Integral manifolds and the reduction principle in stability theory. III

It is shown how, with the help of approximate integral manifolds, to solve the reduction problem in stability theory in the nonsingular critical case. A generalization of the first fundamental Lyapunov-Malkin theorem in critical cases is obtained.Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 43, No. 10, pp. 1324–1329, October, 1991.     

Development of the Bogolyubov-Mitropol'skii method of integral manifolds

A survey is presented of some results relating to the development of the Bogolyubov-Mitropol'skii method of integral manifolds.Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 44, No. 1, pp. 33–46, January, 1992.     

Tetraphenylphosphonium Diiodobromide: Crystal and Molecular Structure

Complex formation in systems containing 3-carboxypropyltriphenylphosphonium or tetraphenylphosphonium bromide, molecular iodine, and chloroform solution was compared. The maximum number of iodine molecules coordinated by bromides in the solution was established by spectrophotometric method using a function of average iodine number and the stability constants of the complexes were determined. The diiodobromide [(C₆H₅)₄P]BrI₂ was studied by X-ray diffraction analysis. The ab initio calculations were performed for [Y(R)₄]I₃ (Y = N, P, As; R = CH₃, C₆H₅). The obtained experimental data and the correlations with the results of quantum-chemical calculations revealed that the tetraphenylphosphonium cation binds diiodobromide anions through the terminal halogen atoms with equal probability.     

On properties of central manifolds of a stationary point

We present results concerning properties of central manifolds of a stationary point. The results are illustrated by examples.     

Bifurcations of rotating structures in a parabolic functional differential equation

We investigate the Andronov-Hopf bifurcation of the birth of a periodic solution from a space-homogeneous stationary solution of the Neumann problem on a disk for a parabolic equation with a transformation of space variables in the case where this transformation is the composition of a rotation by a constant angle and a radial contraction. Under general assumptions, we prove a theorem on the existence of a rotating structure, deduce conditions for its orbital stability, and construct its asymptotic form. __________ Translated from Neliniini Kolyvannya, Vol. 9, No. 2, pp. 155–169, April–June, 2006.