On dynamics of semiconjugated entire functions

Let $g$ and $h$ be transcendental entire functions and let $f$ be a continuous map of the complex plane into itself with $f\circ g=h\circ f.$ Then $g$ and $h$ are said to be semiconjugated by $f$ and $f$ is called a semiconjugacy. We consider the dynamical properties of semiconjugated transcendental entire functions $g$ and $h$ and provide several conditions under which the semiconjugacy $f$ carries Fatou set of one entire function into the Fatou set of other entire function appearing in the semiconjugation. We have also shown that under certain condition on the growth of entire functions appearing in the semiconjugation, the set of asymptotic values of the derivative of composition of the entire functions is bounded.Comment: 6 pages, accepted for publication in J.Ind.Math.Soc. arXiv admin note: substantial text overlap with arXiv:1307.578

Flash of Prompt Photons from the Early Stage of Heavy-Ion Collisions

We briefly recall the tremendous strides in the studies of the parton cascade model made by Klaus Geiger. Next, we argue that photons may provide confirmation of several of these ideas. Thus we know that, copious internetted partonic cascades may develop in the wake of relativistic collisions of nuclei at CERN SPS and BNL RHIC energies, We use the parton cascade model to estimate the emission of single photons generated from such cascades due to the branching of quarks $q \to q \gamma$, scattering of quarks and gluons, and annihilation of quarks. The formation of a hot and dense partonic matter is shown to be preceded by an intense radiation of photons from the QED branching of quarks. This is similar to the QCD branching $q \to qg$ which along with the gluon multiplication ($g \to gg$) which is known to play a crucial role in the formation of the dense partonic plasma.Comment: 14 pages, including 4 figures. Contribution to Proceedings of ``Kay Kay Gee Day- Klaus Kinder-Geiger Memorial Workshop'' held at Brookhaven National Lab, October 23, 199

Scaling of single photon production in hadronic collisions

Scaling of single photon production in $pp$ and $p\overline{p}$ collisions is studied. It is empirically observed the available data scales $\sim \sqrt{s}/p_T^5$ for $x_T=2p_T/\sqrt{s} \leq 0.1$ and $\sim (\sqrt{s})^{3.3}/p_T^9$ for larger $x_T$. The NLO pQCD predictions for $pp$ collisions at $\sqrt{s}$ of 200 and 5500 GeV, relevant for RHIC and LHC energies are seen to closely follow this scaling behaviour. Implications for single photon production in heavy ion collisions are discussed.Comment: 4 pages including 5 figures. Figure 5 changed to include correct two-loop contributions. (Submitted to Eur. Phys. J. C.