On a characterization of the normal distribution by means of identically distributed linear forms

Let X₁, X₂,…, be independent, identically distributed random variables. Suppose that the linear forms L₁ = Σ_j=1^∞a_jX_j and L₂ = Σ_j=1^∞b_jX_j exist with probability one and are identically distributed; necessary and sufficient conditions assuring that X₁ is normally distributed are presented. The result is an extension of a theorem of Linnik (Ukrainian Math. J.5 (1953), 207–243, 247–290) concerning the case that the linear forms L₁ and L₂ have a finite number of nonvanishing components. This proof only makes use of elementary properties of characteristic functions and of meromorphic functions.     

Synthesis,molecular and crystal structures,and characteristic features of electronic structures of salicylamide-based B,Si-containing chelates

The reaction of 4-(2-hydroxybenzoyl)-2,2,6,6-tetramethyl-2,6-disilamorpholine with BF₃Et₂O afforded (O-B)-chelate 4-[2-(difluoroboroxy)benzoyl]-2,2,6,6-tetramethyl-2,6-disilamorpholine. Treatment of the latter with BF₃Et₂O or SOCl₂ gave rise to products of the disilamorpholine ring opening, viz., (O-B) chelate 2-(difluoroboroxy)-N,N-bis(dimethylfluorosilylmethyl)benzamide or 2-(difluoroboroxy)-N, N-bis(dimethylchlorosilylmethyl)benzamide, respectively. The structures of the compounds synthesized were confirmed by X-ray diffraction analysis and ¹H, ¹³C, and ²⁹Si NMR spectroscopy. High-precision X-ray diffraction study and quantum-chemical calculations demonstrated that the coordination OSi bond is absent in the two last-mentioned compounds.Published in Russian in Izvestiya Akademii Nauk. Seriya Khimicheskaya, No. 9, pp. 1846–1853, September, 2004.     

Structure of polynuclear palladium(ii) hydroxocomplexes formed upon alkaline hydrolysis of palladium(ii) chloride complexes

The structure of polynuclear Pd^II hydroxocomplexes (PHC) formed as a result of alkaline hydrolysis of Pd^II chloride complexes was studied by EXAFS, SAXS, and TEM methods. It is established that in aqueous solutions a hydroxocomplex particle is a filament curled into a ball containing about 100 Pd atoms. The filament consists of planar coordination squares of PdO₄ units linkedvia one or two oxygen bridges of different geometry. Aging of samples results in an increase in the number of single bridging ligands and a decrease in the diameter of particles. Interatomic distances around palladium atoms were determined.Translated fromIzvestiya Akademii Nauk. Seriya Khimlcheskaya, No. 10, pp. 1901–1905, October, 1995.     

Mesoporous Titanium-containing Silicas. Synthesis and geometrical characteristics

Mesoporous titanium-containing silicas with TiO₂ contents from 1 up to 70 mol% were prepared. The obtained samples have been characterized by the powder X-ray diffraction data, the diffuse reflectance infrared Fourier transform method, and nitrogen adsorption at 77 K. Specific surface area, total pore volume, distribution pore volume on pore sizes were determined from nitrogen adsorption isotherm for synthesized titanosilicas. This revised version was published online in August 2006 with corrections to the Cover Date.     

Impact of electron-electron interaction on the electron energy distribution function in molecular plasmas under rf field action

Calculations of the electron energy distribution and of relevant macroscopic quantities of collision-dominated, weakly ionized plasmas under rf field action have been performed with increasing degrees of ionization, and the impact of the electron-electron interaction on these quantities was determined. The investigations were performed for the gas plasmas in CO and H₂ as representatives of molecular plasmas The energy distribution and macroscopic quantities are obtained by solving the nonstationary Bolizmann equation for a given rf field and degree of ionization taking into accoung and additional Fokker-Planck term besides the collision integrals for the elastic and the main inelastic collision processes. In these molecular plasmas a remarkable impact of the electron-electron interaction connected with increasing Maxwellization is observed for degrees of ionization greater than 10.     

Pore size distributions in low‐k dielectric thin films from X‐ray porosimetry

X‐ray reflectivity has been used to determine the mass uptake of probe molecules in porous thin films supported on thick silicon wafers. The adsorption occurs by capillary condensation when the films are exposed to probe vapor at controlled partial vapor pressures. The probe solvent partial pressure was varied by mixing saturated air and dry air at constant temperature or by changing sample temperature at a constant vapor concentration. Pore size distribution in the films can be calculated from the probe uptake with typical porosimetric approaches such as the application of the Kelvin equation to convert partial pressure into pore size. For illustration, the pore size distribution of three different nanoporous thin films, the primary candidate of ultra‐low‐k interlevel dielectrics in the next generation of integrated circuit chips, was determined with this technique. These samples represent different generations of low‐k dielectrics developed by industry. © 2002 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 40: 2170–2177, 2002     

Deposition of Oral Bacteria and Polystyrene Particles to Quartz and Dental Enamel in a Parallel Plate and Stagnation Point Flow Chamber

The aim of this paper is to determine to what extent (i) deposition of oral bacteria and polystyrene particles, (ii) onto quartz and dental enamel with and without a salivary conditioning film, (iii) in a parallel plate (PP) and stagnation point (SP) flow chamber and at common Peclet numbers are comparable. All three bacterial strains showed different adhesion behaviors, and even Streptococcus mitis BMS, possessing a similar cell surface hydrophobicity as polystyrene particles, did not mimic polystyrene particles in its adhesion behavior, possibly as a result of the more negative ζ potentials of the polystyrene particles. The stationary endpoint adhesion of all strains, including polystyrene particles, was lower in the presence of a salivary conditioning film, while also desorption probabilities under flow were higher in the presence of a conditioning film than in its absence. Deposition onto quartz and enamel surfaces was different, but without a consistent trend valid for all strains and polystyrene particles. It is concluded that differences in experimental results exist, and the process of bacterial deposition to enamel surfaces cannot be modeled by using polystyrene particles and quartz collector surfaces.     

数均聚合度计算的教学方法

总结毛者提出的线型缩聚中当量系数的新定义及引入缩聚体系单体平均官能度的新方法，本文总结出了一套讲授数均聚合度计算问题的简单方法。     

Studies on the porous structure of di(methacryloyloxymethyl) naphthalene-divinylbenzene copolymers by inverse exclusion chromatography

Summary Using inverse exclusion chromatography the porous structure of the copolymers of di(methacryloyloxymethyl)naphthalenes and divinylbenzene was investigated.In order to determine the pore size distributions of the copolymers, toluene, alkylphenones, phthalates and polystyrene standards were used as the probes.The measurements proved that the existence of micropores depend on the method of copolymerization. The copolymers obtained by suspension and emulsion methods are more or less microporous, but the copolymer prepared by thermal polymerization in mass does not include micropores in its internal structure.     

Single-Molecule single crystals of isotactic polystyrene

Single-molecule single crystals were grown from amorphous droplets of fractionated isotactic polystyrene. The crystals were analyzed by electron microscopy and electron diffraction. The molecular mass distribution could be matched with a statistical analysis of single-molecule particles (amorphous and crystals). Proof was brought that single molecules of isotactic polystyrene do not reach equilibrium dimensions on crystallization, rather assume the lamellar morphology with chain-folded macroconformation, also known from crystallization of polymolecular crystals. © 1994 John Wiley & Sons, Inc.

1 This article is a US Government work and, as such, is in the public domain in the United States of America. US Government contract No. DE-AC05-840R-21400.