(North-Holland Mathematics Studies, Volume 206)
ISBN: 978-0-444-52713-4
ISBN10: 0-444-52713-3 Hardback
Measurements: 9 1/2 X 6 7/16 in
Pages: 378
- Deals systematically with difference equations in normed spaces
- Considers new classes of equations that could not be studied in
the frameworks of ordinary and partial difference equations
- Develops the freezing method and presents recent results on
Volterra discrete equations
- Contains an approach based on the estimates for norms of
operator functions
Description
Many problems for partial difference and integro-difference
equations can be written as difference equations in a normed
space. This book is devoted to linear and nonlinear difference
equations in a normed space. Our aim in this monograph is to
initiate systematic investigations of the global behavior of
solutions of difference equations in a normed space. Our primary
concern is to study the asymptotic stability of the equilibrium
solution. We are also interested in the existence of periodic and
positive solutions. There are many books dealing with the theory
of ordinary difference equations. However there are no books
dealing systematically with difference equations in a normed
space. It is our hope that this book will stimulate interest
among mathematicians to develop the stability theory of abstract
difference equations.
Note that even for ordinary difference equations, the problem of
stability analysis continues to attract the attention of many
specialists despite its long history. It is still one of the most
burning problems, because of the absence of its complete
solution,
but many general results available for ordinary difference
equations
(for example, stability by linear approximation) may be easily
proved for abstract difference equation
Contents
Preface
1. Definitions and Preliminaries
2. Classes of Operators
3. Functions of Finite Matrices
4. Norm Estimates for Operator Functions
5. Spectrum Perturbations
6. Linear Equations with Constant Operators
7. Liapunov's Type Equations
8. Bounds for Spectral Radiuses
9. Linear Equations with Variable Operators
10. Linear Equations with Slowly Varying Coefficients
11. Nonlinear Equations with Autonomous Linear Parts
12. Nonlinear Equations with Time-Variant Linear Parts
13. Higher Order Linear Difference Equations
14. Nonlinear Higher Order Difference Equations
15. Input-to-State Stability
16. Periodic Solutions of Difference Equations and Orbital
Stability
17. Discrete Volterra Equations in Banach Spaces
18. Convolution type Volterra Difference Equations in Euclidean
Spaces and their Perturbations
19 Stieltjes Differential Equations
20 Volterra-Stieltjes Equations
21. Difference Equations with Continuous Time
22. Steady States of Difference Equations
Appendix A
Notes
References
List of Main Symbols
Index
(Studies in the History and Philosophy of Mathematics, Volume 5)
ISBN: 978-0-444-52728-8
ISBN10: 0-444-52728-1 Book/Hardback
Measurements: 5 X 9 15/16 in
Pages: 550
- Over 20 essays by some of the best historians of mathematics
and science, including Ronald Calinger, Peter Hoffmann, Curtis
Wilson, Kim Plofker, Victor Katz, Ruediger Thiele, David
Richeson, Robin Wilson, Ivor Grattan-Guinness and Karin Reich
- New details of Euler’s life in two essays, one by Ronald
Calinger and one he co-authored with Elena Polyakhova
- New information on Euler’s work in differential geometry,
series, mechanics, and other important topics including his
influence in the early 19th century
Description
The year 2007 marks the 300th anniversary of the birth of one of
the Enlightenment’s most important mathematicians and
scientists, Leonhard Euler. This volume is a collection of 24
essays by some of the world’s best Eulerian scholars from seven
different countries about Euler, his life and his work.
Some of the essays are historical, including much previously
unknown information about Euler’s life, his activities in the
St. Petersburg Academy, the influence of the Russian Princess
Dashkova, and Euler’s philosophy. Others describe his influence
on the subsequent growth of European mathematics and physics in
the 19th century. Still others give technical details of Euler’s
innovations in probability, number theory, geometry, analysis,
astronomy, mechanics and other fields of mathematics and science.
Contents
Foreword (C.E. Sandifer and R.E. Bradley)
Introduction (C.E. Sandifer and R.E. Bradley)
Leonhard Euler: Life and Thought (R.S. Calinger)
Leonard Euler and Russia (P. Hoffmann)
Princess Dashkova, Euler, and the Russian Academy of Sciences (R.S.
Calinger and E.N. Polyakhova)
Leonhrd Euler and Philosophy (W. Breidert)
Images of Euler (F. Fasanelli)
Euler and Applications of Analytical Mathematics to Astronomy (C.
Wilson)
Euler and Indian Astronomy (K. Plofker)
Euler and Kinematics (T. Koetsier)
Euler on Rigid Bodies (S.G. Langton)
Euler's Analysis Textbooks (V.J. Katz)
Euler and the Calculus of Variations (R. Thiele)
Euler, D'Alembert and the Logarithm Function (R.E. Bradley)
Some Facets of Euler's Work on Series (C.E. Sandifer)
The Geometry of Leonhard Euler (H.S. White)
Cyclotomy: From Euler through Vandermonde to Gauss (O. Neumann)
Euler and Number Theory: A Study in Mathematical Invention (J.
Suzuki)
Euler and Lotteries (D.R. Bellhouse)
Euler's Science of Combinations (B. Hopkins and R. Wilson)
The Truth about Konigsberg (B. Hopkins and R. Wilson)
The Polyhedral Formula (D. Richeson)
On the Recognition of Euler among the French, 1790-1830 (I.
Grattan-Guinness)
Euler's Influence on the Birth of Vector Mechanics (S. Caparrini)
Euler's Contribution to Differential Geometry and its Reception (K.
Reich)
Euler's Mechanics as a Foundation of Quantum Mechanics (D. Suisky)
Index
Series: Handbook of Computing and Statistics with Applications
ISBN: 978-0-444-52044-9
ISBN10: 0-444-52044-9 Hardback
Measurements: 9 1/2 X 6 7/16 in
Pages: 460
- Covers a wide class of important models
- Models and statistical methods described provide tools for
analyzing a wide spectrum of complicated data
- Includes illustrative examples with real data sets from
business, education, medicine, public health and sociology.
- Demonstrates the use of a wide variety of statistical,
computational, and mathematical techniques.
Description
This Handbook covers latent variable models, which are a flexible
class of models for modeling multivariate data to explore
relationships among observed and latent variables.
Contents
Preface
About the Authors
1. Covariance Structure Models for Maximal Reliability of Unit-weighted
Composites (Peter M. Bentler)
2. Advances in Analysis of Mean and Covariance Structure When
Data are Incomplete (Mortaza Jamshidian, Matthew Mata)
3. Rotation Algorithms: From Beginning to End (Robert I. Jennrich)
4. Selection of Manifest Variables (Yutaka Kano)
5. Bayesian Analysis of Mixtures Structural Equation Models with
Missing Data (Sik-Yum Lee)
6. Local Influence Analysis for Latent Variable Models with
Nonignorable Missing Responses (Bin Lu, Xin-Yuan Song, Sik-Yum
Lee, Fernand Mac-Moune Lai)
7. Goodness-of-fit Measures for Latent Variable Models for Binary
Data (D. Mavridis, Irini Moustaki, Martin Knott)
8. Bayesian Structural Equation Modeling (Jesus Palomo, David B.
Dunson, Ken Bollen)
9. The Analysis of Structural Equation Model with Ranking Data
using Mx (Wai-Yin Poon)
10. Multilevel Structural Equation Modeling (Sophia Rable-Hesketh,
Anders Skrondal, Xiaohui Zheng)
11. Statistical Inference of Moment Structure (Alexander Shapiro)
12. Meta-Analysis and Latent Variables Models for Binary Data (Jian-Qing
Shi)
13. Analysis of Multisample Structural Equation Models with
Applications to Quality of Life Data (Xin-Yuan Song)
14. The Set of Feasible Solutions for Reliability and Factor
Analysis (Jos M.F. ten Berge, Gregor Soean)
15. Nonlinear Structural Equation Modeling as a Statistical
Method (Melanie M. Wall, Yasuo Amemiya)
16. Matrix Methods and Their Applications to Factor Analysis (Haruo
Yanai, Yoshio Takane)
17. Robust Procedures in Structural Equation Modeling (Ke-Hai
Yuan, Peter M. Bentler)
18. Stochastic Approximation Algorithms for Estimation of Spatial
Mixed Models (Hongtu Zhu, Faming Liang, Minggao Gu, Bradley
Peterson)
EMS Monographs in Mathematics
ISBN 978-3-03719-031-9
January 2007, 1000 pages, hardcover, 16.5 cm x 23.5 cm.
The equations describing the motion of a perfect fluid were first
formulated by Euler in 1752. These equations were among the first
partial differential equations to be written down, but, after a
lapse of two and a half centuries, we are still far from
adequately understanding the observed phenomena which are
supposed to lie within their domain of validity.
These phenomena include the formation and evolution of shocks in
compressible fluids, the subject of the present monograph. The
first work on shock formation was done by Riemann in 1858.
However, his analysis was limited to the simplified case of one
space dimension. Since then, several deep physical insights have
been attained and new methods of mathematical analysis invented.
Nevertheless, the theory of the formation and evolution of shocks
in real three-dimensional fluids has remained up to this day
fundamentally incomplete.
This monograph considers the relativistic Euler equations in
three space dimensions for a perfect fluid with an arbitrary
equation of state. We consider initial data for these equations
which outside a sphere coincide with the data corresponding to a
constant state. Under suitable restriction on the size of the
initial departure from the constant state, we establish theorems
that give a complete description of the maximal classical
development. In particular, it is shown that the boundary of the
domain of the maximal classical development has a singular part
where the inverse density of the wave fronts vanishes, signalling
shock formation. The theorems give a detailed description of the
geometry of this singular boundary and a detailed analysis of the
behavior of the solution there. A complete picture of shock
formation in three-dimensional fluids is thereby obtained. The
approach is geometric, the central concept being that of the
acoustical spacetime manifold.
The monograph will be of interest to people working in partial
differential equations in general and in fluid mechanics in
particular.
Contents
EMS Series of Lectures in Mathematics
ISBN 978-3-03719-027-2
January 2007, 264 pages, softcover, 17.0 cm x 24.0 cm.
The theory of empirical processes constitutes the mathematical
toolbox of asymptotic statistics. Its growth was accelerated by
the 1950s work on the Functional Central Limit Theorem and the
Invariance Principle. The theory has developed in parallel with
statistical methodologies, and has been successfully applied to a
large diversity of problems related to the asymptotic behaviour
of statistical procedures.
The three sets of lecture notes in the book offer a wide panorama
of contemporary empirical processes theory. Techniques are
developed in the framework of probability in Banach spaces,
Hungarian-style strong approximations, using tools from general
stochastic process theory. Other tools appear in this text in
connection with historical as well as modern applications, such
as goodness-of-fit tests, density estimation or general M-estimators.
This book gives an excellent overview of the broad scope of the
theory of empirical processes. It will be an invaluable aid for
students and researchers interested in an advanced and well-documented
approach to the selected topics.
Contents