Wiener's test for space-time random walks and its applications

This paper establishes a criterion for whether a -dimensional random walk on the integer lattice visits a space-time subset infinitely often or not. It is a precise analogue of Wiener's test for regularity of a boundary point with respect to the classical Dirichlet problem. The test obtained is applied to strengthen the harder half of Kolmogorov's test for the random walk.

     

Determination of thermodynamic functions of sorption for cyclohexyl-, piperidyl-, morpholyl-, and thiomorpholyl-n-alkanes by capillary gas-liquid chromatography

The values of partial molar free energy (G), enthalpy (H), and entropy (S) of sorption in the homologous series ofN-alkylpiperidines,N-alkylmorpholines,N-alkyl thiomorpholines, and alkylcyclohexanes were determined. It was found that the free energy of sorption is determined to a greater extent by the enthalpy term than by the entropy one. The free energy of sorption of the first homolog decreases when then-alkyl chain is attached directly to the carbon atom of the cycle and increases in the case ofN-alkylsubstituted heterocycles. The influence of the heteroatom nature on intermolecular interactions of homologs with the nonpolar stationary phase was quantitatively estimated on the basis of thermodynamic data.Dead time necessary for calculation of the retention factor was determined by the retention of methane injected into the column simultaneously with the sample.Translated from Izvestiya Akademii Nauk. Seriya Khimicheskaya, No. 8, pp. 2030–2032, August, 1996.     

High-temperature TG/DSC/QMS applications in environmental protection

The decomposition reactions of polystyrene, phenolic resin and a protective undercoating material for automobiles which contains PVC were tested using a new type of thermal analysis — mass spectrometry coupling system for measurements to 1500C or 2000C, which is based on the principle of a two-step skimmer orifice system. The results will be presented, with particular emphasis on the detection sensitivity of the new system for the products of decomposition.The capability of this coupling system to detect even heavy metals such as lead and silver in the waste gases from decomposition or after evaporation at high temperatures will also be demonstrated.     

Surface modified precipitated calcium carbonates at a high degree of dispersion

Calcium carbonates of different degrees of surface hydrophobicity were obtained when sorbic acid or polyoxyethylene glycol were present during the precipitation. In the presence of trace amounts of divalent cations carbonates with high surface hydrophilicity and improved monodisperse character are obtained. Surface modification of the calcium carbonates by several proadhesive compounds can markedly improve the chemical affinity of the carbonates to polymers. Very effective are isostearoyl titanate and two polyoxyethylene compounds. Precipitated calcium carbonates modified with 2 to 3 percent (wt/wt) of isostearoyl titanate increased the tensile strenght of butadiene-styrene rubber by approximately 100%. Polyurethane is only strengthened when 30 wt/wt of a filler are introduced independently of the type proadhesive compounds. The best strength and hysteresis of polyurethanes are obtained with calcium carbonate modified with 2 percent (wt/wt) of polyoxyethylene glycol.     

An Electrostatic Bond Energy Model for Enthalpies of Formation of Chloroalkanes in Gaseous States

An electrostatic bond energy model is formulated to fit the enthalpies of formation and dipole moments of the alkanes and chloroalkanes. In this model, the charge distributions are calculated by an electrostatic approach similar to the "MSE" method, and the enthalpy of formation of a molecule is the sum of the bond energy terms plus the electrostatic energy of the interactions between the charges on all atoms. All parameters of this model are obtained by parameterization. The calculated dipole moments for 13 chloroalkanes and enthalpies of formation for 19 alkanes and non-geminal chloroalkanes agree with the determined values very well. To calculate the enthalpies of formation of geminal chloroalkanes, a correction mainly attributed to the van der Waals interactions in the geminal substituted group, about 24 kJ/mol per pair of geminal chlorine atoms, is introduced.     

Synthesis of derivatives of ketocarboxylic acids by the decomposition of 1,4-cyclohexanedione monoethyleneketal hydroperoxide

The decomposition of 1,4-dihydroxy-1,4-dihydroperoxycyclohexane under the action of FeSO₄ and the decomposition of 1,4-cyclohexanedione monoethyleneketal hydroperoxide under the action of Fe^II salts in the presence of various ligands or under the action of Cu^II sulfate have been studied. A preparative method for the synthesis of derivatives of diketodicarboxylic or -functionally substituted ketocarboxylic acids from 1,4-cyclohexanedione monoethyleneketal has been developed.Translated fromIzvestiya Akademii Nauk. Seriya Khimicheskaya, No. 7, pp. 1231–1235, July, 1993.     

Autocatalytic oxidation of Fe(Phen)3 2+ by bromate in water-in-oil reverse micelles of AOT

Autocatalytic oxidation of ferroin by bromate in water-in-oil reverse micelles of AOT has been studied experimentally and theoretically. The simplest models for this process have been constructed. Analytical solutions for these models were found for some limiting cases. It has been shown that the autocatalytic reaction runs much more slowly in reverse micelles than in water. The dependencies of the maximum reaction rate, _max, the exponent of the increase in ferriin concentration, , and induction period, , on micelle concentration have been obtained at =[H₂O]/[AOT]=4.6. It was found that there is only one theoretical model which can explain the experimental data. The values of the elementary reaction rate constantsk _i were estimated on the basis of the theoretical dependencies of _max and on the constantsk _i . All elementary rate constants turned out to be two or three orders of magnitude smaller than the corresponding constants for the reaction proceeding in water. The decrease in the rate constants is explained by the increase in viscosity and pH in a micellar water core at low .Translated fromIzvestiya Akademii Nauk. Seriya Khimicheskaya, No. 8, pp. 1401–1407, August, 1993.This work was supported by the Russian Foundation for Fundamental Investigations through Research Grant 93-03-4090.     

Phosphorus-containing podands

A number of monopodands havingo-diphenylphosphinyl terminal groups were synthesized by alkylating sodium derivatives of oligoethylene glycols witho-(bromomethyl)phenyldiphenylphosphine. The stability constants of the complexes of these ligands with alkali metal cations at 25 °C were determined conductometrically in a THF—chloroform solution (41, v/v). The complexing ability of monopodands with respect to the cations studied increases monotonically as the number of electron-donating sites increases (from 3 to 8) for all of the cations except Li⁺ and, to some extent, Na⁺. In the case of Li⁺ a smooth decrease in the stability of the complexes is observed. The monopodands obtained in this work differ drastically in this regard from their structural isomers, bis[o-(diphenylphosphinylmethyl)phenyl] ethers of oligoethylene glycols, which had been studied previously.For part 10, see ref. 1.Translated fromIzvestiya Akademii Nauk. Seriya Khimicheskaya, No. 5, pp. 952–956, May, 1993.     

C 1 surface interpolation with constraints

Givenn pairwise distinct and arbitrarily spaced pointsP _i in a domainD of thex–y plane andn real numbersf _i, consider the problem of computing a bivariate functionf(x, y) of classC ¹ inD whose values inP _i are exactlyf _i,i=1,,n, and whose first or second order partial derivatives satisfy appropriate equality and inequality constraints on a given set ofp pointsQ _l inD.In this paper we present a method for solving the above problem, which is designed for extremely large data sets. A step of this method requires the solution of a large scale quadratic programming (QP) problem.The main purpose of this work is to analyse an iterative method for determining the solution of this QP problem: such a method is very efficient and well suited for parallel implementation on a multiprocessor system.Work supported by MURST Project of Computational Mathematics, Italy.     

Langevin dynamic simulation of hysteresis in a field-swept Landau potential

Numerical simulations are done of Langevin dynamics for a uniform-orderparameter, field-swept Landau model,= –|a/2|m ²+|b/4|m ⁴–mh(t) , to study hysteresis effects. The field is swept at a constant rateh(t)=h(0)+ht. The stochastic jump values of the field {h_J from an initially prepared metastable minimumm(0) are recorded, on passage to a global minimum m(). The results are: (a) The mean jump¯h _J(h) increases (hysteresis loop widens) with h, confirming a previous theoretical criterion based on rate competition between field-sweep and inverse mean first-passage time (FPT); (b) The broad jump distribution(h _J,h) is related to intrinsically large FPT fluctuations ( ²–²)/ ² O(1), and can be quantitatively understood. Possible experimental tests of the ideas are indicated.