On L1L^1-estimates of derivatives of univalent rational functions

We study the growth of the quantity $\int_{\mathbb{T}}|R'(z)|\,dm(z)$ for rational functions $R$ of degree $n$, which are bounded and univalent in the unit disk, and prove that this quantity may grow as $n^\gamma$, $\gamma>0$, when $n\to\infty$. Some applications of this result to problems of regularity of boundaries of Nevanlinna domains are considered. We also discuss a related result by Dolzhenko which applies to general (non-univalent) rational functions.Comment: 16 pages, to appear in Journal d'Analyse Mathematiqu

Omega_{ccc} production via fragmentation at LHC

In the framework of the leading order of perturbative QCD and the nonrelativistic quark-diquark model of baryons we have obtained fragmentation function for c-quark to split into Omega_{ccc} baryon. It is shown that at LHC one can expect 3.5 10^3 events with Omega_{ccc} at p_t>5 GeV/c and -1<y<1 per year.Comment: LaTex, 5 pages and 2 figures. Talk presented at XIV Workshop on High Energy Physics and Quantum Field Theory, Moscow, May 27 - June 4, 199