Context. In April 2004 the first image was obtained of a planetary mass companion (now known as 2M1207 b) in orbit around a selfluminous object different from our own Sun (the young brown dwarf 2MASSW J1207334-393254, hereafter 2M1207 A). 2M1207 b probably formed via fragmentation and gravitational collapse, offering proof that such a mechanism can form bodies in the planetary mass regime. Howe...

The purpose of this theoretical work is to establish a connection between the most important properties plane curves: cycloids and sinusoids. For this, drawing mechanism considered, which simultaneously draws sinusoid two cycloids. Based on results obtained using mechanical method obtaining curves, following important, previously unknown, facts are established. Firstly, new in terms that not re...

We study the C2 Ruijsenaars-Schneider(RS) models with interaction potentials of rational and trigonometric types. The Lax pairs for these models are constructed and the involutive Hamiltonians are also given. Taking nonrelativistic limit, we obtain the Lax pair of C2 Calogero-Moser model. PACS: 02.20.+b, 11.10.Lm, 03.80.+r

We introduce the $h$-adic quantum vertex algebras associated with trigonometric $R$-matrices in types $B$, $C$ and $D$, thus generalizing well-known Etingof-Kazhdan construction type $A$. show that restricted modules for affine $D$ are naturally equipped structure of $\phi$-coordinated module aforementioned algebras.

Ray tracing is a well known rendering technique for producing high quality photorealistic pictures. Parametric surfaces are being used extensively in geometric modeling and require fast and robust methods for computing the intersetions of rays with these surfaces. In this paper, we review two recent intersections methods and discuss their problems. Combining and optimizing the advantages of bot...