Power spectrum and anisotropy of super inflation in loop quantum cosmology

We investigate the scalar mode of perturbation of super inflation in the version of loop quantum cosmology in which the gauge invariant holonomy corrections are considered. Given a background solution, we calculate the power spectrum of the perturbation in the classical and LQC conditions. Then we compute the anisotropy originated from the perturbation. It is found that in the presence of the gauge invariant holonomy corrections the power spectrum is exponentially blue and the anisotropy also grows exponentially in the epoch of super inflation.Comment: 12 pages,4 figures,Published versio

Some new applications for heat and fluid flows via fractional derivatives without singular kernel

This paper addresses the mathematical models for the heat-conduction equations and the Navier-Stokes equations via fractional derivatives without singular kernel.Comment: This is a preprint of a paper whose final and definite form will be published in Thermal Science. Paper Submitted 28/ Dec /2016; Revised 20/Jan/2016; Accepted for publication 21/Jan/201

Anatomy of Bs→PVB_s \to PV decays and effects of next-to-leading order contributions in the perturbative QCD factorization approach

In this paper, we will make systematic calculations for the branching ratios and the CP-violating asymmetries of the twenty one $\bar{B}^0_s \to PV$ decays by employing the perturbative QCD (PQCD) factorization approach. Besides the full leading-order (LO) contributions, all currently known next-to-leading order (NLO) contributions are taken into account. We found numerically that: (a) the NLO contributions can provide $\sim 40\%$ enhancement to the LO PQCD predictions for ${\cal B}(\bar{B}_s^0 \to K^0 \bar{K}^{*0})$ and ${\cal B}(\bar{B}_s^0 \to K^{\pm}K^{*\mp})$, or a $\sim 37\%$ reduction to \calb(\bar{B}_s^0 \to \pi^{-} K^{*+}), and we confirmed that the inclusion of the known NLO contributions can improve significantly the agreement between the theory and those currently available experimental measurements, (b) the total effects on the PQCD predictions for the relevant $B\to P$ transition form factors after the inclusion of the NLO twist-2 and twist-3 contributions is generally small in magnitude: less than $10\%$ enhancement respect to the leading order result, (c) for the "tree" dominated decay $\bar B_s^0\to K^+ \rho^-$ and the "color-suppressed-tree" decay $\bar B_s^0\to \pi^0 K^{*0}$, the big difference between the PQCD predictions for their branching ratios are induced by different topological structure and by interference effects among the decay amplitude ${\cal A}_{T,C}$ and ${\cal A}_P$: constructive for the first decay but destructive for the second one, and (d) for \bar{B}_s^0 \to V(\eta, \etar) decays, the complex pattern of the PQCD predictions for their branching ratios can be understood by rather different topological structures and the interference effects between the decay amplitude \cala(V\eta_q) and \cala(V\eta_s) due to the \eta-\etar mixing.Comment: 18 pages, 2 figures, 3 tables. Some modifications of the text. Several new references are adde