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J. Ding

Publications and source records attributed to J. Ding.

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A Quadruple-Phase Strong Mg II Absorber at z~0.9902 Toward PG 1634+706

The z=0.9902 system along the quasar PG 1634+706 line of sight is a strong MgII absorber (W(2796)>0.3A) with only weak CIV absorption (it is ``CIV-deficient''). To study this system, we used high-resolution spectra from both HST/STIS (R=30,000) and Keck/HIRES (R=45,000). These spectra cover key transitions, such as MgI, MgII, FeII, SiII, CII, SiIII, CIII, SiIV, and CIV. Assuming a Haardt and Madau extragalactic background spectrum, we modeled the system with a combination of photoionization and collisional ionization. Based on a comparison of synthetic spectra to the data profiles, we infer the existence of the following four phases of gas: i) Seven MgII clouds have sizes of 1-1000pc and densities of 0.002-0.1/cm^3, with a gradual decrease in density from blue to red. The MgII phase gives rise to most of the CIV absorption and resembles the warm, ionized inter-cloud medium of the Milky Way; ii) Instead of arising in the same phase as MgII, MgI is produced in separate, narrow components with b~0.75km/s. These small MgI pockets (~100AU) could represent a denser phase (~200/cm^3) of the interstellar medium (ISM), analogous to the small-scale structure observed in the Milky Way ISM; iii) A ``broad phase'' with a Doppler parameter, b~60km/s, is required to consistently fit Ly-alpha, Ly-beta, and the higher-order Lyman-series lines. A low metallicity (log Z <= -2) for this phase could explain why the system is ``CIV-deficient'', and also why NV and OVI are not detected. This phase may be a galactic halo or it could represent a diffuse medium in an early-type galaxy; iv) The strong absorption in SiIV relative to CIV could be produced in an extra, collisionally ionized phase with a temperature of T~60,000K. The collisional phase could exist in cooling layers that are shock-heated by supernovae-related processes.

astro-ph↗

Integral Presentations for the Universal R-matrix

We present an integral formula for the universal R-matrix of quantum affine algebra with 'Drinfeld comultiplication'. We show that the properties of the universal R-matrix follow from the factorization properties of the cycles in proper configuration spaces. For general g we conjecture that such cycles exist and unique. For $U_q(\hat{sl}_2)$ describe precisely the cycles and present a new simple expression for the universal R-matrix as a result of calculation of corresponding integrals.

math.QA↗

Factorization of the Universal R-matrix for $U_q(\hat{sl}_2)$

The factorization of the universal R-matrix corresponding to so called Drinfeld Hopf structure is described on the example of quantum affine algebra $U_q(\hat{sl}_2)$. As a result of factorization procedure we deduce certain differential equations on the factors of the universal ${\cal R}$-matrix, which allow to construct uniquely these factors in the integral form.

math.QA↗