Quilts: Central Extensions, Braid Actions, and Finite Groups
Quilts: Central Extensions, Braid Actions, and Finite Groups

Author: Tim Hsu

Publisher: Springer

Published: 2007-05-06

Total Pages: 189

ISBN-13: 3540455809

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Quilts are 2-complexes used to analyze actions and subgroups of the 3-string braid group and similar groups. This monograph establishes the fundamentals of quilts and discusses connections with central extensions, braid actions, and finite groups. Most results have not previously appeared in a widely available form, and many results appear in print for the first time. This monograph is accessible to graduate students, as a substantial amount of background material is included. The methods and results may be relevant to researchers interested in infinite groups, moonshine, central extensions, triangle groups, dessins d'enfants, and monodromy actions of braid groups.

Characters and Cyclotomic Fields in Finite Geometry
Characters and Cyclotomic Fields in Finite Geometry

Author: Bernhard Schmidt

Publisher: Springer

Published: 2004-10-13

Total Pages: 112

ISBN-13: 3540457976

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This monograph contributes to the existence theory of difference sets, cyclic irreducible codes and similar objects. The new method of field descent for cyclotomic integers of presribed absolute value is developed. Applications include the first substantial progress towards the Circulant Hadamard Matrix Conjecture and Ryser`s conjecture since decades. It is shown that there is no Barker sequence of length l with 13

hp-Finite Element Methods for Singular Perturbations
hp-Finite Element Methods for Singular Perturbations

Author: Jens M. Melenk

Publisher: Springer

Published: 2004-10-19

Total Pages: 331

ISBN-13: 354045781X

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Many partial differential equations arising in practice are parameter-dependent problems that are of singularly perturbed type. Prominent examples include plate and shell models for small thickness in solid mechanics, convection-diffusion problems in fluid mechanics, and equations arising in semi-conductor device modelling. Common features of these problems are layers and, in the case of non-smooth geometries, corner singularities. Mesh design principles for the efficient approximation of both features by the hp-version of the finite element method (hp-FEM) are proposed in this volume. For a class of singularly perturbed problems on polygonal domains, robust exponential convergence of the hp-FEM based on these mesh design principles is established rigorously.

Punctured Torus Groups and 2-Bridge Knot Groups (I)
Punctured Torus Groups and 2-Bridge Knot Groups (I)

Author: Hirotaka Akiyoshi

Publisher: Springer

Published: 2007-05-26

Total Pages: 293

ISBN-13: 3540718079

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Here is the first part of a work that provides a full account of Jorgensen's theory of punctured torus Kleinian groups and its generalization. It offers an elementary and self-contained description of Jorgensen's theory with a complete proof. Through various informative illustrations, readers are naturally led to an intuitive, synthetic grasp of the theory, which clarifies how a very simple fuchsian group evolves into complicated Kleinian groups.

Yetter-Drinfel'd Hopf Algebras over Groups of Prime Order
Yetter-Drinfel'd Hopf Algebras over Groups of Prime Order

Author: Yorck Sommerhäuser

Publisher: Springer

Published: 2004-10-19

Total Pages: 161

ISBN-13: 3540454233

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Being the first monograph devoted to this subject, the book addresses the classification problem for semisimple Hopf algebras, a field that has attracted considerable attention in the last years. The special approach to this problem taken here is via semidirect product decompositions into Yetter-Drinfel'd Hopf algebras and group rings of cyclic groups of prime order. One of the main features of the book is a complete treatment of the structure theory for such Yetter-Drinfel'd Hopf algebras.

Lectures on the Automorphism Groups of Kobayashi-Hyperbolic Manifolds
Lectures on the Automorphism Groups of Kobayashi-Hyperbolic Manifolds

Author: Alexander Isaev

Publisher: Springer

Published: 2007-03-11

Total Pages: 149

ISBN-13: 3540691537

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In this monograph the author presents a coherent exposition of recent results on complete characterization of Kobayashi-hyperbolic manifolds with high-dimensional groups of holomorphic automorphisms. These classification results can be viewed as complex-geometric analogues of those known for Riemannian manifolds with high-dimensional isotropy groups that were extensively studied in the 1950s-70s.

Hypoelliptic Estimates and Spectral Theory for Fokker-Planck Operators and Witten Laplacians
Hypoelliptic Estimates and Spectral Theory for Fokker-Planck Operators and Witten Laplacians

Author: Francis Nier

Publisher: Springer

Published: 2005-01-17

Total Pages: 215

ISBN-13: 3540315535

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There has recently been a renewal of interest in Fokker-Planck operators, motivated by problems in statistical physics, in kinetic equations, and differential geometry. Compared to more standard problems in the spectral theory of partial differential operators, those operators are not self-adjoint and only hypoelliptic. The aim of the analysis is to give, as generally as possible, an accurate qualitative and quantitative description of the exponential return to the thermodynamical equilibrium. While exploring and improving recent results in this direction, this volume proposes a review of known techniques on: the hypoellipticity of polynomial of vector fields and its global counterpart, the global Weyl-Hörmander pseudo-differential calculus, the spectral theory of non-self-adjoint operators, the semi-classical analysis of Schrödinger-type operators, the Witten complexes, and the Morse inequalities.

Tutorials in Mathematical Biosciences II
Tutorials in Mathematical Biosciences II

Author: James Sneyd

Publisher: Springer

Published: 2005-06-13

Total Pages: 214

ISBN-13: 3540314385

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This book presents a series of models in the general area of cell physiology and signal transduction, with particular attention being paid to intracellular calcium dynamics, and the role played by calcium in a variety of cell types. Calcium plays a crucial role in cell physiology, and the study of its dynamics lends insight into many different cellular processes. In particular, calcium plays a central role in muscular contraction, olfactory transduction and synaptic communication, three of the topics to be addressed in detail in this book. In addition to the models, much of the underlying physiology is presented, so that readers may learn both the mathematics and the physiology, and see how the models are applied to specific biological questions. It is intended primarily as a graduate text or a research reference. It will serve as a concise and up-to-date introduction to all those who wish to learn about the state of calcium dynamics modeling, and how such models are applied to physiological questions.