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     

Linear optical bullets

We describe a class of spatio-temporal optical pulses that spread neither spatially nor temporarily in linear dispersive media over long propagation distances. These new spatio-temporal pulses, referred to as linear optical bullets, can have any spatio-temporal profile and temporal width, and they carry a finite amount of energy. We also discuss in detail a technique for the experimental realization of linear optical bullets.     

Fractal analysis of RF signals scattered by small-scale ionospheric irregularities

The fractal dimension as a characteristic of an experimental data series is considered. The correlation integral method is used for dimension calculation. It is shown that by the fractal dimension one can identify a variety of ionospheric processes even when the conventional spectral analysis fails. It is found that the realizations corresponding to volume scattering by natural and artificial irregularities have finite dimension, which is significantly different. A technique for preparing experimental data to be processed by the correlation integral method is developed. The influence of the data sampling rate and signal-to-noise ratio on the dimension is analyzed.Radioastronomical Institute, Ukrainian Academy of Sciences, Khar'kov. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 38, No. 6, pp. 557–565, June, 1995.     

Quantum-Chemical Investigation of the Mechanism of Transfer of Fluorine in the Reaction of F‐TEDA‐BF4 with Dimethylenebicyclo[3.3.1]nonane

The mechanism of the reaction of the N-fluoro reagent FTEDABF₄ with dimethylenebicyclo[3.3.1]nonane was investigated by the semiempirical PM3 SCF MO method using the Cramer–Truhlar SM5.42R solvation model. It was shown that the mechanism of addition of the fluorine corresponds to classical S _N 2 nucleophilic substitution involving single-electron transfer synchronous with the cleavage–formation of C—F and N—F bonds.     

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.     

Electrical and Spectral Properties of Complexes of Pyridine N-Oxide Derivatives with Iron Trichloride

Complexes (1 : 2) of iron trichloride with N-oxides of pyridine, picolines, and 2,6-lutidine were studied by optical spectroscopy, dielectrometry, and conductometry. In solid complexes, three crystalline phases are in equilibrium; the nuclei of each of these phases can be detected in the oily state. The enthalpies of the coordination bonds are different in different phases. One of the phases of the 3-picoline N-oxide complex shows a strong orientation disorder; disappearance of the short-range order causes weakening of the coordination bonds by 1.6 kcal. The thermal motion of free base molecules in two phases of the 2,6-lutidine N-oxide complex is gaslike. In the solid phase of this complex, there is a strong distribution of the relaxation frequencies; the mean relaxation frequency is close to 220 Hz. Upon irradiation of the complexes with solar or UV light, specific coloration centers can form. Weak alternating electric fields initiate in some compounds reversible chemical reactions. The intermolecular and charge equilibria in the compounds are very labile; the energy of generation of the low-temperature electrical conductivity in them is close to 0.9 eV.