Linear differential-algebraic equations perturbed by Volterra integral operators

We study linear inhomogeneous vector ordinary differential equations of arbitrary order in which the matrix multiplying the highest derivative of the unknown vector function is singular in the domain where the equations are defined. We also study perturbations (not necessarily small) of such equations, which are linear integro-differential equations with a Volterra operator. We obtain sufficient conditions for the solvability of such equations and give representations of their general solutions; solvability and uniqueness conditions are also given for initial value problems for such equations. The influence of small perturbations of the free term and the initial data on the solution is considered. A numerical method is suggested. The results of numerical experiments are given.     

On limit cycles of systems with a partial integral

For a certain class of two-dimensional autonomous systems of differential equations with an invariant curve that contains ovals, we indicate necessary and sufficient conditions for these ovals to be limit cycles of phase trajectories.     

Features of the ionization mechanism of radical recombination luminescence excitation

A comparison of the temperature-time cycles of radical recombination luminescence (RRL) in atomic hydrogen, based on ZnS and ZnCdS at different partial pressures, is presented. The obtained results allow us to explain the temperature dependences of chemisorption of the charged form of N ⁺ and the optical transition rate upon RRL.     

Mössbauer and Magnetic Studies of Doped Lanthanum Manganite La1 – xCaxMn0.98Fe0.02O3 + δ (x = 0.05, 0.10, 0.20): I. Nonstoichiometric Composition

Journal of Surface Investigation: X-ray, Synchrotron and Neutron Techniques - Mössbauer and magnetic studies of Ca-doped lanthanum manganites...     

Effect of the temperature on the kinetics of the chemisorption of atmospheric oxygen by a sodium dithionite solution

Properties of a 0.0316 mol/l sodium hydroxide solution and the reactivity of reactants involved in the reaction of aerobic oxidation of sodium dithionite are studied over a temperature range of 283–353 K, and changes in motive forces of the rate-limiting, multistage interphase transfer of atmospheric oxygen are estimated. It is established that heating accelerates the adsorption of the gas by the liquid surface by a factor of 18, decreases the solubility of oxygen by a factor of 2, increases the rate of diffusion of oxygen molecules by a factor of 5, and, as a result, increases the absorption of the oxidizer from the air by a factor of 8.     

The processes of benzene alkylation with n-alkenes on the sulfocation exchangers

The processes of benzene alkylation with n-alkenes C₂–C₃ on sulfocation exchangers are developed. The processes are deprived of the strong corrosion aggressiveness, characteristic of the industrial processes with use of AlCl₃ or BF₃, and do not need the periodic burning out of the formed contaminants, that is characteristic of the processes with application of zeolites. Alkylation proceeds in the liquid phase at moderate temperatures: 70–90°C in the case of alkylation with propene and n-butenes, and 130°C for the alkylation with ethylene. With the use of alkane-alkene fractions C₂–C₃ the conversion of alkenes process exceeds 99%, the alkylbenzene to dialkylbenzenes ratio reaches 20–25%. Peralkylation of dialkylbenzenes it not required.     

Effect of hydroxyethylated alkyl phenol and triethanolamine on absorption of atmospheric oxygen by aqueous-alkaline solutions

Changes in the driving force of the multistage interphase transfer of atmospheric oxygen in the presence of a nonionogenic wetting agent and triethanolamine were assessed by using analytical solutions of the film model of mass exchange at the phase boundary to describe the chemisorption uptake of oxygen by a sodium dithionite solution.     

Oxidative Destruction of Anthraquinone and Indigoid Compounds in Aqueous Solutions of Sodium Hydroxymethylsulfinate

Kinetics of quinone-hydroquinone equilibria of tetrabromoindigo, benzopyrene quinone, and dimethoxybenzanthrone in the presence of a reducer and atmospheric oxygen were studied by spectrophotometry. The reason for the destruction of the dyes both in acidic and alkaline media is the molecular oxygen primarily present in the system. The destruction mechanism is considered on an example of disodium 5,5-indigosulfonate.     

On the Relation between the Properties of a Degenerate Linear-Quadratic Control Problem and the Euler–Poisson Equation

Computational Mathematics and Mathematical Physics - A quadratic functional with linear constraints in the form of differential equations with identically degenerate matrices multiplying the...     

Comparison of propagation of a shock wave in a decaying plasma in various gases

The effect of gas humidity and composition on shock wave splitting in the plasma of a decaying glow discharge is investigated in dried and moist air, nitrogen, and argon over various time periods after the discharge termination. The shapes of the signals reflecting the gas pressure distribution behind the shock wave in these media are approximately the same except for some values of decay time comparable to the characteristic time of decay of excited state concentration (including singlet oxygen) after the termination of the discharge (8 ms). The signals in the same four gases are compared quantitatively for different time periods after discharge termination by expanding the signal into a Fourier series. The free term and the second and third modes in the Fourier expansion are compared. Analysis is carried out for up to time periods of 60 ms.