The group of strong Galois objects associated to a cocommutative Hopf quasigroup

Let H be a cocommutative faithfully flat Hopf quasigroup in a strict symmetric monoidal category with equalizers. In this paper we introduce the notion of (strong) Galois H-object and we prove that the set of isomorphism classes of (strong) Galois H-objects is a (group) monoid which coincides, in the Hopf algebra setting, with the Galois group of H-Galois objects introduced by Chase and Sweedler

Organic Molecules in the Galactic Center. Hot Core Chemistry without Hot Cores

We study the origin of large abundances of complex organic molecules in the Galactic center (GC). We carried out a systematic study of the complex organic molecules CH3OH, C2H5OH, (CH3)2O, HCOOCH3, HCOOH, CH3COOH, H2CO, and CS toward 40 GC molecular clouds. Using the LTE approximation, we derived the physical properties of GC molecular clouds and the abundances of the complex molecules.The CH3OH abundance between clouds varies by nearly two orders of magnitude from 2.4x10^{-8} to 1.1x10^{-6}. The abundance of the other complex organic molecules relative to that of CH3OH is basically independent of the CH3OH abundance, with variations of only a factor 4-8. The abundances of complex organic molecules in the GC are compared with those measured in hot cores and hot corinos, in which these complex molecules are also abundant. We find that both the abundance and the abundance ratios of the complex molecules relative to CH3OH in hot cores are similar to those found in the GC clouds. However, hot corinos show different abundance ratios than observed in hot cores and in GC clouds. The rather constant abundance of all the complex molecules relative to CH3OH suggests that all complex molecules are ejected from grain mantles by shocks. Frequent (similar 10^{5}years) shocks with velocities >6km/s are required to explain the high abundances in gas phase of complex organic molecules in the GC molecular clouds. The rather uniform abundance ratios in the GC clouds and in Galactic hot cores indicate a similar average composition of grain mantles in both kinds of regions. The Sickle and the Thermal Radio Arches, affected by UV radiation, show different relative abundances in the complex organic molecules due to the differentially photodissociation of these molecules.Comment: 18 pages, 10 Postscript figures, uses aa.cls, aa.bst, 10pt.rtx, natbib.sty, revsymb.sty revtex4.cls, aps.rtx and aalongtabl.sty. Accepted in A&A 2006. version 2. relocated figures and tables. Language editor suggestions. added reference

Variational approach for walking solitons in birefringent fibres

We use the variational method to obtain approximate analytical expressions for the stationary pulselike solutions in birefringent fibers when differences in both phase velocities and group velocities between the two components and rapidly oscillating terms are taken into account. After checking the validity of the approximation we study how the soliton pulse shape depends on its velocity and nonlinear propagation constant. By numerically solving the propagation equation we have found that most of these stationary solutions are stable.Comment: LaTeX2e, uses graphicx package, 23 pages with 8 figure

ISO observations of the Galactic center Interstellar Medium: neutral gas and dust

The 500 central pc of the Galaxy (hereafter GC) exhibit a widespread gas component with a kinetic temperature of 100-200 K. The bulk of this gas is not associated to the well-known thermal radio continuum or far infrared sources like Sgr A or Sgr B. How this gas is heated has been a longstanding problem. With the aim of studying the thermal balance of the neutral gas and dust in the GC, we have observed 18 molecular clouds located at projected distances far from thermal continuum sources with the Infrared Space Observatory (ISO). In this paper we present observations of several fine structure lines and the full continuum spectra of the dust between 40 and 190 microns. A warm dust component with a temperature between 27 and 42 K is needed to fit the spectra. We have compared the gas and the dust emission with the predictions from J-type and C-type shocks and photodissociation region (PDRs) models. We conclude that the dust and the fine structure lines observations are best explained by a PDR with a density of 10$^3$ cm^-3 and an incident far-ultraviolet field 10$^3$ times higher than the local interstellar radiation field. PDRs can naturally explain the discrepancy between the gas and the dust temperatures. However, these PDRs can only account for 10-30% of the total H2 column density with a temperature of ~ 150 K. We discuss other possible heating mechanisms (short version).Comment: Accepted for publication by A&

Smash (co)products and skew pairings

Let [tau] be an invertible skew pairing on (B,H), where B and H are Hopf algebras in a symmetric monoidal category C with (co)equalizers. Assume that H is quasitriangular. Then we obtain a new algebra structure such that B is a Hopf algebra in the braided category HHYD and there exists a Hopf algebra isomorphism w: B[infinity]H --> B [tau]H in C, where B[infinity]H is a Hopf algebra with (co)algebra structure the smash (co)product and B [tau] H is the Hopf algebra defined by Doi and Takeuchi