorem are to generalize it both in the direction of replacing the homology spheres by spaces of more general topological types and in the direction of replacing the group tl by more general compact groups
25 editions published between 1975 and 2013 in 4 languages and held by 500 WorldCat member libraries worldwide
Historically, applications of algebraic topology to the study of topological transformation groups were originated in the work of L.E. 1. Brouwer on periodic transformations and, a little later, in the beautiful fixed point theorem ofP. A. Smith for prime periodic maps on homology spheres. Upon comparing the fixed point theorem of Smith with its predecessors, the fixed point theorems of Brouwer and Lefschetz, one finds that it is possible, at least for the case of homology spheres, to upgrade the conclusion of mere existence (or nonexistence) to the actual determination of the homology type of the fixed point set, if the map is assumed to be prime periodic. The pioneer result of P.A. Smith clearly suggests a fruitful general direction of studying topological transformation groups in the framework of algebraic topology. Naturally, the immediate problems following the Smith fixed point theorem are to generalize it both in the direction of replacing the homology spheres by spaces of more general topological types and in the direction of replacing the group tl by more general compact groups
The Chern Symposium, 1979 : proceedings of the International Symposium on Differential Geometry in honor of S.S. Chern, held
in Berkeley, California, June 1979 by
Wu Yi Hsiang(
Book
)
21 editions published between 1979 and 1981 in English and held by 339 WorldCat member libraries worldwide
This volume attests to the vitality of differential geometry as it probes deeper into its internal structure and explores ever widening connections with other subjects in mathematics and physics. To most of us Professor S.S. Chern is modern differential geometry, and we, his students, are grateful to him for leading us to this fertile landscape. The aims of the symposium were to review recent developments in geometry and to expose and explore new areas of research. It was our way of honoring Professor Chern upon the occasion of his official retirement as Professor of Mathematics at the University of California. This book is a record of the scientific events of the symposium and reflects Professor Chern's wide interest and influence. The conference also reflected Professor Chern's personality. It was a serious occasion, active yet relaxed, mixed with gentleness and good humor. We wish him good health, a long life, happiness, and a continuation of his extraordinarily deep and original contributions to mathematics. I.M. Singer Contents Real and Complex Geometry in Four Dimensions M.F. ATIYAH. ... Equivariant Morse Theory and the YangMills Equation on Riemann Surfaces RAOUL BaTT .. 11 Isometric Families of Kahler Structures EUGENIO CALABI. . 23 Two Applications of Algebraic Geometry to Entire Holomorphic Mappings MARK GREEN AND PHILLIP GRIFFITHS.  ...  . . 41 The Canonical Map for Certain Hilbert Modular Surfaces F. HIRZEBRUCH ...  ... 75 Tight Embeddings and Maps. Submanifolds of Geometrical Class Three in EN NICOLAAS H. KUIPER
21 editions published between 1979 and 1981 in English and held by 339 WorldCat member libraries worldwide
This volume attests to the vitality of differential geometry as it probes deeper into its internal structure and explores ever widening connections with other subjects in mathematics and physics. To most of us Professor S.S. Chern is modern differential geometry, and we, his students, are grateful to him for leading us to this fertile landscape. The aims of the symposium were to review recent developments in geometry and to expose and explore new areas of research. It was our way of honoring Professor Chern upon the occasion of his official retirement as Professor of Mathematics at the University of California. This book is a record of the scientific events of the symposium and reflects Professor Chern's wide interest and influence. The conference also reflected Professor Chern's personality. It was a serious occasion, active yet relaxed, mixed with gentleness and good humor. We wish him good health, a long life, happiness, and a continuation of his extraordinarily deep and original contributions to mathematics. I.M. Singer Contents Real and Complex Geometry in Four Dimensions M.F. ATIYAH. ... Equivariant Morse Theory and the YangMills Equation on Riemann Surfaces RAOUL BaTT .. 11 Isometric Families of Kahler Structures EUGENIO CALABI. . 23 Two Applications of Algebraic Geometry to Entire Holomorphic Mappings MARK GREEN AND PHILLIP GRIFFITHS.  ...  . . 41 The Canonical Map for Certain Hilbert Modular Surfaces F. HIRZEBRUCH ...  ... 75 Tight Embeddings and Maps. Submanifolds of Geometrical Class Three in EN NICOLAAS H. KUIPER
A concise introduction to calculus by
Wu Yi Hsiang(
Book
)
1 edition published in 1995 in English and held by 195 WorldCat member libraries worldwide
1 edition published in 1995 in English and held by 195 WorldCat member libraries worldwide
Least action principle of crystal formation of dense packing type and the proof of Kepler's conjecture by
Wu Yi Hsiang(
)
8 editions published in 2001 in English and held by 91 WorldCat member libraries worldwide
8 editions published in 2001 in English and held by 91 WorldCat member libraries worldwide
Lectures on Lie groups by
Wu Yi Hsiang(
Book
)
5 editions published between 1999 and 2000 in English and held by 55 WorldCat member libraries worldwide
5 editions published between 1999 and 2000 in English and held by 55 WorldCat member libraries worldwide
Ji he xue de yuan qi yu fa zhan by
Wu Yi Hsiang(
Book
)
6 editions published between 1982 and 1994 in Chinese and held by 27 WorldCat member libraries worldwide
6 editions published between 1982 and 1994 in Chinese and held by 27 WorldCat member libraries worldwide
The Chern Symposium : International Symposium in Global Analysis and Global Geometry held in Berkeley, Calif., June 1979 by
International Symposium on Differential Geometry(
Book
)
6 editions published in 1980 in English and German and held by 24 WorldCat member libraries worldwide
6 editions published in 1980 in English and German and held by 24 WorldCat member libraries worldwide
Shi bian duo xiang han shu by
Wu Yi Hsiang(
Book
)
4 editions published between 1983 and 1992 in Chinese and held by 22 WorldCat member libraries worldwide
4 editions published between 1983 and 1992 in Chinese and held by 22 WorldCat member libraries worldwide
Least action principle of crystal formation of dense packing type and Kepler's conjecture by
Wu Yi Hsiang(
Book
)
1 edition published in 2001 in English and held by 16 WorldCat member libraries worldwide
1 edition published in 2001 in English and held by 16 WorldCat member libraries worldwide
Chen sheng shen wen xuan by
ShiingShen Chern(
Book
)
1 edition published in 1993 in Chinese and held by 13 WorldCat member libraries worldwide
Selected papers of Chern ShiingShen
1 edition published in 1993 in Chinese and held by 13 WorldCat member libraries worldwide
Selected papers of Chern ShiingShen
Lectures on Lie groups by
Wu Yi Hsiang(
)
3 editions published between 2000 and 2017 in English and held by 9 WorldCat member libraries worldwide
This invaluable book provides a concise and systematic introduction to the theory of compact connected Lie groups and their representations, as well as a complete presentation of the structure and classification theory. It uses a nontraditional approach and organization. There is a proper balance between, and a natural combination of, the algebraic and geometric aspects of Lie theory, not only in technical proofs but also in conceptual viewpoints. For example, the orbital geometry of adjoint action, is regarded as the geometric organization of the totality of noncommutativity of a given compact connected Lie group, while the maximal tori theorem of É. Cartan and the Weyl reduction of the adjoint action on G to the Weyl group action on a chosen maximal torus are presented as the key results that provide a clearcut understanding of the orbital geometry
3 editions published between 2000 and 2017 in English and held by 9 WorldCat member libraries worldwide
This invaluable book provides a concise and systematic introduction to the theory of compact connected Lie groups and their representations, as well as a complete presentation of the structure and classification theory. It uses a nontraditional approach and organization. There is a proper balance between, and a natural combination of, the algebraic and geometric aspects of Lie theory, not only in technical proofs but also in conceptual viewpoints. For example, the orbital geometry of adjoint action, is regarded as the geometric organization of the totality of noncommutativity of a given compact connected Lie group, while the maximal tori theorem of É. Cartan and the Weyl reduction of the adjoint action on G to the Weyl group action on a chosen maximal torus are presented as the key results that provide a clearcut understanding of the orbital geometry
A concise introduction to calculus by
Wu Yi Hsiang(
Book
)
8 editions published in 1995 in 3 languages and held by 9 WorldCat member libraries worldwide
8 editions published in 1995 in 3 languages and held by 9 WorldCat member libraries worldwide
Transformation groups on complex Stiefel manifolds by
Wu Yi Hsiang(
Book
)
3 editions published in 1981 in English and held by 6 WorldCat member libraries worldwide
3 editions published in 1981 in English and held by 6 WorldCat member libraries worldwide
Lectures on lie groups (second edition) by
Wu Yi Hsiang(
Book
)
2 editions published between 2016 and 2017 in English and held by 6 WorldCat member libraries worldwide
2 editions published between 2016 and 2017 in English and held by 6 WorldCat member libraries worldwide
Ji he xue de yuan qi yu yan jin by
Wu Yi Hsiang(
Book
)
1 edition published in 1983 in Chinese and held by 5 WorldCat member libraries worldwide
1 edition published in 1983 in Chinese and held by 5 WorldCat member libraries worldwide
Cong suan shu dao dai shu by
Wu Yi Hsiang(
Book
)
1 edition published in 1981 in Chinese and held by 5 WorldCat member libraries worldwide
1 edition published in 1981 in Chinese and held by 5 WorldCat member libraries worldwide
Li qun jiang yi by
Wu Yi Hsiang(
Book
)
1 edition published in 1992 in Chinese and held by 5 WorldCat member libraries worldwide
Ben shu jiang shu li qun de ji ben li lun ji qi ying yong. Gong liu zhang. Di yi zhang jie shao jin zhi qun de xian xing biao shi lun;Di er zhang xiang xi shuo ming ru he qu shi xian li qun jie gou de xian xing hua he li dai shu zai li qun jie gou lun shang de ji ben zhong yao xing;Di san zhang yan tao lian tong jin zhi li qun de ban sui bian huan qun de gui ji he;Di si zhang de chu jin zhi li qun de jie gou he fen lei li lun;Di wu zhang yong dai shu de guan dian, Tao lun fu ban dan li dai shu de jie gou yu fen lei;Di liu zhang ze she ji shi ban dan li dai shu de li lun, Te bie shi ta yu dui cheng kong jian li lun de lian xi
1 edition published in 1992 in Chinese and held by 5 WorldCat member libraries worldwide
Ben shu jiang shu li qun de ji ben li lun ji qi ying yong. Gong liu zhang. Di yi zhang jie shao jin zhi qun de xian xing biao shi lun;Di er zhang xiang xi shuo ming ru he qu shi xian li qun jie gou de xian xing hua he li dai shu zai li qun jie gou lun shang de ji ben zhong yao xing;Di san zhang yan tao lian tong jin zhi li qun de ban sui bian huan qun de gui ji he;Di si zhang de chu jin zhi li qun de jie gou he fen lei li lun;Di wu zhang yong dai shu de guan dian, Tao lun fu ban dan li dai shu de jie gou yu fen lei;Di liu zhang ze she ji shi ban dan li dai shu de li lun, Te bie shi ta yu dui cheng kong jian li lun de lian xi
Xian xing dai shu ji chu li lun by
Wuyi Xiang(
Book
)
1 edition published in 1990 in Chinese and held by 4 WorldCat member libraries worldwide
1 edition published in 1990 in Chinese and held by 4 WorldCat member libraries worldwide
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Related Identities
 Kobayashi, S. Editor
 Singer, I. M. Editor
 Wolf, J.
 Chern, Shiingshen Honoree Dedicatee
 Wu, H.H
 Weinstein, A.
 Atiyah, Michael Francis
 Chern Symposium. <1979, Berkeley, Calif.>.
 莫宗堅
 康明昌 1948
Useful Links
Associated Subjects
Algebra Algebras, Linear Calculus Chern, ShiingShen, China Crystallography, Mathematical Functions of real variables Geometry Geometry, Differential Geometry, Plane Geometry, Solid Global analysis (Mathematics) Global differential geometry Homology theory Kepler's conjecture Lie algebras Lie groups Mathematicians Mathematics Sphere Sphere packings Topological groups Topological transformation groups Transformation groups
Covers
Alternative Names
Hsiang, W.Y.
Hsiang, W. Y. 1937
Hsiang, W. Y. (Wu Yi), 1937
Hsiang Wui
Hsiang, Wu Y. 1937
Hsiang, WuYi 1937
Sân, U I.
Wu Yi Hsiang
Wu, Yihsiang 1937
WuYi Hsiang Amerikaans wiskundige
WuYi Hsiang chinesischUSamerikanischer Mathematiker
Wu Yi Hsiang matemático estadounidense
WuYi Hsiang mathématicien américain
Сян У И
У И Сян
項武義
项武义 1937
Languages