Series: Lecture Notes in Mathematics
Subseries: Fondazione C.I.M.E., Firenze , Vol. 1942
2008, VIII, 174 p., Softcover
ISBN: 978-3-540-78492-0
Due: April 16, 2008
Of the three lecture courses making up the CIME summer school on Fluid Dynamics at Cetraro in 2005 reflected in this volume, the first, due to Sergio Albeverio describes deterministic and stochastic models of hydrodynamics.
In the second course, Franco Flandoli starts from 3D Navier-Stokes equations and ends with turbulence.
Finally,Yakov Sinai, in the 3rd course, describes some rigorous mathematical results for multidimensional Navier-Stokes systems and some recent results on the one-dimensional Burgers equation with random forcing.
Table of contents
Series: Lecture Notes in Mathematics
Subseries: Fondazione C.I.M.E., Firenze , Vol. 1943
2008, XI, 192 p. 33 illus., Softcover
ISBN: 978-3-540-78545-3
Due: April 23, 2008
Nowadays we are facing numerous and important imaging problems: nondestructive testing of materials, monitoring of industrial processes, enhancement of oil production by efficient reservoir characterization, emerging developments in noninvasive imaging techniques for medical purposes - computerized tomography (CT), magnetic resonance imaging (MRI), positron emission tomography (PET), X-ray and ultrasound tomography, etc. In the CIME Summer School on Imaging (Martina Franca, Italy 2002), leading experts in mathematical techniques and applications presented broad and useful introductions for non-experts and practitioners alike to many aspects of this exciting field. The volume contains part of the above lectures completed and updated by additional contributions on other related topics: a general presentation and introduction (Moscoso), X-ray tomography (Natterer), Electromagnetic imaging (Dorn, Bertete-Aguirre, Papanicolaou), coherent imaging in telecommunications in a multiple input-multiple output setup (Dorn), polarization based optical imaging (Moscoso), topological derivatives used in shape reconstruction related to inverse scattering problems (Carpio, Rapun), Point interactions (DellfAntonio, Figari, Teta).
Prologue by the editor (L.L. Bonilla).- Introduction to Image Reconstruction (M. Moscoso).- X-ray Tomography (F. Natterer).- Adjoint Fields and Sensitivities for 3D Electromagnetic Imaging in Isotropic and Anisotropic Media (O. Dorn, H. Bertete-Aguirre, G.C. Papanicolaou).- Polarization-based Optical Imaging (M. Moscoso).- A Brief Review on Point Interactions (G. Dell'Antonia, R. Figar, A. Teta).- Topological derivatives for Shape Reconstruction (A. Carpio, M.L. Rapun).- Time-reversal and the Adjoint Imaging Method with an Application in Telecommunication (O. Dorn).
Original Dutch editions published by Mathematics Institute, University of Utrecht, The Netherlands
2008, Approx. 160 p. 76 illus., Softcover
ISBN: 978-0-387-78130-3
Due: September 2008
A unique place to find classical results in geometry, along with more theorems
Contains a foreword by Robin Hartshorne
Covers a wide range of topics in elementary plane Euclidean geometry
Translator has added historical references and an updated bibliography
This small book has for a long time been a unique place to find classical results from geometry, such as Pythagoras' theorem, the nine-point circle, Morley's triangle, Poncelet's polygons, and many other subjects. In addition, this book contains recent, geometric theorems which have been obtained in this classical field over the past years. There are 27 independent chapters on a wide range of topics in elementary plane Euclidean geometry, at a level just beyond what is usually taught in a good high school or college geometry course. The selection of topics is intelligent, varied, and stimulating. In a small space the author provides many thought-provoking ideas. This book will fit in well with the increasing interest for geometry in research and education. This book was originally published in Dutch, and this will be the first English translation. This translation also includes a new foreword by Robin Hartshorne.
Preface.- The Pythagorean theorem.- Ceva's theorem.- Perpendicular bisectors; concurrence.- The Nine-point circle and euler line.- The Taylor circle.- Coordinate systems with respect to a triangle.- The Area of a triangle as a function of the barycentric coordinates of its vertices.- The Distances from a point to the vertices of a triangle.- The Simson line.- Morley's triangle.- Inequalities in a triangle.- The Mixed area of two parallel polygons.- The Isoperimetric inequaltiy.- Poncelet polygons.- A Closure problem for triangles.- A Class of special triangles.- Two unusual conditions for a triangle.- A Counterpart for the euler line.- Menelaus's theorem; cross-ratios and reciprocation.- The Theorems of desargues, pappus, and pascal.- Inversion.- The Theorems of ptolemy and casey.- Pedal triangles; brocard points.- Isogonal conjugation; the symmedian point.- Isotomic conjugation.- Triangles with two equal angle bisectors.- The Inscribed triangle with the smallest perimeter; the fermat point.- Appendix: remarks and hints.- References.- Index.-
Series: Nonconvex Optimization and Its Applications , Vol. 88
2008, Approx. 310 p., Hardcover
ISBN: 978-3-540-78561-3
Due: May 28, 2008
Invexity and Optimization presents results on invex function and their properties in smooth and nonsmooth cases, pseudolinearity and eta-pseudolinearity. Results on optimality and duality for a nonlinear scalar programming problem are presented, second and higher order duality results are given for a nonlinear scalar programming problem, and saddle point results are also presented. Invexity in multiobjective programming problems and Kuhn-Tucker optimality conditions are given for a multiobjecive programming problem, Wolfe and Mond-Weir type dual models are given for a multiobjective programming problem and usual duality results are presented in presence of invex functions. Continuous-time multiobjective problems are also discussed. Quadratic and fractional programming problems are given for invex functions. Symmetric duality results are also given for scalar and vector cases.
Introduction.- Invex Functions (The Smooth Case).- Pseudolinearity. Invexity and Generalized Monotonicity.- Extensions of Invexity to Nondifferentiable Functions.- Invexity in Nonlinear Programming.- Invex Functions in Multiobjective Programming.- Variational and Control problems involving Invexity.- Invexity For Some Special Functions and Problems.- References.- Index.
Series: Lecture Notes in Mathematics , Vol. 1937
2008, Approx. 220 p., Softcover
ISBN: 978-3-540-78276-6
Due: May 7, 2008
Granular matter displays a variety of peculiarities that distinguish it from other appearances studied in condensed matter physics and renders its overall mathematical modelling somewhat arduous. Prominent directions in the modelling granular flows are analyzed from various points of view. Foundational issues, numerical schemes and experimental results are discussed. The volume furnishes a rather complete overview of the current research trends in the mechanics of granular matter. Various chapters introduce the reader to different points of view and related techniques. New models describing granular bodies as complex bodies are presented. Results on the analysis of the inelastic Boltzmann equations are collected in different chapters. Gallavotti-Cohen symmetry is also discussed.
Preface by Gianfranco Capriz, Pasquale Giovine, Paolo Maria Mariano.- Joe D. Goddard: From granular matter to generalized continuum.- Alexander V. Bobylev, Carlo Cercignani, Irene Martinez Gamba: Generalized kinetic Maxwell models of granular gases.- Giuseppe Toscani: Hydrodynamics from dissipative Boltzmann equation.- Gianfranco Capriz: Bodies with kinetic substructures.- Tommaso Ruggeri: From extended thermodynamics to granular materials.- Ramon Garcia-Rojo, S. McNamara, Hans J. Herrmann: Influence of contact modeling on the macroscopic plastic response of granular soils under cyclic loading.- Alain Barrat, Andrea Puglisi, E. Trizac, Paolo Visco, Frederic van Wijland: Fluctuations in granular gases.- Pasquale Giovine: An extended continuum theory for granular media.- Paolo Maria Mariano: Slow motion in granular matter.- Index.