Yu. Aminov,
Institute of Low Temperature Physics and Engineering,Kharkov, The Ukraine
The Geometry of Submanifolds
Providing a comprehensive presentation of the geometry of submanifolds, this volume expands the classical results in the theory of curves and surfaces. The geometry of submanifolds starts from the idea of the extrinsic geometry of a surface and the theory studies the position and properties of a submanifold
in ambient space, in both local and global aspects. This volume also highlights the contributions made by great geometers, past and present, to the geometry of submanifolds and the developing areas of application.
Contents: Curves ・General Properties of Submanifolds ・ Hypersurfaces ・Submanifolds in Euclidean Space ・
Submanifolds in Riemannian Space ・Two-Dimensional Surfaces in E4 ・Minimal Submanifolds ・Grassman Image of a Submanifold ・Regular Polyhedra in E4 and EN ・Isometric Immersions of Lobachevski Space into Euclidean Spaces
Readership: Researchers in mathematics and geometry.
December, 1999 / 388 pp / Cloth / 90-5699-087-X
Waldschmidt, M., Universite Pierre et Marie Curie, Paris, France
Diophantine Approximation on Linear Algebraic Groups
Transcendence Properties of the Exponential Function in Several Variables
2000. XXVII, 633 pp.
3-540-66785-7
The theory of transcendental numbers is closely related to the study of diophantine approximation. This book deals with values of the usual exponential function ez: a central open problem is the conjecture on algebraic independence of logarithms of algebraic numbers. It includes proofs of the main basic results (theorems of Hermite-Lindemann, Gelfond-Schneider, 6 exponentials theorem), an introduction to height functions and Lehmer's problem, several proofs of Baker's theorem as well as explicit measures of linear independence of logarithms. An original feature is the systematic use, in proofs, of Laurent's interpolation determinants. The
most general result is the so-called Theorem of the Linear Subgroup, an effective version of which is also included. It yields new results of simultaneous approximation and of algebraic independence. Two chapters written by D. Roy provide complete and at the same time simplified proofs of zero estimates (due to Philippon) on linear algebraic groups.
Keywords: Transcendental Numbers Linear Algebraic groups Simultaneous Diophantine Approximation Exponential Functions Measures of Independence
Contents: 1. Introduction and Historical Survey Part I. Linear Independence of Logarithms of Algebraic Numbers 2. Transcendence Proofs in One Variable 3. Heights of Algebraic Numbers 4. The Criterion of Schneider-Lang 5. Zero Estimate 6. Linear Independence of Logarithms of Algebraic Numbers Part II. Measures of Linear Independence 7. A First Measure with a Simple Proof 8. Zero Estimate (Continued), by Damien ROY 9. Refined Measure III. Multiplicities in Higher Dimension 10. Multiplicity Estimates, by Damien ROY 11. Interpolation Determinants with One Derivative 12. On Baker's Method Part IV. The Linear Subgroup Theorem 13. Points Whose Coordinates are Logarithms of Algebraic Numbers 14. Lower Bounds for the Rank of Matrices Part V. Simultaneous Approximation of Values of the Exponential Function in Several Variables 15. A Quantitative Version of the Linear Subgroup Theorem 16. Applications to Diophantine Approximation 17. Algebraic Independence References
Series: Grundlehren der mathematischen Wissenschaften.VOL. 326
Fields: Number Theory; Algebraic Geometry; Group Theory
Written for: Researchers and graduate students in number theory (diophantine equations) and algebraic geometry
Book category: Monograph
Publication language: English
Faraut, J., Universite Pierre et Marie Curie, Paris, France /
Kaneyuki, S., Sophia University,Tokyo, Japan /
Korayi, A., H.H. Lehmann College, New York, USA /
Lu, Q., Academia Sinica, Beijing, China et al.
Analysis and Geometry on Complex Homogeneous Domains
2000. 560 pages. Hardcover
ISBN 3-7643-4138-6
This excellent introductory text covers a number of important areas in complex analysis and geometry.
Written by experts in their respective fields, each of the five chapters unfolds from the basics to the more complex. Unlike other more laborious introductory texts, the exposition here is rapid-paced and efficient,
without compromising proofs and examples that enable the reader to grasp the essentials.
Topics covered include:
Function spaces on complex
semigroups
Graded Lie algebras, related
geometric structures, and
pseudo-Hermitian symmetric spaces
Function spaces on bounded
symmetric domains
Heat kernels of non-compact
symmetric spaces
Jordan triple systems
This volume will be useful as a graduate text for students of Lie group theory with connections to complex analysis, or as a self-study resource for newcomers to the field. Readers will reach the frontiers of the
subject in a considerably shorter time than with existing texts.
Peter Bloomfield (North Carolina State Univ., Raleigh, North Carolina)
Fourier Analysis of Time Series: An Introduction, 2nd Ed.
ISBN: 0-471-88948-2
Hardcover
Published: Jan 2000
Copyright: 2000
Imprint: Wiley-Interscience
A new, revised edition of a yet unrivaled work on frequency domain analysis
Long recognized for his unique focus on frequency domain methods for the analysis of time series data as well as for his applied, easy-to-understand approach, Peter Bloomfield brings his well-known 1976 work thoroughly up to date. With a minimum of mathematics and an engaging, highly rewarding style, Bloomfield provides in-depth discussions of harmonic regression, harmonic analysis, complex demodulation, and spectrum analysis. All methods are clearly illustrated using examples of specific data sets, while ample exercises acquaint readers with Fourier analysis and its applications. The Second Edition: Devotes an entire chapter to complex demodulation Treats harmonic regression in two separate chapters Features a more succinct discussion of the fast Fourier transform Uses S-PLUS commands (replacing FORTRAN) to accommodate programming needs and graphic flexibility Includes Web addresses for all time series data used in the examples
An invaluable reference for statisticians seeking to expand their understanding of frequency domain methods, Fourier Analysis of Time Series, Second Edition also provides easy access to sophisticated statistical tools for scientists and professionals in such areas as atmospheric science, oceanography, climatology, and biology.
Contents
Fitting Sinusoids.
The Search for Periodicity.
Harmonic Analysis.
The Fast Fourier Transform.
Examples of Harmonic Analysis.
Complex Demodulation.
The Spectrum.
Some Stationary Time Series Theory.
Analysis of Multiple Series.
Further Topics.
References.
Indexes.
Subject: Statistics / Statistics Special Topics /
Series Title: Wiley Series in Probability and Mathematical Statistics - Applied Probability and StatisticsSection
Srinivasan, G., editor
From White Dwarfs to Black Holes:
The Legacy of S. Chandrasekhar.
xiv, 240 p., 3 halftones. 1999
Cloth 0-226-76996-8
Paper 0-226-76997-6
From White Dwarfs to Black Holes chronicles the extraordinarily productive scientific career of Subrahmanyan Chandrasekhar, one of the twentieth century's most distinguished astrophysicists. Among
Chandrasekhar's many discoveries were the critical mass that makes a star too massive to become a white dwarf and the mathematical theory of black holes. In 1983 he shared the Nobel Prize for Physics for these and other achievements.
Over the course of more than six decades of active research Chandrasekhar investigated a dizzying array of subjects. G. Srinivasan notes in the preface to this book that "the range of Chandra's contributions
is so vast that no one person in the physics or astronomy community can undertake the task of commenting on his achievements." Thus, in this collection, ten eminent scientists evaluate Chandrasekhar's contributions to
their own fields of specialization. Donald E. Osterbrock closes the volume with a historical discussion of Chandrasekhar's interactions with graduate students during his more than quarter century at Yerkes Observatory.
Contributors are James Binney, John L. Friedman, Norman R. Lebovitz, Donald E. Osterbrock, E. N. Parker, Roger Penrose, A. R. P. Rau, George B. Rybicki, E. E. Salpeter, Bernard F. Schutz, and G. Srinivasan.
Subjects: Physical Sciences: Astronomy and Astrophysics