This is the first book dedicated to applying the Carleman
estimates to coefficient inverse problems. Coefficient inverse
problems consist of determining the variable coefficients of
partial differential equations from the boundary measurements of
their solutions. Such problems arise in a number of applications
of particular interest to natural sciences and technology, such
as medical imaging, underwater acoustics and electromagnetics,
non-destructive evaluation, geophysics of exploration, etc.. The
main difficulty in solving coefficient inverse problems is due to
their nonlinearity and ill-posedness. This monograph presents one
of the most powerful tools for the mathematical treatment of such
problems, the method of Carleman estimates. Originally introduced
in the field of inverse problems by A.L. Bukhgeim and M.V.
Klibanov in 1981, the method of Carleman estimates has become
popular in the applied mathematics community. Written in a
readable and concise manner, the book introduces the reader to
the essence of the techniques used for deriving Carleman
estimates and using them for proofs of global uniqueness and
stability results for coefficient inverse problems. The core of
the book is two most recent advances of the authors. These are
the global uniqueness of a multidimensional coefficient inverse
problem for a nonlinear parabolic equation and the so-called
convexification framework for constructing globally convergent
algorithms for the numerical solution of coefficient inverse
problems. Several applications of the convexification to
magnetotelluric frequency sounding, electrical impedance
tomography, infra-red optical sensing of biotissies, and time
reversal are discussed. The effectiveness of convexification
algorithms is demonstrated in computational experiments.
This monograph is of value and interest to researchers in the
fields of inverse problems in partial differential equations,
numerical methods, mathematical modeling, scientific computing,
in both academia and industry.
2004; vi+280 pages
ISBN 90-6764-405-6
In this volume, an abstract theory of ‘forms’ is
developed, thus providing a conceptually satisfying framework for
the classification of forms of Fermat equations. The classical
results on diagonal forms are extended to the broader class of
all forms of Fermat varieties.
The main topic is the study of forms of the Fermat equation over
an arbitrary field K. Using Galois descent, all such forms are
classified; particularly, a complete and explicit classification
of all cubic binary equations is given. If K is a finite field
containing the d-th roots of unity, the Galois representation on
l-adic cohomology (and so in particular the zeta function) of the
hypersurface associated with an arbitrary form of the Fermat
equation of degree d is computed.
Contents:
Varieties Over Finite Fields and Their Zeta Function
Galois Descent
Nonabelian Cohomology
I-Adic Cohomology
Classification of Forms
Forms of the Fermat Equation I
Binary Cubic Equations
Forms of the Fermat Equation II
Representations of Semidirect Products
I-Adic Cohomology of Fermat Varieties
The Zeta Function of Forms of Fermat Equations
Appendices:
Pseudo-Abelian Categories
Computation of J3F25(1,1,1)
Readership: Researchers and professionals in physics and
mathematics.
220pp (approx.) Pub. date: Scheduled Spring 2005
ISBN 981-256-039-4
The papers contained in this book address problems in one and
several complex variables. The main theme is the extension of
geometric function theory methods and theorems to several complex
variables. The papers present various results on the growth of
mappings in various classes as well as observations about the
boundary behavior of mappings, via developing and using some semi
group methods.
Contents:
Subriemannian Geometry and Subelliptic Partial Differential
Equations (D-C Chang et al.)
Proper Holomorphic Mappings between Some Generalized Hartogs
Triangles (Z Chen)
Invariant Mappings in Geometric Function Theory (C H FitzGerald)
The Distortion Theorems for Convex Mappings in Several Complex
Variables (S Gong)
Basic Properties of Loewner Chains in Several Complex Variables (I
Graham et al.)
A New Inequality and Its Applications (H Ke)
Intermediate Value Theorem for Functions of Classes of Riemann
Surfaces (M Masumoto)
A Hadamard Theorem on Algebraic Curves (S-K Wang & H-P Zhang)
Hodge?Laplace Operator on Complex Finsler Manifolds (C Zhong
& T Zhong)
and other papers
Readership: Graduate students, researchers and academics in
mathematics.
350pp (approx.) Pub. date: Scheduled Winter 2004
ISBN 981-256-023-8
The book collects original research papers on applied
categorical structures, most of which have been presented at the
North-West European Category Seminar 2003 in Berlin. The spectrum
of these mathematical results reflects the varied interests of
Horst Herrlich ? one of the leading category theorists of the
world ? to whom this volume is dedicated in view of his 65th
birthday. The book contains applications of categorical methods
in various branches of mathematics such as algebra, analysis,
logic and topology, as well as fuzzy structures and computer
science. At the end of the book the reader will find a complete
list of Horst Herrlich’s publications.
Contents:
Boole’s Booleanness (B Banaschewski)
Homeomorphically Closed Nearness Spaces (H L Bentley & J W
Carlson)
The Tensor Product of Orthomodular Posets (R Borger)
Saturated Collections of Metrics (E Colebunders et al.)
Topological Structures in Logics (W Gahler)
The Structure of Affine Algebraic Sets (E Giuli)
A Characterization of Co-Retracts of Functional Structures (R
Kaschek)
Introducing Lagois Correspondences (A Melton)
On Coalgebras which are Algebras (H-E Porst & C Dzierzon)
Fibrewise Sobriety (G Richter & A Vauth)
and other papers
Readership: Graduate students, researchers, academics and
lecturers in mathematics and computer science.
350pp (approx.) Pub. date: Scheduled Fall 2004
ISBN 981-256-053-X
In this collection of essays, biographies and Nobel lectures,
ten Nobel Laureates from five continents give various and
startling perspectives on current questions about modernity and
tradition, unity and diversity, integration, identity and
integrity in a multicultural world of change. It is also a book
on self-confidence and presents different ways to self-knowledge
and cultural individuality. Published in print for the first
time, these studies and penetrating observations on topical
issues, written by leading authors and intellectuals from many
distant countries, make up one of the most intriguing and
engaging avowals of our time.
The Nobel Laureates are:
Sir V S Naipaul (United Kingdom, born in Trinidad)
Nadine Gordimer (South Africa)
Derek Walcott (St Lucia)
Naguib Mahfouz (Egypt)
Patrick White (Australia)
Ernest Hemingway (USA)
Grazia Deledda (Sardinia, Italy)
Amartya Sen (United Kingdom and the USA, born in India)
Rabindranath Tagore (India)
Nelson Mandela (South Africa)
Contents:
Two Worlds (V S Naipaul)
The Enigma of Arrival (V S Naipaul)
Writing and Being (N Gordimer)
Nadine Gordimer and the South African Experience (P Wastberg)
A Single, Homeless, Circling Satellite ? Derek Walcott (J Mjoberg)
The Antilles ? Fragments of Epic Memory (D Walcott)
Naguib Mahfouz ? The Son of Two Civilizations (A Hallengren)
Autobiography (P White)
Patrick White ? Existential Explorer (K Hansson)
A Case of Identity ? Ernest Hemingway (A Hallengren)
Voice of Sardinia ? Grazia Deledda (A Hallengren)
Autobiography (A Sen)
Tagore and His India (A Sen)
Nelson Mandela and the Rainbow of Culture (A Hallengren)
Readership: General.
300pp (approx.) Pub. date: Scheduled Winter 2004
ISBN 981-256-038-6
ISBN 981-256-074-2(pbk)
On March 25, 2003 Professor Vernon Hughes of Yale University
passed away in New Haven, Connecticut. His career in physics
extended over more than 50 years, and his highly influential
research work contributed invaluably to numerous fundamental
questions in physics.
This book comprises a compilation of articles covering talks
given at the Vernon Willard Hughes Memorial Symposium, which took
place at Yale University in November 2003. The fascinating
contributions from many leading experimental and theoretical
physicists cover topics in atomic, nuclear and particle physics,
as well as include remarks made by Professor Alan Bromley at the
symposium dinner. The book also features the Biographical Memoirs
of Professor Hughes, written by Professor Robert Adair for the US
National Academy of Sciences, and a complete list of Professor
Hughes’s publications.
Contents:
Vernon Hughes and the Early Years of Molecular Beam Resonance (N
Ramsey)
Recent Developments of the Theory of Muon and Electron g-2 (T
Kinoshita)
Muonium ? The Early Years (R Prepost)
The 46 Years of Muon g-2 (F Farley)
Fundamental Physics with Diatomic Molecules (D DeMille)
Past, Present and Future of Muonium (K Jungmann)
Vernon Hughes and the Quest for the Proton’s Spin (R Jaffe)
Muonium Lifetime and Heavy Quark Decays (W Marciano)
The Spin Structure of the Nucleon: A Hughes Legacy (G Cates)
Exploring the Nucleon Spin: The Next Decade (A Deshpande)
Parity Nonconservation in Electron?Electron Scattering (E Hughes)
Muon g-2: The Last Word (E Sichtermann)
Remarks at the Symposium Dinner (D A Bromley)
Biographical Memoirs of Vernon Willard Hughes for the National
Academy of Sciences (R Adair)
Readership: Graduate students, academics and researchers in high
energy physics, nuclear physics and atomic physics.
300pp (approx.) Pub. date: Scheduled Winter 2004
ISBN 981-256-050-5