Malkina V. Geometrical modelling of scalar and vector fields on a base of the generalized-3vector calculations

Object - processes of a vector, scalar and vtctor-scalar nature; the purpose - to develop bases of the new geometrical device on the ba-sis of the functions offered in the robot general-ized - 3-vector's argument for modelling vector and scalar fields with the given positionally - differential properties; methods - differential and analytical geometry, the theory of ap-proximation, methods of calculations, the func-tional and mathematical analysis, the theory of functions of complex variables, the theory of hypercomplex numbers; theoretical and practi-cal results - the new modelling device, which basis is made constructed in the robot general-ized - 3-vector with calculation is developed, the method of construction approximating vec-tor, scalar or vector-scalar generalized-3-vector's a polynom is developed; novelty - theoretical bases of geometrical modelling of vector and scalar fields for the first time are developed, namely: For the first time special parametrization of new geometrical objects is entered and investigated on the basis of intro-duction of concept generalized 3-vector(О-3-vector) and constructions of system of special operations above these objects, that in aggre-gate makes a basis О-3-vector calculations; bases of the analysis О-3-vector functions for the first time are developed; the general method of geometrical modelling of vector and scalar fields with the given item and linear differential properties on base O-3-vector approximating polynoms for the first time is developed; on the basis of the general method for the first time on base O-3-vector polynoms methods of the de-cision of a task about deformation of an elastic body in movings; for a task about a deflection of a plate; tasks of heat conductivity stationary and non-stationary; for a task about fluctua-tions of a firm body; a degree of introduction - it is introduced in KB "Pivdenne", Dnepropet-rovsk; in KB "Kievpromzv'yazokbud", Kiev; at GRP Avto-ZAZ-Motor, Melitopol; sphere of use - construction of geometrical models of the phenomena and processes on beforehand given linear differential-geometrical characteristics