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Dynamical systems [[electronic resource] ] : methods and applications : theoretical developments and numerical examples / / Alexander G. Ramm, Nguyen S. Hoang
| Dynamical systems [[electronic resource] ] : methods and applications : theoretical developments and numerical examples / / Alexander G. Ramm, Nguyen S. Hoang |
| Autore | Ramm A. G (Alexander G.) |
| Pubbl/distr/stampa | Hoboken, N.J., : Wiley, 2012 |
| Descrizione fisica | 1 online resource (572 p.) |
| Disciplina | 515/.35 |
| Altri autori (Persone) | HoangNguyen S. <1980-> |
| Soggetto topico | Differentiable dynamical systems |
| ISBN |
1-283-42518-1
9786613425188 1-118-19960-X 1-118-19961-8 1-118-19959-6 |
| Formato | Materiale a stampa  |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
Dynamical Systems Method and Applications: Theoretical Developments and Numerical Examples; CONTENTS; List of Figures; List of Tables; Preface; Acknowledgments; PART I; 1 Introduction; 1.1 What this book is about; 1.2 What the DSM (Dynamical Systems Method) is; 1.3 The scope of the DSM; 1.4 A discussion of DSM; 1.5 Motivations; 2 III-posed problems; 2.1 Basic definitions. Examples; 2.2 Variational regularization; 2.3 Quasi-solutions; 2.4 Iterative regularization; 2.5 Quasi-inversion; 2.6 Dynamical systems method (DSM); 2.7 Variational regularization for nonlinear equations
3 DSM for well-posed problems3.1 Every solvable well-posed problem can be solved by DSM; 3.2 DSM and Newton-type methods; 3.3 DSM and the modified Newton's method; 3.4 DSM and Gauss-Newton-type methods; 3.5 DSM and the gradient method; 3.6 DSM and the simple iterations method; 3.7 DSM and minimization methods; 3.8 Ulm's method; 4 DSM and linear ill-posed problems; 4.1 Equations with bounded operators; 4.2 Another approach; 4.3 Equations with unbounded operators; 4.4 Iterative methods; 4.5 Stable calculation of values of unbounded operators; 5 Some inequalities 5.1 Basic nonlinear differential inequality5.2 An operator inequality; 5.3 A nonlinear inequality; 5.4 The Gronwall-type inequalities; 5.5 Another operator inequality; 5.6 A generalized version of the basic nonlinear inequality; 5.6.1 Formulations and results; 5.6.2 Applications; 5.7 Some nonlinear inequalities and applications; 5.7.1 Formulations and results; 5.7.2 Applications; 6 DSM for monotone operators; 6.1 Auxiliary results; 6.2 Formulation of the results and proofs; 6.3 The case of noisy data; 7 DSM for general nonlinear operator equations 7.1 Formulation of the problem. The results and proofs7.2 Noisy data; 7.3 Iterative solution; 7.4 Stability of the iterative solution; 8 DSM for operators satisfying a spectral assumption; 8.1 Spectral assumption; 8.2 Existence of a solution to a nonlinear equation; 9 DSM in Banach spaces; 9.1 Well-posed problems; 9.2 Ill-posed problems; 9.3 Singular perturbation problem; 10 DSM and Newton-type methods without inversion of the derivative; 10.1 Well-posed problems; 10.2 Ill-posed problems; 11 DSM and unbounded operators; 11.1 Statement of the problem; 11.2 Ill-posed problems 12 DSM and nonsmooth operators12.1 Formulation of the results; 12.2 Proofs; 13 DSM as a theoretical tool; 13.1 Surjectivity of nonlinear maps; 13.2 When is a local homeomorphism a global one?; 14 DSM and iterative methods; 14.1 Introduction; 14.2 Iterative solution of well-posed problems; 14.3 Iterative solution of ill-posed equations with monotone operator; 14.4 Iterative methods for solving nonlinear equations; 14.5 Ill-posed problems; 15 Numerical problems arising in applications; 15.1 Stable numerical differentiation; 15.2 Stable differentiation of piecewise-smooth functions 15.3 Simultaneous approximation of a function and its derivative by interpolation polynomials |
| Record Nr. | UNINA-9910139297203321 |
Ramm A. G (Alexander G.)
|
||
| Hoboken, N.J., : Wiley, 2012 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Dynamical systems [[electronic resource] ] : methods and applications : theoretical developments and numerical examples / / Alexander G. Ramm, Nguyen S. Hoang
| Dynamical systems [[electronic resource] ] : methods and applications : theoretical developments and numerical examples / / Alexander G. Ramm, Nguyen S. Hoang |
| Autore | Ramm A. G (Alexander G.) |
| Pubbl/distr/stampa | Hoboken, N.J., : Wiley, 2012 |
| Descrizione fisica | 1 online resource (572 p.) |
| Disciplina | 515/.35 |
| Altri autori (Persone) | HoangNguyen S. <1980-> |
| Soggetto topico | Differentiable dynamical systems |
| ISBN |
1-283-42518-1
9786613425188 1-118-19960-X 1-118-19961-8 1-118-19959-6 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
Dynamical Systems Method and Applications: Theoretical Developments and Numerical Examples; CONTENTS; List of Figures; List of Tables; Preface; Acknowledgments; PART I; 1 Introduction; 1.1 What this book is about; 1.2 What the DSM (Dynamical Systems Method) is; 1.3 The scope of the DSM; 1.4 A discussion of DSM; 1.5 Motivations; 2 III-posed problems; 2.1 Basic definitions. Examples; 2.2 Variational regularization; 2.3 Quasi-solutions; 2.4 Iterative regularization; 2.5 Quasi-inversion; 2.6 Dynamical systems method (DSM); 2.7 Variational regularization for nonlinear equations
3 DSM for well-posed problems3.1 Every solvable well-posed problem can be solved by DSM; 3.2 DSM and Newton-type methods; 3.3 DSM and the modified Newton's method; 3.4 DSM and Gauss-Newton-type methods; 3.5 DSM and the gradient method; 3.6 DSM and the simple iterations method; 3.7 DSM and minimization methods; 3.8 Ulm's method; 4 DSM and linear ill-posed problems; 4.1 Equations with bounded operators; 4.2 Another approach; 4.3 Equations with unbounded operators; 4.4 Iterative methods; 4.5 Stable calculation of values of unbounded operators; 5 Some inequalities 5.1 Basic nonlinear differential inequality5.2 An operator inequality; 5.3 A nonlinear inequality; 5.4 The Gronwall-type inequalities; 5.5 Another operator inequality; 5.6 A generalized version of the basic nonlinear inequality; 5.6.1 Formulations and results; 5.6.2 Applications; 5.7 Some nonlinear inequalities and applications; 5.7.1 Formulations and results; 5.7.2 Applications; 6 DSM for monotone operators; 6.1 Auxiliary results; 6.2 Formulation of the results and proofs; 6.3 The case of noisy data; 7 DSM for general nonlinear operator equations 7.1 Formulation of the problem. The results and proofs7.2 Noisy data; 7.3 Iterative solution; 7.4 Stability of the iterative solution; 8 DSM for operators satisfying a spectral assumption; 8.1 Spectral assumption; 8.2 Existence of a solution to a nonlinear equation; 9 DSM in Banach spaces; 9.1 Well-posed problems; 9.2 Ill-posed problems; 9.3 Singular perturbation problem; 10 DSM and Newton-type methods without inversion of the derivative; 10.1 Well-posed problems; 10.2 Ill-posed problems; 11 DSM and unbounded operators; 11.1 Statement of the problem; 11.2 Ill-posed problems 12 DSM and nonsmooth operators12.1 Formulation of the results; 12.2 Proofs; 13 DSM as a theoretical tool; 13.1 Surjectivity of nonlinear maps; 13.2 When is a local homeomorphism a global one?; 14 DSM and iterative methods; 14.1 Introduction; 14.2 Iterative solution of well-posed problems; 14.3 Iterative solution of ill-posed equations with monotone operator; 14.4 Iterative methods for solving nonlinear equations; 14.5 Ill-posed problems; 15 Numerical problems arising in applications; 15.1 Stable numerical differentiation; 15.2 Stable differentiation of piecewise-smooth functions 15.3 Simultaneous approximation of a function and its derivative by interpolation polynomials |
| Record Nr. | UNINA-9910828885303321 |
|
Ramm A. G (Alexander G.)
|
||
| Hoboken, N.J., : Wiley, 2012 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Random fields estimation [[electronic resource] /] / Alexander G. Ramm
| Random fields estimation [[electronic resource] /] / Alexander G. Ramm |
| Autore | Ramm A. G (Alexander G.) |
| Pubbl/distr/stampa | Hackensack, NJ, : World Scientific, c2005 |
| Descrizione fisica | 1 online resource (388 p.) |
| Disciplina | 519.2 |
| Altri autori (Persone) | RammA. G (Alexander G.). |
| Soggetto topico |
Random fields
Estimation theory |
| Soggetto genere / forma | Electronic books. |
| ISBN |
1-281-89914-3
9786611899141 981-270-315-2 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto | Preface; Contents; 1. Introduction; 2. Formulation of Basic Results; 3. Numerical Solution of the Basic Integral Equation in Distributions; 4. Proofs; 5. Singular Perturbation Theory for a Class of Fredholm Integral Equations Arising in Random Fields Estimation Theory; 6. Estimation and Scattering Theory; 7. Applications; 8. Auxiliary Results; Appendix A Analytical Solution of the Basic Integral Equation for a Class of One-Dimensional Problems; Appendix B Integral Operators Basic in Random Fields Estimation Theory; Bibliographical Notes; Bibliography; Symbols; Index |
| Record Nr. | UNINA-9910450734703321 |
|
Ramm A. G (Alexander G.)
|
||
| Hackensack, NJ, : World Scientific, c2005 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Random fields estimation [[electronic resource] /] / Alexander G. Ramm
| Random fields estimation [[electronic resource] /] / Alexander G. Ramm |
| Autore | Ramm A. G (Alexander G.) |
| Pubbl/distr/stampa | Hackensack, NJ, : World Scientific, c2005 |
| Descrizione fisica | 1 online resource (388 p.) |
| Disciplina | 519.2 |
| Altri autori (Persone) | RammA. G (Alexander G.). |
| Soggetto topico |
Random fields
Estimation theory |
| ISBN |
1-281-89914-3
9786611899141 981-270-315-2 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto | Preface; Contents; 1. Introduction; 2. Formulation of Basic Results; 3. Numerical Solution of the Basic Integral Equation in Distributions; 4. Proofs; 5. Singular Perturbation Theory for a Class of Fredholm Integral Equations Arising in Random Fields Estimation Theory; 6. Estimation and Scattering Theory; 7. Applications; 8. Auxiliary Results; Appendix A Analytical Solution of the Basic Integral Equation for a Class of One-Dimensional Problems; Appendix B Integral Operators Basic in Random Fields Estimation Theory; Bibliographical Notes; Bibliography; Symbols; Index |
| Record Nr. | UNINA-9910784048303321 |
|
Ramm A. G (Alexander G.)
|
||
| Hackensack, NJ, : World Scientific, c2005 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Random fields estimation [[electronic resource] /] / Alexander G. Ramm
| Random fields estimation [[electronic resource] /] / Alexander G. Ramm |
| Autore | Ramm A. G (Alexander G.) |
| Edizione | [1st ed.] |
| Pubbl/distr/stampa | Hackensack, NJ, : World Scientific, c2005 |
| Descrizione fisica | 1 online resource (388 p.) |
| Disciplina | 519.2 |
| Altri autori (Persone) | RammA. G (Alexander G.). |
| Soggetto topico |
Random fields
Estimation theory |
| ISBN |
1-281-89914-3
9786611899141 981-270-315-2 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto | Preface; Contents; 1. Introduction; 2. Formulation of Basic Results; 3. Numerical Solution of the Basic Integral Equation in Distributions; 4. Proofs; 5. Singular Perturbation Theory for a Class of Fredholm Integral Equations Arising in Random Fields Estimation Theory; 6. Estimation and Scattering Theory; 7. Applications; 8. Auxiliary Results; Appendix A Analytical Solution of the Basic Integral Equation for a Class of One-Dimensional Problems; Appendix B Integral Operators Basic in Random Fields Estimation Theory; Bibliographical Notes; Bibliography; Symbols; Index |
| Record Nr. | UNINA-9910822027603321 |
|
Ramm A. G (Alexander G.)
|
||
| Hackensack, NJ, : World Scientific, c2005 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Scattering of acoustic and electromagnetic waves by small impedance bodies of arbitrary shapes : applications to creating new engineered materials / / Alexander G. Ramm
| Scattering of acoustic and electromagnetic waves by small impedance bodies of arbitrary shapes : applications to creating new engineered materials / / Alexander G. Ramm |
| Autore | Ramm A. G (Alexander G.) |
| Pubbl/distr/stampa | New York, New York : , : Momentum Press, , [2013] |
| Descrizione fisica | 1 online resource (262 p.) |
| Disciplina | 531.1133 |
| Soggetto topico | Wave-motion, Theory of |
| Soggetto genere / forma | Electronic books. |
| ISBN | 1-60650-622-6 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
Contents -- Preface -- Introduction --
1. Scalar wave scattering by one small body of an arbitrary shape -- 1.1 Impedance bodies -- 1.2 Acoustically soft bodies (the Dirichlet boundary condition) -- 1.3 Acoustically hard bodies (the Neumann boundary condition) -- 1.4 The interface (transmission) boundary condition -- 1.5 Summary of the results -- 2. Scalar wave scattering by many small bodies of an arbitrary shape -- 2.1 Impedance bodies -- 2.2 The Dirichlet boundary condition -- 2.3 The Neumann boundary condition -- 2.4 The transmission boundary condition -- 2.5 Wave scattering in an inhomogeneous medium -- 2.6 Summary of the results -- 3. Creating materials with a desired refraction coefficient -- 3.1 Scalar wave scattering. Formula for the refraction coefficient -- 3.2 A recipe for creating materials with a desired refraction coefficient -- 3.3 A discussion of the practical implementation of the recipe -- 3.4 Summary of the results -- 4. Wave-focusing materials -- 4.1 What is a wave-focusing material? -- 4.2 Creating wave-focusing materials -- 4.3 Computational aspects of the problem -- 4.4 Open problems -- 4.5 Summary of the results -- 5. Electromagnetic wave scattering by a single small body of an arbitrary shape -- 5.1 The impedance boundary condition -- 5.2 Perfectly conducting bodies -- 5.3 Formulas for the scattered field in the case of EM wave scattering by one impedance small body of an arbitrary shape -- 5.4 Summary of the results -- 6. Many-body scattering problem in the case of small scatterers -- 6.1 Reduction of the problem to linear algebraic system -- 6.2 Derivation of the integral equation for the effective field -- 6.3 Summary of the results -- 7. Creating materials with a desired refraction coefficient -- 7.1 A formula for the refraction coefficient -- 7.2 Formula for the magnetic permeability -- 7.3 Summary of the results -- 8. Electromagnetic wave scattering by many nanowires -- 8.1 Statement of the problem -- 8.2 Asymptotic solution of the problem -- 8.3 Many-body scattering problem equation for the effective field -- 8.4 Physical properties of the limiting medium -- 8.5 Summary of the results -- 9. Heat transfer in a medium in which many small bodies are embedded -- 9.1 Introduction -- 9.2 Derivation of the equation for the limiting temperature -- 9.3 Various results -- 9.4 Summary of the results -- 10. Quantum-mechanical wave scattering by many potentials with small support -- 10.1 Problem formulation -- 10.2 Proofs -- 10.3 Summary of the results -- 11. Some results from the potential theory -- 11.1 Potentials of the simple and double layers -- 11.2 Replacement of the surface potentials -- 11.3 Asymptotic behavior of the solution to the Helmholtz equation under the impedance boundary condition -- 11.4 Some properties of the electrical capacitance -- 11.5 Summary of the results -- 12. Collocation method -- 12.1 Convergence of the collocation method -- 12.2 Collocation method and homogenization -- 12.3 Summary of the results -- 13. Some inverse problems related to small scatterers -- 13.1 Finding the position and size of a small body from the scattering data -- 13.2 Finding small subsurface inhomogeneities -- 13.3 Inverse radio measurements problem -- 13.4 Summary of the results -- Appendix -- A1. Banach and Hilbert spaces -- A2. A result from perturbation theory -- A3. The Fredholm alternative -- Bibliographical notes -- Bibliography -- Index. |
| Record Nr. | UNINA-9910453391503321 |
|
Ramm A. G (Alexander G.)
|
||
| New York, New York : , : Momentum Press, , [2013] | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Scattering of acoustic and electromagnetic waves by small impedance bodies of arbitrary shapes : applications to creating new engineered materials / / Alexander G. Ramm
| Scattering of acoustic and electromagnetic waves by small impedance bodies of arbitrary shapes : applications to creating new engineered materials / / Alexander G. Ramm |
| Autore | Ramm A. G (Alexander G.) |
| Pubbl/distr/stampa | New York, New York : , : Momentum Press, , [2013] |
| Descrizione fisica | 1 online resource (262 p.) |
| Disciplina | 531.1133 |
| Soggetto topico | Wave-motion, Theory of |
| ISBN | 1-60650-622-6 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
Contents -- Preface -- Introduction --
1. Scalar wave scattering by one small body of an arbitrary shape -- 1.1 Impedance bodies -- 1.2 Acoustically soft bodies (the Dirichlet boundary condition) -- 1.3 Acoustically hard bodies (the Neumann boundary condition) -- 1.4 The interface (transmission) boundary condition -- 1.5 Summary of the results -- 2. Scalar wave scattering by many small bodies of an arbitrary shape -- 2.1 Impedance bodies -- 2.2 The Dirichlet boundary condition -- 2.3 The Neumann boundary condition -- 2.4 The transmission boundary condition -- 2.5 Wave scattering in an inhomogeneous medium -- 2.6 Summary of the results -- 3. Creating materials with a desired refraction coefficient -- 3.1 Scalar wave scattering. Formula for the refraction coefficient -- 3.2 A recipe for creating materials with a desired refraction coefficient -- 3.3 A discussion of the practical implementation of the recipe -- 3.4 Summary of the results -- 4. Wave-focusing materials -- 4.1 What is a wave-focusing material? -- 4.2 Creating wave-focusing materials -- 4.3 Computational aspects of the problem -- 4.4 Open problems -- 4.5 Summary of the results -- 5. Electromagnetic wave scattering by a single small body of an arbitrary shape -- 5.1 The impedance boundary condition -- 5.2 Perfectly conducting bodies -- 5.3 Formulas for the scattered field in the case of EM wave scattering by one impedance small body of an arbitrary shape -- 5.4 Summary of the results -- 6. Many-body scattering problem in the case of small scatterers -- 6.1 Reduction of the problem to linear algebraic system -- 6.2 Derivation of the integral equation for the effective field -- 6.3 Summary of the results -- 7. Creating materials with a desired refraction coefficient -- 7.1 A formula for the refraction coefficient -- 7.2 Formula for the magnetic permeability -- 7.3 Summary of the results -- 8. Electromagnetic wave scattering by many nanowires -- 8.1 Statement of the problem -- 8.2 Asymptotic solution of the problem -- 8.3 Many-body scattering problem equation for the effective field -- 8.4 Physical properties of the limiting medium -- 8.5 Summary of the results -- 9. Heat transfer in a medium in which many small bodies are embedded -- 9.1 Introduction -- 9.2 Derivation of the equation for the limiting temperature -- 9.3 Various results -- 9.4 Summary of the results -- 10. Quantum-mechanical wave scattering by many potentials with small support -- 10.1 Problem formulation -- 10.2 Proofs -- 10.3 Summary of the results -- 11. Some results from the potential theory -- 11.1 Potentials of the simple and double layers -- 11.2 Replacement of the surface potentials -- 11.3 Asymptotic behavior of the solution to the Helmholtz equation under the impedance boundary condition -- 11.4 Some properties of the electrical capacitance -- 11.5 Summary of the results -- 12. Collocation method -- 12.1 Convergence of the collocation method -- 12.2 Collocation method and homogenization -- 12.3 Summary of the results -- 13. Some inverse problems related to small scatterers -- 13.1 Finding the position and size of a small body from the scattering data -- 13.2 Finding small subsurface inhomogeneities -- 13.3 Inverse radio measurements problem -- 13.4 Summary of the results -- Appendix -- A1. Banach and Hilbert spaces -- A2. A result from perturbation theory -- A3. The Fredholm alternative -- Bibliographical notes -- Bibliography -- Index. |
| Record Nr. | UNINA-9910790611303321 |
|
Ramm A. G (Alexander G.)
|
||
| New York, New York : , : Momentum Press, , [2013] | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Scattering of acoustic and electromagnetic waves by small impedance bodies of arbitrary shapes : applications to creating new engineered materials / / Alexander G. Ramm
| Scattering of acoustic and electromagnetic waves by small impedance bodies of arbitrary shapes : applications to creating new engineered materials / / Alexander G. Ramm |
| Autore | Ramm A. G (Alexander G.) |
| Pubbl/distr/stampa | New York, New York : , : Momentum Press, , [2013] |
| Descrizione fisica | 1 online resource (262 p.) |
| Disciplina | 531.1133 |
| Soggetto topico | Wave-motion, Theory of |
| ISBN | 1-60650-622-6 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
Contents -- Preface -- Introduction --
1. Scalar wave scattering by one small body of an arbitrary shape -- 1.1 Impedance bodies -- 1.2 Acoustically soft bodies (the Dirichlet boundary condition) -- 1.3 Acoustically hard bodies (the Neumann boundary condition) -- 1.4 The interface (transmission) boundary condition -- 1.5 Summary of the results -- 2. Scalar wave scattering by many small bodies of an arbitrary shape -- 2.1 Impedance bodies -- 2.2 The Dirichlet boundary condition -- 2.3 The Neumann boundary condition -- 2.4 The transmission boundary condition -- 2.5 Wave scattering in an inhomogeneous medium -- 2.6 Summary of the results -- 3. Creating materials with a desired refraction coefficient -- 3.1 Scalar wave scattering. Formula for the refraction coefficient -- 3.2 A recipe for creating materials with a desired refraction coefficient -- 3.3 A discussion of the practical implementation of the recipe -- 3.4 Summary of the results -- 4. Wave-focusing materials -- 4.1 What is a wave-focusing material? -- 4.2 Creating wave-focusing materials -- 4.3 Computational aspects of the problem -- 4.4 Open problems -- 4.5 Summary of the results -- 5. Electromagnetic wave scattering by a single small body of an arbitrary shape -- 5.1 The impedance boundary condition -- 5.2 Perfectly conducting bodies -- 5.3 Formulas for the scattered field in the case of EM wave scattering by one impedance small body of an arbitrary shape -- 5.4 Summary of the results -- 6. Many-body scattering problem in the case of small scatterers -- 6.1 Reduction of the problem to linear algebraic system -- 6.2 Derivation of the integral equation for the effective field -- 6.3 Summary of the results -- 7. Creating materials with a desired refraction coefficient -- 7.1 A formula for the refraction coefficient -- 7.2 Formula for the magnetic permeability -- 7.3 Summary of the results -- 8. Electromagnetic wave scattering by many nanowires -- 8.1 Statement of the problem -- 8.2 Asymptotic solution of the problem -- 8.3 Many-body scattering problem equation for the effective field -- 8.4 Physical properties of the limiting medium -- 8.5 Summary of the results -- 9. Heat transfer in a medium in which many small bodies are embedded -- 9.1 Introduction -- 9.2 Derivation of the equation for the limiting temperature -- 9.3 Various results -- 9.4 Summary of the results -- 10. Quantum-mechanical wave scattering by many potentials with small support -- 10.1 Problem formulation -- 10.2 Proofs -- 10.3 Summary of the results -- 11. Some results from the potential theory -- 11.1 Potentials of the simple and double layers -- 11.2 Replacement of the surface potentials -- 11.3 Asymptotic behavior of the solution to the Helmholtz equation under the impedance boundary condition -- 11.4 Some properties of the electrical capacitance -- 11.5 Summary of the results -- 12. Collocation method -- 12.1 Convergence of the collocation method -- 12.2 Collocation method and homogenization -- 12.3 Summary of the results -- 13. Some inverse problems related to small scatterers -- 13.1 Finding the position and size of a small body from the scattering data -- 13.2 Finding small subsurface inhomogeneities -- 13.3 Inverse radio measurements problem -- 13.4 Summary of the results -- Appendix -- A1. Banach and Hilbert spaces -- A2. A result from perturbation theory -- A3. The Fredholm alternative -- Bibliographical notes -- Bibliography -- Index. |
| Record Nr. | UNINA-9910809871003321 |
|
Ramm A. G (Alexander G.)
|
||
| New York, New York : , : Momentum Press, , [2013] | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Wave scattering by small bodies of arbitrary shapes [[electronic resource] /] / Alexander G. Ramm
| Wave scattering by small bodies of arbitrary shapes [[electronic resource] /] / Alexander G. Ramm |
| Autore | Ramm A. G (Alexander G.) |
| Pubbl/distr/stampa | Hackensack, NJ ; ; London, : World Scientific, c2005 |
| Descrizione fisica | 1 online resource (313 p.) |
| Disciplina | 530.124 |
| Soggetto topico |
Waves - Mathematics
Scattering (Physics) - Mathematics Electrostatics - Mathematics Iterative methods (Mathematics) |
| Soggetto genere / forma | Electronic books. |
| ISBN |
1-281-89696-9
9786611896966 981-270-120-6 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
Preface; Contents; Introduction; Chapter 1 Basic Problems; Chapter 2 Iterative Processes for Solving Fredholm's Integral Equations for Static Problems; Chapter 3 Calculating Electric Capacitance; Chapter 4 Numerical Examples; Chapter 5 Calculating Polarizability Tensors; Chapter 6 Iterative Methods: Mathematical Results; Chapter 7 Wave Scattering by Small Bodies; Chapter 8 Fredholm Alternative and a Characterization of Fredholm Operators; Chapter 9 Boundary-Value Problems in Rough Domains; Chapter 10 Low Frequency Asymptotics; Chapter 11 Finding Small Inhomogeneities from Scattering Data
Chapter 12 Modified Rayleigh Conjecture and Applications Appendix A Optimal with Respect to Accuracy Algorithms for Calculation of Multidimensional Weakly Singular Integrals and Applications to Calculation of Capacitances of Conductors of Arbitrary Shapes; Problems; Bibliographical Notes; Bibliography; List of Symbols; Index |
| Record Nr. | UNINA-9910450677003321 |
|
Ramm A. G (Alexander G.)
|
||
| Hackensack, NJ ; ; London, : World Scientific, c2005 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Wave scattering by small bodies of arbitrary shapes [[electronic resource] /] / Alexander G. Ramm
| Wave scattering by small bodies of arbitrary shapes [[electronic resource] /] / Alexander G. Ramm |
| Autore | Ramm A. G (Alexander G.) |
| Pubbl/distr/stampa | Hackensack, NJ ; ; London, : World Scientific, c2005 |
| Descrizione fisica | 1 online resource (313 p.) |
| Disciplina | 530.124 |
| Soggetto topico |
Waves - Mathematics
Scattering (Physics) - Mathematics Electrostatics - Mathematics Iterative methods (Mathematics) |
| ISBN |
1-281-89696-9
9786611896966 981-270-120-6 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
Preface; Contents; Introduction; Chapter 1 Basic Problems; Chapter 2 Iterative Processes for Solving Fredholm's Integral Equations for Static Problems; Chapter 3 Calculating Electric Capacitance; Chapter 4 Numerical Examples; Chapter 5 Calculating Polarizability Tensors; Chapter 6 Iterative Methods: Mathematical Results; Chapter 7 Wave Scattering by Small Bodies; Chapter 8 Fredholm Alternative and a Characterization of Fredholm Operators; Chapter 9 Boundary-Value Problems in Rough Domains; Chapter 10 Low Frequency Asymptotics; Chapter 11 Finding Small Inhomogeneities from Scattering Data
Chapter 12 Modified Rayleigh Conjecture and Applications Appendix A Optimal with Respect to Accuracy Algorithms for Calculation of Multidimensional Weakly Singular Integrals and Applications to Calculation of Capacitances of Conductors of Arbitrary Shapes; Problems; Bibliographical Notes; Bibliography; List of Symbols; Index |
| Record Nr. | UNINA-9910783915403321 |
|
Ramm A. G (Alexander G.)
|
||
| Hackensack, NJ ; ; London, : World Scientific, c2005 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
