Series: Sources and Studies in the History of Mathematics and Physical Sciences
2009, Approx. 670 p. 49 illus., Hardcover
ISBN: 978-0-387-78955-2
Due: November 2008
For two thousand years, a fundamental ritual of government was the emperor's "granting the seasons" to his people at the New Year by issuing an almanac containing an accurate lunisolar calendar. The high point of this tradition was the "Season-granting system" (Shou-shih li, 1280). Its treatise records detailed instructions for computing eclipses of the sun and moon and motions of the planets, based on a rich archive of observations, some ancient and some new.
Sivin, the West’s leading scholar of the Chinese sciences, not only recreates the project's cultural, political, bureaucratic, and personal dimensions, but translates the extensive treatise and explains every procedure in minimally technical language. The book contains many tables, illustrations, and aids to reference. It is clearly written for anyone who wants to understand the fundamental role of science in Chinese history. There is no comparable study of state science in any other early civilization.
Preface.- Introduction.- Astonomical reform and occupation politics.- Orientation.- The Project: origins and process.- The Astronomers.- The Observatory and its instruments.- The Records.- Evaluation of the season-granting system, part 1.- Evaluation of the season-granting system, part 2.- Canon of the season-granting system, part 1.- Canon of the season-granting system, part 2.- Conclusion.- Appendix a: the instruments of kuo shou-ching.- Appendix b: the account of conduct of kuo shou-ching.- Appendix c: technical terms.- Acknowledgments.- Bibliography.- Index-glossary.-
Series: Lecture Notes in Mathematics , Vol. 1962
2009, Approx. 230 p., Softcover
ISBN: 978-3-540-85993-2
Due: October 30, 2008
In May 2006, The University of Utah hosted an NSF-funded minicourse on stochastic partial differential equations. The goal of this minicourse was to introduce graduate students and recent Ph.D.s to various modern topics in stochastic PDEs, and to bring together several experts whose research is centered on the interface between Gaussian analysis, stochastic analysis, and stochastic partial differential equations. This monograph contains an up-to-date compilation of many of those lectures. Particular emphasis is paid to showcasing central ideas and displaying some of the many deep connections between the mentioned disciplines, all the time keeping a realistic pace for the student of the subject.
Preface.-1. A Primer on stochastic partial differential equations.- 2.The stochastic wave equation.- 3. Application of Malliavin calculus to stochastic partial differential equations.- 4.Some tools and results for parabolic stochastic partial differential equations.- 5. Sample path properties of anisotropic Gaussian random fields.-List of participants.-Index.
Series: Lecture Notes in Mathematics , Vol. 1963
2009, Approx. 240 p., Softcover
ISBN: 978-3-540-85963-5
Due: October 29, 2008
Establishing a new concept of local Lyapunov exponents the author brings together two separate theories, namely Lyapunov exponents and the theory of large deviations.
Specifically, a linear differential system is considered which is controlled by a stochastic process that during a suitable noise-intensity-dependent time is trapped near one of its so-called metastable states. The local Lyapunov exponent is then introduced as the exponential growth rate of the linear system on this time scale. Unlike classical Lyapunov exponents, which involve a limit as time increases to infinity in a fixed system, here the system itself changes as the noise intensity converges, too.
Introduction.- 1. Linear differential systems with parameter excitation.- 2. Locality and time scales of the underlying non-degenerate system.- 3. Exit probabilities for degenerate systems.- 4. Local Lyapunov exponents.- Bibliography.- Index.
Series: International Mathematical Series , Vol. 8,9 & 10
2009, Approx. 1195 p. 3-volume-set.
ISBN: 978-0-387-85791-6
Due: November 2008
Sobolev spaces and inequalities are fundamental tools in the theory of partial differential equations, analysis, differential geometry, mathematical physics, etc. Introduced 70 years ago, they turned out to be extremely useful in many different settings and continue to attract the attention of new generations of mathematicians. Recent advantages in the theory of Sobolev spaces and in applications are presented by globally recognized specialists in topics covering Sobolev-type spaces of functions in metric spaces, various aspects of Sobolev-type inequalities, boundary value problems for differential operators, spectral problems, approximations, optimal control, important problems of mathematical physics, analysis, partial differential equations, geometry, etc.
The book is dedicated to the centenary of S.L. Sobolev and includes biographical articles supplied with the bibliography of Sobolev's works in the 1930s and archive photos of Sobolev previously unpublished in the English-language literature.
Volume I
My Love Affair with the Sobolev Inequality, D.R. Adams.- Maximal Functions in Sobolev Spaces, D. Aalto, J. Kinnunen.- Hardy Type Inequalities Via Riccati and Sturm?Liouville Equations, S. Bobkov, F. Gotze.- Quantitative Sobolev and Hardy Inequalities and Related Symmetrization Principles, A. Cianchi.- Inequalities of Hardy?Sobolev Type in Carnot?Caratheodory Spaces, D. Danielli et al.- Sobolev Embeddings and Hardy Operators, D.E. Edmunds, W.D. Evans.- Sobolev Mappings between Manifolds and Metric Spaces, P. Hajlasz.- A Collection of Sharp Dilation Invariant Integral Inequalities for Differentiable Functions, V. Maz'ya, T. Shaposhnikova.- Optimality of Function Spaces in Sobolev Embeddings, L. Pick.- On the Hardy?Sobolev?Maz'ya Inequality and Its Generalizations, Y. Pinchover, K. Tintarev.- Sobolev Inequalities in Familiar and Unfamiliar Settings, L. Saloff-Coste.- A Universality Property of Sobolev Spaces in Metric Measure Spaces, N. Shanmugalingam.- Cocompact Imbeddings and Structure of Weakly Convergent Sequences, K. Tintarev.
Volume II
On the Mathematical Works of S.L. Sobolev in the 1930s, V. Babich.- Sobolev in Siberia, Y. Reshetnyak.- Boundary Harnack Principle and the Quasihyperbolic Boundary Condition, H. Aikawa.- Sobolev Spaces and their Relatives: local Polynomial Approximation Approach, Y. Brudnyi.- Spectral Stability of Higher Order Uniformly Elliptic Operators, V. Burenkov, P.D. Lamberti.- Conductor Inequalities and Criteria for Sobolev - Lorentz Two - Weight Inequalities, S. Costea, V. Maz'ya.- Besov Regularity for the Poisson Equation in Smooth and Polyhedral Cones, S. Dahlke, W. Sickel.- Variational Approach to Complicated Similarity Solutions of Higher Order Nonlinear Evolution Partial Differential Equations, V. Galaktionov et al.- Lq,p-Cohomology of Riemannian Manifolds with Negative Curvature, V. Gol'dshtein, M. Troyanov.- Volume Growth and Escape Rate of Brownian Motion on a Cartan?Hadamard Manifold, A. Grigor'yan, E. Hsu.- Sobolev Estimates for the Green Potential Associated with the Robin?Laplacian in Lipschitz Domains Satisfying a Uniform Exterior Ball Condition, T. Jakab et al.- Properties of Spectra of Boundary Value Problems in Cylindrical and Quasicylindrical Domains, S. Nazarov.- Estimates for Completeley Integrable Systems of Differential Operators and Applications, Y. Reshetnyak.- Counting Schrodinger Boundstates: Semiclassics and Beyond, G. Rozenblum, M. Solomyak.- Function Spaces on Cellular Domains, H. Triebel.
Volume III
Geometrization of Rings as a Method for Solving Inverse Problems, M. Belishev.- The Ginzburg?Landau Equations for Superconductivity with Random Fluctuations, A. Fursikov et al.- Carleman Estimates with Second Large Parameter for Second Order Operators, V. Isakov, N. Kim.- Sharp Spectral Asymptotics for Dirac Energy, V. Ivrii.- Linear Hyperbolic and Petrowski Type PDEs with Continuous Boundary Control - Boundary Observation Open Loop Map: Implication on Nonlinear Boundary Stabilization with Optimal Decay Rates, I. Lasiecka, R. Triggiani.- Uniform Asymptotics of Green's Kernels for Mixed and Neumann Problems in Domains with Small Holes and Inclusions, V. Maz'ya, A. Movchan.- Finsler Structures and Wave Propagation, M. Taylor.
Series: Lecture Notes in Mathematics , Vol. 1960
2009, Approx. 460 p., Softcover
ISBN: 978-3-540-85419-7
Due: November 26, 2008
Part I.- 1. Derived and Triangulated Categories.- 2. Derived Functors.- 3. Derived Direct and Inverse Image.- 4. Abstract Grothendieck Duality for schemes
Part II.- 1. Commutativity of diagrams constructed from a monoidal pair of pseudofunctors.- 2. Sheaves on ringed sites.- 3. Derived categories and derived functors of sheaves on ringed sites.- 4. Sheaves over a diagram of S-schemes.- 5. The left and right inductions and the direct and inverse images.- 6. Operations on sheaves via the structure data.- 7. Quasi-coherent sheaves over a diagram of schemes.- 8. Derived functors of functors on sheaves of modules over diagrams of schemes.- 9. Simplicial objects.- 10. Descent theory.- 11. Local noetherian property.- 12. Groupoid of schemes.- 13. Boekstedt-Neeman resolutions and hyperExt sheaves.- 14. The right adjoint of the derived direct image functor.- 15. Comparison of local Ext sheaves.- 16. The Composition of two almost-pseudofunctors.- 17. The right adjoint of the derived direct image functor of a morphism of diagrams.- 18. Commutativity of twisted inverse with restrictions.- 19. Open immersion base change.- 20. The existence of compactification and composition data for diagrams of schemes over an ordered finite category.- 21. Flat base change.- 22. Preservation of Quasi-coherent cohomology.- 23. Compatibility with derived direct images.- 24. Compatibility with derived right inductions.- 25. Equivariant Grothendieck's duality.- 26. Morphisms of finite flat dimension.- 27. Cartesian finite morphisms.- 28. Cartesian regular embeddings and cartesian smooth morphisms.- 29. Group schemes flat of finite type.- 30. Compatibility with derived G-invariance.- 31. Equivariant dualizing complexes and canonical modules.- 32. A generalization of Watanabe's theorem.- 33. Other examples of diagrams of schemes