On the maximum principle for doubly nonlinear parabolic equations

For a general class of doubly nonlinear parabolic equations, some versions of the maximum principle are established. They play an important role in studying the regularity of generalized solutions of such equations. In particular, the results obtained can be used in studying equations of the form $$\frac{{\partial u}}{{\partial t}} - div\{ |u|^l |\nabla u\} = 0, m > 1, l > 1 - m.$$ which have numerous applications in the mechanics of continuous media. Bibliography: 17 tiles.     

Methylation of the cyclic homolog of xanthine

Alkylation of the cyclic homolog of xanthine in the methyl iodide-sodium hydride system as a function of the reagent-alkylating system ratio yields different products: for a 13 ratio of reagents, a homolog of caffeine is formed, while for a 12 ratio, a homolog of theobromine is formed. In contrast to xanthine, methylation of its cyclic homolog initially takes place at the imidazole ring and occurs in the sequence N₍₁₎, N₍₄₎, N₍₇₎.A. V. Bogatskii National Academy of Sciences of Ukraine, Odessa 270080. Translated from Khimiya Geterotsiklicheskikh Soedinenii, No. 5, pp. 701–703, May, 1998.     

Effect of interference of quantum states on the broadening of energy levels in a strong electromagnetic field

The wave equation, written down for -functions averaged over the gauge, is solved within the resonance approximation for a number of low levels of a hydrogen-like atom, located in a strong electromagnetic field and undergoing impact action. It is shown that the interference of quantum states, resulting from the interaction of the atom with its surrounding, may lead, depending on the conditions, to a further dependence of the broadening or narrowing of spectral line contours on the external field intensity.Omsk State University. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 11, pp. 8–12, November 1993.     

Electrical conductivity of solutions of the LiIO3-HIO3-H2O system

The electrical conductivity of aqueous LiIO₃ solutions and solutions of the LiIO₃-HIO₃-H₂O system is measured over a wide range of compositions at 25, 50, and 75°C. Isothermal surfaces of electrical conductivity are mapped, and the activation energies of conductivity are calculated. The conductivity isotherms in the LiIO₃-H₂O and HIO₃-H₂O boundary binary systems and in mixed solutions along sections with fixed electrolyte ratios each have a maximum as a function of electrolyte concentration. It is assumed that structure reorganization occurs in solutions in the concentration range corresponding to the peak conductivity. Proton migration features in the solutions in question are considered.     

Calculated structures of asymmetric modifications of cyanospinels

Structural mechanisms of formation of low-symmetry phases of cyanospinels are described in terms of the phenomenological theory of phase transitions. These are examined for transitions from a spinel structure to two cubic and four rhombohedral phases, induced by automorphic irreducible representations 9-2 and 9-3. Atomic coordinates and the symmetry types of occupied positions in asymmetric phases are determined. Criteria for discrimination between the two as well as between the four phases are formulated. The structures of complex cyanides Tl₂Zn(CN)₄ , K₂Zn(CN)₄, K₂Hg(CN)₄, and Rb₂Hg(CN)₄ are calculated. The displacements and irreducible representations inducing transitions from spinel structures to these phases are determined. Novocherkassk State Technological University. Translated fromZhumal Struktumoi Khimii, Vol. 35, No. 5, pp. 41–49, September–October, 1994. Translated by L. Smolina