On the Eigenvalues and Eigenfunctions of the Sturm--Liouville Operator with a Singular Potential

In this paper we consider the Sturm--Liouville operators generated by the differential expression -y+q(x)y and by Dirichlet boundary conditions on the closed interval [0,]. Here q(x) is a distribution of first order,, i.e., q(x)dx L ₂[0,]. Asymptotic formulas for the eigenvalues and eigenfunctions of such operators which depend on the smoothness degree of q(x) are obtained.     

Trace Formula for Sturm--Liouville Operators with Singular Potentials

Mathematical Notes - Suppose that u(x) is a function of bounded variation on the closed interval [0,π], continuous at the endpoints of this interval. Then the Sturm—Liouville operator...     

Introduction of Low-Molecular Digicidylurethane: Effect on the Properties of Oligoetherurethane-Diepoxide Compositions

The preparation of elastomers based on blends containing oligoetherurethane diepoxide (OUDE) and low-molecular-weight diglycidylurethane (DGU) has been described. For both the composition and cured elastomer, the dependence of the properties on the DGU fraction in the initial blend has been studied. It is shown that, at an equimolar ratio of DGU and OUDE, the physicomechanical characteristics properties of the elastomers have been shown to be significantly higher than those for OUDE-based elastomers. A 1.5- to 2-fold decrease in the degree of equilibrium swelling has been observed at a 0.5 mole fraction of DGU, if compared to OUDE-based elastomers.     

Equiconvergence of Spectral Decompositions for Sturm–Liouville Operators with a Distributional Potential in Scales of Spaces

Doklady Mathematics - We study the equiconvergence of spectral decompositions for two Sturm–Liouville operators on the interval [0, π] generated by the differential expressions...     

Radiation-thermal transformations and distillation of lipids and disperse systems on their basis

The radiation-thermal transformations of rape oil under conditions of postradiation distillation, radiation heating, and electron-beam distillation with auxiliary heating were studied. Diesel hydrocarbons were predominant in the condensate distilled off upon combined heating. The concentration of oxygen atoms decreased as a result of radiation-induced decarboxylation and dehydration processes. The irradiation of oil as a constituent of disperse systems facilitated purposeful deoxygenation, a decrease in the viscosity, and an increase in the yield of the gasoline fraction.     

Rate of convergence of the Taylor series for some classes of analytic functions

We study the rate of convergence of the Taylor series for functions from the classes A ^Ψ H _p, p = 1, ∞, in the uniform and integral metrics. Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 50, No. 7, pp. 1001–1003, June, 1998.