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Ideals and Reality : Projective Modules and Number of Generators of Ideals
The book gives a comprehensive introduction to basic commutative algebra, together with the related methods from homological algebra, which will enable students who know only the fundamentals of algebra to enjoy the power of using these tools. At the same time, it also serves as a valuable reference for the research specialist and as potential course material, because the authors present, for the first time in book form, an approach here that is an intermix of classical algebraic K-theory and complete intersection techniques, making connections with the famous results of Forster-Swan and Eisenbud-Evans. A study of projective modules and their connections with topological vector bundles in a form due to Vaserstein is included. Important subsidiary results appear in the copious exercises.
Hypoelliptic estimates and spectral theory for Fokker-Planck operators and witten Laplacians
There has recently been a renewal of interest in Fokker-Planck operators, motivated by problems in statistical physics, in kinetic equations and differential geometry. Compared to more standard problems in the spectral theory of partial differential operators, those operators are not self-adjoint and only hypoelliptic. The aim of the analysis is to give, as generally as possible, an accurate qualitative and quantitative description of the exponential return to the thermodynamical equilibrium. While exploring and improving recent results in this direction this volume proposes a review of known techniques on: the hypoellipticity of polynomial of vector fields and its global counterpart; the global Weyl-Hörmander pseudo-differential calculus, the spectral theory of non-self-adjoint operators, the semi-classical analysis of Schrödinger-type operators.
Hyperbolic Systems of Balance Laws : Lectures given at the C.I.M.E. Summer School held in Cetraro, Italy, July 14-21, 2003
The present Cime volume includes four lectures by Bressan, Serre, Zumbrun and Williams and an appendix with a Tutorial on Center Manifold Theorem by Bressan. Bressan’s notes start with an extensive review of the theory of hyperbolic conservation laws. Then he introduces the vanishing viscosity approach and explains clearly the building blocks of the theory in particular the crucial role of the decomposition by travelling waves. Serre focuses on existence and stability for discrete shock profiles, he reviews the existence both in the rational and in the irrational cases and gives a concise introduction to the use of spectral methods for stability analysis. Finally the lectures by Williams and Zumbrun deal with the stability of multidimensional fronts.
Hyperbolic Problems and Regularity Questions
This book discusses new challenges in the quickly developing field of hyperbolic problems. Particular emphasis lies on the interaction between nonlinear partial differential equations, functional analysis and applied analysis as well as mechanics.The book originates from a recent conference focusing on hyperbolic problems and regularity questions. It is intended for researchers in functional analysis, PDE, fluid dynamics and differential geometry.
Hyperbolic Problems : Theory, Numerics, Applications ; Proceedings of the Eleventh International Conference on Hyperbolic Problems held in Ecole Normale Supérieure, Lyon, July 17-21, 2006
This volume contains papers that were presented at HYP2006, the eleventh international Conference on Hyperbolic Problems: Theory, Numerics and Applications held at the Ecole Normale Supérieure de Lyon, France, July 17-21, 2006. This biennial series of conferences has become one of the most important international events in Applied Mathematics. As computers became more and more powerful, the interplay between theory, modelling, and numerical algorithms gained considerable impact, and the scope of HYP conferences expanded accordingly. The field is currently in interaction with a variety of scientific domains, including fluid dynamics, physics, electromagnetism, chemistry, biology, road and network traffic, and engineering. Many of these papers present new effective numerical methods and their application in various contexts.
Hyperbolic Geometry
The geometry of the hyperbolic plane has been an active and fascinating field of mathematical inquiry for most of the past two centuries. The basic approach taken is to define hyperbolic lines and develop a natural group of transformations preserving hyperbolic lines, and then study hyperbolic geometry as those quantities invariant under this group of transformations. Topics covered include the upper half-plane model of the hyperbolic plane, Möbius transformations, the general Möbius group, and their subgroups preserving the upper half-plane, hyperbolic arc-length and distance as quantities invariant under these subgroups, the Poincaré disc model, convex subsets of the hyperbolic plane, hyperbolic area, the Gauss-Bonnet formula and its applications.
Hyberbolic Conservation Laws in Continuum Physics
This masterly exposition of the mathematical theory of hyperbolic system for conservation laws brings out the intimate connection with continuum thermodynamics, by emphasising issues in which the analysis may reveal something about the physics and, in return, the underlying physical structure may direct and drive the analysis.Theis edition contains chapter recounting the exciting recent developments on the vanishing viscosity method. Numerous new sections have been incorporated in preexisting chapters, to introduce newly derived results or present older material
How to Build a Modern Tontine : Algorithms, Scripts and Tips
This book introduces the modern tontine and its applications in retirement and decumulation. Personal financial management in the later stages of life presents unique challenges, and renowned retirement planning expert Dr. Milevsky proposes the modern tontine as a solution. With the goal of guiding professionals and retirees in more efficient decumulation, the book demonstrates how to build a modern tontine. It is technically oriented, employing a cookbook format, featuring R code, and examining retirement planning through a statistical lens.
How Data Quality Affects our Understanding of the Earnings Distribution
This book demonstrates how data quality issues affect all surveys and proposes methods that can be utilised to deal with the observable components of survey error in a statistically sound manner. This book begins by profiling the post-Apartheid period in South Africa's history when the sampling frame and survey methodology for household surveys was undergoing periodic changes due to the changing geopolitical landscape in the country. This book profiles how different components of error had disproportionate magnitudes in different survey years, including coverage error, sampling error, nonresponse error, measurement error, processing error and adjustment error.
Horizons of Combinatorics
Hungarian mathematics has always been known for discrete mathematics, including combinatorial number theory, set theory and recently random structures, combinatorial geometry as well. The recent volume contains high level surveys on these topics with authors mostly being invited speakers for the conference "Horizons of Combinatorics" held in Balatonalmadi, Hungary in 2006. The collection gives a very good overview of recent trends and results in a large part of combinatorics and related topics, and offers an interesting reading for experienced specialists as well as to young researchers and students.
Homotopy Methods in Topological Fixed and Periodic Points Theory
The notion of a fixed point plays a crucial role in numerous branches of mat- maticsand its applications. Informationabout the existence of such pointsis often the crucial argument in solving a problem. In particular, topological methods of fixed point theory have been an increasing focus of interest over the last century. These topological methods of fixed point theory are divided, roughly speaking, into two types. The ?rst type includes such as the Banach Contraction Principle where the assumptions on the space can be very mild but a small change of the map can remove the fixed point. The second type, on the other hand, such as the Brouwer and Lefschetz Fixed Point Theorems, give the existence of a fixed point not only for a given map but also for any its deformations. This book is an exposition of a part of the topological fixed and periodic point theory, of this second type, based on the notions of Lefschetz and Nielsen numbers. Since both notions are homotopyinvariants, the deformationis used as an essential method, and the assertions of theorems typically state the existence of fixed or periodic points for every map of the whole homotopy class, we refer to them as homotopy methods of the topological fixed and periodic point theory.
Homogenization of Partial Differential Equations
Homogenization is a method for modeling processes in microinhomogeneous media, which are encountered in radiophysics, filtration theory, rheology, elasticity theory, and other domains of mechanics, physics, and technology. These processes are described by PDEs with rapidly oscillating coefficients or boundary value problems in domains with complex microstructure. From the technical point of view, given the complexity of these processes, the best techniques to solve a wide variety of problems involve constructing appropriate macroscopic (homogenized) models. The present monograph is a comprehensive study of homogenized problems, based on the asymptotic analysis of boundary value problems as the characteristic scales of the microstructure decrease to zero. The work focuses on the construction of nonstandard models: non-local models, multicomponent models, and models with memory.
Holomorphic Morse Inequalities and Bergman Kernels
The main analytic tool is the analytic localization technique in local index theory developed by Bismut-Lebeau. The book includes the most recent results in the field and therefore opens perspectives on several active areas of research in complex, Kähler and symplectic geometry. A large number of applications are included, e.g., an analytic proof of the Kodaira embedding theorem, a solution of the Grauert-Riemenschneider and Shiffman conjectures, a compactification of complete Kähler manifolds of pinched negative curvature, the Berezin-Toeplitz quantization, weak Lefschetz theorems, and the asymptotics of the Ray-Singer analytic torsion.
Holomorphic Functions in the Plane and n-dimensional Space
Complex analysis nowadays has higher-dimensional analoga: the algebra of complex numbers is replaced then by the non-commutative algebra of real quaternions or by Clifford algebras. During the last 30 years the so-called quaternionic and Clifford or hypercomplex analysis successfully developed to a powerful theory with many applications in analysis, engineering and mathematical physics. This textbook introduces both to classical and higher-dimensional results based on a uniform notion of holomorphy. Historical remarks, lots of examples, figures and exercises accompany each chapter.
History of Mathematics : A Supplement
This book attempts to fill two gaps which exist in the standard textbooks on the History of Mathematics. One is to provide students with material that could encourage more critical thinking. General textbooks, attempting to cover three thousand years of mathematical history, must necessarily oversimplify almost everything, the practice of which can scarcely promote a critical approach to the subject. For this reason, Craig Smorynski chooses a more narrow but deeper coverage of a few select topics. The second aim of this book is to include the proofs of important results which are typically neglected in the modern history of mathematics curriculum. The most obvious of these is the oft-cited necessity of introducing complex numbers in applying the algebraic solution of cubic equations. This solution, though it is now relegated to courses in the History of Mathematics, was a major occurrence in the history of mathematics.
History of Banach Spaces and Linear Operators
Written by a distinguished specialist in functional analysis, this book presents a comprehensive treatment of the history of Banach spaces and (abstract bounded) linear operators. While other historical texts on the subject focus on developments before 1950, this one is mainly devoted to the second half of the 20th century.Banach space theory is presented in a broad mathematical context, using tools from such areas as set theory, topology, algebra, combinatorics, probability theory, and logic.
High performance computing on vector systems 2007 ; Conference proceedings
The following book presents contributions from the 6th TERAFLOP Workshop which was hosted by Tohoku University in Sendai, Japan in Autumn 2006 and the 7th Workshop in Stuttgart which was held in spring 2007 in Stuttgart. Focus is layed on current applications and future requirements, as well as developments of next generation hardware architectures and installations. The papers presented in this book lay out the wide range of fields in which sustained performance can be achieved if engineering knowledge, numerical mathematics and computer science skills are brought together. With the advent of hybrid systems, the Teraflop workbench project will continue the support of leading edge computations for future applications.
High performance computing on vector systems 2006 ; Proceedings of the High Performance Computing Center Stuttgart, March 2006
With this second issue of "High Performance Computing on Vector Systems ~ Proceedings of the High Performance Computing Center Stuttgart" we con tinue our publication of most recent results in high performance computing and innovative architecture. Together with our book series on "High Perfor mance Computing in Science and Engineering'06 - Transactions of the High Performance Computing Center Stuttgart" this book gives an overview of the most recent developments in high performance computing and its use in scientific and engineering applications. This second issue covers presentations and papers given by scientists in two workshops held at Stuttgart and Tokyo in spring and summer 2006.
High performance computing on vector systems ; Proceedings of the High Performance Computing Center Stuttgart, March 2005
The book presents the state of the art in high performance computing and simulation on modern supercomputer architectures. Innovative application fields like multiphysics simulations and material science are presented.
High performance computing in science and engineering, Munich 2004 ; Transactions of the 2nd Joint HLRB and KONWIHR Status and Result Workshop, March 2-3, 2004, Technical University of Munich, and Leibniz-Rechenzentrum Munich, Germany
Three of the 38 papers deal with computer science, 11 with computational fluid dynamics, two with bio-sciences, six with chemistry, nine with solid-state physics, one with geophysics, four with fundamental physics and two with astrophysics. At a workshop on high performance computing papers should not only have a high scientific quality of the subject addressed, e.g. CFD (Computational Fluid Dynamics), physics, chemistry, but should ecially emphasize the necessity to have access to a high performance computer in order to solve the problem. It should also contain information about the simulation techniques used and about the performance of the computer when using distinc algorithms.
