This monograph is devoted to the nonperturbative dynamics in the Standard Model (SM), the basic theory of allfundamental interactions in nature except gravity. The Standard Model is divided into two parts: the quantum chromodynamics (QCD) and the electro-weak theory (EWT) are well-defined renormalizable theories in which the perturbation theory is valid. However, for the adequate description of the real physics nonperturbative effects are inevitable. This book describes how these nonperturbative effects may be obtained in the framework of spontaneous generation of effective interactions. The well-known example of such effective interaction is provided by the famous Nambu-Jona-Lasinio effective interaction. Also a spontaneous generation of this interaction in the framework of QCD is described and applied to the method for other effective interactions in QCD and EWT. The method is based on N.N. Bogoliubov's conception of compensation equations. As a result we then describe the principal features of the Standard Model, e.g. Higgs sector, and significant nonperturbative effects including recent results obtained at LHC and TEVATRON.

This book describes a program of research in computable structure theory. The goal is to find definability conditions corresponding to bounds on complexity which persist under isomorphism. The results apply to familiar kinds of structures (groups, fields, vector spaces, linear orderings Boolean algebras, Abelian p-groups, models of arithmetic). There are many interesting results already, but there are also many natural questions still to be answered. The book is self-contained in that it includes necessary background material from recursion theory (ordinal notations, the hyperarithmetical hierarchy) and model theory (infinitary formulas, consistency properties).

This book starts with a discussion of nonlinear ordinary differential equations, bifurcation theory and Hamiltonian dynamics. It then embarks on a systematic discussion of the traditional topics of modern nonlinear dynamics -- integrable systems, Poincare maps, chaos, fractals and strange attractors. The Baker s transformation, the logistic map and Lorenz system are discussed in detail in view of their central place in the subject. There is a detailed discussion of solitons centered around the Korteweg-deVries equation in view of its central place in integrable systems. Then, there is a discussion of the Painleve property of nonlinear differential equations which seems to provide a test of integrability. Finally, there is a detailed discussion of the application of fractals and multi-fractals to fully-developed turbulence -- a problem whose understanding has been considerably enriched by the application of the concepts and methods of modern nonlinear dynamics. On the application side, there is a special emphasis on some aspects of fluid dynamics and plasma physics reflecting the author s involvement in these areas of physics. A few exercises have been provided that range from simple applications to occasional considerable extension of the theory. Finally, the list of references given at the end of the book contains primarily books and papers used in developing the lecture material this volume is based on.

This book has grown out of the author s lecture notes for an interdisciplinary graduate-level course on nonlinear dynamics. The basic concepts, language and results of nonlinear dynamical systems are described in a clear and coherent way. In order to allow for an interdisciplinary readership, an informal style has been adopted and the mathematical formalism has been kept to a minimum.

This book is addressed to first-year graduate students in applied mathematics, physics, and engineering, and is useful also to any theoretically inclined researcher in the physical sciences and engineering.

This second edition constitutes an extensive rewrite of the text involving refinement and enhancement of the clarity and precision, updating and amplification of several sections, addition of new material like theory of nonlinear differential equations, solitons, Lagrangian chaos in fluids, and critical phenomena perspectives on the fluid turbulence problem and many new exercises."

The book is about user interfaces to applications that have been designed for social and physical interaction. The interfaces are 'playful', that is, users feel challenged to engage in social and physical interaction because that will be fun. The topics that will be present in this book are interactive playgrounds, urban games using mobiles, sensor-equipped environments for playing, child-computer interaction, tangible game interfaces, interactive tabletop technology and applications, full-body interaction, exertion games, persuasion, engagement, evaluation and user experience. Readers of the book will not only get a survey of state-of-the-art research in these areas, but the chapters in this book will also provide a vision of the future where playful interfaces will be ubiquitous, that is, present and integrated in home, office, recreational, sports and urban environments, emphasizing that in the future in these environments game elements will be integrated and welcomed.

This research monograph is highly contextual in the present era of spatial/spatio-temporal data explosion. The overall text contains many interesting results that are worth applying in practice, while it is also a source of intriguing and motivating questions for advanced research on spatial data science. The monograph is primarily prepared for graduate students of Computer Science, who wish to employ probabilistic graphical models, especially Bayesian networks (BNs), for applied research on spatial/spatio-temporal data. Students of any other discipline of engineering, science, and technology, will also find this monograph useful. Research students looking for a suitable problem for their MS or PhD thesis will also find this monograph beneficial. The open research problems as discussed with sufficient references in Chapter-8 and Chapter-9 can immensely help graduate researchers to identify topics of their own choice. The various illustrations and proofs presented throughout the monograph may help them to better understand the working principles of the models. The present monograph, containing sufficient description of the parameter learning and inference generation process for each enhanced BN model, can also serve as an algorithmic cookbook for the relevant system developers.

The theory of probability and mathematical statistics is becoming an indispensable discipline in many branches of science and engineering. This is caused by increasing significance of various uncertainties affecting performance of complex technological systems. Fundamental concepts and procedures used in analysis of these systems are often based on the theory of probability and mathematical statistics. The book sets out fundamental principles of the probability theory, supplemented by theoretical models of random variables, evaluation of experimental data, sampling theory, distribution updating and tests of statistical hypotheses. Basic concepts of Bayesian approach to probability and two-dimensional random variables, are also covered. Examples of reliability analysis and risk assessment of technological systems are used throughout the book to illustrate basic theoretical concepts and their applications. The primary audience for the book includes undergraduate and graduate students of science and engineering, scientific workers and engineers and specialists in the field of reliability analysis and risk assessment. Except basic knowledge of undergraduate mathematics no special prerequisite is required.

Decision-aid Philippe Vincke Universite Libre de Bruxelles Over the past decade the discipline of multicriteria decision-aid has been extensively developed in the world of mathematics. As its name indicates, multicriteria decision-aid aims to give decision-makers a tool which should enable them to advance in solving decision problems where several points of view must be taken into account. Written by one of the leading authorities in the field, this book provides a unique introduction to the foundations, models and methods of multicriteria decision-aid. Challenging the monocriteria decision-aid approach to problem solving, Vincke presents us with a unique book which deals with preference modelling, the multiple attribute utility theory, the outranking approach and interactive decision-making methods in the same text. Multicriteria Decision-aid is directed at graduates and postgraduates studying in the fields of management, operations research, decision analysis and all those who, in business and administration, wish to take part in decision-making through scientific reasoning.

This is the revised and augmented edition of a now classic book which is an introduction to sub-Markovian kernels on general measurable spaces and their associated homogeneous Markov chains. The first part, an expository text on the foundations of the subject, is intended for post-graduate students. A study of potential theory, the basic classification of chains according to their asymptotic behaviour and the celebrated Chacon-Ornstein theorem are examined in detail.
The second part of the book is at a more advanced level and includes a treatment of random walks on general locally compact abelian groups. Further chapters develop renewal theory, an introduction to Martin boundary and the study of chains recurrent in the Harris sense. Finally, the last chapter deals with the construction of chains starting from a kernel satisfying some kind of maximum principle.

By establishing an alternative foundation of control theory, this thesis represents a significant advance in the theory of control systems, of interest to a broad range of scientists and engineers. While common control strategies for dynamical systems center on the system state as the object to be controlled, the approach developed here focuses on the state trajectory. The concept of precisely realizable trajectories identifies those trajectories that can be accurately achieved by applying appropriate control signals. The resulting simple expressions for the control signal lend themselves to immediate application in science and technology. The approach permits the generalization of many well-known results from the control theory of linear systems, e.g. the Kalman rank condition to nonlinear systems. The relationship between controllability, optimal control and trajectory tracking are clarified. Furthermore, the existence of linear structures underlying nonlinear optimal control is revealed, enabling the derivation of exact analytical solutions to an entire class of nonlinear optimal trajectory tracking problems. The clear and self-contained presentation focuses on a general and mathematically rigorous analysis of controlled dynamical systems. The concepts developed are visualized with the help of particular dynamical systems motivated by physics and chemistry.

This Festschrift resulted from a workshop on "Advanced Modelling in Mathematical Finance" held in honour of Ernst Eberlein's 70th birthday, from 20 to 22 May 2015 in Kiel, Germany. It includes contributions by several invited speakers at the workshop, including several of Ernst Eberlein's long-standing collaborators and former students. Advanced mathematical techniques play an ever-increasing role in modern quantitative finance. Written by leading experts from academia and financial practice, this book offers state-of-the-art papers on the application of jump processes in mathematical finance, on term-structure modelling, and on statistical aspects of financial modelling. It is aimed at graduate students and researchers interested in mathematical finance, as well as practitioners wishing to learn about the latest developments.

The Dirac equation is of fundamental importance for relativistic quantum mechanics and quantum electrodynamics. In relativistic quantum mechanics, the Dirac equation is referred to as one-particle wave equation of motion for electron in an external electromagnetic field. In quantum electrodynamics, exact solutions of this equation are needed to treat the interaction between the electron and the external field exactly. In this monograph, all propagators of a particle, i.e., the various Green's functions, are constructed in a certain way by using exact solutions of the Dirac equation.

"Understanding Complex Urban Systems" takes as its point of departure the insight that the challenges of global urbanization and the complexity of urban systems cannot be understood let alone managed by sectoral and disciplinary approaches alone. But while there has recently been significant progress in broadening and refining the methodologies for the quantitative modeling of complex urban systems, in deepening the theoretical understanding of cities as complex systems, or in illuminating the implications for urban planning, there is still a lack of well-founded conceptual thinking on the methodological foundations and the strategies of modeling urban complexity across the disciplines.

Bringing together experts from the fields of urban and spatial planning, ecology, urban geography, real estate analysis, organizational cybernetics, stochastic optimization, and literary studies, as well as specialists in various systems approaches and in transdisciplinary methodologies of urban analysis, the volume seeks to advance the discussion on multidisciplinary approaches to urban modeling. While engaging with the state of the art in their respective fields, the contributions are specifically written for both experts from a broad range of disciplines as well as for urban practitioners who feel the need for new approaches given the uncertainty of current developments.

The book presents research that contributes to the development of intelligent dialog systems to simplify diverse aspects of everyday life, such as medical diagnosis and entertainment. Covering major thematic areas: machine learning and artificial neural networks; algorithms and models; and social and biometric data for applications in human-computer interfaces, it discusses processing of audio-visual signals for the detection of user-perceived states, the latest scientific discoveries in processing verbal (lexicon, syntax, and pragmatics), auditory (voice, intonation, vocal expressions) and visual signals (gestures, body language, facial expressions), as well as algorithms for detecting communication disorders, remote health-status monitoring, sentiment and affect analysis, social behaviors and engagement. Further, it examines neural and machine learning algorithms for the implementation of advanced telecommunication systems, communication with people with special needs, emotion modulation by computer contents, advanced sensors for tracking changes in real-life and automatic systems, as well as the development of advanced human-computer interfaces. The book does not focus on solving a particular problem, but instead describes the results of research that has positive effects in different fields and applications.

This proceedings volume highlights a selection of papers presented at the 7th International Conference on High Performance Scientific Computing, which took place in Hanoi, Vietnam, during March 19-23, 2018. The conference has been organized by the Institute of Mathematics of the Vietnam Academy of Science and Technology, the Interdisciplinary Center for Scientific Computing (IWR) of Heidelberg University and the Vietnam Institute for Advanced Study in Mathematics. The contributions cover a broad, interdisciplinary spectrum of scientific computing and showcase recent advances in theory, methods, and practical applications. Subjects covered include numerical simulation, methods for optimization and control, machine learning, parallel computing and software development, as well as the applications of scientific computing in mechanical engineering, airspace engineering, environmental physics, decision making, hydrogeology, material science and electric circuits.

Comprehensive and thorough, this monograph emphasizes the main role differential geometry and convex analysis play in the understanding of physical, chemical, and mechanical notions. Central focus is placed on specifying the agreement between the functional framework and its physical necessity and on making clear the intrinsic character of physical elements, independent from specific charts or frames. The book is divided into four sections, covering thermostructure, classical mechanics, fluid mechanics modelling, and behavior laws. An extensive appendix provides notations and definitions as well as brief explanation of integral manifolds, symplectic structure, and contact structure. Plenty of examples are provided throughout the book, and reviews of basic principles in differential geometry and convex analysis are presented as needed. This book is a useful resource for graduate students and researchers in the field.

Neural field theory has a long-standing tradition in the mathematical and computational neurosciences. Beginning almost 50 years ago with seminal work by Griffiths and culminating in the 1970ties with the models of Wilson and Cowan, Nunez and Amari, this important research area experienced a renaissance during the 1990ties by the groups of Ermentrout, Robinson, Bressloff, Wright and Haken. Since then, much progress has been made in both, the development of mathematical and numerical techniques and in physiological refinement und understanding. In contrast to large-scale neural network models described by huge connectivity matrices that are computationally expensive in numerical simulations, neural field models described by connectivity kernels allow for analytical treatment by means of methods from functional analysis. Thus, a number of rigorous results on the existence of bump and wave solutions or on inverse kernel construction problems are nowadays available. Moreover, neural fields provide an important interface for the coupling of neural activity to experimentally observable data, such as the electroencephalogram (EEG) or functional magnetic resonance imaging (fMRI). And finally, neural fields over rather abstract feature spaces, also called dynamic fields, found successful applications in the cognitive sciences and in robotics. Up to now, research results in neural field theory have been disseminated across a number of distinct journals from mathematics, computational neuroscience, biophysics, cognitive science and others. There is no comprehensive collection of results or reviews available yet. With our proposed book Neural Field Theory, we aim at filling this gap in the market. We received consent from some of the leading scientists in the field, who are willing to write contributions for the book, among them are two of the founding-fathers of neural field theory: Shun-ichi Amari and Jack Cowan.

With more and more physicists and physics students exploring the possibility of utilizing their advanced math skills for a career in the finance industry, this much-needed book quickly introduces them to fundamental and advanced finance principles and methods.
Quantitative Finance for Physicists provides a short, straightforward introduction for those who already have a background in physics. Find out how fractals, scaling, chaos, and other physics concepts are useful in analyzing financial time series. Learn about key topics in quantitative finance such as option pricing, portfolio management, and risk measurement. This book provides the basic knowledge in finance required to enable readers with physics backgrounds to move successfully into the financial industry.
* Short, self-contained book for physicists to master basic concepts and quantitative methods of finance
* Growing field-many physicists are moving into finance positions because of the high-level math required
*Draws on the author's own experience as a physicist who moved into a financial analyst position

In this book the dynamics of the non-ideal oscillatory system, in which the excitation is influenced by the response of the oscillator, is presented. Linear and nonlinear oscillators with one or more degrees of freedom interacting with one or more energy sources are treated. This concerns for example oscillating systems excited by a deformed elastic connection, systems excited by an unbalanced rotating mass, systems of parametrically excited oscillator and an energy source, frictionally self-excited oscillator and an energy source, energy harvesting system, portal frame - non-ideal source system, non-ideal rotor system, planar mechanism - non-ideal source interaction. For the systems the regular and irregular motions are tested. The effect of self-synchronization, chaos and methods for suppressing chaos in non-ideal systems are considered. In the book various types of motion control are suggested. The most important property of the non-ideal system connected with the jump-like transition from a resonant state to a non-resonant one is discussed. The so called 'Sommerfeld effect', resonant unstable state and jumping of the system into a new stable state of motion above the resonant region is explained. A mathematical model of the system is solved analytically and numerically. Approximate analytical solving procedures are developed. Besides, simulation of the motion of the non-ideal system is presented. The obtained results are compared with those for the ideal case. A significant difference is evident. The book aims to present the established results and to expand the literature in non-ideal vibrating systems. A further intention of the book is to give predictions of the effects for a system where the interaction between an oscillator and the energy source exist. The book is targeted at engineers and technicians dealing with the problem of source-machine system, but is also written for PhD students and researchers interested in non-linear and non-ideal problems.

This book addresses the peculiarities of nonlinear wave propagation in waveguides and explains how the stratification depends on the waveguide and confinement. An example of this is an optical fibre that does not allow light to pass through a density jump. The book also discusses propagation in the nonlinear regime, which is characterized by a specific waveform and amplitude, to demonstrate so-called solitonic behaviour. In this case, a wave may be strongly localized, and propagates with a weak change in shape. In the waveguide case there are additional contributions of dispersion originating from boundary or asymptotic conditions. Offering concrete guidance on solving application problems, this essentially (more than twice) expanded second edition includes various aspects of guided propagation of nonlinear waves as well as new topics like solitonic behaviour of one-mode and multi-mode excitation and propagation and plasma waveguides, propagation peculiarities of electromagnetic waves in metamaterials, new types of dispersion, dissipation, electromagnetic waveguides, planetary waves and plasma waves interaction.The key feature of the solitonic behaviour is based on Coupled KdV and Coupled NS systems. The systems are derived in this book and solved numerically with the proof of stability and convergence. The domain wall dynamics of ferromagnetic microwaveguides and Bloch waves in nano-waveguides are also included with some problems of magnetic momentum and charge transport.

This book, now in its second edition, introduces the singularity analysis of differential and difference equations via the Painleve test and shows how Painleve analysis provides a powerful algorithmic approach to building explicit solutions to nonlinear ordinary and partial differential equations. It is illustrated with integrable equations such as the nonlinear Schroedinger equation, the Korteweg-de Vries equation, Henon-Heiles type Hamiltonians, and numerous physically relevant examples such as the Kuramoto-Sivashinsky equation, the Kolmogorov-Petrovski-Piskunov equation, and mainly the cubic and quintic Ginzburg-Landau equations. Extensively revised, updated, and expanded, this new edition includes: recent insights from Nevanlinna theory and analysis on both the cubic and quintic Ginzburg-Landau equations; a close look at physical problems involving the sixth Painleve function; and an overview of new results since the book's original publication with special focus on finite difference equations. The book features tutorials, appendices, and comprehensive references, and will appeal to graduate students and researchers in both mathematics and the physical sciences.

These are the Proceedings of the 6th International Symposium on Multibody Systems and Mechatronics (MUSME 2017) which was held in Florianopolis, Brazil, October 24-28, 2017. Topics addressed include analysis and synthesis of mechanisms; dynamics of multibody systems; design algorithms for mechatronic systems; simulation procedures and results; prototypes and their performance; robots and micromachines; experimental validations; theory of mechatronic simulation; mechatronic systems; and control of mechatronic systems. The MUSME 2017 Symposium was one of the activities of the FEIbIM Commission for Mechatronics and IFToMM technical Committees for Multibody Dynamics, Robotics and Mechatronics.

Current research results in stochastic and deterministic global optimization including single and multiple objectives are explored and presented in this book by leading specialists from various fields. Contributions include applications to multidimensional data visualization, regression, survey calibration, inventory management, timetabling, chemical engineering, energy systems, and competitive facility location. Graduate students, researchers, and scientists in computer science, numerical analysis, optimization, and applied mathematics will be fascinated by the theoretical, computational, and application-oriented aspects of stochastic and deterministic global optimization explored in this book. This volume is dedicated to the 70th birthday of Antanas Zilinskas who is a leading world expert in global optimization. Professor Zilinskas's research has concentrated on studying models for the objective function, the development and implementation of efficient algorithms for global optimization with single and multiple objectives, and application of algorithms for solving real-world practical problems.

This volume provides academic discussion on the theory and practice of mathematical analysis of nonlinear and inverse problems in electromagnetics and their applications. From mathematical problem statement to numerical results, the featured articles provide a concise overview of comprehensive approaches to the solution of problems. Articles highlight the most recent research concerning reliable theoretical approaches and numerical techniques and cover a wide range of applications, including acoustics, electromagnetics, optics, medical imaging, and geophysics. The nonlinear and ill-posed nature of inverse problems and the challenges they present when developing new numerical methods are explained, and numerical verification of proposed new methods on simulated and experimental data is provided. Based on the special session of the same name at the 2017 Progress in Electromagnetics Research Symposium, this book offers a platform for interaction between theoretical and practical researchers and between senior and incoming members in the field.

This book collects lecture courses and seminars given at the Les Houches Summer School 2010 on "Quantum Theory: From Small to Large Scales." Fundamental quantum phenomena appear on all scales, from microscopic to macroscopic. Some of the pertinent questions include the onset of decoherence, the dynamics of collective modes, the influence of external randomness and the emergence of dissipative behaviour. Our understanding of such phenomena has been advanced by the study of model systems and by the derivation and analysis of effective dynamics for large systems and over long times. In this field, research in mathematical physics has regularly contributed results that were recognized as essential in the physics community. During the last few years, the key questions have been sharpened and progress on answering them has been particularly strong. This book reviews the state-of-the-art developments in this field and provides the necessary background for future studies. All chapters are written from a pedagogical perspective, making the book accessible to master and PhD students and researchers willing to enter this field.

This book uses the spiral shape as a key to a multitude of strange and seemingly disparate stories about art, nature, science, mathematics, and the human endeavour. In a way, the book is itself organized as a spiral, with almost disconnected chapters circling around and closing in on the common theme. A particular strength of the book is its extremely cross-disciplinary nature - everything is fun, and everything is connected! At the same time, the author puts great emphasis on mathematical and scientific correctness, in contrast, perhaps, with some earlier books on spirals. Subjects include the mathematical properties of spirals, sea shells, sun flowers, Greek architecture, air ships, the history of mathematics, spiral galaxies, the anatomy of the human hand, the art of prehistoric Europe, Alfred Hitchcock, and spider webs, to name a few.