Vanadium valency charge state in solid solutions ScNb2−2xTa2xVO9

Phase equilibria in the Sc₂O₃-V₂O₅-Nb₂O₅-Ta₂O₅ system and properties of ScNb_2−2xTa_2xVO₉ phases were studied by X-ray phase analysis, optical and radio spectroscopy. A continuous series of solid solutions was shown to exist at 0≤x≤1. V(IV) centers with different crystallographic surrounding were detected for all the considered compositions. A correlation between the number of V(IV) ions and the width of the forbidden gap in the solid solutions was found.     

Three-dimensional flow of supersonic jets past bodies

Translated from Aktual'nye Voprosy Prikladnoi Matematiki, pp. 228–235, 1989.     

Global solvability of the Cauchy-Dirichlet problem for nondiagonal parabolic systems with variational structure in the case of two spatial variables

The Cauchy-Dirichlet problem for quasilinear parabolic systems of second-order equations is considered in the case of two spatial variables. Under the condition that the corresponding elliptic operator has variational structure, the global in time solvability is established. The solution is smooth almost everywhere and the number of singular points is finite. Sufficient conditions that guarantee the absence of singular points are given. Bibliography: 23 titles. Translated fromProblemy Matematicheskogo Analiza No. 16, 1997, pp. 3–40.     

Regularity results for quasilinear elliptic systems with nonlinear boundary conditions

It is proved that a solution of the boundary-value problem for a second-order quasilinear system with controlled order of nonlinearity is partially smooth all the way to the boundary of a domain. The boundary condition is imposed by means of a second-order nonlinear operator which can be regarded as a generalization of the “directional derivative” to the case of quasilinear systems. Bibliography: 6 titles. Translated fromProblemy Matematicheskogo Analiza, No. 14, 1995, pp. 23–50.     

Acid-base properties of substituted tetraphenylmethylenediphosphine dioxides

Conclusions Some tetraphenylmethylenediphosphine dioxides, substituted in the methylene bridge, were subjected to potentiometric titration in nitromethane with perchloric acid. The obtained values of the pK _a basicity constants (CH₃NO₂) obey a linear relationship with the ^* constants of the substituents.Translated from Izvestiya Akademii Nauk SSSR, Seriya Khimicheskaya, No. 1, pp. 199–201, January, 1972.     

Lattice Dynamics in LaTa2-2xNb2xVO9-δ (x=0–0.1) Solid Solutions

The oxygen nonstoichiometry (x) of LaTa_2-2xNb_2xVO₉- (x = 0–0.1) solid solutions was studied using Xray phase analysis, vibrational spectroscopy, and radiospectroscopy. A correlation was found between (x) and the unit cell volume V(x) of the solid solutions. It was shown that the infrared spectra of LaTa₂VO₉- change in passing from = 0 to 0. The structural position of the oxygen vacancy in LaTa_2-2xNb_2xVO₉- is discussed.