This bookprovides readers with an overview of recent international research and developments in the teaching and learning of modelling and applications from a variety of theoretical and practical perspectives. There is a strong focus on pedagogical issues for teaching and learning of modelling as well as research into teaching and practice. The teaching of applications of mathematics and mathematical modelling from the early years through primary and secondary school and at tertiary level is rising in prominence in many parts of the world commensurate with an ever-increasing usage of mathematics in business, the environment, industry and everyday life. The authors are all members of the International Community of Teachers of Mathematical Modelling and Applications and important researchers in mathematics education and mathematics. The book will be of interest to teachers, practitioners and researchers in universities, polytechnics, teacher education, curriculum and policy. "

This textbook provides a comprehensive modeling, reformulation and optimization approach for solving production planning and supply chain planning problems, covering topics from a basic introduction to planning systems, mixed integer programming (MIP) models and algorithms through the advanced description of mathematical results in polyhedral combinatorics required to solve these problems. Based on twenty years worth of research in which the authors have played a significant role, the book addresses real life industrial production planning problems (involving complex production structures with multiple production stages) using MIP modeling and reformulation approach. The book provides an introduction to MIP modeling and to planning systems, a unique collection of reformulation results, and an easy to use problem-solving library. This approach is demonstrated through a series of real life case studies, exercises and detailed illustrations. Review by Jakub Marecek (Computer Journal) The emphasis put on mixed integer rounding and mixing sets, heuristics in-built in general purpose integer programming solvers, as well as on decompositions and heuristics using integer programming should be praised... There is no doubt that this volume offers the present best introduction to integer programming formulations of lotsizing problems, encountered in production planning. (2007)

I am gratified that there is sufficient interest in the subject matter so as to support the offering of a second edition of this monograph. The of differential games dynamic interpretation and game theoretic foundation form a powerful and vital methodology for helping us study and understand marketing competition. This second edition offers a blend of what proved to be successful with the first edition and new material. The first two chapters, reviewing empirical and modeling research, have been updated to include contributions in the last decade that have advanced the area. I have not changed the essential content in the duopoly analyses in chapters 3, 4, and 5. A notable addition to the present edition are the new chapters, 6, 7, and 8, which offer analysis of three triopoly models. In the final chapter, I offer my summary view of the area and hope for continued contributions. I want to express my appreciation for the support of Josh Eliashberg, editor of the International Series in Quantitative Marketing, as well as Zachary Rolnik, Director, and David Cella, Publishing Editor, of Kluwer. Their encouragement has provided crucial motivation in this endeavor.

Statistical models and methods for lifetime and other time-to-event data are widely used in many fields, including medicine, the environmental sciences, actuarial science, engineering, economics, management, and the social sciences. For example, closely related statistical methods have been applied to the study of the incubation period of diseases such as AIDS, the remission time of cancers, life tables, the time-to-failure of engineering systems, employment duration, and the length of marriages. This volume contains a selection of papers based on the 1994 International Research Conference on Lifetime Data Models in Reliability and Survival Analysis, held at Harvard University. The conference brought together a varied group of researchers and practitioners to advance and promote statistical science in the many fields that deal with lifetime and other time-to-event-data. The volume illustrates the depth and diversity of the field. A few of the authors have published their conference presentations in the new journal Lifetime Data Analysis (Kluwer Academic Publishers).

This book describes and discusses the properties of heterogeneous materials. The properties considered include the conductivity (thermal, electrical, magnetic), elastic moduli, dielectrical constant, optical properties, mechanical fracture, and electrical and dielectrical breakdown properties. Both linear and nonlinear properties are considered. The nonlinear properties include those with constitutive non-linearities as well as threshold non-linearities, such as brittle fracture and dielectric breakdown. A main goal of this book is to compare two fundamental approaches to describing and predicting materials properties, namely, the continuum mechanics approach, and those based on the discrete models. The latter models include the lattice models and the atomistic approaches. The book provides comprehensive and up to date theoretical and computer simulation analysis of materials' properties. Typical experimental methods for measuring all of these properties are outlined, and comparison is made between the experimental data and the theoretical predictions. Volume I covers linear properties, while Volume II considers non-linear and fracture and breakdown properties, as well as atomistic modeling. This multidisciplinary book will appeal to applied physicists, materials scientists, chemical and mechanical engineers, chemists, and applied mathematicians.

Cardiovascular diseases have a major impact in Western countries. Mathematical models and numerical simulations can aid the understanding of physiological and pathological processes, complementing the information provided to medical doctors by medical imaging and other non-invasive means, and opening the possibility of a better diagnosis and more in-depth surgical planning.This book offers a mathematically sound and up-to-date foundation to the training of researchers, and serves as a useful reference for the development of mathematical models and numerical simulation codes. It is structured into different chapters, written by recognized experts in the field, but it features a common thread with consistency of notation and expressions and systematic cross-referencing. Many fundamental issues are faced, such as: the mathematical representation of vascular geometries extracted from medical images, modelling blood rheology and the complex multilayer structure of the vascular tissue, and its possible pathologies, the mechanical and chemical interaction between blood and vascular walls; the different scales coupling local and systemic dynamics. All these topics introduce challenging mathematical and numerical problems, demanding for advanced analysis and simulation techniques. This book is addressed to graduate students and researchers in the field of bioengineering, applied mathematics and medicine, wishing to engage themselves in the fascinating task of modeling how the cardiovascular system works.

Volume II of this two-volume, interdisciplinary work is a unified presentation of a broad range of state-of-the-art topics in the rapidly growing field of mathematical modeling in the biological sciences. Highlighted throughout are mathematical and computational apporaches to examine central problems in the life sciences, ranging from the organization principles of individual cells to the dynamics of large populations. The chapters are thematically organized into the following main areas: epidemiology, evolution and ecology, immunology, neural systems and the brain, and innovative mathematical methods and education.

The work will be an excellent reference text for a broad audience of researchers, practitioners, and advanced students in this rapidly growing field at the intersection of applied mathematics, experimental biology and medicine, computational biology, biochemistry, computer science, and physics.

Modern methods of filter design and controller design often yield systems of very high order, posing a problem for their implementation. Over the past two decades or so, sophisticated methods have been developed to achieve simplification of filters and controllers. Such methods often come with easy-to-use error bounds, and in the case of controller simplification methods, such error bounds will usually be related to closed-loop properties.This book is the first comprehensive treatment of approximation methods for filters and controllers. It is fully up to date, and it is authored by two leading researchers who have personally contributed to the development of some of the methods. Balanced truncation, Hankel norm reduction, multiplicative reduction, weighted methods and coprime factorization methods are all discussed.The book is amply illustrated with examples, and will equip practising control engineers and graduates for intelligent use of commercial software modules for model and controller reduction.

Multiresolution methods in geometric modelling are concerned with the generation, representation, and manipulation of geometric objects at several levels of detail. Applications include fast visualization and rendering as well as coding, compression, and digital transmission of 3D geometric objects.

This book marks the culmination of the four-year EU-funded research project, Multiresolution in Geometric Modelling (MINGLE). The book contains seven survey papers, providing a detailed overview of recent advances in the various fields within multiresolution modelling, and sixteen additional research papers. Each of the seven parts of the book starts with a survey paper, followed by the associated research papers in that area. All papers were originally presented at the MINGLE 2003 workshop held at Emmanuel College, Cambridge, UK, 9-11 September 2003.

The present volume aims to be a comprehensive survey on the derivation of the equations of motion, both in General Relativity as well as in alternative gravity theories. The topics covered range from the description of test bodies, to self-gravitating (heavy) bodies, to current and future observations. Emphasis is put on the coverage of various approximation methods (e.g., multipolar, post-Newtonian, self-force methods) which are extensively used in the context of the relativistic problem of motion. Applications discussed in this volume range from the motion of binary systems -- and the gravitational waves emitted by such systems -- to observations of the galactic center. In particular the impact of choices at a fundamental theoretical level on the interpretation of experiments is highlighted. This book provides a broad and up-do-date status report, which will not only be of value for the experts working in this field, but also may serve as a guideline for students with background in General Relativity who like to enter this field.

This valuable source for graduate students and researchers provides a comprehensive introduction to current theories and applications in optimization methods and network models. Contributions to this book are focused on new efficient algorithms and rigorous mathematical theories, which can be used to optimize and analyze mathematical graph structures with massive size and high density induced by natural or artificial complex networks. Applications to social networks, power transmission grids, telecommunication networks, stock market networks, and human brain networks are presented. Chapters in this book cover the following topics: Linear max min fairness Heuristic approaches for high-quality solutions Efficient approaches for complex multi-criteria optimization problems Comparison of heuristic algorithms New heuristic iterative local search Power in network structures Clustering nodes in random graphs Power transmission grid structure Network decomposition problems Homogeneity hypothesis testing Network analysis of international migration Social networks with node attributes Testing hypothesis on degree distribution in the market graphs Machine learning applications to human brain network studies This proceeding is a result of The 6th International Conference on Network Analysis held at the Higher School of Economics, Nizhny Novgorod in May 2016. The conference brought together scientists and engineers from industry, government, and academia to discuss the links between network analysis and a variety of fields.

The financial results of any manufacturing company can be dramatically impacted by the repetitive decisions required to control a complex production network be it a network of machines in a factory; a network of factories in a company; or a network of companies in a supply chain. Decision Policies for Production Networks presents recent convergent research on developing policies for operating production networks including details of practical control and decision techniques which can be applied to improve the effectiveness and economic efficiency of production networks worldwide. Researchers and practitioners come together to explore a wide variety of approaches to a range of topics including:

WIP and equipment management policies,

Material release policies,

Machine, factory, and supply chain network policies for delivery in the face of supply and demand variability, and

Conflicts between complex production network models and their controlling policies.

Case studies and relevant mathematical techniques are included to support and explain techniques such as heuristics, global and hierarchical optimization, control theory and filtering approaches related to complex systems or traffic flows. Decision Policies for Production Networks acts as handbook for researchers and practitioners alike, providing findings and information which can be applied to develop methods and advance further research across production networks.
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This book analyzes the use of modeling in charting the survival of financial and industrial enterprises. The author shows how to use models effectively, and goes on to consider the pitfalls that can occur. The book contains plenty of practical examples, making this a useful 'how to' guide.

The aim of the book is to present for non-specialist researchers as well as for experts a comprehensive overview of the background, key ideas, basic methods, implementation details and a selection of solutions offered by a novel technology for the optimisation of the location of dangerous offshore activities in terms of environmental criteria, as developed in the course of the BalticWay project. The book consists of two parts. The first part introduces the basic principles of ocean modeling and depicts the long way from the generic principles to the practical modeling of oil spills and of the propagation of other adverse impacts. The second part focuses on the techniques for solving the inverse problem of the quantification of offshore areas with respect to their potential to serve as a source of environmental danger to vulnerable regions (such as spawning, nursing or also tourist areas). The chapters are written in a tutorial style; they are mostly self-contained and understandable for non-specialist researchers and students. They are carefully peer-reviewed by international experts. The goal was to produce a book that highlights all key steps, methods, models and data sets it is necessary to combine in order to produce a practically usable technology and/or decision support system for a particular sea region. Thus the book is useful not only as a description and a manual of this particular technology but also as a roadmap highlighting the complicated technical issues of ocean modeling for practical purposes. It describes the approaches taken by the authors in an understandable way and thus is useful for educational purposes, such as a course in industrially and environmentally relevant applications of ocean modeling.

This volume was produced in conjunction with the Thematic Program in o-Minimal Structures and Real Analytic Geometry, held from January to June of 2009 at the Fields Institute. Five of the six contributions consist of notes from graduate courses associated with the program: Felipe Cano on a new proof of resolution of singularities for planar analytic vector fields; Chris Miller on o-minimality and Hardy fields; Jean-Philippe Rolin on the construction of o-minimal structures from quasianalytic classes; Fernando Sanz on non-oscillatory trajectories of vector fields; and Patrick Speissegger on pfaffian sets. The sixth contribution, by Antongiulio Fornasiero and Tamara Servi, is an adaptation to the nonstandard setting of A.J. Wilkie's construction of o-minimal structures from infinitely differentiable functions. Most of this material is either unavailable elsewhere or spread across many different sources such as research papers, conference proceedings and PhD theses. This book will be a useful tool for graduate students or researchers from related fields who want to learn about expansions of o-minimal structures by solutions, or images thereof, of definable systems of differential equations.

This work provides a detailed and up-to-the-minute survey of the various stability problems that can affect suspension bridges. In order to deduce some experimental data and rules on the behavior of suspension bridges, a number of historical events are first described, in the course of which several questions concerning their stability naturally arise. The book then surveys conventional mathematical models for suspension bridges and suggests new nonlinear alternatives, which can potentially supply answers to some stability questions. New explanations are also provided, based on the nonlinear structural behavior of bridges. All the models and responses presented in the book employ the theory of differential equations and dynamical systems in the broader sense, demonstrating that methods from nonlinear analysis can allow us to determine the thresholds of instability.

This self-contained book systematically explores the statistical dynamics on and of complex networks having relevance across a large number of scientific disciplines. The theories related to complex networks are increasingly being used by researchers for their usefulness in harnessing the most difficult problems of a particular discipline. The book is a collection of surveys and cutting-edge research contributions exploring the interdisciplinary relationship of dynamics on and of complex networks. Topics covered include complex networks found in nature-genetic pathways, ecological networks, linguistic systems, and social systems-as well as man-made systems such as the World Wide Web and peer-to-peer networks.

The contributed chapters in this volume are intended to promote cross-fertilization in several research areas, and will be valuable to newcomers in the field, experienced researchers, practitioners, and graduate students interested in systems exhibiting an underlying complex network structure in disciplines such as computer science, biology, statistical physics, nonlinear dynamics, linguistics, and the social sciences.

This book provides a survey on different kinds of Feistel ciphers, with their definitions and mathematical/computational properties. Feistel ciphers are widely used in cryptography in order to obtain pseudorandom permutations and secret-key block ciphers. In Part 1, we describe Feistel ciphers and their variants. We also give a brief story of these ciphers and basic security results. In Part 2, we describe generic attacks on Feistel ciphers. In Part 3, we give results on DES and specific Feistel ciphers. Part 4 is devoted to improved security results. We also give results on indifferentiability and indistinguishability.

The classical ARMA models have limitations when applied to the field of financial and monetary economics. Financial time series present nonlinear dynamic characteristics and the ARCH models offer a more adaptive framework for this type of problem. This book surveys the recent work in this area from the perspective of statistical theory, financial models, and applications and will be of interest to theorists and practitioners. From the view point of statistical theory, ARCH models may be considered as specific nonlinear time series models which allow for an exhaustive study of the underlying dynamics. It is possible to reexamine a number of classical questions such as the random walk hypothesis, prediction interval building, presence of latent variables etc., and to test the validity of the previously studied results. There are two main categories of potential applications. One is testing several economic or financial theories concerning the stocks, bonds, and currencies markets, or studying the links between the short and long run. The second is related to the interventions of the banks on the markets, such as choice of optimal portfolios, hedging portfolios, values at risk, and the size and times of block trading.

This volume collects contributions from the speakers at an INdAM Intensive period held at the University of Bari in 2017. The contributions cover several aspects of partial differential equations whose development in recent years has experienced major breakthroughs in terms of both theory and applications. The topics covered include nonlocal equations, elliptic equations and systems, fully nonlinear equations, nonlinear parabolic equations, overdetermined boundary value problems, maximum principles, geometric analysis, control theory, mean field games, and bio-mathematics. The authors are trailblazers in these topics and present their work in a way that is exhaustive and clearly accessible to PhD students and early career researcher. As such, the book offers an excellent introduction to a variety of fundamental topics of contemporary investigation and inspires novel and high-quality research.

3. 8 Problems . . . 66 4 ENABLING REUSE 69 4. 1 Concepts . . . . . . . . 69 4. 2 Exploiting commonality 70 4. 3 Reusable building blocks 71 4. 4 Allowing replaceable components 75 4. 5 Other replaceable entities 79 4. 6 Limiting flexibility . . . 82 4. 7 Other considerations . . 84 4. 8 Language fundamentals 85 4. 9 Problems . . . . . . . . 88 5 FUNCTIONS 91 5. 1 Concepts . . . . . . . . 91 5. 2 Introduction to functions 92 5. 3 An interpolation function 94 5. 4 Multiple return values 96 97 5. 5 Passing records as arguments 5. 6 Using extemal subroutines 100 5. 7 Language fundamentals 102 5. 8 Problems . . . . . . . . 110 6 USING ARRAYS 113 6. 1 Concepts . . . . . . . . . . . . . . . . . . 113 6. 2 Planetary motion: Arrays of components . . 113 6. 3 Simple ID heat transfer: Arrays of variables 120 6. 4 Using arrays with chemical systems 132 6. 5 Language fundamentals 143 6. 6 Problems . . . . . . . . . . . . . . 152 7 HYBRID MODELS 155 7. 1 Concepts . . . . . . . . 155 7. 2 Modeling digital circuits 155 7. 3 Bouncing ball . . . . . . 162 7. 4 Sensor modeling . . . . 166 7. 5 Language fundamentals 178 7. 6 Problems . . . . . . . . 186 8 EXPLORING NONLINEAR BEHAVIOR 189 8. 1 Concepts . . . 189 8. 2 An ideal diode 189 8. 3 Backlash . . . 193 8. 4 Thermal properties 199 Contents vii 8. 5 Hodgkin-Huxley nerve cell models 203 8. 6 Language fundamentals 206 8. 7 Problems . . . . . . . . . . . . . . 210 9 MISCELLANEOUS 213 9. 1 Lookup rules 213 9. 2 Annotations . . 225 Part II Effective Modelica 10 MULTI-DOMAIN MODELING 231 10. 1 Concepts . . . . . . . . . 231 231 10. 2 Conveyor system . . . . .

This book presents solutions to control problems in a number of robotic systems and provides a wealth of worked-out examples with full analytical and numerical details, graphically illustrated to aid in reader comprehension. It also presents relevant studies on and applications of robotic system control approaches, as well as the latest findings from interdisciplinary theoretical studies. Featuring chapters on advanced control (fuzzy, neural, backstepping, sliding mode, adaptive, predictive, diagnosis, and fault-tolerant control), the book will equip readers to easily tailor the techniques to their own applications. Accordingly, it offers a valuable resource for researchers, engineers, and students in the field of robotic systems.

This book deals with methods to evaluate scientific productivity. In the book statistical methods, deterministic and stochastic models and numerous indexes are discussed that will help the reader to understand the nonlinear science dynamics and to be able to develop or construct systems for appropriate evaluation of research productivity and management of research groups and organizations. The dynamics of science structures and systems is complex, and the evaluation of research productivity requires a combination of qualitative and quantitative methods and measures. The book has three parts. The first part is devoted to mathematical models describing the importance of science for economic growth and systems for the evaluation of research organizations of different size. The second part contains descriptions and discussions of numerous indexes for the evaluation of the productivity of researchers and groups of researchers of different size (up to the comparison of research productivities of research communities of nations). Part three contains discussions of non-Gaussian laws connected to scientific productivity and presents various deterministic and stochastic models of science dynamics and research productivity. The book shows that many famous fat tail distributions as well as many deterministic and stochastic models and processes, which are well known from physics, theory of extreme events or population dynamics, occur also in the description of dynamics of scientific systems and in the description of the characteristics of research productivity. This is not a surprise as scientific systems are nonlinear, open and dissipative.

In the ideal world, major decisions would be made based on complete and reliable information available to the decision maker. We live in a world of uncertainties, and decisions must be made from information which may be incomplete and may contain uncertainty. The key mathematical question addressed in this volume is "how to make decision in the presence of quantifiable uncertainty." The volume contains articles on model problems of decision making process in the energy and power industry when the available information is noisy and/or incomplete. The major tools used in studying these problems are mathematical modeling and optimization techniques; especially stochastic optimization. These articles are meant to provide an insight into this rapidly developing field, which lies in the intersection of applied statistics, probability, operations research, and economic theory. It is hoped that the present volume will provide entry to newcomers into the field, and stimulation for further research.

Optimization is presented in most multivariable calculus courses as an application of the gradient, and while this treatment makes sense for a calculus course, there is much more to the theory of optimization. Optimization problems are generated constantly, and the theory of optimization has grown and developed in response to the challenges presented by these problems. This textbook aims to show readers how optimization is done in practice and help them to develop an appreciation for the richness of the theory behind the practice. Exercises, problems (including modeling and computational problems), and implementations are incorporated throughout the text to help students learn by doing. Python notes are inserted strategically to help readers complete computational problems and implementations. The Basics of Practical Optimization, Second Edition is intended for undergraduates who have completed multivariable calculus, as well as anyone interested in optimization. The book is appropriate for a course that complements or replaces a standard linear programming course.