Boundary Value Problems for Ordinary Differential Equations with Deviated Arguments

We discuss differential equations with nonlinear boundary conditions. We formulate sufficient conditions under which problems with deviating arguments have quasisolutions or solutions. To obtain the results, we apply the method of monotone iterations.     

A differential-geometric criterion of the kinematic integrability of nonlinear differential equations

A theorem on the existence of a G-representation and a differential-geometric criterion of the kinematic integrability for nonlinear differential equations from the Λ²-G-classes is proved. Examples of zero-curvature representations and metrics for some equations of mathematical physics are presented. __________ Translated from Fundamental’naya i Prikladnaya Matematika (Fundamental and Applied Mathematics), Vol. 11, No. 1, Geometry, 2005.     

Circular dichroism spectra in mordant azo dyes

The photogyrotropic properties of several mordant yellow azo dyes in gelatin and polymer matrices that are in the normal state or exposed to circularly polarized light are investigated. A model explanation for the experimental data is given.     

Production and properties of metal-carbon composite coatings with a nanocrystalline structure

It is suggested to produce metal-carbon composite coatings by magnetron sputtering of mosaic cathodes, which are Group IV, V, and VI metals. The mosaic structure of the cathode elements are computer-optimized for each of the metals. Reflection electron diffraction studies show that the coatings have the amorphous or nanocrystalline structures, which are thermally stable. The coatings offer specific physical properties, in particular, low friction factor and high hardness.     

Growth and study of single crystals of (Na,K)NbO<Subscript>3</Subscript> solid solutions

(Na, K)NbO₃ crystals with a perovskite structure and a KNbO₃ content up to 40 mol % were grown from flux with the use of the solvent NaBO₂. The dielectric measurements of the crystals grown revealed phase transitions that had never been observed before in ceramic samples.     

Arene sulfenylation by arenesulfenamides and arenesulfenylacetates

Two systems for arene sulfenylation were investigated: arenesulfenamides in the presence of SO₃ and sulfenylacetate complexes with AlBr₃. A preference for the second reagent was demonstrated for sulfenylation of substrates bearing donor substituitents.Translated fromIzvestiya Akademii Nauk. Seriya Khimicheskaya, No. 2, pp. 324–326, February, 1995.     

Inconsistency of a metatheory of Nudel''man

A metatheory of Nudel'man outlined in [1] is proved inconsistent. The groundwork for the proof is the method of arithmetization of metamathematics.Translated fromAlgebra i Logika, Vol. 34, No. 1, pp. 41–43, January–February, 1995.     

Controllability of Functional Integro-Differential Inclusions with an Unbounded Delay

In this paper, a sufficient condition is established for the controllability of neutral functional integro-differential inclusions with an unbounded delay in Banach spaces. The approach used is a fixed-point theorem for condensing maps due to Martelli and the theory of analytic semigroup of linear operators. Communicated by F. Zirilli Research supported by NNSF of China, by the Teaching and Research Award Program for Outstanding Young Teachers in Higher Education Institutions of the Ministry of Education of China, and by the Qing Lan Talent Engineering Fund QL-05-164 of Lanzhou Jiaotong University. The authors are grateful to Professor F. Zirilli and two anonymous referees for valuable suggestions improving this paper.