Author: Vassily Olegovich Manturov
Publisher: World Scientific
ISBN: 9811220131
Category : Mathematics
Languages : en
Pages : 387
Book Description
This book contains an in-depth overview of the current state of the recently emerged and rapidly growing theory of Gnk groups, picture-valued invariants, and braids for arbitrary manifolds. Equivalence relations arising in low-dimensional topology and combinatorial group theory inevitably lead to the study of invariants, and good invariants should be strong and apparent. An interesting case of such invariants is picture-valued invariants, whose values are not algebraic objects, but geometrical constructions, like graphs or polyhedra.In 2015, V O Manturov defined a two-parametric family of groups Gnk and formulated the following principle: if dynamical systems describing a motion of n particles possess a nice codimension 1 property governed by exactly k particles then these dynamical systems possess topological invariants valued in Gnk.The book is devoted to various realisations and generalisations of this principle in the broad sense. The groups Gnk have many epimorphisms onto free products of cyclic groups; hence, invariants constructed from them are powerful enough and easy to compare. However, this construction does not work when we try to deal with points on a 2-surface, since there may be infinitely many geodesics passing through two points. That leads to the notion of another family of groups — Γnk, which give rise to braids on arbitrary manifolds yielding invariants of arbitrary manifolds.
Mods!
Author: Richard Barnes
Publisher: Plexus Publishing
ISBN: 0859658708
Category : Music
Languages : en
Pages : 149
Book Description
The sixties were possibly the greatest decade of last century – an exciting time for music and youth. No other youth culture has personified this more than the Mods, who emerged in the early years of the decade as followers of fashion and soul music and who became the style leaders for this new youth culture. This lavish pictorial history contains over 150 photographs of the original Mods, celebrating their thrilling and unique way of life.
Publisher: Plexus Publishing
ISBN: 0859658708
Category : Music
Languages : en
Pages : 149
Book Description
The sixties were possibly the greatest decade of last century – an exciting time for music and youth. No other youth culture has personified this more than the Mods, who emerged in the early years of the decade as followers of fashion and soul music and who became the style leaders for this new youth culture. This lavish pictorial history contains over 150 photographs of the original Mods, celebrating their thrilling and unique way of life.
I'm One
Author: Horst A. Friedrichs
Publisher: Prestel Publishing
ISBN: 9783791348209
Category : Mod culture (Subculture)
Languages : en
Pages : 0
Book Description
This rare collection of photographs provides a sensitive portrayal of Britain's Mod community from the past decade and a unique insight into the diversity of the contemporary Mod scene.
Publisher: Prestel Publishing
ISBN: 9783791348209
Category : Mod culture (Subculture)
Languages : en
Pages : 0
Book Description
This rare collection of photographs provides a sensitive portrayal of Britain's Mod community from the past decade and a unique insight into the diversity of the contemporary Mod scene.
The Vehicle Selection Matrix
Art Sales
Access
Author:
Publisher:
ISBN:
Category : American periodicals
Languages : en
Pages : 1050
Book Description
Publisher:
ISBN:
Category : American periodicals
Languages : en
Pages : 1050
Book Description
Invariants And Pictures: Low-dimensional Topology And Combinatorial Group Theory
Author: Vassily Olegovich Manturov
Publisher: World Scientific
ISBN: 9811220131
Category : Mathematics
Languages : en
Pages : 387
Book Description
This book contains an in-depth overview of the current state of the recently emerged and rapidly growing theory of Gnk groups, picture-valued invariants, and braids for arbitrary manifolds. Equivalence relations arising in low-dimensional topology and combinatorial group theory inevitably lead to the study of invariants, and good invariants should be strong and apparent. An interesting case of such invariants is picture-valued invariants, whose values are not algebraic objects, but geometrical constructions, like graphs or polyhedra.In 2015, V O Manturov defined a two-parametric family of groups Gnk and formulated the following principle: if dynamical systems describing a motion of n particles possess a nice codimension 1 property governed by exactly k particles then these dynamical systems possess topological invariants valued in Gnk.The book is devoted to various realisations and generalisations of this principle in the broad sense. The groups Gnk have many epimorphisms onto free products of cyclic groups; hence, invariants constructed from them are powerful enough and easy to compare. However, this construction does not work when we try to deal with points on a 2-surface, since there may be infinitely many geodesics passing through two points. That leads to the notion of another family of groups — Γnk, which give rise to braids on arbitrary manifolds yielding invariants of arbitrary manifolds.
Publisher: World Scientific
ISBN: 9811220131
Category : Mathematics
Languages : en
Pages : 387
Book Description
This book contains an in-depth overview of the current state of the recently emerged and rapidly growing theory of Gnk groups, picture-valued invariants, and braids for arbitrary manifolds. Equivalence relations arising in low-dimensional topology and combinatorial group theory inevitably lead to the study of invariants, and good invariants should be strong and apparent. An interesting case of such invariants is picture-valued invariants, whose values are not algebraic objects, but geometrical constructions, like graphs or polyhedra.In 2015, V O Manturov defined a two-parametric family of groups Gnk and formulated the following principle: if dynamical systems describing a motion of n particles possess a nice codimension 1 property governed by exactly k particles then these dynamical systems possess topological invariants valued in Gnk.The book is devoted to various realisations and generalisations of this principle in the broad sense. The groups Gnk have many epimorphisms onto free products of cyclic groups; hence, invariants constructed from them are powerful enough and easy to compare. However, this construction does not work when we try to deal with points on a 2-surface, since there may be infinitely many geodesics passing through two points. That leads to the notion of another family of groups — Γnk, which give rise to braids on arbitrary manifolds yielding invariants of arbitrary manifolds.
The Reference Catalogue of Current Literature
Web Data Mining
Author: Bing Liu
Publisher: Springer Science & Business Media
ISBN: 3642194605
Category : Computers
Languages : en
Pages : 637
Book Description
Liu has written a comprehensive text on Web mining, which consists of two parts. The first part covers the data mining and machine learning foundations, where all the essential concepts and algorithms of data mining and machine learning are presented. The second part covers the key topics of Web mining, where Web crawling, search, social network analysis, structured data extraction, information integration, opinion mining and sentiment analysis, Web usage mining, query log mining, computational advertising, and recommender systems are all treated both in breadth and in depth. His book thus brings all the related concepts and algorithms together to form an authoritative and coherent text. The book offers a rich blend of theory and practice. It is suitable for students, researchers and practitioners interested in Web mining and data mining both as a learning text and as a reference book. Professors can readily use it for classes on data mining, Web mining, and text mining. Additional teaching materials such as lecture slides, datasets, and implemented algorithms are available online.
Publisher: Springer Science & Business Media
ISBN: 3642194605
Category : Computers
Languages : en
Pages : 637
Book Description
Liu has written a comprehensive text on Web mining, which consists of two parts. The first part covers the data mining and machine learning foundations, where all the essential concepts and algorithms of data mining and machine learning are presented. The second part covers the key topics of Web mining, where Web crawling, search, social network analysis, structured data extraction, information integration, opinion mining and sentiment analysis, Web usage mining, query log mining, computational advertising, and recommender systems are all treated both in breadth and in depth. His book thus brings all the related concepts and algorithms together to form an authoritative and coherent text. The book offers a rich blend of theory and practice. It is suitable for students, researchers and practitioners interested in Web mining and data mining both as a learning text and as a reference book. Professors can readily use it for classes on data mining, Web mining, and text mining. Additional teaching materials such as lecture slides, datasets, and implemented algorithms are available online.
Arts & Decoration
Index of Army Motion Pictures, Film Strips, Slides, and Phono-recordings
Author: United States. Department of the Army
Publisher:
ISBN:
Category : Motion pictures
Languages : en
Pages : 572
Book Description
Publisher:
ISBN:
Category : Motion pictures
Languages : en
Pages : 572
Book Description