Lattice gas state functions

State equations for simple lattice systems are constructed by extending the Gibbs method to a non-equilibrium system.In memory of D. N. Zubarev, teacher and scientist, whose advice and attention are gratefully remembered.The idea of constructing such a model (on the basis of the vacancy model of condensed matter proposed by the author) belongs to D. N. Zubarev.Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 105, No. 3, pp. 478–490, December, 1995.     

On the function of action on a manifold of ground state solutions

The functions of action and energy are introduced on a manifold of ground states of the Euclidian scalar field functional of action. The differential identity connecting these two functions is proved.Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 105, No. 3, pp. 438–449, December, 1995.     

Estimating the observation parameters of a switching Poisson stream at random moments

We investigate the properties of maximum likelihood estimators in observation schemes of random variables that arrive at random time moments on a Poisson trajectory defined on some ergodic process.Translated from Vychislitel'naya i Prikladnaya Matematika, No. 59, pp. 98–105, 1986.     

ASYMPTOTIC BEHAVIOUR OF THE SOLUTIONS OF A CERTAIN FOURTH-ORDER DIFFERENTIAL EQUATION

The present paper establishes sufficient conditions for the uniformly bounded of any solution of (1.1) and which tend to zero as t → ∞.     

NONLOCAL INITIAL PROBLEM FOR NONLINEAR NONAUTONOMOUS DIFFERENTIAL EQUATIONS IN A BANACH SPACE

The nonlocal initial problem for nonlinear nonautonomous evolution equati-ons in a Banach space is considered. It is assumed that the nonlinearities havethe local Lipschitz properties. The existence and uniqueness of mild solutionsare proved. Applications to integro-differential equations are discussed.The main tool in the paper is the normalizing mapping (the generalizednorm).     

Spectroscopic study on the complex formation of chromogenic bridged calixarenes with aliphatic amines

The complex formation between chromogenic capped calix 4 arene derivatives comprising indophenol indicator group(s), and aliphatic amines has been studied by UV/Vis spectroscopy. The equilibrium constants have been determined in ethanol, and—for one ligand—also in dimethylsulfoxide. The results have been interpreted in terms of various types of host–guest interactions and of steric effects.     

Mechanism of Interaction of γ-Halogenated Salts of Pyrylium and Benzopyrylium with Aromatic Amines

Stoichiometry and kinetics of reactions of 2,6-diphenyl-4-chloropyrylium, 4-chloroflavylium, 4-bromoflavylium, and 4-iodoflavylium perchlorates with nucleophiles N,N-dimethylaniline and n-phenylenediamine are studied using cyclic voltammetry and spectroscopy. Nucleophilic substitution in these compounds proceeds via the formation of a charge-transfer complex, which converts into a radical ion pair as a result of the electron transfer. Heterolytic clevage of the C–Hal bond occurs at the stage of pyranyl (flavanyl) radical.