This book provides the mathematical foundations for Feynman's operator calculus and for the Feynman path integral formulation of quantum mechanics as a natural extension of analysis and functional analysis to the infinite-dimensional setting. In one application, the results are used to prove the last two remaining conjectures of Freeman Dyson for quantum electrodynamics. In another application, the results are used to unify methods and weaken domain requirements for non-autonomous evolution equations. Other applications include a general theory of Lebesgue measure on Banach spaces with a Schauder basis and a new approach to the structure theory of operators on uniformly convex Banach spaces. This book is intended for advanced graduate students and researchers.

The present volume contains the Proceedings of the International Conference on Spectral Theory and Mathematical Physics held in Santiago de Chile in November 2014. Main topics are: Ergodic Quantum Hamiltonians, Magnetic Schroedinger Operators, Quantum Field Theory, Quantum Integrable Systems, Scattering Theory, Semiclassical and Microlocal Analysis, Spectral Shift Function and Quantum Resonances. The book presents survey articles as well as original research papers on these topics. It will be of interest to researchers and graduate students in Mathematics and Mathematical Physics.

The book discusses three classes of problems: the generalized Nash equilibrium problems, the bilevel problems and the mathematical programming with equilibrium constraints (MPEC). These problems interact through their mathematical analysis as well as their applications. The primary aim of the book is to present the modern tool of variational analysis and optimization, which are used to analyze these three classes of problems. All contributing authors are respected academicians, scientists and researchers from around the globe. These contributions are based on the lectures delivered by experts at CIMPA School, held at the University of Delhi, India, from 25 November-6 December 2013, and peer-reviewed by international experts. The book contains five chapters. Chapter 1 deals with nonsmooth, nonconvex bilevel optimization problems whose feasible set is described by using the graph of the solution set mapping of a parametric optimization problem. Chapter 2 describes a constraint qualification to MPECs considered as an application of calmness concept of multifunctions and is used to derive M-stationarity conditions for MPEC. Chapter 3 discusses the first- and second-order optimality conditions derived for a special case of a bilevel optimization problem in which the constraint set of the lower level problem is described as a general compact convex set. Chapter 4 concentrates the results of the modelization and analysis of deregulated electricity markets with a focus on auctions and mechanism design. Chapter 5 focuses on optimization approaches called reflection methods for protein conformation determination within the framework of matrix completion. The last chapter (Chap. 6) deals with the single-valuedness of quasimonotone maps by using the concept of single-directionality with a special focus on the case of the normal operator of lower semi-continuous quasiconvex functions.

This book explains - in simple terms and with almost no mathematics - the physics behind recent and glamorous discoveries in Cosmology, Quantum Mechanics, Elementary Particles (e.g. Higgs bosons) and Complexity Theory. En route it delves into the historical landmarks and revolutions that brought about our current understanding of the universe. The book is written mainly for those with little scientific background, both college students and lay readers alike, who are curious about the world of modern physics. Unsolved problems are highlighted and the philosophical implications of the sometimes astounding modern discoveries are discussed. Along the way the reader gains an insight into the mindset and methodology of a physicist.

This textbook takes the reader on a tour of the most important landmarks of theoretical physics: classical, quantum, and statistical mechanics, relativity, electrodynamics, as well as the most modern and exciting of all: elementary particles and the physics of fractals. The second edition has been supplemented with a new chapter devoted to concise though complete presentation of dynamical systems, bifurcations and chaos theory. The treatment is confined to the essentials of each area, presenting all the central concepts and equations at an accessible level. Chapters 1 to 4 contain the standard material of courses in theoretical physics and are supposed to accompany lectures at the university; thus they are rather condensed. They are supposed to fill one year of teaching. Chapters 5 and 6, in contrast, are written less condensed since this material may not be part of standard lectures and thus could be studied without the help of a university teacher. An appendix on elementary particles lies somewhere in between: It could be a summary of a much more detailed course, or studied without such a course. Illustrations and numerous problems round off this unusual textbook. It will ideally accompany the students all along their course in theoretical physics and prove indispensable in preparing and revising the exams. It is also suited as a reference for teachers or scientists from other disciplines who are interested in the topic.

Gradiometry is a multidisciplinary area that combines theoretical and applied physics, ultra-low noise electronics, precision engineering, and advanced signal processing. All physical fields have spatial gradients that fall with distance from their sources more rapidly than the field strength itself. This makes the gradient measurements more difficult. However, there has been a considerable investment, both in terms of time and money, into the development of various types of gradiometers driven by the extremely valuable type of information that is contained in gradients. Applications include the search for oil, gas, and mineral resources, GPS-free navigation, defence, space missions, medical research, and some other applications. The author describes gravity gradiometers, magnetic gradiometers, and electromagnetic (EM) gradiometers. The first two types do not require any active sources of the primary physical fields whose gradients are measured, such as gravity field and ambient magnetic field. EM gradiometers do require a primary EM field, pulsed, or sinusoidal, which propagates through media and creates a secondary EM field. The latter one contains information about the non uniformness of electromagnetically active media such as conductivity and magnetic permeability contrasts. These anomalies are the boundaries of mineral deposits, oil and gas traps, underground water reserves, buried artifacts, unexploded ordnance (UXO), nuclear submarines, and even cancerous human tissue. This book provides readers with a comprehensive introduction, history, potential applications, and current developments in relation to some of the most advanced technologies in the 21st Century. Most of the developments are strictly controlled by Defence Export Control rules and regulations, introduced in all developed countries that typically require permission to transfer relevant information from one country to another. The book is based on the materials that have been available in public domain such as scientific journals, conferences, extended abstracts, and online presentations. In addition, medical applications of EM gradiometers are exempt from any control, and some new results relevant to breast cancer early detection research are published in this book for the first time.

This book presents a selection of the best contributions to GIREP EPEC 2015, the Conference of the International Research Group on Physics Teaching (GIREP) and the European Physical Society's Physics Education Division (EPS PED). It introduces readers interested in the field to the problem of identifying strategies and tools to improve physics teaching and learning so as to convey Key Competences and help students acquire them. The main topic of the conference was Key Competences (KC) in physics teaching and learning in the form of knowledge, skills and attitudes that are fundamental for every member of society. Given the role of physics as a field strongly connected not only to digital competence but also to several other Key Competences, this conference provided a forum for in-depth discussions of related issues.

This book is an exploration of philosophical questions about infinity. Graham Oppy examines how the infinite lurks everywhere, both in science and in our ordinary thoughts about the world. He also analyses the many puzzles and paradoxes that follow in the train of the infinite. Even simple notions, such as counting, adding and maximising present serious difficulties. Other topics examined include the nature of space and time, infinities in physical science, infinities in theories of probability and decision, the nature of part/whole relations, mathematical theories of the infinite, and infinite regression and principles of sufficient reason.

This volume presents the proceedings of the 11th Conference on Problems and Methods in Mathematical Physics (11th TMP), held in Chemnitz, March 25-28, 1999. The conference was dedicated to the memory of Siegfried PrAssdorf, who made important contributions to the theory and numerical analysis of operator equations and their applications in mathematical physics and mechanics. The main part of the book comprises original research papers. The topics are ranging from integral and pseudodifferential equations, boundary value problems, operator theory, boundary element and wavelet methods, approximation theory and inverse problems to various concrete problems and applications in physics and engineering, and reflect PrAssdorf's broad spectrum of research activities. The volume also contains articles describing the life and mathematical achievements of Siegfried PrAssdorf and includes a list of his publications. The book is addressed to a wide audience in the mathematical and engineering sciences.

This book introduces the fundamentals of computer vision (CV), with a focus on extracting useful information from digital images and videos. Including a wealth of methods used in detecting and classifying image objects and their shapes, it is the first book to apply a trio of tools (computational geometry, topology and algorithms) in solving CV problems, shape tracking in image object recognition and detecting the repetition of shapes in single images and video frames. Computational geometry provides a visualization of topological structures such as neighborhoods of points embedded in images, while image topology supplies us with structures useful in the analysis and classification of image regions. Algorithms provide a practical, step-by-step means of viewing image structures. The implementations of CV methods in Matlab and Mathematica, classification of chapter problems with the symbols (easily solved) and (challenging) and its extensive glossary of key words, examples and connections with the fabric of CV make the book an invaluable resource for advanced undergraduate and first year graduate students in Engineering, Computer Science or Applied Mathematics. It offers insights into the design of CV experiments, inclusion of image processing methods in CV projects, as well as the reconstruction and interpretation of recorded natural scenes.

Measurement is an essential activity in every branch of technology and science, the fourth edition of this successful text has been extensively extended and updated to include new developments in measurement devices and technology. Principles of Measurement Systems, 4/e provides a coherent and integrated approach to the topic, covering the main techniques and devices used, together with relevant theory applications, for both mechanical and electronic systems.

An increasing complexity of models used to predict real-world systems leads to the need for algorithms to replace complex models with far simpler ones, while preserving the accuracy of the predictions. This three-volume handbook covers methods as well as applications. This third volume focuses on applications in engineering, biomedical engineering, computational physics and computer science.

This book is based on the idea that Boltzmann-like modelling methods can be developed to design, with special attention to applied sciences, kinetic-type models which are called generalized kinetic models. In particular, these models appear in evolution equations for the statistical distribution over the physical state of each individual of a large population. The evolution is determined both by interactions among individuals and by external actions.

Considering that generalized kinetic models can play an important role in dealing with several interesting systems in applied sciences, the book provides a unified presentation of this topic with direct reference to modelling, mathematical statement of problems, qualitative and computational analysis, and applications. Models reported and proposed in the book refer to several fields of natural, applied and technological sciences. In particular, the following classes of models are discussed: population dynamics and socio-economic behaviours, models of aggregation and fragmentation phenomena, models of biology and immunology, traffic flow models, models of mixtures and particles undergoing classic and dissipative interactions.

This monograph discusses recent advances in ergodic theory and dynamical systems. As a mixture of survey papers of active research areas and original research papers, this volume attracts young and senior researchers alike. Contents: Duality of the almost periodic and proximal relations Limit directions of a vector cocycle, remarks and examples Optimal norm approximation in ergodic theory The iterated Prisoner's Dilemma: good strategies and their dynamics Lyapunov exponents for conservative twisting dynamics: a survey Takens' embedding theorem with a continuous observable

Dynamical Symmetry Breaking and the Onset of Chaos in the Interacting Boson Model of Nuclei; Y. Alhassid. Generating the Spectrum of Nonlinear Hamiltonians; L.Ya. Baranov, R.D. Levine. Dynamical Symmetry and String Theory; I. Bars. U(7) Spectrum Generating Algebra for Rotations and Vibrations in Triatomic Molecules; R. Bijker, et al. Algebraic Treatment of Collective Excitations in Baryon Spectroscopy; R. Bijker, A. Leviatan. Can Iachello's Idea of a Spectral Supersymmetry be Extended into the Relativistic Domain; A. Bohm, L.C. Biedenharn. Low Lying Electric Dipole Excitations and the Interacting Boson Model; P. von Brentano, et al. Effective Charges, the Valence pn Interaction, and the IBM; R.F. Casten, A. Wolf. Dynamical Symmetries in Superdeformed Nuclei; J.A. Cizewski. Dynamical Algebras and Syperalgebras for Interacting Itinerant Many-Electron Systems; A. Danani, M. Rasetti. Number and Isospin Dependence of the IBM3 Hamiltonian; J.P. Elliott, et al. 43 additional articles. Index.

This book advocates the importance and value of errors for the progress of scientific research! Hans Kricheldorf explains that most of the great scientific achievements are based on an iterative process (an 'innate self-healing mechanism'): errors are committed, being checked over and over again, through which finally new findings and knowledge can arise. New ideas are often first confronted with refusal. This is so not only in real life, but also in scientific and medical research. The author outlines in this book how great ideas had to ripen over time before winning recognition and being accepted. The book showcases in an entertaining way, but without schadenfreude, that even some of the most famous discoverers may appear in completely different light, when regarding errors they have committed in their work. This book is divided into two parts. The first part creates a fundament for the discussion and understanding by introducing important concepts, terms and definitions, such as (natural) sciences and scientific research, laws of nature, paradigm shift, and progress (in science). It compares natural sciences with other scientific disciplines, such as historical research or sociology, and examines the question if scientific research can generate knowledge of permanent validity. The second part contains a collection of famous fallacies and errors from medicine, biology, chemistry, physics and geology, and how they were corrected. Readers will be astonished and intrigued what meanders had to be explored in some cases before scientists realized facts, which are today's standard and state-of-the-art of science and technology. This is an entertaining and amusing, but also highly informative book not only for scientists and specialists, but for everybody interested in science, research, their progress, and their history!

This book focuses on the theory of the Zakharov system in the context of plasma physics. It has been over 40 years since the system was first derived by V. E. Zakharov - and in the course of those decades, many innovative achievements with major impacts on other research fields have been made. The book represents a first attempt to highlight the mathematical theories that are most important to researchers, including the existence and unique problems, blow-up, low regularity, large time behavior and the singular limit. Rather than attempting to examine every aspect of the Zakharov system in detail, it provides an effective road map to help readers access the frontier of studies on this system.

This book offers a timely overview of fractional calculus applications, with a special emphasis on fractional derivatives with Mittag-Leffler kernel. The different contributions, written by applied mathematicians, physicists and engineers, offers a snapshot of recent research in the field, highlighting the current methodological frameworks together with applications in different fields of science and engineering, such as chemistry, mechanics, epidemiology and more. It is intended as a timely guide and source of inspiration for graduate students and researchers in the above-mentioned areas.