Solubility in the LaCl<Subscript>3</Subscript>-GdCl<Subscript>3</Subscript>-HCl-H<Subscript>2</Subscript>O system at 25°C

Solubility has been studied in the LaCl₃-GdCl₃-HCl-H₂O quaternary water-salt system at 25°C along the 40±0.2% HCl section; the system is of the eutonic type. The composition of the eutonic solution is as follows: LaCl₃·7H₂O-4.50, GdCl₃·6H₂O, 0.52; HCl, 37.99; and H₂O, 56.99 wt %.     

A cohomological index of Fuller type for set-valued dynamical systems

In the paper we develop the theory of a cohomological index of the Fuller type detecting periodic orbits of a set-valued dynamical system generated by a differential inclusion or a differential equation without the uniqueness of solutions. The theory presented is applied to establish a general result on the existence of bifurcation of periodic orbits from an equilibrium point of a differential inclusion.     

Method of calculating aerodynamic coefficients of some three-dimensional bodies with arbitrary cross section

We consider a method of calculating the aerodynamic coefficients of bodies with arbitrary cross section. The method is carried out on electronic computers, and calculations for bodies with different aspect ratios and shapes are carried out by way of example. The effectiveness of the method is demonstrated by a comparison of the calculated results with the results of a systematic experiment.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 6, pp. 92–98, November–December, 1977.     

On the linear stability study of zonal incompressible flows on a sphere

The normal mode (linear) stability of zonal flows of a nondivergent fluid on a rotating sphere is considered. The spherical harmonics are used as the basic functions on the sphere. The stability matrix representing in this basis the vorticity equation operator linearized about a zonal flow is analyzed in detail using the recurrent formula derived for the nonlinear triad interaction coefficients. It is shown that the zonal flow having the form of a Legendre polynomial P_n(μ) of degree n is stable to infinitesimal perturbations of every invariant set I_m with |m| ≥ n. For each zonal number m, I_m is here the span of all the spherical harmonics $Y^{m}_{k}(x)$, whose degree k is greater than or equal to m. It is also shown that such small-scale perturbations are stable not only exponentially, but also algebraically. © 1998 John Wiley & Sons, Inc. Numer Methods Partial Differential Eq 14: 649–665, 1998     

Photodegradation of CuBi2O4 Films Evidenced by Fast Formation of Metallic Bi using Operando Surface-sensitive X-ray Scattering**

CuBi₂O₄ has recently emerged as a promising photocathode for photo-electrochemical (PEC) water splitting. However, its fast degradation under operation currently poses a limit to its application. Here, we report a novel method to study operando the semiconductor-electrolyte interface during PEC operation by surface-sensitive high-energy X-ray scattering. We find that a fast decrease in the generated photocurrents correlates directly with the formation of a metallic Bi phase. We further show that the slower formation of metallic Cu, as well as the dissolution of the electrode in contact with the electrolyte, further affect the CuBi₂O₄ activity and morphology. Our study provides a comprehensive picture of the degradation mechanisms affecting CuBi₂O₄ electrodes under operation and poses the methodological basis to investigate the photocorrosion processes affecting a wide range of PEC materials.