Series: Frontiers in Mathematics
2009, Approx. 180 p., Softcover
ISBN: 978-3-7643-9999-3
Due: February 2009
The book discusses in detail the extension of the Schwarz--Pick inequality to higher order derivatives of analytic functions with given images. This is a first systematic presentation of the main results in this area. The book contains the materials from the work of many researchers and, in particular, authors' investigations in the last ten years with a new unified approach.
The book will be of interest for researchers and postgraduate students in function theory and hyperbolic geometry. The reader will find a number of historical remarks on the Schwarz Lemma as well as many interesting results of geometric function theory including the attractive steps on coefficient problems from Bieberbach to de Branges, applications of some hyperbolic characteristics of domains via Beardon-Pommerenke's theorem, a new interpretation of coefficient estimates as certain properties of the Poincare metric, a successful combination of the classical ideas of Littlewood, Lowner and Teichmuller with modern approaches. The last chapter of the book contains a discussion of problems that are still open.
1. Introduction.- 2. Basic coefficient inequalities.- 3. The Poincare metric.- 4. Basic Schwarz-Pick type inequalities.- 5. Punishing factors for special cases.- 6. Multiply connected domains.- 7. Related results.- 8. Some open problems.
Series: Birkhauser Advanced Texts / Basler Lehrbucher
2009, Approx. 300 p., Hardcover
ISBN: 978-3-7643-9981-8
Due: February 2009
Simple presentation
Large spectrum of issues on elliptic equations
Many original results
Independent chapters
The aim of this book is to introduce the reader to different topics of the theory of elliptic partial differential equations by avoiding technicalities and refinements. Apart from the basic theory of equations in divergence form it includes subjects such as singular perturbation problems, homogenization, computations, asymptotic behaviour of problems in cylinders, elliptic systems, nonlinear problems, regularity theory, Navier-Stokes system, p-Laplace equation. Just a minimum on Sobolev spaces has been introduced, and work or integration on the boundary has been carefully avoided to keep the reader's attention on the beauty and variety of these issues.
The chapters are relatively independent of each other and can be read or taught separately. Numerous results presented here are original and have not been published elsewhere. The book will be of interest to graduate students and faculty members specializing in partial differential equations.
Preface.- I. Basic techniques.- 1. Hilbert space techniques.- 2. A survey of essential analysis.- 3. Weak formulation of elliptic problems.- 4. Elliptic problems in divergence form.- 5. Singular perturbation problems.- 6. Problems in large cylinders.- 7. Periodic problems.- 8. Homogenization.- 9. Eigenvalues.- 10. Numerical computations.- II. More advanced theory.- 11. Nonlinear problems.- 12. L(infinity)-estimates.- 13. Linear elliptic systems.- 14. The stationary Navier?Stokes system.- 15. Some more spaces.- 16. Regularity theory.- 17. The p-Laplace equation.- 18. The strong maximum principle.- 19. Problems in the whole space.- A. Fixed point theorems.- Bibliography.- Index.
During the past decade there has been an explosion in computation and information technology.
With it have come vast amounts of data in a variety of fields such as medicine, biology, finance, and
marketing. The challenge of understanding these data has led to the development of new tools in
the field of statistics, and spawned new areas such as data mining, machine learning, and bioinformatics.
Many of these tools have common underpinnings but are often expressed with different
terminology. This book describes the important ideas in these areas in a common conceptual
framework. While the approach is statistical, the emphasis is on concepts rather than mathematics.
Many examples are given, with a liberal use of color graphics. It should be a valuable resource
for statisticians and anyone interested in data mining in science or industry. The book’s coverage
is broad, from supervised learning (prediction) to unsupervised learning.
7 Topics include neural networks, support vector
machines, classification trees and boosting - the
first comprehensive treatment of this topic in any
book 7 Includes over 200 pages of four-color
graphics
Fields of interest
Statistical Theory and Methods
Target groups
Researchers and graduate students
Type of publication
Contributed volume
Mathematics
Due February 2009
2009. XXII, 562 p. Hardcover
ISBN 978-0-387-84857-0
Series: Frontiers in Mathematics
2009, Approx. 130 p., Softcover
ISBN: 978-3-0346-0001-9
Due: March 2009
The monograph provides the first full discussion of flag-transitive Steiner designs. This is a central part of the study of highly symmetric combinatorial configurations at the interface of several mathematical disciplines, like finite or incidence geometry, group theory, combinatorics, coding theory, and cryptography. In a sufficiently self-contained and unified manner the classification of all flag-transitive Steiner designs is presented. This recent result settles interesting and challenging questions that have been object of research for more than 40 years. Its proof combines methods from finite group theory, incidence geometry, combinatorics, and number theory.
The book contains a broad introduction to the topic, along with many illustrative examples. Moreover, a census of some of the most general results on highly symmetric Steiner designs is given in a survey chapter.
The monograph is addressed to graduate students in mathematics and computer science as well as established researchers in design theory, finite or incidence geometry, coding theory, cryptography, algebraic combinatorics, and more generally, discrete mathematics.
Graduate students in mathematics and computer science; established researchers in design theory, finite or incidence geometry, coding theory, cryptography, algebraic combinatorics, and more generally, discrete mathematics
Preface.- 1. Incidence Structures and Steiner Designs.- 2. Permutation Groups and Group Actions.- 3. Number Theoretical Tools.- 4. Highly Symmetric Steiner Designs.- 5. A Census of Highly Symmetric Steiner Designs.- 6. The Classification of Flag-transitive Steiner Quadruple Systems.- 7. The Classification of Flag-transitive Steiner 3-Designs.- 8. The Classification of Flag-transitive Steiner 4-Designs.- 9. The Classification of Flag-transitive Steiner 5-Designs.- 10. The Non-Existence of Flag-transitive Steiner 6-Designs.- References.- Index.
Series: Frontiers in Mathematics
2009, Approx. 185 p., Softcover
ISBN: 978-3-7643-9989-4
Due: January 2009
The book generalizes the well-known regularity of ring elements to regularity of homomorphisms in module categories, and further to regularity of morphisms in any category. Regular homomorphisms are characterized in terms of decompositions of domain and codomain, and numerous other results are presented. While the theory is well developed in module categories many questions remain about generalizations and extensions to other categories. The book only requires the knowledge of a basic course in modern algebra. It is written clearly, with great detail, and is accessible to students and researchers alike.
Researchers and students in algebra and potentially other fields
Series: Springer Series in Statistics
2009, XII, 384 p., Hardcover
ISBN: 978-0-387-88145-4
Due: April 2009
In the past decade, the study of networks has increased dramatically. Researchers from across the sciences?including biology and bioinformatics, computer science, economics, engineering, mathematics, physics, sociology, and statistics?are more and more involved with the collection and statistical analysis of network-indexed data. As a result, statistical methods and models are being developed in this area at a furious pace, with contributions coming from a wide spectrum of disciplines.
This book provides an up-to-date treatment of the foundations common to the statistical analysis of network data across the disciplines. The material is organized according to a statistical taxonomy, although the presentation entails a conscious balance of concepts versus mathematics. In addition, the examples?including extended cases studies?are drawn widely from the literature. This book should be of substantial interest both to statisticians and to anyone else working in the area of ‘network science.’
The coverage of topics in this book is broad, but unfolds in a systematic manner, moving from descriptive (or exploratory) methods, to sampling, to modeling and inference. Specific topics include network mapping, characterization of network structure, network sampling, and the modeling, inference, and prediction of networks, network processes, and network flows. This book is the first such resource to present material on all of these core topics in one place.
Introduction and overview.- Preliminaries.- Mapping networks.- Descriptive analysis of network graph characteristics.- Sampling and estimation in network graphs.- Models for network graphs.- Network topology inference.- Modeling and prediction for processes on network graphs.- Analysis of network flow data.- Graphical models