Connection formulae for asymptotics of the fifth Painlevé transcendent on the imaginary axis: I

Leading terms of asymptotic expansions for the general complex solutions of the fifth Painlevé equation as are found. These asymptotics are parameterized by monodromy data of the associated linear ODE, The parameterization allows one to derive connection formulae for the asymptotics. We provide numerical verification of the results. Important special cases of the connection formulae are also considered.     

Structure and acid-basic properties of the surface of titanium oxides modified by phosphorus and aluminum and prepared by the alkoxo method

An alkoxo method for the preparatio of single-phase titanium oxides modified by phosphorus and aluminum is proposed and the mechanism of oxide formation is investigated. Structural studies showed that the sizes of the anatase microcrystallite grains and mesopores in the systems are characterized by a uniform distribution. The nature of the modifying agent and the conditions of synthesis influence the interatomic distances and the dimension ofc, the tetragonal unit cell constant of anatase. Published inIzvestiya Akademiii Nauk. seriya Khimicheskaya, No. 11, pp 1829–1834, November, 2000.