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In this book an account of the growth theory of subharmonic functions is given, which is directed towards its applications to entire functions of one and several complex variables. The presentation aims at converting the noble art of constructing an entire function with prescribed asymptotic behaviour to a handicraft. For this one should only construct the limit set that describes the asymptotic behaviour of the entire function. All necessary material is developed within the book, hence it will be most useful as a reference book for the construction of entire functions.

Electronic books. -- local. --- Potential theory (Mathematics). --- Subharmonic functions. --- Subharmonic functions --- Operations Research --- Civil & Environmental Engineering --- Engineering & Applied Sciences --- Potential theory (Mathematics) --- Green's operators --- Green's theorem --- Potential functions (Mathematics) --- Potential, Theory of --- Functions, Subharmonic --- Mathematics. --- Potential Theory. --- Mathematical analysis --- Mechanics --- Functions of real variables

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Aimed at graduate students and researchers in mathematics, physics, and engineering, this book presents a clear path from calculus to classical potential theory and beyond, moving the reader into a fertile area of mathematical research as quickly as possible. The author revises and updates material from his classic work, Introduction to Potential Theory (1969), to provide a modern text that introduces all the important concepts of classical potential theory. In the first half of the book, the subject matter is developed meticulously from first principles using only calculus. Commencing with the inverse square law for gravitational and electromagnetic forces and the divergence theorem of the calculus, the author develops methods for constructing solutions of Laplace’s equation on a region with prescribed values on the boundary of the region. The second half addresses more advanced material aimed at those with a background of a senior undergraduate or beginning graduate course in real analysis. For specialized regions, namely spherical chips, solutions of Laplace’s equation are constructed having prescribed normal derivatives on the flat portion of the boundary and prescribed values on the remaining portion of the boundary. By means of transformations known as diffeomorphisms, these solutions are morphed into local solutions on regions with curved boundaries. The Perron-Weiner-Brelot method is then used to construct global solutions for elliptic partial differential equations involving a mixture of prescribed values of a boundary differential operator on part of the boundary and prescribed values on the remainder of the boundary.

Electronic books. -- local. --- Mathematics. --- Potential theory (Mathematics). --- Potential theory (Mathematics) --- Operations Research --- Civil & Environmental Engineering --- Engineering & Applied Sciences --- Green's operators --- Green's theorem --- Potential functions (Mathematics) --- Potential, Theory of --- Math --- Partial differential equations. --- Applied mathematics. --- Engineering mathematics. --- Physics. --- Engineering. --- Potential Theory. --- Mathematical Methods in Physics. --- Engineering, general. --- Partial Differential Equations. --- Applications of Mathematics. --- Science --- Construction --- Industrial arts --- Technology --- Natural philosophy --- Philosophy, Natural --- Physical sciences --- Dynamics --- Engineering --- Engineering analysis --- Mathematical analysis --- Mechanics --- Partial differential equations --- Mathematics --- Mathematical physics. --- Differential equations, partial. --- Physical mathematics --- Physics

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This volume gives an introduction to a fascinating research area to applied mathematicians. It is devoted to providing the exposition of promising analytical and numerical techniques for solving challenging biomedical imaging problems, which trigger the investigation of interesting issues in various branches of mathematics.

Biomedical engineering --- Electrical impedance tomography --- Imaging systems in medicine --- Diagnostic Imaging --- Tomography --- Electronics, Medical --- Models, Theoretical --- Electric Impedance --- Diagnostic Techniques and Procedures --- Investigative Techniques --- Electric Conductivity --- Electronics --- Electricity --- Physics --- Analytical, Diagnostic and Therapeutic Techniques and Equipment --- Diagnosis --- Electromagnetic Phenomena --- Natural Science Disciplines --- Physical Phenomena --- Disciplines and Occupations --- Phenomena and Processes --- Biology - General --- Biomedical Engineering --- Health & Biological Sciences --- Biology --- Mathematical models --- Electrical impedance tomography. --- Mathematical models. --- Applied potential tomography --- Electrical impedance imaging --- Clinical engineering --- Medical engineering --- Mathematics. --- Radiology. --- Differential equations. --- Partial differential equations. --- Potential theory (Mathematics). --- Biomathematics. --- Mathematical and Computational Biology. --- Potential Theory. --- Ordinary Differential Equations. --- Partial Differential Equations. --- Imaging / Radiology. --- Mathematics --- Green's operators --- Green's theorem --- Potential functions (Mathematics) --- Potential, Theory of --- Mathematical analysis --- Mechanics --- Partial differential equations --- 517.91 Differential equations --- Differential equations --- Radiological physics --- Radiation --- Math --- Science --- Bioengineering --- Biophysics --- Engineering --- Medicine --- Differential Equations. --- Differential equations, partial. --- Radiology, Medical. --- Clinical radiology --- Radiology, Medical --- Radiology (Medicine) --- Medical physics

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The present book discusses the Kuhn-Tucker Optimality, Karush-Kuhn-Tucker Necessary and Sufficient Optimality Conditions in presence of various types of generalized convexity assumptions. Wolfe-type Duality, Mond-Weir type Duality, Mixed type Duality for Multiobjective optimization problems such as Nonlinear programming problems, Fractional programming problems, Nonsmooth programming problems, Nondifferentiable programming problems, Variational and Control problems under various types of generalized convexity assumptions.

Convex functions. --- Convexity spaces. --- Mathematical optimization. --- Optimization (Mathematics) --- Optimization techniques --- Optimization theory --- Systems optimization --- Functions, Convex --- Mathematics. --- Operations research. --- Decision making. --- Potential theory (Mathematics). --- Mathematical models. --- Calculus of variations. --- Potential Theory. --- Mathematical Modeling and Industrial Mathematics. --- Calculus of Variations and Optimal Control; Optimization. --- Operation Research/Decision Theory. --- Isoperimetrical problems --- Variations, Calculus of --- Maxima and minima --- Models, Mathematical --- Simulation methods --- Green's operators --- Green's theorem --- Potential functions (Mathematics) --- Potential, Theory of --- Mathematical analysis --- Mechanics --- Deciding --- Decision (Psychology) --- Decision analysis --- Decision processes --- Making decisions --- Management --- Management decisions --- Choice (Psychology) --- Problem solving --- Operational analysis --- Operational research --- Industrial engineering --- Management science --- Research --- System theory --- Math --- Science --- Decision making --- Operations research --- System analysis --- Functions of real variables --- Operations Research/Decision Theory.