Horvath, Janos (Ed.)

A Panorama of Hungarian Mathematics in the Twentieth Century, I

Series: Bolyai Society Mathematical Studies, Vol. 14
2005, 580 p., Hardcover
ISBN: 3-540-28945-3

About this book

A glorious period of Hungarian mathematics started in 1900 when Lipot Fejer discovered the summability of Fourier series.This was followed by the discoveries of his disciples in Fourier analysis and in the theory of analytic functions. At the same time Frederic (Frigyes) Riesz created functional analysis and Alfred Haar gave the first example of wavelets. Later the topics investigated by Hungarian mathematicians broadened considerably, and included topology, operator theory, differential equations, probability, etc. The present volume, the first of two, presents some of the most remarkable results achieved in the twentieth century by Hungarians in analysis, geometry and stochastics.

The book is accessible to anyone with a minimum knowledge of mathematics. It is supplemented with an essay on the history of Hungary in the twentieth century and biographies of those mathematicians who are no longer active. A list of all persons referred to in the chapters concludes the volume.

Written for:
Scientists, researchers, graduate students, lecturers interested in the history of mathematics in Hungary

Keywords:
Analysis
Geometry
History of Mathematics
Hungarian Mathematics
Stochastics

Kaski, Petteri, Ostergard, Patric R.J.

Classification Algorithms for Codes and Designs

Series: Algorithms and Computation in Mathematics, Vol. 15
XII, 412 p. 62 illus., 2006, XII, 412 p. 62 illus. with DVD-ROM., Hardcover
ISBN: 3-540-28990-9

About this book

This book considers one of the basic problems in discrete mathematics: given a collection of constraints, describe up to isomorphism all the objects that meet them. Only a handful of classification results for combinatorial objects are dated before the mid-20th century; indeed, it is through modern computers and recent developments in algorithms that this topic has flourished and matured. This book is the first comprehensive reference on combinatorial classification algorithms, with emphasis on both the general theory and application to central families of combinatorial objects, in particular, codes and designs.

The accompanying DVD provides an exhaustive catalogue of combinatorial objects with small parameters.

The book will be of great interest to researchers and can be used as course material for graduate courses in both computer science and mathematics.

Written for:
Graduate students and researchers in mathematics, computer science, electrical engineering, signal processing and telecommunication

Keywords:
algorithms
classification
codes
combinatorics
designs

Macheras, Panos, Iliadis, Athanassios

Modeling in Biopharmaceutics, Pharmacokinetics and Pharmacodynamics
Homogeneous and Heterogeneous Approaches

Series: Interdisciplinary Applied Mathematics, Vol. 30
2005, XX, 444 p. 118 illus., Hardcover
ISBN: 0-387-28178-9

About this book

The subject of Modeling in Biopharmaceutics, Pharmacokinetics and Pharmacodynamics is the state of the art of modeling approaches in Biopharmaceutics, Pharmacokinetics and Pharmacodynamics (BPP). The book discusses ways in which classical and non-classical mathematical models may be used to describe drug processes and therapeutic effect in the human body. It is divided into four parts, the first dealing with the fundamental principles of fractals, diffusion and nonlinear dynamics, the second with drug dissolution, release and absorption, the third with empirical, compartmental and stochastic pharmacokinetic models, and the fourth with classical and non-classical aspects of pharmacodynamics. The book is intended to introduce the concepts of fractals, anomalous diffusion and the associated non classical kinetics, and stochastic modeling, within nonlinear dynamics and illuminate with their use the intrinsic complexity of drug processes in homogeneous and heterogeneous media. In parallel fashion, the book also covers all classical models that have direct relevance and application to the biopharmaceutics, pharmacokinetics and pharmacodynamics.

This timely and useful book will appeal to researchers and graduate students in pharmacology, pharmaceutical sciences, physiology, applied mathematics, and biomathematical statistics.

Table of contents

The geometry of nature.- Diffusion and kinetics.- Nonlinear dynamics.- Drug release.- Drug dissolution.- Oral drug absorption.- Empirical models.- Deterministic compartmental models.- Stochastic compartmental models.- Classical pharmacodynamics.- Nonclassical pharmacodynamics.- Appendices (A-H).

Blackadar, Bruce

Operator Algebras
Theory of C*-Algebras and von Neumann Algebras

Series: Encyclopaedia of Mathematical Sciences, Vol. 122
Volume package: Operator Algebras and Non-Commutative Geometry
2006, XX, 517 p., Hardcover
ISBN: 3-540-28486-9

About this book

This book is the most comprehensive treatment available of the general theory of C*-algebras and von Neumann algebras. Beginning with the basics, the theory is developed through such topics as tensor products, nuclearity and exactness, crossed products, classification of injective factors, K-theory, finiteness, stable rank, and quasidiagonality.

The presentation concentrates on carefully and precisely explaining the main features of each part of the theory of operator algebras; most important arguments are at least outlined, and many are presented in full detail, so the volume is much more than a mere survey.

Table of contents

Jorgensen, Palle E.T.

Analysis and Probability
Wavelets, Signals, Fractals

Series: Graduate Texts in Mathematics, Vol. 234
2006, Approx. 270 p. 35 illus., Hardcover
ISBN: 0-387-29519-4

About this textbook

This text, combining analysis and tools from mathematical probability, focuses on a systematic and novel exposition of a recent trend in pure and applied mathematics. The emphasis is on the unity of basis constructions and their expansions (bases which are computationally efficient), and on their use in several areas: from wavelets to fractals. The aim of this book is to show how to use processes from probability, random walks on branches, and their path-space measures in the study of convergence questions from harmonic analysis, with particular emphasis on the infinite products that arise in the analysis of wavelets. The book brings together tools from engineering (especially signal/image processing) and mathematics (harmonic analysis and operator theory).

Table of contents

Acknowledgments.- Introduction: Measures on Path Space.- List of Figures.- Index of Symbols.- Transition Probabilities: Random Walk.- N0 vs. Z.- A Case Study: Duality for the Cantor Sets.- Infinite Products.- The Minimal Eigenfunction.- Generalizations and Applications.- Pyramids and Operators.- Pairs of Representations of the Cuntz Algebras On and their Application to Multiresolutions.- Appendix: Polyphase Matrices and the Operator Algebra ON.- References.- Comments on Signal-Processing Terminology.- Afterword: Computational Math.- List of Names and Discoveries.- General Index.