A HYPERBOLIC TANGENT YIELD FUNCTION OF FLORIDA CITRUS

This study models Florida citrus production as a function of the age profile of a given tree stock. The age relationship is estimated using a modified hyperbolic tangent function and the parameters is solved by Spatial Process Models and Maximum Likelihood approach. The estimation is based on the production data of four citrus varieties in 25 regions of Florida from 1992 to 2005. The results show smooth S-shaped yield curves of Florida citrus. This analysis offers yield function of citrus as the first step for statistical modeling of the risks associated with citrus cancers aimed at pricing insurance rates.yield function, citrus, hyperbolic tangent, insurance, spatial autoregressive, Demand and Price Analysis,

The NLO contributions to the scalar pion form factors and the O(αs2){\cal O}(\alpha_s^2) annihilation corrections to the B→ππB\to \pi\pi decays

In this paper, by employing the $k_{T}$ factorization theorem, we made the first calculation for the space-like scalar pion form factor $Q^2 F(Q^2)$ at the leading order (LO) and the next-to-leading order (NLO) level, and then found the time-like scalar pion form factor $F'^{(1)}_{\rm a,I}$ by analytic continuation from the space-like one. From the analytical evaluations and the numerical results, we found the following points: (a) the NLO correction to the space-like scalar pion form factor has an opposite sign with the LO one but is very small in magnitude, can produce at most $10\%$ decrease to LO result in the considered $Q^2$ region; (b) the NLO time-like scalar pion form factor $F'^{(1)}_{\rm a,I}$ describes the ${\cal O}(\alpha_s^2)$ contribution to the factorizable annihilation diagrams of the considered $B \to \pi\pi$ decays, i.e. the NLO annihilation correction; (c) the NLO part of the form factor $F'^{(1)}_{\rm a,I}$ is very small in size, and is almost independent with the variation of cutoff scale $\mu_0$, but this form factor has a large strong phase around $-55^\circ$ and may play an important role in producing large CP violation for $B\to \pi\pi$ decays; and (d) for $B^0 \to \pi^+\pi^-$ and $\pi^0\pi^0$ decays, the newly known NLO annihilation correction can produce only a very small enhancement to their branching ratios, less than $3\%$ in magnitude, and therefore we could not interpret the well-known $\pi\pi$-puzzle by the inclusion of this NLO correction to the factorizable annihilation diagrams.Comment: 26 pages, 12 figures, 1 Table; Minor correction

Modelling and interpreting the dependence of clustering on the spectral energy distributions of galaxies

We extend our previous physically-based halo occupation distribution models to include the dependence of clustering on the spectral energy distributions of galaxies. The high resolution Millennium Simulation is used to specify the positions and the velocities of the model galaxies. The stellar mass of a galaxy is assumed to depend only on M_{infall}, the halo mass when the galaxy was last the central dominant object of its halo. Star formation histories are parametrized using two additional quantities that are measured from the simulation for each galaxy: its formation time (t_{form}), and the time when it first becomes a satellite (t_{infall}). Central galaxies begin forming stars at time t_{form} with an exponential time scale tau_c. If the galaxy becomes a satellite, its star formation declines thereafter with a new time scale tau_s. We compute 4000 \AA break strengths for our model galaxies using stellar population synthesis models. By fitting these models to the observed abundances and projected correlations of galaxies as a function of break strength in the Sloan Digital Sky Survey, we constrain tau_c and tau_s as functions of galaxy stellar mass. We find that central galaxies with large stellar masses have ceased forming stars. At low stellar masses, central galaxies display a wide range of different star formation histories, with a significant fraction experiencing recent starbursts. Satellite galaxies of all masses have declining star formation rates, with similar e-folding times, tau_s ~ 2.5Gyr. One consequence of this long e-folding time is that the colour-density relation is predicted to flatten at redshifts > 1.5, because star formation in the majority of satellites has not yet declined by a significant factor. This is consistent with recent observational results from the DEEP and VVDS surveys.Comment: 14 pages, 11 figures, submitted to MNRA

Synthesis of a ditopic homooxacalix[3]arene for fluorescence enhanced detection of heavy and transition metal ions

A pyrene-appended ratiometric fluorescent chemosensor L based on a synthetic approach of insulating the fluorophore from the ionophore by a specific molecular spacer has been synthesised and characterised. The fluorescence spectra changes of L suggested that the chemosensor can detect heavy and transition metal (HTM) ions ratiometrically and with variable sensitivity according to the substituents present. ¹H NMR titration experiments indicated that the three triazole ligands prefer binding with Hg²⁺, Pb²⁺ and Zn²⁺, resulting in a conformational change that produces monomer emission of the pyrene accompanied by the excimer quenching. However, the addition of Fe³⁺, which may be accommodated by the cavity of L, makes the pyrene units move closer to each other, and a discernible increase in the emission intensity of the static excimer is observed. Therefore, it is believed that the ditopic scaffold of the calix[3]arene as a specific molecular spacer here plays an important role in the blocking of the heavy atom effect of HTM ions by insulating the fluorophore from the ionophore given the long distance between the metal cation and the pyrene moiety