July 2004, ISBN 1-4020-2205-0, Hard cover
Book Series: Fundamental Theories of Physics : Volume 141
This book presents the most recent advances in complex Finsler
geometry and related geometries: the geometry of complex
Lagrange, Hamilton and Cartan Spaces. The last three spaces were
initially introduced to and have been investigated by the author
of the present volume over the past several years. This book will
acquaint the reader with: - a survey of some basic results from
complex manifolds and the complex vector bundles theory, - the
geometry of holomorphic tangent bundles, - an analysis of the
main results in complex Finsler geometry, - a study of the
geometry of complex Lagrange and generalized Lagrange Spaces. Of
special interest are their holomorphic subspaces, - the
construction of the complex Hamilton geometry, - the complex
Finsler vector bundles. Audience: Geometers, complex analysts,
and physicists in quantum field theory and in theoretical
mechanics will find this book of interest. The volume can be also
used as a supplementary graduate text.
June 2004, ISBN 1-4020-2188-7, Hard cover
Book Series: Nato Science Series: Ii: Mathematics, Physics and
Chemistry : Volume 153
Leading scientists discuss the most recent physical and
experimental results in the physics of Bose-Einstein condensate
theory, the theory of nonlinear lattices (including quantum and
nonlinear lattices), and nonlinear optics and photonics.
Classical and quantum aspects of the dynamics of nonlinear waves
are considered. The contributions focus on the Gross-Pitaevskii
equation and on the quantum nonlinear Schrodinger equation.
Recent experimental results on atomic condensates and hydrogen
bonded systems are reviewed. Particular attention is given to
nonlinear matter waves in periodic potential.
Preface. Contributing Authors. - I: Nonlinear Waves. General
Topics. Towards algebro-geometric integration of the Gross-Pitaevskii
equation; V.Z. Enolskii. On modeling adiabatic N-soliton
interactions; V.S. Gerdjikov. Dynamical stabilization of
nonlinear waves; F. Abdullaev. Solitons as strange attractors; N.
Akhmediev, et al. Multidimensional solitons and vortices in
periodic potentials; B.B. Baizakov, et al. Globally-linked vortex
clusters; L.-C. Crasovan, et al. Solutions of the logarithmic
Schrodinger equation in a rotating harmonic trap; I. Bialynicki-Birula,
T. Sowinski. Linear and nonlinear bound states in curved
waveguides; Yu.B. Gaididei, et al. Numerical study of a nonlocal
sine-Gordon equation; G. Alfimov, et al. From nonlocality to
fractional calculus; L. Vazquez. On 3+1 dimensional Friedman-Robertson-Walker
universes with matter; T. Christodoulakis, et al. Stochastic
effects on the Eckhaus equation; S. De Lillo, G. Sanchini.
Modulational instability of some nonlinear nuclear continuum and
discrete models; D. Grecu, A. Visinescu. Scattering of NLS
solitons with bound quantum states; A. Ludu. "Oscillator-Wave"
model: Multiple attractors and strong stability; V. Damgov, P.
Trenchev. - II: Bose-Einstein Condensates and Matter Waves. Bose-Einstein
condensation: the odd nonlinear quantum mechanics; L.P.
Pitaevskii. Statistical mechanics of quantum integrable systems;
M. Wadati, et al. Bose-Einstein condensates in an optical
lattice; C. Fort, L. Fallani. Bose-Einstein condensates in
optical lattices in the nonlinear regime; O. Morsch, E. Arimondo.
Quantum bound states and matter waves delocalizations; M. Salerno.
Control of matter waves in optical lattices by Feshbach
resonance; V.A. Brazhnyi, V.V. Konotop. Two-component Bose-Einstein
condensates in optical lattices; N.A. Kostov, et al. Shock waves
in Bose-Einstein condensates; A.M. Kamchatnov, et al. - III:
Nonlinear Optics and Photonics. Stopping and bending light in 2D
photonic structures; A.B. Aceves, T. Dohnal. Model of the two
level quantum dots ensemble interacting with ultra-short pulse of
coherent radiation; A.I. Maimistov. Enhanced optical transmission
via tunnel coupling in surface polaritronic crystals; S.A.
Darmanyan, et al. Liquid light in cubic-quintic nonlinear optical
materials; H. Michinel, et al. Optical pulse evolution toward
light bullet and vortex solution; V. Skarka, et al. The
description of extremely short pulses in non-resonant media in
frame of Maxwell-Duffing-type models; E.V. Kazantseva. Statistics
of three interacting optical solitons; S. Boscolo, et al.
Statistical study of Raman scattering in optical fibers affected
by random conditions; J. Villarroel. Electromagnetics of
unharmonic waves - exactly solvable model; A. Shvartsburg. - IV:
Nonlinear Waves in Discrete Systems. Quantum breathers in an
attractive fermionic Hubbard model; J.C. Eilbeck, F. Palermo.
Energy localization and first order phase transition in solids
and molecules; S. Takeno, T. Suzuki. Soliton dynamics in randomly
perturbed discrete lattices; J. Garnier. Ultrafast electron
transfer: The standard theory revisited; S. Aubry. Nonlinear
spectroscopy study of vibrational self-trapping in hydrogen
bonded crystals; J. Edler, P. Hamm. Quantum anharmonic phonons in
the Fermi-Pasta-Ulam chain; J. Szeftel. Dynamics of the perturbed
Ablowitz-Ladik soliton beyond the adiabatic approximation; E.V.
Doktorov, et al. Travelling waves in a perturbed discrete sine-Gordon
equation; V.M. Rothos, M. Feckan. Dynamics of multicomponent
solitons in perturbed ladder lattices; O.O. Vakhnenko. Miwa's
representation of the Volterra hierarchy; V.E. Vekslerchik.
Moving topological solitons in the discrete Klein-Gordon
equation; Ya. Zolotaryuk. Dynamics of discrete solitons in media
with varying nonlinearity; F.Kh. Abdullaev, et al. On continuous
limits of some generalized compressible Heisenberg spin chains; N.S.
Serikbaev, et al. On the geometry of stationary Heisenberg
ferromagnets; F.K. Rahimov, et al. - Index.
June 2004, ISBN 1-4020-2030-9, Hard cover
Book Series: Mathematics and its Applications : Volume 567
In contrast to other books devoted to the averaging method and
the method of integral manifolds, in the present book we study
oscillation systems with many varying frequencies. In the process
of evolution, systems of this type can pass from one resonance
state into another. This fact considerably complicates the
investigation of nonlinear oscillations. In the present
monograph, a new approach based on exact uniform estimates of
oscillation integrals is proposed. On the basis of this approach,
numerous completely new results on the justification of the
averaging method and its applications are obtained and the
integral manifolds of resonance oscillation systems are studied.
This book is intended for a wide circle of research workers,
experts, and engineers interested in oscillation processes, as
well as for students and post-graduate students specialized in
ordinary differential equations. This book opens new
possibilities of the application of the averaging method to the
solution of problems in mechanics, radio engineering, and control.
Contents and Contributors
Introduction. 1: Averaging Method in Oscillation Systems with
Variable Frequencies. 1. Uniform Estimates for One-Dimensional
Oscillation Integrals. 2. Justification of Averaging Method for
Oscillation Systems with omega = omega(tau). 3. Investigation of
Two-Frequency Systems. 4. Justification of Averaging Method for
Oscillation Systems with omega = omega(x, tau). 5. Averaging over
All Fast Variables in Multifrequency Systems of Higher
Approximation. 2: Averaging Method in Multipoint Problems. 6.
Boundary-Value Problems for Oscillation Systems with Frequencies
Dependent on Time Variable. 7. Theorem on Justification of
Averaging Method on Entire Axis. 8. Multipoint Problem for
Resonance Multifrequency Systems. 9. Estimates of the Error of
Averaging Method for Multipoint Problems in Critical Case. 10.
Theorems on Existence of Solutions of Boundary-Value Problems. 11.
Boundary-Value Problems with Parameters. 3: Integral Manifolds.
12. Auxiliary Statements. 13. Construction of Successive
Approximations. 14. Existence of Integral Manifold. 15.
Conditional Asymptotic Stability of Integral Manifold. 16.
Smoothness of Integral Manifold. 17. Asymptotic Expansion of
Integral Manifold. 18. Decomposition of Equations in the
Neighborhood of Asymptotically Stable Integral Manifold. 19.
Proof of Theorem 18.1. 20. Investigation of Second-Order
Oscillation Systems. 21. Weakening of Conditions in the Theorem
on Integral Manifold. 4: Investigation of a Dynamical System in
the Neighborhood of Quasiperiodic Trajectory. 22. Statement and
General description of the Problem. 23. Theorem on Reducibility.
24. Variational Equation and Theorem on Attraction to
Quasiperiodic Solutions. 25. Behavior of Trajectories under Small
Perturbations of a Dynamical System. 26. The Case of a Toroidal
Manifold Filled with Trajectories of General Form. 27. Discrete
Dynamical System in the Neighborhood of a Quasiperiodic
Trajectory. References
June 2004, ISBN 1-4020-1963-7, Hard cover
Book Series: Mathematics and its Applications : Volume 571
Young measures are now a widely used tool in the Calculus of
Variations, in Control Theory, in Probability Theory and other
fields. They are known under different names such as "relaxed
controls", "fuzzy random variables" and many other
names. This monograph provides a unified presentation of the
theory, along with new results and applications in various fields.
It can serve as a reference on the subject. Young measures are
presented in a general setting which includes finite and for the
first time infinite dimensional spaces: the fields of
applications of Young measures (Control Theory, Calculus of
Variations, Probability Theory...) are often concerned with
problems in infinite dimensional settings. The theory of Young
measures is now well understood in a finite dimensional setting,
but open problems remain in the infinite dimensional case. We
provide several new results in the general frame, which are new
even in the finite dimensional setting, such as characterizations
of convergence in measure of Young measures (Chapter 3) and
compactness criteria (Chapter 4).These results are established
under a different form (and with less details and developments)
in recent papers by the same authors. We also provide new
applications to Visintin and Reshetnyak type theorems (Chapters 6
and 8), existence of solutions to differential inclusions (Chapter
7), dynamical programming (Chapter 8) and the Central Limit
Theorem in locally convex spaces (Chapter 9).
October 2004, ISBN 1-4020-2770-2, Hard cover
Book Series: Nato Science Series: Ii: Mathematics, Physics and
Chemistry : Volume 179
This volume is the conference proceedings of the NATO ARW during
August 2001 at Kananaskis Village, Canada on "New Techniques
in Topological Quantum Field Theory". This conference
brought together specialists from a number of different fields
all related to Topological Quantum Field Theory. The theme of
this conference was to attempt to find new methods in quantum
topology from the interaction with specialists in these other
fields. The featured articles include papers by V.Vassiliev on
combinatorial formulas for cohomology of spaces of Knots, the
computation of Ohtsuki series by N. Jacoby and R. Lawrence, and a
paper by M. Asaeda and J. Przytycki on the torsion conjecture for
Khovanov homology by Shumakovitch. Moreover, There are articles
on more classical topics related to manifolds and braid groups by
such well known authors as D. Rolfsen, H. Zieschang and F. Cohen.
Contents and Contributors
Table of Contents Editorial Combinatorial Formulas for Cohomology
of spaces of Knots V. Vassiliev On the Homology of Spaces of Long
Knots; V. Tourtchine Some computations of Ohtsuki series: N.
Jacoby and R. Lawrence From 3-moves to Lagrangian tangles and
cubic skein modules; J. Przytycki On Spin and Complex Spin
Borromean Surgeries; F. Deloup Khovanov homology: torsion and
thickness; Marta M. Asaeda and Jozef II. Przytycki Khovanov
Homology for Knots and Links up to 11 Crossings; D. Bar Natan.
Perturbative Quantum Field Theory and L Algebras; L. lonescu A
linking form conjecture for 3-manifolds; J. Bryden and F. Deloup
Mappings of non-zero degree between 3-manifolds: a new
obstruction; D. Rolfsen On braid groups, homotopy groups, and
modular forms; F. Cohen A note on symplectic circle actions and
Massey products; Z. Stipiei and A. Tralle Realization of
Primitive Branched Coverings over Closed Surfaces; S.A.Bogatyi ,
D.L. Goncalves, E.A. Kudryavtseva, H. Zieschang Cohomology Rings
of Oriented Seifert Manifolds with mod p Coefficients; J. Bryden
On cyclic covers of the Riemann sphere and a related class of
curves; S. Kallel, D. Sjerve, Y. Song
May 2004, ISBN 0-306-48433-1, Paperback
By assuming it is possible to understand regression analysis
without fully comprehending all its underlying proofs and
theories, this introduction to the widely used statistical
technique is accessible to readers who may have only a
rudimentary knowledge of mathematics. Chapters discuss:
Contents
The Origins and Uses of Regression Analysis. Basic Matrix Algebra:
Manipulating Vectors. The Mean and Variance of a Variable.
Regression Models and Linear Functions. Errors of Prediction and
Least-Squares Estimation. Least-Squares Regression and Covariance.
Covariance and Linear Independence. Separating Explained and
Error Variance. Transforming Variables to Standard Form.
Regression Analysis with Standardized Variables. Populations,
Samples, and Sampling Distributions. Sampling Distributions and
Test Statistics. Testing Hypotheses Using the t Test. The t Test
for the Simple Regression Coefficient. More Matrix Algebra:
Manipulating Matrices. The Multiple Regression Model. Normal
equations and Partial Regression Coefficients. Partial Regression
and Residualized Variables. The Coefficient of Determination in
Multiple Regression. Standard Errors of Partial Regression
Coefficients. The Incremental Contributions of Variables. Testing
Simple Hypotheses Using the F Test. Testing Compound Hypotheses
Using the F Test. Testing Hypotheses in Nested Regression Models.
Testing for Interaction in Multiple Regression. Nonlinear
Relationships and Variable Transformations. 13 Additional
Chapters. Appendices. Index.