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Elsevier

Academic Press

  • Solution of Equations and Systems of Equations

    Pure and Applied Mathematics: A Series of Monographs and Textbooks, Vol. 9
    • 2nd Edition
    • A. M. Ostrowski
    • Paul A. Smith + 1 more
    • English
    Solution of Equations and Systems of Equations, Second Edition deals with the Laguerre iteration, interpolating polynomials, method of steepest descent, and the theory of divided differences. The book reviews the formula for confluent divided differences, Newton's interpolation formula, general interpolation problems, and the triangular schemes for computing divided differences. The text explains the method of False Position (Regula Falsi) and cites examples of computation using the Regula Falsi. The book discusses iterations by monotonic iterating functions and analyzes the connection of the Regula Falsi with the theory of iteration. The text also explains the idea of the Newton-Raphson method and compares it with the Regula Falsi. The book also cites asymptotic behavior of errors in the Regula Falsi iteration, as well as the theorem on the error of the Taylor approximation to the root. The method of steepest descent or gradient method proposed by Cauchy ensures "global convergence" in very general conditions. This book is suitable for mathematicians, students, and professor of calculus, and advanced mathematics.

  • Topics in Optimization

    • 1st Edition
    • George Leitmann
    • English
    Mathematics in Science and Engineering, Volume 31: Topics in Optimization compiles contributions to the field of optimization of dynamical systems. This book is organized into two parts. Part 1 covers reported investigations that are based on variational techniques and constitute essentially extensions of the classical calculus of variations. The contributions to optimal control theory and its applications, where the arguments are primarily geometric in nature, are discussed in Part 2. This volume specifically discusses the inequalities in a variational problem, singular extremals, mathematical foundations of system optimization, and synthesis of optimal controls. This publication is recommended for both theoreticians and practitioners.

  • Elementary Theory

    Fundamentals of the Theory of Operator Algebras
    • 1st Edition
    • Richard V. Kadison + 1 more
    • Samuel Eilenberg + 1 more
    • English
    Fundamentals of the Theory of Operator Algebras, Volume I: Elementary Theory provides information pertinent to the fundamental aspects of the theory of operator algebras. This book discusses the finite-dimensional linear algebra. Organized into five chapters, this volume begins with an overview of the fundamental aspects of linear functional analysis that are needed in the study of operator algebras. This text then discusses the continuous linear operators, continuous linear functionals, weak topologies, and convexity in the context of linear topological spaces. Other chapters consider the elementary geometry of Hilbertspaces and the simplest properties of Hilbert space operators. This book discusses as well algebras that have a Banach-space structure relative to which the multiplication is continuous. The final chapter deals with those C*-algebras that are strong-operator closed in their action on some Hilbert space, which play a fundamental role in the subject. This book is a valuable resource for mathematicians.

  • Real-Variable Methods in Harmonic Analysis

    • 1st Edition
    • Alberto Torchinsky
    • Samuel Eilenberg + 1 more
    • English
    Real-Variable Methods in Harmonic Analysis deals with the unity of several areas in harmonic analysis, with emphasis on real-variable methods. Active areas of research in this field are discussed, from the Calderón-Zygmund theory of singular integral operators to the Muckenhoupt theory of Ap weights and the Burkholder-Gundy theory of good ? inequalities. The Calderón theory of commutators is also considered. Comprised of 17 chapters, this volume begins with an introduction to the pointwise convergence of Fourier series of functions, followed by an analysis of Cesàro summability. The discussion then turns to norm convergence; the basic working principles of harmonic analysis, centered around the Calderón-Zygmund decomposition of locally integrable functions; and fractional integration. Subsequent chapters deal with harmonic and subharmonic functions; oscillation of functions; the Muckenhoupt theory of Ap weights; and elliptic equations in divergence form. The book also explores the essentials of the Calderón-Zygmund theory of singular integral operators; the good ? inequalities of Burkholder-Gundy; the Fefferman-Stein theory of Hardy spaces of several real variables; Carleson measures; and Cauchy integrals on Lipschitz curves. The final chapter presents the solution to the Dirichlet and Neumann problems on C1-domains by means of the layer potential methods. This monograph is intended for graduate students with varied backgrounds and interests, ranging from operator theory to partial differential equations.

  • Physics of Geomagnetic Phenomena

    International Geophysics Series, Vol. 2
    • 1st Edition
    • S. Matsushita + 1 more
    • English
    Physics of Geomagnetic Phenomena, Volume II covers the advances in geomagnetism and the penetrations into the generation of geomagnetic field phenomena. This book is composed of three chapters and begins with a discussion on various types of phenomenal disturbances, such as ionospheric and geomagnetic disturbance, aurora, and storm. The next chapter describes certain aspects of space geomagnetism based on satellite and rocket observations. This chapter also examines the origins of geomagnetic disturbance phenomena. The last chapter surveys the problems connected with studies of geomagnetic storms and auroras, along with a hydromagnetic model of these phenomena. This book will be of value to physicists, theoreticians, and scientists in allied fields of geomagnetism.

  • Physics of the Aurora and Airglow

    International Geophysics Series, Vol. 2
    • 1st Edition
    • Joseph W. Chamberlain
    • J. Van Mieghem
    • English
    International Geophysics Series, Volume 2: Physics of the Aurora and Airglow explores certain physical aspects of aurora and airglow. This volume is composed of 13 chapters and begins with surveys of the theory and spectroscopic and photometric analyses of radiation from the upper atmosphere. The subsequent chapters treat the geographic distribution of aurora and its physical processes in the atmosphere. Other chapters examine the theory of hydrogen emission in aurora, resonance scattering by atmospheric sodium, the excitation of the oxygen red lines in the airglow, and an atlas of the auroral spectrum. A chapter focuses on the analysis of twilight observations for emission heights. The concluding chapters discuss the theory of day airglow, as well as the spectral photometry and excitation of the nightglow. This book is of value to geophysicists, theoreticians, and scientists of the allied fields of geophysics.

  • Atomic and Molecular Processes

    • 1st Edition
    • D.R. Bates
    • English
    Atomic and Molecular Processes focuses on radiative and collisional processes involving atoms or molecules, including photoionization, elastic and inelastic scattering of electrons, energy loss by slow electrons, excitation, ionization, detachment, charge transfer, elastic scattering, and chemical reactions. The selection first offers information on forbidden and allowed transitions, including forbidden transitions in diatomic molecular spectra; forbidden transitions in crystals; calculations of atomic line strengths; and measurements of atomic transition probabilities. The book also ponders on photoionization processes, photodetachment, and high temperature shock waves. The manuscript elaborates on electronic and ionic recombination, elastic scattering of electrons, and the motions of slow electrons in gases. The book also evaluates the theory of excitation and ionization by electron impact; measurement of collisional excitation and ionization cross sections; and spectral line broadening in plasmas. The selection is a dependable reference for readers interested in atomic and molecular processes.

  • Physics of Geomagnetic Phenomena

    International Geophysics Series, Vol. 1
    • 1st Edition
    • S. Matsushita + 1 more
    • English
    Physics of Geomagnetic phenomena, Volume I covers the significant advances in geomagnetism and the penetrations into the generation of geomagnetic field phenomena. This volume is composed of three chapters. Chapter I deals briefly with the discovery and developments in geomagnetism, followed by discussions on some fundamental topics of the field, including the aurora and geomagnetic storms. This chapter also considers the instruments, geomagnetic stations, and the correlations between geomagnetic indices. Chapter II describes the magnetic properties of minerals and various processes of acquisition of remanent magnetization. This chapter also provides palaeomagnetic data for the direction and intensity of the geomagnetic field in ancient times. Chapter III explores geomagnetic variations caused by solar flares and eclipses. This book will prove useful to physicists, students in upper atmospheric and space topics, and scientists in allied fields with a background in geomagnetism.

  • Atmosphere—Ocean Dynamics

    • 1st Edition
    • Adrian E. Gill
    • William L. Donn
    • English
    Atmosphere-Ocean Dynamics deals with a systematic and unified approach to the dynamics of the ocean and atmosphere. The book reviews the relationship of the ocean-atmosphere and how this system functions. The text explains this system through radiative equilibrium models; the book also considers the greenhouse effect, the effects of convection and of horizontal gradients, and the variability in radiative driving of the earth. Equations in the book show the properties of a material element, mass conservation, the balance of scalar quantity (such as salinity), and the mathematical behavior of the ocean and atmosphere. The book also addresses how the ocean-atmosphere system tends to adjust to equilibrium, both in the absence and presence of driving forces such as gravity. The text also explains the effect of the earth's rotation on the system, as well as the application of forced motions such as that produced by wind or temperature changes. The book explains tropical dynamics and the effects of variation of the Coriolis parameter with latitude. The text will be appreciated by meteorologists, environmentalists, students studying hydrology, and people working in general earth sciences.

  • The Upper Atmosphere

    Meteorology and Physics
    • 1st Edition
    • Richard A. Craig
    • J. Van Mieghem
    • English
    The Upper Atmosphere: Meteorology and Physics focuses on the study of the characteristics, movements, composition, and observations of the upper atmosphere. The book first offers information on the meteorological conditions in the lower stratosphere and the structure and circulation of the upper stratosphere and the mesosphere. Topics include balloon sounding systems, climatology of the lower stratosphere, disturbed circulation of the lower stratosphere, rocket measurements, and frequent measurements with balloons and meteorological rockets. The text then ponders on the sun's radiation and the upper atmosphere and composition of the stratosphere and mesosphere. The manuscript elaborates on the composition and structure of the thermosphere, including photochemical processes, diffusion, composition and structure measurements, and structure of the thermosphere. The text also ponders on radiative processes and heat transfer; atmospheric tides and winds in the lower thermosphere; and transport of properties in the upper atmosphere. The publication is a valuable source of information for readers interested in the meteorology and physics of the upper atmosphere.

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