Stationary Distribution Function Estimation for Ergodic Diffusion Process

The problem of nonparametric stationary distribution function estimation by the observations of an ergodic diffusion process is considered. The local asymptotic minimax lower bound on the risk of all the estimators is found and it is proved that the empirical distribution function is asymptotically efficient in the sense of this bound.     

Optimization of the synthesis of non-symmetrical alkyl dimethyl sulfonium halides

This work is aimed at the optimization of the yield and purity of non-symmetrical trialkyl sulfonium halide salts. The effects of parameters such as solvent, temperature and concentration were studied. The products were carefully analyzed and the crystal structure of [{n-CH₃(CH₂)₁₅}(CH₃)₂S]Br determined. The overall aim of the present study is future syntheses of low-dimensional magnetic materials.     

Multiplicity of zeros and discrete orthogonal polynomials

We consider a problem of bounding the maximal possible multiplicity of a zero of some expansions Σ a_iF_i(x), at a certain point c, depending on the chosen family {imi}. The most important example is a polynomial with c = 1. It is shown that this question naturally leads to discrete orthogonal polynomials. Using this connection we derive some new bounds, in particular on the multiplicity of the zero at one of a polynomial with a prescribed norm. 30C15, 33C47     

Calculation of the infrared spectrum and density of the vibrational states of an SiO2 melt by molecular dynamics

The density of the vibrational states of an SiO₂ melt under various PT conditions, the distributions of the Si-O-Si and O-Si-O angles in it, and its IR absorption spectra have been calculated by molecular dynamics with the use of a pairwise additive Born-Mayer potential. A comparison with the experimental data reveals that the ionic approximation selected is capable of basically reproducing the structural and spectroscopic properties of the melt, but the distributions of the bond angles are considerably broader than the experimentally determined distributions, and the absorption band caused by the stretching vibrations is not displayed in the calculated spectrum. The disparities indicated are apparently due to the isotropic nature of the potential of the interparticle interactions.V. I. Vernadskii Institute of Geochemistry and Analytical Chemistry, Academy of Sciences of the USSR, Moscow. Translated from Teoreticheskaya i Éksperimental'naya Khimiya, Vol. 27, No. 4, pp. 467–470, July–August, 1991. Original article submitted October 12, 1990.     

The preparation and X-ray structural study of complexes that catalyze isocyanate cyclotrimerization

A 11-complex of trinitrophenol with benzyldimethylamine (1) and a 111-complex, the product of the interaction of benzyldimethylamine, glycidyl phenyl ether, and phenol (2), have been synthesized and characterized by means of X-ray analysis. Complex1 is a precursor for the catalysts of selective isocyanate cyclotrimerization, while complex2 is one of those catalysts. In the crystal structure complex1 forms H-bonded cationic-anionic aggregates with proton transfer from phenol to the N-atom of the tertiary amine. Complex2 crystallizes as a monohydrate (2a) with a strong H-bond between the quaternary ammonium and phenolic components, and exists in crystals in the form of globular H-bonded dimeric hydrates. Possible pathways of dissociation of complex2a are discussed. The data obtained may be used as a basis for further interpretation of the regularities of cyclotrimerization of isocyanates catalyzed by complexes of this type.Translated fromIzvestiya Akademii Nauk. Seriya Khimicheskaya, No 1, pp. 92–97, January, 1993.     

Large effect of polydispersity on defect concentrations in colloidal crystals

We compute the equilibrium concentration of stacking faults and point defects in polydisperse hard-sphere crystals. We find that, while the concentration of stacking faults remains similar to that of monodisperse hard-sphere crystals, the concentration of vacancies decreases by about a factor of 2. Most strikingly, the concentration of interstitials in the maximally polydisperse crystal may be some six orders of magnitude larger than in a monodisperse crystal. We show that this dramatic increase in interstitial concentration is due to the increased probability of finding small particles and that the small-particle tail of the particle size distribution is crucial for the interstitial concentration in a colloidal crystal.     

Mechanistic characterization of aerobic alcohol oxidation catalyzed by Pd(OAc)(2)/pyridine including identification of the catalyst resting state and the origin of nonlinear [catalyst] dependence

The Pd(OAc)(2)/pyridine catalyst system is one of the most convenient and versatile catalyst systems for selective aerobic oxidation of organic substrates. This report describes the catalytic mechanism of Pd(OAc)(2)/pyridine-mediated oxidation of benzyl alcohol, which has been studied by gas-uptake kinetic methods and (1)H NMR spectroscopy. The data reveal that turnover-limiting substrate oxidation by palladium(II) proceeds by a four-step pathway involving (1) formation of an adduct between the alcohol substrate and the square-planar palladium(II) complex, (2) proton-coupled ligand substitution to generate a palladium-alkoxide species, (3) reversible dissociation of pyridine from palladium(II) to create a three-coordinate intermediate, and (4) irreversible beta-hydride elimination to produce benzaldehyde. The catalyst resting state, characterized by (1)H NMR spectroscopy, consists of an equilibrium mixture of (py)(2)Pd(OAc)(2), 1, and the alcohol adduct of this complex, 1xRCH(2)OH. These in situ spectroscopic data provide direct support for the mechanism proposed from kinetic studies. The catalyst displays higher turnover frequency at lower catalyst loading, as revealed by a nonlinear dependence of the rate on [catalyst]. This phenomenon arises from a competition between forward and reverse reaction steps that exhibit unimolecular and bimolecular dependences on [catalyst]. Finally, overoxidation of benzyl alcohol to benzoic acid, even at low levels, contributes to catalyst deactivation by formation of a less active palladium benzoate complex.     

Modification of Non-Hydrolytic Sol-Gel Derived Alumina by Solvent Treatments

The effect of wetting non-hydrolytic derived alumina xerogels with water and organic solvents in the 20–70°C range on the alumina's properties was investigated. Wetting with organic solvents does not affect the alumina. However, contact with water was found to change the sharp crystallization at 800°C to a continuous crystallization starting at 450°C. Water treatment for a day at room temperature (RT) followed by second calcination decreased the surface area by 10%. This decrease in surface area is less pronounced with increasing wetting periods. On the other hand water treatment at 50–70°C followed by a second calcination resulted in a surface area increase of up to 15%. Upon water treatment the total pore volume has decreased from 0.65 (cm³/gr) to 0.48 (cm³/gr) and the average pore size decreased from 6.8 nm to 4.1 nm. The Cl content was found to be uneffected by the water treatment, remaining at 2.5% wt. Wetting with water at elevated temperature (70°C) accelerated the morphological changes, eliminating the crystallization peak at 800°C in one hour. A dissolution-reprecipitation mechanism is suggested to explain the results. In addition, Mass-Spectroscopy of the effluent gas during heat treatment revealed the emission of CO₂ and water upon phase transition into -Al₂O₃, at 1150–1300°C.     

The reaction of propane sultone with cuanosine,adenosine, and related compounds

Propane sultone (3-hydroxypropanesulfonic acid-γ-lactone) which is a monofunctional directacting alkylating carcinogen, has been shown to react irreversibly with DNA from various sources in vitro. It reacts with guanosine in DMSO to yield the N-7 alkyl nucleoside, while reaction with 2′-deoxyguanosine yields the corresponding N-7 alkyl purine. Evidence for the structure of these products and of one formed when adenosine and propane sultone react is presented.     

Tensor products of coherent configurations

A Cartesian decomposition of a coherent configuration ✗ is defined as a special set of its parabolics that form a Cartesian decomposition of the underlying set. It turns out that every tensor decomposition of ✗ comes from a certain Cartesian decomposition. It is proved that if the coherent configuration ✗ is thick, then there is a unique maximal Cartesian decomposition of ✗; i.e., there is exactly one internal tensor decomposition of ✗ into indecomposable components. In particular, this implies an analog of the Krull–Schmidt theorem for the thick coherent configurations. A polynomial-time algorithm for finding the maximal Cartesian decomposition of a thick coherent configuration is constructed.