Two central problems in the pure theory of economic growth are analysed in this monograph: 1) the dynamic laws governing the economic growth processes, 2) the kinematic and geometric properties of the set of solutions to the dynamic systems. With allegiance to rigor and the emphasis on the theoretical fundamentals of prototype mathematical growth models, the treatise is written in the theorem-proof style. To keep the exposition orderly and as smooth as possible, the economic analysis has been separated from the purely mathematical issues, and hence the monograph is organized in two books. Regarding the scope and content of the two books, an "Introduction and Over view" has been prepared to offer both motivation and a brief account. The introduc tion is especially designed to give a recapitulation of the mathematical theory and results presented in Book II, which are used as the unifying mathematical framework in the analysis and exposition of the different economic growth models in Book I. Economists would probably prefer to go directly to Book I and proceed by consult ing the mathematical theorems of Book II in confirming the economic theorems in Book I. Thereby, both the independence and interdependence of the economic and mathematical argumentations are respected."

This monograph is an exposition of a novel method for solving inverse problems, a method of parameter estimation for time series data collected from simulations of real experiments. These time series might be generated by measuring the dynamics of aircraft in flight, by the function of a hidden Markov model used in bioinformatics or speech recognition or when analyzing the dynamics of asset pricing provided by the nonlinear models of financial mathematics. Dynamic Systems Models demonstrates the use of algorithms based on polynomial approximation which have weaker requirements than already-popular iterative methods. Specifically, they do not require a first approximation of a root vector and they allow non-differentiable elements in the vector functions being approximated. The text covers all the points necessary for the understanding and use of polynomial approximation from the mathematical fundamentals, through algorithm development to the application of the method in, for instance, aeroplane flight dynamics or biological sequence analysis. The technical material is illustrated by the use of worked examples and methods for training the algorithms are included. Dynamic Systems Models provides researchers in aerospatial engineering, bioinformatics and financial mathematics (as well as computer scientists interested in any of these fields) with a reliable and effective numerical method for nonlinear estimation and solving boundary problems when carrying out control design. It will also be of interest to academic researchers studying inverse problems and their solution.

This book, intended for researchers and graduate students in physics, applied mathematics and engineering, presents a detailed comparison of the important methods of solution for linear differential and difference equations - variation of constants, reduction of order, Laplace transforms and generating functions - bringing out the similarities as well as the significant differences in the respective analyses. Equations of arbitrary order are studied, followed by a detailed analysis for equations of first and second order. Equations with polynomial coefficients are considered and explicit solutions for equations with linear coefficients are given, showing significant differences in the functional form of solutions of differential equations from those of difference equations. An alternative method of solution involving transformation of both the dependent and independent variables is given for both differential and difference equations. A comprehensive, detailed treatment of Green's functions and the associated initial and boundary conditions is presented for differential and difference equations of both arbitrary and second order. A dictionary of difference equations with polynomial coefficients provides a unique compilation of second order difference equations obeyed by the special functions of mathematical physics. Appendices augmenting the text include, in particular, a proof of Cramer's rule, a detailed consideration of the role of the superposition principal in the Green's function, and a derivation of the inverse of Laplace transforms and generating functions of particular use in the solution of second order linear differential and difference equations with linear coefficients.

This monograph presents the newly developed method of rigged Hilbert spaces as a modern approach in singular perturbation theory. A key notion of this approach is the Lax-Berezansky triple of Hilbert spaces embedded one into another, which specifies the well-known Gelfand topological triple. All kinds of singular interactions described by potentials supported on small sets (like the Dirac -potentials, fractals, singular measures, high degree super-singular expressions) admit a rigorous treatment only in terms of the equipped spaces and their scales. The main idea of the method is to use singular perturbations to change inner products in the starting rigged space, and the construction of the perturbed operator by the Berezansky canonical isomorphism (which connects the positive and negative spaces from a new rigged triplet). The approach combines three powerful tools of functional analysis based on the Birman-Krein-Vishik theory of self-adjoint extensions of symmetric operators, the theory of singular quadratic forms, and the theory of rigged Hilbert spaces. The book will appeal to researchers in mathematics and mathematical physics studying the scales of densely embedded Hilbert spaces, the singular perturbations phenomenon, and singular interaction problems.

This text discusses mathematical modelling, analysis and control of the immune system and disease dynamics. The purpose of the book is the practical application of mathematics to immunology and medicine in order to establish a basis for more effective treatment, to provide a tutorial systematic description of how the immune system controls diseases and to present several significant examples such as malignant tumour dynamics and control, and viral hepatitis. The book is multidisciplinary in content, with the intended readers including biomathematicians, biologists and physicists. It combines immunological principles, mathematical models, computer simulations and methods of analysis.

This volume contains the proceedings of the 19th International Conference on Difference Equations and Applications, held at Sultan Qaboos University, Muscat, Oman in May 2013. The conference brought together experts and novices in the theory and applications of difference equations and discrete dynamical systems. The volume features papers in difference equations and discrete time dynamical systems with applications to mathematical sciences and, in particular, mathematical biology, ecology, and epidemiology. It includes four invited papers and eight contributed papers. Topics covered include: competitive exclusion through discrete time models, Benford solutions of linear difference equations, chaos and wild chaos in Lorenz-type systems, advances in periodic difference equations, the periodic decomposition problem, dynamic selection systems and replicator equations, and asymptotic equivalence of difference equations in Banach Space. This book will appeal to researchers, scientists, and educators who work in the fields of difference equations, discrete time dynamical systems and their applications.

The purpose of this monograph is to show how a compliant offshore structure in an ocean environment can be modeled in two and three di mensions. The monograph is divided into five parts. Chapter 1 provides the engineering motivation for this work, that is, offshore structures. These are very complex structures used for a variety of applications. It is possible to use beam models to initially study their dynamics. Chapter 2 is a review of variational methods, and thus includes the topics: princi ple of virtual work, D'Alembert's principle, Lagrange's equation, Hamil ton's principle, and the extended Hamilton's principle. These methods are used to derive the equations of motion throughout this monograph. Chapter 3 is a review of existing transverse beam models. They are the Euler-Bernoulli, Rayleigh, shear and Timoshenko models. The equa tions of motion are derived and solved analytically using the extended Hamilton's principle, as outlined in Chapter 2. For engineering purposes, the natural frequencies of the beam models are presented graphically as functions of normalized wave number and geometrical and physical pa rameters. Beam models are useful as representations of complex struc tures. In Chapter 4, a fluid force that is representative of those that act on offshore structures is formulated. The environmental load due to ocean current and random waves is obtained using Morison's equa tion. The random waves are formulated using the Pierson-Moskowitz spectrum with the Airy linear wave theory."

This book is an intellectually stimulating excursion into mathematical machines and structures capable for a universal computation. World top experts in computer science and mathematics overview exciting and intriguing topics of logical theory of monoids, geometry of Gauss word, philosophy of mathematics in computer science, asynchronous and parallel P-systems, decidability in cellular automata, splicing systems, reversible Turing machines, information flows in two-way finite automata, prime generators in automaton arrays, Grossone and Turing machines, automaton models of atomic lattices. The book is full of visually attractive examples of mathematical machines, open problems and challenges for future research. Those interested in the advancement of a theory of computation, philosophy of mathematics, future and emergent computing paradigms, architectures and implementations will find the book vital for their research and development.

This thesis describes the development of biophysically detailed computer models of the human atria and torso to study the underlying mechanisms of cardiac diseases, some of the most common causes of morbidity and mortality. This is a cross-disciplinary project, involving fundamentals of cardiac electrophysiology, physics of excitable media, applied mathematics and high performance scientific computing and visualisation. The author uses computer models to provide insights into the underlying mechanisms of the genesis of atrial fibrillation and develops novel techniques for the monitoring of atrial tachycardia.

For more than 250 years partial di?erential equations have been clearly the most important tool available to mankind in order to understand a large variety of phenomena, natural at ?rst and then those originating from - man activity and technological development. Mechanics, physics and their engineering applications were the ?rst to bene't from the impact of partial di?erential equations on modeling and design, but a little less than a century ago the Schr] odinger equation was the key opening the door to the application of partial di?erential equations to quantum chemistry, for small atomic and molecular systems at ?rst, but then for systems of fast growing complexity. The place of partial di?erential equations in mathematics is a very particular one: initially, the partial di?erential equations modeling natural phenomena were derived by combining calculus with physical reasoning in order to - press conservation laws and principles in partial di?erential equation form, leading to the wave equation, the heat equation, the equations of elasticity, the Euler and Navier-Stokes equations for ?uids, the Maxwell equations of electro-magnetics, etc. It is in order to solve 'constructively' the heat equation that Fourier developed the series bearing his name in the early 19th century; Fourier series (and later integrals) have played (and still play) a fundamental roleinbothpureandappliedmathematics, includingmanyareasquiteremote from partial di?erential equations. On the other hand, several areas of mathematics such as di?erential ge- etry have bene?ted from their interactions with partial di?erential equations."

Agent-based modeling/simulation is an emergent approach to the analysis of social and economic systems. It provides a bottom-up experimental method to be applied to social sciences such as economics, management, sociology and politics as well as some engineering fields dealing with social activities. This book includes selected papers presented at the Eighth International Workshop on Agent-Based Approaches in Economic and Social Complex Systems held in Tokyo, Japan, in 2013. At the workshop, 23 reviewed full papers were presented and of those, 13 were selected to be included in this volume.

The Applications of Computer Algebra (ACA) conference covers a wide range of topics from Coding Theory to Differential Algebra to Quantam Computing, focusing on the interactions of these and other areas with the discipline of Computer Algebra. This volume provides the latest developments in the field as well as its applications in various domains, including communications, modelling, and theoretical physics. The book will appeal to researchers and professors of computer algebra, applied mathematics, and computer science, as well as to engineers and computer scientists engaged in research and development.

This contributed volume comprises research articles and reviews on topics connected to the mathematical modeling of cellular systems. These contributions cover signaling pathways, stochastic effects, cell motility and mechanics, pattern formation processes, as well as multi-scale approaches. All authors attended the workshop on "Modeling Cellular Systems" which took place in Heidelberg in October 2014. The target audience primarily comprises researchers and experts in the field, but the book may also be beneficial for graduate students.

This monograph provides a definitive overview of recent advances in the stability and oscillation of autonomous delay differential equations. Topics include linear and nonlinear delay and integrodifferential equations, which have potential applications to both biological and physical dynamic processes. Chapter 1 deals with an analysis of the dynamical characteristics of the delay logistic equation, and a number of techniques and results relating to stability, oscillation and comparison of scalar delay and integrodifferential equations are presented. Chapter 2 provides a tutorial-style introduction to the study of delay-induced Hopf bifurcation to periodicity and the related computations for the analysis of the stability of bifurcating periodic solutions. Chapter 3 is devoted to local analyses of nonlinear model systems and discusses many methods applicable to linear equations and their perturbations. Chapter 4 considers global convergence to equilibrium states of nonlinear systems, and includes oscillations of nonlinear systems about their equilibria. Qualitative analyses of both competitive and cooperative systems with time delays feature in both Chapters 3 and 4. Finally, Chapter 5 deals with recent developments in models of neutral differential equations and their applications to population dynamics. Each chapter concludes with a number of exercises and the overall exposition recommends this volume as a good supplementary text for graduate courses. For mathematicians whose work involves functional differential equations, and whose interest extends beyond the boundaries of linear stability analysis.

This authored monograph provides a detailed discussion of the boundary layer flow due to a moving plate. The topical focus lies on the 2- and 3-dimensional case, considering axially symmetric and unsteady flows. The author derives a criterion for the self-similar and non-similar flow, and the turbulent flow due to a stretching or shrinking sheet is also discussed. The target audience primarily comprises research experts in the field of boundary layer flow, but the book will also be beneficial for graduate students.

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 contributes to the developing dialogue between cognitive science and social sciences. It focuses on a central issue in both fields, i.e. the nature and the limitations of the rationality of beliefs and action. The development of cognitive science is one of the most important and fascinating intellectual advances of recent decades, and social scientists are paying increasing attention to the findings of this new branch of science that forces us to consider many classical issues related to epistemology and philosophy of action in a new light. Analysis of the concept of rationality is a leitmotiv in the history of the social sciences and has involved endless disputes. Since it is difficult to give a precise definition of this concept, and there is a lack of agreement about its meaning, it is possible to say that there is a 'mystery of rationality'. What is it to be rational? Is rationality merely instrumental or does it also involve the endorsement of values, i.e. the choice of goals? Should we consider rationality to be a normative principle or a descriptive one? Can rationality be only Cartesian or can it also be argumentative? Is rationality a conscious skill or a partly tacit one? This book, which has been written by an outstanding collection of authors, including both philosophers and social scientists, tries to make a useful contribution to the debates on these problems and shed some light on the mystery of rationality. The target audience primarily comprises researchers and experts in the field.

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.

Understanding and predicting the performance of electromechanical systems is crucially important in the design of many modern products, and today s engineers and researchers are constantly seeking methods for optimizing these complex systems.

This important text/reference highlights a unique combination of numerical tools and strategies for handling the challenges of multiphysics simulation. As multiphysics simulation is a broad and rapidly growing field, requiring an array of technical skills in different intersecting disciplines, this book presents a specific focus on electromechanical systems as the target application.

Topics and features: introduces the concept of design via simulation, along with the role of multiphysics simulation in today s engineering environment; discusses the importance of structural optimization techniques in the design and development of electromechanical systems; provides an overview of the physics commonly involved with electromechanical systems for applications such as electronics, magnetic components, RF components, actuators, and motors; reviews the governing equations for the simulation of related multiphysics problems; outlines relevant (topology and parametric size) optimization methods for electromechanical systems; describes in detail several multiphysics simulation and optimization example studies in both two and three dimensions, with sample numerical code.

Researchers and engineers in industry and academia will find this work to be an invaluable reference on advanced electromechanical system design. The book is also suitable for students at undergraduate and graduate level, and many of the design examples will be of interest to anyone curious about the unique design solutions that arise from the coupling of optimization methods with multiphysics simulation techniques."

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 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.

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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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.