Download or read book An Exponential Function Approach To Parabolic Equations written by Chin-yuan Lin and published by World Scientific. This book was released on 2014-08-08 with total page 174 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume is on initial-boundary value problems for parabolic partial differential equations of second order. It rewrites the problems as abstract Cauchy problems or evolution equations, and then solves them by the technique of elementary difference equations. Because of this, the volume assumes less background and provides an easy approach for readers to understand.
Download or read book Bloch type Periodic Functions Theory And Applications To Evolution Equations written by Yong-kui Chang and published by World Scientific. This book was released on 2022-07-13 with total page 209 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph aims to provide for the first time a unified and homogenous presentation of the recent works on the theory of Bloch periodic functions, their generalizations, and their applications to evolution equations. It is useful for graduate students and beginning researchers as seminar topics, graduate courses and reference text in pure and applied mathematics, physics, and engineering.
Download or read book Blow up Theories for Semilinear Parabolic Equations written by Bei Hu and published by Springer Science & Business Media. This book was released on 2011-03-23 with total page 137 pages. Available in PDF, EPUB and Kindle. Book excerpt: There is an enormous amount of work in the literature about the blow-up behavior of evolution equations. It is our intention to introduce the theory by emphasizing the methods while seeking to avoid massive technical computations. To reach this goal, we use the simplest equation to illustrate the methods; these methods very often apply to more general equations.
Download or read book Differential Sheaves And Connections A Natural Approach To Physical Geometry written by Anastasios Mallios and published by World Scientific. This book was released on 2015-09-17 with total page 302 pages. Available in PDF, EPUB and Kindle. Book excerpt: This unique book provides a self-contained conceptual and technical introduction to the theory of differential sheaves. This serves both the newcomer and the experienced researcher in undertaking a background-independent, natural and relational approach to 'physical geometry'. In this manner, this book is situated at the crossroads between the foundations of mathematical analysis with a view toward differential geometry and the foundations of theoretical physics with a view toward quantum mechanics and quantum gravity. The unifying thread is provided by the theory of adjoint functors in category theory and the elucidation of the concepts of sheaf theory and homological algebra in relation to the description and analysis of dynamically constituted physical geometric spectrums.
Download or read book Functional Equations And Inequalities Solutions And Stability Results written by John Michael Rassias and published by World Scientific Publishing Company. This book was released on 2017-03-20 with total page 397 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume covers the topic in functional equations in a broad sense and is written by authors who are in this field for the past 50 years. It contains the basic notions of functional equations, the methods of solving functional equations, the growth of functional equations in the last four decades and an extensive reference list on fundamental research papers that investigate the stability results of different types of functional equations and functional inequalities. This volume starts by taking the reader from the fundamental ideas to higher levels of results that appear in recent research papers. Its step-by-step expositions are easy for the reader to understand and admire the elegant results and findings on the stability of functional equations.
Download or read book Introduction To Matrix Theory With Applications In Economics And Engineering Second Edition written by Ferenc Szidarovszky and published by World Scientific. This book was released on 2022-12-19 with total page 469 pages. Available in PDF, EPUB and Kindle. Book excerpt: Linear algebra and matrix theory are among the most important and most frequently applied branches of mathematics. They are especially important in solving engineering and economic models, where either the model is assumed linear, or the nonlinear model is approximated by a linear model, and the resulting linear model is examined.This book is mainly a textbook, that covers a one semester upper division course or a two semester lower division course on the subject.The second edition will be an extended and modernized version of the first edition. We added some new theoretical topics and some new applications from fields other than economics. We also added more difficult exercises at the end of each chapter which require deep understanding of the theoretical issues. We also modernized some proofs in the theoretical discussions which give better overview of the study material. In preparing the manuscript we also corrected the typos and errors, so the second edition will be a corrected, extended and modernized new version of the first edition.
Download or read book Discrete Approximation Theory written by George A Anastassiou and published by World Scientific. This book was released on 2016-09-29 with total page 347 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this monograph, we present the authors' recent work of the last seven years in Approximation Theory. Chapters are self-contained and can be read independently and advanced courses can be taught out of this book. Here our generalized discrete singular operators are of the following types: Picard, Gauss-Weierstrass and Poisson-Cauchy operators. We treat both the unitary and non-unitary, univariate and multivariate cases of these operators, which are not necessarily positive operators. The book's results are expected to find applications in many areas of pure and applied mathematics, and statistics. As such, it is suitable for researchers, graduate students, and seminars of related subjects, and serves well as an invaluable resource for all science libraries.
Download or read book Stochastic Models With Applications To Genetics Cancers Aids And Other Biomedical Systems Second Edition written by Wai-yuan Tan and published by World Scientific. This book was released on 2015-10-28 with total page 523 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents a systematic treatment of Markov chains, diffusion processes and state space models, as well as alternative approaches to Markov chains through stochastic difference equations and stochastic differential equations. It illustrates how these processes and approaches are applied to many problems in genetics, carcinogenesis, AIDS epidemiology and other biomedical systems.One feature of the book is that it describes the basic MCMC (Markov chain and Monte Carlo) procedures and illustrates how to use the Gibbs sampling method and the multilevel Gibbs sampling method to solve many problems in genetics, carcinogenesis, AIDS and other biomedical systems.As another feature, the book develops many state space models for many genetic problems, carcinogenesis, AIDS epidemiology and HIV pathogenesis. It shows in detail how to use the multilevel Gibbs sampling method to estimate (or predict) simultaneously the state variables and the unknown parameters in cancer chemotherapy, carcinogenesis, AIDS epidemiology and HIV pathogenesis. As a matter of fact, this book is the first to develop several state space models for many genetic problems, carcinogenesis and other biomedical problems.To emphasize special applications to medical problems, in this new edition the book has added a new chapter to illustrate how to develop biologically-supported stochastic models and state space models of carcinogenesis in human beings. Specific examples include hidden Markov models and state space models for human colon cancer, human liver cancer and some human pediatric cancers such as retinoblastoma and hepatoblastoma. The book also gives examples to illustrate how to develop procedures to assess cancer risk of environmental agents through initiation-promotion protocols.
Download or read book Frontiers In Approximation Theory written by George A Anastassiou and published by World Scientific. This book was released on 2015-06-23 with total page 229 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph presents the author's work of the last five years in approximation theory. The chapters are self-contained and can be read independently. Readers will find the topics covered are diverse and advanced courses can be taught out of this book.The first part of the book is dedicated to fractional monotone approximation theory introduced for the first time by the author, taking the related ordinary theory of usual differentiation at the fractional differentiation level with polynomials and splines as approximators. The second part deals with the approximation by discrete singular operators of the Favard style, for example, of the Picard and Gauss-Weierstrass types. Then, it continues in a very detailed and extensive chapter on approximation by interpolating operators induced by neural networks, a connection to computer science. This book ends with the approximation theory and functional analysis on time scales, a very modern topic, detailing all the pros and cons of this method.The results in this book are expected to find applications in many areas of pure and applied mathematics. So far, very little is written about fractional approximation theory which is at its infancy. As such, it is suitable for researchers, graduate students, and performing seminars as well as an invaluable resource for all science libraries.
Download or read book Frontiers In Time Scales And Inequalities written by George A Anastassiou and published by World Scientific. This book was released on 2015-08-06 with total page 289 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph contains the author's work of the last four years in discrete and fractional analysis. It introduces the right delta and right nabla fractional calculus on time scales and continues with the right delta and right nabla discrete fractional calculus in the Caputo sense. Then, it shows representation formulae of functions on time scales and presents Ostrowski type inequalities, Landau type inequalities, Grüss type and comparison of means inequalities, all these over time scales. The volume continues with integral operator inequalities and their multivariate vectorial versions using convexity of functions, again all these over time scales. It follows the Grüss and Ostrowski type inequalities involving s-convexity of functions; and also examines the general case when several functions are involved. Then, it presents the general fractional Hermite-Hadamard type inequalities using m-convexity and (s, m)-convexity. Finally, it introduces the reduction method in fractional calculus and its connection to fractional Ostrowski type inequalities is studied.This book's results are expected to find applications in many areas of pure and applied mathematics, especially in difference equations and fractional differential equations. The chapters are self-contained and can be read independently, and advanced courses can be taught out of it. It is suitable for researchers, graduate students, seminars of the above subjects, and serves well as an invaluable resource for all science libraries.
Download or read book Elliptic Parabolic Equations written by Zhuoqun Wu and published by World Scientific. This book was released on 2006 with total page 428 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides an introduction to elliptic and parabolic equations. While there are numerous monographs focusing separately on each kind of equations, there are very few books treating these two kinds of equations in combination. This book presents the related basic theories and methods to enable readers to appreciate the commonalities between these two kinds of equations as well as contrast the similarities and differences between them.
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
Download or read book Finite Difference Methods for Ordinary and Partial Differential Equations written by Randall J. LeVeque and published by SIAM. This book was released on 2007-09-06 with total page 342 pages. Available in PDF, EPUB and Kindle. Book excerpt: Introductory textbook from which students can approach more advance topics relating to finite difference methods.
Download or read book Ultrasonics International 87 written by Sam Stuart and published by Elsevier. This book was released on 2013-09-17 with total page 974 pages. Available in PDF, EPUB and Kindle. Book excerpt: Ultrasonics International 87 contains the Proceedings of the Ultrasonics International Conference and Exhibition held at London, United Kingdom on July 1987. The conference discussed and reviewed some of the developments in the field of ultrasonics. The compendium consists of over 150 contributed papers, four invited papers and three plenary papers. Topics discussed include generation of unipolar ultrasonic pulses by signal processing; scattering of longitudinal waves by partially closed slots; piezoelectric materials for ultrasonic transducers; and measuring turbulent flow characteristics using a multi- dimensional ultrasonic probe. Fiber optic sensors, medical imaging and inverse methods, and laser generation of ultrasound are covered as well. Physicians, technicians, researchers, and physical scientists will find the book insightful.
Download or read book Mathematical Analysis and Its Applications written by S. M. Mazhar and published by Elsevier. This book was released on 2014-05-17 with total page 443 pages. Available in PDF, EPUB and Kindle. Book excerpt: Mathematical Analysis and its Applications covers the proceedings of the International Conference on Mathematical Analysis and its Applications. The book presents studies that discuss several mathematical analysis methods and their respective applications. The text presents 38 papers that discuss topics, such as approximation of continuous functions by ultraspherical series and classes of bi-univalent functions. The representation of multipliers of eigen and joint function expansions of nonlocal spectral problems for first- and second-order differential operators is also discussed. The book will be of great interest to researchers and professionals whose work involves the use of mathematical analysis.
Download or read book Parabolic Wave Equations with Applications written by Michael D. Collins and published by Springer Nature. This book was released on 2019-11-04 with total page 141 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book introduces parabolic wave equations, their key methods of numerical solution, and applications in seismology and ocean acoustics. The parabolic equation method provides an appealing combination of accuracy and efficiency for many nonseparable wave propagation problems in geophysics. While the parabolic equation method was pioneered in the 1940s by Leontovich and Fock who applied it to radio wave propagation in the atmosphere, it thrived in the 1970s due to its usefulness in seismology and ocean acoustics. The book covers progress made following the parabolic equation’s ascendancy in geophysics. It begins with the necessary preliminaries on the elliptic wave equation and its analysis from which the parabolic wave equation is derived and introduced. Subsequently, the authors demonstrate the use of rational approximation techniques, the Padé solution in particular, to find numerical solutions to the energy-conserving parabolic equation, three-dimensional parabolic equations, and horizontal wave equations. The rest of the book demonstrates applications to seismology, ocean acoustics, and beyond, with coverage of elastic waves, sloping interfaces and boundaries, acousto-gravity waves, and waves in poro-elastic media. Overall, it will be of use to students and researchers in wave propagation, ocean acoustics, geophysical sciences and more.
Download or read book Thermodynamics in Geochemistry written by Gregor Munro Anderson and published by Oxford University Press, USA. This book was released on 1993 with total page 609 pages. Available in PDF, EPUB and Kindle. Book excerpt: Annotation This textbook and reference outlines the principles and applications of thermodynamics in geochemistry.
