A note on q-Bernstein polynomials

In this paper we constructed new q-extension of Bernstein polynomials. Fron those q-Berstein polynomials, we give some interesting properties and we investigate some applications related this q-Bernstein polynomials.Comment: 13 page

The Effects of the Massless O(alpha_s^2), O(\alpha\alpha_s), O(\alpha^2) QCD and QED Corrections and of the Massive Contributions to Gamma(H^0\rightarrow b\overline{b})

We consider in detail various theoretical uncertainties of the perturbative predictions for the decay width of $H^0\rightarrow b\overline{b}$ process in the region $50\ GeV< M_H\leq 2M_W$. We calculate the order $O(\alpha_s^2)$-contributions to the expression for $\Gamma_{Hb\overline{b}}$ through the pole quark mass and demonstrate that they are important for the elimination of the numerical difference between the corresponding expression and the one through the running $b$-quark mass. The order $O(\alpha\alpha_s)$ and $O(\alpha^2)$ massless and order $O(m_b^2/M_H^2)$ massive corrections to $\Gamma_{Hb\overline{b}}$ are also calculated. The importance of the latter contributions for modeling of the threshold effects is demonstrated. The troubles with identifying of the 4 recent L3 events $e^+e^-\rightarrow l^+l^-\gamma\gamma$ with the decay of a Standard Higgs boson are discussed.Comment: 16 pages, 6 figures (can be optained by mail after the request from the authers, e-mails: [email protected]; [email protected]); LATEX, modified version of ENSLAPP.-A.-407/92 preprin

Photoproduction off the nucleon revisited: Evidence for a narrow N(1688) resonance?

Revised analysis of $\Sigma$ beam asymmetry for the $\eta$ photoproduction on the free proton reveals a structure at $W\sim 1.69$ GeV. Fit of the experimental data based on the E429 solution of the SAID partial wave analysis suggests a narrow ($\Gamma \leq 25$ MeV) resonance. Possible candidates are $P_{11}, P_{13}$, or $D_{13}$ resonances. The result is considered in conjunction with the recent evidence for a bump-like structure at $W\sim 1.67 - 1.68$ GeV in the quasi-free $\eta$ photoproduction on the neutron.Comment: Contribution to the Workshop on the Physics of the Excited Nucleons NSTAR2007, Bonn, Germany, Sept. 5 - 8 2007. To be published in Eur.Phys.J.