Magnetic and catalytic properties of the Ni system on kieselgur

The composition, crystal structure, and character of the magnetic susceptibility of nickel—kieselgur catalyst were studied. The connectivity of the activity and selectivity of the nickel catalyst with local and collective properties of the catalyst surface was established. It was discovered that under the influence of a reaction medium, the magnetic properties of the catalyst differ substantially from its initial properties, due to the formation of clusters on the surface forming an active phase.     

Domain instabilities in the planar texture of smectic A liquid crystals

Domain instabilities have been observed in the planar texture of smectic A liquid crystals. The influence of the material parameters and of the applied field on the characteristics of this phenomena have been studied.     

The System Ga2S3?Pr2O3

The diagram of state of Ga₂S₃? Pr₂O₃ has been investigated by the methods of differential thermal, high-temperature differential thermal, X-ray diffraction, microstructural and thermodynamic analyses and by measurement of microhardness of the samples. It has been found that the system is eutectic, the solubility on the part of Ga₂S₃ at 295 K reaches 8 mol.%. In the system the existence of one incongruently-melting compound of Ga₂S₃ · 2 Pr₂O₃ was found.     

Oxidation of the cyclopentanone and cyclohexanone alkyl derivatives in a pseudohomogeneous system without a phase transfer agent

The reaction of catalytic oxidation of C₅–C₁₂ alkyl- and cycloalkylcyclopentanones and -cyclohexanones to lactones in a pseudohomogeneous system without the participation of phase transfer agents was investigated. It was established that the catalytic systems prepared on the basis of molybdenum and tungsten blue (MeO _n Br _m , where Me = Mo, W, n = 1, 2, m = 2, 3) and H₃PO₄ deposited on powdered activated carbon AG-3 at 40–60°C, at 5–6 h duration exhibit a high selectivity in the reaction of nucleophilic addition of oxygen to the ketones with the formation of the valero- and caprolactones.     

Adjoint Coexhausters in Nonsmooth Analysis and Extremality Conditions

In the classical (“smooth”) mathematical analysis, a differentiable function is studied by means of the derivative (gradient in the multidimensional space). In the case of nondifferentiable functions, the tools of nonsmooth analysis are to be employed. In convex analysis and minimax theory, the corresponding classes of functions are investigated by means of the subdifferential (it is a convex set in the dual space), quasidifferentiable functions are treated via the notion of quasidifferential (which is a pair of sets). To study an arbitrary directionally differentiable function, the notions of upper and lower exhausters (each of them being a family of convex sets) are used. It turns out that conditions for a minimum are described by an upper exhauster, while conditions for a maximum are stated in terms of a lower exhauster. This is why an upper exhauster is called a proper one for the minimization problem (and an adjoint exhauster for the maximization problem) while a lower exhauster will be referred to as a proper one for the maximization problem (and an adjoint exhauster for the minimization problem). The directional derivatives (and hence, exhausters) provide first-order approximations of the increment of the function under study. These approximations are positively homogeneous as functions of direction. They allow one to formulate optimality conditions, to find steepest ascent and descent directions, to construct numerical methods. However, if, for example, the maximizer of the function is to be found, but one has an upper exhauster (which is not proper for the maximization problem), it is required to use a lower exhauster. Instead, one can try to express conditions for a maximum in terms of upper exhauster (which is an adjoint one for the maximization problem). The first to get such conditions was Roshchina. New optimality conditions in terms of adjoint exhausters were recently obtained by Abbasov. The exhauster mappings are, in general, discontinuous in the Hausdorff metric, therefore, computational problems arise. To overcome these difficulties, the notions of upper and lower coexhausters are used. They provide first-order approximations of the increment of the function which are not positively homogeneous any more. These approximations also allow one to formulate optimality conditions, to find ascent and descent directions (but not the steepest ones), to construct numerical methods possessing good convergence properties. Conditions for a minimum are described in terms of an upper coexhauster (which is, therefore, called a proper coexhauster for the minimization problem) while conditions for a maximum are described in terms of a lower coexhauster (which is called a proper one for the maximization problem). In the present paper, we derive optimality conditions in terms of adjoint coexhausters.     

Fatty Acids of Vegetable Oils as Components of Anti-Wear Diesel-Fuel Additives

Russian Journal of Applied Chemistry - Comparative study of fatty acids isolated from vegetable (sunflower and cotton-seed) oils and tall oil fatty acids was carried out as regards the possibility...     

Fredholm quasilinear manifolds and degree of a Fredholm quasilinear mapping between them

A new class of Banach manifolds and a new class of mappings between them are presented, and the theory of degree of such mappings is given.