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Curves, Plane --- Courbes planes --- Fractals --- Fractales --- Courbes algébriques

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Mathematical control systems --- cryptografie --- Curves, Elliptic --- Elliptic curves --- Coding theory --- 512.7 --- 519.72 --- 512.7 Algebraic geometry. Commutative rings and algebras --- Algebraic geometry. Commutative rings and algebras --- 519.72 Information theory: mathematical aspects --- Information theory: mathematical aspects --- Curves, Algebraic --- Data compression (Telecommunication) --- Digital electronics --- Information theory --- Machine theory --- Signal theory (Telecommunication) --- Computer programming --- Codage --- Courbes elliptiques

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This book focuses on the formulation of mathematical models for the light curves of eclipsing binary stars, and on the algorithms for generating such models. Since information gained from binary systems provides much of what we know of the masses, luminosities, and radii of stars, such models are acquiring increasing importance in studies of stellar structure and evolution. As in other areas of science, the computer revolution has given many astronomers tools that previously only specialists could use; anyone with access to a set of data can now expect to be able to model it. This book will provide astronomers, both amateur and professional, with a guide for - specifying an astrophysical model for a set of observations - selecting an algorithm to determine the parameters of the model - estimating the errors of the parameters It is written for readers with knowledge of basic calculus and linear algebra; appendices cover mathematical details on such matters as optimization, coordinate systems, and specific models. While emphasizing the physical and mathematical framework, the discussion remains close to the problems if actual implementation. It begins with an overview of the problem and a discussion of the observational data that form the basis of any model. The treatment then turns to the direct problem (computing the light curve and other observables from the a given set of parameters) and then to the indirect problem (determining a best-fit set of parameters from the data). The book concludes with chapters on specific models and approaches and the authors' views on the structure of future light- curve programs.

Eclipsing binaries --- Etoiles doubles photométriques --- Light curves --- Courbes de lumière --- Light curves. --- Etoiles doubles photométriques --- Courbes de lumière --- Observations, Astronomical. --- Astronomy—Observations. --- Astrophysics. --- Astronomy, Observations and Techniques. --- Astrophysics and Astroparticles. --- Astronomical physics --- Astronomy --- Cosmic physics --- Physics --- Astronomical observations --- Observations, Astronomical

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This volume contains the expanded versions of the lectures given by the authors at the C.I.M.E. instructional conference held in Cetraro, Italy, from July 12 to 19, 1997. The papers collected here are broad surveys of the current research in the arithmetic of elliptic curves, and also contain several new results which cannot be found elsewhere in the literature. Owing to clarity and elegance of exposition, and to the background material explicitly included in the text or quoted in the references, the volume is well suited to research students as well as to senior mathematicians.

Curves, Elliptic --- Mathematical Theory --- Geometry --- Mathematics --- Physical Sciences & Mathematics --- Number theory. --- Algebraic geometry. --- Number Theory. --- Algebraic Geometry. --- Algebraic geometry --- Number study --- Numbers, Theory of --- Algebra --- Mathematics. --- Geometry, Algebraic. --- Math --- Science --- Géométrie algébrique --- Géométrie algébrique --- Courbes elliptiques --- Nombres, Théorie des