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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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This book is comprehensive in its classical mathematical physics presentation, providing the reader with detailed instructions for obtaining Green's functions from scratch. Green's functions is an instrument easily accessible to practitioners who are engaged in design and exploitation of machines and structures in modern engineering practice. To date, there are no books available on the market that are devoted to the Green's function formalism for equations covered in this volume. The reader, with an undergraduate background in applied mathematics, can become an active user of the Green's function approach. For the first time, Green's functions are discussed for a specific class of problems dealing with potential fields induced in thin-wall structures and therefore, the reader will have first-hand access to a novel issue. This Work is accessible to researchers in applied mathematics, mechanics, and relevant disciplines such as engineering, as well as to upper level undergraduates and graduate students.
Mathematics. --- Differential equations. --- Partial differential equations. --- Numerical analysis. --- Partial Differential Equations. --- Ordinary Differential Equations. --- Classical Mechanics. --- Numerical Analysis. --- Partial differential equations --- 517.91 Differential equations --- Differential equations --- Math --- Science --- Mathematical analysis --- Differential equations, partial. --- Differential Equations. --- Mechanics. --- Classical mechanics --- Newtonian mechanics --- Physics --- Dynamics --- Quantum theory --- Green's functions. --- Functions, Green's --- Functions, Induction --- Functions, Source --- Green functions --- Induction functions --- Source functions --- Potential theory (Mathematics)
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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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Boundary value problems. --- Green's functions. --- Mathematical physics. --- Boundary value problems --- Green's functions --- Mathematical physics --- 517.95 --- 517.95 Partial differential equations --- Partial differential equations --- Physical mathematics --- Physics --- Boundary conditions (Differential equations) --- Differential equations --- Functions of complex variables --- Initial value problems --- Functions, Green's --- Functions, Induction --- Functions, Source --- Green functions --- Induction functions --- Source functions --- Potential theory (Mathematics) --- Mathematics
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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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Non-Abelian gauge theories, such as quantum chromodynamics (QCD) or electroweak theory, are best studied with the aid of Green's functions that are gauge-invariant off-shell, but unlike for the photon in quantum electrodynamics, conventional graphical constructions fail. The Pinch Technique provides a systematic framework for constructing such Green's functions, and has many useful applications. Beginning with elementary one-loop examples, this book goes on to extend the method to all orders, showing that the Pinch Technique is equivalent to calculations in the background field Feynman gauge. The Pinch Technique Schwinger-Dyson equations are derived, and used to show how a dynamical gluon mass arises in QCD. Applications are given to the center vortex picture of confinement, the gauge-invariant treatment of resonant amplitudes, the definition of non-Abelian effective charges, high-temperature effects, and even supersymmetry. This book is ideal for elementary particle theorists and graduate students.
Quantum chromodynamics --- Gauge fields (Physics) --- Green's functions. --- Gauge invariance. --- Functions, Green's --- Functions, Induction --- Functions, Source --- Green functions --- Induction functions --- Source functions --- Differential equations --- Potential theory (Mathematics) --- Gage invariance --- Gauge transformations --- Invariance, Gauge --- Electromagnetism --- Symmetry (Physics) --- Transformations (Mathematics) --- Fields, Gauge (Physics) --- Gage fields (Physics) --- Gauge theories (Physics) --- Field theory (Physics) --- Group theory --- Chromodynamics, Quantum --- QCD (Nuclear physics) --- Particles (Nuclear physics) --- Quantum electrodynamics --- Mathematics.
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warmtetransmissie --- warmteoverdracht --- warmteleer --- warmtegeleidbaarheid --- Pneumatic energy. Refrigeration --- thermodynamics --- Thermodynamics --- thermodynamica --- warmteberekening --- 536.2 --- Green's functions --- Heat --- -#KVIV:BB --- Electromagnetic waves --- Physics --- Cold --- Combustion --- Fire --- Temperature --- Thermochemistry --- Functions, Green's --- Functions, Induction --- Functions, Source --- Green functions --- Induction functions --- Source functions --- Differential equations --- Potential theory (Mathematics) --- Heat conduction. Heat transfer --- Conduction --- -Mathematics --- Green's functions. --- Mathematics. --- 536.2 Heat conduction. Heat transfer --- #KVIV:BB --- Conduction&delete& --- Mathematics
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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
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Quasiconformal mappings. --- Green's functions. --- Jump processes. --- 51 <082.1> --- Mathematics--Series --- Quasiconformal mappings --- Jump processes --- Applications quasi conformes --- Green, Fonctions de --- Processus de sauts --- Complex analysis --- Computer architecture. Operating systems --- Green's functions --- Functions, Green's --- Functions, Induction --- Functions, Source --- Green functions --- Induction functions --- Source functions --- Differential equations --- Potential theory (Mathematics) --- Mappings, Quasiconformal --- Conformal mapping --- Functions of complex variables --- Geometric function theory --- Mappings (Mathematics) --- Processes, Jump --- Markov processes
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Electromagnetic theory --- Green's functions. --- Boundary value problems. --- Théorie électromagnétique --- Green, Fonctions de --- Problèmes aux limites --- Mathematics. --- Mathématiques --- Boundary value problems --- -Green's functions --- Functions, Green's --- Functions, Induction --- Functions, Source --- Green functions --- Induction functions --- Source functions --- Differential equations --- Potential theory (Mathematics) --- Light, Electromagnetic theory of --- Electric fields --- Magnetic fields --- Boundary conditions (Differential equations) --- Functions of complex variables --- Mathematical physics --- Initial value problems --- Mathematics --- Green's functions --- Green, Fonctions de. --- Problèmes aux limites. --- Mathématiques.