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     

Oxidation of olefins with alkanesulfoperacids

Alkanesulfonic peracids RSO₄H effectively oxidize olefins to the corresponding epoxides. The kinetics and mechanism of this reaction are studied. It was shown that both the monomer and dimer form of the peracid act as oxidizing agents. The dependence of the weight constant of the reaction of monomer RSO₄H with substituted acyclic olefins on the structure of the latter is described by the Taft equation. A linear correlation is established between log k₂ and the inductive constants of the substituents on the oxygen atom in the peracid.Translated from Izvestiya Akademii Nauk SSSR, Seriya Khimicheskaya, No. 2, pp. 333–337, February, 1991.     

On the mechanism of phenol ozonolysis

The mechanisms of liquid-phase phenol ozonation are revised. A new mechanism in which a significant role is played by free-radical reactions is suggested for this process.     

2,12‐Dichloro‐10,20‐diphenyl‐5,7,15,17‐tetrahydro‐6H,16H‐dibenzo[d,l][1,9,2,6,10,14]dioxotetraazacyclohexadecine‐6,16‐dione dioxane solvate as a potential macrocyclic hexadentate ligand

The macrocyclic title compound crystallizes as a dioxane solvate, C₃₀H₂₂Cl₂N₄O₄·C₄H₈O₂, with two independent formula units in the unit cell. The observed syn conformation is controlled by both intramolecular N—H...O hydrogen bonds and intermolecular C—H...π interactions. The relative macrocyclic inner bore is estimated to be 4.19 Å. In the crystal structure, molecules form dimers via intermolecular C—H...π interactions, and these dimers are, in turn, linked to form columns along the a axis by intermolecular C—H...O hydrogen bonds. Both X‐ray diffraction analysis and density functional theory (DFT) calculations reveal that the macrocycle possesses very high flexibility. This property, as well as the presence of six donor atoms accessible for coordination, makes the title macrocycle a very promising ligand for complexation with the majority of transition metals.     

Kinetics and products of the reaction of diazo compounds with SO2

Data were obtained on the composition of products and kinetics of the reaction of SO₂ with Ph(R)CN₂ (R=Ph, Me) in solutions of isooctane, 1,4-di-oxane, and ethanol at 295 K. A mechanism was proposed for the process in accordance with which the sulfene being formed participates in concurrent reactions with the starting reagents. The relative rate constants for the process stages were determined.Translated from Izvestiya Akademii Nauk SSSR, Seriya Khimicheskaya, No. 11, pp. 2496–2500, November, 1990.     

Chemiluminescent studies for the kinetics of decomposition of Di-(tert-butyl)-trioxide

Thermolysis of di-(tert-butyl)-trioxide produces IR and visible chemiluminescence (CL) which may be ascribed to emission by singlet oxygen (IR-CL) and triplet acetone (vis. CL).     

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.