Submillimeter molecular line observations of cometary Levy (1990c)

Observations of HCN and H2CO in Comet Levy (1990c) obtained at the Caltech Submillimeter Observatory during August 1990 are presented. The HCN J=3-2 rotational line was measured at high spectral resolution (0.1 km/s) and mapped at 13 points over a region of approximately 1.5 arcmin. Analysis of the line profile and the map suggest only slight deviations from the distribution expected for isotropic outgassing of HCN from the nucleus at a velocity of 0.7 plus or minus 0.1 km/s. Observations of the HCN J=4-3 and H2CO5(sub 15)4(sub 14) transitions were obtained simultaneously on two days following the HCN J=3-2 measurements. These transitions are the first submillimeter spectral lines to be detected in a comet. Five point maps of the emission show good consistency between the J=3-2 and J=4-3 HCN observations for an HCN production rate of 2 x 10(exp 26) and a rotational temperature of approximately 30 K. The map of H2CO emission indicates that it is more extended than the prediction of models in which H2CO originates entirely from the nucleus. H2CO may also originate from an extended source in the coma

Synthetic horizontal branch morphology for different metallicities and ages under tidally enhanced stellar wind

It is believed that, except for metallicity, some other parameters are needed to explain the horizontal branch (HB) morphology of globular clusters (GCs). Furthermore, these parameters are considered to be correlated with the mass loss of the red giant branch (RGB) stars. In our previous work, we proposed that tidally enhanced stellar wind during binary evolution may affect the HB morphology by enhancing the mass loss of the red giant primary. As a further study, we now investigate the effects of metallicity and age on HB morphology by considering tidally enhanced stellar winds during binary evolution. We incorporated the tidally enhanced-stellar-wind model into Eggleton's stellar evolution code to study the binary evolution. To study the effects of metallicity and age on our final results, we conducted two sets of model calculations: (i) for a fixed age, we used three metallicities, namely Z=0.0001, 0.001, and 0.02. (ii) For a fixed metallicity, Z=0.001, we used five ages in our model calculations: 14, 13, 12, 10, and 7 Gyr. We found that HB morphology of GCs becomes bluer with decreasing metallicity, and old GCs present bluer HB morphology than young ones. These results are consistent with previous work. Although the envelope-mass distributions of zero-age HB stars produced by tidally enhanced stellar wind are similar for different metallicities, the synthetic HB under tidally enhanced stellar wind for Z=0.02 presented a distinct gap between red and blue HB. However, this feature was not seen clearly in the synthetic HB for Z=0.001 and 0.0001. We also found that higher binary fractions may make HB morphology become bluer, and we discussed the results with recent observations.Comment: 16 pages, 6 figures, 3 tables, accepted for publication in Astronomy & Astrophysic

On a refinement of Wilf-equivalence for permutations

Recently, Dokos et al. conjectured that for all $k, m\geq 1$, the patterns $12\ldots k(k+m+1)\ldots (k+2)(k+1)$ and $(m+1)(m+2)\ldots (k+m+1)m\ldots 21$ are $maj$-Wilf-equivalent. In this paper, we confirm this conjecture for all $k\geq 1$ and $m=1$. In fact, we construct a descent set preserving bijection between $12\ldots k (k-1)$-avoiding permutations and $23\ldots k1$-avoiding permutations for all $k\geq 3$. As a corollary, our bijection enables us to settle a conjecture of Gowravaram and Jagadeesan concerning the Wilf-equivalence for permutations with given descent sets

[Colored solutions of Yang-Baxter equation from representations of U_{q}gl(2)]

We study the Hopf algebra structure and the highest weight representation of a multiparameter version of $U_{q}gl(2)$. The commutation relations as well as other Hopf algebra maps are explicitly given. We show that the multiparameter universal ${\cal R}$ matrix can be constructed directly as a quantum double intertwiner, without using Reshetikhin's transformation. An interesting feature automatically appears in the representation theory: it can be divided into two types, one for generic $q$, the other for $q$ being a root of unity. When applying the representation theory to the multiparameter universal ${\cal R}$ matrix, the so called standard and nonstandard colored solutions $R(\mu,\nu; {\mu}', {\nu}')$ of the Yang-Baxter equation is obtained.Comment: [14]pages, latex, no figure

Y(so(5)) symmtry of the nonlinear Schro¨\ddot{o}dinger model with four-cmponents

The quantum nonlinear Schr$\ddot{o}$dinger(NLS) model with four-component fermions exhibits a $Y(so(5))$ symmetry when considered on an infintite interval. The constructed generators of Yangian are proved to satisfy the Drinfel'd formula and furthermore, the $RTT$ relation with the general form of rational R-matrix given by Yang-Baxterization associated with $so(5)$ algebraic structure.Comment: 10 pages, no figure