Billiard and the five-gap theorem

بررسی فرایند نورد متقارن ورق های سه لایه با استفاده از تابع جریان و تئوری حد بالا

In this paper, a mathematical model for symmetrical multi-layer sheet rolling, in which the layers are unbounded before rolling, by using the upper bound method and stream function theorem is proposed. Using this model, we can investigate the plastic deformation behavior of sheets at the roll gap during rolling. Effect of various rolling conditions such as initial and final thickness and flow s...

Spectral analysis of the transfer operator for the Lorentz gas

We study the billiard map associated with both the finiteand infinite-horizon Lorentz gases having smooth scatterers with strictly positive curvature. We introduce generalized function spaces (Banach spaces of distributions) on which the transfer operator is quasicompact. The mixing properties of the billiard map then imply the existence of a spectral gap and related statistical properties such...

Monoids in the fundamental group . . .

We study monoids generated by Zariski-van Kampen generators in the 17 fundamental groups of the complement of logarithmic free divisors in C listed by Sekiguchi (Theorem 1). Five of them are Artin monoids and eight of them are free abelian monoids. The remaining four monoids are not Gaußian and, hence, are neither Garside nor Artin (Theorem 2). However, we introduce, similarly to Artin monoids,...

Generation of the Ahlfors Five Islands Theorem

Poncelet’s theorem and Billiard knots

Let D be any elliptic right cylinder. We prove that every type of knot can be realized as the trajectory of a ball in D. This proves a conjecture of Lamm and gives a new proof of a conjecture of Jones and Przytycki. We use Jacobi’s proof of Poncelet’s theorem by means of elliptic functions. keywords: Poncelet’s theorem, Jacobian elliptic functions, Billiard knots , Lissajous knots, Cylinder kno...