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

On the freeness of anticyclotomic selmer groups of modular forms

We establish the freeness of certain anticyclotomic Selmer groups of modular forms. The freeness of these Selmer groups plays a key role in the Euler system arguments introduced by Bertolini and Darmon in their work on the anticyclotomic main conjecture for modular forms. In particular, our result fills some implicit gaps which appeared in generalizations of the Bertolini-Darmon result to the case where the associated residual representation is not minimally ramified. The removal of such a minimal ramification hypothesis is essential for applications involving congruences of modular forms.Accepted manuscrip

Measuring |V_{td} / V_{ub}| through B -> M \nu \bar\nu (M=\pi,K,\rho,K^*) decays

We propose a new method for precise determination of |V_{td} / V_{ub}| from the ratios of branching ratios BR(B -> \rho \nu \bar \nu ) / BR(B ->\rho l \nu ) and BR(B -> \pi \nu \bar \nu ) / BR(B -> \pi l \nu ). These ratios depend only on the ratio of the Cabibbo-Kobayashi-Maskawa (CKM) elements |V_{td} / V_{ub}|$ with little theoretical uncertainty, when very small isospin breaking effects are neglected. As is well known, |V_{td} / V_{ub}| equals to (\sin \gamma) / (\sin \beta) for the CKM version of CP-violation within the Standard Model. We also give in detail analytical and numerical results on the differential decay width d\Gamma(B -> K^* \nu \bar \nu ) / dq^2 and the ratio of the differential rates dBR(B -> \rho \nu \bar \nu )/dq^2 / dBR(B -> K^* \nu \bar \nu )/dq^2 as well as BR(B -> \rho \nu \bar \nu ) / BR(B -> K^* \nu \bar \nu) and BR(B -> \pi \nu \bar \nu ) / BR(B -> K \nu \bar \nu).Comment: LaTeX with 2 figures, 12 page

General polygamy inequality of multi-party quantum entanglement

Using entanglement of assistance, we establish a general polygamy inequality of multi-party entanglement in arbitrary dimensional quantum systems. For multi-party closed quantum systems, we relate our result with the monogamy of entanglement to show that the entropy of entanglement is an universal entanglement measure that bounds both monogamy and polygamy of multi-party quantum entanglement.Comment: 4 pages, 1 figur