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Shape and shape theory [[electronic resource] /] / D.G. Kendall ... [et al.]
| Shape and shape theory [[electronic resource] /] / D.G. Kendall ... [et al.] |
| Autore | Kendall D. G (David George), <1918-2007.> |
| Pubbl/distr/stampa | Chichester ; ; New York, : Wiley, c1999 |
| Descrizione fisica | 1 online resource (328 p.) |
| Disciplina | 514.24 |
| Altri autori (Persone) | KendallD. G <1918-2007.> (David George) |
| Collana | Wiley series in probability and statistics |
| Soggetto topico |
Shape theory (Topology)
Topological spaces |
| ISBN |
1-282-30738-X
9786612307386 0-470-31700-0 0-470-31784-1 |
| Formato | Materiale a stampa  |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
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 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 |
| Record Nr. | UNINA-9910139884103321 |
Kendall D. G (David George), <1918-2007.>
|
||
| Chichester ; ; New York, : Wiley, c1999 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Shape and shape theory [[electronic resource] /] / D.G. Kendall ... [et al.]
| Shape and shape theory [[electronic resource] /] / D.G. Kendall ... [et al.] |
| Autore | Kendall D. G (David George), <1918-2007.> |
| Pubbl/distr/stampa | Chichester ; ; New York, : Wiley, c1999 |
| Descrizione fisica | 1 online resource (328 p.) |
| Disciplina | 514.24 |
| Altri autori (Persone) | KendallD. G <1918-2007.> (David George) |
| Collana | Wiley series in probability and statistics |
| Soggetto topico |
Shape theory (Topology)
Topological spaces |
| ISBN |
1-282-30738-X
9786612307386 0-470-31700-0 0-470-31784-1 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
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 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 |
| Record Nr. | UNINA-9910829937303321 |
|
Kendall D. G (David George), <1918-2007.>
|
||
| Chichester ; ; New York, : Wiley, c1999 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Shape and shape theory / / D.G. Kendall ... [et al.]
| Shape and shape theory / / D.G. Kendall ... [et al.] |
| Autore | Kendall D. G (David George), <1918-2007.> |
| Pubbl/distr/stampa | Chichester ; ; New York, : Wiley, c1999 |
| Descrizione fisica | 1 online resource (328 p.) |
| Disciplina | 514/.24 |
| Collana | Wiley series in probability and statistics |
| Soggetto topico |
Shape theory (Topology)
Topological spaces |
| ISBN |
1-282-30738-X
9786612307386 0-470-31700-0 0-470-31784-1 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
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 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 |
| Record Nr. | UNINA-9910877287003321 |
|
Kendall D. G (David George), <1918-2007.>
|
||
| Chichester ; ; New York, : Wiley, c1999 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||