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1. |
Record Nr. |
UNISA996466772703316 |
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Autore |
Fröhlich Steffen |
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Titolo |
Coulomb Frames in the Normal Bundle of Surfaces in Euclidean Spaces [[electronic resource] ] : Topics from Differential Geometry and Geometric Analysis of Surfaces / / by Steffen Fröhlich |
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Pubbl/distr/stampa |
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Berlin, Heidelberg : , : Springer Berlin Heidelberg : , : Imprint : Springer, , 2012 |
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ISBN |
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Edizione |
[1st ed. 2012.] |
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Descrizione fisica |
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1 online resource (XIV, 117 p.) |
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Collana |
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Lecture Notes in Mathematics, , 0075-8434 ; ; 2053 |
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Disciplina |
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Soggetti |
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Differential geometry |
Partial differential equations |
Functions of complex variables |
Differential Geometry |
Partial Differential Equations |
Functions of a Complex Variable |
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Lingua di pubblicazione |
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Formato |
Materiale a stampa |
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Livello bibliografico |
Monografia |
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Note generali |
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Bibliographic Level Mode of Issuance: Monograph |
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Nota di bibliografia |
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Includes bibliographical references (p. 107-111) and index. |
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Nota di contenuto |
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Surface Geometry -- Elliptic Systems -- Normal Coulomb Frames in R4 -- Normal Coulomb Frames in Rn+2. |
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Sommario/riassunto |
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This book is intended for advanced students and young researchers interested in the analysis of partial differential equations and differential geometry. It discusses elementary concepts of surface geometry in higher-dimensional Euclidean spaces, in particular the differential equations of Gauss-Weingarten together with various integrability conditions and corresponding surface curvatures. It includes a chapter on curvature estimates for such surfaces, and, using results from potential theory and harmonic analysis, it addresses geometric and analytic methods to establish the existence and regularity of Coulomb frames in their normal bundles, which arise as critical points for a functional of total torsion. |
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2. |
Record Nr. |
UNINA9910778218403321 |
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Autore |
Roach G. F (Gary Francis) |
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Titolo |
Wave scattering by time dependent perturbations [[electronic resource] ] : an introduction / / G.F. Roach |
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Pubbl/distr/stampa |
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Princeton, N.J., : Princeton University Press, 2007 |
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ISBN |
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1-282-15878-3 |
9786612158780 |
1-4008-2816-3 |
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Edizione |
[Course Book] |
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Descrizione fisica |
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1 online resource (300 p.) |
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Collana |
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Princeton series in applied mathematics |
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Disciplina |
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Soggetti |
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Waves - Mathematics |
Scattering (Physics) - Mathematics |
Perturbation (Mathematics) |
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Lingua di pubblicazione |
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Formato |
Materiale a stampa |
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Livello bibliografico |
Monografia |
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Note generali |
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Description based upon print version of record. |
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Nota di bibliografia |
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Includes bibliographical references (p. [275]-283) and index. |
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Nota di contenuto |
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Frontmatter -- Contents -- Preface -- Chapter One. Introduction and Outline of Contents -- Chapter Two. Some Aspects of Waves on Strings -- Chapter Three. Mathematical Preliminaries -- Chapter Four. Spectral Theory and Spectral Decompositions -- Chapter Five. On Nonautonomous Problems -- Chapter Six. On Scattering Theory Strategies -- Chapter Seven. Echo Analysis -- Chapter Eight. Wave Scattering from Time-Periodic Perturbations -- Chapter Nine Concerning Inverse Problems -- Chapter Ten. Some Remarks on Scattering in Other Wave Systems -- Chapter Eleven. Commentaries and Appendices -- Bibliography -- Index |
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Sommario/riassunto |
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This book offers the first comprehensive introduction to wave scattering in nonstationary materials. G. F. Roach's aim is to provide an accessible, self-contained resource for newcomers to this important field of research that has applications across a broad range of areas, including radar, sonar, diagnostics in engineering and manufacturing, geophysical prospecting, and ultrasonic medicine such as sonograms. New methods in recent years have been developed to assess the structure and properties of materials and surfaces. When light, sound, or some other wave energy is directed at the material in question, |
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"imperfections" in the resulting echo can reveal a tremendous amount of valuable diagnostic information. The mathematics behind such analysis is sophisticated and complex. However, while problems involving stationary materials are quite well understood, there is still much to learn about those in which the material is moving or changes over time. These so-called non-autonomous problems are the subject of this fascinating book. Roach develops practical strategies, techniques, and solutions for mathematicians and applied scientists working in or seeking entry into the field of modern scattering theory and its applications. Wave Scattering by Time-Dependent Perturbations is destined to become a classic in this rapidly evolving area of inquiry. |
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