The main purpose of this book is to show how ideas from combinatorial group theory have spread to two other areas of mathematics: the theory of Lie algebras and affine algebraic geometry. Some of these ideas, in turn, came to combinatorial group theory from low-dimensional topology in the beginning of the 20th Century.
Examines the relationship between three different areas of mathematics and theoretical computer science: combinatorial group theory, cryptography, and complexity theory. It explores how non-commutative (infinite) groups can be used in public key cryptography. It also shows that there is remarkable feedback from cryptography to combinatorial group theory because some of the problems motivated by cryptography appear to be new to group theory.
This volume consists of contributions by speakers at the AMS Special Session on Combinatorial and Statistical Group Theory held at New York University. Readers will find a variety of contributions, including survey papers on applications of group theory in cryptography, research papers on various aspects of statistical group theory, and papers on more traditional combinatorial group theory. The book is suitable for graduate students and research mathematicians interested in group theory and its applications to cryptography.
A Special Session on affine and algebraic geometry took place at the first joint meeting between the American Mathematical Society (AMS) and the Real Sociedad Matematica Espanola (RSME) held in Seville (Spain). This volume contains articles by participating speakers at the Session. The book contains research and survey papers discussing recent progress on the Jacobian Conjecture and affine algebraic geometry and includes a large collection of open problems. It is suitable for graduate students and research mathematicians interested in algebraic geometry.
AMS Special Session Geometric Group Theory, April 21-22, 2001, Las Vegas, Nevada, AMS Special Session Computational Group Theory, April 28-29, 2001, Hoboken, New Jersey
AMS Special Session Geometric Group Theory, April 21-22, 2001, Las Vegas, Nevada, AMS Special Session Computational Group Theory, April 28-29, 2001, Hoboken, New Jersey
This book gives a nice overview of the diversity of current trends in computational and statistical group theory. It presents the latest research and a number of specific topics, such as growth, black box groups, measures on groups, product replacement algorithms, quantum automata, and more. It includes contributions by speakers at AMS Special Sessions at The University of Nevada (Las Vegas) and the Stevens Institute of Technology (Hoboken, NJ). It is suitable for graduate students and research mathematicians interested in group theory.
This book is about relations between three different areas of mathematics and theoretical computer science: combinatorial group theory, cryptography, and complexity theory. It is explored how non-commutative (infinite) groups, which are typically studied in combinatorial group theory, can be used in public key cryptography. It is also shown that there is a remarkable feedback from cryptography to combinatorial group theory because some of the problems motivated by cryptography appear to be new to group theory, and they open many interesting research avenues within group theory. Then, complexity theory, notably generic-case complexity of algorithms, is employed for cryptanalysis of various cryptographic protocols based on infinite groups, and the ideas and machinery from the theory of generic-case complexity are used to study asymptotically dominant properties of some infinite groups that have been applied in public key cryptography so far. Its elementary exposition makes the book accessible to graduate as well as undergraduate students in mathematics or computer science.
The main purpose of this book is to show how ideas from combinatorial group theory have spread to two other areas of mathematics: the theory of Lie algebras and affine algebraic geometry. Some of these ideas, in turn, came to combinatorial group theory from low-dimensional topology in the beginning of the 20th Century.
AMS Special Session Geometric Group Theory, April 21-22, 2001, Las Vegas, Nevada, AMS Special Session Computational Group Theory, April 28-29, 2001, Hoboken, New Jersey
AMS Special Session Geometric Group Theory, April 21-22, 2001, Las Vegas, Nevada, AMS Special Session Computational Group Theory, April 28-29, 2001, Hoboken, New Jersey
This book gives a nice overview of the diversity of current trends in computational and statistical group theory. It presents the latest research and a number of specific topics, such as growth, black box groups, measures on groups, product replacement algorithms, quantum automata, and more. It includes contributions by speakers at AMS Special Sessions at The University of Nevada (Las Vegas) and the Stevens Institute of Technology (Hoboken, NJ). It is suitable for graduate students and research mathematicians interested in group theory.
This volume consists of contributions by speakers at the AMS Special Session on Combinatorial and Statistical Group Theory held at New York University. Readers will find a variety of contributions, including survey papers on applications of group theory in cryptography, research papers on various aspects of statistical group theory, and papers on more traditional combinatorial group theory. The book is suitable for graduate students and research mathematicians interested in group theory and its applications to cryptography.
Examines the relationship between three different areas of mathematics and theoretical computer science: combinatorial group theory, cryptography, and complexity theory. It explores how non-commutative (infinite) groups can be used in public key cryptography. It also shows that there is remarkable feedback from cryptography to combinatorial group theory because some of the problems motivated by cryptography appear to be new to group theory.
This book shows new directions in group theory motivated by computer science. It reflects the transition from geometric group theory to group theory of the 21st century that has strong connections to computer science. Now that geometric group theory is drifting further and further away from group theory to geometry, it is natural to look for new tools and new directions in group theory which are present.
Covering relations between three different areas of mathematics and theoretical computer science, this book explores how non-commutative (infinite) groups, which are typically studied in combinatorial group theory, can be used in public key cryptography.
Professor Skripov obtained worldwide recognition with his monograph "Metastable liquids", published in English by Wiley & Sons. Based upon this work and another monograph published only in Russia, this book investigates the behavior of melting line and the properties of the coexisting crystal and liquid phase of simple substances across a wide range of pressures, including metastable states of the coexisting phases. The authors derive new relations for the thermodynamic similarity for liquid-vapour phase transition, as well as describing solid-liquid, liquid-vapor and liquid-liquid phase transitions for binary systems employing the novel methodology of thermodynamic similarity.
In this well-written presentation, motivated by numerous examples and problems, the authors introduce the basic theory of braid groups, highlighting several definitions that show their equivalence; this is followed by a treatment of the relationship between braids, knots and links. Important results then treat the linearity and orderability of the subject. Relevant additional material is included in five large appendices. Braid Groups will serve graduate students and a number of mathematicians coming from diverse disciplines.
Readers intent on mastering the basics should start by reading the first few overview chapters and then delve into the descriptions of specific current applications to see how they actually work. Important future applications are also outlined, including information storage, materials for computer memories, quantum computers, isotopic fibers, isotopic optoelectronics, and quantum electronics.
This book describes new trends in the nanoscience of isotopic materials science. Assuming a background in graduate condensed matter physics and covering the fundamental aspects of isotopic materials science from the very beginning, it equips readers to engage in high-level professional research in this area. The book ́s main objective is to provide insight into the question of why solids are the way they are, either because of how their atoms are bonded with one another, because of defects in their structure, or because of how they are produced or processed. Accordingly, it explores the science of how atoms interact, connects the results to real materials properties, and demonstrates the engineering concepts that can be used to produce or improve semiconductors by design. In addition, it shows how the concepts discussed are applied in the laboratory. The book addresses the needs of researchers, graduate students and senior undergraduate students alike. Although primarily written for materials science audience, it will be equally useful to those teaching in electrical engineering, materials science or even chemical engineering or physics curricula. In order to maintain the focus on materials concepts, however, the book does not burden the reader with details of many of the derivations and equations nor does it delve into the details of electrical engineering topics.
Presenting some of the most recent results of Russian research into shock compression, as well as historical overviews of the Russian research programs into shock compression, this volume will provide Western researchers with many novel ideas and points of view. The chapters in this volume are written by leading Russian specialists various fields of high-pressure physics and form accounts of the main researches on the behavior of matter under shock-wave interaction. The experimental portions contain results of studies of shock compression of metals to high and ultra-high pressure, shock initiation of polymorphic transformations, strength, fracture and fragmentation under shock compression, and detonation of condensed explosives. There are also chapters on theoretical investigations of shock-wave compression and plasma states in regimes of high-pressure and high- temperature. The topics of the book are of interest to scientists and engineers concerned with questions of material behavior under impulsive loading and to the equation of state of matter. Application is to questions of high-speed impact, inner composition of planets, verification of model representations of material behavior under extreme 1oading conditions, syntheses of new materials, development of new technologies for material processing, etc. Russian research differs from much of the Western work in that it has traditionally been wider-ranging and more directed to extremes of response than to precise characterization of specific materials and effects. Western scientists could expect to benefit from the perspective gained from close knowledge of the Russian work.
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