On the differences and similarities of the first order delay and ordinary differential equations

The present paper is the first step in the systematic study of differences and similarities of the first order delay and ordinary differential equations. The continuous dependence of solutions to DDE on the time delay tending to zero is discussed and theorems guaranteeing continuous dependence are proved. The properties of nonnegativity and the blow-up phenomena for the solution to delay differential equation are studied. Conditions guaranteeing boundness of the solution to DDE are stated. Delay differential equations are considered in Rn as well as in Lp.     

Convergence criteria for branched continued fractions with nonnegative components

For branched continued fractions with nonnegative components and a fixed or variable number of branchings we establish necessary and sufficient conditions for their approximants to be well-defined. We study necessary and sufficient conditions for convergence that are multivariable analogs of the known Seidel-Stern and Stern criteria for continued fractions with positive elements. Translated fromMatematichni Metodi ta Fiziko-Mekhanichni Polya, Vol. 40, No. 2, 1997, pp. 7–13.     

Ethyl 4-thi0cyanato-3-oxo-2-arylhydrazono-1-butanoates in heterocyclization reactions

Conclusions Substituted 1,3-oxathiolanes or substituted 2-chloro-1,3-thiazoles are formed in the reaction of ethyl 4-thiocyanato-3-oxo-2-arylhydrazono-1-butanoates with gaseous HCl in absolute benzene, depending on the electron-donor properties of the substituents in the arylhydrazone.Translated from Izvestiya Akademii Nauk SSSR, Seriya Khimicheskaya, No. 7, pp. 1612–1618, July, 1988.     

Mössbauer effect studies of Tb<Subscript>0.27</Subscript>Dy<Subscript>0.73</Subscript>(Fe<Subscript>1−<Emphasis Type="Italic">x</Emphasis></Subscript>Co<Subscript><Emphasis Type="Italic">x</Emphasis></Subscript>)2 intermetallics at 295 K

The synthesis of materials and the studies of crystal structure and ⁵⁷Fe Mössbauer effect were performed for Tb_0.27Dy_0.73(Fe_1?x Co _x )₂ intermetallics. Terfenol-D (Tb_0.27Dy_0.73Fe₂) is the starting compound of this Fe/Co-substituted series. X-ray measurements showed evidence of a pure cubic Laves phase C15, MgCu₂-type, and unit cell parameters were determined across the series. A Co substitution introduced local area, at sub-nanoscale, with random Fe/Co neighbourhoods of the ⁵⁷Fe atoms.Mössbauer effect spectra for the Tb_0.27Dy_0.73(Fe_1?x Co _x )₂ series at room temperature are composed of a number of locally originated subspectra due to the random distribution of Fe and Co atoms in the transition metal sublattice, and due to [1 1 1] an easy axis of magnetization. Isomer shift, magnetic hyperfine field and quadrupole interaction parameter were obtained from the spectra, both for the local area and for the bulk sample.As a result of Fe/Co substitution, a Slater-Pauling-type curve for the average magnetic hyperfine field vs. Co content was observed. It was found that the magnetic hyperfine fields corresponding to the local area also create a dependence of the Slater-Pauling-type vs. Co contribution in the Fe/Co neighbourhoods.     

Photoelectric properties of Al/In<Subscript>2</Subscript>Se<Subscript>3</Subscript> Schottky barriers

We used directional solidification of the melt to grow single crystals of the binary compound In2Se3 and then determined the composition of the crystals obtained and their structure. From Hall effect measurements, we determined the type of conductivity, the concentration, and the Hall mobility of the free electrons in the single crystals obtained, on which we developed photosensitive Al/In₂Se₃ Schottky barriers for the first time and determined their photoelectric properties. We established that the indicated barriers can be used to design broadband optical photoconverters based on In₂Se₃ single crystals. __________ Translated from Zhurnal Prikladnoi Spektroskopii, Vol. 75, No. 3, pp. 425–427, May–June, 2008.     

Study of active carbons by X-ray methods

The X-ray scattering properties of carbon black and charcoals, activated chemically and by steam have been studied in a transmission arrangement. The radial distribution functions calculated from the experimental data indicate that the majority of carbon atoms in chemically activated samples have sp³ configurations, characteristic of strained ring systems. Activation by steam produces a small amount of crystalline graphite. Most of the carbon atoms in carbon black are in an sp²-hybrid state, apparently because of the presence of contaminating atoms in appreciable amount, although no crystalline graphite can be detected.