The theory of the numerical-analytic method: Achievements and new trends of development. VII

For the numerical-analytic method suggested by A. M. Samoilenko in 1965, we analyze the application to abstract differential equations, implicit equations, and control problems. Institute of Mathematics, Ukrainian Academy of Sciences, Kiev. Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 51, No. 9, pp. 1244–1261, September, 1999.     

The theory of the numerical-analytic method: Achievements and new trends of development. V

We analyze the application of the numerical-analytic method proposed by A. M. Samoilenko in 1965 to difference equations. Institute of Mathematics, Ukrainian Academy of Sciences, Kiev. Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 51, No. 5, pp. 663–673, May, 1999.     

The theory of the numerical-analytic method: Achievements and new trends of development. VI

We analyze the application of the numerical-analytic method proposed by A.M. Samoilenko in 1965 to multipoint boundary-value problems. Institute of Mathematics, Ukrainian Academy of Sciences, Kiev. Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 51, No. 7, pp. 960–971, July, 1999.     

Existence and Extendability of Solutions of the Equation g(t,x) = 0

We consider the problem of extendability and existence of solutions of the equation g(t, x) = 0 on the maximum interval of their definition.     

The Reduction Method in the Theory of Lie-Algebraically Integrable Oscillatory Hamiltonian Systems

We study the problem of the complete integrability of nonlinear oscillatory dynamical systems connected, in particular, both with the Cartan decomposition of a Lie algebra is the Lie algebra of a fixed subgroup with respect to an involution : G G on the Lie group G, and with a Poisson action of special type on a symplectic matrix manifold.     

Kinetic Parameters of Silver Electrodeposition from Nitrate Melts

The system Ag/KNO₃–NaNO₃–AgNO₃is studied in an open bath in air by various experimental methods. The limiting diffusion currents of the silver electrodeposition are determined by a galvanodynamic method at various linear current sweep rates. The diffusion coefficient of Ag⁺ions in equimolar KNO₃–NaNO₃melt is determined by a potentiodynamic method at linear potential sweep. The exchange currents on a silver support are determined by the method of two current pulses.     

Order parameter and barrier height in LaSrMnO cluster glasses

Using the results of magnetization measurements of LaSrMnO cluster glasses, it is shown that the concentration of frozen magnetic moments exponentially decreases with the increase of temperature. We find that temperature dependence of the order parameter q, of the form q−q(T)∼T−5/2, is universal characteristic of the investigated cluster glasses and that the barrier height Δ closely follows the quadratic relation to the temperature, Δ≈BT².