Hardcover
ISBN 978-3-11-022612-6
Series: [de Gruyter Proceedings in Mathematics]
to be published October 2010
This volume contains the proceedings of the conference "Casimir Force, Casimir Operators and the Riemann Hypothesis * Mathematics for Innovation in Industry and Science" held in November 2009 in Fukuoka (Japan). The motive for the conference was the celebration of the 100th birthday of Casimir and the 150th birthday of the Riemann hypothesis.
The conference focused on the following topics:
Casimir operators in harmonic analysis and representation theory
Number theory, in particular zeta functions and cryptography
Casimir force in physics and its relation with nano-science
Mathematical biology
Importance of mathematics for innovation in industry
The latter topic was inspired both by the call for innovation in industry worldwide and by the fact that Casimir, who was the director of Philips research for a long time in his career, had an outspoken opinion on the importance of fundamental science for industry.
These proceedings are of interest both to research mathematicians and to those interested in the role science, and in particular mathematics, can play in innovation in industry.
Hardcover
ISBN 978-3-11-025020-6
Series: de Gruyter Series in Nonlinear Analysis and Applications 13
to be published December 2010
Discussion of stability questions for optimization problems provides new insights and opens up new ways of dealing with applications.
Local uniform convexity of a convex function turns out to be equivalent to strong solvability of corresponding convex optimization problems.
New analysis shows that a reflexive and strictly convex Orlicz space is already an E-space.
New application of the uniform boundedness principle of Banach together with the Banach-Steinhaus theorem, both extended to families of convex functions.
This is an essentially self-contained book on the theory of convex functions and convex optimization in Banach spaces, with a special interest in Orlicz spaces. It is as well suited for students of the second half of undergraduate studies focusing on approximate algorithms based on the stability principles developed in this text and the solution of the corresponding nonlinear equations, as also it provides a rich set of material for a master course on linear and nonlinear functional analysis.
Additionally it offers novel aspects for the specialist: a synopsis of the geometry of Banach spaces, aspects of stability and the duality of different levels of differentiability and convexity. And it provides a novel approach to the fundamental theorems of Variational Calculus based on the principle of pointwise minimization of the Lagrangian on the one hand and convexification by quadratic supplements using the classical Legendre-Ricatti equation on the other.
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2009; 347 pp; hardcover
ISBN-13: 978-81-85931-94-4
This is part one of a two-volume introduction to real analysis and is intended for honours undergraduates who have already been exposed to calculus. The emphasis is on rigour and on foundations. The material starts at the very beginning--the construction of the number systems and set theory--then goes on to the basics of analysis (limits, series, continuity, differentiation, Riemann integration), through to power series, several variable calculus and Fourier analysis, and finally to the Lebesgue integral. These are almost entirely set in the concrete setting of the real line and Euclidean spaces, although there is some material on abstract metric and topological spaces. There are also appendices on mathematical logic and the decimal system. The entire text (omitting some less central topics) can be taught in two quarters of twenty-five to thirty lectures each.
The course material is deeply intertwined with the exercises, as it is intended that the student actively learn the material (and practice thinking and writing rigorously) by proving several of the key results in the theory.
In the second edition, several typos and other errors have been corrected.
Volume 1
*Introduction
*Starting at the beginning: The natural numbers
*Set theory
*Integers and rationals
*The real numbers
*Limits of sequences
*Series
*Infinite sets
*Continuous functions on mathbf{R}
*Differentiation of functions
*The Riemann integral
*Appendix A: The basics of mathematical logic
*Appendix B: The decimal system
Tata Institute of Fundamental Research
2010; 540 pp; hardcover
ISBN-13: 978-81-8487-085-5
Expected publication date is August 20, 2010.
This is the proceedings of the International Colloquium organized by the Tata Institute of Fundamental Research in January 2008, one of a series of colloquia going back to 1956. It covers a wide spectrum of mathematics, ranging over algebraic geometry, topology, automorphic forms, and number theory.
Algebraic cycles form the basis for the construction of motives, and conjectures about motives depend ultimately on important problems related to algebraic cycles, such as the Hodge and the Tate conjectures. Shimura varieties provide interesting, nontrivial instances of these fundamental problems. On the other hand, the motives of Shimura varieties are of great interest in automorphic forms and number theory.
This volume features refereed articles by leading experts in these fields. The articles contain original results as well as expository material.
Graduate students and research mathematicians interested in cycles, motives, and Shimura varieties.
* D. Arapura -- Mixed Hodge structures associated to geometric variations
* M. Asakura and K. Sato -- Beilinson's Tate conjecture for K_2 of elliptic surface: Survey and examples
* E. Ghate -- On the freeness of the integral cohomology groups of Hilbert-Blumenthal varieties as Hecke modules
* P. Griffiths -- Singularities of admissible normal functions
* G. Harder -- Arithmetic aspects of rank one Eisenstein cohomology
* K. Kimura -- A remark on the second Abel-Jacobi map
* A. Krishna and V. Srinivas -- Zero cycles on singular affine varieties
* M. Levine -- Tate motives and the fundamental group
* S.-J. Kang and J. D. Lewis -- Beilinson's Hodge conjecture for K_{1} revisited
* S. Kimura and J. P. Murre -- On natural isomorphisms of finite dimensional motives and applications to the Picard motives
* A. Miller -- Chow motives of mixed Shimura varieties
* A. Neeman -- Dualizing complexes--the modern way
* A. Rosenschon and V. Srinivas -- The Griffiths group of the generic abelian 3-fold
* R. Sreekantan -- Non-Archimedean regulator maps and special values of L-functions
* T. Terasoma -- The Artin-Schreier DGA and the \mathbf{F}_p-fundamental group of an \mathbf{F}_p scheme
Publication Details
Advanced Lectures in Mathematics, Vol. 13
Softcover. 431 pages. 4 pages of color photographs.
ISBN: 978-1-57146-204-6
Published: August 2010
Full Description
Geometric Analysis combines differential equations and differential geometry. An important aspect is to solve geometric problems by studying differential equations. Besides some known linear differential operators such as the Laplace operator, many differential equations arising from differential geometry are nonlinear. A particularly important example is the Monge-Ampere equation. Applications to geometric problems have also motivated new methods and techniques in differential equations. The field of geometric analysis is broad and has had many striking applications.
This handbook of geometric analysis - the second to be published in the ALM series - provides introductions to and surveys of important topics in geometric analysis and their applications to related fields. It can be used as a reference by graduate students and researchers.
Heat Kernels on Metric Measure Spaces with Regular Volume Growth
Alexander Grigor'yan
A Convexity Theorem and Reduced Delzant Spaces
Bong H. Lian and Bailin Song
Localization and some Recent Applications
Bong H. Lian and Kefeng Liu
Gromov-Witten Invariants of Toric Calabi-Yau Threefolds
Chiu-Chu Melissa Liu
Survey on Affine Spheres
John Loftin
Convergence and Collapsing Theorems in Riemannian Geometry
Xiaochun Rong
Geometric Transformations and Soliton Equations
Chuu-Lian Terng
Affine Integral Geometry from a Differentiable Viewpoint
Deane Yang
Classification of Fake Projective Planes
Sai-Kee Yeung
Publication Details
Advanced Lectures in Mathematics, Vol. 14
Softcover. 472 pages. 4 pages of color photographs.
ISBN: 978-1-57146-205-3
Published: August 2010
Full Description
Geometric Analysis combines differential equations and differential geometry. An important aspect is to solve geometric problems by studying differential equations. Besides some known linear differential operators such as the Laplace operator, many differential equations arising from differential geometry are nonlinear. A particularly important example is the Monge-Ampere equation. Applications to geometric problems have also motivated new methods and techniques in differential equations. The field of geometric analysis is broad and has had many striking applications.
This handbook of geometric analysis - the third to be published in the ALM series - provides introductions to and surveys of important topics in geometric analysis and their applications to related fields. It can be used as a reference by graduate students and researchers.
A Survey of Einstein Metrics on 4-manifolds
Michael T. Anderson
Sphere Theorems in Geometry
Simon Brendle and Richard Schoen
Curvature Flows and CMC Hypersurfaces
Claus Gerhardt
Geometric Structures on Riemannian Manifolds
Naichung Conan Leung
Symplectic Calabi-Yau Surfaces
Tian-Jun Li
Lectures on Stability and Constant Scalar Curvature
D.H. Phong and Jacob Sturm
Analytic Aspect of Hamilton's Ricci Flow
Xi-Ping Zhu
ISBN: 978-0-470-60970-5
Hardcover
736 pages
January 2011
This Third Edition includes basic modern tools of computational mathematics for boundary value problems and also provides the foundational mathematical material necssary to understand and use the tools. Central to the text is a down-to-earth approach that shows readers how to use differential and integral equations when tackling significant problems in the physical sciences, engineering, and applied mathematics, and the book maintains a careful balance between sound mathematics and meaningful applications. A new co-author, Michael J. Holst, has been added to this new edition, and together he and Ivar Stakgold incorporate recent developments that have altered the field of applied mathematics, particularly in the areas of approximation methods and theory including best linear approximation in linear spaces; interpolation of functions in Sobolev Spaces; spectral, finite volume, and finite difference methods; techniques of nonlinear approximation; and Petrov-Galerkin and Galerkin methods for linear equations.
Additional topics have been added including weak derivatives and Sobolev Spaces, linear functionals, energy methods and A Priori estimates, fixed-point techniques, and critical and super-critical exponent problems.
The authors have revised the complete book to ensure that the notation throughout remained consistent and clear as well as adding new and updated references. Discussions on modeling, Fourier analysis, fixed-point theorems, inverse problems, asymptotics, and nonlinear methods have also been updated.