Groups and Geometric Analysis: Integral Geometry, Invariant Differential Operators, and Spherical Functions, Sigurdur Helgason
Автор: Gilkey, Peter B. Название: Geometry of spherical space form groups, the ISBN: 9813220783 ISBN-13(EAN): 9789813220782 Издательство: World Scientific Publishing Рейтинг: Цена: 26928.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание:
This volume focuses on discussing the interplay between the analysis, as exemplified by the eta invariant and other spectral invariants, the number theory, as exemplified by the relevant Dedekind sums and Rademacher reciprocity, the algebraic topology, as exemplified by the equivariant bordism groups, K-theory groups, and connective K-theory groups, and the geometry of spherical space forms, as exemplified by the Smith homomorphism. These are used to study the existence of metrics of positive scalar curvature on spin manifolds of dimension at least 5 whose fundamental group is a spherical space form group.
This volume is a completely rewritten revision of the first edition. The underlying organization is modified to provide a better organized and more coherent treatment of the material involved. In addition, approximately 100 pages have been added to study the existence of metrics of positive scalar curvature on spin manifolds of dimension at least 5 whose fundamental group is a spherical space form group. We have chosen to focus on the geometric aspect of the theory rather than more abstract algebraic constructions (like the assembly map) and to restrict our attention to spherical space forms rather than more general and more complicated geometrical examples to avoid losing contact with the fundamental geometry which is involved.
Автор: Yang, Lei (peking Univ, China) Название: Hessian polyhedra, invariant theory and appell hypergeometric functions ISBN: 981320947X ISBN-13(EAN): 9789813209473 Издательство: World Scientific Publishing Рейтинг: Цена: 21384.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание:
Our book gives the complex counterpart of Klein's classic book on the icosahedron. We show that the following four apparently disjoint theories: the symmetries of the Hessian polyhedra (geometry), the resolution of some system of algebraic equations (algebra), the system of partial differential equations of Appell hypergeometric functions (analysis) and the modular equation of Picard modular functions (arithmetic) are in fact dominated by the structure of a single object, the Hessian group ����′216. It provides another beautiful example on the fundamental unity of mathematics.
Описание: The book presents integral formulations for partial differential equations, with the focus on spherical and plane integral operators. The integral relations are obtained for different elliptic and parabolic equations, and both direct and inverse mean value relations are studied. The derived integral equations are used to construct new numerical methods for solving relevant boundary value problems, both deterministic and stochastic based on probabilistic interpretation of the spherical and plane integral operators.
Exact Solutions and Invariant Subspaces of Nonlinear Partial Differential Equations in Mechanics and Physics is the first book to provide a systematic construction of exact solutions via linear invariant subspaces for nonlinear differential operators. Acting as a guide to nonlinear evolution equations and models from physics and mechanics, the book focuses on the existence of new exact solutions on linear invariant subspaces for nonlinear operators and their crucial new properties.
This practical reference deals with various partial differential equations (PDEs) and models that exhibit some common nonlinear invariant features. It begins with classical as well as more recent examples of solutions on invariant subspaces. In the remainder of the book, the authors develop several techniques for constructing exact solutions of various nonlinear PDEs, including reaction-diffusion and gas dynamics models, thin-film and Kuramoto-Sivashinsky equations, nonlinear dispersion (compacton) equations, KdV-type and Harry Dym models, quasilinear magma equations, and Green-Naghdi equations. Using exact solutions, they describe the evolution properties of blow-up or extinction phenomena, finite interface propagation, and the oscillatory, changing sign behavior of weak solutions near interfaces for nonlinear PDEs of various types and orders. The techniques surveyed in Exact Solutions and Invariant Subspaces of Nonlinear Partial Differential Equations in Mechanics and Physics serve as a preliminary introduction to the general theory of nonlinear evolution PDEs of different orders and types.
Автор: Crabb Название: The Geometric Hopf Invariant and Surgery Theory ISBN: 3319713051 ISBN-13(EAN): 9783319713052 Издательство: Springer Рейтинг: Цена: 19564.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: Written by leading experts in the field, this monograph provides homotopy theoretic foundations for surgery theory on higher-dimensional manifolds. Presenting classical ideas in a modern framework, the authors carefully highlight how their results relate to (and generalize) existing results in the literature.
Автор: Wallach, Nolan R. Название: Geometric invariant theory ISBN: 3319659057 ISBN-13(EAN): 9783319659053 Издательство: Springer Рейтинг: Цена: 8384.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: Geometric Invariant Theory (GIT) is developed in this text within the context of algebraic geometry over the real and complex numbers. It contains two chapters developing material in complex and real algebraic geometry and algebraic groups that are difficult to find in the literature.
Автор: Mumford, David Fogarty, John Kirwan, Frances Название: Geometric invariant theory ISBN: 3642634001 ISBN-13(EAN): 9783642634000 Издательство: Springer Рейтинг: Цена: 19564.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: This standard reference on applications of invariant theory to the construction of moduli spaces is a systematic exposition of the geometric aspects of classical theory of polynomial invariants. This new, revised edition is completely updated and enlarged with an additional chapter on the moment map by Professor Frances Kirwan.
Автор: Claus M?ller Название: Analysis of Spherical Symmetries in Euclidean Spaces ISBN: 0387949496 ISBN-13(EAN): 9780387949499 Издательство: Springer Рейтинг: Цена: 21661.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: Offers a fresh and direct approach to the theories of special functions with emphasis on spherical symmetry in Euclidean spaces of arbitrary dimensions. This work uses elementary concepts to present the spherical harmonics in a theory of invariants of the orthogonal group. It is particularly important for the complexification of the Funk-Hecke.
Автор: Efthimiou Costas Et Al Название: Spherical Harmonics In P Dimensions ISBN: 9814596698 ISBN-13(EAN): 9789814596695 Издательство: World Scientific Publishing Рейтинг: Цена: 9821.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: The current book makes several useful topics from the theory of special functions, in particular the theory of spherical harmonics and Legendre polynomials in arbitrary dimensions, available to undergraduates studying physics or mathematics. With this audience in mind, nearly all details of the calculations and proofs are written out, and extensive background material is covered before exploring the main subject matter.
Автор: Gilberto Bini; Fabio Felici; Margarida Melo; Filip Название: Geometric Invariant Theory for Polarized Curves ISBN: 3319113364 ISBN-13(EAN): 9783319113364 Издательство: Springer Рейтинг: Цена: 4890.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание:
Introduction.- Singular Curves.- Combinatorial Results.- Preliminaries on GIT.- Potential Pseudo-stability Theorem.- Stabilizer Subgroups.- Behavior at the Extremes of the Basic Inequality.- A Criterion of Stability for Tails.- Elliptic Tails and Tacnodes with a Line.- A Strati_cation of the Semistable Locus.- Semistable, Polystable and Stable Points (part I).- Stability of Elliptic Tails.- Semistable, Polystable and Stable Points (part II).- Geometric Properties of the GIT Quotient.- Extra Components of the GIT Quotient.- Compacti_cations of the Universal Jacobian.- Appendix: Positivity Properties of Balanced Line Bundles.
Автор: Simon Hubbert; Qu?c Th?ng Le Gia; Tanya M. Morton Название: Spherical Radial Basis Functions, Theory and Applications ISBN: 3319179381 ISBN-13(EAN): 9783319179384 Издательство: Springer Рейтинг: Цена: 6986.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: This book is the first to be devoted to the theory and applications of spherical (radial) basis functions (SBFs), which is rapidly emerging as one of the most promising techniques for solving problems where approximations are needed on the surface of a sphere.
Описание: Preface.- Introduction.- Preliminaries.- Geometric Invariant Theory.- Moduli Space of Vector Bundles.- Unstability Correspondence.- Stratifications on the Moduli Space of Higgs Bundles.- References.- Index.
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