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Bulletin
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Mathematics and Music
In Western Civilization Mathematics and Music have a long and interesting history in common, with several interactions, traditionally associated with the name of Pythagoras but also with a significant number of other mathematicians, like Leibniz, for instance. Mathematical models can be found for almost all levels of musical activities from composition to sound production by traditional instruments or by digital means. Modern music theory has been incorporating more and more mathematical content during the last decades. This book offers a journey into recent work relating music and mathematics. It contains a large variety of articles, covering the historical aspects, the influence of logic and mathematical thought in composition, perception and understanding of music and the computational aspects of musical sound processing. The authors illustrate the rich and deep interactions that exist between Mathematics and Music.
Bulletin
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Mathematical Models for Phase Change Problems
This monograph collects research and expository articles reflect ing the interaction and the cooperation of different groups in several European institut ions concerning current research on mathematical models for the behaviour of materials with phase change. These papers were presented and discussed in a Workshop held at Obidos, Portugal, du ring the first three days of October, 1988, and grew out of a two year period of intensive exploitation of differ ent abilities and mathematical experiences of the six participating groups, namely, in the University of Augsburg, wh ich was the co ordination center of this project, the Laboratoire Central des Ponts et Chaussees of Paris, the Aristoteles ...
Dirichlet Forms
The theory of Dirichlet forms has witnessed recently some very important developments both in theoretical foundations and in applications (stochasticprocesses, quantum field theory, composite materials,...). It was therefore felt timely to have on this subject a CIME school, in which leading experts in the field would present both the basic foundations of the theory and some of the recent applications. The six courses covered the basic theory and applications to: - Stochastic processes and potential theory (M. Fukushima and M. Roeckner) - Regularity problems for solutions to elliptic equations in general domains (E. Fabes and C. Kenig) - Hypercontractivity of semigroups, logarithmic Sobolev inequalities and relation to statistical mechanics (L. Gross and D. Stroock). The School had a constant and active participation of young researchers, both from Italy and abroad.
Nonlinear Evolution Equations And Their Applications - Proceedings Of The Luso-chinese Symposium
This book discusses recent trends and developments in the area of nonlinear evolution equations. It is a collection of invited lectures on the following topics: nonlinear parabolic equations (systems); nonlinear hyperbolic systems; free boundary problems; conservation laws and shock waves; travelling and solitary waves; regularity, stability and singularity, etc.
The Arts of Ornamental Geometry
This collective study focuses on a unique anonymous medieval document on ornamental geometry featuring geometrical constructions and textual instructions in Persian. Selections from the unpublished work of Alpay Özdural (d. 2003) on this subject have been updated with original contributions by Jan P. Hogendijk, Elaheh Kheirandish, Gülru Necipoğlu, and Wheeler M. Thackston. The chapters interpreting this fascinating document are followed, for the first time, by a facsimile, transcription, and translation, as well as drawings of incised construction lines invisible in the photographed facsimile. This publication intersects with the current interest in Islamic geometrical patterning as an in...
