1 citations · 1 across the 3 of their papers we have counts for
6 papers · 1 filter
On the correlations of directions in the Euclidean plane
Florin P. Boca, Alexandru Zaharescu
We study the correlations of directions in the Euclidean plane, where is a point in a fixed disc, is an integer lattice point in the square , and $Q\to…
The correlations of Farey fractions
Florin P. Boca, Alexandru Zaharescu
We prove that all correlations of the sequence of Farey fractions exist and provide formulas for the correlation measures.
The distribution of the free path lengths in the periodic two-dimensional Lorentz gas in the small-scatterer limit
Florin P. Boca, Alexandru Zaharescu
We study the free path length and the geometric free path length in the model of the periodic two-dimensional Lorentz gas (Sinai billiard). We give a complete and rigorous proof fo…
On the distribution of the Farey sequence with odd denominators
F. P. Boca, C. Cobeli, A. Zaharescu
We prove some asymptotic results on the distribution of h-tuples of consecutive Farey fractions of order Q with odd denominators as .
On the index of Farey sequences
F. P. Boca, R. N. Gologan, A. Zaharescu
We prove some asymptotic formulae concerning the distribution of the index of Farey fractions of order Q as .
The average length of a trajectory in a certain billiard in a flat two-torus
Florin P. Boca, Radu N. Gologan, Alexandru Zaharescu
We remove a small disc from the flat two-dimensional torus and consider a point-like particle that starts moving from the center of the disc with linear trajectory. We provide asym…