Non-linear Elliptic Equations in Conformal Geometry
Non-linear Elliptic Equations in Conformal Geometry

Author: Sun-Yung A. Chang

Publisher: European Mathematical Society

Published: 2004

Total Pages: 106

ISBN-13: 9783037190067

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Non-linear elliptic partial differential equations are an important tool in the study of Riemannian metrics in differential geometry, in particular for problems concerning the conformal change of metrics in Riemannian geometry. In recent years the role played by the second order semi-linear elliptic equations in the study of Gaussian curvature and scalar curvature has been extended to a family of fully non-linear elliptic equations associated with other symmetric functions of the Ricci tensor. A case of particular interest is the second symmetric function of the Ricci tensor in dimension four closely related to the Pfaffian. In these lectures, starting from the background material, the author reviews the problem of prescribing Gaussian curvature on compact surfaces. She then develops the analytic tools (e.g., higher order conformal invariant operators, Sobolev inequalities, blow-up analysis) in order to solve a fully nonlinear equation in prescribing the Chern-Gauss-Bonnet integrand on compact manifolds of dimension four. The material is suitable for graduate students and research mathematicians interested in geometry, topology, and differential equations.

Theoretical Fluid Dynamics
Theoretical Fluid Dynamics

Author: Achim Feldmeier

Publisher: Springer Nature

Published: 2020-03-17

Total Pages: 580

ISBN-13: 3030310221

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This textbook gives an introduction to fluid dynamics based on flows for which analytical solutions exist, like individual vortices, vortex streets, vortex sheets, accretions disks, wakes, jets, cavities, shallow water waves, bores, tides, linear and non-linear free-surface waves, capillary waves, internal gravity waves and shocks. Advanced mathematical techniques ("calculus") are introduced and applied to obtain these solutions, mostly from complex function theory (Schwarz-Christoffel theorem and Wiener-Hopf technique), exterior calculus, singularity theory, asymptotic analysis, the theory of linear and nonlinear integral equations and the theory of characteristics. Many of the derivations, so far contained only in research journals, are made available here to a wider public.

Harmonic and Applied Analysis
Harmonic and Applied Analysis

Author: Filippo De Mari

Publisher: Springer Nature

Published: 2021-12-13

Total Pages: 316

ISBN-13: 3030866645

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Deep connections exist between harmonic and applied analysis and the diverse yet connected topics of machine learning, data analysis, and imaging science. This volume explores these rapidly growing areas and features contributions presented at the second and third editions of the Summer Schools on Applied Harmonic Analysis, held at the University of Genova in 2017 and 2019. Each chapter offers an introduction to essential material and then demonstrates connections to more advanced research, with the aim of providing an accessible entrance for students and researchers. Topics covered include ill-posed problems; concentration inequalities; regularization and large-scale machine learning; unitarization of the radon transform on symmetric spaces; and proximal gradient methods for machine learning and imaging.

Electromagnetic Fields
Electromagnetic Fields

Author: Jean G. Van Bladel

Publisher: John Wiley & Sons

Published: 2007-05-23

Total Pages: 1171

ISBN-13: 0470124571

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Professor Jean Van Bladel, an eminent researcher and educator in fundamental electromagnetic theory and its application in electrical engineering, has updated and expanded his definitive text and reference on electromagnetic fields to twice its original content. This new edition incorporates the latest methods, theory, formulations, and applications that relate to today's technologies. With an emphasis on basic principles and a focus on electromagnetic formulation and analysis, Electromagnetic Fields, Second Edition includes detailed discussions of electrostatic fields, potential theory, propagation in waveguides and unbounded space, scattering by obstacles, penetration through apertures, and field behavior at high and low frequencies.

Multiscale Methods
Multiscale Methods

Author: G A Pavliotis

Publisher: Springer Science & Business Media

Published: 2008-02-19

Total Pages: 314

ISBN-13: 0387738282

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This introduction to multiscale methods gives you a broad overview of the methods’ many uses and applications. The book begins by setting the theoretical foundations of the methods and then moves on to develop models and prove theorems. Extensive use of examples shows how to apply multiscale methods to solving a variety of problems. Exercises then enable you to build your own skills and put them into practice. Extensions and generalizations of the results presented in the book, as well as references to the literature, are provided in the Discussion and Bibliography section at the end of each chapter.With the exception of Chapter One, all chapters are supplemented with exercises.

Complex Geometry and Dynamics
Complex Geometry and Dynamics

Author: John Erik Fornæss

Publisher: Springer

Published: 2015-11-05

Total Pages: 316

ISBN-13: 3319203371

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This book focuses on complex geometry and covers highly active topics centered around geometric problems in several complex variables and complex dynamics, written by some of the world’s leading experts in their respective fields. This book features research and expository contributions from the 2013 Abel Symposium, held at the Norwegian University of Science and Technology Trondheim on July 2-5, 2013. The purpose of the symposium was to present the state of the art on the topics, and to discuss future research directions.

Approaches to the Qualitative Theory of Ordinary Differential Equations
Approaches to the Qualitative Theory of Ordinary Differential Equations

Author: Tong-Ren Ding

Publisher: World Scientific

Published: 2007

Total Pages: 394

ISBN-13: 981270468X

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This book is an ideal text for advanced undergraduate students and graduate students with an interest in the qualitative theory of ordinary differential equations and dynamical systems. Elementary knowledge is emphasized by the detailed discussions on the fundamental theorems of the Cauchy problem, fixed-point theorems (especially the twist theorems), the principal idea of dynamical systems, the nonlinear oscillation of Duffing's equation, and some special analyses of particular differential equations. It also contains the latest research by the author as an integral part of the book.

Non-equilibrium Evaporation and Condensation Processes
Non-equilibrium Evaporation and Condensation Processes

Author: Yuri B. Zudin

Publisher: Springer

Published: 2019-03-12

Total Pages: 414

ISBN-13: 3030138151

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This monograph is focused mostly on the exposition of analytical methods for the solution of problems of strong phase change. A new theoretical model is proved useful in describing, with acceptable accuracy, problems of strong evaporation and condensation. The book is the first to treat the problem of asymmetry for evaporation/condensation. A semi-empirical model for the process is proposed for purposes of practical calculation of the process of strong evaporation. The “limiting schemes” of the vapor bubble growth are analyzed. The thermo-hydrodynamic problem of evaporating meniscus of a thin liquid film on a heated surface is considered. A theoretical analysis of the problem of evaporation of a drop levitating over a vapor cushion is performed. The problem of vapor condensation upon a transversal flow around a horizontal cylinder is considered. The second edition is extended by (i) the conjugate “strong evaporation - heat conduction” problem, (ii) the influence of accommodation coefficients on intensive processes of evaporation and condensation, (iii) the problem of supersonic condensation. This book is the first to present a comprehensive theoretical approach of boiling problems: nucleate boiling, superfluid helium phase transition, similarity between pseudo-boiling and subcritical pressure nucleate boiling. The target audience primarily comprises research experts in the field of thermodynamics and fluid dynamics, but the book may also be beneficial for graduate students.