Generalizing the Pareto to the log-Pareto model and statistical inference

In this article we introduce a full-fledged statistical model of log-Pareto distribution functions (dfs) parametrized by two shape parameters and a scale parameter. Pareto dfs can be regained in the limit by varying parameters of log-Pareto dfs, whence the log-Pareto model can be regarded as an extension of the Pareto model. Log-Pareto dfs are first of all obtained by means of exponential transformations of Pareto dfs. We also indicate an iterated application of such a procedure. A class of generalized log-Pareto dfs is considered as well. In addition, power-pot (p-pot) stable dfs – related to p-max stable dfs – are introduced and log-Pareto dfs are identified as special cases. A modification of a quick (systematic) estimator is proposed as an initial estimator for the numerical computation of the maximum likelihood estimator (MLE) in the 3-parameter model.      

The role of self-trapped excitons and defects in the formation of nanogratings in fused silica

We investigate the role of self-trapped excitons (STEs) and defects in the formation of femtosecond laser pulse induced nanogratings (NGs) in fused silica. Our experiments reveal strongly enhanced NG formation for pulse separations up to the STE lifetime. In addition, the absorption spectra show that the weaker cumulative action of laser pulses for longer temporal separations is predominantly mediated by dangling-bond-type lattice defects that emerge from decaying STEs.     

Small-Molecule Diffusion in Semicrystalline Polymers as Revealed by Experimental and Simulation Studies

Summary: Diffusion of n-hexane in poly(ethylene-co-1-hexene)s with 15–75 wt.% crystallinity was studied by desorption experiments analyzing data using the Fickian equations with a concentration dependent diffusivity. The effect of the impenetrable crystalline phase on the penetrant diffusivity (D) is described by D = D_a/(τβ), where D_a is the diffusivity of the amorphous polymer, τ is the geometrical impedance factor and β is a factor describing the constraining effect of the crystals on the non-crystalline phase. For a polymer with 75 wt.% crystallinity, τβ varied markedly with penetrant concentration (v_1a) in the penetrable phase: 1000 (v_1a = 0) and 10 (v_1a = 0.15). This penetrant-uptake had no effect on the gross crystal morphology, i.e. β must be strongly dependent on v_1a. Samples saturated in n-hexane exhibited a penetrant-induced loosening of the interfacial structure, as revealed by an increase in crystal density that require an increased mobility in the interfacial component and by a decrease in the intensity of the asymmetric X-ray scattering associated with the interfacial component. The geometrical impedance factor has been modelled by mimicking spherulite growth and τ was obtained as the ratio of the diffusivities of the fully amorphous and semicrystalline systems. The maximum τ obtained from these simulations is ca. ten, which suggests that β in the systems with v_1a = 0.15 takes values close to unity. The simulations showed that the geometrical impedance factor is insensitive to the ratio of the crystal width and the crystal thickness. A free path length scaling parameter characteristic of the amorphous phase correlated with τ.     

Fluorenyl based syndiotactic specific metallocene catalysts structural features,origin of syndiospecificity

The stereochemistry of propylene insertion/propagation reactions with a variety of C_s symmetric fluorenyl- containing single site catalysts is discussed. Our recent results indicate that independent of the chemical composition of the ancillary ligand fragments, or nature of the transition metal, active sites with local C_s symmetry and enantiotopic coordination positions behave syndioselectively in the general context of chain migratory insertion mechanism. Perfect bilateral symmetry neither exists nor is required in these processes. In this context the mechanism of syndiospecific polymerization is revisited by taking into account the structural characteristics and catalytic behavior of the original metallocene based (η⁵-C₅H₄-CMe₂-η⁵-C₁₃H₈) MCl₂/ MAO; M = Zr ( 1 ), Hf ( 2 ) catalyst systems and new syndiotactic specific systems including (η⁵-C₅H₄-CPh2-η5-3,6-di-tBut-C₁₃H₆)ZrCl₂ ( 3 ), η¹,η⁵-(μMe₂Si)(3,6-di-tBut-Flu)(t-ButN)MCl₂/ MAO; M =Ti ( 4 ), Zr ( 5 ) and η¹,η⁵-(μMe₂Si)(2,7-di-tBut-Flu)(t-ButN)MCl₂/ MAO; M = Ti ( 6 ), Zr ( 7 ).     

ChemInform Abstract: Ab initio study of the Two Iso‐electronic Molecules NpO‐4 and UO2‐4O.

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