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On multiplicative (generalized) - derivations and central valued conditions in prime rings

Sandhu Gurninder S., Ayran Ayşe, Aydin Neşet

Journal of Mathematics and Applications

2021

Vol. 44

93--105

Let R be a prime ring with multiplicative (generalized)- derivations (F, f) and (G, g) on R. This paper gives a number of central valued algebraic identities involving F and G that are equivalent to the commutativity of R under some suitable assumptions. Moreover, in order to optimize our results, we show that the assumptions taken cannot be relaxed.

The existence and uniqueness of solution of one coupled plate thermomechanics problem

Krysko V. A., Awrejcewicz J., Bruk V. M.

Journal of Applied Analysis

2002

Vol. 8, nr 1

129-139

The thermo-elastic plate system of equations is analysed. The sufficient conditions of existence, uniqueness and continuity dependence on initial data of the Cauchy problem solutions for differential-operational equation of mixed type (a part of the equation of hyperbolic type, and a part of parabolic type) are given in this paper. If the operational coefficients are suitably chosen, the investigated equation can be used to obtain a differential equation describing vibrations of a plate — the modified Germain-Lagrange equation of hyperbolic type. Moreover, in order to define the temperature field, one can use a three-dimensional equation of thermal conductivity (a parabolic equation).