Two monotonic functions involving gamma function and volume of unit ball

In present paper, we prove the monotonicity of two functions involving the gamma function $\Gamma(x)$ and relating to the $n$-dimensional volume of the unit ball $\mathbb{B}^n$ in $\mathbb{R}^n$.Comment: 7 page

Effect of sodium hexametaphosphate and trisodium phosphate on dispersion of polycarboxylate superplasticizer

The high fluidity cement-based material has been widely used in indoor floor, grout, pumping concrete and self-compacting concrete. Efficiently dispersing the cement grains is essential for the practical application of this kind of material. Generally, the retarder can enhance the initial dispersion of PCE system because of the reduced consumption of superplasticizer and free water as well as the delayed formation of the hydration products at the very beginning of hydration. Both sodium hexametaphosphate (SHMP) and trisodium phosphate (TSP) are commonly used retarders. However, SHMP can enhance the initial dispersion of PCE while TSP cannot; this phenomenon cannot be simply explained from the retarding effect. It is proposed in this paper that the different behavior of SHMP and TSP could be related to the water/solid interface performance. The adsorption behavior was analyzed with TOC, ICP and XPS. The adsorption model was then proposed to explain the mechanism. The results show that TSP can reduce the initial dispersing ability of PCE while SHMP can enhance it. Both TSP and SHMP can reduce the adsorption capacity of PCE, but increase the thickness of adsorption layer. This phenomenon indicates that phosphates, which can be quickly precipitated and partly cover the PCE layer, may increase the ineffective adsorption to reduce the initial dispersing ability of the PCE system; on the contrary, for those phosphates, which can be combined with Ca2+ and preferentially adsorb onto the surface of cement grains, can avoid the ineffective adsorption to enhance the initial dispersing ability of the PCE system. The results suggest that the dispersing ability of PCE-retarder system is not completely dependent on the total adsorption amount of PCE or the thickness of adsorption layer, but mainly depends on the effective adsorption amount

Spin and lattice excitations of a BiFeO3 thin film and ceramics

We present a comprehensive study of polar and magnetic excitations in BiFeO3 ceramics and a thin film epitaxially grown on an orthorhombic (110) TbScO3 substrate. Infrared reflectivity spectroscopy was performed at temperatures from 5 to 900 K for the ceramics and below room temperature for the thin film. All 13 polar phonons allowed by the factor-group analysis were observed in theceramic samples. The thin-film spectra revealed 12 phonon modes only and an additional weak excitation, probably of spin origin. On heating towards the ferroelectric phase transition near 1100 K, some phonons soften, leading to an increase in the static permittivity. In the ceramics, terahertz transmission spectra show five low-energy magnetic excitations including two which were not previously known to be infrared active; at 5 K, their frequencies are 53 and 56 cm-1. Heating induces softening of all magnetic modes. At a temperature of 5 K, applying an external magnetic field of up to 7 T irreversibly alters the intensities of some of these modes. The frequencies of the observed spin excitations provide support for the recently developed complex model of magnetic interactions in BiFeO3 (R.S. Fishman, Phys. Rev. B 87, 224419 (2013)). The simultaneous infrared and Raman activity of the spin excitations is consistent with their assignment to electromagnons

Monotonicity results and bounds for the inverse hyperbolic sine

In this note, we present monotonicity results of a function involving to the inverse hyperbolic sine. From these, we derive some inequalities for bounding the inverse hyperbolic sine.Comment: 3 page

Ratio of Hadronic Decay Rates of J\psi and \psi(2S) and the \rho\pi Puzzle

The so-called \rho\pi puzzle of J\psi and \psi(2S) decays is examined using the experimental data available to date. Two different approaches were taken to estimate the ratio of J\psi and \psi(2S) hadronic decay rates. While one of the estimates could not yield the exact ratio of \psi(2S) to J\psi inclusive hadronic decay rates, the other, based on a computation of the inclusive ggg decay rate for \psi(2S) (J\psi) by subtracting other decay rates from the total decay rate, differs by two standard deviations from the naive prediction of perturbative QCD, even though its central value is nearly twice as large as what was naively expected. A comparison between this ratio, upon making corrections for specific exclusive two-body decay modes, and the corresponding experimental data confirms the puzzles in J\psi and \psi(2S) decays. We find from our analysis that the exclusively reconstructed hadronic decays of the \psi(2S) account for only a small fraction of its total decays, and a ratio exceeding the above estimate should be expected to occur for a considerable number of the remaining decay channels. We also show that the recent new results from the BES experiment provide crucial tests of various theoretical models proposed to explain the puzzle.Comment: 8 pages, no figure, 4 table

The 13N(d,n)14O Reaction and the Astrophysical 13N(p,g)14O Reaction Rate

$^{13}$N($p,\gamma$)$^{14}$O is one of the key reactions in the hot CNO cycle which occurs at stellar temperatures around $T_9$ $\geq$ 0.1. Up to now, some uncertainties still exist for the direct capture component in this reaction, thus an independent measurement is of importance. In present work, the angular distribution of the $^{13}$N($d,n$)$^{14}$O reaction at $E_{\rm{c.m.}}$ = 8.9 MeV has been measured in inverse kinematics, for the first time. Based on the distorted wave Born approximation (DWBA) analysis, the nuclear asymptotic normalization coefficient (ANC), $C^{^{14}O}_{1,1/2}$, for the ground state of $^{14}$O $\to$ $^{13}$N + $p$ is derived to be $5.42 \pm 0.48$ fm$^{-1/2}$. The $^{13}$N($p,\gamma$)$^{14}$O reaction is analyzed with the R-matrix approach, its astrophysical S-factors and reaction rates at energies of astrophysical relevance are then determined with the ANC. The implications of the present reaction rates on the evolution of novae are then discussed with the reaction network calculations.Comment: 17 pages and 8 figure