Perthame, Benoit

Transport Equations in Biology

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.

Pont, Jean-Claude (Ed.)

Complete Works of Charles-Francois Sturm

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.


Toft, Joachim; Wong, Man Wah; Zhu, Hongmei (Eds.)

Modern Trends in Pseudo-Differential Operators

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.

Emel'yanov, Eduard Yu.

Non-spectral Asymptotic Analysis of One-Parameter Operator Semigroups

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



Ma, Xiaonan, Marinescu, George

Holomorphic Morse Inequalities and Bergman Kernels

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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