This is the second of three volumes containing the proceedings of the International Colloquium 'Free Boundary Problems: Theory and Applications', held in Montreal from June 13 to June 22, 1990. The main theme of this volume is the concept of free boundary problems associated with solids. The first free boundary problem, the freezing of water - the Stefan problem - is the prototype of solidification problems which form the main part of this volume. The two sections treting this subject cover a large variety of topics and procedures, ranging from a theoretical mathematical treatment of solvability to numerical procedures for practical problems. Some new and interesting problems in solid mechanics are discussed in the first section while in the last section the important new subject of solid-solid-phase transition is examined.

These two volumes consist of chapters written by students and colleagues of W.K. Estes. The books' contributors -- themselves eminent figures in the field -- reflect on Estes' sweeping contributions to mathematical as well as cognitive and experimental psychology. As indicated by their titles, Volume I features mathematical and theoretical essays, and Volume II presents cognitive and experimental essays. Both volumes contain insightful literature reviews as well as descriptions of exciting new theoretical and empirical advances. Many of the essays also incorporate personal reminiscences reflecting the authors' fond affection for their illustrious mentor.

A best-seller in its French edition, the construction of this book is original and its success in the French market demonstrates its appeal. It is based on three principles: 1. An organization of the chapters by families of algorithms : exhaustive search, divide and conquer, etc. At the contrary, there is no chapter only devoted to a systematic exposure of, say, algorithms on strings. Some of these will be found in different chapters. 2. For each family of algorithms, an introduction is given to the mathematical principles and the issues of a rigorous design, with one or two pedagogical examples. 3. For its most part, the book details 150 problems, spanning on seven families of algorithms. For each problem, a precise and progressive statement is given. More important, a complete solution is detailed, with respect to the design principles that have been presented ; often, some classical errors are pointed at. Roughly speaking, two thirds of the book are devoted to the detailed rational construction of the solutions.

This book focuses on the class of large-scale stochastic systems, which has dominated the attention of many academic and research groups. It discusses distributed-sensor networks, decentralized detection theory, and econometric models with integrated and decentralized policymakers.

Discrete Mathematics for New Technology has been designed to cover the core mathematics requirement for undergraduate computer science students in the UK and the USA. This has been approached in a comprehensive way whilst maintaining an easy to follow progression from the basic mathematical concepts covered by the GCSE in the UK and by high-school algebra in the USA, to the more sophisticated mathematical concepts examined in the latter stages of the book. The rigorous treatment of theory is punctuated by frequent use of pertinent examples. This is then reinforced with exercises to allow the reader to achieve a "feel" for the subject at hand. Hints and solutions are provided for these brain-teasers at the end of the book. Although aimed primarily at computer science students, the structured development of the mathematics enables this text to be used by undergraduate mathematicians, scientists and others who require an understanding of discrete mathematics. The topics covered include: logic and the nature of mathematical proof set theory, relations and functions, matrices and systems of linear equations, algebraic structures, Boolean algebras and a thorough treatise on graph theory. The authors have extensive experience of teaching undergraduate mathematics at colleges and universities in the British and American systems. They have developed and taught courses for a varied of non-specialists and have established reputations for presenting rigorous mathematical concepts in a manner which is accessible to this audience. Their current research interests lie in the fields of algebra, topology and mathematics education. Discrete Mathematics for New Technology is therefore a rare thing; areadable, friendly textbook designed for non-mathematicians, presenting material which is at the foundations of mathematics itself. It is essential reading.

This volume provides a comprehensive introduction to module theory and the related part of ring theory, including original results as well as the most recent work. It is a useful and stimulating study for those new to the subject as well as for researchers and serves as a reference volume. Starting form a basic understanding of linear algebra, the theory is presented and accompanied by complete proofs. For a module M, the smallest Grothendieck category containing it is denoted by o[M] and module theory is developed in this category. Developing the techniques in o[M] is no more complicated than in full module categories and the higher generality yields significant advantages: for example, module theory may be developed for rings without units and also for non-associative rings. Numerous exercises are included in this volume to give further insight into the topics covered and to draw attention to related results in the literature.

Features Provides an accessible introduction to mathematics in art Supports the narrative with a self-contained mathematical theory, with complete proofs of the main results (including the classification theorem for similarities) Presents hundreds of figures, illustrations, computer-generated graphics, designs, photographs, and art reproductions, mainly presented in full color Includes 21 projects and about 280 exercises, about half of which are fully solved Covers Euclidean geometry, golden section, Fibonacci numbers, symmetries, tilings, similarities, fractals, cellular automata, inversion, hyperbolic geometry, perspective drawing, Platonic and Archimedean solids, and topology New to the Second Edition New exercises, projects and artworks Revised, reorganised and expanded chapters More use of color throughout

Order stars is a recently developed technique to analyze and explain the behaviour of numerical methods. The main idea is to explore different features of numerical algorithms as properties of analytical functions in various portions of the complex plane. Thus, for example, the order of some numerical methods for ordinary differential equations can be translated to the language of approximation theory - specifically, to the question of how well a given rational function R approximates the exponential. Likewise, stability properties of the underlying method can be expressed as some other features of the function R. In this formulation, order stars establish the relationship between order and stability, helping in the search for better and more efficient computational algorithms.

New Edition! Completely Revised and Updated
Chemical Graph Theory, 2nd Edition is a completely revised and updated edition of a highly regarded book that has been widely used since its publication in 1983. This unique book offers a basic introduction to the handling of molecular graphs - mathematical diagrams representing molecular structures. Using mathematics well within the vocabulary of most chemists, this volume elucidates the structural aspects of chemical graph theory: (1) the relationship between chemical and graph-theoretical terminology, elements of graph theory, and graph-theoretical matrices; (2) the topological aspects of the Hückel theory, resonance theory, and theories of aromaticity; and (3) the applications of chemical graph theory to structure-property and structure-activity relationships and to isomer enumeration. An extensive bibliography covering the most relevant advances in theory and applications is one of the book's most valuable features. This volume is intended to introduce the entire chemistry community to the applications of graph theory and will be of particular interest to theoretical organic and inorganic chemists, physical scientists, computational chemists, and those already involved in mathematical chemistry.

- the book provides a unique overview of the NCBI resources, including BLAST (which are foundational to bioinformatics), and how to use them, making it a great introduction to bioinformatics and a great resource for those just starting in an industry lab - whereas many bioinformatics books try to cover every aspect of the topic and easily confuse readers, this is highly practical and focuses on key resources and tools, and how to use them - the companion website contains tutorials, R and Python codes, instructor materials including slides, exercises, and problems for students

Covers ODEs and PDEs-in One TextbookUntil now, a comprehensive textbook covering both ordinary differential equations (ODEs) and partial differential equations (PDEs) didn't exist. Fulfilling this need, Ordinary and Partial Differential Equations provides a complete and accessible course on ODEs and PDEs using many examples and exercises as well as intuitive, easy-to-use software. Teaches the Key Topics in Differential Equations The text includes all the topics that form the core of a modern undergraduate or beginning graduate course in differential equations. It also discusses other optional but important topics such as integral equations, Fourier series, and special functions. Numerous carefully chosen examples offer practical guidance on the concepts and techniques. Guides Students through the Problem-Solving Process Requiring no user programming, the accompanying computer software allows students to fully investigate problems, thus enabling a deeper study into the role of boundary and initial conditions, the dependence of the solution on the parameters, the accuracy of the solution, the speed of a series convergence, and related questions. The ODE module compares students' analytical solutions to the results of computations while the PDE module demonstrates the sequence of all necessary analytical solution steps.

Structural dynamics is a complex and increasingly important field of civil/structural engineering. The aim of this concise book is to demonstrate to practising engineers and advanced students that the dynamic response of structural systems can be understood without advanced techniques of analysis and impenetrable detail.

Construction Mathematics is an introductory level mathematics text, written specifically for students of construction and related disciplines. Learn by tackling exercises based on real-life construction maths. Examples include: costing calculations, labour costs, cost of materials and setting out of building components. Suitable for beginners and easy to follow throughout. Learn the essential basic theory along with the practical necessities. The second edition of this popular textbook is fully updated to match new curricula, and expanded to include even more learning exercises. End of chapter exercises cover a range of theoretical as well as practical problems commonly found in construction practice, and three detailed assignments based on practical tasks give students the opportunity to apply all the knowledge they have gained. Construction Mathematics addresses all the mathematical requirements of Level 2 construction NVQs from City & Guilds/CITB and Edexcel courses, including the BTEC First Diploma in Construction. Additional coverage of the core unit Mathematics in Construction and the Built Environment from BTEC National Construction, Civil Engineering and Building Services courses makes this an essential revision aid for students who do not have Level 2 mathematics experience before commencing their BTEC National studies. This is also the ideal primer for any reader who wishes to refresh their mathematics knowledge before going into a construction HNC or BSc.

The core content of even the most intricate intellectual edifices is often a simple fact or idea. So is it with quantum mechanics; the entire mathematical fabric of the formal description of quantum mechanics stems essentially from the fact that quantum probabilities interfere (i.e., from the superposition principle). This book is dedicated to substantiating this claim. In the process, the book tries to demonstrate how the factual content of quantum mechanics can be transcribed in the formal language of vector spaces and linear transformations by disentangling the empirical content from the usual formal description. More importantly, it tries to bring out what this transcription achieves. The book uses a pedagogic strategy which reverse engineers the postulates of quantum mechanics to device a schematic outline of the empirical content of quantum mechanics from which the postulates are then reconstructed step by step. This strategy is adopted to avoid the disconcerting details of actual experiments (however simplified) to spare the beginner of issues that lurk in the fragile foundations of the subject. In the Copenhagen interpretation of quantum mechanics, the key idea is measurement. But "measurement" carries an entirely different meaning from the connotation that the term carries elsewhere in physics. This book strives to underline this as strongly as possible. The book is intended as an undergraduate text for a first course in quantum mechanics. Since the book is self contained, it may also be used by enthusiastic outsiders interested to get a glimpse of the core content of the subject. Features: Demonstrates why linear algebra is the appropriate mathematical language for quantum mechanics. Uses a reconstructive approach to motivate the postulates of quantum mechanics. Builds the vocabulary of quantum mechanics by showing how the entire body of its conceptual ingredients can be constructed from the single notion of quantum measurement.

Includes over 250 solved problems to supplement graduate-level courses in fluid mechanics and turbomachinery. Enables students to practice applying key concepts of fluid mechanics and the governing conservation laws to solve real-world problems. Uses the physics-first approach, allowing for a good understanding of the problem physics and the results obtained. Covers problems on flowpath aerodynamics design. Covers problems on secondary air systems modeling of gas turbines.

1) Presents a new type of S-N equation 2) Discusses empirical fracture equations of mixed mode crack 3) Applies the Wohler Curve Methods for a Low/Medium/High cycle fatigue in metallic materials 4) Enables the reader to analyse failure and fracture in metallic materials

Designed as an introduction to numerical methods for students, this book combines mathematical correctness with numerical performance, and concentrates on numerical methods and problem solving. It applies actual numerical solution strategies to formulated process models to help identify and solve chemical engineering problems. Second edition comes with additional chapter on numerical integration and section on boundary value problems in the relevant chapter. Additional material on general modelling principles, mass/energy balances and separate section on DAE's is also included. Case study section has been extended with additional examples.

This book investigates why economics makes less visible progress over time than scientific fields with a strong practical component, where interactions with physical technologies play a key role. The thesis of the book is that the main impediment to progress in economics is "false feedback", which it defines as the false result of an empirical study, such as empirical evidence produced by a statistical model that violates some of its assumptions. In contrast to scientific fields that work with physical technologies, false feedback is hard to recognize in economics. Economists thus have difficulties knowing where they stand in their inquiries, and false feedback will regularly lead them in the wrong directions. The book searches for the reasons behind the emergence of false feedback. It thereby contributes to a wider discussion in the field of metascience about the practices of researchers when pursuing their daily business. The book thus offers a case study of metascience for the field of empirical economics. The main strength of the book are the numerous smaller insights it provides throughout. The book delves into deep discussions of various theoretical issues, which it illustrates by many applied examples and a wide array of references, especially to philosophy of science. The book puts flesh on complicated and often abstract subjects, particularly when it comes to controversial topics such as p-hacking. The reader gains an understanding of the main challenges present in empirical economic research and also the possible solutions. The main audience of the book are all applied researchers working with data and, in particular, those who have found certain aspects of their research practice problematic.

The text covers a wide range of topics such as mathematical modeling of crop pest control management, water resources management, impact of anthropogenic activities on atmospheric carbon dioxide concentrations, impact of climate changes on melting of glaciers and polar bear populations, dynamics of slow-fast predator-prey system and spread and control of HIV epidemic. It emphasizes the use of mathematical modeling to investigate the fluid flow problems including the breaking of viscoelastic jet, instability arising in nanofiber, flow in an annulus channel, and thermal instability in nano-fluids in a comprehensive manner. This book will be a readily accessible source of information for the students, researchers and policymakers interested in the application of mathematical and computational modeling techniques to investigate various biological and engineering phenomena. Features Focuses on the current modeling and computational trends to investigate various ecological, epidemiological, and engineering systems. Presents the mathematical modeling of a wide range of ecological and environmental issues including crop pest control management, water resources management, the effect of anthropogenic activities on atmospheric carbon dioxide concentrations, and impact of climate changes on melting of glaciers and polar bear population. Covers a wide range of topics including the breaking of viscoelastic jet, instability arising in nanofiber, flow in an annulus channel, and thermal instability in nano-fluids. Examines evolutionary models i.e., models of time-varying processes. Highlights the recent developments in the analytical methods to investigate the nonlinear dynamical systems. Showcases diversified applications of computational techniques to solve practical biological and engineering problems. The book focuses on the recent research developments in the mathematical modeling and scientific computing of biological and engineering systems. It will serve as an ideal reference text for senior undergraduate, graduate students, and researchers in diverse fields including ecological engineering, environmental engineering, computer engineering, mechanical engineering, mathematics, and fluid dynamics.

Risk Measures and Insurance Solvency Benchmarks: Fixed-Probability Levels in Renewal Risk Models is written for academics and practitioners who are concerned about potential weaknesses of the Solvency II regulatory system. It is also intended for readers who are interested in pure and applied probability, have a taste for classical and asymptotic analysis, and are motivated to delve into rather intensive calculations. The formal prerequisite for this book is a good background in analysis. The desired prerequisite is some degree of probability training, but someone with knowledge of the classical real-variable theory, including asymptotic methods, will also find this book interesting. For those who find the proofs too complicated, it may be reassuring that most results in this book are formulated in rather elementary terms. This book can also be used as reading material for basic courses in risk measures, insurance mathematics, and applied probability. The material of this book was partly used by the author for his courses in several universities in Moscow, Copenhagen University, and in the University of Montreal. Features Requires only minimal mathematical prerequisites in analysis and probability Suitable for researchers and postgraduate students in related fields Could be used as a supplement to courses in risk measures, insurance mathematics and applied probability.

This monograph provides a careful review of the major statistical techniques used to analyze regression data with nonconstant variability and skewness. The authors have developed statistical techniques--such as formal fitting methods and less formal graphical techniques-- that can be applied to many problems across a range of disciplines, including pharmacokinetics, econometrics, biochemical assays, and fisheries research.

While the main focus of the book in on data transformation and weighting, it also draws upon ideas from diverse fields such as influence diagnostics, robustness, bootstrapping, nonparametric data smoothing, quasi-likelihood methods, errors-in-variables, and random coefficients. The authors discuss the computation of estimates and give numerous examples using real data. The book also includes an extensive treatment of estimating variance functions in regression.

Classical mechanics is a subject that is teeming with life. However, most of the interesting results are scattered around in the specialist literature, which means that potential readers may be somewhat discouraged by the effort required to obtain them. Addressing this situation, Hamiltonian Dynamical Systems includes some of the most significant papers in Hamiltonian dynamics published during the last 60 years. The book covers bifurcation of periodic orbits, the break-up of invariant tori, chaotic behavior in hyperbolic systems, and the intricacies of real systems that contain coexisting order and chaos. It begins with an introductory survey of the subjects to help readers appreciate the underlying themes that unite an apparently diverse collection of articles. The book concludes with a selection of papers on applications, including in celestial mechanics, plasma physics, chemistry, accelerator physics, fluid mechanics, and solid state mechanics, and contains an extensive bibliography. The book provides a worthy introduction to the subject for anyone with an undergraduate background in physics or mathematics, and an indispensable reference work for researchers and graduate students interested in any aspect of classical mechanics.

This new book aims to provide to both beginners and experts with a completely algorithmic approach to data analysis and conceptual modeling, database design, implementation, and tuning, starting from vague and incomplete customer requests and ending with IBM DB/2, Oracle, MySQL, MS SQL Server, or Access based software applications. A rich panoply of solutions to actual useful data sub-universes (e.g. business, university, public and home library, geography, history, etc.) is provided, constituting a powerful library of examples. Four data models are presented and used: the graphical Entity-Relationship, the mathematical EMDM, the physical Relational, and the logical deterministic deductive Datalogones. For each one of them, best practice rules, algorithms, and the theory beneath are clearly separated. Four case studies, from a simple public library example, to a complex geographical study are fully presented, on all needed levels. Several dozens of real life exercises are proposed, out of which at least one per chapter is completely solved. Both major historical and up-to-date references are provided for each of the four data models considered. The book provides a library of useful solutions to real-life problems and provides valuable knowledge on data analysis and modeling, database design, implementation, and fine tuning.

Although there has been a surge of interest in density estimation in recent years, much of the published research has been concerned with purely technical matters with insufficient emphasis given to the technique's practical value. Furthermore, the subject has been rather inaccessible to the general statistician.

The account presented in this book places emphasis on topics of methodological importance, in the hope that this will facilitate broader practical application of density estimation and also encourage research into relevant theoretical work. The book also provides an introduction to the subject for those with general interests in statistics. The important role of density estimation as a graphical technique is reflected by the inclusion of more than 50 graphs and figures throughout the text.

Several contexts in which density estimation can be used are discussed, including the exploration and presentation of data, nonparametric discriminant analysis, cluster analysis, simulation and the bootstrap, bump hunting, projection pursuit, and the estimation of hazard rates and other quantities that depend on the density. This book includes general survey of methods available for density estimation. The Kernel method, both for univariate and multivariate data, is discussed in detail, with particular emphasis on ways of deciding how much to smooth and on computation aspects. Attention is also given to adaptive methods, which smooth to a greater degree in the tails of the distribution, and to methods based on the idea of penalized likelihood.

Features Provides a uniquely historical perspective on the mathematical underpinnings of a comprehensive list of games Suitable for a broad audience of differing mathematical levels. Anyone with a passion for games, game theory, and mathematics will enjoy this book, whether they be students, academics, or game enthusiasts Covers a wide selection of topics at a level that can be appreciated on a historical, recreational, and mathematical level.