Series:De Gruyter Series in Discrete Mathematics and Applications 3
This book indends to cover an area of great current interest, namely the interplay between combinatorics, coding theory, and cryptography. This is a rich field with high relevance for information theory and communication technology. This book therefore appeals to graduate students and researchers in discrete mathematics, information theory, and electrical engineering.
The book, strikes a good balance between theoretical material and applications. There is a first part devoted to the background and also recent results on combinatorial designs. There are wellknown applications of combinatorial designs to coding theory and cryptography. These as well as new developments are covered in the second and third part of the proposed book.
There is a good portion of material in this book that is not treated elsewhere in the expository literature. This makes the book a unique entry in its kind. Although the topic is important, there are very few books that offer the same level of depth in the specific applications covered in this textbook. In particular, some key features that make this book unique in the fields of Combinatorial Design Theory, Coding Theory and Cryptography are:
Combinatorial algorithms for compatible sequences and related complexity analysis
State-of-the-art coverage of results for classes of combinatorial designs
Competent metaheuristic algorithms for combinatorial designs for
the first time
Dozen of constructions for self-dual and quasi-cyclic codes
Overview of private-key and secret-sharing cryptography in Design Theory
The book is intended for both an academic and a professional audience. Mathematicians, computer scientists, practitioners and researchers, senior undergraduate and postgraduate students could benefit from the theoretical material and applications of this book. The textbook may serve as a standard course for combinatorial designs, coding theory and cryptography, as an excellent reference for the researcher and as a comprehensive guide for the enthusiastic practitioner.
To be published: July 2014
ISBN: 978-3-11-029408-8
24 x 17 cmApprox. xx, 500 pages
Language: English
Type of Publication: Monograph
Keywords: Combinatorial Design Theory, Coding Theory; Cryptography; Combinatorial algorithms
Series:De Gruyter Studies in Mathematics 57
The book gives a systematical presentation of stochastic approximation methods for discrete time Markov price processes. Advanced methods combining backward recurrence algorithms for computing of option rewards and general results on convergence of stochastic space skeleton and tree approximations for option rewards are applied to a variety of models of multivariate modulated Markov price processes. The principal novelty of presented results is based on consideration of multivariate modulated Markov price processes and general pay-off functions, which can depend not only on price but also an additional stochastic modulating index component, and use of minimal conditions of smoothness for transition probabilities and pay-off functions, compactness conditions for log-price processes and rate of growth conditions for pay-off functions. The volume presents results on structural studies of optimal stopping domains, Monte Carlo based approximation reward algorithms, and convergence of American-type options for autoregressive and continuous time models, as well as results of the corresponding experimental studies.
To be published: July 2014
ISBN: 978-3-11-032968-1
24 x 17 cmApprox. x, 490 pages
Language: English
Type of Publication: Monograph
Keywords: American option, Optimal stopping, Convergence of rewards, Markov chain, Approximation algorithm
Series:De Gruyter Expositions in Mathematics 59
The topic of this book is located at the intersection of complex analysis, operator theory and partial differential equations. First we investigate the canonical solution operator to d-bar restricted to Bergman spaces of holomorphic L2 functions in one and several complex variables. These operators are Hankel operators of special type. In the following we consider the general d-bar-complex and derive properties of the complex Laplacian on L2 spaces of bounded pseudoconvex domains and on weighted L2 spaces.
The main part is devoted to compactness of the d-bar-Neumann operator. The last part will contain a detailed account of the application of the d-bar-methods to Schrodinger operators, Pauli and Dirac operators and to Witten-Laplacians.
To be published: July 2014ISBN: 978-3-11-031530-1
24 x 17 cmApprox. x, 290 pages
Language: English
Type of Publication: Monograph
Keywords: d-bar Neumann Problem; Inhomogeneous Cauchy-Riemann Equation; Hankel Operator; Compactness; Schrodinger Operator; Witten Laplacian
Series:De Gruyter Expositions in Mathematics 11
"This book draws a colorful and widespread picture of global affine hypersurface theory up to the most recent state. [...] Moreover, the recent development revealed that affine differential geometry - as differential geometry in general - has an exciting intersection area with other fields of interest, like partial differential equations, global analysis, convex geometry and Riemann surfaces (in the complex- analytic sense).
The core of the text is devoted to four important subfields [...]: Affine hyperspheres; Rigidity and uniqueness theorems; Variational problems and affine maximal surfaces; Geometric inequalities. There is a comprehensive introduction [...], starting at the level of students with a general background in Euclidean differential geometry and basic Riemannian geometry. [...] The bibliography contains about 625 items [...], such that researchers and newcomers are provided with an almost complete list, starting right with the beginnings.
The book is written in a clear style, and almost all proofs are carried out in detail. Even auxiliary parts from other fields are explained and sometimes proved. This underlines in addition, how close this field is to the broad flow of modern mathematics. [...] Summary: This is a fine book, inviting to an active and interesting field of research."
To be published: November 2014ISBN: 978-3-11-026667-2
24 x 17 cmApprox. x, 400 pages
Language: English
Type of Publication: Monograph
Keywords: Affine differential geometry; Global differential geometry; Hypersurfaces
Heritage of European Mathematics
ISBN 978-3-03719-126-2
November 2013, 3963 pages, hardcover, 17 x 24 cm.
Jacques Tits was awarded the Wolf Prize in 1993 and the Abel Prize (jointly with John Thompson) in 2008. The impact of his contributions in algebra, group theory and geometry made over a span of more than five decades is incalculable. Many fundamental developments in several fields of mathematics have their origin in ideas of Tits. A number of Titsf papers mark the starting point of completely new directions of research. Outstanding examples are papers on quadratic forms, on Kac?Moody groups and on what subsequently became known as the Tits-alternative.
These volumes contain an almost complete collection of Titsf mathematical writings. They include, in particular, a number of published and unpublished manuscripts which have not been easily accessible until now. This collection of Titsf contributions in one place makes the evolution of his mathematical thinking visible. The development of his theory of buildings and BN-pairs and its bearing on the theory of algebraic groups, for example, reveal a fascinating story. Along with Titsf mathematical writings, these volumes contain biographical data, survey articles on aspects of Titsf work and comments by the editors on the content of some of his papers.
With the publication of these volumes, a major piece of 20th century mathematics
is being made available to a wider audience