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This book provides a complete and exhaustive study of the Green’s functions. Professor Cabada first proves the basic properties of Green's functions and discusses the study of nonlinear boundary value problems. Classic methods of lower and upper solutions are explored, with a particular focus on monotone iterative techniques that flow from them. In addition, Cabada proves the existence of positive solutions by constructing operators defined in cones. The book will be of interest to graduate students and researchers interested in the theoretical underpinnings of boundary value problem solutions.

Green's functions. --- Differential equations. --- 517.91 Differential equations --- Differential equations --- Functions, Green's --- Functions, Induction --- Functions, Source --- Green functions --- Induction functions --- Source functions --- Mathematics. --- Operator theory. --- Functions of complex variables. --- Ordinary Differential Equations. --- Several Complex Variables and Analytic Spaces. --- Operator Theory. --- Potential theory (Mathematics) --- Differential Equations. --- Differential equations, partial. --- Functional analysis --- Partial differential equations --- Complex variables --- Elliptic functions --- Functions of real variables

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Green's Function and Boundary Elements of Multifield Materials contains a comprehensive treatment of multifield materials under coupled thermal, magnetic, electric, and mechanical loads. Its easy-to-understand text clarifies some of the most advanced techniques for deriving Green's function and the related boundary element formulation of magnetoelectroelastic materials: Radon transform, potential function approach, Fourier transform. Our hope in preparing this book is to attract interested readers and researchers to a new field that continues to provide fascinating and technologically i

Materials science --- Green's functions. --- Boundary element methods. --- Mathematics. --- BEM (Engineering analysis) --- BIE analysis --- BIE methods --- Boundary element analysis --- Boundary elements methods --- Boundary integral equation analysis --- Boundary integral equation methods --- Boundary integral methods --- Numerical analysis --- Functions, Green's --- Functions, Induction --- Functions, Source --- Green functions --- Induction functions --- Source functions --- Differential equations --- Potential theory (Mathematics) --- Material science --- Physical sciences

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Advances in semiconductor technology have made possible the fabrication of structures whose dimensions are much smaller than the mean free path of an electron. This book gives a thorough account of the theory of electronic transport in such mesoscopic systems. After an initial chapter covering fundamental concepts, the transmission function formalism is presented, and used to describe three key topics in mesoscopic physics: the quantum Hall effect; localisation; and double-barrier tunnelling. Other sections include a discussion of optical analogies to mesoscopic phenomena, and the book concludes with a description of the non-equilibrium Green's function formalism and its relation to the transmission formalism. Complete with problems and solutions, the book will be of great interest to graduate students of mesoscopic physics and nanoelectronic device engineering, as well as to established researchers in these fields.

Electron transport. --- Semiconductors. --- Green's functions. --- Mesoscopic phenomena (Physics) --- Crystalline semiconductors --- Semi-conductors --- Semiconducting materials --- Semiconductor devices --- Crystals --- Electrical engineering --- Electronics --- Solid state electronics --- Electrons --- Energy-band theory of solids --- Free electron theory of metals --- Transport theory --- Phenomena, Mesoscopic (Physics) --- Physics --- Functions, Green's --- Functions, Induction --- Functions, Source --- Green functions --- Induction functions --- Source functions --- Differential equations --- Potential theory (Mathematics) --- Materials --- Electron transport --- Semiconductors

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This book is a systematic study of the classical and quantum theories of gauge systems. It starts with Dirac's analysis showing that gauge theories are constrained Hamiltonian systems. The classical foundations of BRST theory are then laid out with a review of the necessary concepts from homological algebra. Reducible gauge systems are discussed, and the relationship between BRST cohomology and gauge invariance is carefully explained. The authors then proceed to the canonical quantization of gauge systems, first without ghosts (reduced phase space quantization, Dirac method) and second in the BRST context (quantum BRST cohomology). The path integral is discussed next. The analysis covers indefinite metric systems, operator insertions, and Ward identities. The antifield formalism is also studied and its equivalence with canonical methods is derived. The examples of electromagnetism and abelian 2-form gauge fields are treated in detail. The book gives a general and unified treatment of the subject in a self-contained manner. Exercises are provided at the end of each chapter, and pedagogical examples are covered in the text.

Gauge fields (Physics) --- Abelian constraints. --- Berezin integral. --- Canonical Hamiltonian. --- Fourier transformation. --- Gauss law. --- Gaussian average. --- Green functions. --- Heisenberg algebra. --- Jacobi identity. --- Kunneth formula. --- Lagrange multipliers. --- Pauli matrices. --- antighost number. --- auxiliary fields. --- boundary operator. --- cohomology. --- convolution. --- derivations. --- differential. --- doublet. --- effective action. --- extended action. --- exterior product. --- harmonic states. --- involution. --- left derivatives. --- local commutativity. --- nontrivial cycle. --- superdomain.

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Finite element method --- Green's functions --- Microwave integrated circuits --- Méthode des éléments finis --- Green, Fonctions de --- Mathematical models --- -Integrated circuits --- Microwave circuits --- Functions, Green's --- Functions, Induction --- Functions, Source --- Green functions --- Induction functions --- Source functions --- Differential equations --- Potential theory (Mathematics) --- FEA (Numerical analysis) --- FEM (Numerical analysis) --- Finite element analysis --- Numerical analysis --- Isogeometric analysis --- Finite element method. --- Green's functions. --- Mathematical models. --- -Mathematical models --- Méthode des éléments finis --- Integrated circuits