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Título : Applied Pseudoanalytic Function Theory Tipo de documento: documento electrónico Autores: Vladislav V. Kravchenko ; SpringerLink (Online service) Editorial: Basel : Birkhäuser Basel Fecha de publicación: 2009 Colección: Frontiers in Mathematics, ISSN 1660-8046 Número de páginas: XII, 184 p Il.: online resource ISBN/ISSN/DL: 978-3-0346-0004-0 Idioma : Inglés (eng) Palabras clave: Mathematics Functions of complex variables Operator theory Partial differential equations Physics Differential Equations Mathematical Methods in Theory a Complex Variable Several Variables and Analytic Spaces Clasificación: 51 Matemáticas Resumen: Pseudoanalytic function theory generalizes and preserves many crucial features of complex analytic function theory. The Cauchy-Riemann system is replaced by a much more general first-order system with variable coefficients which turns out to be closely related to important equations of mathematical physics. This relation supplies powerful tools for studying and solving Schrödinger, Dirac, Maxwell, Klein-Gordon and other equations with the aid of complex-analytic methods. The book is dedicated to these recent developments in pseudoanalytic function theory and their applications as well as to multidimensional generalizations. It is directed to undergraduates, graduate students and researchers interested in complex-analytic methods, solution techniques for equations of mathematical physics, partial and ordinary differential equations Nota de contenido: Pseudoanalytic Function Theory and Second-order Elliptic Equations -- Definitions and Results from Bers’ Theory -- Solutions of Second-order Elliptic Equations as Real Components of Complex Pseudoanalytic Functions -- Formal Powers -- Cauchy’s Integral Formula -- Complex Riccati Equation -- Applications to Sturm-Liouville Theory -- A Representation for Solutions of the Sturm-Liouville Equation -- Spectral Problems and Darboux Transformation -- Applications to Real First-order Systems -- Beltrami Fields -- Static Maxwell System in Axially Symmetric Inhomogeneous Media -- Hyperbolic Pseudoanalytic Functions -- Hyperbolic Numbers and Analytic Functions -- Hyperbolic Pseudoanalytic Functions -- Relationship between Hyperbolic Pseudoanalytic Functions and Solutions of the Klein-Gordon Equation -- Bicomplex and Biquaternionic Pseudoanalytic Functions and Applications -- The Dirac Equation -- Complex Second-order Elliptic Equations and Bicomplex Pseudoanalytic Functions -- Multidimensional Second-order Equations En línea: http://dx.doi.org/10.1007/978-3-0346-0004-0 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=33994 Applied Pseudoanalytic Function Theory [documento electrónico] / Vladislav V. Kravchenko ; SpringerLink (Online service) . - Basel : Birkhäuser Basel, 2009 . - XII, 184 p : online resource. - (Frontiers in Mathematics, ISSN 1660-8046) .
ISBN : 978-3-0346-0004-0
Idioma : Inglés (eng)
Palabras clave: Mathematics Functions of complex variables Operator theory Partial differential equations Physics Differential Equations Mathematical Methods in Theory a Complex Variable Several Variables and Analytic Spaces Clasificación: 51 Matemáticas Resumen: Pseudoanalytic function theory generalizes and preserves many crucial features of complex analytic function theory. The Cauchy-Riemann system is replaced by a much more general first-order system with variable coefficients which turns out to be closely related to important equations of mathematical physics. This relation supplies powerful tools for studying and solving Schrödinger, Dirac, Maxwell, Klein-Gordon and other equations with the aid of complex-analytic methods. The book is dedicated to these recent developments in pseudoanalytic function theory and their applications as well as to multidimensional generalizations. It is directed to undergraduates, graduate students and researchers interested in complex-analytic methods, solution techniques for equations of mathematical physics, partial and ordinary differential equations Nota de contenido: Pseudoanalytic Function Theory and Second-order Elliptic Equations -- Definitions and Results from Bers’ Theory -- Solutions of Second-order Elliptic Equations as Real Components of Complex Pseudoanalytic Functions -- Formal Powers -- Cauchy’s Integral Formula -- Complex Riccati Equation -- Applications to Sturm-Liouville Theory -- A Representation for Solutions of the Sturm-Liouville Equation -- Spectral Problems and Darboux Transformation -- Applications to Real First-order Systems -- Beltrami Fields -- Static Maxwell System in Axially Symmetric Inhomogeneous Media -- Hyperbolic Pseudoanalytic Functions -- Hyperbolic Numbers and Analytic Functions -- Hyperbolic Pseudoanalytic Functions -- Relationship between Hyperbolic Pseudoanalytic Functions and Solutions of the Klein-Gordon Equation -- Bicomplex and Biquaternionic Pseudoanalytic Functions and Applications -- The Dirac Equation -- Complex Second-order Elliptic Equations and Bicomplex Pseudoanalytic Functions -- Multidimensional Second-order Equations En línea: http://dx.doi.org/10.1007/978-3-0346-0004-0 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=33994 Ejemplares
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Título : Approximation of Additive Convolution-Like Operators : Real C*-Algebra Approach Tipo de documento: documento electrónico Autores: Victor D. Didenko ; SpringerLink (Online service) ; Silbermann, Bernd Editorial: Basel : Birkhäuser Basel Fecha de publicación: 2008 Colección: Frontiers in Mathematics, ISSN 1660-8046 Número de páginas: XII, 306 p Il.: online resource ISBN/ISSN/DL: 978-3-7643-8751-8 Idioma : Inglés (eng) Palabras clave: Mathematics Algebra Integral equations transforms Operational calculus Operator theory Partial differential Numerical analysis Theory Analysis Equations Transforms, Calculus Differential Clasificación: 51 Matemáticas Resumen: Various aspects of numerical analysis for equations arising in boundary integral equation methods have been the subject of several books published in the last 15 years [95, 102, 183, 196, 198]. Prominent examples include various classes of o- dimensional singular integral equations or equations related to single and double layer potentials. Usually, a mathematically rigorous foundation and error analysis for the approximate solution of such equations is by no means an easy task. One reason is the fact that boundary integral operators generally are neither integral operatorsof the formidentity plus compact operatornor identity plus an operator with a small norm. Consequently, existing standard theories for the numerical analysis of Fredholm integral equations of the second kind are not applicable. In the last 15 years it became clear that the Banach algebra technique is a powerful tool to analyze the stability problem for relevant approximation methods [102, 103, 183, 189]. The starting point for this approach is the observation that the ? stability problem is an invertibility problem in a certain BanachorC -algebra. As a rule, this algebra is very complicated – and one has to ?nd relevant subalgebras to use such tools as local principles and representation theory. However,invariousapplicationsthereoftenarisecontinuousoperatorsacting on complex Banach spaces that are not linear but only additive – i. e. , A(x+y)= Ax+Ay for all x,y from a given Banach space. It is easily seen that additive operators 1 are R-linear provided they are continuous Nota de contenido: Complex and Real Algebras -- Approximation of Additive Integral Operators on Smooth Curves -- Approximation Methods for the Riemann-Hilbert Problem -- Piecewise Smooth and Open Contours -- Approximation Methods for the Muskhelishvili Equation -- Numerical Examples En línea: http://dx.doi.org/10.1007/978-3-7643-8751-8 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=34416 Approximation of Additive Convolution-Like Operators : Real C*-Algebra Approach [documento electrónico] / Victor D. Didenko ; SpringerLink (Online service) ; Silbermann, Bernd . - Basel : Birkhäuser Basel, 2008 . - XII, 306 p : online resource. - (Frontiers in Mathematics, ISSN 1660-8046) .
ISBN : 978-3-7643-8751-8
Idioma : Inglés (eng)
Palabras clave: Mathematics Algebra Integral equations transforms Operational calculus Operator theory Partial differential Numerical analysis Theory Analysis Equations Transforms, Calculus Differential Clasificación: 51 Matemáticas Resumen: Various aspects of numerical analysis for equations arising in boundary integral equation methods have been the subject of several books published in the last 15 years [95, 102, 183, 196, 198]. Prominent examples include various classes of o- dimensional singular integral equations or equations related to single and double layer potentials. Usually, a mathematically rigorous foundation and error analysis for the approximate solution of such equations is by no means an easy task. One reason is the fact that boundary integral operators generally are neither integral operatorsof the formidentity plus compact operatornor identity plus an operator with a small norm. Consequently, existing standard theories for the numerical analysis of Fredholm integral equations of the second kind are not applicable. In the last 15 years it became clear that the Banach algebra technique is a powerful tool to analyze the stability problem for relevant approximation methods [102, 103, 183, 189]. The starting point for this approach is the observation that the ? stability problem is an invertibility problem in a certain BanachorC -algebra. As a rule, this algebra is very complicated – and one has to ?nd relevant subalgebras to use such tools as local principles and representation theory. However,invariousapplicationsthereoftenarisecontinuousoperatorsacting on complex Banach spaces that are not linear but only additive – i. e. , A(x+y)= Ax+Ay for all x,y from a given Banach space. It is easily seen that additive operators 1 are R-linear provided they are continuous Nota de contenido: Complex and Real Algebras -- Approximation of Additive Integral Operators on Smooth Curves -- Approximation Methods for the Riemann-Hilbert Problem -- Piecewise Smooth and Open Contours -- Approximation Methods for the Muskhelishvili Equation -- Numerical Examples En línea: http://dx.doi.org/10.1007/978-3-7643-8751-8 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=34416 Ejemplares
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Título : Artinian Modules over Group Rings Tipo de documento: documento electrónico Autores: Leonid A. Kurdachenko ; SpringerLink (Online service) ; Javier Otal ; Igor Ya Subbotin Editorial: Basel : Birkhäuser Basel Fecha de publicación: 2007 Colección: Frontiers in Mathematics, ISSN 1660-8046 Número de páginas: XII, 247 p Il.: online resource ISBN/ISSN/DL: 978-3-7643-7765-6 Idioma : Inglés (eng) Palabras clave: Mathematics Algebra Clasificación: 51 Matemáticas Nota de contenido: Modules with chain conditions -- Ranks of groups -- Some generalized nilpotent groups -- Artinian modules and the socle -- Reduction to subgroups of finite index -- Modules over Dedekind domains -- The Kovacs-Newman theorem -- Hartley’s classes of modules -- The injectivity of some simple modules -- Direct decompositions in artinian modules -- On the countability of artinian modules over FC-hypercentral groups -- Artinian modules over periodic abelian groups -- Nearly injective modules -- Artinian modules over abelian groups of finite section rank -- The injective envelopes of simple modules over group rings -- Quasifinite modules -- Some applications: splitting over the locally nilpotent residual En línea: http://dx.doi.org/10.1007/978-3-7643-7765-6 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=34684 Artinian Modules over Group Rings [documento electrónico] / Leonid A. Kurdachenko ; SpringerLink (Online service) ; Javier Otal ; Igor Ya Subbotin . - Basel : Birkhäuser Basel, 2007 . - XII, 247 p : online resource. - (Frontiers in Mathematics, ISSN 1660-8046) .
ISBN : 978-3-7643-7765-6
Idioma : Inglés (eng)
Palabras clave: Mathematics Algebra Clasificación: 51 Matemáticas Nota de contenido: Modules with chain conditions -- Ranks of groups -- Some generalized nilpotent groups -- Artinian modules and the socle -- Reduction to subgroups of finite index -- Modules over Dedekind domains -- The Kovacs-Newman theorem -- Hartley’s classes of modules -- The injectivity of some simple modules -- Direct decompositions in artinian modules -- On the countability of artinian modules over FC-hypercentral groups -- Artinian modules over periodic abelian groups -- Nearly injective modules -- Artinian modules over abelian groups of finite section rank -- The injective envelopes of simple modules over group rings -- Quasifinite modules -- Some applications: splitting over the locally nilpotent residual En línea: http://dx.doi.org/10.1007/978-3-7643-7765-6 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=34684 Ejemplares
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Título : Differential Geometry of Lightlike Submanifolds Tipo de documento: documento electrónico Autores: Krishan L. Duggal ; SpringerLink (Online service) ; Bayram Sahin Editorial: Basel : Birkhäuser Basel Fecha de publicación: 2010 Colección: Frontiers in Mathematics, ISSN 1660-8046 Número de páginas: 488 p Il.: online resource ISBN/ISSN/DL: 978-3-0346-0251-8 Idioma : Inglés (eng) Palabras clave: Mathematics Differential geometry Geometry Clasificación: 51 Matemáticas Resumen: This is the first systematic account of the main results in the theory of lightlike submanifolds of semi-Riemannian manifolds which have a geometric structure, such as almost Hermitian, almost contact metric or quaternion Kähler. Using these structures, the book presents interesting classes of submanifolds whose geometry is very rich. The book also includes hypersurfaces of semi-Riemannian manifolds, their use in general relativity and Osserman geometry, half-lightlike submanifolds of semi-Riemannian manifolds, lightlike submersions, screen conformal submersions, and their applications in harmonic maps. Basic constructions and definitions are presented as preliminary background in every chapter. The presentation explores applications and suggests several open questions. This self-contained monograph provides up-to-date research in lightlike geometry and is intended for graduate students and researchers just entering this field Nota de contenido: Preliminaries -- Lightlike hypersurfaces -- Applications of lightlike hypersurfaces -- Half-lightlike submanifolds -- Lightlike submanifolds -- Submanifolds of indefinite Kähler manifolds -- Submanifolds of indefinite Sasakian manifolds -- Submanifolds of indefinite quaternion Kähler manifolds -- Applications of lightlike geometry En línea: http://dx.doi.org/10.1007/978-3-0346-0251-8 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=33671 Differential Geometry of Lightlike Submanifolds [documento electrónico] / Krishan L. Duggal ; SpringerLink (Online service) ; Bayram Sahin . - Basel : Birkhäuser Basel, 2010 . - 488 p : online resource. - (Frontiers in Mathematics, ISSN 1660-8046) .
ISBN : 978-3-0346-0251-8
Idioma : Inglés (eng)
Palabras clave: Mathematics Differential geometry Geometry Clasificación: 51 Matemáticas Resumen: This is the first systematic account of the main results in the theory of lightlike submanifolds of semi-Riemannian manifolds which have a geometric structure, such as almost Hermitian, almost contact metric or quaternion Kähler. Using these structures, the book presents interesting classes of submanifolds whose geometry is very rich. The book also includes hypersurfaces of semi-Riemannian manifolds, their use in general relativity and Osserman geometry, half-lightlike submanifolds of semi-Riemannian manifolds, lightlike submersions, screen conformal submersions, and their applications in harmonic maps. Basic constructions and definitions are presented as preliminary background in every chapter. The presentation explores applications and suggests several open questions. This self-contained monograph provides up-to-date research in lightlike geometry and is intended for graduate students and researchers just entering this field Nota de contenido: Preliminaries -- Lightlike hypersurfaces -- Applications of lightlike hypersurfaces -- Half-lightlike submanifolds -- Lightlike submanifolds -- Submanifolds of indefinite Kähler manifolds -- Submanifolds of indefinite Sasakian manifolds -- Submanifolds of indefinite quaternion Kähler manifolds -- Applications of lightlike geometry En línea: http://dx.doi.org/10.1007/978-3-0346-0251-8 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=33671 Ejemplares
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Título : Extremum Problems for Eigenvalues of Elliptic Operators Tipo de documento: documento electrónico Autores: Antoine Henrot ; SpringerLink (Online service) Editorial: Basel : Birkhäuser Basel Fecha de publicación: 2006 Colección: Frontiers in Mathematics, ISSN 1660-8046 Número de páginas: X, 202 p. 16 illus Il.: online resource ISBN/ISSN/DL: 978-3-7643-7706-9 Idioma : Inglés (eng) Palabras clave: Mathematics Operator theory Potential (Mathematics) Theory Clasificación: 51 Matemáticas Resumen: Problems linking the shape of a domain or the coefficients of an elliptic operator to the sequence of its eigenvalues are among the most fascinating of mathematical analysis. In this book, we focus on extremal problems. For instance, we look for a domain which minimizes or maximizes a given eigenvalue of the Laplace operator with various boundary conditions and various geometric constraints. We also consider the case of functions of eigenvalues. We investigate similar questions for other elliptic operators, such as the Schrödinger operator, non homogeneous membranes, or the bi-Laplacian, and we look at optimal composites and optimal insulation problems in terms of eigenvalues. Providing also a self-contained presentation of classical isoperimetric inequalities for eigenvalues and 30 open problems, this book will be useful for pure and applied mathematicians, particularly those interested in partial differential equations, the calculus of variations, differential geometry, or spectral theory Nota de contenido: Eigenvalues of elliptic operators -- Tools -- The first eigenvalue of the Laplacian-Dirichlet -- The second eigenvalue of the Laplacian-Dirichlet -- The other Dirichlet eigenvalues -- Functions of Dirichlet eigenvalues -- Other boundary conditions for the Laplacian -- Eigenvalues of Schrödinger operators -- Non-homogeneous strings and membranes -- Optimal conductivity -- The bi-Laplacian operator En línea: http://dx.doi.org/10.1007/3-7643-7706-2 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=35034 Extremum Problems for Eigenvalues of Elliptic Operators [documento electrónico] / Antoine Henrot ; SpringerLink (Online service) . - Basel : Birkhäuser Basel, 2006 . - X, 202 p. 16 illus : online resource. - (Frontiers in Mathematics, ISSN 1660-8046) .
ISBN : 978-3-7643-7706-9
Idioma : Inglés (eng)
Palabras clave: Mathematics Operator theory Potential (Mathematics) Theory Clasificación: 51 Matemáticas Resumen: Problems linking the shape of a domain or the coefficients of an elliptic operator to the sequence of its eigenvalues are among the most fascinating of mathematical analysis. In this book, we focus on extremal problems. For instance, we look for a domain which minimizes or maximizes a given eigenvalue of the Laplace operator with various boundary conditions and various geometric constraints. We also consider the case of functions of eigenvalues. We investigate similar questions for other elliptic operators, such as the Schrödinger operator, non homogeneous membranes, or the bi-Laplacian, and we look at optimal composites and optimal insulation problems in terms of eigenvalues. Providing also a self-contained presentation of classical isoperimetric inequalities for eigenvalues and 30 open problems, this book will be useful for pure and applied mathematicians, particularly those interested in partial differential equations, the calculus of variations, differential geometry, or spectral theory Nota de contenido: Eigenvalues of elliptic operators -- Tools -- The first eigenvalue of the Laplacian-Dirichlet -- The second eigenvalue of the Laplacian-Dirichlet -- The other Dirichlet eigenvalues -- Functions of Dirichlet eigenvalues -- Other boundary conditions for the Laplacian -- Eigenvalues of Schrödinger operators -- Non-homogeneous strings and membranes -- Optimal conductivity -- The bi-Laplacian operator En línea: http://dx.doi.org/10.1007/3-7643-7706-2 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=35034 Ejemplares
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