Geometry Of Crystallographic Groups
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Geometry Of Crystallographic Groups
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Author : Andrzej Szczepański
language : en
Publisher: World Scientific
Release Date : 2012
Geometry Of Crystallographic Groups written by Andrzej Szczepański and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012 with Mathematics categories.
Crystallographic groups are groups which act in a nice way and via isometries on some n-dimensional Euclidean space. This book gives an example of the torsion free crystallographic group with a trivial center and a trivial outer automorphism group.
Geometry Of Crystallographic Groups Second Edition
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Author : Andrzej Szczepanski
language : en
Publisher:
Release Date : 2024-09-30
Geometry Of Crystallographic Groups Second Edition written by Andrzej Szczepanski and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-09-30 with categories.
It is eleven years since the First Edition of Geometry of Crystallographic Groups appeared. This Second Edition expands on the first, providing details of a new result of automorphism of crystallographic groups, and on Hantzsche-Wendt groups/manifolds.Crystalographic groups are groups which act via isometries on some n-dimensional Euclidean space, so-named because in three dimensions they occur as the symmetry groups of a crystal. There are short introductions to the theme before every chapter, and a list of conjectures and open projects at the end of the book.Geometry of Crystallographic Groups is suitable as a textbook for students, containing basic theory of crystallographic groups. It is also suitable for researchers in the field, discussing in its second half more advanced and recent topics.
Introduction To Crystal Geometry
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Author : Martin Julian Buerger
language : en
Publisher:
Release Date : 1971
Introduction To Crystal Geometry written by Martin Julian Buerger and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1971 with Science categories.
Geometric Crystallography
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Author : P. Engel
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Geometric Crystallography written by P. Engel and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Science categories.
In the last decade mathematical crystallography has found increasing interest. Siginificant results have been obtained by algebraic, geometric, and group theoretic methods. Also classical crystallography in three-dimen sional Euclidean space has been extended to higher dimen sions in order to understand better the dimension independent crystallographic properties. The aim of this note is to introduce the reader to the fascinating and rich world of geometric crystallography. The prerequisites for reading it are elementary geometry and topological notations, and basic knowledge of group theory and linear algebra. Crystallography is geometric by its nature. In many cases, geometric arguments are the most appropriate and can thus best be understood. Thus the geometric point of view is emphasized here. The approach is axiomatic start ing from discrete point sets in Euclidean space. Symmetry comes in very soon and plays a central role. Each chapter starts with the necessary definitions and then the subject is treated in two- and three-dimensional space. Subsequent sections give an extension to higher dimensions. Short historical remarks added at the end of the chapters will show the development of the theory. The chapters are main ly self-contained. Frequent cross references, as well as an extended subject index, will help the reader who is only interested in a particular subject.
Groups And Geometry
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Author : Roger C. Lyndon
language : en
Publisher: Cambridge University Press
Release Date : 1985-03-14
Groups And Geometry written by Roger C. Lyndon and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1985-03-14 with Mathematics categories.
This 1985 book is an introduction to certain central ideas in group theory and geometry. Professor Lyndon emphasises and exploits the well-known connections between the two subjects and leads the reader to the frontiers of current research at the time of publication.
Point Groups Space Groups Crystals Molecules
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Author : R. Mirman
language : en
Publisher: World Scientific
Release Date : 1999
Point Groups Space Groups Crystals Molecules written by R. Mirman and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 1999 with Science categories.
This book is by far the most comprehensive treatment of point and space groups, and their meaning and applications. Its completeness makes it especially useful as a text, since it gives the instructor the flexibility to best fit the class and goals. The instructor, not the author, decides what is in the course. And it is the prime book for reference, as material is much more likely to be found in it than in any other book; it also provides detailed guides to other sources.Much of what is taught is folklore, things everyone knows are true, but (almost?) no one knows why, or has seen proofs, justifications, rationales or explanations. (Why are there 14 Bravais lattices, and why these? Are the reasons geometrical, conventional or both? What determines the Wigner-Seitz cells? How do they affect the number of Bravais lattices? Why are symmetry groups relevant to molecules whose vibrations make them unsymmetrical? And so on). Here these analyses are given, interrelated, and in-depth. The understanding so obtained gives a strong foundation for application and extension. Assumptions and restrictions are not merely made explicit, but also emphasized.In order to provide so much information, details and examples, and ways of helping readers learn and understand, the book contains many topics found nowhere else, or only in obscure articles from the distant past. The treatment is (often completely) different from those elsewhere. At least in the explanations, and usually in many other ways, the book is completely new and fresh. It is designed to inform, educate and make the reader think. It strongly emphasizes understanding.The book can be used at many levels, by many different classes of readers ? from those who merely want brief explanations (perhaps just of terminology), who just want to skim, to those who wish the most thorough understanding.
Groups
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Author : R. P. Burn
language : en
Publisher: Cambridge University Press
Release Date : 1987-09-03
Groups written by R. P. Burn and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1987-09-03 with Mathematics categories.
Following the same successful approach as Dr. Burn's previous book on number theory, this text consists of a carefully constructed sequence of questions that will enable the reader, through participation, to study all the group theory covered by a conventional first university course. An introduction to vector spaces, leading to the study of linear groups, and an introduction to complex numbers, leading to the study of Möbius transformations and stereographic projection, are also included. Quaternions and their relationships to 3-dimensional isometries are covered, and the climax of the book is a study of the crystallographic groups, with a complete analysis of these groups in two dimensions.
Orientations And Rotations
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Author : Adam Morawiec
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-04-17
Orientations And Rotations written by Adam Morawiec and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-04-17 with Science categories.
Essentially, Orientations and Rotations treats the mathematical and computational foundations of texture analysis. It contains an extensive and thorough introduction to parameterizations and geometry of the rotation space. Since the notions of orientations and rotations are of primary importance for science and engineering, the book can be useful for a very broad audience using rotations in other fields.
N Dimensional Crystallography
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Author : R. L. E. Schwarzenberger
language : en
Publisher: Pitman Publishing
Release Date : 1980
N Dimensional Crystallography written by R. L. E. Schwarzenberger and has been published by Pitman Publishing this book supported file pdf, txt, epub, kindle and other format this book has been release on 1980 with Mathematics categories.
Geometry Of Crystallographic Groups
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Author : Andrzej Szczepanski
language : en
Publisher: World Scientific
Release Date : 2012
Geometry Of Crystallographic Groups written by Andrzej Szczepanski and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012 with Mathematics categories.
Crystallographic groups are groups which act in a nice way and via isometries on some n-dimensional Euclidean space. They got their name, because in three dimensions they occur as the symmetry groups of a crystal (which we imagine to extend to infinity in all directions). The book is divided into two parts. In the first part, the basic theory of crystallographic groups is developed from the very beginning, while in the second part, more advanced and more recent topics are discussed. So the first part of the book should be usable as a textbook, while the second part is more interesting to researchers in the field. There are short introductions to the theme before every chapter. At the end of this book is a list of conjectures and open problems. Moreover there are three appendices. The last one gives an example of the torsion free crystallographic group with a trivial center and a trivial outer automorphism group.This volume omits topics about generalization of crystallographic groups to nilpotent or solvable world and classical crystallography.We want to emphasize that most theorems and facts presented in the second part are from the last two decades. This is after the book of L Charlap OC Bieberbach groups and flat manifoldsOCO was published.