Inverse and Ill-Posed Problems Series
The problems of determining coefficients of hyperbolic equations
and systems from additional information on their solutions are of
great practical significance. As a rule, the desired coefficients
are important characteristics of the media under consideration.
In this monograph, dynamic type of inverse problems in which the
additional information is given by the trace of the direct
problem solution on a (usually time-like) surface of the domain
is considered.
In this book theoretical and numerical background of the direct
methods are discussed. Theorems of convergence, conditional
stability and other properties of the mentioned above methods are
formulated and proven.
This book is of value and interest for students, postgraduate
students, engineers, and researchers who are interested in the
theory and numerics of inverse problems for hyperbolic equations.
2005; viii+180 pages
ISBN 90-6764-416-1
Series: Advanced Courses in Mathematics - CRM Barcelona,
2004, VII, 182 p., Softcover
ISBN: 3-7643-7216-8
About this book
The subject of this book is stochastic partial differential
equations, in particular, reaction-diffusion equations, Burgers
and Navier-Stokes equations and the corresponding Kolmogorov
equations. For each case the transition semigroup is considered
and irreducibility, the strong Feller property, and invariant
measures are investigated. Moreover, it is proved that the
exponential functions provide a core for the infinitesimal
generator. As a consequence, it is possible to study Sobolev
spaces with respect to invariant measures and to prove a basic
formula of integration by parts (the so-called "carre du
champs identity". Several results were proved by the author
and his collaborators and appear in book form for the first time.
Presenting the basic elements of the theory in a simple and
compact way, the book covers a one-year course directed to
graduate students in mathematics or physics. The only
prerequisites are basic probability (including finite dimensional
stochastic differential equations), basic functional analysis and
some elements of the theory of partial differential equations.
Table of contents
Introduction and Preliminaries.- Stochastic Perturbations of
Linear Equations.- Stochastic Differential Equations with
Lipschitz Nonlinearities.- Reaction-Diffusion Equations.- The
Stochastic Burgers Equation.- The Stochastic 2D Navier-Stokes
Equation.- Bibliography.- Index.
2005, XIV, 390 p. 106 illus. 2 tabs. With CD-ROM., Softcover
ISBN: 0-8176-3223-9
About this textbook
Over two hundred novel and innovative computer algebra worksheets
or "recipes" will enable readers in engineering,
physics, and mathematics to easily and rapidly solve and explore
most problems they encounter in their mathematical physics
studies. While the aim of this text is to illustrate
applications, a brief synopsis of the fundamentals for each topic
is presented, the topics being organized to correlate with those
found in traditional mathematical physics texts. The recipes are
presented in the form of stories and anecdotes, a pedagogical
approach that makes a mathematically challenging subject easier
and more fun to learn.
Key features:
* Uses the MAPLE computer algebra system to allow the reader to
easily and quickly change the mathematical models and the
parameters and then generate new answers
* No prior knowledge of MAPLE is assumed; the relevant MAPLE
commands are introduced on a need-to-know basis
* All recipes are contained on a CD-ROM provided with the text
* All MAPLE commands are indexed for easy reference
* A classroom-tested story/anecdote format is used, accompanied
with amusing or thought-provoking quotations
* Study problems, which are presented as Supplementary Recipes,
are fully solved and annotated and also provided on the CD-ROM
This is a self-contained and standalone text, similar in style
and format to Computer Algebra Recipes: A Gourmet's Guide to
Mathematical Models of Science (ISBN 0-387-95148-2), Springer New
York 2001 and Computer Algebra Recipes for Classical Mechanics (ISBN
0-8176-4291-9), Birkhauser 2003. Computer Algebra Recipes for
Mathematical Physics may be used in the classroom, for self-study,
as a reference, or as a text for an online course.
Series: Progress in Nonlinear Differential Equations and Their
Applications, Vol. 61
2005, XIV, 282 p., Hardcover
ISBN: 3-7643-7165-X
About this book
Vsevolod Alekseevich Solonnikov is known as one of the
outstanding mathematicians from the St. Petersburg Mathematical
School. His remarkable results on exact estimates of solutions to
boundary and initial-boundary value problems for linear elliptic,
parabolic, Stokes and Navier-Stokes systems, his methods and
contributions to the inverstigation of free boundary problems, in
particular in fluid mechanics, are well known to specialists all
over the world.
The International Conference on "Trends in Partial
Differential Equations of Mathematical Physics" was held on
the occasion of his 70th birthday in Obidos (Portugal) from June
7 to 10, 2003. The conference consisted of thirty-eight invited
and contributed lectures and gathered, in the charming and unique
medieval town of Obidos, about sixty participants from fifteen
countries.
This book contains twenty original contributions on many topics
related to V.A. Solonnikov's work, selected from the invited
talks of the conference.
Table of contents
Preface.- Contributions by S.N. Antonsev, J.I. Di-az, H.B. de
Oliveira - M. Bonforte, G. Grillo - L. Brandolese - L.
Consiglieri, J.F. Rodrigues, T. Shilkin - I.V. Denisova - D.
Andreucci, P. Bisegna, E. DiBenedetto - C. Ebmeyer - A. Fasano, M.
Primicero - E.V. Frolova - D.A. Gomes - G. Guidoboni, M. Padula -
Li Tatsien - A. Mahalov, B. Nicolaenko, C. Bardos, F. Golse - P.B.
Mucha - J. Neustupa, P. Penel - M. Padula - D.L. Rapoport - R.
Rautmann - S. Shmarev - H.-J. Kuo, N.S. Trudinger.
Series: International Series of Numerical Mathematics, Vol.
149
2005, Approx. 248 p., Hardcover
ISBN: 3-7643-7208-7
About this book
The book provides a summary of recent developments in modeling
epitaxial growth, with emphasis on multi-scale approaches and
numerical methods. It presents a compact overview and can serve
as an introduction for applied mathematicians, theoretical
physicists and computational material scientists into this highly
active interdisciplinary field of research.
Written for:
Biologists, people from education and research with background in
applied mathematics, theoretical physics, materials science,
nanotechnology
Table of contents
Introduction.- Discrete atomic models.- Discrete-continuous
models.- Continuous models.- Connections between discrete-atomic
and discrete continuous models.- Connections between discrete
continuous and continuous models.
Series: Trends in Mathematics,
2005, XXVIII, 297 p., Hardcover
ISBN: 3-7643-7214-1
About this book
The articles in this volume study various cohomological aspects
of algebraic varieties:
- characteristic classes of singular varieties;
- geometry of flag varieties;
- cohomological computations for homogeneous spaces;
- K-theory of algebraic varieties;
- quantum cohomology and Gromov-Witten theory.
The main purpose is to give comprehensive introductions to the
above topics through a series of "friendly" texts
starting from a very elementary level and ending with the
discussion of current research. In the articles, the reader will
find classical results and methods as well as new ones. Numerous
examples will help to understand the mysteries of the
cohomological theories presented. The book will be a useful guide
to research in the above-mentioned areas. It is adressed to
researchers and graduate students in algebraic geometry,
algebraic topology, and singularity theory, as well as to
mathematicians interested in homogeneous varieties and symmetric
functions. Most of the material exposed in the volume has not
appeared in books before.
Contributors:
Paolo Aluffi/Michel Brion/Anders Skovsted Buch/Haibao Duan/Ali
Ulas Ozgur Kisisel
Piotr Pragacz/Jorg Schurmann/Marek Szyjewski/Harry Tamvakis
Table of contents
Preface.- Notes on the Life and Work of A. Grothendieck.-
Characteristic Classes of Singular Varieties.- Lectures on the
Geometry of Flag Varieties.- Combinatorial K-Theory.- Morse
Functions and Cohomology of Homogeneous Spaces.- Integrable
Systems and Gromov-Witten Theory.- Multiplying Schubert Classes.-
Lectures on Characteristic Classes of Constructible Functions.-
Algebraic K-Theory of Schemes.- Gromov-Witten Invariants and
Quantum Cohomology of Grassmannians.
Series: Einstein Studies, Preliminary entry 11
2005, Approx. 510 p. 20 illus., Hardcover
ISBN: 0-8176-4380-X
About this book
This volume from the Einstein Series is based largely on papers
presented at the Sixth International Conference on the History of
General Relativity, held in Amsterdam on June 26-29, 2002. These
contributions from notable experts offer both new and historical
insights on gravitation, general relativity, cosmology, unified
field theory, and the history of science.
Topics discussed include the prehistory of special relativity,
early attempts at a relativistic theory of gravitation, the
beginnings of general relativity, the problem of motion in the
context of relativity, conservation laws, the axiomatization of
relativity, classical and contemporary cosmology, gravitation and
electromagnetism, quantum gravity, and relativity as seen through
the eyes of the public and renowned relativists.
Contributors include: K. Brading; G. Gale; H.F.M. Goenner; J.
Goldberg; S. Katzir; D. Kennefick; H. Kragh; C. Lehner; U. Majer;
J. Mattingly; E.T. Newman; J.D. Norton; J. Renn; R. Rynasiewicz;
J.M. Sanchez-Ron; T. Sauer; C. Smeenk; J. Stachel; M. Wazeck; and
D. Wunsch.
Table of contents
Preface * Stachel: Fresnel's (Dragging) Coefficient as a
Challenge to 19th Century Optics of Moving Bodies * Katzir:
Poincare's Relativistic Theory of Gravitation * Renn: Standing on
the Shoulders of a Dwarf: General Relativity?A Triumph of
Einstein and Grossman's Erroneous Entwurf Theory * Renn: Before
the Riemann Tensor: The Emergence of Einstein's Double Strategy *
Norton: A Conjecture on Einstein, the Independent Reality of
Spacetime Coordinate Systems and the Disaster of 1913 * Lehner:
Einstein and the Principle of General Relativity, 1916-1921 *
Kennefick: Einstein and the Problem of Motion: A Small Clue *
Brading: A Note on General Relativity, Energy Conservation, and
Noether's Theorems * Rynasiewicz: Weyls vs. Reichenbach on
Lichtgeometrie * Gale: Dingle and de Sitter Against the
Metaphysicians, or Two Ways to Keep Modern Cosmology Physical *
Kragh: George Gamow and the 'Factual Approach' to Relativistic
Cosmology * Sanchez-Ron: George McVittie, The Uncompromising
Empiricist * Smeenk: False Vacuum: Early Universe Cosmology and
the Development of Inflation * Majer and Sauer: Hilbert's 'World
Equations' and His Vision of a Unified Science * Wunsch:
Einstein, Kaluza and the Fifth Dimension * Goenner: Large Unified
Field Theory: Early History and Interplay between Mathematics and
Physics * Mattingly: Is Quantum Gravity Necessary? * Wazeck:
Einstein in the Daily Press: A Glimpse into the Gehrcke Papers *
Goldberg: Syracuse: 1949-1952 * Newman: A Biased and Personal
Description of GR at Syracuse University, 1951-1961