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Author : H Begehr
Publisher : CRC Press
Page : 286 pages
File Size : 51,7 Mb
Release : 2023-06-16
Category : Mathematics
ISBN : 9781000951516
Complex analytical methods are a powerful tool for special partial differential equations and systems. To make these methods applicable for a wider class, transformations and transmutations are used.
Author : H Begehr
Publisher : CRC Press
Page : 286 pages
File Size : 54,9 Mb
Release : 1993-09-23
Category : Mathematics
ISBN : 0582091098
Complex analytical methods are a powerful tool for special partial differential equations and systems. To make these methods applicable for a wider class, transformations and transmutations are used.
Author : Heinrich G. W. Begehr,Robert P. Gilbert
Publisher : Chapman and Hall/CRC
Page : 424 pages
File Size : 55,7 Mb
Release : 1992-12-14
Category : Mathematics
ISBN : UOM:39015029241083
A broad ranging collection of recent results in the subject covering areas from plane elasticity to second and higher order elliptic equations. The chapters may be read individually, providing a more accessible forum for the applications.
Author : H Begehr
Publisher : CRC Press
Page : 280 pages
File Size : 45,6 Mb
Release : 2023-06-16
Category : Mathematics
ISBN : 9781000946550
Complex analytical methods are a powerful tool for special partial differential equations and systems. To make these methods applicable for a wider class, transformations and transmutations are used.
Author : Heinrich G. W. Begehr
Publisher : Unknown
Page : 0 pages
File Size : 46,6 Mb
Release : 2019
Category : MATHEMATICS
ISBN : 1003417019
Complex analytical methods are a powerful tool for special partial differential equations and systems. To make these methods applicable for a wider class, transformations and transmutations are used.
Author : H Begehr
Publisher : Chapman and Hall/CRC
Page : 280 pages
File Size : 49,6 Mb
Release : 1993-09-23
Category : Mathematics
ISBN : 0582091098
Complex analytical methods are a powerful tool for special partial differential equations and systems. To make these methods applicable for a wider class, transformations and transmutations are used.
Author : Heinrich G. W. Begehr
Publisher : Unknown
Page : 0 pages
File Size : 46,5 Mb
Release : 1992
Category : Differential equations, Partial
ISBN : LCCN:90013592
Author : Saburou Saitoh
Publisher : CRC Press
Page : 289 pages
File Size : 46,8 Mb
Release : 2020-11-25
Category : Mathematics
ISBN : 9781000115246
The general theories contained in the text will give rise to new ideas and methods for the natural inversion formulas for general linear mappings in the framework of Hilbert spaces containing the natural solutions for Fredholm integral equations of the first kind.
Author : Vladislav V. Kravchenko,Sergei M. Sitnik
Publisher : Springer Nature
Page : 685 pages
File Size : 46,8 Mb
Release : 2020-04-11
Category : Mathematics
ISBN : 9783030359140
Transmutation operators in differential equations and spectral theory can be used to reveal the relations between different problems, and often make it possible to transform difficult problems into easier ones. Accordingly, they represent an important mathematical tool in the theory of inverse and scattering problems, of ordinary and partial differential equations, integral transforms and equations, special functions, harmonic analysis, potential theory, and generalized analytic functions. This volume explores recent advances in the construction and applications of transmutation operators, while also sharing some interesting historical notes on the subject.
Author : Saburou Saitoh,Yoshihiro Sawano
Publisher : Springer
Page : 452 pages
File Size : 50,6 Mb
Release : 2016-10-14
Category : Mathematics
ISBN : 9789811005305
This book provides a large extension of the general theory of reproducing kernels published by N. Aronszajn in 1950, with many concrete applications.In Chapter 1, many concrete reproducing kernels are first introduced with detailed information. Chapter 2 presents a general and global theory of reproducing kernels with basic applications in a self-contained way. Many fundamental operations among reproducing kernel Hilbert spaces are dealt with. Chapter 2 is the heart of this book.Chapter 3 is devoted to the Tikhonov regularization using the theory of reproducing kernels with applications to numerical and practical solutions of bounded linear operator equations.In Chapter 4, the numerical real inversion formulas of the Laplace transform are presented by applying the Tikhonov regularization, where the reproducing kernels play a key role in the results.Chapter 5 deals with ordinary differential equations; Chapter 6 includes many concrete results for various fundamental partial differential equations. In Chapter 7, typical integral equations are presented with discretization methods. These chapters are applications of the general theories of Chapter 3 with the purpose of practical and numerical constructions of the solutions.In Chapter 8, hot topics on reproducing kernels are presented; namely, norm inequalities, convolution inequalities, inversion of an arbitrary matrix, representations of inverse mappings, identifications of nonlinear systems, sampling theory, statistical learning theory and membership problems. Relationships among eigen-functions, initial value problems for linear partial differential equations, and reproducing kernels are also presented. Further, new fundamental results on generalized reproducing kernels, generalized delta functions, generalized reproducing kernel Hilbert spaces, andas well, a general integral transform theory are introduced.In three Appendices, the deep theory of Akira Yamada discussing the equality problems in nonlinear norm inequalities, Yamada's unified and generalized inequalities for Opial's inequalities and the concrete and explicit integral representation of the implicit functions are presented.
Author : Elina Shishkina,Sergei Sitnik
Publisher : Academic Press
Page : 594 pages
File Size : 43,8 Mb
Release : 2020-07-24
Category : Mathematics
ISBN : 9780128204078
Transmutations, Singular and Fractional Differential Equations with Applications to Mathematical Physics connects difficult problems with similar more simple ones. The book's strategy works for differential and integral equations and systems and for many theoretical and applied problems in mathematics, mathematical physics, probability and statistics, applied computer science and numerical methods. In addition to being exposed to recent advances, readers learn to use transmutation methods not only as practical tools, but also as vehicles that deliver theoretical insights. Presents the universal transmutation method as the most powerful for solving many problems in mathematics, mathematical physics, probability and statistics, applied computer science and numerical methods Combines mathematical rigor with an illuminating exposition full of historical notes and fascinating details Enables researchers, lecturers and students to find material under the single "roof"
Author : Pei Dang,Min Ku,Tao Qian,Luigi G. Rodino
Publisher : Birkhäuser
Page : 609 pages
File Size : 53,6 Mb
Release : 2017-04-18
Category : Mathematics
ISBN : 9783319488127
This book presents a collection of papers from the 10th ISAAC Congress 2015, held in Macau, China. The papers, prepared by respected international experts, address recent results in Mathematics, with a special focus on Analysis. By structuring the content according to the various mathematical topics, the volume offers specialists and non-specialists alike an excellent source of information on the state-of-the-art in Mathematical Analysis and its interdisciplinary applications.
Author : Armand Wirgin
Publisher : World Scientific
Page : 300 pages
File Size : 50,8 Mb
Release : 2003-01-13
Category : Mathematics
ISBN : 9789814486743
This book concerns the mathematical analysis — modeling physical concepts, existence, uniqueness, stability, asymptotics, computational schemes, etc. — involved in predicting complex mechanical/acoustical behavior/response and identifying or optimizing mechanical/acoustical systems giving rise to phenomena that are either observed or aimed at. The forward problems consist in solving generally coupled, nonlinear systems of integral or partial (integer or fractional) differential equations with nonconstant coefficients. The identification/optimization of the latter, of the driving terms and/or of the boundary conditions, all of which are often affected by random perturbations, forms the class of related inverse or control problems. Contents:Imaging Methods in Random Media (J Berryman et al.)Resonances of an Elastic Plate in a Duct, in the Presence of a Uniform Flow (A S B-B Dhia & J-F Mercier)First Order Asymptotic Modelling of a Nuclear Waste Repository (A Bourgeat et al.)Recovery of the Poroelastic Parameters of Cancellous Bone Using Low Frequency Acoustic Interrogation (J L Buchanan et al.)Trapping Regions for Discontinuously Coupled Dynamic Systems (S Carl & J W Jerome)Differential Calculi (R Carroll)Homogenizing a Flow of an Incompressible Inviscid Fluid Through an Elastic Porous Media (T Clopeau & A Mickelic)On the Hardy Spaces of Harmonic and Monogenic Functions in the Unit Ball of RM+1 (R Delanghe)A Model for Porous Ductile Viscoplastic Solids including Void Shape Effects (L Flandi & J-B Leblond)Acoustic Wave Propagation in a Composite of Two Different Poroelastic Materials with a very Rough Periodic Interface: a Homogenization Approach (R Gilbert & M-J Ou)A Survey of Pointwise Interpolation Inequalities for Integer and Fractional Derivatives (V Maz'ya & T Shaposhnikova)Recent Progress in the Theoretical and Numerical Modelling of Thin-Layer Flow (L Schwartz)and other papers Readership: Researchers, academics and graduate students in the fields of analysis and differential equations, applied mathematics, mechanics and mathematical physics. Keywords:Analysis;Integral and Partial Differential Equations;Solid and Fluid Mechanics
Author : Armand Wirgin
Publisher : World Scientific
Page : 301 pages
File Size : 48,9 Mb
Release : 2002
Category : Science
ISBN : 9789812382641
At head of title: Proceedings of the International Conference to celebrate Robert P. Gilbert's 70th birthday.
Author : Heinrich Begehr,A. Okay Celebi,W. Tutschke
Publisher : Springer Science & Business Media
Page : 331 pages
File Size : 48,8 Mb
Release : 2013-12-01
Category : Mathematics
ISBN : 9781461332916
This volume is a collection of manscripts mainly originating from talks and lectures given at the Workshop on Recent Trends in Complex Methods for Par tial Differential Equations held from July 6 to 10, 1998 at the Middle East Technical University in Ankara, Turkey, sponsored by The Scientific and Tech nical Research Council of Turkey and the Middle East Technical University. This workshop is a continuation oftwo workshops from 1988 and 1993 at the In ternational Centre for Theoretical Physics in Trieste, Italy entitled Functional analytic Methods in Complex Analysis and Applications to Partial Differential Equations. Since classical complex analysis of one and several variables has a long tra dition it is of high level. But most of its basic problems are solved nowadays so that within the last few decades it has lost more and more attention. The area of complex and functional analytic methods in partial differential equations, however, is still a growing and flourishing field, in particular as these methods are not only applied. Whithin the framework of holomorphic functions but are also combined with properties of generalized analytic functions. This can be seen by the many books which recently were published in this field and also by the proceedings in this ISAAC series and the ISAAC congresses and workshops.