Asymptotic results for weighted means of linear combinations of independent Poisson random variables

ABSTRACT

In this paper we prove the large deviation principle for a class of weighted means of linear combinations of independent Poisson distributed random variables, which converge weakly to a normal distribution. The interest in these linear combinations is motivated by the diffusion approximation in Lansky [On approximations of Stein's neuronal model, J. Theoret. Biol. 107 (1984), pp. 631–647] of the Stein's neuronal model (see Stein [A theoretical analysis of neuronal variability, Biophys. J. 5 (1965), pp. 173–194]). We also prove an analogue result for sequences of multivariate random variables based on the diffusion approximation in Tamborrino, Sacerdote, and Jacobsen [Weak convergence of marked point processes generated by crossings of multivariate jump processes. Applications to neural network modeling, Phys. D 288 (2014), pp. 45–52]. The weighted means studied in this paper generalize the logarithmic means. We also investigate moderate deviations.     

Isolation of Bisphenol A-Tolerating/degrading Shewanella haliotis Strain MH137742 from an Estuarine Environment

Applied Biochemistry and Biotechnology - The human exposure to bisphenol A (BPA) occurs frequently. Once, this compound was one of the highest volume chemicals produced worldwide and used as a...     

Reactions with a Metalloid Tin Cluster {Sn10[Si(SiMe3)3]4}2−: Ligand Elimination versus Coordination Chemistry

Chemistry that uses metalloid tin clusters as a starting material is of fundamental interest towards understanding the reactivity of such compounds. Since we identified {Sn₁₀[Si(SiMe₃)₃]₄}^2? 7 as an ideal candidate for such reactions, we present a further step in the understanding of metalloid tin cluster chemistry. In contrast to germanium chemistry, ligand elimination seems to be a major reaction channel, which leads to the more open metalloid cluster {Sn₁₀[Si(SiMe₃)₃]₃}^? 9 , in which the Sn core is only shielded by three Si(SiMe₃)₃ ligands. Compound 9 is obtained through different routes and is crystallised together with two different countercations. Besides the structural characterisation of this novel metalloid tin cluster, the electronic structure is analysed by ¹¹⁹Sn Mössbauer spectroscopy. Additionally, possible reaction pathways are discussed. The presented first step into the chemistry of metalloid tin clusters thus indicates that, with respect to metalloid germanium clusters, more reaction channels are accessible, thereby leading to a more complex reaction system.     

Study of the initial stage of manganese dioxide electrodeposition on a rotating ring-disk electrode

The initial stage of electrodeposition of manganese dioxide has been studied on the platinum disk electrode and on the ring-disk electrode. Two current maxima were observed on the anodic voltammograms. It has been shown that the first rise in the current is associated with the formation of manganese dioxide (MD) nuclei on the electrode surface, and the second with their growth at the border between MnO₂ and bare platinum due to an increase in the perimeter of the nuclei. Electrodeposition on bare platinum proceeds at a higher rate than on the surface of growing MD. This is explained by the difference in the reaction mechanisms on these substrates. The first stage of the process on the growing MD is the chemisorption of Mn(II) ions with the formation of Mn(III) ions, which are then electrochemically oxidized to MD. Chemisorption is the slowest step in the whole process.     

Crystallization of the mesomorphic form and control of the molecular structure for tailoring the mechanical properties of isotactic polypropylene

The combination of the control of the concentration of stereodefects in isotactic polypropylene using metallocene catalysts and the crystallization via the mesophase is a strategy to tailor the mechanical properties. Stiff materials, flexible materials, and thermoplastic elastomers can be produced depending only on the concentration of rr stereodefects. Modulus, ductility, and strength can be modulated through the crystallization of α and γ forms or of the mesophase. Different morphologies are observed depending on the stereoregularity and conditions of crystallization. Crystals of the mesomorphic form always exhibit a nodular morphology, accounting for the similar good deformability of all quenched samples, whatever the concentration of stereodefects. The mesophase transforms by thermal treatments into the α form preserving the nodular morphology, with increase of strength while maintaining the ductility typical of the mesophase. Annealing of the mesophase permits a precise adjustment of crystallinity and size of nodular crystals offering additional options to modify the mechanical properties. © 2014 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2014 , 52, 677–699     

Thickness dependence of thermally induced changes in surface and bulk properties of Nafion® nanofilms

Thermally induced changes in surface wettability, dewetting behavior, and proton transport of “self‐assembled” nanothin Nafion^® films (4–300 nm) on SiO₂ substrate is reported. Thermal annealing induces switching of the surface wettability of 55 nm and thinner films from hydrophilic to super‐hydrophobic. Thickness dependence of this behavior is observed with higher annealing temperature required for lower thickness films, indicating highly restrictive mobility of Nafion^® ionomer as film thickness decreases. Dewetting is only observed for 4‐nm thin film. Significant suppression in proton conductivity upon thermal annealing was noted. Similarly, two other bulk properties, water uptake and swelling, were found to decrease upon annealing. This work reports a systematic examination of the thickness dependence of thermally induced changes in both surface and bulk properties of ultra‐thin Nafion^®. © 2016 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2016 , 54, 1267–1277