Association of Formaldehyde in Aqueous-Alcoholic Systems

In the neutral systems formaldehyde-water-alcohol (methanol, ethanol, ethylene glycol) at 25°C, formaldehyde is preferentially present as hemiacetals. The mean equilibrium constants of step polycondensation of formaldehyde are calculated.     

Formation of Cyclic Oligomers in Concentrated Aqueous Solutions of Formaldehyde

An MNDO calculation gave the formation enthalpies of the components of equilibrium mixtures in concentrated aqueous acid solutions of formaldehyde. The results of this study suggest that intramolecular cyclization of linear oligomers with 5 and 9 CH₂O units, respectively, is the most plausible mechanism of formation of cyclic oligomers of formaldehyde — trioxane and tetraoxane. Ring protonation by the hydroxonium ion with ring opening is the most energetically favorable route of cyclic acetal decomposition.     

Electrical conductances of aqueous Na2SO4, H2SO4, and their mixtures: limiting equivalent ion conductances, dissociation constants, and speciation to 673 K and 28 MPa

The electrical conductivities of aqueous solutions of Na(2)SO(4), H(2)SO(4), and their mixtures have been measured at 373-673 K at 12-28 MPa in dilute solutions for molalities up to 10(-2) mol kg(-1). These conductivities have been fit to the conductance equation of Turq et al.(1) with a consensus mixing rule and mean spherical approximation activity coefficients. Provided the concentration is not too high, all of the data can be fitted by a solution model that includes ion association to form NaSO(4)(-), Na(2)SO(4)(0), HSO(4)(-), H(2)SO(4)(0), and NaHSO(4)(0). The adjustable parameters of this model are the dissociation constants of the SO(4)(-) species and the H(+), SO(4)(-2), and HSO(4)(-) conductances (ion mobilities) at infinite dilution. For the 673 K and 230 kg m(-3) state point with the lowest dielectric constant, epsilon = 3.5, where the Coulomb interactions are the strongest, this model does not fit the experimental data above a solution molality of 0.016. Including the species H(9)(SO(4))(5)(-) gave satisfactory fits to the conductance data at the higher concentrations.     

Effect of mechanical activation on the catalytic, physical and chemical properties of copper oxide

Mechano-chemical activation of copper oxide powders leads to structural disordering of the near-surface layers of particles and, thus, to considerable variations in the catalytic properties of copper oxide.

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Laser-quality oxide Y<Subscript>3</Subscript>Al<Subscript>5</Subscript>O<Subscript>12</Subscript> ceramics. Comparative studies of its basic characteristics and laser ceramics of a known manufacturer

The effect of sintering aids of SiO₂, ZrO₂, B₂O₃, and MgO oxides on the optimum sintering temperature, ceramics grain growth, total volume of residual pores, and optical quality of obtained ceramics is studied. The best combinations of sintering aids are found; as a result, YAG:Nd (1 at%) samples of ceramics of high optical quality are obtained. An original method for characterizing laser properties of ceramics is developed. Comparative measurements of main laser characteristics of the obtained ceramics and ceramics of the Konoshima Chemical Corp. Ltd wellknown in the world practice, are performed.     

Tamm states in zigzag carbon nanotubes: Analytic estimates in the Hückel approximation

The frontier molecular orbitals of [C _n ] _q hydrocarbons, fragments of (n, 0) nanotubes, were considered. Asymptotic estimates for two different sets of frontier molecular orbitals were obtained in the Hückel approximation. The problem was shown to be equivalent to the search for model polyene levels with alternating resonance parameters (β and β′ = γβ). The γ parameter was determined by the symmetry type of molecular orbitals and took on values from 0 to 2. The problem was reduced to an analysis of a regular linear polyene with a modified terminal atom by taking alternant symmetry into account. The states of the system were classified according to quasi-momentum Θ values, which could be complex. Solutions with a complex Θ value were localized at tube ends and could be interpreted as Tamm states. The criterion of the appearance of Tamm solutions for the problem under consideration was formulated, γ < 1 − 1/(q + 2). The conclusion was drawn that these states for an arbitrary [C _n ] _q fragment lied close to the Fermi level, and their energies were described by the asymptotic equation α ± βρ^{(q + 1)}. Delocalized levels were always situated farther from the Fermi level than Tamm states.     

Series in the Haar system

We obtain some results concerning the unconditional convergence of series in the Haar system in the metric of L(0, 1).Translated from Matematicheskie Zametki, Vol. 10, No. 4, pp. 369–374, October, 1971.     

Inscribed Balls and Their Centers

A ball of maximal radius inscribed in a convex closed bounded set with a nonempty interior is considered in the class of uniformly convex Banach spaces. It is shown that, under certain conditions, the centers of inscribed balls form a uniformly continuous (as a set function) set-valued mapping in the Hausdorff metric. In a finite-dimensional space of dimension n, the set of centers of balls inscribed in polyhedra with a fixed collection of normals satisfies the Lipschitz condition with respect to sets in the Hausdorff metric. A Lipschitz continuous single-valued selector of the set of centers of balls inscribed in such polyhedra can be found by solving n + 1 linear programming problems.     

Growth Conditions on a Function and the Error Bound Condition

Mathematical Notes - An Erratum to this paper has been published: https://doi.org/10.1134/S0001434618010261