This book-unique in the literature-provides readers with the mathematical background needed to design many of the optical combinations that are used in astronomical telescopes and cameras. The results presented in the work were obtained by using a different approach to third-order aberration theory as well as the extensive use of the software package Mathematica (R). Replete with workout examples and exercises, Geometric Optics is an excellent reference for advanced graduate students, researchers, and practitioners in applied mathematics, engineering, astronomy, and astronomical optics. The work may be used as a supplementary textbook for graduate-level courses in astronomical optics, optical design, optical engineering, programming with Mathematica, or geometric optics.

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.

Recent groundbreaking discoveries in physics, including the discovery of the Higgs Boson and gravitational waves, have relied on chi-squared analysis and model testing, a data analysis method. This is the first book to make chi-squared model testing accessible to students in introductory physics lab courses and others who need to learn this method, such as beginning researchers in astrophysics and particle physics, beginners in data science, and lab students in other experimental sciences. For over a decade, Harvard University's introductory physics lab sequence has made chi-squared model testing its central theme. Written by two faculty members, the book is based on years of experience teaching students learn how to think like scientists by testing their models using chi-squared analysis. By including uncertainties in the curve fitting technique, chi-squared data analysis improves on the centuries old ordinary least squares and linear regression methods and combines best fit parameter estimation and model testing in one method. A toolkit of essential statistical and experimental concepts is developed from the ground up with novel features to interest even those familiar with the material. The presentation of one and two parameter chi-squared model testing, requiring only elementary probability and algebra, is followed by case studies that apply the methods to simple introductory physics lab experiments. More challenging topics requiring calculus are addressed in an advanced topic chapter. This self-contained and student-friendly introduction includes a glossary, end of chapter problems with complete solutions, and software scripts available in several popular programming languages that the reader can use for chi-squared model testing.

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.

The point of departure in the present book is that the decision-makers involved in the evaluation of alternatives under conflicting criteria express their preferential judgement by estimating ratios of subjective values or differences of the corresponding logarithms, the so-called grades. Three MCDA methods are studied in detail; the Simple Multi-Attribute Rating Technique SMART, and the Additive and the Multiplicative AHP, both pairwise-comparison methods which do not suffer from the well-known shortcomings of the original Analytic Hierarchy Process. Context-related preference modeling on the basis of psychophysical research in visual perception and motor skills is extensively discussed in the introductory chapters. Thereafter many extensions of the ideas are presented via case studies in university administration, health care, environmental assessment, budget allocation, and energy planning at the national and the European level. The issues under consideration are: group decision-making with inhomogeneous power distributions, the search for a compromise solution, resource allocation and fair distribution, scenario analysis in long-term planning, conflict analysis via the pairwise comparison of concessions and multi-objective optimization. The final chapters are devoted to the fortunes of MCDA in the hands of its designers. Audience: The book presents methods for decision support and their applications in the fields of university administration, health care, environmental assessment, budget allocation, and strategic energy planning and will be of value to practitioners, students and researchers in these and related fields.

The field of large-scale dimensional metrology (LSM) deals with objects that have linear dimensions ranging from tens to hundreds of meters. It has recently attracted a great deal of interest in many areas of production, including the automotive, railway, and shipbuilding sectors. Distributed Large-Scale Dimensional Metrology introduces a new paradigm in this field that reverses the classical metrological approach: measuring systems that are portable and can be easily moved around the location of the measured object, which is preferable to moving the object itself. Distributed Large-Scale Dimensional Metrology combines the concepts of distributed systems and large scale metrology at the application level. It focuses on the latest insights and challenges of this new generation of systems from the perspective of the designers and developers. The main topics are: coverage of measuring area, sensors calibration, on-line diagnostics, probe management, and analysis of metrological performance. The general descriptions of each topic are further enriched by specific examples concerning the use of commercially available systems or the development of new prototypes. This will be particularly useful for professional practitioners such as quality engineers, manufacturing and development engineers, and procurement specialists, but Distributed Large-Scale Dimensional Metrology also has a wealth of information for interested academics.

Features Self-contained book suitable for graduate students and post-doctoral fellows in financial mathematics and data science, as well as for practitioners working in the financial industry who deal with big data All results are presented visually to aid in understanding of concepts.

Using examples from finance and modern warfare to the flocking of birds and the swarming of bacteria, the collected research in this volume demonstrates the common methodological approaches and tools for modeling and simulating collective behavior.

Thetopics presented point toward new and challenging frontiers of applied mathematics, making the volume a useful referencetext forapplied mathematicians, physicists, biologists, and economists involved in the modeling of socio-economic systems."

Knowledge acquisition is one of the most important aspects influencing the quality of methods used in artificial intelligence and the reliability of expert systems. The various issues dealt with in this volume concern many different approaches to the handling of partial knowledge and to the ensuing methods for reasoning and decision making under uncertainty, as applied to problems in artificial intelligence. The volume is composed of the invited and contributed papers presented at the Workshop on Mathematical Models for Handling Partial Knowledge in Artificial Intelligence, held at the Ettore Majorana Center for Scientific Culture of Erice (Sicily, Italy) on June 19-25, 1994, in the framework of the International School of Mathematics "G.Stampacchia." It includes also a transcription of the roundtable held during the workshop to promote discussions on fundamental issues, since in the choice of invited speakers we have tried to maintain a balance between the various schools of knowl edge and uncertainty modeling. Choquet expected utility models are discussed in the paper by Alain Chateauneuf: they allow the separation of perception of uncertainty or risk from the valuation of outcomes, and can be of help in decision mak ing. Petr Hajek shows that reasoning in fuzzy logic may be put on a strict logical (formal) basis, so contributing to our understanding of what fuzzy logic is and what one is doing when applying fuzzy reasoning."

The correlations between physical systems provide significant information about their collective behaviour - information that is used as a resource in many applications, e.g. communication protocols. However, when it comes to the exploitation of such correlations in the quantum world, identification of the associated 'resource' is extremely challenging and a matter of debate in the quantum community. This dissertation describes three key results on the identification, detection, and quantification of quantum correlations. It starts with an extensive and accessible introduction to the mathematical and physical grounds for the various definitions of quantum correlations. It subsequently focusses on introducing a novel unified picture of quantum correlations by taking a modern resource-theoretic position. The results show that this novel concept plays a crucial role in the performance of collaborative quantum computations that is not captured by the standard textbook approaches. Further, this new perspective provides a deeper understanding of the quantum-classical boundary and paves the way towards establishing a resource theory of quantum computations.

Graph Separators with Applications is devoted to techniques for obtaining upper and lower bounds on the sizes of graph separators - upper bounds being obtained via decomposition algorithms. The book surveys the main approaches to obtaining good graph separations, while the main focus of the book is on techniques for deriving lower bounds on the sizes of graph separators. This asymmetry in focus reflects our perception that the work on upper bounds, or algorithms, for graph separation is much better represented in the standard theory literature than is the work on lower bounds, which we perceive as being much more scattered throughout the literature on application areas. Given the multitude of notions of graph separator that have been developed and studied over the past (roughly) three decades, there is a need for a central, theory-oriented repository for the mass of results. The need is absolutely critical in the area of lower-bound techniques for graph separators, since these techniques have virtually never appeared in articles having the word separator' or any of its near-synonyms in the title. Graph Separators with Applications fills this need.

This book is about the pattern formation and the evolution of crack propagation in engineering materials and structures, bridging mathematical analyses of cracks based on singular integral equations, to computational simulation of engineering design. The first two parts of this book focus on elasticity and fracture and provide the basis for discussions on fracture morphology and its numerical simulation, which may lead to a simulation-based fracture control in engineering structures. Several design concepts are discussed for the prevention of fatigue and fracture in engineering structures, including safe-life design, fail-safe design, damage tolerant design.

After starting with basic elasticity and fracture theories in parts one and two, this book focuses on the fracture morphology that develops due to the propagation of brittle cracks or fatigue cracks.

In part three, the mathematical analysis of a curved crack is precisely described, based on the perturbation method. The stability theory of interactive cracks propagating in brittle solids may help readers to understand the formation of a fractal-like cracking patterns in brittle solids, while the stability theory of crack paths helps to identify the straight versus sharply curved or sometimes wavy crack paths observed in brittle solids.

In part four, the numerical simulation method of a system of multiple cracks is introduced by means of the finite element method, which may be used for the better implementation of fracture control in engineering structures.

This book is part of a series on Mathematics for Industry and will appeal to structural engineers seeking to understand the basic backgrounds of analyses, but also to mathematicians with an interest in how such mathematical solutions are evaluated in industrial applications."

This book is addressed to scientists, engineers and students of engineering departments, who make use of modelling and computer simulation. Since more and more physical experiments are being replaced by computer simulations the use of mathematical models of various engineering systems has become an especially important area of research. The book is devoted to selected problems of various engineering domains, such as control, electrical engineering or electrical metrology. They are based on different mathematical fields such as matrix theory, differential equations, function approximation with applications in dynamic modelling, methods of simplifying high-order models, determining mapping errors of simplified models, their optimization and the synthesis of suitable input signals. The book is easy to read and understand because all the needed mathematical transformations and formula are derived and explained by means of the examples enclosed.

This book covers algorithms and discretization procedures for the solution of nonlinear progamming, semi-infinite optimization and optimal control problems. Among the important features included are the theory of algorithms represented as point-to-set maps, the treatment of min-max problems with and without constraints, the theory of consistent approximation which provides a framework for the solution of semi-infinite optimization, optimal control, and shape optimization problems with very general constraints, using simple algorithms that call standard nonlinear programming algorithms as subroutines, the completeness with which algorithms are analysed, and chapter 5 containing mathematical results needed in optimization from a large assortment of sources. Readers will find of particular interest the exhaustive modern treatment of optimality conditions and algorithms for min-max problems, as well as the newly developed theory of consistent approximations and the treatment of semi-infinite optimization and optimal control problems in this framework. This book presents the first treatment of optimization algorithms for optimal control problems with state-trajectory and control constraints, and fully accounts for all the approximations that one must make in their solution.It is also the first to make use of the concepts of epi-convergence and optimality functions in the construction of consistent approximations to infinite dimensional problems.

Presenting techniques, case-studies and methodologies that combine the use of simulation approaches with optimization techniques for facing problems in manufacturing, logistics, or aeronautical problems, this book provides solutions to common industrial problems in several fields, which range from manufacturing to aviation problems, where the common denominator is the combination of simulation's flexibility with optimization techniques' robustness. Providing readers with a comprehensive guide to tackle similar issues in industrial environments, this text explores novel ways to face industrial problems through hybrid approaches (simulation-optimization) that benefit from the advantages of both paradigms, in order to give solutions to important problems in service industry, production processes, or supply chains, such as scheduling, routing problems and resource allocations, among others.

This book gives an overview of the state of the art in five different approaches to social science simulation on the individual level. The volume contains microanalytical simulation models designed for policy implementation and evaluation, multilevel simulation methods designed for detecting emergent phenomena, dynamical game theory applications, the use of cellular automata to explain the emergence of structure in social systems, and multi-agent models using the experience from distributed artificial intelligence applied to special phenomena. The book collects the results of an international conference which brought together social scientists and computer scientists both engaged in a wide range of simulation approaches for the first time.

The theory of constructive (recursive) models follows from works of Froehlich, Shepherdson, Mal'tsev, Kuznetsov, Rabin, and Vaught in the 50s. Within the framework of this theory, algorithmic properties of abstract models are investigated by constructing representations on the set of natural numbers and studying relations between algorithmic and structural properties of these models. This book is a very readable exposition of the modern theory of constructive models and describes methods and approaches developed by representatives of the Siberian school of algebra and logic and some other researchers (in particular, Nerode and his colleagues). The main themes are the existence of recursive models and applications to fields, algebras, and ordered sets (Ershov), the existence of decidable prime models (Goncharov, Harrington), the existence of decidable saturated models (Morley), the existence of decidable homogeneous models (Goncharov and Peretyat'kin), properties of the Ehrenfeucht theories (Millar, Ash, and Reed), the theory of algorithmic dimension and conditions of autostability (Goncharov, Ash, Shore, Khusainov, Ventsov, and others), and the theory of computable classes of models with various properties. Future perspectives of the theory of constructive models are also discussed. Most of the results in the book are presented in monograph form for the first time. The theory of constructive models serves as a basis for recursive mathematics. It is also useful in computer science, in particular, in the study of programming languages, higher level languages of specification, abstract data types, and problems of synthesis and verification of programs. Therefore, the book will be usefulfor not only specialists in mathematical logic and the theory of algorithms but also for scientists interested in the mathematical fundamentals of computer science. The authors are eminent specialists in mathematical logic. They have established fundamental results on elementary theories, model theory, the theory of algorithms, field theory, group theory, applied logic, computable numberings, the theory of constructive models, and the theoretical computer science.

Accelerated degradation of soils and surface waters produce increasing problems in many parts of the world. Within this context, the book addresses the topic Application of Physically Based Soil Erosion Models in order to present some essential tools for improving land-use strategies and conservation measures. Over the last 20 years, the need for more accurate assessments of soil losses and sediment yields has led to the development of some highly complex, process-based soil erosion models. In 14 papers, specialists from 5 European countries, the USA and Brazil report on practical applications of these models and give insight into the latest developments. This book will help to implement state-of-the-art soil erosion prediction technologies within soil and water conservation planning and assessment. Hence, the book should be of special interest to agricultural and environmental engineers, hydrologists, soil scientists and geoscientists.

The book covers nonlinear physical problems and mathematical modeling, including molecular biology, genetics, neurosciences, artificial intelligence with classical problems in mechanics and astronomy and physics. The chapters present nonlinear mathematical modeling in life science and physics through nonlinear differential equations, nonlinear discrete equations and hybrid equations. Such modeling can be effectively applied to the wide spectrum of nonlinear physical problems, including the KAM (Kolmogorov-Arnold-Moser (KAM)) theory, singular differential equations, impulsive dichotomous linear systems, analytical bifurcation trees of periodic motions, and almost or pseudo- almost periodic solutions in nonlinear dynamical systems.

This book builds inviscid flow analysis from an undergraduate-level treatment of potential flow to the level required for research. The tools covered in this book allow the reader to develop physics-based mathematical models for a variety of flows, including attached and separated flows past wings, fins, and blades of various shapes undergoing arbitrary motions. The book covers all of the ingredients of these models: the solution of potential flows about arbitrary body shapes in two- and three-dimensional contexts, with a particular focus on conformal mapping in the plane; the decomposition of the flow into contributions from ambient vorticity and body motion; generalized edge conditions, of which the Kutta condition is a special case; and the calculation of force and moment, with extensive treatments of added mass and the influence of fluid vorticity. The book also contains an extensive primer with all of the necessary mathematical tools. The concepts are demonstrated on several example problems, both classical and modern.

This award-winning thesis investigates the mechanisms underlying cardiac arrhythmia development and termination from an entirely new perspective. By viewing the heart as a complex system, the author uses theoretical tools from nonlinear dynamics combined with numerical simulations and experiments to achieve insights into the relationship between its structure and dynamics, thereby paving the way towards innovative low-energy defibrillation strategies. The work tackles, among other things: the effect of substrate heterogeneity on the spatial-temporal dynamics of cardiac arrhythmias and ways in which weak pulsed electric fields can be used to control these dynamics in heterogeneous cardiac tissue. The long-term vision of this research is to replace the current strategy of applying painful and sometimes tissue damaging electric shock - currently the only reliable way to terminate life-threatening fibrillation - by a more subtle but equally effective intervention. The book maps out a number of promising research directions for biophysicists and medical researchers working on the origins and treatment of cardiac arrhythmias.

This textbook presents the motion of pure nonlinear oscillatory systems and various solution procedures which give the approximate solutions of the strong nonlinear oscillator equations. It presents the author's original method for the analytical solution procedure of the pure nonlinear oscillator system. After an introduction, the physical explanation of the pure nonlinearity and of the pure nonlinear oscillator is given. The analytical solution for free and forced vibrations of the one-degree-of-freedom strong nonlinear system with constant and time variable parameters is considered. In this second edition of the book, the number of approximate solving procedures for strong nonlinear oscillators is enlarged and a variety of procedures for solving free strong nonlinear oscillators is suggested. A method for error estimation is also given which is suitable to compare the exact and approximate solutions. Besides the oscillators with one degree-of-freedom, the one and two mass oscillatory systems with two-degrees-of-freedom and continuous oscillators are considered. The chaos and chaos suppression in ideal and non-ideal mechanical systems is explained. In this second edition more attention is given to the application of the suggested methodologies and obtained results to some practical problems in physics, mechanics, electronics and biomechanics. Thus, for the oscillator with two degrees-of-freedom, a generalization of the solving procedure is performed. Based on the obtained results, vibrations of the vocal cord are analyzed. In the book the vibration of the axially purely nonlinear rod as a continuous system is investigated. The developed solving procedure and the solutions are applied to discuss the muscle vibration. Vibrations of an optomechanical system are analyzed using the oscillations of an oscillator with odd or even quadratic nonlinearities. The extension of the forced vibrations of the system is realized by introducing the Ateb periodic excitation force which is the series of a trigonometric function. The book is self-consistent and suitable for researchers and as a textbook for students and also professionals and engineers who apply these techniques to the field of nonlinear oscillations.

This book reports on advanced theories and cutting-edge applications in the field of soft computing. The individual chapters, written by leading researchers, are based on contributions presented during the 4th World Conference on Soft Computing, held May 25-27, 2014, in Berkeley. The book covers a wealth of key topics in soft computing, focusing on both fundamental aspects and applications. The former include fuzzy mathematics, type-2 fuzzy sets, evolutionary-based optimization, aggregation and neural networks, while the latter include soft computing in data analysis, image processing, decision-making, classification, series prediction, economics, control, and modeling. By providing readers with a timely, authoritative view on the field, and by discussing thought-provoking developments and challenges, the book will foster new research directions in the diverse areas of soft computing.

In the eighties, a group of theoretical physicists introduced several models for certain disordered systems, called "spin glasses". These models are simple and rather canonical random structures, that physicists studied by non-rigorous methods. They predicted spectacular behaviors, previously unknown in probability theory. They believe these behaviors occur in many models of considerable interest for several branches of science (statistical physics, neural networks and computer science). This book introduces in a rigorous manner this exciting new area to the mathematically minded reader. It requires no knowledge whatsoever of any physics, and contains proofs in complete detail of much of what is rigorously known on spin glasses at the time of writing.

Self-organizing maps (SOM) have proven to be of significant economic value in the areas of finance, economic and marketing applications. As a result, this area is rapidly becoming a non-academic technology. This book looks at near state-of-the-art SOM applications in the above areas, and is a multi-authored volume, edited by Guido Deboeck, a leading exponent in the use of computational methods in financial and economic forecasting, and by the originator of SOM, Teuvo Kohonen. The book contains chapters on applications of unsupervised neural networks using Kohonen's self-organizing map approach.