This monograph presents a new model of mathematical structures called weak n-categories. These structures find their motivation in a wide range of fields, from algebraic topology to mathematical physics, algebraic geometry and mathematical logic. While strict n-categories are easily defined in terms associative and unital composition operations they are of limited use in applications, which often call for weakened variants of these laws. The author proposes a new approach to this weakening, whose generality arises not from a weakening of such laws but from the very geometric structure of its cells; a geometry dubbed weak globularity. The new model, called weakly globular n-fold categories, is one of the simplest known algebraic structures yielding a model of weak n-categories. The central result is the equivalence of this model to one of the existing models, due to Tamsamani and further studied by Simpson. This theory has intended applications to homotopy theory, mathematical physics and to long-standing open questions in category theory. As the theory is described in elementary terms and the book is largely self-contained, it is accessible to beginning graduate students and to mathematicians from a wide range of disciplines well beyond higher category theory. The new model makes a transparent connection between higher category theory and homotopy theory, rendering it particularly suitable for category theorists and algebraic topologists. Although the results are complex, readers are guided with an intuitive explanation before each concept is introduced, and with diagrams showing the interconnections between the main ideas and results.

The flagship monograph addressing the spheroidal wave function and its pertinence to computational electromagnetics

Spheroidal Wave Functions in Electromagnetic Theory presents in detail the theory of spheroidal wave functions, its applications to the analysis of electromagnetic fields in various spheroidal structures, and provides comprehensive programming codes for those computations.

The topics covered in this monograph include:

• Spheroidal coordinates and wave functions
• Dyadic Green’s functions in spheroidal systems
• EM scattering by a conducting spheroid
• EM scattering by a coated dielectric spheroid
• Spheroid antennas
• SAR distributions in a spheroidal head model

The programming codes and their applications are provided online and are written in Mathematica 3.0 or 4.0. Readers can also develop their own codes according to the theory or routine described in the book to find subsequent solutions of complicated structures.

Spheroidal Wave Functions in Electromagnetic Theory is a fundamental reference for scientists, engineers, and graduate students practicing modern computational electromagnetics or applied physics.

The power engineering domain is facing huge challenges, with an increasing interest in intermittent renewable energies which are imposing major technical limitations. Operating ever closer to their limits, the industry-standard AC power grids are subject to instabilities. This book presents an insight into DC grid systems, offering interesting issues to well controlled power grids, in contrast to current AC systems which provide the simplest and most economic connection method for short distances.

This handbook covers basic concepts in mechanical engineering and mechatronics, including stress and strain, mechanics of solids, internal combustion engines, refrigeration, fluid mechanics, control systems, actuation, robotics, electro-mechanical systems, hydraulics, and more. Using step by step examples and numerous illustrations, the book is designed with a "self-teaching" methodology, including a variety of exercises with corresponding answers to enhance mastery of the content. Mechanical engineering and mechatronics concepts provide the skill sets in cross-disciplinary subjects which are needed in modern manufacturing industries. Features Covers basic concepts in mechanical engineering and mechatronics, including stress and strain, mechanics of solids, internal combustion engines, refrigeration, fluid mechanics, control systems, actuation, robotics, and electro-mechanical systems Includes a variety of exercises (with answers), such as conceptual questions, multiple choice, and fill-in the blanks, to enhance mastery of the content

Topics of complex system physics and their interdisciplinary applications to different problems in seismology, biology, economy, sociology, energy and nanotechnology are covered in this new work from renowned experts in their fields. Inparticular, contributed papers contain original results on network science, earthquake dynamics, econophysics, sociophysics, nanoscience and biological physics. Most of the papers use interdisciplinary approaches based on statistical physics, quantum physics and other topics of complex system physics.Papers on econophysics and sociophysics are focussed on societal aspects of physics such as, opinion dynamics, public debates and financial and economic stability. This work will be of interest to statistical physicists, economists, biologists, seismologists and all scientists working in interdisciplinary topics of complexity."

Our knowledge of objects of complex and potential analysis has been enhanced recently by ideas and constructions of theoretical and mathematical physics, such as quantum field theory, nonlinear hydrodynamics, material science. These are some of the themes of this refereed collection of papers, which grew out of the first conference of the European Science Foundation Networking Programme 'Harmonic and Complex Analysis and Applications' held in Norway 2007.

Volume 1 of the Handbook of Colloid and Interface Science is a survey of the theory of colloids in a variety of fields, as well as theircharacterization by rheology. It is an ideal reference work for research scientists, universities, and industry practitioners looking for a complete understanding of how colloids and interfaces behave.

The Shaggy Steed is an unassuming figure from Irish folklore who reveals himself as an inspiring teacher of the forces hidden in the universe. This book celebrates an unassuming bit of physics that also turns out to be an inspiring teacher. The two-body problem - the motion of two bodies bound by the inverse-square force of gravity and electricity - is the Shaggy Steed of physics, guiding the reader to an understanding of both the forces and the mathematical beauty hidden in the physical world.

Encouraged to share his memories of Michael Faraday (1791 1867), John Hall Gladstone (1827 1902) published in 1872 this short work about his late friend's life and career. Faraday's successor as Fullerian Professor of Chemistry at the Royal Institution, Gladstone discusses how Faraday approached science, and the value of his discoveries. Offering informed insights into Faraday's character, Gladstone includes a number of extracts from personal letters. The work also includes a translation of part of the eulogy given by Jean-Baptiste Dumas at the Academie des Sciences, as well as an anonymous poem honouring Faraday and published in Punch shortly after his death. An appendix lists the numerous learned societies to which Faraday belonged. Also reissued in this series are The Life and Letters of Faraday (1870), compiled by Henry Bence Jones, and John Tyndall's Faraday as a Discoverer (1868)."

Professor Atiyah is one of the greatest living mathematicians and is well known throughout the mathematical world. He is a recipient of the Fields Medal, the mathematical equivalent of the Nobel Prize, and is still at the peak of his career. His huge number of published papers, focusing on the areas of algebraic geometry and topology, have here been collected into six volumes, divided thematically for easy reference by individuals interested in a particular subject.
This sixth volume in Michael Atiyah's collected works contains a selection of his publications since 1987, including his work on skyrmions, "Atiyah's axioms" for topological quantum field theories, monopoles, knots, K-theory, equivariant problems, point particles, and M-theory.

Toeplitz and Toeplitz-related systems arise in a variety of applications in mathematics and engineering, especially in signal and image processing. This book deals primarily with iterative methods for solving Toeplitz and Toeplitz-related linear systems, discussing both the algorithms and their convergence theories. A basic knowledge of real analysis, elementary numerical analysis and linear algebra is assumed. The first part of the book (chapters one and two) gives a brief review of some terms and results in linear algebra and the conjugate gradient method, which are important topics for handling the mathematics later on in the book. The second part of the book (chapters three to seven) presents the theory of using iterative methods for solving Toeplitz and Toeplitz-related systems. The third part of the book (chapters eight to twelve) presents recent results from applying the use of iterative methods in different fields of applications, such as partial differential equations, signal and image processing, integral equations and queuing networks. These chapters provide research and application-oriented readers with a thorough understanding of using iterative methods, enabling them not only to apply these methods to the problems discussed but also to derive and analyze new methods for other types of problems and applications.

Demonstrating many fundamental concepts of physics and engineering through the working principles of popular science toys is inexpensive, quickly reaching the senses and inspiring a better learning. The systematic way of setting theoretical model equations for the toys provides a remarkable experience in constructing model equations for physical and engineering systems.Given that most science toys are based on the principles of physics, and to cater to the needs of graduate and master-level programme students in physics and engineering, the present book covers more than 40 wide ranging popular toys. For each toy various features are presented including history, construction, working principle, theoretical model, a solved problem and 5-10 exercises.A course on The Physics of Toys can be designed based on the proposed book to be taught as a full course at graduate and master-level and even to students who have never been exposed to physics. Further, the features of the toys covered in this book can be used to illustrate various concepts and principles in different branches of physics and engineering.

This book is a concise introduction to the key concepts of classical field theory for beginning graduate students and advanced undergraduate students who wish to study the unifying structures and physical insights provided by classical field theory without dealing with the additional complication of quantization. In that regard, there are many important aspects of field theory that can be understood without quantizing the fields. These include the action formulation, Galilean and relativistic invariance, traveling and standing waves, spin angular momentum, gauge invariance, subsidiary conditions, fluctuations, spinor and vector fields, conservation laws and symmetries, and the Higgs mechanism, all of which are often treated briefly in a course on quantum field theory.

This book is the second of a two volume series. Covering a range of subjects from operator theory and classical harmonic analysis to Banach space theory, this book features fully-refereed, high-quality papers exploring new results and trends in weighted norm inequalities, Schur-Agler class functions, complex analysis, dynamical systems, and dyadic harmonic analysis. Graduate students and researchers in analysis will find inspiration in the articles collected in this volume, which emphasize the remarkable connections between harmonic analysis and operator theory. A survey of the two weight problem for the Hilbert transform and an expository article on the Clark model to the case of non-singular measures and applications to the study of rank-one perturbations are included. The material for this volume is based on the 13th New Mexico Analysis Seminar held at the University of New Mexico, April 3-4, 2014 and on several special sections of the Western Spring Sectional Meeting at the University of New Mexico, April 4-6,2014. During the event, participants honored the memory of Cora Sadosky-a great mathematician who recently passed away and who made significant contributions to the field of harmonic analysis. Cora was an exceptional scientist and human being. She was a world expert in harmonic analysis and operator theory, publishing over fifty-five research papers and authoring a major textbook in the field. Participants of the conference include new and senior researchers, recent doctorates as well as leading experts in the area.

First published in 1868, soon after the death of Michael Faraday (1791 1867), this short work assesses the discoveries made by a humble bookbinder who became one of the foremost scientific investigators of the nineteenth century. Eminently qualified, John Tyndall (1820 93), who received Faraday's support in taking up the professorship of natural philosophy at the Royal Institution in 1853, gives an informed appraisal of a remarkable scientific career. The protege of Sir Humphry Davy, Faraday went on to carry out pioneering work in the fields of electromagnetism, diamagnetism and electrolysis. Tyndall focuses here on Faraday's research, describing his influences and how he approached his investigations, although insights into his character are also incorporated: 'Underneath his sweetness and gentleness was the heat of a volcano.' Also reissued in this series are The Life and Letters of Faraday (1870), compiled by Henry Bence Jones, and John Hall Gladstone's Michael Faraday (1872)."

From the reviews: "A unique feature of this book is the nice blend of engineering vividness and mathematical rigour. [...] The authors are to be congratulated for their valuable contribution to the literature in the area of theoretical thermoelasticity and vibration of plates." Journal of Sound and Vibration

This textbook provides everything you need to get through a basic physics course. It guides students through all the essentials with a concise review of the concept, simple illustrations to demonstrate it, worked problems to showcase how to apply it, and a short quiz for self-testing. Whereas other standard books can be overwhelming to students, the author shares what has worked with his own students, trimming back unnecessary detail and focusing on the core basic physical concepts required to gain solid footing. The full range of topics are addressed in a manner that facilitates understanding and will encourage students to continue forward with their learning.

This volume presents lectures given at the Wisla 19 Summer School: Differential Geometry, Differential Equations, and Mathematical Physics, which took place from August 19 - 29th, 2019 in Wisla, Poland, and was organized by the Baltic Institute of Mathematics. The lectures were dedicated to symplectic and Poisson geometry, tractor calculus, and the integration of ordinary differential equations, and are included here as lecture notes comprising the first three chapters. Following this, chapters combine theoretical and applied perspectives to explore topics at the intersection of differential geometry, differential equations, and mathematical physics. Specific topics covered include: Parabolic geometry Geometric methods for solving PDEs in physics, mathematical biology, and mathematical finance Darcy and Euler flows of real gases Differential invariants for fluid and gas flow Differential Geometry, Differential Equations, and Mathematical Physics is ideal for graduate students and researchers working in these areas. A basic understanding of differential geometry is assumed.

This state of the art book takes an applications based approach to teaching mathematics to engineering and applied sciences students. The book lays emphasis on associating mathematical concepts with their physical counterparts, training students of engineering in mathematics to help them learn how things work. The book covers the concepts of number systems, algebra equations and calculus through discussions on mathematics and physics, discussing their intertwined history in a chronological order. The book includes examples, homework problems, and exercises. This book can be used to teach a first course in engineering mathematics or as a refresher on basic mathematical physics. Besides serving as core textbook, this book will also appeal to undergraduate students with cross-disciplinary interests as a supplementary text or reader.

This book reconceptualizes the ancient philosophy of 'dualism' and a 'trinity' applied to classical and quantum nonequilibrium phenomena. In addition to classical mechanics and electrodynamics, a remarkable connection of this philosophy with quantum mechanics is established, which can be useful for quantum computing and the development of quantum artificial intelligence. Packed with the recent theoretical models, quantum simulations of black holes, and experimental observations of quantum phase transitions, this book brings a holistic approach that can be useful to refine the concept of the 'Creation', i.e., the evolution of the Universe from the condensed state of matter, and explain the artificial vision. The approch is:

Unique: Connects ancient philosophy, classical and quantum mechanics, materials, and the latest quantum technologies

Novelty: High level of scientific interpretation of ancient philosophy, creation, interactions, and disorder

Multidisciplinary: Guides students to learn quantum simulations and develop philosophical ideas

The book contains over ten years of in-depth research by the author on the ancient eastern (Indian) philosophy and the latest scientific research in condensed matter and quantum technology. This book will simplify the picture of ancient eastern philosophy, which can be read by the general audience, particularly undergraduate/postgraduate students interested in quantum information science without any mathematical treatment. However, some parts of the book will be ideal for senior academicians and professional researchers in both worlds.

Table of Contents

Preamble: Philosophy through careful observation and self-realization—the birth of cycles. 1. Creation? A cosmic model: Birth of Matter and Mind: Two Cycles 2. Background/history—Understanding creation: Gods and Goddesses. 3. Life Begins on Earth—Creation of the Devices, Deities, and the Concept of God: Creation of Cycles 4. Theory of evolution—(Sankhya) Philosophy of dualism: Creation of a Cycle 5. Interactions at the Macroscale—Classical mechanics—Equilibrium and Rotation: One Cycle 6. Energy/Light and Space (Matter) Application in Condensed Matter Physics: Two Cycles 7.Condensed matter physics—Creation of particles—Bosonic vs. fermionic: One and a half cycle 8: Creation through interactions at the microscale—Quantum mechanics 9. Space–Time Distortion: Black holes, Condensates, and quantum devices 10. Quantum Simulation, Artificial Intelligence, and Vision . Conclusion References.

This textbook serves as an introduction to groups, rings, fields, vector and tensor spaces, algebras, topological spaces, differentiable manifolds and Lie groups --- mathematical structures which are foundational to modern theoretical physics. It is aimed primarily at undergraduate students in physics and mathematics with no previous background in these topics. Applications to physics --- such as the metric tensor of special relativity, the symplectic structures associated with Hamilton's equations and the Generalized Stokes's Theorem --- appear at appropriate places in the text. Worked examples, end-of-chapter problems (many with hints and some with answers) and guides to further reading make this an excellent book for self-study. Upon completing this book the reader will be well prepared to delve more deeply into advanced texts and specialized monographs in theoretical physics or mathematics.

This book collects a selection of papers presented at ELECTRIMACS 2019, the 13th international conference of the IMACS TC1 Committee, held in Salerno, Italy, on 21st-23rd May 2019. The conference papers deal with modelling, simulation, analysis, control, power management, design optimization, identification and diagnostics in electrical power engineering. The main application fields include electric machines and electromagnetic devices, power electronics, transportation systems, smart grids, electric and hybrid vehicles, renewable energy systems, energy storage, batteries, supercapacitors and fuel cells, and wireless power transfer. The contributions included in Volume 1 are particularly focused on electrical engineering simulation aspects and innovative applications.