Series: Advances in Mathematical Fluid Mechanics
2006, Approx. 210 p., Hardcover
ISBN: 3-7643-7741-0
Due: October 2006
About this book
This volume collects the contributions of a Conference held in
June 2005 at the laboratoire Paul Painleve (UMR CNRS 8524) in
Lille, France. The meeting was intended to review hot topics and
future trends in fluid dynamics, with the objective to foster
exchanges of various viewpoints (e.g. theoretical, and numerical)
on the addressed questions.
Written for:
Researchers, graduate students
Keywords:
Mach number
compressible models
coriolis force
critical thresholds
fluid dynamics
incompressible models
multiphase flows
phase transitions
vortex sheets
2007, Approx. 350 p., 50 illus., Hardcover
ISBN: 0-8176-4526-8
Due: May 2007
About this textbook
Classical mechanics is one of those special occurrences in
science where interdisciplinary contributions have come together
in a perfect blend, providing a most elegant and penetrating
example of "modeling" in science. Following Lagrangrian
principles, the author employs mathematics not only as a "unifying"
language, but also to exemplify its role as a catalyst behind new
concepts and discoveries, such as the d'Alembert principle,
complex systems dynamics, and Hamiltonian mechanics. Today, these
same dynamics are now being focused to address other
interdisciplinary areas of research in fields such as biology and
chemistry.
Key topics and features:
* Revisits beautiful classical material, including gyroscopes,
precessions, spinning tops, effects of rotation of the Earth on
gravity motions, and variational principles
* Analytical mechanics, such as Lagrange's equations, are
explicitly derived, placing them on sound mathematical and
physical ground
* Attention to the topic of "small oscillations and
stability", intended to serve as groundwork to the atomic
theory of vibrations of atoms in molecules
* Hamilton-Jacobi mechanics is treated with an eye to recent
developments in the solvability of Hamilton?Jacobi PDEs
Offering a rigorous mathematical treatment of the subject and
requiring of the reader only a solid background in introductory
physics, multivariable calculus, and linear algebra, Classical
Mechanics can serve as a text for advanced undergraduates and
graduate students in mathematics, physics, engineering, and the
natural sciences, as well as an excellent reference for applied
mathematicians and mathematical physicists.
Written for:
advanced undergraduates and graduate students in mathematics,
math physics, physics, engineering, and math biology
Table of contents
Preface.- Geometry of Motion.- Constraints and Lagrangian
Coordinates.- Dynamics of a Point Mass.- Geometry of Masses.-
Systems Dynamics.- The Lagrange Equations.- Precessions.-
Variational Principles.- Bibliography.- Index.
2007, 50 illus., Softcover
ISBN: 0-8176-4527-6
Due: December 2006
About this textbook
This challenging problem book by renowned US Olympiad coaches,
mathematics teachers, and researchers develops a multitude of
problem-solving skills needed to excel in mathematical contests
and in mathematical research in number theory. Offering
inspiration and intellectual delight, the problems throughout the
book encourage students to express their ideas in writing to
explain how they conceive problems, what conjectures they make,
and what conclusions they reach. Applying specific techniques and
strategies, readers will acquire a solid understanding of the
fundamental concepts and ideas of number theory.
Key features:
* Contains problems developed for various mathematical contests,
including the International Mathematical Olympiad (IMO)
* Builds a bridge between ordinary high school examples and
exercises in number theory and more sophisticated, intricate and
abstract concepts and problems up to the mathematical contest
level
* Begins by familiarizing students with typical examples that
illustrate central themes, followed by numerous carefully
selected problems and extensive discussions of their solutions
* Gathers unconventional, essay-type, non-routine examples,
exercises and problems, many presented in an original fashion
* Engages students in creative thinking and stimulates them to
express their comprehension and mastery of the material beyond
the classroom
104 Number Theory Problems is a valuable resource for advanced
high school students, undergraduates, instructors, mathematics
coaches preparing to participate in mathematical contents, and
those contemplating future research in number theory and its
related areas.
Written for:
Advanced high school students, undergraduates, mathematics
majors, instructors, mathematics coaches
Table of contents
Preface.- Notation.- Number Theory Fundamentals.- Introductory
Problems.- Advanced Problems.- Solutions to Introductory Problems.-
Solutions to Advanced Problems.- Glossary.- References.- Subject
Index.
Series: Applied and Numerical Harmonic Analysis
2007, Approx. 615 p., Hardcover
ISBN: 3-7643-7777-1
Due: November 2006
About this book
This volume reflects the latest developments in the area of
wavelet analysis and its applications. Since the corner-stone
lecture of Yves Meyer presented at the ICM 1990 in Kyoto, in some
extent, wavelet analysis has often been said to be mainly an
applied area. However, a significant percentage of contributors
now are prominent mathematicians working mainly in theoretical
mathematical areas, and the concept of wavelets continuously
stretches across various disciplines of mathematics.
Written for:
Postgraduates and researchers in harmonic and wavelet analysis
Keywords:
harmonic analysis
numerical analysis
wavelets
Table of contents
Preface.- I. Wavelet Theory.- 1. Approximation and Fourier
Analysis - 2. Construction of Wavelets and Frame Theory - 3.
Fractal and Multifractal Theory, Wavelet Algorithms, Wavelets in
Numerical Analysis - 4. Time-Frequency Analysis, Adaptive
Representation of Nonlinear and Non-stationary Signals.- II.
Wavelet Applications.
Series: Cornerstones
2007, Approx. 650 p., 10 illus., Hardcover
ISBN: 0-8176-4522-5
Due: March 2007
Table of contents
Preface.-Guide for the Reader.-Transition to Modern Number Theory.-Wedderburn?Artin
Ring Theory.-Brauer Group.-Homological Algebra.-Three Theorems in
Algebraic Number Theory.-Reinterpretation with Adeles and Ideles.-Infinite
Field Extensions.-Background for Algebraic Geometry.-The Number
Theory of Algebraic Curves.-Methods of Algebraic Geometry.-Index.
Series: Oberwolfach Seminars , Vol. 35
2007, Approx. 400 p., Softcover
ISBN: 3-7643-7805-0
Due: January 2007
About this textbook
This book surveys results on the physical and mathematical
modeling as well as the numerical simulation of hemodynamical
flows, i.e., of fluid and structural mechanical processes
occurring in the human blood circuit. The topics treated are
continuum mechanical description, choice of suitable liquid and
wall models, mathematical analysis of coupled models, numerical
methods for flow simulation, parameter identification and model
calibration, fluid-solid interaction, mathematical analysis of
piping systems, particle transport in channels and pipes,
artificial boundary conditions, and many more. Hemodynamics is an
area of active current research, and this book provides an entry
into the field for graduate students and researchers. It has
grown out of a series of lectures given by the authors at the
Oberwolfach Research Institute in November, 2005.
Keywords:
Hemodynamical Flow
Modeling
finite element method
fluid-solid interaction
non-Newtonian flow
numerical flow simulation
Table of contents
Preface.- Continuum mechanical description of blood flow.-
Mechanical models of blood vessel walls.- Analysis of Newtonian
and non-Newtonian fluid models.- Numerical methods for flow
simulation.- Aspects of mesh and model adaptivity.- Particle
transport in viscous flows.- Flows through systems of pipes.-
Fluid-structure interaction in blood vessels.
Series: Progress in Mathematics , Vol. 282
2007, Approx. 240 p., 10 illus., Hardcover
ISBN: 0-8176-4524-1
Due: April 2007
About this book
This book is a self-contained monograph on spectral theory for
non-compact Riemann surfaces, focused on the infinite-volume case.
A hyperbolic surface of infinite volume provides for a
qualitatively different context from either the compact or finite-volume
cases, a context in which spectral theory of the Laplacian
operator emerges as scattering theory.
Scattering theory, in particular the theory of resonances, is of
great interest in physics, geometry, and analytic number theory.
By focusing on the scattering theory of hyperbolic surfaces, this
work provides a compelling introductory example which will be
accessible to a broad audience. The book opens with an
introduction to the geometry of hyperbolic surfaces. Then a
thorough development of the spectral theory of a geometrically
finite hyperbolic surface of infinite volume is given, which
serves also as an attractive introduction to geometric scattering
theory and the theory of resonances. The final sections of the
recent developments, for which no thorough expository account
exists, include resonance counting (illustrating techniques
developed for potential and obstacle scattering), analysis of the
Selberg zeta function, the Poisson formula relating the resonance
set to the length spectrum, and the proof that the resonance set
determines a surface up to finitely many possibilities.
The book draws on techniques from functional analysis and
differential geometry, as well as some techniques from algebra
and number theory. Thus it should appeal to graduate students and
researchers from a wide range of backgrounds.
Table of contents
Preface.-Hyperbolic surfaces.-Geometry of H.-Fuchsian groups.-Geometric
finiteness.-Classification of hyperbolic ends.-Length spectrum
and Selbergfs zeta function.-Review of the Compact Case.-Spectral
theory for compact manifolds.-Selbergfs trace formula for
compact surfaces.-Consequences of the trace formula.-Review of
the finite-volume case.-Finite-volume hyperbolic surfaces.-Spectral
theory.-Selbergfs trace formula.-Scattering Theory in Model
Cases.-Spectral theory of H.-Scattering theory on H.-Hyperbolic
cylinders.-Funnels.-Parabolic cylinder.-Scattering Theory for
infinite-volume hyperbolic surfaces.-Compactification.-Continuation
of the resolvent.-Resolvent asymptotics and the stretched product.-Structure
of the resolvent kernel.-Discrete and continuous spectrum.-Generalized
eigenfunctions.-Scattering matrix.-Structure of kernels in the
conformally compact case.-Resonances and scattering poles.-Multiplicities
of resonances.-Scattering poles.-Half-integer points.-Coincidence
of resonances and scattering poles.-Upper bound on the density of
resonances.-Infinite-volume spectral geometry.-Relative
scattering determinant.-Regularized traces.-The resolvent 0-trace
calculation.-Structure of Selbergfs zeta function.-The Poisson
formula for resonances.-Application.-Lower bounds on the density.-Weyl
formula for the scattering phase.-The length spectrum.-Finiteness
of isospectral classes.- Appendix A Functional analysis.-Basic
spectral theory.-Analytic Fredholm theorem.-Operator residues and
multiplicities.-Appendix B Asymptotic expansions.-References.-Index.