Series: Lecture Notes in Mathematics, Vol. 2040
Subseries: C.I.M.E. Foundation Subseries
1st Edition., 2011, X, 308 p. 74 illus., 25 in color.
Softcover, ISBN 978-3-642-24078-2
Due: December 31, 2011
This book is a collection of lecture notes for the CIME course on "Multiscale and Adaptivity: Modeling, Numerics and Applications," held in Cetraro (Italy), in July 2009.
Complex systems arise in several physical, chemical, and biological processes, in which length and time scales may span several orders of magnitude. Traditionally, scientists have focused on methods that are particularly applicable in only one regime, and knowledge of the system on one scale has been transferred to another scale only indirectly.
Even with modern computer power, the complexity of such systems precludes their being treated directly with traditional tools, and new mathematical and computational instruments have had to be developed to tackle such problems. The outstanding and internationally renowned lecturers, coming from different areas of Applied Mathematics, have themselves contributed in an essential way to the development of the theory and techniques that constituted the subjects of the courses.
AdaptiveWavelet Methods.- Heterogeneous Mathematical Models in Fluid Dynamics and Associated Solution Algorithms.- Primer of Adaptive Finite Element Methods.- Mathematically Founded Design of Adaptive Finite Element Software.
Series: Lecture Notes in Mathematics, Vol. 2042
2012, 2012, X, 176 p. 22 illus., 11 in color.
Softcover, ISBN 978-3-642-24408-7
Due: January 31, 2012
This volume presents a mathematical development of a recent approach to
the modeling and simulation of turbulent flows based on methods for the
approximate solution of inverse problems. The resulting Approximate Deconvolution
Models or ADMs have some advantages over more commonly used turbulence
models ? as well as some disadvantages. Our goal in this book is to provide
a clear and complete mathematical development of ADMs, while pointing out
the difficulties that remain. In order to do so, we present the analytical
theory of ADMs, along with its connections, motivations and complements
in the phenomenology of and algorithms for ADMs.
1 Introduction.- 2 Large Eddy Simulation.- 3 Approximate Deconvolution Operators and Models.- 4 Phenomenology of ADMs.- 5 Time Relaxation Truncates Scales.- 6 The Leray-Deconvolution Regularization.- 7 NS-alpha- and NS-omega-Deconvolution Regularizations.
Series: Lecture Notes in Mathematics, Vol. 2043
1st Edition., 2011, X, 206 p. 26 illus., 11 in color.
Softcover, ISBN 978-3-642-24414-8
Due: December 31, 2011
Partial differential equations of mixed elliptic-hyperbolic type arise in diverse areas of physics and geometry, including fluid and plasma dynamics, optics, cosmology, traffic engineering, projective geometry, geometric variational theory, and the theory of isometric embeddings. And yet even the linear theory of these equations is at a very early stage. This text examines various Dirichlet problems that can be formulated for Keldysh-type equations, one of the two main classes of linear elliptic-hyperbolic equations. Open boundary conditions (in which data are prescribed on only part of the boundary) and closed boundary conditions (in which data are prescribed on the entire boundary) are both considered. Emphasis is placed on the formulation of boundary conditions for which solutions can be shown to exist in an appropriate function space, and specific applications to plasma physics, optics, and analysis on projective spaces are discussed.
1 Introduction.- 2 Mathematical Preliminaries.- 3 The Equation of Cinquini-Cibrario.- 4 The Cold Plasma Model.- 5 Light near a Caustic.- 6 Projective Geometry.
Series: International Series of Numerical Mathematics, Vol. 161
1st Edition., 2012, 300 p.
ISBN 978-3-0348-0248-2
Due: January 19, 2012
Inequalities are an essential component occurring in various mathematical areas. On the one hand, they form a highly important collection of tools e.g. for proving analytic or stochastic theorems or for deriving error estimates in numerical mathematics, and on the other hand they also constitute a fascinating and challenging research field of their own. Inequalities also appear directly in mathematical models for many kinds of applications e.g. from science, engineering, and economics. This volume reflects all these aspects of the area. Classical inequalities related to means or to convexity are addressed as well as inequalities arising in the field of ordinary and partial differential equations, like Sobolev or Hardy-type inequalities, and inequalities occurring in geometrical contexts. Within the last five decades, great contributions to the field of inequalities have been made by late Wolfgang Walter. His book on differential and integral inequalities was a real breakthrough in the 1970fs and has generated a vast variety of further research in this field. He also organized six of the seven gGeneral Inequalitiesh Conferences held at Oberwolfach between 1976 and 1995, and co-edited their proceedings volumes. He participated as an honorary member of the Scientific Committee in the gGeneral Inequalities 8h conference in Hungary. As a recognition of his great achievements, this volume is dedicated to Wolfgang Walterfs memory. The gGeneral Inequalitiesh meetings found their continuation in the gConferences on Inequalities and Applicationsh which, so far, have been held twice in Hungary. This volume contains some contributions of the participants of the second of these conferences which took place in Hajduszoboszlo in September 2010, as well as additional articles written upon invitation. These contributions reflect many theoretical and practical aspects in the field of inequalities, and will be useful for researchers and lecturers, as well as for students who want to familiarize themselves with the area.
Contents.- Preface.- Wolfgang Walter.- Conference on Inequalities and Applications '10.- Boundary Value Problems.- Numerical Methods.- Geometric and Norm Inequalities.- Generalized Convexity.- Convexity and Related Inequalities.- Other Equations and Inequalities.
Volume package: Mathematical Analysis
2012, 2012, XIV, 391p. 106 illus..
ISBN 978-0-8176-8309-2
Due: December 28, 2011
Provides theoretical foundation for analysis of functions of several variables
Motivates the topics with examples, observations, exercises, and illustrations
Includes appendix of mathematicians who made important contributions to analysis
Exciting historical background motivates the subject
Mathematical Analysis: Foundations and Advanced Techniques for Functions of Several Variables builds upon the basic ideas and techniques of differential and integral calculus for functions of several variables, as outlined in an earlier introductory volume. The presentation is largely focused on the foundations of measure and integration theory.
Preface.- Spaces of Summable Functions and Partial Differential Equations.- Convex Sets and Convex Functions.- The Formalism of the Calculus of Variations.- Differential Forms.- Measures and Integrations.- Hausdorff and Radon Measures.- Mathematicians and Other Scientists.- Bibliographical Notes.- Index.
Series: Universitext
1st Edition., 2012, XII, 332 p. 17 illus., 4 in color.
Softcover, ISBN 978-1-4614-1808-5
Due: February 3, 2012
Contains a rapid introduction to complex algebraic geometry Includes background material on topology, manifold theory and sheaf theory
Analytic and algebraic approaches are developed somewhat in parallel
Easy-going style will not intimidate newcomers to algebraic geometry
This textbook is a strong addition to existing introductory literature on algebraic geometry. The authorfs treatment combines the study of algebraic geometry with differential and complex geometry and unifies these subjects using sheaf-theoretic ideas. It is also an ideal text for showing students the connections between algebraic geometry, complex geometry, and topology, and brings the reader close to the forefront of research in Hodge theory and related fields. Unique features of this textbook: - Contains a rapid introduction to complex algebraic geometry - Includes background material on topology, manifold theory and sheaf theory - Analytic and algebraic approaches are developed somewhat in parallel The presentation is easy going, elementary, and well illustrated with examples. gAlgebraic Geometry over the Complex Numbersh is intended for graduate level courses in algebraic geometry and related fields. It can be used as a main text for a second semester graduate course in algebraic geometry with emphasis on sheaf theoretical methods or a more advanced graduate course on algebraic geometry and Hodge Theory.
Preface.- 1. Plane Curves.- 2. Manifolds and Varieties via Sheaves.- 3. More Sheaf Theory.- 4. Sheaf Cohomology.- 5. de Rham Cohomoloy of Manifolds.- 6. Riemann Surfaces.- 7. Simplicial Methods.- 8. The Hodge Theorem for Riemann Manifolds.- 9. Toward Hodge Theory for Complex Manifolds.- 10. Kahler Manifolds.- 11. A Little Algebraic Surface Theory.- 12. Hodge Structures and Homological Methods.- 13. Topology of Families.- 14. The Hard Lefschez Theorem.- 15. Coherent Sheaves.- 16. Computation of Coherent Sheaves.- 17. Computation of some Hodge numbers.- 18. Deformation Invariance of Hodge Numbers.- 19. Analogies and Conjectures.- References.- Index.