Download or read book Hypersingular Integrals and Their Applications written by Stefan Samko and published by CRC Press. This book was released on 2001-10-25 with total page 382 pages. Available in PDF, EPUB and Kindle. Book excerpt: Hypersingular integrals arise as constructions inverse to potential-type operators and are realized by the methods of regularization and finite differences. This volume develops these approaches in a comprehensive treatment of hypersingular integrals and their applications. The author is a renowned expert on the topic. He explains the basics before building more sophisticated ideas, and his discussions include a description of hypersingular integrals as they relate to functional spaces. Hypersingular Integrals and Their Applications also presents recent results and applications that will prove valuable to graduate students and researchers working in mathematical analysis.
Download or read book Hypersingular Integral Equations and Their Applications written by I.K. Lifanov and published by CRC Press. This book was released on 2003-12-29 with total page 416 pages. Available in PDF, EPUB and Kindle. Book excerpt: A number of new methods for solving singular and hypersingular integral equations have emerged in recent years. This volume presents some of these new methods along with classical exact, approximate, and numerical methods. The authors explore the analysis of hypersingular integral equations based on the theory of pseudodifferential operators and co
Download or read book Advanced Ferroelectric And Piezoelectric Materials With Improved Properties And Their Applications written by Ivan A Parinov and published by World Scientific. This book was released on 2024-03-14 with total page 312 pages. Available in PDF, EPUB and Kindle. Book excerpt: Discover the latest advances in ferroelectric and piezoelectric material sciences with this comprehensive monograph, divided into six chapters, each offering unique insights into the field.Chapter 1 delves into the manufacture and study of new ceramic materials, focusing on complex oxides of various metals (Aurivillius phases). The authors explore layered bismuth titanates and niobates, known for their high Curie temperature, and discuss how varying their chemical composition can lead to significant changes in their electrophysical properties. Chapter 2 explores the fascinating world of ferroelectrics — dielectrics with spontaneous polarization. Mathematical models and approaches of fractional calculus are used to understand the process of polarization switching in these materials, shedding light on the fractality of electrical responses. In Chapter 3, readers gain valuable insights into the inhomogeneous polarization process of polycrystalline ferroelectrics, a crucial stage in creating piezoceramic samples for energy converters. The authors present a comprehensive mathematical model that allows the determination of various characteristics, including dielectric and piezoelectric hysteresis loops and the effect of attenuation processes.Chapter 4 focuses on state-of-the-art piezoelectric energy harvesting, discussing theoretical, experimental, and computer modelling approaches. The authors discuss piezoelectric generators (PEGs) of different types (cantilever, stack and axis) and nonlinear effects arising at their operation. Chapter 5 presents expanded test and finite element models for cantilever-type and axial-type PEGs with active elements. The studies cover various structural and electric schemes of the PEGs with proof mass, bimorph and cylindrical piezoelectric elements, and excitation loads. Finally, Chapter 6 reviews some results in the last five years, obtained in modelling the vibration of devices from piezoactive materials, including five important effects: piezoelectric, flexoelectric, pyroelectric, piezomagnetic and flexomagnetic.As a diverse addition to the literature, this book is a relevant resource for researchers, engineers, and students seeking to expand their knowledge of cutting-edge developments in this exciting field.
Download or read book Singular Integral Operators Factorization and Applications written by Albrecht Böttcher and published by Birkhäuser. This book was released on 2012-12-06 with total page 393 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains the proceedings of the International Workshop on Operator Theory and Applications held at the University of Algarve in Faro, Portugal, September 12-15, in the year 2000. The main topics of the conference were !> Factorization Theory; !> Factorization and Integrable Systems; !> Operator Theoretical Methods in Diffraction Theory; !> Algebraic Techniques in Operator Theory; !> Applications to Mathematical Physics and Related Topics. A total of 94 colleagues from 21 countries participated in the conference. The major part of participants came from Portugal (32), Germany (17), Israel (6), Mexico (6), the Netherlands (5), USA (4) and Austria (4). The others were from Ukraine, Venezuela (3 each), Spain, Sweden (2 each), Algeria, Australia, Belorussia, France, Georgia, Italy, Japan, Kuwait, Russia and Turkey (one of each country). It was the 12th meeting in the framework of the IWOTA conferences which started in 1981 on an initiative of Professors 1. Gohberg (Tel Aviv) and J. W. Helton (San Diego). Up to now, it was the largest conference in the field of Operator Theory in Portugal.
Download or read book Fractional Integrals and Potentials written by Boris Rubin and published by CRC Press. This book was released on 1996-06-24 with total page 428 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume presents recent developments in the fractional calculus of functions of one and several real variables, and shows the relation of this field to a variety of areas in pure and applied mathematics. Beyond some basic properties of fractional integrals in one and many dimensions, it contains a mathematical theory of certain important weakly singular integral equations of the first kind arising in mechanics, diffraction theory and other areas of mathematical physics. The author focuses on explicit inversion formulae that can be obtained by making use of the classical Marchaudís approach and its generalization, leading to wavelet type representations.
Download or read book Bessel Functions and Their Applications written by B G Korenev and published by CRC Press. This book was released on 2002-07-25 with total page 290 pages. Available in PDF, EPUB and Kindle. Book excerpt: Bessel functions are associated with a wide range of problems in important areas of mathematical physics. Bessel function theory is applied to problems of acoustics, radio physics, hydrodynamics, and atomic and nuclear physics. Bessel Functions and Their Applications consists of two parts. In Part One, the author presents a clear and rigorous intro
Download or read book Physics and Mechanics of New Materials and Their Applications written by Ivan A. Parinov and published by Springer Nature. This book was released on 2021-08-10 with total page 601 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents selected peer-reviewed contributions from the 2020 International Conference on “Physics and Mechanics of New Materials and Their Applications”, PHENMA 2020 (26–29 March 2021, Kitakyushu, Japan), focusing on processing techniques, physics, mechanics, and applications of advanced materials. The book describes a broad spectrum of promising nanostructures, crystal structures, materials, and composites with unique properties. It presents nanotechnological design approaches, environmental-friendly processing techniques, and physicochemical as well as mechanical studies of advanced materials. The selected contributions describe recent progress in computational materials science methods and algorithms (in particular, finite-element and finite-difference modelling) applied to various technological, mechanical, and physical problems. The presented results are important for ongoing efforts concerning the theory, modelling, and testing of advanced materials. Other results are devoted to promising devices with higher accuracy, increased longevity, and greater potential to work effectively under critical temperatures, high pressure, and in aggressive environments.
Download or read book Fractional Integrals Potentials and Radon Transforms written by Boris Rubin and published by CRC Press. This book was released on 2024-08-14 with total page 565 pages. Available in PDF, EPUB and Kindle. Book excerpt: Fractional Integrals, Potentials, and Radon Transforms, Second Edition presents recent developments in the fractional calculus of functions of one and several real variables, and shows the relation of this field to a variety of areas in pure and applied mathematics. In this thoroughly revised new edition, the book aims to explore how fractional integrals occur in the study of diverse Radon type transforms in integral geometry. Beyond some basic properties of fractional integrals in one and many dimensions, this book also contains a mathematical theory of certain important weakly singular integral equations of the first kind arising in mechanics, diffraction theory and other areas of mathematical physics. The author focuses on explicit inversion formulae that can be obtained by making use of the classical Marchaud’s approach and its generalization, leading to wavelet type representations. New to this Edition Two new chapters and a new appendix, related to Radon transforms and harmonic analysis of linear operators commuting with rotations and dilations have been added. Contains new exercises and bibliographical notes along with a thoroughly expanded list of references. This book is suitable for mathematical physicists and pure mathematicians researching in the area of integral equations, integral transforms, and related harmonic analysis.
Download or read book Equations with Involutive Operators written by Nikolai Karapetiants and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 444 pages. Available in PDF, EPUB and Kindle. Book excerpt: This self-contained title demonstrates an important interplay between abstract and concrete operator theory. Key ideas are developed in a step-by-step approach, beginning with required background and historical material, and culminating in the final chapters with state-of-the-art topics. Good examples, bibliography and index make this text a valuable classroom or reference resource.
Download or read book Inverse Spectral Problems for Linear Differential Operators and Their Applications written by V A Yurko and published by CRC Press. This book was released on 2000-01-18 with total page 268 pages. Available in PDF, EPUB and Kindle. Book excerpt: Aims to construct the inverse problem theory for ordinary non-self-adjoint differential operators of arbitary order on the half-line and on a finite interval. The book consists of two parts: in the first part the author presents a general inverse problem of recovering differential equations with integrable coefficients when the behaviour of the spe
Download or read book Differential and Integral Inequalities written by Dorin Andrica and published by Springer Nature. This book was released on 2019-11-14 with total page 848 pages. Available in PDF, EPUB and Kindle. Book excerpt: Theories, methods and problems in approximation theory and analytic inequalities with a focus on differential and integral inequalities are analyzed in this book. Fundamental and recent developments are presented on the inequalities of Abel, Agarwal, Beckenbach, Bessel, Cauchy–Hadamard, Chebychev, Markov, Euler’s constant, Grothendieck, Hilbert, Hardy, Carleman, Landau–Kolmogorov, Carlson, Bernstein–Mordell, Gronwall, Wirtinger, as well as inequalities of functions with their integrals and derivatives. Each inequality is discussed with proven results, examples and various applications. Graduate students and advanced research scientists in mathematical analysis will find this reference essential to their understanding of differential and integral inequalities. Engineers, economists, and physicists will find the highly applicable inequalities practical and useful to their research.
Download or read book Introduction to Radon Transforms written by Boris Rubin and published by Cambridge University Press. This book was released on 2015-11-12 with total page 595 pages. Available in PDF, EPUB and Kindle. Book excerpt: A comprehensive introduction to basic operators of integral geometry and the relevant harmonic analysis for students and researchers.
Download or read book Advances in Harmonic Analysis and Operator Theory written by Alexandre Almeida and published by Springer Science & Business Media. This book was released on 2013-01-31 with total page 389 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume is dedicated to Professor Stefan Samko on the occasion of his seventieth birthday. The contributions display the range of his scientific interests in harmonic analysis and operator theory. Particular attention is paid to fractional integrals and derivatives, singular, hypersingular and potential operators in variable exponent spaces, pseudodifferential operators in various modern function and distribution spaces, as well as related applications, to mention but a few. Most contributions were firstly presented in two conferences at Lisbon and Aveiro, Portugal, in June‒July 2011.
Download or read book Thirteen Papers in Analysis written by R. R. Suncheleev and published by American Mathematical Soc.. This book was released on 1986 with total page 396 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Differential Equations and Function Spaces written by Sergeĭ Lʹvovich Sobolev and published by American Mathematical Soc.. This book was released on 1992 with total page 270 pages. Available in PDF, EPUB and Kindle. Book excerpt: This commemorative volume honours the memory of S. L. Sobolev by presenting eighteen papers reflecting the area of Sobolev's main contributions: applications of functional analysis to differential equations. The papers examine various problems in the theory of partial differential equations (linear and non-linear) and the theory of differentiable functions of several real variables. Applications to problems of mathematical physics and approximate methods of conformal mapping are also treated.
Download or read book Geometric Analysis and Integral Geometry written by Eric Todd Quinto and published by American Mathematical Soc.. This book was released on 2013 with total page 299 pages. Available in PDF, EPUB and Kindle. Book excerpt: Provides an historical overview of several decades in integral geometry and geometric analysis as well as recent advances in these fields and closely related areas. It contains several articles focusing on the mathematical work of Sigurdur Helgason, including an overview of his research by Gestur Olafsson and Robert Stanton.
Download or read book Integral Operators in Non Standard Function Spaces written by Vakhtang Kokilashvili and published by Birkhäuser. This book was released on 2016-05-11 with total page 585 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book, the result of the authors' long and fruitful collaboration, focuses on integral operators in new, non-standard function spaces and presents a systematic study of the boundedness and compactness properties of basic, harmonic analysis integral operators in the following function spaces, among others: variable exponent Lebesgue and amalgam spaces, variable Hölder spaces, variable exponent Campanato, Morrey and Herz spaces, Iwaniec-Sbordone (grand Lebesgue) spaces, grand variable exponent Lebesgue spaces unifying the two spaces mentioned above, grand Morrey spaces, generalized grand Morrey spaces, and weighted analogues of some of them. The results obtained are widely applied to non-linear PDEs, singular integrals and PDO theory. One of the book's most distinctive features is that the majority of the statements proved here are in the form of criteria. The book is intended for a broad audience, ranging from researchers in the area to experts in applied mathematics and prospective students.
