Ion solvation of aqueous solutions of alkali, alkaline earth, and transition metal halides

The published data on the density and velocity of ultrasound are used to determine the ion solvation parameters of sodium, magnesium, and cobalt chlorides. It is shown that the solvation of typical coordination compounds, such as cobalt chloride, is determined by the same underlying systems and interactions as that of electrolytes with ions of alkali and alkaline earth metals.     

Mathematical modeling of flow in sound-absorbing structures of resonance type in the presence of a grazing flow

Sound-absorbing structures of resonance type are studied on the basis of integration of the unsteady Reynolds-averaged Navier-Stokes equations. The formation of the boundary layer over a sound-absorbing panel is compared with that on a flat plate in the presence of an incident wave. The dependence of the panel reflection coefficient on the presence of a grazing flow and the boundary layer thickness is investigated. The results of the numerical experiment are compared with the available experimental data.     

Mathematical modeling of polymer film casting under biaxial stretching taking into account heat transfer

Polymer film casting is studied using a modified Vinogradov-Pokrovskii rheologicalmodel with heat transfer taken into account. Dependences of the film temperature, velocity, and width on the distance to the extruder exit was obtained and the effect of model parameters on these dependences was examined.     

A sharp bound for the degree of proper monomial mappings between balls

The authors prove that a proper monomial holomorphic mapping from the two-ball to the N-ball has degree at most 2N-3, and that this result is sharp. The authors first show that certain group-invariant polynomials (related to Lucas polynomials) achieve the bound. To establish the bound the authors introduce a graph-theoretic approach that requires determining the number of sinks in a directed graph associated with the quotient polynomial. The proof also relies on a result of the first author that expresses all proper polynomial holomorphic mappings between balls in terms of tensor products.     

On distributive modules and rings

In this paper we study ω-distributive modules, where ω is a cardinal number. We extend a characterization of distributive modules to ω-distributive modules. In particular, the case in which ω = n is a finite cardinal is considered. We apply the results to the case n = 2, obtaining new characterizations for distributive modules and rings. Special attention is given to saturated submodules and ideals.     

On bases of identities of finite inverse semigroups with solvable subgroups

It is shown that every finite inverse semigroup having only solvable subgroups, viewed as a semigroup with the additional unary operation of inversion, has no finite basis of identities, unless it is a strict inverse semigroup.