M. Yan — Page 2 | Searcharxiv

arXiv2001

Physical Conditions in the Foreground Gas of Reflection Nebulae: NGC 2023, vdB 102, and NGC 7023

High resolution optical spectra of HD 37903 and HD 147009, which illuminate the reflection nebulae, NGC 2023 and vdB 102, were obtained for comparison with our results for HD 200775 and NGC 7023. Ground-based measurements of the molecules, CH, C$_2$, and CN, and the atoms, Na I and K I, were analyzed to extract physical conditions in the foreground cloud. Estimates of the gas density, gas temperature and flux of ultraviolet radiation were derived and were compared with the results from infrared and radio studies of the main molecular cloud. The conditions are similar to those found in studies of diffuse clouds. The foreground material is less dense than the gas in the molecular cloud behind the star(s). The gas temperature was set at 40 K, the temperature determined for the foreground gas in NGC 7023. The flux of ultraviolet radiation was found to be less intense than in the molecular material behind the star(s). The column densities of Na I and K I were reproduced reasonably well when the extinction curve for the specific line of sight was adopted. We obtained NEWSIPS data from the IUE archive for HD 37903 and HD 200775. The ultraviolet data on C I and CO allow extraction of the physical conditions by alternate methods. General agreement among the various diagnostics was found, leading to self-consistent pictures of the foreground photodissociation regions. An Appendix describes checks on the usefulness of IUE NEWSIPS data for interstellar studies. (Abridged)

astro-ph↗

arXiv1999

On Hopf algebras with positive bases

We show that if a finite dimensional Hopf algebra over ${\bf C}$ has a basis such that all the structure constants are non-negative, then the Hopf algebra must be given by a finite group $G$ and a factorization $G=G_+G_-$ into two subgroups. We also show that Hopf algebras in the category of finite sets with correspondences as morphisms are classified in the similar way. Our results can be used to explain some results in Hopf algebras from set-theoretical viewpoint.

math.QA↗

arXiv1999

Quasi-triangular structures on Hopf algebras with positive bases

A basis B of a finite dimensional Hopf algebra H is said to be positive if all the structure constants of H relative to B are non-negative. A quasi-triangular structure $R\in H\otimes H$ is said to be positive with respect to B if it has non-negative coefficients in the basis $B \otimes B$ of $H\otimes H$. In our earlier work, we have classified all finite dimensional Hopf algebras with positive bases. In this paper, we classify positive quasi-triangular structures on such Hopf algebras. A consequence of this classification is a new way of constructing set-theoretical solutions of the Yang-Baxter equation.

math.QA↗