Series: Frontiers in Mathematics
2007, VIII, 198 p., 28 illus., Softcover
ISBN-10: 3-7643-7841-7
ISBN-13: 978-3-7643-7841-7
About this book
This book presents models written as partial differential
equations and originating from various questions in population
biology, such as physiologically structured equations, adaptive
dynamics, and bacterial movement. Its purpose is to derive
appropriate mathematical tools and qualitative properties of the
solutions (long time behavior, concentration phenomena,
asymptotic behavior, regularizing effects, blow-up or dispersion).
Original mathematical methods described are, among others, the
generalized relative entropy method - a unique method to tackle
most of the problems in population biology, the description of
Dirac concentration effects using a new type of Hamilton-Jacobi
equations, and a general point of view on chemotaxis including
various scales of description leading to kinetic, parabolic or
hyperbolic equations.
Table of contents
Preface.- 1. From Differential Equations to Structured Population
Dynamics.- 2. Adaptive Dynamics; an Asymptotic Point of View.- 3.
Population Balance Equations: the Renewal Equation.- 4.
Population Balance Equations: Size Structure.- 5. Cell Motion and
Chemotaxis.- 6. General Mathematical Tools.- Bibliography.- Index.
2007, Approx. 255 p., Hardcover
ISBN-10: 3-7643-7989-8
ISBN-13: 978-3-7643-7989-6
About this book
Charles Francois Sturm was born in Geneva, Switzerland, on
September 29, 1803. He obtained his scientific education in this
city and Geneva honoured his memory on the occasion of the 200th
anniversary of his birth by a colloquium and workshop in Geneva
held in 2003.
This volume is based on lectures presented at this colloquium.
The focus is on C.F. Sturm's own work. The book contains
particular reproductions of his scientific publications. Sturm
contributed notably to geometry, algebra, analysis, optics,
mechanics, other work in physics (particularly fluid mechanics
and speed of sound in water).
These original papers are accompanied by contributions from
internationally renowned experts thereby deepening topics like
differential equations, optics and algebraic curves. The volume
complements the book on the development of Sturm-Liouville theory
(ISBN 978-3-7643-7066-4) that also originates from that
colloquium.
Table of contents
Introduction.- Six contributing articles on Sturms work.-
Collected papers.
Series: Operator Theory: Advances and Applications , Vol. 172
2007, Approx. 360 p., Hardcover
ISBN-10: 3-7643-8097-7
ISBN-13: 978-3-7643-8097-7
A Birkhauser book
About this book
The ISAAC Group in Pseudo-Differential Operators (IGPDO) met at
the Fifth ISAAC Congress held at Universita di Catania in Italy
in July, 2005. This volume consists of papers based on lectures
given at the special session on pseudodifferential operators and
invited papers that bear on the themes of IGPDO.
Nineteen peer-reviewed papers represent modern trends in pseudo-differential
operators. Topics include partial differential equations, global
analysis, geometry, quantization, Wigner transforms, Weyl
transforms on Lie groups, mathematical physics and timefrequency
analysis. The articles will be of interest to graduate students
and researchers in analysis, mathematical physics and
mathematical sciences. This collection of essays and research
articles under the banner of IGPDO is a valuable complement to
the volumes "Advances in Pseudo-Differential Operators"
and "Pseudo-Differential Operators and Related Topics"
published in the same series in 2004 and 2006, respectively.
Table of contents
Preface.- Contributions by P. Boggiatto, E. Buzano, M. Cappiello,
R.D. Carmichael, E. Cordero, G. De Donno, A. Eida, G. Garello, J.B.
Gil, T. Gramchev, K. Grochenig, C. Iwasaki, Yu.I. Karlovich, T.
Krainer, C.-I. Martin, A. Mendoza, A. Morando, A. Oliaro, S.
Pilipovic, P. Popivanov, V.S. Rabinovich, S. Roch, L. Rodino, M.
Ruzhansky, B.-W. Schulze, M. Sugimoto, J. Tie, J. Toft, V.
Turunen, M.W. Wong, H. Zhu.
Series: Operator Theory: Advances and Applications , Vol. 173
2007, Approx. 180 p., Hardcover
ISBN-10: 3-7643-8095-0
ISBN-13: 978-3-7643-8095-3
About this book
In this book, non-spectral methods are presented and discussed
that have been developed over the last two decades for the
investigation of asymptotic behavior of operator semigroups. This
concerns in particular Markov semigroups in L1-spaces, motivated
by applications to probability theory and dynamical systems.
Recently many results on the asymptotic behaviour of Markov
semigroups were extended to positive semigroups in Banach
lattices with order-continuous norm, and to positive semigroups
in non-commutative L1-spaces. Related results, historical notes,
exercises, and open problems accompany each chapter.
Table of contents
Winner of the Ferran Sunyer i Balaguer Prize 2006
Series: Progress in Mathematics , Vol. 254
2007, Approx. 280 p., Hardcover
ISBN-10: 3-7643-8096-9
ISBN-13: 978-3-7643-8096-0
A Birkhauser book
About this book
This book examines holomorphic Morse inequalities and the
asymptotic expansion of the Bergman kernel on manifolds by using
the heat kernel. It opens perspectives on several active areas of
research in complex, Kahler and symplectic geometry. A large
number of applications are also included, such as an analytic
proof of Kodaira's embedding theorem, a solution of the Grauert-Riemenschneider
and Shiffman conjectures, compactification of complete Kahler
manifolds of pinched negative curvature, Berezin-Toeplitz
quantization, weak Lefschetz theorems, and asymptotics of the Ray-Singer
analytic torsion.
Table of contents
0. Introduction.- 1. Demailly's Holomorphic Morse Inequalities.-
2. Characterization of Moishezon Manifolds.- 3. Holomorphic Morse
Inequalities on Non-compact Manifolds.- 4. Asymptotic Expansion
of the Bergman Kernel.- 5. Kodaira Map.- 6. Bergman Kernel on Non-compact
Manifolds.- 7. Toeplitz Operators.- 8. Bergman Kernels on
Symplectic Manifolds.- Appendix.- A. Sobolev Spaces - B. Elements
of Analytic and Hermitian Geometry - C. Spectral Analysis of Self-adjoint
Operators - D. Heat Kernel and Finite Propagation Speed - E.
Harmonic Oscillator.
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