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Author : Francesco Maggi
Publisher : Cambridge University Press
Page : 475 pages
File Size : 41,7 Mb
Release : 2012-08-09
Category : Mathematics
ISBN : 9781107021037
An engaging graduate-level introduction that bridges analysis and geometry. Suitable for self-study and a useful reference for researchers.
Author : Francesco Maggi
Publisher : Cambridge University Press
Page : 475 pages
File Size : 43,5 Mb
Release : 2012-08-09
Category : Mathematics
ISBN : 9781139560894
The marriage of analytic power to geometric intuition drives many of today's mathematical advances, yet books that build the connection from an elementary level remain scarce. This engaging introduction to geometric measure theory bridges analysis and geometry, taking readers from basic theory to some of the most celebrated results in modern analysis. The theory of sets of finite perimeter provides a simple and effective framework. Topics covered include existence, regularity, analysis of singularities, characterization and symmetry results for minimizers in geometric variational problems, starting from the basics about Hausdorff measures in Euclidean spaces and ending with complete proofs of the regularity of area-minimizing hypersurfaces up to singular sets of codimension 8. Explanatory pictures, detailed proofs, exercises and remarks providing heuristic motivation and summarizing difficult arguments make this graduate-level textbook suitable for self-study and also a useful reference for researchers. Readers require only undergraduate analysis and basic measure theory.
Author : Andrea Braides,Margherita Solci
Publisher : Springer Nature
Page : 134 pages
File Size : 43,7 Mb
Release : 2021-03-23
Category : Mathematics
ISBN : 9783030699178
This book introduces the reader to important concepts in modern applied analysis, such as homogenization, gradient flows on metric spaces, geometric evolution, Gamma-convergence tools, applications of geometric measure theory, properties of interfacial energies, etc. This is done by tackling a prototypical problem of interfacial evolution in heterogeneous media, where these concepts are introduced and elaborated in a natural and constructive way. At the same time, the analysis introduces open issues of a general and fundamental nature, at the core of important applications. The focus on two-dimensional lattices as a prototype of heterogeneous media allows visual descriptions of concepts and methods through a large amount of illustrations.
Author : Washek F. Pfeffer
Publisher : CRC Press
Page : 259 pages
File Size : 52,9 Mb
Release : 2016-02-03
Category : Mathematics
ISBN : 9781466507210
This book is devoted to a detailed development of the divergence theorem. The framework is that of Lebesgue integration- no generalized Riemann integrals of Henstock-Kurzweil variety are involved.In Part I the divergence theorem is established by a combinatorial argument involving dyadic cubes. Only elementary properties of the Lebesgue integral an
Author : Abderrahim Elmoataz,Jalal Fadili,Yvain Quéau,Julien Rabin,Loïc Simon
Publisher : Springer Nature
Page : 584 pages
File Size : 43,9 Mb
Release : 2021-04-29
Category : Computers
ISBN : 9783030755492
This book constitutes the proceedings of the 8th International Conference on Scale Space and Variational Methods in Computer Vision, SSVM 2021, which took place during May 16-20, 2021. The conference was planned to take place in Cabourg, France, but changed to an online format due to the COVID-19 pandemic. The 45 papers included in this volume were carefully reviewed and selected from a total of 64 submissions. They were organized in topical sections named as follows: scale space and partial differential equations methods; flow, motion and registration; optimization theory and methods in imaging; machine learning in imaging; segmentation and labelling; restoration, reconstruction and interpolation; and inverse problems in imaging.
Author : M. P. Brodmann,R. Y. Sharp
Publisher : Cambridge University Press
Page : 128 pages
File Size : 45,8 Mb
Release : 2012-11-15
Category : Mathematics
ISBN : 9781139788649
This second edition of a successful graduate text provides a careful and detailed algebraic introduction to Grothendieck's local cohomology theory, including in multi-graded situations, and provides many illustrations of the theory in commutative algebra and in the geometry of quasi-affine and quasi-projective varieties. Topics covered include Serre's Affineness Criterion, the Lichtenbaum–Hartshorne Vanishing Theorem, Grothendieck's Finiteness Theorem and Faltings' Annihilator Theorem, local duality and canonical modules, the Fulton–Hansen Connectedness Theorem for projective varieties, and connections between local cohomology and both reductions of ideals and sheaf cohomology. The book is designed for graduate students who have some experience of basic commutative algebra and homological algebra and also experts in commutative algebra and algebraic geometry. Over 300 exercises are interspersed among the text; these range in difficulty from routine to challenging, and hints are provided for some of the more difficult ones.
Author : Velimir Jurdjevic
Publisher : Cambridge University Press
Page : 437 pages
File Size : 51,8 Mb
Release : 2016-07-04
Category : Mathematics
ISBN : 9781107113886
Blending control theory, mechanics, geometry and the calculus of variations, this book is a vital resource for graduates and researchers in engineering, mathematics and physics.
Author : Dorina Mitrea,Irina Mitrea,Marius Mitrea
Publisher : Springer Nature
Page : 940 pages
File Size : 41,9 Mb
Release : 2022-11-04
Category : Mathematics
ISBN : 9783031059506
This monograph presents a comprehensive, self-contained, and novel approach to the Divergence Theorem through five progressive volumes. Its ultimate aim is to develop tools in Real and Harmonic Analysis, of geometric measure theoretic flavor, capable of treating a broad spectrum of boundary value problems formulated in rather general geometric and analytic settings. The text is intended for researchers, graduate students, and industry professionals interested in applications of harmonic analysis and geometric measure theory to complex analysis, scattering, and partial differential equations. Volume I establishes a sharp version of the Divergence Theorem (aka Fundamental Theorem of Calculus) which allows for an inclusive class of vector fields whose boundary trace is only assumed to exist in a nontangential pointwise sense.
Author : Robin Pemantle,Mark C. Wilson
Publisher : Cambridge University Press
Page : 395 pages
File Size : 48,9 Mb
Release : 2013-05-31
Category : Mathematics
ISBN : 9781107031579
Aimed at graduate students and researchers in enumerative combinatorics, this book is the first to treat the analytic aspects of combinatorial enumeration from a multivariate perspective.
Author : R. M. Dudley
Publisher : Cambridge University Press
Page : 485 pages
File Size : 46,5 Mb
Release : 2014-02-24
Category : Mathematics
ISBN : 9780521498845
This expanded edition of the classic work on empirical processes now boasts several new proved theorems not in the first.
Author : Ivan Arzhantsev
Publisher : Cambridge University Press
Page : 539 pages
File Size : 52,6 Mb
Release : 2015
Category : Mathematics
ISBN : 9781107024625
This book provides a largely self-contained introduction to Cox rings and their applications in algebraic and arithmetic geometry.
Author : Bodil Branner,Núria Fagella
Publisher : Cambridge University Press
Page : 433 pages
File Size : 51,6 Mb
Release : 2014-01-23
Category : Mathematics
ISBN : 9781107042919
A comprehensive introduction to quasiconformal surgery in holomorphic dynamics. Contains a wide variety of applications and illustrations.
Author : Amritanshu Prasad
Publisher : Cambridge University Press
Page : 205 pages
File Size : 40,7 Mb
Release : 2015-02-05
Category : Mathematics
ISBN : 9781107082052
This book examines the fundamental results of modern combinatorial representation theory. The exercises are interspersed with text to reinforce readers' understanding of the subject. In addition, each exercise is assigned a difficulty level to test readers' learning. Solutions and hints to most of the exercises are provided at the end.
Author : Juan José Marín,José María Martell,Dorina Mitrea,Irina Mitrea,Marius Mitrea
Publisher : Springer Nature
Page : 605 pages
File Size : 41,9 Mb
Release : 2022-09-29
Category : Mathematics
ISBN : 9783031082344
This monograph provides a state-of-the-art, self-contained account on the effectiveness of the method of boundary layer potentials in the study of elliptic boundary value problems with boundary data in a multitude of function spaces. Many significant new results are explored in detail, with complete proofs, emphasizing and elaborating on the link between the geometric measure-theoretic features of an underlying surface and the functional analytic properties of singular integral operators defined on it. Graduate students, researchers, and professionals interested in a modern account of the topic of singular integral operators and boundary value problems – as well as those more generally interested in harmonic analysis, PDEs, and geometric analysis – will find this text to be a valuable addition to the mathematical literature.
Author : Marcelo Viana
Publisher : Cambridge University Press
Page : 217 pages
File Size : 40,7 Mb
Release : 2014-07-24
Category : Mathematics
ISBN : 9781107081734
Covers the fundamental aspects of the classical theory and introduces significant recent developments. Based on the author's graduate course.
