On the construction of direct and reverse relations of linear control systems

We suggest a constructive method for finding controls D(x) that take zero of the phase space of a complete reachable linear control system with constant coefficients and with a conical set of control constraints to each point x of the phase space. The method is based on the idea of successive reduction of the problem dimension.     

Multidimensional exact solutions to the reaction-diffusion system with power-law nonlinear terms

We study a nonlinear reaction-diffusion system that is modeled by a system of parabolic equations with power-law nonlinear terms. The proposed construction of exact solutions enables us to split the process of finding the components depending on time and the spatial coordinates. We construct multiparametric families of exact solutions in elementary functions. The cases are elaborated of blow-up solutions as well as exact solutions time-periodic but spatially anisotropic.     

On the phase superlattice in a vanadium dioxide film

A statistical theory has been proposed for the formation of a heterostructure of alternating metallic and semiconducting phases in a single-crystal VO₂ film on a substrate. The size distribution function of metallic domains is found as a function of temperature. The temperature dependence of the intensity of light transmitted through the film I(T) is obtained. The depth and width of the dip in curve I(T) near a phase transition, calculated in the framework of the developed theory, agree with the experimental data.     

Quantum-chemical study of lutetium and ytterbium bis- and tetrakis(phthalocyaninates)

DFT calculations with B3LYP and PBE0 functionals have been carried out to determine the structural parameters, vibrational frequencies, and quadrupole moments of double-decker heavy lanthanide phthalocyaninates Pc₂Lu, (Pc₂Lu)⁺, (Pc₂Lu)^–, Pc₂Yb, (Pc₂Yb)⁺, and (Pc₂Yb)^–. Free valence of the Pc moiety [0.5 in Pc₂Lu and Pc₂Yb; 1.0 in (Pc₂Lu)⁺ and (Pc₂Yb)⁺] is delocalized in small fractions over the carbon atoms. The Pc₂Lu и Pc₂Yb molecules have a high electron affinity (3.2 eV) and a low ionization potential (6.1–6.3 eV). Calculations predict formation of quadruple-decker supercomplex Yb(Pc₂Lu)₂ from two Pc₂Lu molecules and an Yb atom via an exothermic process. The equilibrium structure of the molecules and ions can be characterized by D_4d point symmetry group.     

Geometries and NMR properties of cisplatin and transplatin revisited at the four-component relativistic level

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Banach limits: Invariance and functional characteristics

Banach limits invariant with respect to the Cesàro transform are studied. New functional characteristics of Banach limits are introduced and studied.     

Mass Spectrometric Study of the Alkaline-Earth Metal Phosphates Thermal Dissociation

Abstract

The study of the stability of polyvalent metal phosphates showed that at high temperatures they dissociate witn a conversion of the phosphorus oxides into a vapour.     

Quantitative analysis of the fractionation of finely dispersed particles in a centrifugal separator

The kinetic characteristics of solid microparticles moving in the interdisk flow of a liquid separator with conical inserts were analyzed. On this basis, a technique was substantiated and calculation was performed for the process of isolation of particles with desired size from a finely dispersed powder in a liquid suspension.