Corrado De Concini University of Rome, Italy
Freddy Van Oystaeyen University of Antwerp/UIA, Belgium
Nikolai Vavilov / Anatoly Yakovlev St Petersburg State University, Russia

Noncommutative Algebra and Geometry

Series: Lecture Notes in Pure and Applied Mathematics Volume: 243

ISBN: 082472349X
Publication Date: 9/1/2005
Number of Pages: 272

Presents selected papers from a conference held in St. Petersburg, Russia, in honor of Dr. Z. Borevich
Organized under the framework of the European Science Foundation's "Noncommuntative Geometry" program
Presents topics including algebraic groups, algebraic number theory, rings, and modules
Features a wide range of international contributors

A valuable addition to the Lecture Notes in Pure and Applied Mathematics series, this reference results from a conference held in St. Petersburg, Russia, in honor of Dr. Z. Borevich. This volume is mainly devoted to the contributions related to the European Science Foundation workshop, organized under the framework of noncommuntative geometry and integrated in the Borevich meeting. The topics presented, including algebraic groups and representations, algebraic number theory, rings, and modules, are a timely distillation of recent work in the field. Featuring a wide range of international experts as contributors, this book is an ideal reference for mathematicians in algebra and algebraic geometry.

Table of Contents

Finite Galois Stable Subgroups of Gln. Derived Categories for Nodal Rings and Projective Configurations. Crowns in Profinite Groups and Applications. The Galois Structure of Ambiguous Ideals in Cyclic Extensions of Degree 8. An Introduction to Noncommutative Deformations of Modules. Symmetric Functions, Noncommutative Symmetric Functions and Quasisymmetric Functions II. Quotient Grothendieck Representations. On the Strong Rigidity of Solvable Lie Algebras. The Role of Bergman in Invesigating Identities in Matrix Algebras with Symplectic Involution. The Triangular Structure of Ladder Functors. Noncommutative Algebraic Geometry and Commutative Desingularizations.

Santiago Alves Tavares University of Florida, Gainesville, USA

Generation of Multivariate Hermite Interpolating Polynomials

Series: Pure and Applied Mathematics Volume: 274

ISBN: 1584885726
Publication Date: 8/23/2005
Number of Pages: 704

Presents a fresh approach to the approximate solution of differential equations
Supplies algorithms and pseudocode for generating constrained numbers and Hermite interpolating polynomials
Contains detailed examples that clarify the algorithms and aid in troubleshooting the development of computer code
Demonstrates several applications of the algorithms, with both one-dimensional and multivariate examples

Generation of Multivariate Hermite Interpolating Polynomials advances the study of approximate solutions to partial differential equations by presenting a novel approach that employs Hermite interpolating polynomials and bysupplying algorithms useful in applying this approach.

Organized into three sections, the book begins with a thorough examination of constrained numbers, which form the basis for constructing interpolating polynomials. The author develops their geometric representation in coordinate systems in several dimensions and presents generating algorithms for each level number. He then discusses their applications in computing the derivative of the product of functions of several variables and in the construction of expression for n-dimensional natural numbers. Section II focuses on the construction of Hermite interpolating polynomials, from their characterizing properties and generating algorithms to a graphical analysis of their behavior.

The final section of the book is dedicated to the application of Hermite interpolating polynomials to linear and nonlinear differential equations in one or several variables. Of particular interest is an example based on the author's thermal analysis of the space shuttle during reentry to the earth's atmosphere, wherein he uses the polynomials developed in the book to solve the heat transfer equations for the heating of the lower surface of the wing.

Table of Contents

CONSTRAINED NUMBERS. Constrained Coordinate System. Generation of the Coordinate System. Natural Coordinates. Computation of the Number of Elements. An Ordering Relation. Application to Symbolic Computation of Derivatives. HERMITE INTERPOLATING POLYNOMIALS. Multivariate Hermite Interpolating Polynomials. Generation of the Hermite Interpolating Polynomials. Hermite Interpolating Polynomials: The Classical and Present Approaches. Normalized Symmetric Square Domain. Rectangular Non-Symmetric Domain. Generic Domains. Extensions of the Constrained Numbers. Field of the Complex Numbers. Analysis of the Behavior of the Hermite Interpolating Polynomials. SELECTED APPLICATIONS. Construction of the Approximate Solution. One-Dimensional Two Point Boundary Value Problems. Application to Problems with Several Variables. Thermal Analysis of the Surface of the Space Shuttle.

Ruey S. Tsay

Analysis of Financial Time Series, 2nd Edition

ISBN: 0-471-69074-0
Hardcover
605 pages
August 2005

Gain the statistical tools and techniques you need to understand today's financial markets with the Second Edition of this critically acclaimed book.
You ll find a comprehensive and systematic introduction to financial econometric models and their applications in modeling and predicting financial time series data. This edition continues to emphasize empirical financial data and focuses on real-world examples. You ll master key aspects of financial time series, including volatility modeling, neural network applications, market microstructure and high-frequency financial data, continuous-time models and Ito's Lemma, Value at Risk, multiple returns analysis, financial factor models, and econometric modeling via computation-intensive methods.

This is an ideal textbook for MBA students and a key reference for researchers and professionals in business and finance. Order your copy today.

Table of contents

Preface.
Preface to First Edition.
1. Financial Time Series and Their Characteristics.
2. Linear Time Series Analysis and Its Applications.
3. Conditional Heteroscedastic Models.
4. Nonlinear Models and Their Applications.
5. High-Frequency Data Analysis and Market Microstructure.
6. Continuous-Time Models and Their Applications.
7. Extreme Values, Quantile Estimation, and Value at Risk.
8. Multivariate Time Series Analysis and Its Applications.
9. Principal Component Analysis and Factor Models.
10. Multivariate Volatility Models and Their Applications.
11. State-Space Models and Kalman Filter.
12. Markov Chain Monte Carlo Methods with Applications.
Index.


Edited by Anthony C. Davison, Yadolah Dodge, and Nanny Wermuth

Celebrating Statistics
Papers in honour of Sir David Cox on his 80th birthday

0-19-856654-9
Publication date: 22 September 2005
272 pages, 234mm x 156mm
Series: Oxford Statistical Science Series

Description

A tribute to Sir David Cox, who has had an immense influence on modern statistics
Each chapter is carefully crafted and collectively present current developments across a wide range of research areas from epidemiology, environmental science, finance, computing and medicine.

Sir David Cox is among the most important statisticians of the past half-century. He has made pioneering and highly influential contributions to a uniquely wide range of topics in statistics and applied probability. His teaching has inspired generations of students, and many well-known researchers have begun as his graduate students or have worked with him at early stages of their careers. Legions of others have been stimulated and enlightened by the clear, concise, and direct exposition exemplified by his many books, papers, and lectures. This book presents a collection of chapters by major statistical researchers who attended a conference held at the University of Neuchatel in July 2004 to celebrate David Cox's 80th birthday. Each chapter is carefully crafted and collectively present current developments across a wide range of research areas from epidemiology, environmental science, finance, computing and medicine.

Edited by Anthony Davison, Ecole Polytechnique Federale de Lausanne, Switzerland; Yadolah Dodge, University of Neuchatel, Switzerland; and N. Wermuth, Goteborg University, Sweden, with chapters by Ole E. Barndorff-Nielsen, Sarah C. Darby, Christina Davies, Peter J. Diggle, David Firth, Peter Hall, Valerie S. Isham, Kung-Yee Liang, Peter McCullagh, Paul McGale, Amilcare Porporato, Nancy Reid, Brian D. Ripley, Ignacio Rodriguez-Iturbe, Andrea Rotnitzky, Neil Shephard, Scott L. Zeger, and including a brief biography of David Cox, this book is suitable for students of statistics, epidemiology, environmental science, finance, computing and medicine, and academic and practising statisticians.

Readership: Ideal for students of statistics, epidemiology, environmental science, finance, computing and medicine, and academic and practising statisticians.

Contents

Preface
Yadolah Dodge: Biography
Valerie Isham: STOCHASTIC MODELS FOR EPIDEMICS
Amilcare Porporato and Ignacio Rodriguez-Iturbe: STOCHASTIC SOIL MOISTURE DYNAMICS AND VEGETATION RESPONSE
Nancy Reid: THEORETICAL STATISTICS AND ASYMPTOTICS
Peter McCullagh: EXCHANGEABILITY AND REGRESSION MODELS
Andrea Rotnitzky: ON SEMIPARAMETRIC INFERENCE Andrea Rotnitzky
Peter Hall: ON NONPARAMETRIC STATISTICAL METHODS
David Firth: SOME TOPICS IN SOCIAL STATISTICS
Scott Zeger, Peter Diggle, and Kung-Yee Liang: BIOSTATISTICS: THE NEAR FUTURE
Sarah Darby, Christina Davies, and Paul McGale: THE EARLY BREAST CANCER TRIALISTS' COLLABORATIVE GROUP: A BRIEF HISTORY OF RESULTS TO DATE
Brian D. Ripley: HOW COMPUTING HAS CHANGED STATISTICS
Neil Shephard: ARE THERE DISCONTINUITIES IN FINANCIAL PRICES?
Ole Eiler Barndorff-Nielsen: ON SOME CONCEPTS OF INFINITE DIVISIBILITY AND THEIR ROLES IN TURBULENCE, FINANCE AND QUANTUM STOCHASTICS
Bibliography

B. L. Moiseiwitsch

Integral Equations

ISBN: 0486441628
Page Count: 176
Dimensions: 5 3/8 x 8 1/2

The integral equation approach to solving problems specifically includes the boundary conditions--a valuable advantage. It also leads naturally to the solution of the problem (under suitable conditions) in the form of an infinite series. Geared toward upper-level undergraduate students, this text focuses chiefly upon linear integral equations. It begins with a straightforward account, accompanied by simple examples of a variety of integral equations and the methods of their solution. The treatment becomes gradually more abstract, with discussions of Hilbert space and linear operators, the resolvent, Fredholm theory, and the Hilbert-Schmidt theory of linear operators in Hilbert space. 1977 ed.

Table of Contents

Preface
1. Classification of integral equations
2. Connection with differential equations
3. Integral equations of the convolution type
4. Method of successive approximations
5. Integral equations with singular kernels
6. Hilbert space
7. Linear operators in Hilbert space
8. The resolvent
9. Fredholm theory
10. Hilbert-Schmidt theory
Bibliography
Index