Inverse limits provide a powerful tool for constructing complicated spaces from simple ones. Theyalso turn the study of a dynamical system consisting of a space and a self-map into a study of a (likely more complicated) space and a self-homeomorphism. In four chapters along with an appendix containing background material the authors develop the theory of inverse limits. The bookbegins with an introduction through inverse limits on 0,1] before moving to a general treatment of the subject. Special topics in continuum theory complete thebook. Although it is not a book on dynamics, the influence of dynamics can be seen throughout; for instance, it includes studies of inverse limits with maps from families of maps that are of interest to dynamicists such as the logistic and the tent families.

This book will serve as a useful reference to graduate students and researchers in continuum theory and dynamical systems. Researchers working in applied areas who are discovering inverse limits in their work will also benefit from this book. "

Stochastic analysis has a variety of applications to biological systems as well as physical and engineering problems, and its applications to finance and insurance have bloomed exponentially in recent times. The goal of this book is to present a broad overview of the range of applications of stochastic analysis and some of its recent theoretical developments. This includes numerical simulation, error analysis, parameter estimation, as well as control and robustness properties for stochastic equations. The book also covers the areas of backward stochastic differential equations via the (non-linear) G-Brownian motion and the case of jump processes. Concerning the applications to finance, many of the articles deal with the valuation and hedging of credit risk in various forms, and include recent results on markets with transaction costs.

This volume presents the state-of-the-art in selected topics across modern nuclear physics, covering fields of central importance to research and illustrating their connection to many different areas of physics. It describes recent progress in the study of superheavy and exotic nuclei, which is pushing our knowledge to ever heavier elements and neutron-richer isotopes. Extending nuclear physics to systems that are many times denser than even the core of an atomic nucleus, one enters the realm of the physics of neutron stars and possibly quark stars, a topic that is intensively investigated with many ground-based and outer-space research missions as well as numerous theoretical works. By colliding two nuclei at very high ultra-relativistic energies one can create a fireball of extremely hot matter, reminiscent of the universe very shortly after the big bang, leading to a phase of melted hadrons and free quarks and gluons, the so-called quark-gluon plasma. These studies tie up with effects of crucial importance in other fields. During the collision of heavy ions, electric fields of extreme strength are produced, potentially destabilizing the vacuum of the atomic physics system, subsequently leading to the decay of the vacuum state and the emission of positrons. In neutron stars the ultra-dense matter might support extremely high magnetic fields, far beyond anything that can be produced in the laboratory, significantly affecting the stellar properties. At very high densities general relativity predicts the stellar collapse to a black hole. However, a number of current theoretical activities, modifying Einstein's theory, point to possible alternative scenarios, where this collapse might be avoided. These and related topics are addressed in this book in a series of highly readable chapters. In addition, the book includes fundamental analyses of the practicalities involved in transiting to an electricity supply mainly based on renewable energies, investigating this scenario less from an engineering and more from a physics point of view. While the topics comprise a large scope of activities, the contributions also show an extensive overlap in the methodology and in the analytical and numerical tools involved in tackling these diverse research fields that are the forefront of modern science.

"Networks of Echoes: Imitation, Innovation and Invisible Leaders" is a mathematically rigorous and data rich book on a fascinating area of the science and engineering of social webs. There are hundreds of complex network phenomena whose statistical properties are described by inverse power laws. The phenomena of interest are not arcane events that we encounter only fleetingly, but are events that dominate our lives. We examine how this intermittent statistical behavior intertwines itself with what appears to be the organized activity of social groups. The book is structured as answers to a sequence of questions such as: How are decisions reached in elections and boardrooms? How is the stability of a society undermined by zealots and committed minorities and how is that stability re-established? Can we learn to answer such questions about human behavior by studying the way flocks of birds retain their formation when eluding a predator? These questions and others are answered using a generic model of a complex dynamic network one whose global behavior is determined by a symmetric interaction among individuals based on social imitation. The complexity of the network is manifest in time series resulting from self-organized critical dynamics that have divergent first and second moments, are non-stationary, non-ergodic and non-Poisson. How phase transitions in the network dynamics influence such activity as decision making is a fascinating story and provides a context for introducing many of the mathematical ideas necessary for understanding complex networks in general. The decision making model (DMM) is selected to emphasize that there are features of complex webs that supersede specific mechanisms and need to be understood from a general perspective. This insightful overview of recent tools and their uses may serve as an introduction and curriculum guide in related courses."

This book contains the results in numerical analysis and optimization presented at the ECCOMAS thematic conference "Computational Analysis and Optimization" (CAO 2011) held in Jyvaskyla, Finland, June 9-11, 2011. Both the conference and this volume are dedicated to Professor Pekka Neittaanmaki on the occasion of his sixtieth birthday. It consists of five parts that are closely related to his scientific activities and interests: Numerical Methods for Nonlinear Problems; Reliable Methods for Computer Simulation; Analysis of Noised and Uncertain Data; Optimization Methods; Mathematical Models Generated by Modern Technological Problems. The book also includes a short biography of Professor Neittaanmaki.

This book presents various computationally efficient component- and system-level design optimization methods for advanced electrical machines and drive systems. Readers will discover novel design optimization concepts developed by the authors and other researchers in the last decade, including application-oriented, multi-disciplinary, multi-objective, multi-level, deterministic, and robust design optimization methods. A multi-disciplinary analysis includes various aspects of materials, electromagnetics, thermotics, mechanics, power electronics, applied mathematics, manufacturing technology, and quality control and management. This book will benefit both researchers and engineers in the field of motor and drive design and manufacturing, thus enabling the effective development of the high-quality production of innovative, high-performance drive systems for challenging applications, such as green energy systems and electric vehicles.

This book gives an introduction to the finite element method as a general computational method for solving partial differential equations approximately. Our approach is mathematical in nature with a strong focus on the underlying mathematical principles, such as approximation properties of piecewise polynomial spaces, and variational formulations of partial differential equations, but with a minimum level of advanced mathematical machinery from functional analysis and partial differential equations.In principle, the material should be accessible to students with only knowledge of calculus of several variables, basic partial differential equations, and linear algebra, as the necessary concepts from more advanced analysis are introduced when needed. Throughout the text we emphasize implementation of the involved algorithms, and have therefore mixed mathematical theory with concrete computer code using the numerical software MATLAB is and its PDE-Toolbox.We have also had the ambition to cover some of the most important applications of finite elements and the basic finite element methods developed for those applications, including diffusion and transport phenomena, solid and fluid mechanics, and also electromagnetics.

Mathematical inequalities are essential tools in mathematics, natural science and engineering. This book gives an overview on recent advances. Some generalizations and improvements for the classical and well-known inequalities are described. They will be applied and further developed in many fields. Applications of the inequalities to entropy theory and quantum physics are also included.

This book provides a self-contained presentation of the physical and mathematical laws governing complex systems. Complex systems arising in natural, engineering, environmental, life and social sciences are approached from a unifying point of view using an array of methodologies such as microscopic and macroscopic level formulations, deterministic and probabilistic tools, modeling and simulation. The book can be used as a textbook by graduate students, researchers and teachers in science, as well as non- experts who wish to have an overview of one of the most open, markedly interdisciplinary and fast-growing branches of present-day science.

This book offers a comprehensive treatment of nonlocal elasticity theory as applied to the prediction of the mechanical characteristics of various types of biological and non-biological nanoscopic structures with different morphologies and functional behaviour. It combines fundamental notions and advanced concepts, covering both the theory of nonlocal elasticity and the mechanics of nanoscopic structures and systems. By reporting on recent findings and discussing future challenges, the book seeks to foster the application of nonlocal elasticity based approaches to the emerging fields of nanoscience and nanotechnology. It is a self-contained guide, and covers all relevant background information, the requisite mathematical and computational techniques, theoretical assumptions, physical methods and possible limitations of the nonlocal approach, including some practical applications. Mainly written for researchers in the fields of physics, biophysics, mechanics, and nanoscience, as well as computational engineers, the book can also be used as a reference guide for senior undergraduate and graduate students, as well as practicing engineers working in a range of areas, such as computational condensed matter physics, computational materials science, computational nanoscience and nanotechnology, and nanomechanics.

'Rough Computing' explores the application of rough set theory, which has attracted attention because of the ability to enhance databases by allowing for the management of uncertainty, a comparative analysis between rough sets, and other intelligent data analysis.

Combining control theory and modeling, this textbook introduces and builds on methods for simulating and tackling concrete problems in a variety of applied sciences. Emphasizing "learning by doing," the authors focus on examples and applications to real-world problems. An elementary presentation of advanced concepts, proofs to introduce new ideas, and carefully presented MATLAB(r) programs help foster an understanding of the basics, but also lead the way to new, independent research.

With minimal prerequisites and exercises in each chapter, this work serves as an excellent textbook and referencefor graduate and advanced undergraduatestudents, researchers, and practitioners in mathematics, physics, engineering, computer science, as well as biology, biotechnology, economics, and finance."

This book describes five qualitative investment decision-making methods based on the hesitant fuzzy information. They are: (1) the investment decision-making method based on the asymmetric hesitant fuzzy sigmoid preference relations, (2) the investment decision-making method based on the hesitant fuzzy trade-off and portfolio selection, (3) the investment decision-making method based on the hesitant fuzzy preference envelopment analysis, (4) the investment decision-making method based on the hesitant fuzzy peer-evaluation and strategy fusion, and (5) the investment decision-making method based on the EHVaR measurement and tail analysis.

This volume reports results from the German research initiative MUNA (Management and Minimization of Errors and Uncertainties in Numerical Aerodynamics), which combined development activities of the German Aerospace Center (DLR), German universities and German aircraft industry. The main objective of this five year project was the development of methods and procedures aiming at reducing various types of uncertainties that are typical of numerical flow simulations. The activities were focused on methods for grid manipulation, techniques for increasing the simulation accuracy, sensors for turbulence modelling, methods for handling uncertainties of the geometry and grid deformation as well as stochastic methods for quantifying aleatoric uncertainties.

This volume contains a contemporary, integrated description of the processes of language. These range from fast scales (fractions of a second) to slow ones (over a million years). The contributors, all experts in their fields, address language in the brain, production of sentences and dialogues, language learning, transmission and evolutionary processes that happen over centuries or millenia, the relation between language and genes, the origins of language, self-organization, and language competition and death. The book as a whole will help to show how processes at different scales affect each other, thus presenting language as a dynamic, complex and profoundly human phenomenon.

This thesis demonstrates techniques that provide faster and more accurate solutions to a variety of problems in machine learning and signal processing. The author proposes a "greedy" algorithm, deriving sparse solutions with guarantees of optimality. The use of this algorithm removes many of the inaccuracies that occurred with the use of previous models.

The subject of fractional calculus and its applications (that is, convolution-type pseudo-differential operators including integrals and derivatives of any arbitrary real or complex order) has gained considerable popularity and importance during the past three decades or so, mainly due to its applications in diverse fields of science and engineering. These operators have been used to model problems with anomalous dynamics, however, they also are an effective tool as filters and controllers, and they can be applied to write complicated functions in terms of fractional integrals or derivatives of elementary functions, and so on.This book will give readers the possibility of finding very important mathematical tools for working with fractional models and solving fractional differential equations, such as a generalization of Stirling numbers in the framework of fractional calculus and a set of efficient numerical methods. Moreover, we will introduce some applied topics, in particular fractional variational methods which are used in physics, engineering or economics. We will also discuss the relationship between semi-Markov continuous-time random walks and the space-time fractional diffusion equation, which generalizes the usual theory relating random walks to the diffusion equation. These methods can be applied in finance, to model tick-by-tick (log)-price fluctuations, in insurance theory, to study ruin, as well as in macroeconomics as prototypical growth models.All these topics are complementary to what is dealt with in existing books on fractional calculus and its applications. This book was written with a trade-off in mind between full mathematical rigor and the needs of readers coming from different applied areas of science and engineering. In particular, the numerical methods listed in the book are presented in a readily accessible way that immediately allows the readers to implement them on a computer in a programming language of their choice. Numerical code is also provided.

This book is a concise introduction to electromagnetics and electromagnetic fields that covers the aspects of most significance for engineering applications by means of a rigorous, analytical treatment. After an introduction to equations and basic theorems, topics of fundamental theoretical and applicative importance, including plane waves, transmission lines, waveguides and Green's functions, are discussed in a deliberately general way. Care has been taken to ensure that the text is readily accessible and self-consistent, with conservation of the intermediate steps in the analytical derivations. The book offers the reader a clear, succinct course in basic electromagnetic theory. It will also be a useful lookup tool for students and designers.

This is the first book devoted to the task of computing integrability structures by computer. The symbolic computation of integrability operator is a computationally hard problem and the book covers a huge number of situations through tutorials. The mathematical part of the book is a new approach to integrability structures that allows to treat all of them in a unified way. The software is an official package of Reduce. Reduce is free software, so everybody can download it and make experiments using the programs available at our website.

Dynamics of Information Systems: Algorithmic Approaches presents recent developments and results found by participants of the Fourth International Conference on the Dynamics of Information Systems, which took place at the University of Florida, Gainesville FL, USA on February 20-22, 2012. The purpose of this conference was to bring together scientists and engineers from industry, government, and universities to exchange knowledge and results in a broad range of topics relevant to the theory and practice of the dynamics of information systems. Dynamics of Information plays an increasingly critical role in our society. The influence of information on social, biological, genetic, and military systems must be better understood to achieve large advances in the capability and understanding of these systems. Applications are widespread and include: detection of terrorist networks, design of highly efficient businesses, computer networks, quantum entanglement, genome modeling, multi-robotic systems, and industrial and manufacturing safety. The book contains state-of-the-art work on theory and practice relevant to the dynamics of information systems. It covers algorithmic approaches to numerical computations with infinite and infinitesimal numbers; presents important problems arising in service-oriented systems, such as dynamic composition and analysis of modern service-oriented information systems and estimation of customer service times on a rail network from GPS data; addresses the complexity of the problems arising in stochastic and distributed systems; and discusses modulating communication for improving multi-agent learning convergence. Network issues-in particular minimum-risk maximum-clique problems, vulnerability of sensor networks, influence diffusion, community detection, and link prediction in social network analysis, as well as a comparative analysis of algorithms for transmission network expansion planning-are described in later chapters.

This book addresses the basics of interval/fuzzy set theory, artificial neural networks (ANN) and computational methods. It presents step-by-step modeling for application problems along with simulation and numerical solutions. In general, every science and engineering problem is inherently biased by uncertainty, and there is often a need to model, solve and interpret problems in the world of uncertainty. At the same time, exact information about models and parameters of practical applications is usually not known and precise values do not exist. This book discusses uncertainty in both data and models. It consists of seven chapters covering various aspects of fuzzy uncertainty in application problems, such as shallow water wave equations, static structural problems, robotics, radon diffusion in soil, risk of invasive alien species and air quality quantification. These problems are handled by means of advanced computational and fuzzy theory along with machine intelligence when the uncertainties involved are fuzzy. The proposed computational methods offer new fuzzy computing methods that help other areas of knowledge construction where inexact information is present.

Quarks are the main constituents of protons and neutrons and hence are important building blocks of all the matter that surrounds us. However, quarks have the intriguing property that they never appear as isolated single particles but only in bound states. This phenomenon is called confinement and has been a central research topic of elementary particle physics for the last few decades. In order to find the mechanism that forbids the existence of free quarks many approaches and ideas are being followed, but by now it has become clear that they are not mutually exclusive but illuminate the problem from different perspectives. Two such confinement scenarios are investigated in this thesis: Firstly, the importance of Abelian field components for the low-energy regime is corroborated, thus supporting the dual superconductor picture of confinement and secondly, the influence of the Gribov horizon on non-perturbative solutions is studied.

Imagine yourself as a military officer in a conflict zone trying to identify locations of weapons caches supporting road-side bomb attacks on your country's troops. Or imagine yourself as a public health expert trying to identify the location of contaminated water that is causing diarrheal diseases in a local population. Geospatial abduction is a new technique introduced by the authors that allows such problems to be solved. Geospatial Abduction provides the mathematics underlying geospatial abduction and the algorithms to solve them in practice; it has wide applicability and can be used by practitioners and researchers in many different fields. Real-world applications of geospatial abduction to military problems are included. Compelling examples drawn from other domains as diverse as criminology, epidemiology and archaeology are covered as well. This book also includes access to a dedicated website on geospatial abduction hosted by University of Maryland. Geospatial Abduction targets practitioners working in general AI, game theory, linear programming, data mining, machine learning, and more. Those working in the fields of computer science, mathematics, geoinformation, geological and biological science will also find this book valuable.