Discrete time Bogoyavlensky lattices

Discretizations of the Bogoyavlensky lattices are introduced, belonging to the same hierarchies as the continuous--time systems. The construction exemplifies the general scheme for integrable discretization of systems on Lie algebras with $r$--matrix Poisson brackets. An initial value problem for the difference equations is solved in terms of a factorization problem in a group. Interpolating Hamiltonian flow is found.Comment: 22 pages, LaTeX, revised version (the third lattice discretized now!

X-ray Development of the Classical Nova V2672 Ophiuchi with Suzaku

We report the Suzaku detection of a rapid flare-like X-ray flux amplification early in the development of the classical nova V2672 Ophiuchi. Two target-of-opportunity ~25 ks X-ray observations were made 12 and 22 days after the outburst. The flux amplification was found in the latter half of day 12. Time-sliced spectra are characterized by a growing supersoft excess with edge-like structures and a relatively stable optically-thin thermal component with Ka emission lines from highly ionized Si. The observed spectral evolution is consistent with a model that has a time development of circumstellar absorption, for which we obtain the decline rate of ~10-40 % in a time scale of 0.2 d on day 12. Such a rapid drop of absorption and short-term flux variability on day 12 suggest inhomogeneous ejecta with dense blobs/holes in the line of sight. Then on day 22 the fluxes of both supersoft and thin-thermal plasma components become significantly fainter. Based on the serendipitous results we discuss the nature of this source in the context of both short- and long-term X-ray behavior.Comment: To appear in PASJ; 9 pages, 5 figures, 2 table

Contribution of Type Ia and Type II Supernovae for Intra-Cluster Medium Enrichment

The origin of the chemical composition of the intracluster medium (ICM) is discussed in this paper. In particular, the contribution from Type Ia supernovae (SNe Ia) to the ICM enrichment is shown to exist by adopting the fitting formulas which have been used in the analysis of the solar system abundances. Our analysis means that we can use the frequency of SNe Ia relative to SNe II as the better measure than $M_{Fe, SN Ia}/M_{Fe, total}$ for estimating the contribution of SNe Ia. Moreover, the chemical compositions of ICMs are shown to be similar to that of the solar system abundances. We can also reproduce the sulfur/iron abundance ratio within a factor of 2, which means that the abundance problem of sulfur needs not to be emphasized too strongly. We need more precise observations to conclude whether ICMs really suffer the shortage problem of sulfur or not.Comment: 20 pages, LaTeX text and 15 postscript figures. Accepted for publication in Astrophysical Journa

Age Dating of a High-Redshift QSO B1422+231 at Z=3.62 and its Cosmological Implications

The observed Fe II(UV+optical)/Mg II lambda lambda 2796,2804 flux ratio from a gravitationally lensed quasar B1422+231 at z=3.62 is interpreted in terms of detailed modeling of photoionization and chemical enrichment in the broad-line region (BLR) of the host galaxy. The delayed iron enrichment by Type Ia supernovae is used as a cosmic clock. Our standard model, which matches the Fe II/Mg II ratio, requires the age of 1.5 Gyr for B1422+231 with a lower bound of 1.3 Gyr, which exceeds the expansion age of the Einstein-de Sitter Omega_0=1 universe at a redshift of 3.62 for any value of the Hubble constant in the currently accepted range, H_0=60-80 km,s^{-1},Mpc^{-1}. This problem of an age discrepancy at z=3.62 can be unraveled in a low-density Omega_0<0.2 universe, either with or without a cosmological constant, depending on the allowable redshift range of galaxy formation. However, whether the cosmological constant is a required option in modern cosmology awaits a thorough understanding of line transfer processes in the BLRs.Comment: 7 pages including 3 figures, to appear in ApJ Letter

An Algebraic Model for the Multiple Meixner Polynomials of the First Kind

An interpretation of the multiple Meixner polynomials of the first kind is provided through an infinite Lie algebra realized in terms of the creation and annihilation operators of a set of independent oscillators. The model is used to derive properties of these orthogonal polynomials

The algebra of dual -1 Hahn polynomials and the Clebsch-Gordan problem of sl_{-1}(2)

The algebra H of the dual -1 Hahn polynomials is derived and shown to arise in the Clebsch-Gordan problem of sl_{-1}(2). The dual -1 Hahn polynomials are the bispectral polynomials of a discrete argument obtained from a q-> -1 limit of the dual q-Hahn polynomials. The Hopf algebra sl_{-1}(2) has four generators including an involution, it is also a q-> -1 limit of the quantum algebra sl_{q}(2) and furthermore, the dynamical algebra of the parabose oscillator. The algebra H, a two-parameter generalization of u(2) with an involution as additional generator, is first derived from the recurrence relation of the -1 Hahn polynomials. It is then shown that H can be realized in terms of the generators of two added sl_{-1}(2) algebras, so that the Clebsch-Gordan coefficients of sl_{-1}(2) are dual -1 Hahn polynomials. An irreducible representation of H involving five-diagonal matrices and connected to the difference equation of the dual -1 Hahn polynomials is constructed.Comment: 15 pages, Some minor changes from version #