Spectroscopic and photoluminescence characteristics of Dy ions in lead containing sodium fluoroborate glasses for laser materials

Lead containing calcium zinc sodium fluoroborate (LCZSFB) glasses doped with different concentrations of trivalent dysprosium ions were prepared and investigated by the XRD, FTIR, optical absorption, photoluminescence and decay curve analysis. The experimentally determined oscillator strengths have been determined by measuring the areas under the absorption peaks and the Judd–Ofelt (J–O) intensity parameters were calculated using the least squares fit method. From the evaluated J–O parameters the radiative transition probability rates, radiative lifetimes and branching ratios were calculated for ⁴F_9/2 excited level. Room temperature photoluminescence spectra for different concentrations of Dy³⁺-doped LCZSFB glasses were obtained by exciting the glass samples at 386 nm. The intensity of Dy³⁺ emission spectra increases with increasing concentration of 0.1, 0.25, 0.5 and 1.0 mol% and beyond 1.0 mol% the concentration quenching is observed. The measuring branching ratios are reasonably high for transitions ⁴F_9/2→⁶H_15/2 and ⁶H_13/2, suggesting that the emission at 484 and 576 nm, respectively, can give rise to lasing action in the visible region. From the visible emission spectra, yellow–blue (Y/B) intensity ratios and chromaticity color coordinates were also estimated. The lifetimes of ⁴F_9/2 metastable state for the samples with different concentrations were also measured and discussed.     

Dynamic multiscaling in two-dimensional fluid turbulence

We obtain, by extensive direct numerical simulations, time-dependent and equal-time structure functions for the vorticity, in both quasi-Lagrangian and Eulerian frames, for the direct-cascade regime in two-dimensional fluid turbulence with air-drag-induced friction. We show that different ways of extracting time scales from these time-dependent structure functions lead to different dynamic-multiscaling exponents, which are related to equal-time multiscaling exponents by different classes of bridge relations; for a representative value of the friction we verify that, given our error bars, these bridge relations hold.     

On generalisations of Stieltjes transform

In this paper two different generalisations of the Stieltjes transform have been given along with their inversion formulae. The results are given in the form of two theorems. These two theorems yield many known generalisations of the transform in question as particular cases on specializing the parameters involved therein.     

The role of higher-multipolar and repulsive forces in the calculation of collision-broadened line-widths of linear molecules

Collision-broadened line widths in CO-CO₂ and CO-O₂ collisions have been calculated by incorporating interactions due to octopoles and hexadecapoles and short range repulsive interactions into Anderson's theory. It is shown how these higher-order interactions can be manipulated to yield good agreement with experimental data. A critical evaluation of this totally empirical manipulation suggests that a thorough revision of the theory is required for all but simple dipole-dipole interactions. In the process of the evaluation, the values of the multipole moments are discussed.     

A novel technique for measurement of self-generated magnetic fields and the plasma density in laser produced plasmas from the Faraday rotation using two color probes

Diagnostic information about the self-generated magnetic fields (SGMF) generated in laser produced plasmas is normally obtained by measuring the Faraday rotation angle (FRA) of a linearly polarized laser probe beam passing through the plasma. Simultaneous recording of the corresponding interferogram is required to get the density information necessary for estimating the magnetic field. The problem with this method is that the visibility of the fringes in the interferogram can be poor, and the SGMF cannot be calculated in the regions where the interference fringes are not observable. In this paper, we propose a new method to obtain the density distribution and the SGMF from two simultaneous measurements of FRA using two probe beams of different colors, which allows one to calculate the SGMF without the need of interferometry.     

On a Markoff-like chain

Set {I_r = θ|θ = [a₀, a₁, a₂, …, a_n, …] with a_n ≥ r from some point on}. In the context of I₁ (the set of all irrational numbers) the chain of approximation theorems is the well-known Markoff chain (J. W. S. Cassels, “An Introduction to Diophantine Approximation,” Cambridge Tracts No. 45, Cambridge, 1959). The purpose of this paper is to find the chain of approximation theorems when restricted to I_r with r ≥ 2.     

On the minimum degree,edge-connectivity and connectivity of power graphs of finite groups

In this paper, the minimum degree of power graphs of certain cyclic groups, abelian p-groups, dihedral groups and dicyclic groups are obtained. It is ascertained that the edge-connectivity and minimum degree of power graphs are equal, and consequently, the minimum disconnecting sets of power graphs of the aforementioned groups are determined. In order to investigate the equality of connectivity and minimum degree of power graphs, certain necessary conditions for finite groups and a necessary and su?cient condition for finite cyclic groups are obtained. Moreover, the equality is discussed for the power graphs of abelian p-groups, dihedral groups and dicyclic groups.     

Comparison of Gelfand-Tsetlin Bases for Alternating and Symmetric Groups

Young’s orthogonal basis is a classical basis for an irreducible representation of a symmetric group. This basis happens to be a Gelfand-Tsetlin basis for the chain of symmetric groups. It is well-known that the chain of alternating groups, just like the chain of symmetric groups, has multiplicity-free restrictions for irreducible representations. Therefore each irreducible representation of an alternating group also admits Gelfand-Tsetlin bases. Moreover, each such representation is either the restriction of, or a subrepresentation of, the restriction of an irreducible representation of a symmetric group. In this article, we describe a recursive algorithm to write down the expansion of each Gelfand-Tsetlin basis vector for an irreducible representation of an alternating group in terms of Young’s orthogonal basis of the ambient representation of the symmetric group. This algorithm is implemented with the Sage Mathematical Software.