Series: Monografie Matematyczne, Vol. 66
2005, XIV, 453 p., Hardcover
ISBN: 3-7643-2431-7
About this book
This book gives a thorough and self contained presentation of H1 its known isomorphic invariants and a complete classification of H1 on spaces of homogeneous type. The necessary background is developed from scratch. This includes a detailed discussion of the Haar system, together with the operators that can be built from it (averaging projections, rearrangement operators, paraproducts, Calderon-Zygmund singular integrals). Complete proofs are given for the classical martingale inequalities of C. Fefferman, Burkholder, and Khinchine-Kahane, and for large deviation inequalities. Complex interpolation is treated. Througout, special attention is given to the combinatorial methods developed in the field. An entire chapter is devoted to study the "Combinatorics of coloured dyadic Intervals".
Written for:
Graduates, postgraduates and researchers in Functional Analysis, Harmonic Analysis, Stochastic Analysis and Combinatorics
Table of contents
Preface.- 1. The Haar System: Basic Facts and Classical results.- 2. Projections, Isomorphisms, and Interpolation.- 3. Combinatorics of Colored Dyadic Intervals.- 4. Martingale H^1 Spaces.- 5. Isomorphic Invariants for H^1.- 6. Atomic H^1 Spaces.- Bibliography.- List of Symbols.- Index.
Series: International Series of Numerical Mathematics, Vol. 149
2005, VIII, 237 p., Hardcover
ISBN: 3-7643-7208-7
About this book
Epitaxy is a very active area of theoretical research since several years. It is experimentally well-explored and technologically relevant for thin film growth. Recently powerful numerical techniques in combination with a deep understanding of the physical and chemical phenomena during the growth process offer the possibility to link atomistic effects at the surface to the macroscopic morphology of the film. The goal of this book is to summarize recent developments in this field, with emphasis on multiscale approaches and numerical methods. It covers atomistic, step-flow, and continuum models and provides a compact overview of these approaches. It also serves as an introduction into this highly active interdisciplinary field of research for applied mathematicians, theoretical physicists and computational materials scientists.
Written for:
Biologists, people from education and research with background in applied mathematics, theoretical physics, materials science, nanotechnology
Table of contents
Introduction.- Discrete atomic models.- Discrete continuous models.- Continuous models.- Connections between discrete atomic and discrete continuous models.- Connections between discrete continuous and continuous models.
Expected publication date is July 28, 2005
Description
Arithmetic noncommutative geometry uses ideas and tools from noncommutative geometry to address questions in a new way and to re-interpret results and constructions from number theory and arithmetic algebraic geometry. This general philosophy is applied to the geometry and arithmetic of modular curves and to the fibers at Archimedean places of arithmetic surfaces and varieties.
Noncommutative geometry can be expected to say something about topics of arithmetic interest because it provides the right framework for which the tools of geometry continue to make sense on spaces that are very singular and apparently very far from the world of algebraic varieties. This provides a way of refining the boundary structure of certain classes of spaces that arise in the context of arithmetic geometry.
With a foreword written by Yuri Manin and a brief introduction to noncommutative geometry, this book offers a comprehensive account of the cross fertilization between two important areas, noncommutative geometry and number theory. It is suitable for graduate students and researchers interested in these areas
Contents
Ouveture
Noncommutative modular curves
Quantum statistical mechanics and Galois theory
Noncommutative geometry at arithmetic infinity
Vistas
Bibliography
Details:
Series: University Lecture Series,Volume: 36
Publication Year: 2005
ISBN: 0-8218-3833-4
Paging: approximately 144 pp.
Binding: Softcover
Expected publication date is July 1, 2005
Description
Idempotent mathematics is a rapidly developing new branch of the mathematical sciences that is closely related to mathematical physics. The existing literature on the subject is vast and includes numerous books and journal papers.
A workshop was organized at the Erwin Schrodinger Institute for Mathematical Physics (Vienna) to give a snapshot of modern idempotent mathematics. This volume contains articles stemming from that event. Also included is an introductory paper by G. Litvinov and additional invited contributions.
The resulting volume presents a comprehensive overview of the state of the art. It is suitable for graduate students and researchers interested in idempotent mathematics and tropical mathematics.
Contents
G. L. Litvinov -- The Maslov's dequantization, idempotent and tropical mathematics: A very brief introduction
M. Akian, S. Gaubert, and V. Kolokoltsov -- Set coverings and invertibility of functional Galois connections
M. Akian, S. Gaubert, and C. Walsh -- Discrete max-plus spectral theory
A. Baklouti -- Dequantization of coadjoint orbits: Moment sets and characteristic varieties
P. Butkovic -- On the combinatorial aspects of max-algebra
G. Cohen, S. Gaubert, J.-P. Quadrat, and I. Singer -- Max-plus convex sets and functions
A. Di Nola and B. Gerla -- Algebras of Lukasiewicz's logic and their semiring reducts
W. H. Fleming and W. M. McEneaney -- Max-plus approaches to continuous space control and dynamic programming
K. Khanin, D. Khmelev, and A. Sobolevskii -- A blow-up phenomenon in the Hamilton-Jacobi equation in an unbounded domain
G. L. Litvinov and G. B. Shpiz -- The dequantization transform and generalized Newton polytopes
P. Loreti and M. Pedicini -- An object-oriented approach to idempotent analysis: Integral equations as optimal control problems
P. Lotito, J.-P. Quadrat, and E. Mancinelli -- Traffic assignment & Gibbs-Maslov semirings
D. McCaffrey -- Viscosity solutions on Lagrangian manifolds and connections with tunnelling operators
E. Pap -- Applications of the generated pseudo-analysis to nonlinear partial differential equations
E. Pap -- A generalization of the utility theory using a hybrid idempotent-probabilistic measure
M. Passare and A. Tsikh -- Amoebas: Their spines and their contours
J. Richter-Gebert, B. Sturmfels, and T. Theobald -- First steps in tropical geometry
I. V. Roublev -- On minimax and idempotent generalized weak solutions to the Hamilton-Jacobi equation
E. Wagneur -- Dequantisation: Semi-direct sums of idempotent semimodules
J. van der Woude and G. J. Olsder -- On (min,max,+)-inequalities
K. Zimmermann -- Solution of some max-separable optimization problems with inequality constraints
Details:
Series: Contemporary Mathematics,Volume: 377
Publication Year: 2005
ISBN: 0-8218-3538-6
Paging: 370 pp.
Binding: Softcover
Expected publication date is July 31, 2005
Description
Since the pioneering works of Novikov and Maltsev, group theory has been a testing ground for mathematical logic in its many manifestations, from the theory of algorithms to model theory. The interaction between logic and group theory led to many prominent results which enriched both disciplines.
This volume reflects the major themes of the American Mathematical Society/Association for Symbolic Logic Joint Special Session (Baltimore, MD), Interactions between Logic, Group Theory and Computer Science. Included are papers devoted to the development of techniques used for the interaction of group theory and logic. It is suitable for graduate students and researchers interested in algorithmic and combinatorial group theory.
A complement to this work is Volume 349 in the AMS series, Contemporary Mathematics, Computational and Experimental Group Theory, which arose from the same meeting and concentrates on the interaction of group theory and computer science.
Contents
R. H. Gilman -- Formal languages and their application to combinatorial group theory
A. G. Myasnikov, V. N. Remeslennikov, and D. E. Serbin -- Regular free
length functions on Lyndon's free \mathbb{Z}[t]-group F^{\mathbb{Z}[t]}
I. Chiswell -- A-free groups and tree-free groups
O. Kharlampovich and A. G. Myasnikov -- Effective JSJ decompositions
O. Kharlampovich and A. Myasnikov -- Algebraic geometry over free groups: Lifting solutions into generic points
E. S. Esyp, I. V. Kazatchkov, and V. N. Remeslennikov -- Divisibility theory and complexity of algorithms for free partially commutative groups
Details:
Series: Contemporary Mathematics, Volume: 378
Publication Year: 2005
ISBN: 0-8218-3618-8
Paging: 348 pp.
Binding: Softcover