Topological Invariants For Projection Method Patterns
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Topological Invariants For Projection Method Patterns
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Author : Alan Forrest
language : en
Publisher: American Mathematical Soc.
Release Date : 2002
Topological Invariants For Projection Method Patterns written by Alan Forrest and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2002 with Mathematics categories.
This memoir develops, discusses and compares a range of commutative and non-commutative invariants defined for projection method tilings and point patterns. The projection method refers to patterns, particularly the quasiperiodic patterns, constructed by the projection of a strip of a high dimensional integer lattice to a smaller dimensional Euclidean space. In the first half of the memoir the acceptance domain is very general - any compact set which is the closure of its interior - while in the second half the authors concentrate on the so-called canonical patterns. The topological invariants used are various forms of $K$-theory and cohomology applied to a variety of both $C DEGREES*$-algebras and dynamical systems derived from such a p
Topological Invariants For Projection Method Patterns
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Author : Alan Forrest
language : en
Publisher:
Release Date : 2014-09-11
Topological Invariants For Projection Method Patterns written by Alan Forrest and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-09-11 with Aperiodic tilings categories.
General introduction Topological spaces and dynamical systems Groupoids, $C^\ast$-algebras, and their invariants Approaches to Calculation I: Cohomology for codimension one Approaches to Calculation II: Infinitely generated cohomology Approaches to Calculation III: Cohomology for small codimension Bibliography.
Mathematics Of Aperiodic Order
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Author : Johannes Kellendonk
language : en
Publisher: Birkhäuser
Release Date : 2015-06-05
Mathematics Of Aperiodic Order written by Johannes Kellendonk and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-06-05 with Mathematics categories.
What is order that is not based on simple repetition, that is, periodicity? How must atoms be arranged in a material so that it diffracts like a quasicrystal? How can we describe aperiodically ordered systems mathematically? Originally triggered by the – later Nobel prize-winning – discovery of quasicrystals, the investigation of aperiodic order has since become a well-established and rapidly evolving field of mathematical research with close ties to a surprising variety of branches of mathematics and physics. This book offers an overview of the state of the art in the field of aperiodic order, presented in carefully selected authoritative surveys. It is intended for non-experts with a general background in mathematics, theoretical physics or computer science, and offers a highly accessible source of first-hand information for all those interested in this rich and exciting field. Topics covered include the mathematical theory of diffraction, the dynamical systems of tilings or Delone sets, their cohomology and non-commutative geometry, the Pisot substitution conjecture, aperiodic Schrödinger operators, and connections to arithmetic number theory.
Radially Symmetric Patterns Of Reaction Diffusion Systems
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Author : Arnd Scheel
language : en
Publisher: American Mathematical Soc.
Release Date : 2003
Radially Symmetric Patterns Of Reaction Diffusion Systems written by Arnd Scheel and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003 with Mathematics categories.
Includes a paper that studies bifurcations of stationary and time-periodic solutions to reaction-diffusion systems. This title develops a center-manifold and normal form theory for radial dynamics which allows for a complete description of radially symmetric patterns.
Abstract Band Method Via Factorization Positive And Band Extensions Of Multivariable Almost Periodic Matrix Functions And Spectral Estimation
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Author : L. Rodman
language : en
Publisher: American Mathematical Soc.
Release Date : 2002
Abstract Band Method Via Factorization Positive And Band Extensions Of Multivariable Almost Periodic Matrix Functions And Spectral Estimation written by L. Rodman and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2002 with Mathematics categories.
In this work, versions of an abstract scheme are developed, which are designed to provide a framework for solving a variety of extension problems. The abstract scheme is commonly known as the band method. The main feature of the new versions is that they express directly the conditions for existence of positive band extensions in terms of abstract factorizations (with certain additional properties). The results prove, amongst other things, that the band extension is continuous in an appropriate sense.
Extending Intersection Homology Type Invariants To Non Witt Spaces
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Author : Markus Banagl
language : en
Publisher: American Mathematical Soc.
Release Date : 2002
Extending Intersection Homology Type Invariants To Non Witt Spaces written by Markus Banagl and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2002 with Mathematics categories.
Intersection homology theory provides a way to obtain generalized Poincare duality, as well as a signature and characteristic classes, for singular spaces. For this to work, one has had to assume however that the space satisfies the so-called Witt condition. We extend this approach to constructing invariants to spaces more general than Witt spaces.
Invariants Of Boundary Link Cobordism
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Author : Desmond Sheiham
language : en
Publisher: American Mathematical Soc.
Release Date : 2003
Invariants Of Boundary Link Cobordism written by Desmond Sheiham and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003 with Mathematics categories.
An $n$-dimensional $\mu$-component boundary link is a codimension $2$ embedding of spheres $L=\sqcup_{\mu}S DEGREESn \subset S DEGREES{n+2}$ such that there exist $\mu$ disjoint oriented embedded $(n+1)$-manifolds which span the components of $L$. This title proceeds to compute the isomorphism class of $C_{
Topology Of Tiling Spaces
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Author : Lorenzo Adlai Sadun
language : en
Publisher: American Mathematical Soc.
Release Date : 2008
Topology Of Tiling Spaces written by Lorenzo Adlai Sadun and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008 with Mathematics categories.
"This book is an introduction to the topology of tiling spaces, with a target audience of graduate students who wish to learn about the interface of topology with aperiodic order. It isn't a comprehensive and cross-referenced tome about everything having to do with tilings, which would be too big, too hard to read, and far too hard to write! Rather, it is a review of the explosion of recent work on tiling spaces as inverse limits, on the cohomology of tiling spaces, on substitution tilings and the role of rotations, and on tilings that do not have finite local complexity. Powerful computational techniques have been developed, as have new ways of thinking about tiling spaces." "The text contains a generous supply of examples and exercises."--BOOK JACKET.
On The Splitting Of Invariant Manifolds In Multidimensional Near Integrable Hamiltonian Systems
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Author : Pierre Lochak
language : en
Publisher: American Mathematical Soc.
Release Date : 2003
On The Splitting Of Invariant Manifolds In Multidimensional Near Integrable Hamiltonian Systems written by Pierre Lochak and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003 with Mathematics categories.
Presents the problem of the splitting of invariant manifolds in multidimensional Hamiltonian systems, stressing the canonical features of the problem. This book offers introduction of a canonically invariant scheme for the computation of the splitting matrix.
Exponentially Small Splitting Of Invariant Manifolds Of Parabolic Points
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Author :
language : en
Publisher: American Mathematical Soc.
Release Date :
Exponentially Small Splitting Of Invariant Manifolds Of Parabolic Points written by and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on with categories.