This is the first book to comprehensively cover chromatic polynomials of graphs. It includes most of the known results and unsolved problems in the area of chromatic polynomials. Dividing the book into three main parts, the authors take readers from the rudiments of chromatic polynomials to more complex topics: the chromatic equivalence classes of graphs and the zeros and inequalities of chromatic polynomials. The early material is well suited to a graduate level course while the latter parts will be an invaluable resource for postgraduate students and researchers in combinatorics and graph theory.

In addition to explaining and modeling unexplored phenomena in nature and society, chaos uses vital parts of nonlinear dynamical systems theory and established chaotic theory to open new frontiers and fields of study. Handbook of Applications of Chaos Theory covers the main parts of chaos theory along with various applications to diverse areas. Expert contributors from around the world show how chaos theory is used to model unexplored cases and stimulate new applications. Accessible to scientists, engineers, and practitioners in a variety of fields, the book discusses the intermittency route to chaos, evolutionary dynamics and deterministic chaos, and the transition to phase synchronization chaos. It presents important contributions on strange attractors, self-exciting and hidden attractors, stability theory, Lyapunov exponents, and chaotic analysis. It explores the state of the art of chaos in plasma physics, plasma harmonics, and overtone coupling. It also describes flows and turbulence, chaotic interference versus decoherence, and an application of microwave networks to the simulation of quantum graphs. The book proceeds to give a detailed presentation of the chaotic, rogue, and noisy optical dissipative solitons; parhelic-like circle and chaotic light scattering; and interesting forms of the hyperbolic prism, the Poincare disc, and foams. It also covers numerous application areas, from the analysis of blood pressure data and clinical digital pathology to chaotic pattern recognition to economics to musical arts and research.

Conveniently grouping methods by techniques, such as chi-squared and empirical distributionfunction, and also collecting methods of testing for specific famous distributions, this useful reference is the first comprehensive review of the extensive literature on the subject. It surveysthe leading methods of testing fit . .. provides tables to make the tests available . .. assessesthe comparative merits of different test procedures . .. and supplies numerical examples to aidin understanding these techniques.Goodness-of-Fit Techniques shows how to apply the techniques . .. emphasizes testing for thethree major distributions, normal, exponential, and uniform . .. discusses the handling of censoreddata .. . and contains over 650 bibliographic citations that cover the field.Illustrated with tables and drawings, this volume is an ideal reference for mathematical andapplied statisticians, and biostatisticians; professionals in applied science fields, including psychologists,biometricians , physicians, and quality control and reliability engineers; advancedundergraduate- and graduate-level courses on goodness-of-fit techniques; and professional seminarsand symposia on applied statistics, quality control, and reliability.

Extremal Optimization: Fundamentals, Algorithms, and Applications introduces state-of-the-art extremal optimization (EO) and modified EO (MEO) solutions from fundamentals, methodologies, and algorithms to applications based on numerous classic publications and the authors' recent original research results. It promotes the movement of EO from academic study to practical applications. The book covers four aspects, beginning with a general review of real-world optimization problems and popular solutions with a focus on computational complexity, such as "NP-hard" and the "phase transitions" occurring on the search landscape. Next, it introduces computational extremal dynamics and its applications in EO from principles, mechanisms, and algorithms to the experiments on some benchmark problems such as TSP, spin glass, Max-SAT (maximum satisfiability), and graph partition. It then presents studies on the fundamental features of search dynamics and mechanisms in EO with a focus on self-organized optimization, evolutionary probability distribution, and structure features (e.g., backbones), which are based on the authors' recent research results. Finally, it discusses applications of EO and MEO in multiobjective optimization, systems modeling, intelligent control, and production scheduling. The authors present the advanced features of EO in solving NP-hard problems through problem formulation, algorithms, and simulation studies on popular benchmarks and industrial applications. They also focus on the development of MEO and its applications. This book can be used as a reference for graduate students, research developers, and practical engineers who work on developing optimization solutions for those complex systems with hardness that cannot be solved with mathematical optimization or other computational intelligence, such as evolutionary computations.

At the heart of modern cryptographic algorithms lies computational number theory. Whether you're encrypting or decrypting ciphers, a solid background in number theory is essential for success. Written by a number theorist and practicing cryptographer, Cryptanalysis of Number Theoretic Ciphers takes you from basic number theory to the inner workings of ciphers and protocols.

First, the book provides the mathematical background needed in cryptography as well as definitions and simple examples from cryptography. It includes summaries of elementary number theory and group theory, as well as common methods of finding or constructing large random primes, factoring large integers, and computing discrete logarithms. Next, it describes a selection of cryptographic algorithms, most of which use number theory. Finally the book presents methods of attack on the cryptographic algorithms and assesses their effectiveness. For each attack method the author lists the systems it applies to and tells how they may be broken with it.

Computational number theorists are some of the most successful cryptanalysts against public key systems. Cryptanalysis of Number Theoretic Ciphers builds a solid foundation in number theory and shows you how to apply it not only when breaking ciphers, but also when designing ones that are difficult to break.

This monograph covers some of the most important developments in Ramsey theory from its beginnings in the early 20th century via its many breakthroughs to recent important developments in the early 21st century.

The book first presents a detailed discussion of the roots of Ramsey theory before offering a thorough discussion of the role of parameter sets. It presents several examples of structures that can be interpreted in terms of parameter sets and features the most fundamental Ramsey-type results for parameter sets: Hales-Jewett's theorem and Graham-Rothschild s Ramsey theorem as well as their canonical versions and several applications. Next, the book steps back to the most basic structure, to sets. It reviews classic results as well as recent progress on Ramsey numbers and the asymptotic behavior of classical Ramsey functions. In addition, it presents product versions of Ramsey's theorem, a combinatorial proof of the incompleteness of Peano arithmetic, provides a digression to discrepancy theory and examines extensions of Ramsey's theorem to larger cardinals. The next part of the book features an in-depth treatment of the Ramsey problem for graphs and hypergraphs. It gives an account on the existence of sparse and restricted Ramsey theorem's using sophisticated constructions as well as probabilistic methods. Among others it contains a proof of the induced Graham-Rothschild theorem and the random Ramsey theorem. The book closes with a chapter on one of the recent highlights of Ramsey theory: a combinatorial proof of the density Hales-Jewett theorem.

This book provides graduate students as well as advanced researchers with a solid introduction and reference to the field."

Putting the G into CAGD, the authors provide a much-needed practical and basic introduction to computer-aided geometric design. This book will help readers understand and use the elements of computer-aided geometric design, curves and surfaces, without the mathematical baggage that is necessary only for more advanced work. Though only minimal background in mathematics is needed to understand the bookis concepts, the book covers an amazing array of topics such as Bezier and B-spline curves and their corresponding surfaces, subdivision surfaces, and NURBS (Non-Uniform Rational B-Splines). Also included are techniques such as interpolation and least squares methods.

Dirk van Dalen's biography studies the fascinating life of the famous Dutch mathematician and philosopher Luitzen Egbertus Jan Brouwer. Brouwer belonged to a special class of genius; complex and often controversial and gifted with a deep intuition, he had an unparalleled access to the secrets and intricacies of mathematics. Most mathematicians remember L.E.J. Brouwer from his scientific breakthroughs in the young subject of topology and for the famous Brouwer fixed point theorem. Brouwer's main interest, however, was in the foundation of mathematics which led him to introduce, and then consolidate, constructive methods under the name 'intuitionism'. This made him one of the main protagonists in the 'foundation crisis' of mathematics. As a confirmed internationalist, he also got entangled in the interbellum struggle for the ending of the boycott of German and Austrian scientists. This time during the twentieth century was turbulent; nationalist resentment and friction between formalism and intuitionism led to the Mathematische Annalen conflict ('The war of the frogs and the mice'). It was here that Brouwer played a pivotal role. The present biography is an updated revision of the earlier two volume biography in one single book. It appeals to mathematicians and anybody interested in the history of mathematics in the first half of the twentieth century.

Algorithms that control the computational processes relating sensors and actuators are indispensable for robot navigation and the perception of the world in which they move. Therefore, a deep understanding of how algorithms work to achieve this control is essential for the development of efficient and usable robots in a broad field of applications. An interdisciplinary group of scientists gathers every two years to document the progress in algorithmic foundations of robotics. This volume addresses in particular the areas of control theory, computational and differential geometry in robotics, and applications to core problems such as motion planning, navigation, sensor-based planning, and manipulation.

This book is a history of artificial intelligence, that audacious effort to duplicate in an artifact what we consider to be our most important property-our intelligence. It is an invitation for anybody with an interest in the future of the human race to participate in the inquiry.

A revised and expanded advanced-undergraduate/graduate text (first ed., 1978) about optimization algorithms for problems that can be formulated on graphs and networks. This edition provides many new applications and algorithms while maintaining the classic foundations on which contemporary algorithm

Recognized as a "Recommended" title by Choice for their April 2021 issue. Choice is a publishing unit at the Association of College & Research Libraries (ACR&L), a division of the American Library Association. Choice has been the acknowledged leader in the provision of objective, high-quality evaluations of nonfiction academic writing. Metaheuristic optimization is a higher-level procedure or heuristic designed to find, generate, or select a heuristic (partial search algorithm) that may provide a sufficiently good solution to an optimization problem, especially with incomplete or imperfect information or limited computation capacity. This is usually applied when two or more objectives are to be optimized simultaneously. This book is presented with two major objectives. Firstly, it features chapters by eminent researchers in the field providing the readers about the current status of the subject. Secondly, algorithm-based optimization or advanced optimization techniques, which are applied to mostly non-engineering problems, are applied to engineering problems. This book will also serve as an aid to both research and industry. Usage of these methodologies would enable the improvement in engineering and manufacturing technology and support an organization in this era of low product life cycle. Features: Covers the application of recent and new algorithms Focuses on the development aspects such as including surrogate modeling, parallelization, game theory, and hybridization Presents the advances of engineering applications for both single-objective and multi-objective optimization problems Offers recent developments from a variety of engineering fields Discusses Optimization using Evolutionary Algorithms and Metaheuristics applications in engineering

Practical Handbook of Genetic Algorithms, Volume 3: Complex Coding Systems contains computer-code examples for the development of genetic algorithm systems - compiling them from an array of practitioners in the field. Each contribution of this singular resource includes: unique code segments documentation description of the operations performed rationale for the chosen approach problems the code overcomes or addresses Practical Handbook of Genetic Algorithms, Volume 3: Complex Coding Systems complements the first two volumes in the series by offering examples of computer code. The first two volumes dealt with new research and an overview of the types of applications that could be taken with GAs. This volume differs from its predecessors by specifically concentrating on specific functions in genetic algorithms, serving as the only compilation of useful and usable computer code in the field.

"Contains the contributions of 45 internationally distinguished mathematicians covering all areas of approximation theory-written in honor of the pioneering work of Arun K. Varma to the fields of interpolation and approximation of functions, including Birhoff interpolation and approximation by spline functions."

This latest collection of puzzles from the internationally acclaimed puzzlemaster Nob Yoshigahara covers a wide variety of puzzles from physical to visual, conceptual to mathematical. Solutions are provided in a separate section, which will help novices get on the right track, and will give seasoned aficionados a chance to check their work.

This story of a highly intelligent observer of the turbulent 20th century who was intimately involved as the secretary and bodyguard to Leon Trotsky is based on extensive interviews with the subject, Jean van Heijenoort, and his family, friends, and colleagues. The author has captured the personal drama and the professional life of her protagonist--ranging from the political passion of a young intellectual to the scientific and historic work in the most abstract and yet philosophically important area of logic--in a very readable narrative.

Logic is now widely recognized to be one of the foundational disciplines of computing with applications in virtually all aspects of the subject, from software engineering and hardware development to programming languages and artificial intelligence. There is a growing need for an in-depth survey of the applications of logic in AI and computer science. The Handbook of Logic in Artificial Intelligence and Logic Programming and its companion, Handbook of Logic in Computer Science, have been created in response to this need. This book is a combination of authoritative exposition, comprehensive survey, and fundamental research that explores underlying unifying themes in the various subject areas. Chapters have been written by an internationally renowned team of researchers and are coordinated in terms of the theories discussed and the examples offered. This book will be of interest to graduate students and researchers in all areas of artificial intelligence, computer science, and logic, as well as to logicians and mathematicians.

This volume focuses on the important mathematical idea of functions that, with the technology of computers and calculators, can be dynamically represented in ways that have not been possible previously. The book's editors contend that as result of recent technological developments combined with the integrated knowledge available from research on teaching, instruction, students' thinking, and assessment, curriculum developers, researchers, and teacher educators are faced with an unprecedented opportunity for making dramatic changes.
The book presents content considerations that occur when the mathematics of graphs and functions relate to curriculum. It also examines content in a carefully considered integration of research that conveys where the field stands and where it might go. Drawing heavily on their own work, the chapter authors reconceptualize research in their specific areas so that this knowledge is integrated with the others' strands. This model for synthesizing research can serve as a paradigm for how research in mathematics education can -- and probably should -- proceed.

Nonlinear Dynamics of Reservoir Mixtures provides an overview of modeling techniques for solving nonlinear problems in hydrodynamics, with an emphasis on compositional flows in porous reservoirs. The volume focuses on nonlinear wave techniques for simulating and predicting fluid dynamic processes in petroleum reservoirs and discusses general applications of these models for other fluids.
Topics covered include inhomogeneous space structures in reservoir processes, gradient models for analyzing changes in thermodynamic and hydrodynamic fluid properties, phase transition dynamics in fluids and rock minerals, and wetting phenomena. The book also discusses the stages involved in developing compositional simulators for enhanced oil recovery and describes applications used in hydrocarbon fields in the former USSR.
Nonlinear Dynamics of Reservoir Mixtures provides excellent reference material for mathematicians, petroleum engineers, exploration geophysicists, and mechanical engineers. It is also a useful compositional modeling text for graduate students in the earth sciences and in petroleum and chemical engineering.

This graduate level text is distinguished both by the range of topics and the novelty of the material it treats--more than half of the material in it has previously only appeared in research papers. The first half of this book introduces the characteristic and matchings polynomials of a graph. It is instructive to consider these polynomials together because they have a number of properties in common. The matchings polynomial has links with a number of problems in combinatorial enumeration, particularly some of the current work on the combinatorics of orthogonal polynomials. This connection is discussed at some length, and is also in part the stimulus for the inclusion of chapters on orthogonal polynomials and formal power series. Many of the properties of orthogonal polynomials are derived from properties of characteristic polynomials. The second half of the book introduces the theory of polynomial spaces, which provide easy access to a number of important results in design theory, coding theory and the theory of association schemes. This book should be of interest to second year graduate text/reference in mathematics.

Examines partitions and covers of graphs and digraphs, latin squares, pairwise balanced designs with prescribed block sizes, ranks and permanents, extremal graph theory, Hadamard matrices and graph factorizations. This book is designed to be of interest to applied mathematicians, computer scientists and communications researchers.

This handsome book is aimed towards those with an intermediate skill level, but the origami basics included at the start of the book make it accessible to beginners. A number of beautiful models are offered, ranging from cubes to prisms to dodecahedra. As with the author's two previous books, Origami Inspirations provides step-by-step instructions and color distribution suggestions to create the more than 30 intricate designs presented. The book also includes a chapter featuring designs by origami artists from around the world, and these projects provide a happy complement to the author's own exciting inspirations in the rest of the book.

In the theory of splines, a function is approximated piece-wise by (usually cubic) polynomials. Quasi-splines is the natural extension of this, allowing us to use any useful class of functions adapted to the problem.
Approximation with Quasi-Splines is a detailed account of this highly useful technique in numerical analysis.
The book presents the requisite approximation theorems and optimization methods, developing a unified theory of one and several variables. The author applies his techniques to the evaluation of definite integrals (quadrature) and its many-variables generalization, which he calls "cubature."
This book should be required reading for all practitioners of the methods of approximation, including researchers, teachers, and students in applied, numerical and computational mathematics.

Principles of Scientific Methods focuses on the fundamental principles behind scientific methods. The book refers to "science" in a broad sense, including natural science, physics, mathematics, statistics, social science, political science, and engineering science. A principle is often abstract and has broad applicability while a method is usually concrete and specific. The author uses many concrete examples to explain principles and presents analogies to connect different methods or problems to arrive at a general principle or a common notion. He mainly discusses a particular method to address the great idea behind the method, not the method itself. The book shows how the principles are not only applicable to scientific research but also to our daily lives. The author explains how scientific methods are used for understanding how and why things happen, making predictions, and learning how to prevent mistakes and solve problems. Studying the principles of scientific methods is to think about thinking and to enlighten our understanding of scientific research. Scientific principles are the foundation of scientific methods. In this book, you'll see how the principles reveal the big ideas behind our scientific discoveries and reflect the fundamental beliefs and wisdoms of scientists. The principles make the scientific methods coherent and constitute the source of creativity.

This richly illustrated book provides step-by-step instructions for the construction of over 30 different modular origami structures. The author describes basic folding techniques required to construct themodules that are used as building blocks to construct complex ornamental models. The diagrams are clear, crisp, and easy to follow, and are accompanied by inspiring color photographs. Additional tips encourage the reader to design their own original creations. Advance Praise for Marvelous Modular Origami "A must-have for any modular origami polyhedra enthusiast." -Rona Gurkewitz, co-author of Multimodular Origami Polyhedra "The models are paper folding in its purest form. They range from simple Sonobe to floral and geometrical constructions. All are eye-catching and satisfying to fold, and the finished constructions are pleasing to behold. Also included are short sections on the mathematics behind the shapes and optimum color choices." -David Petty, author of Origami A-B-C "In this colorful book, you'll find wonderful original origami modular creations. Meenakshi's clear instructions and helpful hints will have you zipping through these modules as well as improvising your own." -Rachel Katz, co-author of FUN FOLDS: Language Learning Through Paper Folding "Marvelous Modular Origami is a colorful addition to the literature of mathematical origami." -Florence Temko, author of many origami and other craft books