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Uniform Stationary Phase Method
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Book Synopsis Uniform Stationary Phase Method by : Vladimir Andreevich Borovikov
Download or read book Uniform Stationary Phase Method written by Vladimir Andreevich Borovikov and published by . This book was released on 1994 with total page 252 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph expounds an original asymptotic stationary phase method for the evaluation of integrals of rapidly oscillating functions, which should be beneficial in wave radiation, propagation and diffraction research. It is self-contained, with theory, formulae and tabulated co-efficients.
Book Synopsis Nanomaterials in Chromatography by : Chaudhery Mustansar Hussain
Download or read book Nanomaterials in Chromatography written by Chaudhery Mustansar Hussain and published by Elsevier. This book was released on 2018-06-08 with total page 554 pages. Available in PDF, EPUB and Kindle. Book excerpt: Nanomaterials in Chromatography: Current Trends in Chromatographic Research Technology and Techniques provides recent advancements in the wide variety of chromatographic techniques applied to nanotechnology. As nanomaterials’ unique properties can improve detection sensitivity and miniaturize the devices used in analytical procedures, they can substantially affect the evaluation and analysis ability of scientists and researchers and foster exciting developments in separation science. The book includes chapters on such crucial topics as the use of nanomaterials in sample preparation and the legalization of nanomaterials, along with a section on reducing the cost of the analysis process, both in terms of chemicals and time consumption. Presents several techniques for nanomaterials in chromatography, including well-known materials like carbon nanomaterials and functionalized nanomaterials Includes suggested readings at the end of each chapter for those who need further information or specific details, from standard handbooks, to journal articles Covers not only applications of nanomaterials in chromatography, but also their environmental impact in terms of toxicity and economic effects
Book Synopsis Electromagnetic Radiation, Scattering, and Diffraction by : Prabhakar H. Pathak
Download or read book Electromagnetic Radiation, Scattering, and Diffraction written by Prabhakar H. Pathak and published by John Wiley & Sons. This book was released on 2021-12-21 with total page 1156 pages. Available in PDF, EPUB and Kindle. Book excerpt: Electromagnetic Radiation, Scattering, and Diffraction Discover a graduate-level text for students specializing in electromagnetic wave radiation, scattering, and diffraction for engineering applications In Electromagnetic Radiation, Scattering and Diffraction, distinguished authors Drs. Prabhakar H. Pathak and Robert J. Burkholder deliver a thorough exploration of the behavior of electromagnetic fields in radiation, scattering, and guided wave environments. The book tackles its subject from first principles and includes coverage of low and high frequencies. It stresses physical interpretations of the electromagnetic wave phenomena along with their underlying mathematics. The authors emphasize fundamental principles and provide numerous examples to illustrate the concepts contained within. Students with a limited undergraduate electromagnetic background will rapidly and systematically advance their understanding of electromagnetic wave theory until they can complete useful and important graduate-level work on electromagnetic wave problems. Electromagnetic Radiation, Scattering and Diffraction also serves as a practical companion for students trying to simulate problems with commercial EM software and trying to better interpret their results. Readers will also benefit from the breadth and depth of topics, such as: Basic equations governing all electromagnetic (EM) phenomena at macroscopic scales are presented systematically. Stationary and relativistic moving boundary conditions are developed. Waves in planar multilayered isotropic and anisotropic media are analyzed. EM theorems are introduced and applied to a variety of useful antenna problems. Modal techniques are presented for analyzing guided wave and periodic structures. Potential theory and Green's function methods are developed to treat interior and exterior EM problems. Asymptotic High Frequency methods are developed for evaluating radiation Integrals to extract ray fields. Edge and surface diffracted ray fields, as well as surface, leaky and lateral wave fields are obtained. A collective ray analysis for finite conformal antenna phased arrays is developed. EM beams are introduced and provide useful basis functions. Integral equations and their numerical solutions via the method of moments are developed. The fast multipole method is presented. Low frequency breakdown is studied. Characteristic modes are discussed. Perfect for graduate students studying electromagnetic theory, Electromagnetic Radiation, Scattering, and Diffraction is an invaluable resource for professional electromagnetic engineers and researchers working in this area.
Book Synopsis The Selected Works of Roderick S C Wong by : Dan Dai
Download or read book The Selected Works of Roderick S C Wong written by Dan Dai and published by World Scientific. This book was released on 2015-08-06 with total page 1557 pages. Available in PDF, EPUB and Kindle. Book excerpt: This collection, in three volumes, presents the scientific achievements of Roderick S C Wong, spanning 45 years of his career. It provides a comprehensive overview of the author's work which includes significant discoveries and pioneering contributions, such as his deep analysis on asymptotic approximations of integrals and uniform asymptotic expansions of orthogonal polynomials and special functions; his important contributions to perturbation methods for ordinary differential equations and difference equations; and his advocation of the Riemann–Hilbert approach for global asymptotics of orthogonal polynomials. The book is an essential source of reference for mathematicians, statisticians, engineers, and physicists. It is also a suitable reading for graduate students and interested senior year undergraduate students. Contents:Volume 1:The Asymptotic Behaviour of μ(z, β,α)A Generalization of Watson's LemmaLinear Equations in Infinite MatricesAsymptotic Solutions of Linear Volterra Integral Equations with Singular KernelsOn Infinite Systems of Linear Differential EquationsError Bounds for Asymptotic Expansions of HankelExplicit Error Terms for Asymptotic Expansions of StieltjesExplicit Error Terms for Asymptotic Expansions of MellinAsymptotic Expansion of Multiple Fourier TransformsExact Remainders for Asymptotic Expansions of FractionalAsymptotic Expansion of the Hilbert TransformError Bounds for Asymptotic Expansions of IntegralsDistributional Derivation of an Asymptotic ExpansionOn a Method of Asymptotic Evaluation of Multiple IntegralsAsymptotic Expansion of the Lebesgue Constants Associated with Polynomial InterpolationQuadrature Formulas for Oscillatory Integral TransformsGeneralized Mellin Convolutions and Their Asymptotic Expansions,A Uniform Asymptotic Expansion of the Jacobi Polynomials with Error BoundsAsymptotic Expansion of a Multiple IntegralAsymptotic Expansion of a Double Integral with a Curve of Stationary PointsSzegö's Conjecture on Lebesgue Constants for Legendre SeriesUniform Asymptotic Expansions of Laguerre PolynomialsTransformation to Canonical Form for Uniform Asymptotic ExpansionsMultidimensional Stationary Phase Approximation: Boundary Stationary PointTwo-Dimensional Stationary Phase Approximation: Stationary Point at a CornerAsymptotic Expansions for Second-Order Linear Difference EquationsAsymptotic Expansions for Second-Order Linear Difference Equations, IIAsymptotic Behaviour of the Fundamental Solution to ∂u/∂t = –(–Δ)muA Bernstein-Type Inequality for the Jacobi PolynomialError Bounds for Asymptotic Expansions of Laplace ConvolutionsVolume 2:Asymptotic Behavior of the Pollaczek Polynomials and Their ZerosJustification of the Stationary Phase Approximation in Time-Domain AsymptoticsAsymptotic Expansions of the Generalized Bessel PolynomialsUniform Asymptotic Expansions for Meixner Polynomials"Best Possible" Upper and Lower Bounds for the Zeros of the Bessel Function Jν(x)Justification of a Perturbation Approximation of the Klein–Gordon EquationSmoothing of Stokes's Discontinuity for the Generalized Bessel Function. IIUniform Asymptotic Expansions of a Double Integral: Coalescence of Two Stationary PointsUniform Asymptotic Formula for Orthogonal Polynomials with Exponential WeightOn the Asymptotics of the Meixner–Pollaczek Polynomials and Their ZerosGevrey Asymptotics and Stieltjes Transforms of Algebraically Decaying FunctionsExponential Asymptotics of the Mittag–Leffler FunctionOn the Ackerberg–O'Malley ResonanceAsymptotic Expansions for Second-Order Linear Difference Equations with a Turning PointOn a Two-Point Boundary-Value Problem with Spurious SolutionsShooting Method for Nonlinear Singularly Perturbed Boundary-Value ProblemsVolume 3:Asymptotic Expansion of the Krawtchouk Polynomials and Their ZerosOn a Uniform Treatment of Darboux's MethodLinear Difference Equations with Transition PointsUniform Asymptotics for Jacobi Polynomials with Varying Large Negative Parameters — A Riemann–Hilbert ApproachUniform Asymptotics of the Stieltjes–Wigert Polynomials via the Riemann–Hilbert ApproachA Singularly Perturbed Boundary-Value Problem Arising in Phase TransitionsOn the Number of Solutions to Carrier's ProblemAsymptotic Expansions for Riemann–Hilbert ProblemsOn the Connection Formulas of the Third Painlevé TranscendentHyperasymptotic Expansions of the Modified Bessel Function of the Third Kind of Purely Imaginary OrderGlobal Asymptotics for Polynomials Orthogonal with Exponential Quartic WeightThe Riemann–Hilbert Approach to Global Asymptotics of Discrete Orthogonal Polynomials with Infinite NodesGlobal Asymptotics of the Meixner PolynomialsAsymptotics of Orthogonal Polynomials via Recurrence RelationsUniform Asymptotic Expansions for the Discrete Chebyshev PolynomialsGlobal Asymptotics of the Hahn PolynomialsGlobal Asymptotics of Stieltjes–Wigert Polynomials Readership: Undergraduates, gradudates and researchers in the areas of asymptotic approximations of integrals, singular perturbation theory, difference equations and Riemann–Hilbert approach. Key Features:This book provides a broader viewpoint of asymptoticsIt contains about half of the papers that Roderick Wong has written on asymptoticsIt demonstrates how analysis is used to make some formal results mathematically rigorousThis collection presents the scientific achievements of the authorKeywords:Asymptotic Analysis;Perturbation Method;Special Functions;Orthogonal Polynomials;Integral Transforms;Integral Equations;Ordinary Differential Equations;Difference Equations;Riemann–Hilbert Problem
Book Synopsis Physical Methods in Modern Chemical Analysis V2 by : Theodore Kuwana
Download or read book Physical Methods in Modern Chemical Analysis V2 written by Theodore Kuwana and published by Elsevier. This book was released on 2012-12-02 with total page 424 pages. Available in PDF, EPUB and Kindle. Book excerpt: Physical Methods in Modern Chemical Analysis, Volume 2 covers the fundamental principles, the instrumentation or necessary equipment, and applications of selected physical methods. This volume contains five chapters, and deals first with the theory, instrumentation, column features, and applications of high-performance liquid chromatography. The next two chapters survey the principles, experimental aspects, procedures, and specific applications of X-ray photoelectron spectroscopy and X-ray diffraction methods. A chapter discusses the technical and theoretical aspects of ion cyclotron resonance, with a special emphasis on its application in gas phase ion and neutral compounds analysis. The last chapter explores the apparatus and experimental procedures in refractive index measurements. This book will be of value to analytical chemists and analytical chemistry researchers.
Book Synopsis Differential Equations & Asymptotic Theory in Mathematical Physics by : Zhen Hua
Download or read book Differential Equations & Asymptotic Theory in Mathematical Physics written by Zhen Hua and published by World Scientific. This book was released on 2004 with total page 390 pages. Available in PDF, EPUB and Kindle. Book excerpt: This lecture notes volume encompasses four indispensable mini courses delivered at Wuhan University with each course containing the material from five one-hour lectures. Readers are brought up to date with exciting recent developments in the areas of asymptotic analysis, singular perturbations, orthogonal polynomials, and the application of Gevrey asymptotic expansion to holomorphic dynamical systems. The book also features important invited papers presented at the conference. Leading experts in the field cover a diverse range of topics from partial differential equations arising in cancer biology to transonic shock waves. The proceedings have been selected for coverage in: . OCo Index to Scientific & Technical Proceedings- (ISTP- / ISI Proceedings). OCo Index to Scientific & Technical Proceedings (ISTP CDROM version / ISI Proceedings). OCo CC Proceedings OCo Engineering & Physical Sciences."
Book Synopsis Airy Functions and Applications to Physics (2nd Edition) by :
Download or read book Airy Functions and Applications to Physics (2nd Edition) written by and published by World Scientific. This book was released on 2010 with total page 213 pages. Available in PDF, EPUB and Kindle. Book excerpt: "Addressed mainly to physicist and chemical physicist, this textbook is the result of a broad compilation of current knowledge on analytical properties of Airy functions. In particular, the calculus implying the Airy functions is developed with care. In the latter chapters, examples are given to succinctly illustrate the use of Airy functions in classical and quantum physics. The physicist, for instance in fluid mechanics, can find what he is looking for, in the references for works of molecular physics or in physics of surfaces, and vice versa."--Publisher's website
Download or read book Advances in Applied Mechanics written by and published by Academic Press. This book was released on 2017-10-27 with total page 120 pages. Available in PDF, EPUB and Kindle. Book excerpt: Advances in Applied Mechanics, Volume 50, draws together recent, significant advances in various topics in applied mechanics. Published since 1948, the book aims to provide authoritative review articles on topics in the mechanical sciences. While the book is ideal for scientists and engineers working in various branches of mechanics, it is also beneficial to professionals who use the results of investigations in mechanics in various applications, such as aerospace, chemical, civil, environmental, mechanical and nuclear engineering. Includes contributions from world-leading experts that are acquired by invitation only Beneficial to scientists, engineers and professionals who use the results of investigations in mechanics in various applications, such as aerospace, chemical, civil, environmental, mechanical and nuclear engineering Covers not only traditional topics, but also important emerging fields
Book Synopsis Asymptotic Methods For Integrals by : Nico M Temme
Download or read book Asymptotic Methods For Integrals written by Nico M Temme and published by World Scientific. This book was released on 2014-10-31 with total page 628 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book gives introductory chapters on the classical basic and standard methods for asymptotic analysis, such as Watson's lemma, Laplace's method, the saddle point and steepest descent methods, stationary phase and Darboux's method. The methods, explained in great detail, will obtain asymptotic approximations of the well-known special functions of mathematical physics and probability theory. After these introductory chapters, the methods of uniform asymptotic analysis are described in which several parameters have influence on typical phenomena: turning points and transition points, coinciding saddle and singularities. In all these examples, the special functions are indicated that describe the peculiar behavior of the integrals.The text extensively covers the classical methods with an emphasis on how to obtain expansions, and how to use the results for numerical methods, in particular for approximating special functions. In this way, we work with a computational mind: how can we use certain expansions in numerical analysis and in computer programs, how can we compute coefficients, and so on.
Book Synopsis Methods of Noncommutative Analysis by : Vladimir E. Nazaikinskii
Download or read book Methods of Noncommutative Analysis written by Vladimir E. Nazaikinskii and published by Walter de Gruyter. This book was released on 2011-06-24 with total page 385 pages. Available in PDF, EPUB and Kindle. Book excerpt: The series is devoted to the publication of monographs and high-level textbooks in mathematics, mathematical methods and their applications. Apart from covering important areas of current interest, a major aim is to make topics of an interdisciplinary nature accessible to the non-specialist. The works in this series are addressed to advanced students and researchers in mathematics and theoretical physics. In addition, it can serve as a guide for lectures and seminars on a graduate level. The series de Gruyter Studies in Mathematics was founded ca. 35 years ago by the late Professor Heinz Bauer and Professor Peter Gabriel with the aim to establish a series of monographs and textbooks of high standard, written by scholars with an international reputation presenting current fields of research in pure and applied mathematics. While the editorial board of the Studies has changed with the years, the aspirations of the Studies are unchanged. In times of rapid growth of mathematical knowledge carefully written monographs and textbooks written by experts are needed more than ever, not least to pave the way for the next generation of mathematicians. In this sense the editorial board and the publisher of the Studies are devoted to continue the Studies as a service to the mathematical community. Please submit any book proposals to Niels Jacob. Titles in planning include Mark M. Meerschaert, Alla Sikorskii, and Mohsen Zayernouri, Stochastic Models for Fractional Calculus, second edition (2018) Flavia Smarazzo and Alberto Tesei, Measure Theory: Radon Measures, Young Measures and Applications to Parabolic Problems (2019) Elena Cordero and Luigi Rodino, Time-Frequency Analysis of Operators (2019) Kezheng Li, Group Schemes and Their Actions (2019; together with Tsinghua University Press) Kai Liu, Ilpo Laine, and Lianzhong Yang, Complex Differential-Difference Equations (2021) Rajendra Vasant Gurjar, Kayo Masuda, and Masayoshi Miyanishi, Affine Space Fibrations (2022)
Book Synopsis Parabolic Equation Methods for Electromagnetic Wave Propagation by : Mireille Levy
Download or read book Parabolic Equation Methods for Electromagnetic Wave Propagation written by Mireille Levy and published by IET. This book was released on 2000 with total page 360 pages. Available in PDF, EPUB and Kindle. Book excerpt: Provides scientists and engineers with a tool for accurate assessment of diffraction and ducting on radio and radar systems. The author gives the mathematical background to parabolic equations modeling and describes simple parabolic equation algorithms before progressing to more advanced topics such as domain truncation, the treatment of impedance boundaries, and the implementation of very fast hybrid methods combining ray-tracing and parabolic equation techniques. The last three chapters are devoted to scattering problems, with application to propagation in urban environments and to radar-cross- section computation. Annotation copyrighted by Book News, Inc., Portland, OR
Book Synopsis Fluid Transport in Nanoporous Materials by : Wm. Curtis Conner
Download or read book Fluid Transport in Nanoporous Materials written by Wm. Curtis Conner and published by Springer Science & Business Media. This book was released on 2006-03-10 with total page 708 pages. Available in PDF, EPUB and Kindle. Book excerpt: This NATO ASI involved teachings and perspectives of the state-of-the-art in experimental and theoretical understandings of transport in nanoporous solids. This workshop brought together the top scientists and engineers in each area to discuss the similarities and differences in each technique and theory. The lectures truly bridge the gaps between these related areas and approaches. The applications in future separations, catalysis, the environment and energy needs are obvious. The solids comprised the newly developing molecular sieves, biological systems and polymeric solids. Transport in single particles, in membranes and in commercial applications were reviewed and analyzed, placing each in context. Techniques such as uptake, Chromatographic, Frequency Response, NMR, Neutron Scattering and Infrared spectroscopies are discussed for mixtures as well as for single components. Theoretical approaches such as Density Functional Theory, Statistical Mechanics, Molecular Dynamics and Maxwell-Stefan Theory are employed to analyze the diffusional transport in confined environments, spanning from sub-nanometers to centimetre scales. In all cases the theories are related to the experiments. These lectures present a uniquq opportunity to learn the various theoretical and experimental approaches to analyze and understand transport in nanoporous materials.
Book Synopsis Electromagnetic Boundary Problems by : Edward F. Kuester
Download or read book Electromagnetic Boundary Problems written by Edward F. Kuester and published by CRC Press. This book was released on 2015-10-28 with total page 266 pages. Available in PDF, EPUB and Kindle. Book excerpt: Electromagnetic Boundary Problems introduces the formulation and solution of Maxwell's equations describing electromagnetism. Based on a one-semester graduate-level course taught by the authors, the text covers material parameters, equivalence principles, field and source (stream) potentials, and uniqueness, as well as:Provides analytical solutions
Book Synopsis Guiding, Diffraction, and Confinement of Optical Radiation by : Salvatore Solimeno
Download or read book Guiding, Diffraction, and Confinement of Optical Radiation written by Salvatore Solimeno and published by Elsevier. This book was released on 2012-12-02 with total page 635 pages. Available in PDF, EPUB and Kindle. Book excerpt: Guiding, Diffraction, and Confinement of Optical Radiation presents a wide array of research studies on optics and electromagnetism. This book is organized into eight chapters that cover the problems related to optical radiation propagation and confinement. Chapter I examines the general features of electromagnetic propagation and introduces the basic concepts pertaining to the description of the electromagnetic field and its interaction with matter. Chapter II is devoted to asymptotic methods of solution of the wave equation, with particular emphasis on the asymptotic representation of the field in the form of the Luneburg-Kline series. This chapter also looks into a number of optical systems characterized by different refractive index distributions relying on the eikonal equation. Chapter III deals with stratified media, such as the multilayered thin films, metallic and dielectric reflectors, and interference filters. Chapters IV and V discuss the problem of propagation and diffraction integrals. Chapter VI describes the scattering from obstacles and the metallic and dielectric gratings. Chapters VII considers the passive and active resonators employed in connection with laser sources for producing a confinement near the axis of an optical cavity and Fabry-Perot interferometers and mainly relies on the use of diffraction theory. Chapter VIII presents the analytic approach to the study of transverse confinement near the axis of a dielectric waveguide hinges on the introduction of modal solutions of the wave equation. This book will be of value to quantum electronics engineers, physicists, researchers, and optics and electromagnetism graduate students.
Book Synopsis Quantum Dots: Fundamentals, Applications, and Frontiers by : Bruce A. Joyce
Download or read book Quantum Dots: Fundamentals, Applications, and Frontiers written by Bruce A. Joyce and published by Springer Science & Business Media. This book was released on 2006-03-30 with total page 401 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains papers delivered at a NATO Advanced Research Workshop and provides a broad introduction to all major aspects of quantum dot structures. Such structures have been produced for studies of basic physical phenomena, for device fabrication and, on a more speculative level, have been suggested as components of a solid-state realization of a quantum computer. The book is structured so that the reader is introduced to the methods used to produce and control quantum dots, followed by discussions of their structural, electronic, and optical properties. It concludes with examples of how their optical properties can be used in practical devices, including lasers and light-emitting diodes operating at the commercially important wavelengths of 1.3 Am and 1.55 Am."
Book Synopsis Instrumental Thin-Layer Chromatography by : Colin Poole
Download or read book Instrumental Thin-Layer Chromatography written by Colin Poole and published by Elsevier. This book was released on 2014-09-22 with total page 665 pages. Available in PDF, EPUB and Kindle. Book excerpt: Instrumental Thin-Layer Chromatography delivers comprehensive coverage of this separation tool with particular emphasis on how this tool can be used in advanced laboratories and integrated into problem-solving scenarios. Significant improvements in instrumentation have outpaced the development of information resources that describe the latest state-of-the-art and demonstrate the full capabilities of TLC. This book provides a contemporary picture of the fundamentals and practical applications of TLC at a level suitable for the needs of professional scientists with interests in project management where TLC is a common tool. Compact, highly focused chapters convey essential information that defines modern TLC and how it can be effectively implemented in most areas of laboratory science. Numerous figures and tables provide access to material not normally found in a single source yet are required by working scientists. Contributions written by recognized authoritative and visionary experts Focuses on state-of-the-art instrumental thin-layer chromatography and advanced applications across many areas Provides guidance on the analysis of complex, dirty mixtures of compounds Offers a cost-effective analytic technique for laboratories working under strict budgets
Book Synopsis IUTAM Symposium on Asymptotics, Singularities and Homogenisation in Problems of Mechanics by : A.B. Movchan
Download or read book IUTAM Symposium on Asymptotics, Singularities and Homogenisation in Problems of Mechanics written by A.B. Movchan and published by Springer. This book was released on 2006-05-09 with total page 624 pages. Available in PDF, EPUB and Kindle. Book excerpt: Proceedings of the IUTAM Symposium held in Liverpool, UK, 8-11 July 2002
