Theoretical analysis of structure and energetics of intermediates in catalytic reactions of alkanesulfonylation

Combined methods of quantum chemistry and molecular mechanics have been used to investigate the structure and energetics of formation of sulfene, and also N-methanesulfonylpyridinium and oxypyridinium halides, which are intermediates in catalytic alkanesulfonylation reactions. The potential energy surface of ion-ion interactions of N-methanesulfonylpyridinium halides has been analyzed. The results have been applied in identifying kinetically indistinguishable mechanisms of general basic and nucleophilic catalysis in processes of alkanesulfonylation of phenols.Institute of Physical Organic Chemistry and Coal Tar Chemistry, Academy of Sciences of the Ukrainian SSR, Donetsk. Donetsk University. Translated from Teoreticheskaya i Eksperimental'naya Khimiya, Vol. 27, No. 2, pp. 159–165, March–April, 1991. Original article submitted November 9, 1989.     

Influence of the structure of monoalkyl substituted ketenes upon the rate of their spontaneous hydrolysis in water

The kinetics of spontaneous hydrolysis of monoalkylsubstituted ketenes has been studied. The influence of inductive and steric effects of substituents upon the rate has been quantitatively estimated in terms of -analysis. Increasing length and branching of alkyl substiuents decrease the rate of ketene hydrolysis.     

Limiting behavior of the solutions to linear second-order parabolic equations

We study the properties of solutions to parabolic equations in smooth cylindrical domains and establish the conditions for the existence of limiting nontangents andL ₂-limits ast 0.Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 45, No. 7, pp. 1029–1038, July, 1993.     

Keller–Osserman estimates and removability result for the anisotropic porous medium equation with gradient absorption term

We study “large” nonnegative solutions for a class of quasilinear equations model of which is We give a sufficient condition on the exponents and for the removability of isolated singularities.     

N-SULPHONYL PYRIDINIUM SALTS IN THE HETARYLATION REACTION

Abstract

Hetarylation of organic CH-acids by a sumultaneous action on them with N-heteroaromatic compounds and acylating agents, carboxylic chlorides and chlorides of acids of phosphorus (III and V) is known.     

The index of a critical point for densely defined operators of type in Banach spaces

The purpose of this paper is to demonstrate that it is possible to define and compute the index of an isolated critical point for densely defined operators of type acting from a real, reflexive and separable Banach space into This index is defined via a degree theory for such operators which has been recently developed by the authors. The calculation of the index is achieved by the introduction of a special linearization of the nonlinear operator at the critical point. This linearization is a new tool even for continuous everywhere defined operators which are not necessarily Fréchet differentiable. Various cases of operators are considered: unbounded nonlinear operators with unbounded linearization, bounded nonlinear operators with bounded linearization, and operators in Hilbert spaces. Examples and counterexamples are given in 2,$"> illustrating the main results. The associated bifurcation problem for a pair of operators is also considered. The main results of the paper are substantial extensions and improvements of the classical results of Leray and Schauder (for continuous operators of Leray-Schauder type) as well as the results of Skrypnik (for bounded demicontinuous mappings of type Applications to nonlinear Dirichlet problems have appeared elsewhere.

     

A necessary condition for the regularity of a boundary point for degenerating parabolic equations with measurable coefficients

We prove a necessary condition for the regularity of a point on a cylindrical boundary for solutions of second-order quasilinear parabolic equations of divergent form whose coefficients have a superlinear growth relative to derivatives with respect to space variables. This condition coincides with the sufficient condition proved earlier by the author. Thus, we establish a criterion for the regularity of a boundary point similar to the well-known Wiener criterion for the Laplace equation.Translated from Ukrainskyi Matematychnyi Zhurnal, Vol. 56, No. 6, pp. 818–836, June, 2004.