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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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Stable Lévy processes and related stochastic processes play an important role in stochastic modelling in applied sciences, in particular in financial mathematics. This book is about the potential theory of stable stochastic processes. It also deals with related topics, such as the subordinate Brownian motions (including the relativistic process) and Feynman–Kac semigroups generated by certain Schroedinger operators. The authors focus on classes of stable and related processes that contain the Brownian motion as a special case. This is the first book devoted to the probabilistic potential theory of stable stochastic processes, and, from the analytical point of view, of the fractional Laplacian. The introduction is accessible to nonspecialists and provides a general presentation of the fundamental objects of the theory. Besides recent and deep scientific results the book also provides a didactic approach to its topic, as all chapters have been tested on a wide audience, including young mathematicians at a CNRS/HARP Workshop, Angers 2006. The reader will gain insight into the modern theory of stable and related processes and their potential analysis with a theoretical motivation for the study of their fine properties.
Functional analysis.  Potential theory (Mathematics).  Stochastic process.  Potential theory (Mathematics)  Functional analysis  Civil & Environmental Engineering  Mathematics  Mathematical Statistics  Operations Research  Engineering & Applied Sciences  Physical Sciences & Mathematics  Green's operators  Green's theorem  Potential functions (Mathematics)  Potential, Theory of  Functional calculus  Mathematics.  Mathematical models.  Probabilities.  Probability Theory and Stochastic Processes.  Mathematical Modeling and Industrial Mathematics.  Potential Theory.  Probability  Statistical inference  Combinations  Chance  Least squares  Mathematical statistics  Risk  Models, Mathematical  Simulation methods  Mathematical analysis  Mechanics  Math  Science  Calculus of variations  Functional equations  Integral equations  Distribution (Probability theory.  Distribution functions  Frequency distribution  Characteristic functions  Probabilities  Analyse fonctionnelle.
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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 PerronWeinerBrelot 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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Serge Alinhac (1948–) received his PhD from l'Université ParisSud XI (Orsay). After teaching at l'Université Paris Diderot VII and Purdue University, he has been a professor of mathematics at l'Université ParisSud XI (Orsay) since 1978. He is the author of Blowup for Nonlinear Hyperbolic Equations (Birkhäuser, 1995) and Pseudodifferential Operators and the Nash–Moser Theorem (with P. Gérard, American Mathematical Society, 2007). His primary areas of research are linear and nonlinear partial differential equations. This excellent introduction to hyperbolic differential equations is devoted to linear equations and symmetric systems, as well as conservation laws. The book is divided into two parts. The first, which is intuitive and easy to visualize, includes all aspects of the theory involving vector fields and integral curves; the second describes the wave equation and its perturbations for two or threespace dimensions. Over 100 exercises are included, as well as "do it yourself" instructions for the proofs of many theorems. Only an understanding of differential calculus is required. Notes at the end of the selfcontained chapters, as well as references at the end of the book, enable easeofuse for both the student and the independent researcher.
Differential equations, Hyperbolic.  Differential equations, Hyperbolic  Mathematics  Physical Sciences & Mathematics  Calculus  Differential equations, Partial.  Hyperbolic differential equations  Partial differential equations  Mathematics.  Mathematical analysis.  Analysis (Mathematics).  Partial differential equations.  Potential theory (Mathematics).  Analysis.  Partial Differential Equations.  Potential Theory.  Green's operators  Green's theorem  Potential functions (Mathematics)  Potential, Theory of  Mathematical analysis  Mechanics  517.1 Mathematical analysis  Math  Science  Differential equations, Partial  Global analysis (Mathematics).  Differential equations, partial.  Analysis, Global (Mathematics)  Differential topology  Functions of complex variables  Geometry, Algebraic
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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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This proceedings volume consists of papers presented at the Variational Analysis and Aerospace Engineering conference held in Erice, Italy in September 2007 at the International School of Mathematics, Guido Stampacchia. The workshop provided a platform for aerospace engineers and mathematicians (from universities, research centers and industry) to discuss the advanced problems requiring an extensive application of mathematics. Important mathematical methods have been developed and extensively applied in the field of aerospace engineering. Topics and contributions at the workshop concentrated on the most advanced mathematical methods in engineering such as computational fluid dynamics methods, the introduction of new materials, theory of optimization, optimization methods applied in aerodynamics, theory of structures, space missions, flight mechanics, theories of control, algebraic geometry for CAD applications, and variational methods and applications. Advanced graduate students, researchers, and professionals in mathematics and engineering will find this volume useful. This work is dedicated to Professor Angelo Miele, an eminent mathematician and engineer, on the occasion of his 85th birthday.
Aerospace engineering.  Calculus of variations.  Computational fluid dynamics.  Geometry, Algebraic.  Mathematical optimization.  Calculus of variations  Aerospace engineering  Computational fluid dynamics  Mathematical optimization  Geometry, Algebraic  Applied Mathematics  Engineering & Applied Sciences  CFD (Computational fluid dynamics)  Fluid dynamics  Computer simulation  Data processing  Mathematics.  Computer simulation.  Potential theory (Mathematics).  Applied mathematics.  Engineering mathematics.  Mathematical models.  Automotive engineering.  Mathematical Modeling and Industrial Mathematics.  Potential Theory.  Simulation and Modeling.  Applications of Mathematics.  Appl.Mathematics/Computational Methods of Engineering.  Automotive Engineering.  Engineering.  Mathematical and Computational Engineering.  Construction  Industrial arts  Technology  Engineering  Engineering analysis  Mathematical analysis  Math  Science  Computer modeling  Computer models  Modeling, Computer  Models, Computer  Simulation, Computer  Electromechanical analogies  Mathematical models  Simulation methods  Modelintegrated computing  Green's operators  Green's theorem  Potential functions (Mathematics)  Potential, Theory of  Mechanics  Mathematics  Models, Mathematical
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The present book discusses the KuhnTucker Optimality, KarushKuhnTucker Necessary and Sufficient Optimality Conditions in presence of various types of generalized convexity assumptions. Wolfetype Duality, MondWeir 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.
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