In 1988, E. Verlinde gave a remarkable conjectural formula for the dimension of conformal blocks over a smooth curve in terms of representations of affine Lie algebras. Verlinde's formula arose from physical considerations, but it attracted further attention from mathematicians when it was realized that the space of conformal blocks admits an interpretation as the space of generalized theta functions. A proof followed through the work of many mathematicians in the 1990s. This book gives an authoritative treatment of all aspects of this theory. It presents a complete proof of the Verlinde formula and full details of the connection with generalized theta functions, including the construction of the relevant moduli spaces and stacks of G-bundles. Featuring numerous exercises of varying difficulty, guides to the wider literature and short appendices on essential concepts, it will be of interest to senior graduate students and researchers in geometry, representation theory and theoretical physics.

The book is concerned with mathematical modelling of supersonic and hyper sonic flows about bodies. Permanent interest in this topic is stimulated, first of all, by aviation and aerospace engineering. The designing of aircraft and space vehicles requires a more precise prediction of the aerodynamic and heat transfer characteristics. Together with broadening of the flight condition range, this makes it necessary to take into account a number of gas dynamic and physical effects caused by rarefaction, viscous-inviscid interaction, separation, various physical and chemical processes induced by gas heating in the intensive bow shock wave. The flow field around a body moving at supersonic speed can be divided into three parts, namely, shock layer, near wake including base flow, and far wake. The shock layer flow is bounded by the bow shock wave and the front and lat eral parts of the body surface. A conventional approach to calculation of shock layer flows consists in a successive solution of the inviscid gas and boundary layer equations. When the afore-mentioned effects become important, implementation of these models meets difficulties or even becomes impossible. In this case, one has to use a more general approach based on the viscous shock layer concept."

Despite successes of modern physics, the existence of dark energy and matter is indicative that conventional mechanical accounting is lacking. The most basic of all mechanical principles is Newton's second law, and conventionally, energy is just energy whether particle or wave energy. In this monograph, Louis de Broglie's idea of simultaneous existence of both particle and associated wave is developed, with a novel proposal to account for mass and energy through a combined particle-wave theory. Newton's second law of motion is replaced by a fully Lorentz invariant reformulation inclusive of both particles and waves. The model springs from continuum mechanics and forms a natural extension of special relativistic mechanics. It involves the notion of "force in the direction of time" and every particle has both particle and wave energies, arising as characteristics of space and time respectively. Dark matter and energy then emerge as special or privileged states occurring for alignments of spatial forces with the force in the direction of time. Dark matter is essentially a backward wave and dark energy a forward wave, both propagating at the speed of light. The model includes special relativistic mechanics and Schroedinger's quantum mechanics, and the major achievements of mechanics and quantum physics. Our ideas of particles and waves are not yet properly formulated, and are bound up with the speed of light as an extreme limit and particle-wave demarcation. Sub-luminal particles have an associated superluminal wave, so if sub-luminal waves have an associated superluminal particle, then there emerges the prospect for faster than light travel with all the implications for future humanity. Carefully structured over special relativity and quantum mechanics, Mathematics of Particle-Wave Mechanical Systems is not a completed story, but perhaps the first mechanical model within which such exalted notions might be realistically and soberly examined. If ultimately the distant universe become accessible, this will necessitate thinking differently about particles, waves and the role imposed by the speed of light. The text constitutes a single proposal in that direction and a depository for mathematically related results. It will appeal to researchers and students of mathematical physics, applied mathematics and engineering mechanics.

The topics of this set of student-oriented books are presented in a discursive style that is readable and easy to follow. Numerous clearly stated, completely worked out examples together with carefully selected problem sets with answers are used to enhance students' understanding and manipulative skill. The goal is to help students feel comfortable and confident in using advanced mathematical tools in junior, senior, and beginning graduate courses.

For more than five decades Bertram Kostant has been one of the major architects of modern Lie theory. Virtually all his papers are pioneering with deep consequences, many giving rise to whole new fields of activities. His interests span a tremendous range of Lie theory, from differential geometry to representation theory, abstract algebra, and mathematical physics. It is striking to note that Lie theory (and symmetry in general) now occupies an ever increasing larger role in mathematics than it did in the fifties. Now in the sixth decade of his career, he continues to produce results of astonishing beauty and significance for which he is invited to lecture all over the world. This is the fourth volume (1985-1995) of a five-volume set of Bertram Kostant's collected papers. A distinguished feature of this fourth volume is Kostant's commentaries and summaries of his papers in his own words.

The theory of complex functions is a strikingly beautiful and powerful area of mathematics. Some particularly fascinating examples are seemingly complicated integrals which are effortlessly computed after reshaping them into integrals along contours, as well as apparently difficult differential and integral equations, which can be elegantly solved using similar methods. To use them is sometimes routine but in many cases it borders on an art. The goal of the book is to introduce the reader to this beautiful area of mathematics and to teach him or her how to use these methods to solve a variety of problems ranging from computation of integrals to solving difficult integral equations. This is done with a help of numerous examples and problems with detailed solutions.

The Edexcel A level Lab Books support students in completing the A level Core Practical requirements. This lab book includes: all the instructions students need to perform the Core Practicals, consistent with our A level online teaching resources writing frames for students to record their results and reflect on their work CPAC Skills Checklists, so that students can track the practical skills they have learned, in preparation for their exams practical skills practice questions a full set of answers. This lab book is designed to help students to: structure their A level lab work to ensure that they cover the Core Practical assessment criteria track their progress in the development of A level practical skills create a record of all of the Core Practical work they will have completed, in preparation for revision.

For more than five decades Bertram Kostant has been one of the major architects of modern Lie theory. Virtually all his papers are pioneering with deep consequences, many giving rise to whole new fields of activities. His interests span a tremendous range of Lie theory, from differential geometry to representation theory, abstract algebra, and mathematical physics. It is striking to note that Lie theory (and symmetry in general) now occupies an ever increasing larger role in mathematics than it did in the fifties. Now in the sixth decade of his career, he continues to produce results of astonishing beauty and significance for which he is invited to lecture all over the world. This is the fifth volume (1995-2005) of a five-volume set of Bertram Kostant's collected papers. A distinguished feature of this fifth volume is Kostant's commentaries and summaries of his papers in his own words.

An account of Newton's life and work.

Modern Physics, Second Edition provides a clear, precise, and contemporary introduction to the theory, experiment, and applications of modern physics. Ideal for both physics majors and engineers, this eagerly awaited second edition puts the modern back into modern physics courses. Pedagogical features throughout the text focus the reader on the core concepts and theories while offering optional, more advanced sections, examples, and cutting-edge applications to suit a variety of students and courses. Critically acclaimed for his lucid style, in the second edition, Randy Harris applies the same insights into recent developments in physics, engineering, and technology.

This is the best seller in this market. It provides a comprehensive introduction to complex variable theory and its applications to current engineering problems. It is designed to make the fundamentals of the subject more easily accessible to students who have little inclination to wade through the rigors of the axiomatic approach. Modeled after standard calculus books-both in level of exposition and layout-it incorporates physical applications throughout the presentation, so that the mathematical methodology appears less sterile to engineering students.

For more than five decades Bertram Kostant has been one of the major architects of modern Lie theory. Virtually all his papers are pioneering with deep consequences, many giving rise to whole new fields of activities. His interests span a tremendous range of Lie theory, from differential geometry to representation theory, abstract algebra, and mathematical physics. It is striking to note that Lie theory (and symmetry in general) now occupies an ever increasing larger role in mathematics than it did in the fifties. Now in the sixth decade of his career, he continues to produce results of astonishing beauty and significance for which he is invited to lecture all over the world. This is the third volume (1975-1985) of a five-volume set of Bertram Kostant's collected papers. A distinguished feature of this third volume is Kostant's commentaries and summaries of his papers in his own words.

This book highlights two essential analyses of data collected during the LHCb experiment, based on the Large Hadron Collider at CERN. The first comprises the first observation and studies of matter-antimatter asymmetries in two three-body b-baryon decays, paving the way for more precise measurements of the relatively unknown decay properties of b-baryon decays. The second is an analysis of a charged B meson decay to three charged pions, where previously large matter-antimatter asymmetries were observed in a model-independent analysis. Here a model of the decay amplitude is constructed using the unitarity-conserving 'K-matrix' model for the scalar contributions, so as to gain an understanding of how the previously observed matter-antimatter asymmetries arise; further, the model's construction yields the most precise and comprehensive study of this decay mode to date.

After the advent of the industrial revolution, the world experienced a rapid change in technology and lifestyle, which has led to a dramatic increase in energy demand. Unfortunately, many of the energy resources used in the past have negatively impacted the environment, from greenhouse gases to the depletion of natural resources. Society now faces the challenge of ensuring sustainable and clean energy production so that society may receive efficient energy without damaging the Earth's health. In order to promote an environmentally healthy society, strategic green policies must be developed. Eco-Friendly and Agile Energy Strategies and Policy Development establishes interdisciplinary coverage in sustainable energy development by strategic thinking and lifestyle changes by designing agile energy strategies and policies. It offers research, experiences, and lessons learned that offer integrated conceptual and empirical contributions from different interrelated fields. Covering topics such as energy security risks, green economy, and solar power plants, this premier reference source is an indispensable resource for engineers, government officials, business leaders, environmentalist organizations, economists, sociologists, students and educators of higher education, libraries, researchers, and academicians.

Concise, balanced, and fundamentals-based resource providing coverage of power system operation and planning, including simulations using PSS(R)E software Electric Power Systems with Renewables provides a comprehensive treatment of various topics related to power systems with an emphasis on renewable energy integration into power systems. The updated use cases and methods in the book build upon the climate change science and renewables currently being integrated with the grid and the ability to manage resilience for electrifying transportation and related power systems as societies identify more ways to move towards a carbon-free future. Simulation examples and software support are provided by integrating the educational version of PSS(R)E. The newly revised edition includes new topics on the intelligent use of PSS(R)E simulation software, presents a short introduction to Python (a widely used software in the power industry), and provides new examples and back-of-the-chapter homework problems to further aid in information retention. Written by two highly qualified authors with significant experience in the field, Electric Power Systems with Renewables also contains information on: Electric energy and the environment, covering hydro power, fossil-fuel based power plants, nuclear power, renewable energy, and distributed generation (DG) Power flow in power system networks covers basic power flow equations, the Newton-Raphson procedure, sensitivity analysis, and a new remote bus voltage control concept Transformers and generators in power systems, covering basic principles of operation, a simplified transformer model, and per-unit representation High voltage DC (HVDC) transmission systems, -current-link, and voltage-link systems Associated with this textbook, there is a website from which the simulation files can be downloaded for use in PSS(R)E and Python. It also contains short videos to simplify the use of these software. This website will be regularly updated. Electric Power Systems with Renewables serves as a highly useful textbook for both undergraduate and graduate students in Electrical and Computer Engineering (ECE). It is also an appropriate resource for students outside of ECE who have the prerequisites, such as in mechanical, civil, and chemical engineering. Practicing engineers will greatly benefit with its industry-relevant approach to meet the present-day needs.

This clear, concise Complete Revision & Practice book from CGP is a perfect way to prepare for the Edexcel A-Level Physics exams - it covers every topic from both years of the course. It's fully up-to-date for the new exam specifications for 2015 and beyond, with straightforward explanations, helpful examples and full-colour diagrams throughout. Practice questions and exam-style questions (with answers) are included for every topic, and the book is rounded off with a section of in-depth advice on Practical Skills. And finally, a free Online Edition of the whole book is included - just use the code printed inside the book to access it on your PC, Mac or tablet!

Classical mechanics is a subject that is teeming with life. However, most of the interesting results are scattered around in the specialist literature, which means that potential readers may be somewhat discouraged by the effort required to obtain them. Addressing this situation, Hamiltonian Dynamical Systems includes some of the most significant papers in Hamiltonian dynamics published during the last 60 years. The book covers bifurcation of periodic orbits, the break-up of invariant tori, chaotic behavior in hyperbolic systems, and the intricacies of real systems that contain coexisting order and chaos. It begins with an introductory survey of the subjects to help readers appreciate the underlying themes that unite an apparently diverse collection of articles. The book concludes with a selection of papers on applications, including in celestial mechanics, plasma physics, chemistry, accelerator physics, fluid mechanics, and solid state mechanics, and contains an extensive bibliography. The book provides a worthy introduction to the subject for anyone with an undergraduate background in physics or mathematics, and an indispensable reference work for researchers and graduate students interested in any aspect of classical mechanics.

These Proceedings cover various topics in modern physics in which group theoretical methods can be applied effectively. The two volumes, containing over 100 papers, cover such areas as representation theory, the theory and applications of dynamical symmetries and coherent states, symmetries in atomic, molecular, nuclear and elementary particle physics, field theory including gauge theories, supersymmetry and supergravity, general relativity and cosmology, the theory of space groups and its applications to solid state physics and phase transitions, the problems of quantum and classical mechanics and paraxial optics, and the theory of nonlinear equations and solitons.

The development and use of medical and dental materials are highly interdisciplinary endeavors which require expertise in chemistry, materials science, medicine and/or dentistry, mechanics and design engineering. The Symposium upon which this treatise is based was organized to bring members from these communities together to explore problems of mutual interest. The biomaterials which are used in medical or dental prostheses must not only exhibit structural stability and provide the desired function, but they must also perform over extended periods of time in the environment of the body. The latter is a very stringent requirement. The oral and other physiological environments are designed by nature to break down many organic substances. Also of importance is the requirement that materials used in the prosthesis not have a deleterious effect on body tissues. Most foreign (to the body) substances are somewhat toxic to human tissues; in fact, few factors are more limiting in the medical prosthesis field than the biocompatibility problem. Some of these problems and the attempts to solve them are discussed in this volume.

This book presents the mathematical study of vortices of the two-dimensional Ginzburg-Landau model, an important phenomenological model used to describe superconductivity. The vortices, identified as quantized amounts of vorticity of the superconducting current localized near points, are the objects of many observational and experimental studies, both past and present. The Ginzburg-Landau functionals considered include both the model cases with and without a magnetic field. The book acts a guide to the various branches of Ginzburg-Landau studies, provides context for the study of vortices, and presents a list of open problems in the field.

This book focuses on the ellipsoidal function, which serves as an evolution and extension of the circular function (trigonometric function) and elliptic function. It presents an in-depth discussion of the ellipsoidal function (algebra) theory and the conformal mapping (geometry) theory of the ellipsoid function, demonstrating the outstanding performance of the ellipsoid function response filter. Applications of the ellipsoidal function include the capacitance of ellipsoidal conductors and the surface area of ellipsoids, which in turn correspond to ellipsoidal integrals of the first kind and the second kind, respectively. The book offers a valuable reference guide for undergraduates, graduate students and researchers in the related fields.