Limit theorems on locally compact Abelian groups

We prove limit theorems for row sums of a rowwise independent infinitesimal array of random variables with values in a locally compact Abelian group. First we give a proof of Gaiser's theorem [4, Satz 1.3.6], since it does not have an easy access and it is not complete. This theorem gives sufficient conditions for convergence of the row sums, but the limit measure cannot have a nondegenerate idempotent factor. Then we prove necessary and sufficient conditions for convergence of the row sums, where the limit measure can be also a nondegenerate Haar measure on a compact subgroup. Finally, we investigate special cases: the torus group, the group of p ‐adic integers and the p ‐adic solenoid. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Electrical and memory properties of silicon nitride structures with embedded Si nanocrystals

In this work, the electrical and memory behaviour of metal-silicon nitride-silicon structures with an embedded nanocrystalline silicon layer, which either consists of separated silicon nanocrystals, or is a continuous nanocrystalline layer, are presented. The structures were prepared by low-pressure chemical vapour deposition (LPCVD). The effect of the duration of deposition and the structure of the nanocrystalline layer were studied. The writing/erasing behaviour was similar for all the structures, but the retention properties were much worse in the structure with a continuous nanocrystalline layer, than in the structures with separated Si nanocrystals. This indicates that Si nanocrystals play role in charge storage in the studied structures.     

The Accuracy of Cauchy Approximation for the Windings of Planar Brownian Motion

Periodica Mathematica Hungarica -     

Carbon nanotube synthesis on oxidized porous silicon

Carbon nanotubes were grown on thermally oxidized porous silicon by catalytic chemical vapor deposition from the mixture of ferrocene and xylene precursor. The growth rate of carbon nanotubes showed dependence on the oxidation extent of porous silicon. On pristine porous silicon surfaces, only poor nanotube growth was observed, whilst samples oxidized in air at 200, 400, 600 and 800 °C prior to the deposition process proved to be suitable substrates for carbon nanotube synthesis. Networks of carbon tubes with diameter of ∼40 and ∼10 nm observed on the surfaces of samples were investigated by electron microscopy and by energy dispersive X-ray analysis.     

Optimal Bounds for Cauchy Approximations for the Winding Distribution of Planar Brownian Motion

Optimal nonuniform bounds are given for the remainder terms in Spitzer's theorem, which gives some final answer to the question of Cauchy approximations for the winding distribution of planar Brownian motion. As a corollary, a large deviation result is presented. Optimal nonuniform bounds for the approximations of the density are also derived.     

Aryl C-H amination by diruthenium nitrides in the solid state and in solution at room temperature: experimental and computational study of the reaction mechanism

Diruthenium azido complexes Ru(2)(DPhF)(4)N(3) (1a, DPhF = N,N'-diphenylformamidinate) and Ru(2)(D(3,5-Cl(2))PhF)(4)N(3) (1b, D(3,5-Cl(2))PhF = N,N'-bis(3,5-dichlorophenyl)formamidinate) have been investigated by thermolytic and photolytic experiments to investigate the chemical reactivity of the corresponding diruthenium nitride species. Thermolysis of 1b at ~100 °C leads to the expulsion of N(2) and isolation of Ru(2)(D(3,5-Cl(2))PhF)(3)NH(C(13)H(6)N(2)Cl(4)) (3b), in which a nitrogen atom has been inserted into one of the proximal aryl C-H bonds of a D(3,5-Cl(2))PhF ligand. A similar C-H insertion product is obtained upon thawing a frozen CH(2)Cl(2) solution of the nitride complex Ru(2)(DPhF)(4)N (2a), formed via photolysis at -196 °C of 1a to yield Ru(2)(DPhF)(3)NH(C(13)H(10)N(2)) (3a). Evidence is provided here that both reactions proceed via direct intramolecular attack of an electrophilic terminal nitrido nitrogen atom on a proximal aryl ring. Thermodynamic and kinetic data for this reaction are obtained from differential scanning calorimetric measurements and thermal gravimetric analysis of the thermolysis of Ru(2)(D(3,5-Cl(2))PhF)(4)N(3), and by Arrhenius/Eyring analysis of the conversion of Ru(2)(DPhF)(4)N to its C-H insertion product, respectively. These data are used to develop a detailed, experimentally validated DFT reaction pathway for N(2) extrusion and C-H functionalization from Ru(2)(D(3,5-Cl(2))PhF)(4)N(3). The diruthenium nitrido complex is an intermediate in the calculated reaction pathway, and the C-H functionalization event shares a close resemblance to a classical electrophilic aromatic substitution mechanism.     

Asymmetric integral as a limit of generated Choquet integrals based on absolutely monotone real set functions

We introduce a generated Choquet integral with respect to absolutely monotone and sign stable set functions. Another type of integrals defined with respect to such a set function is obtained as a limit of an appropriate sequence of generated Choquet integrals.     

On Aggregation of Subcritical Galton–Watson Branching Processes with Regularly Varying Immigration

Lithuanian Mathematical Journal - Abstract. We study an iterated temporal and contemporaneous aggregation of N independent copies of a strongly stationary subcritical Galton–Watson branching...     

A note on kernels and Sperner’s Lemma

The kernel-solvability of perfect graphs was first proved by Boros and Gurvich, and later Aharoni and Holzman gave a shorter proof. Both proofs were based on Scarf’s Lemma. In this note we show that a very simple proof can be given using a polyhedral version of Sperner’s Lemma. In addition, we extend the Boros–Gurvich theorem to h-perfect graphs and to a more general setting.