Sever S. Dragomir / Themistocles M. Rassias

Ostrowski Type Inequalities and Applications
in Numerical Integration

April 2002, ISBN 1-4020-0562-8, Hardbound

Integral inequalities involving functions with bounded derivatives, otherwise known as Ostrowski-type integral inequalities, have enjoyed a surge in popularity. This field has developed significantly over the last few years, and has yielded many new results and powerful applications in numerical integration, probability theory and stochastics, statistics, information theory, and integral operator theory.

The main aim of the present work is to present a number of selected results on Ostrowski-type integral inequalities. Results for univariate and multivariate real functions and their natural applications in the error analysis of numerical quadratures for both simple and multiple integrals as well as for the Riemann-Stieltjes integral are given. Topics dealt with include generalisations of the Ostrowski inequality and its applications; integral inequalities for n-times differentiable mappings; three-point quadrature rules; product-branched Peano kernels and numerical integration; Ostrowski-type inequalities for multiple integrals; results for double integrals based on an Ostrowski-type inequality; product inequalities and weighted quadrature; and some inequalities for the Riemann-Stieltjes integral.

This book is intended for researchers and graduate students working in the fields of integral inequalities, approximation theory, applied mathematics, probability theory and stochastics, and numerical analysis.

Contents

List of Figures. List of Tables. Preface. List of Symbols. 1. Generalizations of the Ostrowski Inequality and Applications; S.S. Dragomir, T.M. Rassias. 2. Integral Inequalities for Η-Times Differentiable Mappings; A. Sofo. 3. Three Point Quadrature Rules; P. Cerone, S.S. Dragomir. 4. Product Branched Peano Kernels and Numerical Integration; P. Cerone. 5. Ostrowski Type Inequalities for Multiple Integrals; N.S. Barnett, et al. 6. Results for Double Integrals Based on an Ostrowski Type Inequality; G. Hanna. 7. Product Inequalities and Weighted Quadrature; J. Roumeliotis. 8. Some Inequalities for the Riemann-Stieltjes Integral; S.S. Dragomir, T.M. Rassias. Index.

Francesco Paoli

Substructural Logics: A Primer

May 2002, ISBN 1-4020-0605-5, Hardbound

Book Series: TRENDS IN LOGIC : Volume 13

Substructural logics are by now one of the most prominent branches of the research field usually labelled as "nonclassical logics" - and perhaps of logic tout court. Over the last few decades a vast amount of research papers and even some books have been devoted to this subject. The aim of the present book is to give a comprehensive account of the "state of the art" of substructural logics, focusing both on their proof theory (especially on sequent calculi and their generalizations) and on their semantics (both algebraic and relational).

Readership: This textbook is designed for a wide readership: graduate students in either philosophy, mathematics, theoretical computer science or theoretical linguistics with no previous knowledge of the subject (except for a working knowledge of elementary logic) will be gradually introduced into the field starting from its basic foundations; specialists and researchers in the area will find an up-to-date survey of the most important current research topics and problems.

Contents

Preface. Part I: The philosophy of substructural logics. 1. The role of structural rules in sequent calculi. Part II: The proof theory of substructural logics. 2. Basic proof systems for substructural logics. 3. Cut elimination and the decision problem. 4. Other formalisms. Part III: The algebra of substructural logics. 5. Algebraic structures. 6. Algebraic semantics. 7. Relational semantics. Appendix A: Basic glossary of algebra and graph theory. Appendix B: Other substructural logics. Bibliography. Index of subjects.

Alejandro Maass / Servet Martinez / Jaime San Martin

Dynamics and Randomness

May 2002, ISBN 1-4020-0591-1, Hardbound

Book Series: NONLINEAR PHENOMENA AND COMPLEX SYSTEMS : Volume 7

This book contains the lectures given at the Conference on Dynamics and Randomness held at the Centro de Modelamiento Matematico of the Universidad de Chile, on December 11-15, 2000. This meeting brought together mathematicians, theoretical physicists, and theoretical computer scientists, and graduate students interested in fields related to probability theory, ergodic theory, and symbolic and topological dynamics. Each chapter is devoted to one of these subjects. Some papers are structured as surveys, presenting at the same time an original point of view and showing mostly new results.

Audience: This volume will appeal to researchers and practitioners working in probability theory, stochastic processes, information theory, coding theory, statistical physics, and thermodynamics.

Contents

Dimension-Like Characteristics of Invariant Sets in Dynamical Systems; V. Afraimovich, J. Urias. Positive K-Theory and Symbolic Dynamics; M. Boyle. Combinatorial and Dynamical Study of Substitutions around the Theorem of Cobham; F. Durand. Irreducibility, Homoclinic Points and Adjoint Actions of Algebraic d-Actions of Rank One; M. Einsiedler, K. Schmidt. Old an New Tools in the Theory of Filtrations; M. Emery. Information Compression and Retention in Dynamical Processes; K. Petersen. Unique Equilibrium States; R.R. Phelps. Poincare Inequalities and Spectral Gap, Concentration Phenomenon for g-Measures; B. Schmitt.