Spectral Geometry Of Shapes

Author : Jing Hua,Zichun Zhong
Publisher : Academic Press
Page : 152 pages
File Size : 44,7 Mb
Release : 2020-01-15
Category : Computers
ISBN : 9780128138427

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Spectral Geometry of Shapes by Jing Hua,Zichun Zhong Pdf

Spectral Geometry of Shapes presents unique shape analysis approaches based on shape spectrum in differential geometry. It provides insights on how to develop geometry-based methods for 3D shape analysis. The book is an ideal learning resource for graduate students and researchers in computer science, computer engineering and applied mathematics who have an interest in 3D shape analysis, shape motion analysis, image analysis, medical image analysis, computer vision and computer graphics. Due to the rapid advancement of 3D acquisition technologies there has been a big increase in 3D shape data that requires a variety of shape analysis methods, hence the need for this comprehensive resource. Presents the latest advances in spectral geometric processing for 3D shape analysis applications, such as shape classification, shape matching, medical imaging, etc. Provides intuitive links between fundamental geometric theories and real-world applications, thus bridging the gap between theory and practice Describes new theoretical breakthroughs in applying spectral methods for non-isometric motion analysis Gives insights for developing spectral geometry-based approaches for 3D shape analysis and deep learning of shape geometry

Author : Antoine Henrot
Publisher : De Gruyter Open
Page : 0 pages
File Size : 40,6 Mb
Release : 2017
Category : Mathematics
ISBN : 3110550881

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Shape Optimization and Spectral Theory by Antoine Henrot Pdf

"Shape optimization and spectral theory" is a survey book aiming to give an overview of recent results in spectral geometry and its links with shape optimization. It covers most of the issues which are important for people working in PDE and differential geometry interested in sharp inequalities and qualitative behaviour for eigenvalues of the Laplacian with different kind of boundary conditions (Dirichlet, Robin and Steklov). This includes: existence of optimal shapes, their regularity, the case of special domains like triangles, isospectrality, quantitative form of the isoperimetric inequalities, optimal partitions, universal inequalities and numerical results. Much progress has been made in these extremum problems during the last ten years and this edited volume presents a valuable update to a wide community interested in these topics. List of contributors Antunes Pedro R.S., Ashbaugh Mark, Bonnaillie-Noël Virginie, Brasco Lorenzo, Bucur Dorin, Buttazzo Giuseppe, De Philippis Guido, Freitas Pedro, Girouard Alexandre, Helffer Bernard, Kennedy James, Lamboley Jimmy, Laugesen Richard S., Oudet Edouard, Pierre Michel, Polterovich Iosif, Siudeja Bartlomiej A., Velichkov Bozhidar

Author : Pierre H. Berard
Publisher : Unknown
Page : 292 pages
File Size : 41,9 Mb
Release : 2014-01-15
Category : Electronic
ISBN : 3662162350

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Spectral Geometry by Pierre H. Berard Pdf

Author : Michael Levitin,Dan Mangoubi,Iosif Polterovich
Publisher : American Mathematical Society
Page : 346 pages
File Size : 55,6 Mb
Release : 2023-11-30
Category : Mathematics
ISBN : 9781470475253

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Topics in Spectral Geometry by Michael Levitin,Dan Mangoubi,Iosif Polterovich Pdf

It is remarkable that various distinct physical phenomena, such as wave propagation, heat diffusion, electron movement in quantum mechanics, oscillations of fluid in a container, can be described using the same differential operator, the Laplacian. Spectral data (i.e., eigenvalues and eigenfunctions) of the Laplacian depend in a subtle way on the geometry of the underlying object, e.g., a Euclidean domain or a Riemannian manifold, on which the operator is defined. This dependence, or, rather, the interplay between the geometry and the spectrum, is the main subject of spectral geometry. Its roots can be traced to Ernst Chladni's experiments with vibrating plates, Lord Rayleigh's theory of sound, and Mark Kac's celebrated question “Can one hear the shape of a drum?” In the second half of the twentieth century spectral geometry emerged as a separate branch of geometric analysis. Nowadays it is a rapidly developing area of mathematics, with close connections to other fields, such as differential geometry, mathematical physics, partial differential equations, number theory, dynamical systems, and numerical analysis. This book can be used for a graduate or an advanced undergraduate course on spectral geometry, starting from the basics but at the same time covering some of the exciting recent developments which can be explained without too many prerequisites.

Author : Robert Brooks,Carolyn Gordon,Peter A. Perry
Publisher : American Mathematical Soc.
Page : 299 pages
File Size : 52,8 Mb
Release : 1994
Category : Mathematics
ISBN : 9780821851852

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Geometry of the Spectrum by Robert Brooks,Carolyn Gordon,Peter A. Perry Pdf

Spectral geometry runs through much of contemporary mathematics, drawing on and stimulating developments in such diverse areas as Lie algebras, graph theory, group representation theory, and Riemannian geometry. The aim is to relate the spectrum of the Laplace operator or its graph-theoretic analogue, the adjacency matrix, to underlying geometric and topological data. This volume brings together papers presented at the AMS-IMS-SIAM Joint Summer Research Conference on Spectral Geometry, held in July 1993 at the University of Washington in Seattle. With contributions from some of the top experts in the field, this book presents an excellent overview of current developments in spectral geometry.

Author : Alex Barnett
Publisher : American Mathematical Soc.
Page : 339 pages
File Size : 50,5 Mb
Release : 2012
Category : Mathematics
ISBN : 9780821853191

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Spectral Geometry by Alex Barnett Pdf

This volume contains the proceedings of the International Conference on Spectral Geometry, held July 19-23, 2010, at Dartmouth College, Dartmouth, New Hampshire. Eigenvalue problems involving the Laplace operator on manifolds have proven to be a consistently fertile area of geometric analysis with deep connections to number theory, physics, and applied mathematics. Key questions include the measures to which eigenfunctions of the Laplacian on a Riemannian manifold condense in the limit of large eigenvalue, and the extent to which the eigenvalues and eigenfunctions of a manifold encode its geometry. In this volume, research and expository articles, including those of the plenary speakers Peter Sarnak and Victor Guillemin, address the flurry of recent progress in such areas as quantum unique ergodicity, isospectrality, semiclassical measures, the geometry of nodal lines of eigenfunctions, methods of numerical computation, and spectra of quantum graphs. This volume also contains mini-courses on spectral theory for hyperbolic surfaces, semiclassical analysis, and orbifold spectral geometry that prepared the participants, especially graduate students and young researchers, for conference lectures.

Author : Stig I. Andersson,Michel L. Lapidus
Publisher : Springer Science & Business Media
Page : 220 pages
File Size : 55,7 Mb
Release : 1997-10
Category : Mathematics
ISBN : 376435755X

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Progress in Inverse Spectral Geometry by Stig I. Andersson,Michel L. Lapidus Pdf

most polynomial growth on every half-space Re (z)::::: c. Moreover, Op(t) depends holomorphically on t for Re t > O. General references for much of the material on the derivation of spectral functions, asymptotic expansions and analytic properties of spectral functions are [A-P-S] and [Sh], especially Chapter 2. To study the spectral functions and their relation to the geometry and topology of X, one could, for example, take the natural associated parabolic problem as a starting point. That is, consider the 'heat equation': (%t + p) u(x, t) = 0 { u(x, O) = Uo(x), tP which is solved by means of the (heat) semi group V(t) = e-; namely, u(-, t) = V(t)uoU- Assuming that V(t) is of trace class (which is guaranteed, for instance, if P has a positive principal symbol), it has a Schwartz kernel K E COO(X x X x Rt, E* (R)E), locally given by 00 K(x, y; t) = L>-IAk( k (R) 'Pk)(X, y), k=O for a complete set of orthonormal eigensections 'Pk E COO(E). Taking the trace, we then obtain: 00 tA Op(t) = trace(V(t)) = 2:: >- k. k=O Now, using, e. g., the Dunford calculus formula (where C is a suitable curve around a(P)) as a starting point and the standard for- malism of pseudodifferential operators, one easily derives asymptotic expansions for the spectral functions, in this case for Op.

Author : E. Brian Davies,Yu Safarov,London Mathematical Society,International Centre for Mathematical Sciences
Publisher : Cambridge University Press
Page : 344 pages
File Size : 49,8 Mb
Release : 1999-09-30
Category : Mathematics
ISBN : 9780521777490

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Spectral Theory and Geometry by E. Brian Davies,Yu Safarov,London Mathematical Society,International Centre for Mathematical Sciences Pdf

This volume brings together lectures from an instructional meeting on spectral theory and geometry held under the auspices of the International Centre for Mathematical Sciences in Edinburgh. The contributions here come from world experts and many are much expanded versions of the lectures they gave. Together they survey the core material and go beyond to reach deeper results. For graduate students and experts alike, this book will be a highly useful resource.

Author : Anonim
Publisher : Elsevier
Page : 706 pages
File Size : 42,8 Mb
Release : 2019-10-16
Category : Mathematics
ISBN : 9780444641410

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Processing, Analyzing and Learning of Images, Shapes, and Forms: Part 2 by Anonim Pdf

Processing, Analyzing and Learning of Images, Shapes, and Forms: Part 2, Volume 20, surveys the contemporary developments relating to the analysis and learning of images, shapes and forms, covering mathematical models and quick computational techniques. Chapter cover Alternating Diffusion: A Geometric Approach for Sensor Fusion, Generating Structured TV-based Priors and Associated Primal-dual Methods, Graph-based Optimization Approaches for Machine Learning, Uncertainty Quantification and Networks, Extrinsic Shape Analysis from Boundary Representations, Efficient Numerical Methods for Gradient Flows and Phase-field Models, Recent Advances in Denoising of Manifold-Valued Images, Optimal Registration of Images, Surfaces and Shapes, and much more. Covers contemporary developments relating to the analysis and learning of images, shapes and forms Presents mathematical models and quick computational techniques relating to the topic Provides broad coverage, with sample chapters presenting content on Alternating Diffusion and Generating Structured TV-based Priors and Associated Primal-dual Methods

Author : Xue-Cheng Tai
Publisher : North Holland
Page : 704 pages
File Size : 49,8 Mb
Release : 2019-10
Category : Electronic
ISBN : 9780444641403

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Processing, Analyzing and Learning of Images, Shapes, and Forms: by Xue-Cheng Tai Pdf

Processing, Analyzing and Learning of Images, Shapes, and Forms: Part 2, Volume 20, surveys the contemporary developments relating to the analysis and learning of images, shapes and forms, covering mathematical models and quick computational techniques. Chapter cover Alternating Diffusion: A Geometric Approach for Sensor Fusion, Generating Structured TV-based Priors and Associated Primal-dual Methods, Graph-based Optimization Approaches for Machine Learning, Uncertainty Quantification and Networks, Extrinsic Shape Analysis from Boundary Representations, Efficient Numerical Methods for Gradient Flows and Phase-field Models, Recent Advances in Denoising of Manifold-Valued Images, Optimal Registration of Images, Surfaces and Shapes, and much more. Covers contemporary developments relating to the analysis and learning of images, shapes and forms Presents mathematical models and quick computational techniques relating to the topic Provides broad coverage, with sample chapters presenting content on Alternating Diffusion and Generating Structured TV-based Priors and Associated Primal-dual Methods

Author : Dr. Martin Concoyle
Publisher : Trafford Publishing
Page : 795 pages
File Size : 44,6 Mb
Release : 2014-01-16
Category : Education
ISBN : 9781490723716

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Partitioning a Many-Dimensional Containment Space by Dr. Martin Concoyle Pdf

This book is an introduction to the simple math patterns used to describe fundamental, stable, spectral-orbital physical systems (represented as discrete hyperbolic shapes). The containment set has many dimensions, and these dimensions possess macroscopic geometric properties (which are discrete hyperbolic shapes). Thus, it is a description that transcends the idea of materialism (i.e., it is higher-dimensional), and it can also be used to model a life-form as a unified, high-dimension, geometric construct, which generates its own energy and which has a natural structure for memory, where this construct is made in relation to the main property of the description being the spectral properties of both material systems and of the metric-spaces that contain the material systems, where material is simply a lower dimension metric-space and where both material components and metric-spaces are in resonance with the containing space.

Author : Douglas D Hunter
Publisher : Trafford Publishing
Page : 970 pages
File Size : 49,6 Mb
Release : 2006-12-22
Category : Philosophy
ISBN : 9781412240437

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The Authority of Material Vs. the Spirit by Douglas D Hunter Pdf

A new mathematically-based structure for language allows for a new context with which one can make verifiable predictions about: material, life, mind, and the spiritual intent of (creative) existence.

Author : Peter B. Gilkey
Publisher : Unknown
Page : 128 pages
File Size : 51,7 Mb
Release : 1995
Category : Electronic
ISBN : 0849378710

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Spectral Geometry by Peter B. Gilkey Pdf

Author : Peter B. Gilkey
Publisher : Unknown
Page : 90 pages
File Size : 46,8 Mb
Release : 1993
Category : Differential geometry
ISBN : UOM:39015037459982

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Applications of Spectral Geometry to Geometry and Topology by Peter B. Gilkey Pdf

Author : Dmitri Fursaev,Dmitri Vassilevich
Publisher : Springer
Page : 288 pages
File Size : 49,7 Mb
Release : 2011-07-02
Category : Science
ISBN : 940070206X

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Operators, Geometry and Quanta by Dmitri Fursaev,Dmitri Vassilevich Pdf

This book gives a detailed and self-contained introduction into the theory of spectral functions, with an emphasis on their applications to quantum field theory. All methods are illustrated with applications to specific physical problems from the forefront of current research, such as finite-temperature field theory, D-branes, quantum solitons and noncommutativity. In the first part of the book, necessary background information on differential geometry and quantization, including less standard material, is collected. The second part of the book contains a detailed description of main spectral functions and methods of their calculation. In the third part, the theory is applied to several examples (D-branes, quantum solitons, anomalies, noncommutativity). This book addresses advanced graduate students and researchers in mathematical physics with basic knowledge of quantum field theory and differential geometry. The aim is to prepare readers to use spectral functions in their own research, in particular in relation to heat kernels and zeta functions.