2012, VIII, 268 p. 20 illus.
ISBN 978-0-8176-8270-5
Due: December 28, 2011
Introduces differentiable manifolds using a theoretical physics approach; unique book in the literature
Provides a collection of exercises of varying degrees of difficulty
Includes applications to differential geometry and general relativity
This textbook gives a concise introduction to the theory of differentiable manifolds, focusing on their applications to differential equations, differential geometry, and Hamiltonian mechanics.
The work’s first three chapters introduce the basic concepts of the theory, such as differentiable maps, tangent vectors, vector and tensor fields, differential forms, local one-parameter groups of diffeomorphisms, and Lie derivatives. These tools are subsequently employed in the study of differential equations (Chapter 4), connections (Chapter 5), Riemannian manifolds (Chapter 6), Lie groups (Chapter 7), and Hamiltonian mechanics (Chapter 8). Throughout, the book contains examples, worked out in detail, as well as exercises intended to show how the formalism is applied to actual computations and to emphasize the connections among various areas of mathematics.
Differentiable Manifolds is addressed to advanced undergraduate or beginning graduate students in mathematics or physics. Prerequisites include multivariable calculus, linear algebra, differential equations, and (for the last chapter) a basic knowledge of analytical mechanics.
Content Level ≫ Graduate
Keywords ≫ Euler equations - Hamiltonian mechanics - Lie derivatives - Riemannian manifolds - differentiable manifolds - differential forms - time-dependent formalism
Related subjects ≫ Birkhauser Mathematics - Birkhauser Physics
Preface.-1 Manifolds.- 2 Lie Derivatives.- 3 Differential Forms.- 4 Integral Manifolds.- 5 Connections .- 6. Riemannian Manifolds.- 7 Lie Groups.- 8 Hamiltonian Classical Mechanics.- References.-Index.
Series: Progress in Mathematics, Vol. 295
2012, XX, 230 p. 1 illus.
ISBN 978-0-8176-8273-6
Due: December 28, 2011
.An outgrowth of a two-week summer session at Jacobs University in Bremen,
Germany in 2009 ("Structures in Lie Theory, Crystals, Derived Functors,
Harish?Chandra Modules, Invariants and Quivers"), this volume consists
of expository and research articles that highlight the various Lie algebraic
methods used in mathematical research today. Key topics discussed include
spherical varieties, Littelmann Paths and Kac-Moody Lie algebras, finite
W-algebras, modular representations and primitive ideals, representation
theory of Artin algebras and quivers, Kac-Moody superalgebras, categories
of Harish?Chandra modules, cohomological methods, and cluster algebras.
Content Level ≫ Research
Keywords ≫ Kac?Moody superalgebras - Lie algebraic methods - representation theory - spherical varieties - vertex algebras
Related subjects ≫ Birkhauser Mathematics
Preface.- Part I: The Courses.- 1 Spherical Varieties.- 2 Consequences of the Littelmann Path Model for the Structure of the Kashiwara B(∞) Crystal.- 3 Structure and Representation Theory of Kac?Moody Superalgebras.- 4 Categories of Harish?Chandra Modules.- 5 Generalized Harish?Chandra Modules.- Part II: The Papers.- 6 B-Orbits of 2-Nilpotent Matrices.- 7 The Weyl Denominator Identity for Finite-Dimensional Lie Superalgebras.- 8 Hopf Algebras and Frobenius Algebras in Finite Tensor Categories.- 9 Mutation Classes of 3 x 3 Generalized Cartan Matrices.- 10 Contractions and Polynomial Lie Algebras.
Sries: Applied Mathematical Sciences, Vol. 179
2011, 400 p.
Hardcover, ISBN 978-0-387-87713-6
Due: October 20, 2011
This book contains the description of basic models of interfacial convection used on different spatial scales. It presents a variety of physical mechanisms and types of instability characteristic for liquid systems with interfaces. The book summarizes results obtained in the field of interfacial convection during a number of decades, including recent developments in exploration of microfluidic convective flows.
Mathematicians, physicists and engineers working in the field of fluid dynamics would find this book helpful to understand the mechanical approaches which are used for studying convective flows and to understand the underlying physical phenomena.
This new edition includes significant progress achieved in studying phenomena in ultra-thin films, in systems with phase transitions, multicomponent systems, and nanosuspensions.
Introduction.- Types of convective instabilities in systems with an interface.- Benard problem in multilayer systems with undeformable interfaces.- Benard problem in multilayer systems with deformable interfaces.- Stability of flows.- Outlook.
Published 15th March 2012 by CRC Press 420 pages
Series: Chapman & Hall/CRC Monographs on Statistics & Applied Probability
Hardback: 978-1-4398205-0-6:
Description
Requiring only a background in mathematical statistics or analysis, this book provides the first comprehensive look at the statistics of manifolds. It presents location and spread parameters for distribution on manifolds, followed by key large sample theory results. The text also addresses inference of two samples, nonparametric MANOVA, principal component analysis, and density estimation on manifolds. A special section is dedicated to a nonparametric statistical analysis on certain special manifolds arising in statistics. The final part of the text focuses on concrete applications in astronomy, image analysis, medical imaging, bioinformatics, and pattern recognition.
Published 15th April 2012 by Chapman & Hall
Hardback: 978-1-4398574-2-7
This text emphasizes the special functions that are used in complex analysis. Starting with the algebraic system of complex numbers, it offers an entry-level course on complex analysis of one variable. It presents the study of analytic functions, conformal mapping, analysis of singularities, and the computation of various integrals. The final three chapters introduce more advanced topics and applications. The book provides examples of applications to various physical problems and explains how to use MathematicaR, Maple?, and MATLAB
This monograph strives to introduce a solid foundation on the usage of Grobner bases in ring theory by focusing on noncommutative associative algebras defined by relations over a field K. It also reveals the intrinsic structural properties of Grobner bases, presents a constructive PBW theory in a quite extensive context and, along the routes built via the PBW theory, the book demonstrates novel methods of using Grobner bases in determining and recognizing many more structural properties of algebras, such as the Gelfand?Kirillov dimension, Noetherianity, (semi-)primeness, PI-property, finiteness of global homological dimension, Hilbert series, (non-)homogeneous p-Koszulity, PBW-deformation, and regular central extension.
With a self-contained and constructive Grobner basis theory for algebras with a skew multiplicative K-basis, numerous illuminating examples are constructed in the book for illustrating and extending the topics studied. Moreover, perspectives of further study on the topics are prompted at appropriate points. This book can be of considerable interest to researchers and graduate students in computational (computer) algebra, computational (noncommutative) algebraic geometry; especially for those working on the structure theory of rings, algebras and their modules (representations).
The Γ-Leading Homogeneous Algebra AΓLH
Grobner Bases: Conception and Construction
Grobner Basis Theory Meets PBW Theory
Using ABLH in Terms of Grobner Bases
Recognizing (Non-)Homogeneous p-Koszulity via ABLH
A Study of Rees Algebra by Grobner Bases
Looking for More Grobner Bases
Researchers and graduate students in computational (computer) algebra, computational (noncommutative) algebraic geometry.
295pp (approx.) Pub. date: Aug 2011
ISBN: 978-981-4365-13-0
981-4365-13-0