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Record Nr. |
UNINA9910139884103321 |
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Autore |
Kendall D. G (David George), <1918-2007.> |
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Titolo |
Shape and shape theory [[electronic resource] /] / D.G. Kendall ... [et al.] |
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Pubbl/distr/stampa |
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Chichester ; ; New York, : Wiley, c1999 |
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ISBN |
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1-282-30738-X |
9786612307386 |
0-470-31700-0 |
0-470-31784-1 |
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Descrizione fisica |
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1 online resource (328 p.) |
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Collana |
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Wiley series in probability and statistics |
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Altri autori (Persone) |
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KendallD. G <1918-2007.> (David George) |
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Disciplina |
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Soggetti |
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Shape theory (Topology) |
Topological spaces |
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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. [293]-297) and index. |
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Nota di contenuto |
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Shape and Shape Theory; Contents; Preface; Chapter 1 Shapes and Shape Spaces; 1.1 Origins; 1.2 Some preliminary observations; 1.3 A matrix representation for the shape of a k-ad; 1.4 'Elementary' shape spaces Σk1 and Σk2; 1.5 The Fubini-Study metric on Σk2; 1.6 The proof of Casson's theorem; Chapter 2 The Global Structure of Shape Spaces; 2.1 The problem; 2.2 When is a space familiar; 2.3 CW complexes; 2.4 A cellular decomposition of the unit sphere; 2.5 The cellular decomposition of shape spaces; 2.6 Inclusions and isometries; 2.7 Simple connectivity and higher homotopy groups |
2.8 The mapping cone decomposition2.9 Homotopy type and Casson's theorem; Chapter 3 Computing the Homology of Cell Complexes; 3.1 The orientation of certain spaces; 3.2 The orientation of spherical cells; 3.3 The boundary of an oriented cell; 3.4 The chain complex, homology and cohomology groups; 3.5 Reduced homology; 3.6 The homology exact sequence for shape spaces; 3.7 Applications of the exact sequence; 3.8 Topological invariants that distinguish between shape spaces; Chapter 4 A Chain Complex for Shape Spaces; 4.1 The chain complex; 4.2 The space of unoriented shapes |
4.3 The boundary map in the chain complex4.4 Decomposing the chain |
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complex; 4.5 Homology and cohomology of the spaces; 4.6 Connectivity of shape spaces; 4.7 Limits of shape spaces; Chapter 5 The Homology Groups of Shape Spaces; 5.1 Spaces of shapes in 2-space; 5.2 Spaces of shapes in 3-space; 5.3 Spaces of shapes in 4-space; 5.4 Spaces of unoriented shapes in 2-space; 5.5 Spaces of unoriented shapes in 3-space; 5.6 Spaces of unoriented shapes in 4-space; 5.7 Decomposing the essential complexes; 5.8 Closed formulae for the homology groups; 5.9 Duality in shape spaces |
Chapter 6 Geodesics in Shape Spaces6.1 The action of SO(m) on the pre-shape sphere; 6.2 Viewing the induced Riemannian metric through horizontal geodesics; 6.3 The singular points and the nesting principle; 6.4 The distance between shapes; 6.5 The set of geodesics between two shapes; 6.6 The non-uniqueness of minimal geodesics; 6.7 The cut locus in shape spaces; 6.8 The distances and projections to lower strata; Chapter 7 The Riemannian Structure of Shape Spaces; 7.1 The Riemannian metric; 7.2 The metric re-expressed through natural local vector fields; 7.3 The Riemannian curvature tensor |
Chapter 8 Induced Shape-Measures8.1 Geometric preliminaries; 8.2 The shape-measure on Σkm induced by k labelled iid isotropic Gaussian distributions on Rm; 8.3 Shape-measures on Σm+1m of Poisson-Delaunay tiles; 8.4 Shape-measures on Σk2 induced by k labelled iid non-isotropic Gaussian distributions on R2; 8.5 Shape-measures on Σk2 induced by complex normal distributions; 8.6 The shape-measure on Σ32 induced by three labelled iid uniform distributions in a compact convex set |
8.7 The shape-measure on Σ32 induced by three labelled iid uniform distributions in a convex polygon. I: the singular tessellation |
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Sommario/riassunto |
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Shape and Shape Theory D. G. Kendall Churchill College, University of Cambridge, UK D. Barden Girton College, University of Cambridge, UK T. K. Carne King's College, University of Cambridge, UK H. Le University of Nottingham, UK The statistical theory of shape is a relatively new topic and is generating a great deal of interest and comment by statisticians, engineers and computer scientists. Mathematically, 'shape' is the geometrical information required to describe an object when location, scale and rotational effects are removed. The theory was pioneered by Professor David Kendall to solve p |
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2. |
Record Nr. |
UNINA9910962694103321 |
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Autore |
Toro Iniesta J. C. del (Jose Carlos) |
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Titolo |
Introduction to spectropolarimetry / / Jose Carlos del Toro Iniesta |
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Pubbl/distr/stampa |
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Cambridge : , : Cambridge University Press, , 2003 |
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ISBN |
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1-107-13539-7 |
1-280-43456-2 |
9786610434565 |
0-511-17899-9 |
0-511-04278-7 |
0-511-14892-5 |
0-511-30612-1 |
0-511-53625-9 |
0-511-05454-8 |
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Edizione |
[1st ed.] |
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Descrizione fisica |
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1 online resource (xvi, 227 pages) : digital, PDF file(s) |
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Disciplina |
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Soggetti |
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Astrophysical spectropolarimetry |
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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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Title from publisher's bibliographic system (viewed on 05 Oct 2015). |
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Nota di bibliografia |
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Includes bibliographical references and index. |
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Nota di contenuto |
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1. Historical introduction -- 2. A review of some basic concepts -- 3. The polarization properties of quasi-monochromatic light -- 4. Linear optical systems acting on polarized light -- 5. Solar polarimetry -- 6. Absorption and dispersion -- 7. The radiative transfer equation -- 8. The RTE in the presence of a magnetic field -- 9. Solving the radiative transfer equation -- 10. Stokes spectrum diagnostics -- 11. Inversion of the RTE. |
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Sommario/riassunto |
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Spectropolarimetry embraces the most complete and detailed measurement and analysis of light, as well as its interaction with matter. This book provides an introductory overview of the area, which plays an increasingly important role in modern solar observations. Chapters include a comprehensive description of the polarization state of polychromatic light and its measurement, an overview of astronomical (solar) polarimetry, the radiative transfer equation for polarized light, and the formation of spectral lines in the presence of a |
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magnetic field. Most topics are dealt with within the realm of classical physics, although a small amount of quantum mechanics is introduced where necessary. This text will be a valuable reference for graduates and researchers in astrophysics, solar physics and optics. |
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