Auto-parallel equation as Euler-Lagrange's equation in spaces with affine connections and metrics

The auto-parallel equation over spaces with affine connections and metrics is considered as a result of the application of the method of Lagrangians with covariant derivatives (MLCD) on a given Lagrangian density.Comment: 19 pages, LaTe

Reionization: Characteristic Scales, Topology and Observability

Recently the numerical simulations of the process of reionization of the universe at z>6 have made a qualitative leap forward, reaching sufficient sizes and dynamic range to determine the characteristic scales of this process. This allowed making the first realistic predictions for a variety of observational signatures. We discuss recent results from large-scale radiative transfer and structure formation simulations on the observability of high-redshift Ly-alpha sources. We also briefly discuss the dependence of the characteristic scales and topology of the ionized and neutral patches on the reionization parameters.Comment: 4 pages, 5 figures (4 in color), to appear in Astronomy and Space Science special issue "Space Astronomy: The UV window to the Universe", proceedings of 1st NUVA Conference ``Space Astronomy: The UV window to the Universe'' in El Escorial (Spain

cis-(6RS,13RS)-3,3,10,10-Tetramethyl-6,13-diphenyl-1,8-dioxa-4,11-diazacyclotetradecane-2,5,9,12-tetraone and two of its precursors

The title macrocycle, C26H30N2O6, (VI), was obtained by ;direct amide cyclization' from the linear precursor 3-hydroxy-N-[1-methyl-1-(N-methyl-N-phenylcarbamoyl)ethyl]-2-phenylpropanamide, the N-methylanilide of rac-2-methyl-2-[(3-hydroxy-2-phenylpropanoyl)amino]propanoic acid, C13H17NO4, (IV). The reaction proceeds via the intermediate rac-2-(2-hydroxy-1-phenylethyl)-4,4-dimethyl-1,3-oxazol-5(4H)-one, C13H15NO3, (V), which was synthesized independently and whose structure was also established. Unlike all previously described analogues, the title macrocycle has the cis-diphenyl configuration. The 14-membered ring has a distorted rectangular diamond-based [3434] configuration and intermolecular N-H...O hydrogen bonds link the molecules into a three-dimensional framework. The propanoic acid precursor forms a complex series of intermolecular hydrogen bonds, each of which involves pairwise association of molecules and which together result in the formation of extended two-dimensional sheets. The oxazole intermediate forms centrosymmetric hydrogen-bonded dimers in the solid state

Flows and particles with shear-free and expansion-free velocities in (L^-_n,g)- and Weyl's spaces

Conditions for the existence of flows with non-null shear-free and expansion-free velocities in spaces with affine connections and metrics are found. On their basis, generalized Weyl's spaces with shear-free and expansion-free conformal Killing vectors as velocity's vectors of spinless test particles moving in a Weyl's space are considered. The necessary and sufficient conditions are found under which a free spinless test particle could move in spaces with affine connections and metrics on a curve described by means of an auto-parallel equation. In Weyl's spaces with Weyl's covector, constructed by the use of a dilaton field, the dilaton field appears as a scaling factor for the rest mass density of the test particle. PACS numbers: 02.40.Ky, 04.20.Cv, 04.50.+h, 04.90.+eComment: 20 pages, LaTeX, to appear in Classical and Quantum Gravity. arXiv admin note: substantial text overlap with arXiv:gr-qc/001104

Raman and Infrared-Active Phonons in Hexagonal HoMnO3_3 Single Crystals: Magnetic Ordering Effects

Polarized Raman scattering and infrared reflection spectra of hexagonal HoMnO$_3$ single crystals in the temperature range 10-300 K are reported. Group-theoretical analysis is performed and scattering selection rules for the second order scattering processes are presented. Based on the results of lattice dynamics calculations, performed within the shell model, the observed lines in the spectra are assigned to definite lattice vibrations. The magnetic ordering of Mn ions, which occurs below T$_N$=76 K, is shown to effect both Raman- and infrared-active phonons, which modulate Mn-O-Mn bonds and, consequently, Mn exchange interaction.Comment: 8 pages, 6 figure

Mixing and Accretion in lambda Bootis Stars

Strong evidence for deep mixing has been uncovered for slowly rotating F, and A stars of the main sequence. As the accretion/diffusion model for the formation of lboo stars is heavily dependent on mixing in superficial regions, such deep mixing may have important repercussions on our understanding of these stars. It is shown that deep mixing at a level similar to that of FmAm stars increases the amount of matter that needs to be accreted by the stars with respect with the standard models by some three orders of magnitude. It is also shown that significantly larger accretion rates have to be maintained, as high as $10^{-11}$~M_\sun yr^{-1}, to prevent meridional circulation from canceling the effect of accretion. The existence of old ($\approx 1$~Gyr) is not a likely outcome of the present models for accretion/diffusion with or without deep mixing. It is argued that lboo stars are potentially very good diagnostics of mixing mechanisms in moderately fast rotators.Comment: To appear in Astrophysical Journal Letters. 4 pages, 2 fgure

Frames of reference in spaces with affine connections and metrics

A generalized definition of a frame of reference in spaces with affine connections and metrics is proposed based on the set of the following differential-geometric objects: (a) a non-null (non-isotropic) vector field, (b) the orthogonal to the vector field sub space, (c) an affine connection and the related to it covariant differential operator determining a transport along the given non-null vector filed. On the grounds of this definition other definitions related to the notions of accelerated, inertial, proper accelerated and proper inertial frames of reference are introduced and applied to some mathematical models for the space-time. The auto-parallel equation is obtained as an Euler-Lagrange's equation. Einstein's theory of gravitation appears as a theory for determination of a special frame of reference (with the gravitational force as inertial force) by means of the metrics and the characteristics of a material distribution. PACS numbers: 0490, 0450, 1210G, 0240VComment: 17 pages, LaTeX 2