Bøger i Bolyai Society Mathematical Studies serien

With the advent of digital computers more than half a century ago, - searchers working in a wide range of scienti?c disciplines have obtained an extremely powerful tool to pursue deep understanding of natural processes in physical, chemical, and biological systems. Computers pose a great ch- lenge to mathematical sciences, as the range of phenomena available for rigorous mathematical analysis has been enormously expanded, demanding the development of a new generation of mathematical tools. There is an explosive growth of new mathematical disciplines to satisfy this demand, in particular related to discrete mathematics. However, it can be argued that at large mathematics is yet to provide the essential breakthrough to meet the challenge. The required paradigm shift in our view should be compa- ble to the shift in scienti?c thinking provided by the Newtonian revolution over 300 years ago. Studies of large-scale random graphs and networks are critical for the progress, using methods of discrete mathematics, probabil- tic combinatorics, graph theory, and statistical physics. Recent advances in large scale random network studies are described in this handbook, which provides a signi?cant update and extension - yond the materials presented in the "e;Handbook of Graphs and Networks"e; published in 2003 by Wiley. The present volume puts special emphasis on large-scale networks and random processes, which deemed as crucial for - tureprogressinthe?eld. Theissuesrelatedtorandomgraphsandnetworks pose very di?cult mathematical questions.

Exploring the connections between arithmetic and geometric properties of algebraic varieties has been the object of much fruitful study for a long time, especially in the case of curves. The aim of the Summer School and Conference on "e;Higher Dimensional Varieties and Rational Points"e; held in Budapest, Hungary during September 2001 was to bring together students and experts from the arithmetic and geometric sides of algebraic geometry in order to get a better understanding of the current problems, interactions and advances in higher dimension. The lecture series and conference lectures assembled in this volume give a comprehensive introduction to students and researchers in algebraic geometry and in related fields to the main ideas of this rapidly developing area.

Discrete mathematics and theoretical computer science are closely linked research areas with strong impacts on applications and various other scientific disciplines. Both fields deeply cross fertilize each other. One of the persons who particularly contributed to building bridges between these and many other areas is Laszlo Lovasz, a scholar whose outstanding scientific work has defined and shaped many research directions in the last 40 years. A number of friends and colleagues, all top authorities in their fields of expertise and all invited plenary speakers at one of two conferences in August 2008 in Hungary, both celebrating Lovasz's 60th birthday, have contributed their latest research papers to this volume. This collection of articles offers an excellent view on the state of combinatorics and related topics and will be of interest for experienced specialists as well as young researchers.

Since his death in 1996, many scientific meetings have been dedicated to the memory of Paul Erdös. From July 4 to 11, 1999, the conference "Paul Erdös and his Mathematics" was held in Budapest, with the ambitious goal of showing the whole range of Erdös' work - a difficult task in view of Erdös' versatility and his broad scope of interest in mathematics. According to this goal, the topics of lectures, given by the leading specialists of the subjects, included number theory, combinatorics, analysis, set theory, probability, geometry and areas connecting them, like ergodic theory. The conference has contributed to changing the common view that Erdös worked only in combinatorics and combinatorial number theory. In the present two volumes, the editors have collected, besides some personal reminiscences by Paul's old friends, mainly survey articles on his work, and on areas he initiated or worked in.

This volume collects together research and survey papers written by invited speakers of the conference celebrating the 70th birthday of László Lovász.The topics covered include classical subjects such as extremal graph theory, coding theory, design theory, applications of linear algebra and combinatorial optimization, as well as recent trends such as extensions of graph limits, online or statistical versions of classical combinatorial problems, and new methods of derandomization.László Lovász is one of the pioneers in the interplay between discrete and continuous mathematics, and is a master at establishing unexpected connections, “building bridges” between seemingly distant fields. His invariably elegant and powerful ideas have produced new subfields in many areas, and his outstanding scientific work has defined and shaped many research directions in the last 50 years. The 14 contributions presented in this volume, all of which are connected to László Lovász''s areas of research, offer an excellent overview of the state of the art of combinatorics and related topics and will be of interest to experienced specialists as well as young researchers.

This volume collects together research and survey papers written by invited speakers of the conference celebrating the 70th birthday of László Lovász.The topics covered include classical subjects such as extremal graph theory, coding theory, design theory, applications of linear algebra and combinatorial optimization, as well as recent trends such as extensions of graph limits, online or statistical versions of classical combinatorial problems, and new methods of derandomization.László Lovász is one of the pioneers in the interplay between discrete and continuous mathematics, and is a master at establishing unexpected connections, "building bridges" between seemingly distant fields. His invariably elegant and powerful ideas have produced new subfields in many areas, and his outstanding scientific work has defined and shaped many research directions in the last 50 years. The 14 contributions presented in this volume, all of which are connected to László Lovász's areas of research, offer an excellent overview of the state of the art of combinatorics and related topics and will be of interest to experienced specialists as well as young researchers.

This volume contains 17 surveys that cover many recent developments in Discrete Geometry and related fields. Besides presenting the state-of-the-art of classical research subjects like packing and covering, it also offers an introduction to new topological, algebraic and computational methods in this very active research field.

Discrete Mathematics and theoretical computer science are closely linked research areas with strong impacts on applications and various other scientific disciplines.

Szemeredi's influence on today's mathematics, especially in combinatorics, additive number theory, and theoretical computer science, is enormous.

These topics include 3-dimensional and higher dimensional contact topology, Fukaya categories, asymptotically holomorphic methods in contact topology, bordered Floer homology, embedded contact homology, and flexibility results for Stein manifolds.

The present volume is a collection of a dozen survey articles, dedicated to the memory of the famous Hungarian geometer, Laszlo Fejes Toth, on the 99th anniversary of his birth. The mathematical work and perspectives of all editors and most contributors of this volume were deeply influenced by Laszlo Fejes Toth.

The present publication contains a special collection of research and review articles on deformations of surface singularities, that put together serve as an introductory survey of results and methods of the theory, as well as open problems and examples.

Algebraic logic is a subject in the interface between logic, algebra and geometry, it has strong connections with category theory and combinatorics.

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.

The present publication contains a special collection of research and review articles on deformations of surface singularities, that put together serve as an introductory survey of results and methods of the theory, as well as open problems and examples.

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.

Paul Erdoes was one of the most influential mathematicians of the twentieth century, whose work in number theory, combinatorics, set theory, analysis, and other branches of mathematics has determined the development of large areas of these fields.

This book collects survey papers in the fields of entropy, search and complexity, summarizing the latest developments in their respective areas. More than half of the papers belong to search theory which lies on the borderline of mathematics and computer science, information theory and combinatorics, respectively.

The present volume is a collection of a dozen survey articles, dedicated to the memory of the famous Hungarian geometer, Laszlo Fejes Toth, on the 99th anniversary of his birth. The mathematical work and perspectives of all editors and most contributors of this volume were deeply influenced by Laszlo Fejes Toth.

These topics include 3-dimensional and higher dimensional contact topology, Fukaya categories, asymptotically holomorphic methods in contact topology, bordered Floer homology, embedded contact homology, and flexibility results for Stein manifolds.

Algebraic logic is a subject in the interface between logic, algebra and geometry, it has strong connections with category theory and combinatorics.

This volume honours the eminent mathematicians Vera Sos and Andras Hajnal. Also presented are cutting edge expository research papers with new theorems and proofs in the area of the classical Hungarian subjects, like extremal combinatorics, colorings, combinatorial number theory, etc.

This book collects survey papers in the fields of entropy, search and complexity, summarizing the latest developments in their respective areas. More than half of the papers belong to search theory which lies on the borderline of mathematics and computer science, information theory and combinatorics, respectively.

Hungarian mathematics has always been known for discrete mathematics, including combinatorial number theory, set theory and recently random structures, and combinatorial geometry.

This volume honours the eminent mathematicians Vera Sos and Andras Hajnal. Also presented are cutting edge expository research papers with new theorems and proofs in the area of the classical Hungarian subjects, like extremal combinatorics, colorings, combinatorial number theory, etc.

Hungarian mathematics has always been known for discrete mathematics, including combinatorial number theory, set theory and recently random structures, and combinatorial geometry.