A certain connection between starlike and convex functions

AbstractWe define two certain classes of functions S∗(α, β) and C(α, β) and obtain a certain connection between these classes

Applications of a Subordination Theorem

AbstractThe object of the present paper is to give applications of a subordination theorem due to Hallenbeck and Ruscheweyh [Proc. Amer. Math. Soc.52 (1975), Theorem 1]. Our results have some interesting corollaries and examples as special cases

Three Generation Long-wavelength Vacuum Oscillation Solution to the Solar Neutrino Problem

We investigate the current status of the long-wavelength vacuum oscillation solution to the solar neutrino problem and to what extent the presence of a third neutrino can affect and modify it. Assuming that the smaller mass squared difference that can induce such oscillations, $\Delta m^2_{12}$, is in the range $10^{-11}-10^{-8}$ eV$^2$ and the larger one, $\Delta m^2_{23}$, in the range relevant to atmospheric neutrino observations, we analyze the most recent solar neutrino data coming from Homestake, SAGE, GALLEX, GNO and Super-Kamiokande experiments in the context of three neutrino generations. We include in our vacuum oscillation analysis the MSW effect in the Sun, which is relevant for some of the parameter space scrutinized. We have also performed, as an extreme exercise, the fit without Homestake data. % While we found that the MSW effect basically does not affect the best fitted parameters, it significantly modifies the allowed parameter space for $\Delta m^2_{12}$ larger than $\sim 3 \times 10^{-10}$ eV$^2$, in good agreement with the result obtained by A. Friedland in the case of two generations. % Although the presence of a third neutrino does not essentially improve the quality of the fit, the solar neutrino data alone can give an upper bound on $\theta_{13}$, which is constrained to be less than $\sim 60^\circ$ at 95 % C.L.Comment: 35 pages, 14 png figures: good quality postscript figures can be found in http://neutrinos.if.usp.br/gefan/papers/publicados/ps/GNZ

Study of a Neutrino Mass Texture Generated in Supergravity with Bilinear R-Parity Violation

We study a particular texture of the neutrino mass matrix generated in supergravity with bilinear R-Parity violation. The relatively high value of $\tan\beta$ makes the one-loop contribution to the neutrino mass matrix as important as the tree-level one. The atmospheric angle is nearly maximal, and its deviation from maximal mixing is related to the smallness of the ratio between the solar and atmospheric mass scales. There is also a common origin for the small values of the solar and reactor angles, but the later is much smaller due the large mass ratio between the lightest two neutrinos. There is a high dependence of the neutrino mass differences on the scalar mass $m_0$ and the gaugino mass $M_{1/2}$, but a smaller one of the mixing angles on the same sugra parameters. Measurements of branching ratios for the neutralino decays can give important information on the parameters of the model. There are good prospects at a future Linear Collider for these measurements, but a more detailed analysis is necessary for the LHC.Comment: 21 pages, 9 figure