This reference book, which has found wide use as a text, provides an answer to the needs of graduate physical mathematics students and their teachers. The present edition is a thorough revision of the first, including a new chapter entitled Connections on Principle Fibre Bundles'' which includes sections on holonomy, characteristic classes, invariant curvature integrals and problems on the geometry of gauge fields, monopoles, instantons, spin structure and spin connections. Many paragraphs have been rewritten, and examples and exercises added to ease the study of several chapters. The index includes over 130 entries.

Numbers ... , natural, rational, real, complex, p-adic .... What do you know about p-adic numbers? Probably, you have never used any p-adic (nonrational) number before now. I was in the same situation few years ago. p-adic numbers were considered as an exotic part of pure mathematics without any application. I have also used only real and complex numbers in my investigations in functional analysis and its applications to the quantum field theory and I was sure that these number fields can be a basis of every physical model generated by nature. But recently new models of the quantum physics were proposed on the basis of p-adic numbers field Qp. What are p-adic numbers, p-adic analysis, p-adic physics, p-adic probability? p-adic numbers were introduced by K. Hensel (1904) in connection with problems of the pure theory of numbers. The construction of Qp is very similar to the construction of (p is a fixed prime number, p = 2,3,5, ... ,127, ... ). Both these number fields are completions of the field of rational numbers Q. But another valuation 1 . Ip is introduced on Q instead of the usual real valuation 1 . I* We get an infinite sequence of non isomorphic completions of Q : Q2, Q3, ... , Q127, ... , IR = Qoo* These fields are the only possibilities to com plete Q according to the famous theorem of Ostrowsky.

This is a unique approach to noise theory and its application to physical measurements that will find its place among the graduate course books. In a very systematic way, the foundations are laid and applied in a way that the book will also be useful to those not focusing on optics. Exercises and solutions help students to deepen their knowledge.

We live in complicated, dangerous times. They are also hyper-technical times. As citizens who will elect future presidents of the most powerful and influential country in the world, we need to know truly understand, not just rely on television's talking heads if Iran's nascent nuclear capability is a genuine threat to the West, if biochemical weapons are likely to be developed by terrorists, if there are viable alternatives to fossil fuels that should be nurtured and supported by the government, if nuclear power should be encouraged, and if global warming is actually happening. This book is written in everyday, nontechnical language on the science behind the concerns that our nation faces in the immediate future. Even active readers of serious journalism will be surprised by the lessons that the book contains. It is "must-have" information for all presidents and citizens of the twenty-first century."

Energy and environmental finance (EEF) is an emerging global phenomenon. During the last few decades, many countries started monitoring EEF practices. Major components of these practices include costs, fraud, scandals, and more. Among several problems, the most prevalent is the lack of awareness about the issues of EEF among various stakeholders. The Handbook of Research on Energy and Environmental Finance 4.0 is an international reference that provides understanding and lessons learned in all aspects of EEF in individual, organizational, and societal experiences. This book examines research in the shape of experience, implementation, and application. Covering topics such as clean power, energy poverty, and environmental degradation, this book is a dynamic resource for academicians, researchers, professionals who work within the domains of EEF, EEF regulators, scholars of EEF, managers involved in EEF organizations, law practitioners involved in EEF regulations, auditors involved in audit and control systems of EEF, university professors, and students pursuing studies and research in EEF.

This book features 13 papers presented at the Fifth International Symposium on Recurrence Plots, held August 2013 in Chicago, IL. It examines recent applications and developments in recurrence plots and recurrence quantification analysis (RQA) with special emphasis on biological and cognitive systems and the analysis of coupled systems using cross-recurrence methods. Readers will discover new applications and insights into a range of systems provided by recurrence plot analysis and new theoretical and mathematical developments in recurrence plots. Recurrence plot based analysis is a powerful tool that operates on real-world complex systems that are nonlinear, non-stationary, noisy, of any statistical distribution, free of any particular model type and not particularly long. Quantitative analyses promote the detection of system state changes, synchronized dynamical regimes or classification of system states. The book will be of interest to an interdisciplinary audience of recurrence plot users and researchers interested in time series analysis of complex systems in general.

The aim of the present book is to show, in a broad and yet deep way, the state of the art in computational science and engineering. Examples of topics addressed are: fast and accurate numerical algorithms, model-order reduction, grid computing, immersed-boundary methods, and specific computational methods for simulating a wide variety of challenging problems, problems such as: fluid-structure interaction, turbulent flames, bone-fracture healing, micro-electro-mechanical systems, failure of composite materials, storm surges, particulate flows, and so on. The main benefit offered to readers of the book is a well-balanced, up-to-date overview over the field of computational science and engineering, through in-depth articles by specialists from the separate disciplines.

The contributions gathered in this volume provide introductions to current problems in geospace electromagnetic radiation, guides to the associated literature and tutorial reviews of the relevant space physics. Students and scientists working on various aspects of the terrestrial aurora or magnetospheric and near-Earth heliospheric high-frequency waves will find this volume an indispensable companion for their studies.

This book provides a chronological introduction to modern atomic theory, which represented an attempt to reconcile the ancient doctrine of atomism with careful experiments-performed during the 19th century-on the flow of heat through substances and across empty space. Included herein are selections from classic texts such as Carnot's Reflection on the Motive Power of Fire, Clausius' Mechanical Theory of Heat, Rutherford's Nuclear Constitution of Atoms, Planck's Atomic Theory of Matter and Heisenberg's Copenhagen Interpretation of Quantum Theory. Each chapter begins with a short introduction followed by a reading selection. Carefully crafted study questions draw out key points in the text and focus the reader's attention on the author's methods, analysis and conclusions. Numerical and laboratory exercises at the end of each chapter test the reader's ability to understand and apply key concepts from the text. Heat, Radiation and Quanta is the last of four volumes in A Student's Guide through the Great Physics Texts. The book comes from a four-semester undergraduate physics curriculum designed to encourage a critical and circumspect approach to natural science while at the same time preparing students for advanced coursework in physics. This book is particularly suitable as a college-level textbook for students of the natural sciences, history or philosophy. It might also serve as a textbook for advanced high-school or home-schooled students, or as a thematically-organized source-book for scholars and motivated lay-readers. In studying the classic scientific texts included herein, the reader will be drawn toward a lifetime of contemplation.

Combined into one volume for the first time, the updated and clarified "Exercises for the Feynman Lectures on Physics" provides comprehensive, hands-on practice in all the most important areas of physics--from Newtonian mechanics through the theory of relativity and quantum mechanics.
A perfect complement to "The Feynman Lectures on Physics," these exercises have all been assigned in Caltech's mandatory two-year introductory physics course, either when Richard Feynman was teaching it, or during the nearly two decades that followed when "The Feynman Lectures on Physics" was used as the textbook. With this modern, easy-to-use volume, students of physics will have a chance to apply what they have learned in the "Lectures" and to enhance and reinforce the concepts taught by the inimitable Richard Feynman.

Devices and Related Properties.- The Properties of the Pseudospark Discharge.- Review of Superdense Glow Discharge.- Basic Mechanisms Contributing to the Hollow Cathode Effect.- Cathode-Related Processes in High-Current Density, Low Pressure Glow Discharges.- Comparison of Electrode Effects in High-Pressure and Low-Pressure Gas Discharges Like Spark-Gap and Pseudospark.- Experimental Review.- Mapping and Modeling of the Cathode Fall and Negative Glow Regions.- Emission Spectroscopy in Optically Thick Gas Discharges.- An Analysis of the High Current Glow Discharge Operation of the BLT Switch.- Laser-Induced Fluorescence Measurements of Number Densities of Neutral and Ionized Metal Atoms.- Streamers in Atmospheric Pressure N2: Empirical Results.- Theoretical Modeling.- The Solution of the Continuity Equations in Ionization and Plasma Growth.- Scaling Parameters for Optically Triggered Hollow Cathode Switches Obtained by Computer Simulation.- A Physical Model of Prebreakdown in the Hollow Cathode Pseudospark Discharge Based on Numerical Simulations.- Self-Consistent Models of DC and Transient Glow Discharges.- Weak Collisions in Strong Double Layers.- The Effect of Pendel Electrons on Breakdown and Sustainment of a Hollow Cathode Discharge.- A Two-Electron-Group Model for a High Current Pseudospark or Back- Lighted Thyratron Plasma.- Electron Ionization Rate Coefficients at Very High E/N.- New Applications.- Plasma-Based Device Concepts Based on the Pseudospark and BLT.- Emittance Measurement of a Pseudospark-Produced Electron Beam.- New Ways of Electron Emission for Power Switching and Electron Beam Generation.

Density functional theory (DFT) has become the standard workhorse for quantum mechanical simulations as it offers a good compromise between accuracy and computational cost.
However, there are many important systems for which DFT performs very poorly, most notably strongly-correlated materials, resulting in a significant recent growth in interest in 'beyond DFT' methods. The widely used DFT+U technique, in particular, involves the addition of explicit Coulomb repulsion terms to reproduce the physics of spatially-localised electronic subspaces.
The magnitude of these corrective terms, measured by the famous Hubbard U parameter, has received much attention but less so for the projections used to delineate these subspaces.
The dependence on the choice of these projections is studied in detail here and a method to overcome this ambiguity in DFT+U, by self-consistently determining the projections, is introduced.
The author shows how nonorthogonal representations for electronic states may be used to construct these projections and, furthermore, how DFT+U may be implemented with a linearly increasing cost with respect to system size.
The use of nonorthogonal functions in the context of electronic structure calculations is extensively discussed and clarified, with new interpretations and results, and, on this topic, this work may serve as a reference for future workers in the field."

This book is aimed at researchers, industry professionals and students interested in the broad ranges of disciplines related to condition monitoring of machinery working in non-stationary conditions. Each chapter, accepted after a rigorous peer-review process, reports on a selected, original piece of work presented and discussed at the International Conference on Condition Monitoring of Machinery in Non-stationary Operations, CMMNO'2018, held on June 20 - 22, 2018, in Santander, Spain. The book describes both theoretical developments and a number of industrial case studies, which cover different topics, such as: noise and vibrations in machinery, conditioning monitoring in non-stationary operations, vibro-acoustic diagnosis of machinery, signal processing, application of pattern recognition and data mining, monitoring and diagnostic systems, faults detection, dynamics of structures and machinery, and mechatronic machinery diagnostics.

Drawing examplesfrom mathematics, physics, chemistry, biology, engineering, economics, medicine, politics, and sports, this book illustrates how nonlinear dynamics plays a vital role in our world. Examples cover a wide range from the spread and possible control of communicable diseases, to the lack of predictability in long-range weather forecasting, to competition between political groups and nations.

After an introductorychapter that explores what it means to be nonlinear, the book covers the mathematical conceptssuch as limit cycles, fractals, chaos, bifurcations, and solitons, that will be applied throughout the book. Numerous computer simulations and exercises allow students to explore topics in greater depth using the Maple computer algebra system. The mathematical level of the text assumes prior exposure to ordinary differential equations and familiarity with the wave and diffusion equations.No prior knowledge of Maple is assumed.

The book may be used at the undergraduate or graduate level to prepare science and engineering students for problems in the "real world," or for self-study by practicing scientists and engineers."

Aimed at graduates and potential researchers, this is a comprehensive introduction to the mathematical aspects of spin glasses and neural networks. It should be useful to mathematicians in probability theory and theoretical physics, and to engineers working in theoretical computer science.

This book helps advanced undergraduate, graduate and postdoctoral students in their daily work by offering them a compendium of numerical methods. The choice of methods pays significant attention to error estimates, stability and convergence issues as well as to the ways to optimize program execution speeds. Many examples are given throughout the chapters, and each chapter is followed by at least a handful of more comprehensive problems which may be dealt with, for example, on a weekly basis in a one- or two-semester course. In these end-of-chapter problems the physics background is pronounced, and the main text preceding them is intended as an introduction or as a later reference. Less stress is given to the explanation of individual algorithms. It is tried to induce in the reader an own independent thinking and a certain amount of scepticism and scrutiny instead of blindly following readily available commercial tools.

S.L. Sobolev (1908-1989) was a great mathematician of the twentieth century. His selected works included in this volume laid the foundations for intensive development of the modern theory of partial differential equations and equations of mathematical physics, and they were a gold mine for new directions of functional analysis and computational mathematics. The topics covered in this volume includes Sobolev's fundamental works on equations of mathematical physics, computational mathematics, and cubature formulas. Some of the articles are generally unknown to mathematicians because they were published in journals that are difficult to access.

The rare earths play a unique role in science. These seventeen related elements afford a panoply of subtle variations deriving from the systematic development of their electronic configurations, allowing a test of theory with excellent resolution. In contrast they find widespread use in even the most mundane processes such as steel making, for polishing materials and gasoline cracking catalysts. In between are exotic uses such as TV screen phosphors, lasers, high strength permanent magnets and chemical probes.
This multi-volume handbook covers the entire rare earth field in an integrated manner. Each chapter is a comprehensive up-to-date, critical review of a particular segment of the field. The work offers the researcher and graduate student alike, a complete and thorough coverage of this fascinating field.
. Authoritative
. Comprehensive
. Up-to-date
. Critical
. Reliable

This book, part of the seriesContributions in Mathematical and Computational Sciences, reviews recent developments in the theory of vertex operator algebras (VOAs) and their applications to mathematics and physics.

The mathematical theory of VOAs originated from the famous monstrous moonshine conjectures of J.H. Conway and S.P. Norton, which predicted a deep relationship between the characters of the largest simple finite sporadic group, the Monster and the theory of modular forms inspired by the observations of J. MacKay and J. Thompson.

The contributions are based on lectures delivered at the 2011 conference on Conformal Field Theory, Automorphic Forms and Related Topics, organized by the editors as part of a special program offered at Heidelberg University that summer under the sponsorship of the Mathematics Center Heidelberg (MATCH)."

"Geometry and Physics" addresses mathematicians wanting to understand modern physics, and physicists wanting to learn geometry. It gives an introduction to modern quantum field theory and related areas of theoretical high-energy physics from the perspective of Riemannian geometry, and an introduction to modern geometry as needed and utilized in modern physics. Jurgen Jost, a well-known research mathematician and advanced textbook author, also develops important geometric concepts and methods that can be used for the structures of physics. In particular, he discusses the Lagrangians of the standard model and its supersymmetric extensions from a geometric perspective."

Synchronization of chaotic systems, a patently nonlinear phenomenon, has emerged as a highly active interdisciplinary research topic at the interface of physics, biology, applied mathematics and engineering sciences. In this connection, time-delay systems described by delay differential equations have developed as particularly
suitable tools for modeling specific dynamical systems. Indeed, time-delay is ubiquitous in many physical systems, for example due to finite
switching speeds of amplifiers in electronic circuits, finite lengths of vehicles in traffic flows, finite signal propagation times in biological networks and circuits, and quite generally whenever memory effects are relevant.
This monograph presents the basics of chaotic time-delay systems and their synchronization with an emphasis on the effects of time-delay feedback which give rise to new collective dynamics.
Special attention is devoted to scalar chaotic/hyperchaotic time-delay
systems, and some higher order models, occurring in different branches of science and technology as well as to the synchronization of their coupled versions.

Last but not least, the presentation as a whole strives for a balance between the necessary mathematical description of the basics
and the detailed presentation of real-world applications.

This is the first comprehensive biography of a major, but neglected, figure of his age. John Theophilus Desaguliers made his mark on the eighteenth century in several diverse ways. He was an assistant to Sir Isaac Newton and later elucidated the difficult concepts of Newtonian physics in private lectures. He was a member of the Royal Society, and was presented with the Society's highest honour, the Copley Medal, no less than three times. He was a pioneering engineer: the water supply of Edinburgh, the ventilation of the Houses of Parliament and the first Westminster Bridge all owed him a debt. In a different sphere, Desaguliers became the third Grand Master of the Grand Lodge of the Freemasons which was founded in 1717. He is remembered worldwide for his seminal influence during those early days of Freemasonry. He also wrote poetry and had an influential circle of patrons, including George I and Frederick, Prince of Wales (whom he initiated as a Mason at a specially convened lodge at Kew). This biography, based on original research, describes a charismatic character who was a major figure of his age.

Modern cosmology is a quickly developing ?eld of research. New technical devices and tools supply the community with new experimental data measured with high accuracy. The self-consistent explanation of these data needs t- oretical models that are based on hypothetical predictions of particle theory. In their turn, such predictions imply cosmology for their probe. Speci?c st- ies of the cosmological consequences of particle theory, linking them to their observable signatures, are actual. This boiling kettle of theoretical research and experimental efforts produces ideas that will be preserved for following generations. The aim of this book is to acquaint the reader with some of these ideas, - fering nontrivial ways to probe the physical basis of modern cosmology. An extensive review of the newest ideas in modern cosmology, e. g. , related with the development of the M-brane theory, lies beyond the scope of our book, which is aimed at providing a ?rmly established system of probes for these ideas, linking their predictions to their possible experimental test. We use the framework of in?ationary paradigm to reveal the phenomena that can shed light on the physical origin of the observed Universe, of its matter content and large-scale structure. The crucial role of quantum ?uctuations in creation of our Universe and in possible features, re?ecting cosmological impact of microphysics, is discussed. These features are shown to be accessible to - perimental test in the near future.

The European Conferences on Numerical Mathematics and Advanced Applications (ENUMATH) are a series of conferences held every two years to provide a forum for discussion of new trends in numerical mathematics and challenging scientific and industrial applications at the highest level of international expertise. ENUMATH 2011 was hosted by the University of Leicester (UK) from the 5th to 9th September 2011. This proceedings volume contains more than 90 papers by speakers of the conference and gives an overview of recent developments in scientific computing, numerical analysis, and practical use of modern numerical techniques and algorithms in various applications. New results on finite element methods, multiscale methods, numerical linear algebra, and finite difference schemes are presented. A range of applications include computational problems from fluid dynamics, materials, image processing, and molecular dynamics.

This self-contained book is devoted to the study of the acoustic wave equations and the Maxwell system, the two most common waves equations that are encountered in physics or in engineering. It presents a detailed analysis of their mathematical and physical properties. In particular, the author focuses on the study of the harmonic exterior problems, building a mathematical framework which provides the existence and uniqueness of the solutions. This book will serve as a useful introduction to wave problems for graduate students in mathematics, physics, and engineering.