Method of fictitious regions for one class of fourth-order quasilinear elliptical equations

We investigate the application of the fictitious region method to fourth-order quasilinear elliptical equations with Dirichlet and Neumann conditions. Convergence bounds are established for two versions of the fictitious region method.Translated from Vychislitel'naya i Prikladnaya Matematika, No. 56, pp. 21–29, 1985     

Chaotic oscillations and noise transformations in a simple dissipative system with delayed feedback

We analyze the statistical behavior of signals in nonlinear circuits with delayed feedback in the presence of external Markovian noise. For the special class of circuits with intense phase mixing we develop an approach for the computation of the probability distributions and multitime correlation functions based on the random phase approximation. Both Gaussian and Kubo-Andersen models of external noise statistics are analyzed and the existence of the stationary (asymptotic) random process in the long-time limit is shown. We demonstrate that a nonlinear system with chaotic behavior becomes a noise amplifier with specific statistical transformation properties.     

Reaction of furan compounds with hydrogen peroxide in the presence of vanadium catalysts

The reactions of furan and a number of its derivatives (furfural, furan-2-carboxylic acid, 2-furfuryl alcohol, and others), in systems containing H₂O₂ and vanadium compounds, proceed through a mechanism of radical hydoxylation of the furan ring with the formation of 5-hydroxy-2(5H)-furanone and maleic acid. The total yield and ratio of the synthesized compounds depend on the reaction conditions.Translated from Khimiya Geterotsiklicheskikh Soedinenii, No. 11, pp. 1462–1467, November, 1991.     

Method of homogeneous solutions under non-smooth loads

We consider a two-dimensional problem concerned with static deformation of an elastic halfstrip under the action of a self-equilibrated load at its end. A method is proposed for regularization of series over homogeneous solutions in the case of non-smooth prescribed loads. An example is given of a load for which divergence obtains for a series over homogeneous solutions for the stress field at the end of the halfstrip.Translated from Teoreticheskaya i Prikladnaya Mekhanika, No. 19, pp. 111–116, 1988.     

Fluorescent spectroscopy of 3-aminophthalimide molecules cooled in an ultrasonic jet

Translated from Zhurnal Prikladnoi Spektroskopii, Vol. 50, No. 3, pp. 385–391, March, 1989.     

Exact solution of a quasipotential equation that describes a bound state of spinor particles

Theoretical and Mathematical Physics -     

Certain problems of the approximation of functions in two variables by Fourier-Hermite sums in the space L 2(Γ², e -x ² -y ²)

Summary We give an exact estimate of the deviation of the "triangular" partial sums of the double Fourier-Hermite series of functions of the class L^r₂(D) in the space L₂(Γ2, e^-x2-y2).