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a perfect lens that would be able to resolve details even smaller than the wavelengths of light used to create the image; see [ 22 ]. The behavior in complex scenarios, such as the propagation of light through materials that alternate between standard materials and metamaterials, is complex and interesting. Motivated by this new discovery in physics, we introduce and study a new billard-type dynamical system. 1.2 Tiling billiards We formulate a model for light passing between two media with refraction coefficient – 1, which we call tiling billiards , defined as

Volume 3, Issue 4 2007 Article 4 Journal of Quantitative Analysis in Sports Position Play in Carom Billiards as a Markov Process Mathieu Bouville, Institute of Materials Research and Engineering Recommended Citation: Bouville, Mathieu (2007) "Position Play in Carom Billiards as a Markov Process," Journal of Quantitative Analysis in Sports: Vol. 3: Iss. 4, Article 4. DOI: 10.2202/1559-0410.1075 ©2007 American Statistical Association. All rights reserved. Position Play in Carom Billiards as a Markov Process Mathieu Bouville Abstract Position play is a key feature

Peter H. Richter8, Andreas Wittek8, Mikhail P. Kharlamovb, and Alexej P. Kharlamov0 a Institut für Theoretische Physik and Institut für Dynamische Systeme, University of Bremen, Postfach 330440, D-28334 Bremen b Institute of Mechanical Engineering, University of Volgograd, GUS-400 119 Volgograd, Russia c Physico-Technical Institute of the Ukrainian Academy of Science, Donetsk 340006, Ukraine Z. Naturforsch. 50a, 693-710 (1995); received February 28, 1995 Dedicated to Professor Siegfried Großmann on the occasion of his 65th birthday Integrable billiards in

Energy Surfaces of Ellipsoidal Billiards Jan Wiersig and Peter H. Richter Institut für Theoretische Physik and Institut für Dynamische Systeme, University of Bremen, Postfach 330 440, 28334 Bremen, Germany Z. Naturforsch. 51 a , 219-241 (1996); received March 14, 1996 Energy surfaces in the space of action variables are calculated and graphically presented for general triaxial ellipsoidal billiards. As was demonstrated by Jacobi in 1838, the system may be integrated in terms of hyperelliptic functions. The actual computation, however, has never been done

Discrete Math. Appl., Vol. 12, No.5, pp. 501-514 (2002) ©VSP2002. On w-languages of special billiards B. F. MELNIKOV Abstract - We consider non-deterministic initial finite automata without final states and the w-languages determined by such automata. For such w-languages, we consider the so-called lan- guages of obstructions. We define and analyse billiard w-languages determined in a special way for each n ?: 3 over an alphabet consisting of n letters. Each w-word of such w-language can be obtained with the use of infinite number of reflections of a point

• 1 • The Lemon Tree Billiards House The Lemon Tree Billiards House is on the first floor of an old concrete building on King Street, between Aloha Electronics and Uncle Phil’s Flowers. The building is old and the pool hall isn’t very large—just nine tables, a ceiling fan, and a soda machine. No one seems to know how the place got its name. Some say it used to be a Korean bar. Others say it was a funeral home. But all seem to agree that it has a lousy name for a pool hall. At one point someone circu- lated a petition requesting the name be changed. But Mr. Kong

60 Other Summer Sports Roller Skating, Walking, Billiards, Tree Climbing, Kite Flying, Steer Wrestling, Fairgrounds sana rahman In this chapter, catastrophic injuries sustained in various sports and recreational activities will be discussed including, roller skating, walking, tree climbing, billiards, kite flying, steer wrestling in rodeos, and injuries sustained at fairgrounds (Table 60.1). In general, these activities are mainly summer activities, and are therefore included in this category. None of these activities had a sufficient number of injuries in our

C h a p t e r 4 Social Cues and Outside Pockets Billiards, Blithedale, and Targeted Potential Often the given writer who first gave vigor to the equation did not, however, intend it as a “bridge” in this historical sense, as a way of abandoning one position and taking up its opposite. Rather he cher- ished it precisely because this midway quality itself was his position. — Kenneth Burke, A Grammar of Motives (1969) Standing at a sturdy and handsome bagatelle table, a caricatured Abraham Lincoln leans into his shot, an intense but comfortable look of focus

Abstract

Groping our way toward a theory of singular spaces with positive scalar curvatures we look at the Dirac operator and a generalized Plateau problem in Riemannian manifolds with corners. Using these, we prove that the set of C 2-smooth Riemannian metrics g on a smooth manifold X, such that scalg(x) ≥ κ(x), is closed under C 0-limits of Riemannian metrics for all continuous functions κ on X. Apart from that our progress is limited but we formulate many conjectures. All along, we emphasize geometry, rather than topology of manifolds with their scalar curvatures bounded from below.