(050) 303-03-10

Ali Avaz oglu Babayev
Ph.D. in Mathematical and Physical Sciences, docent

10

Structural problem of functional algebras and many valued logics; history of science and engineering (investigation of mathematical and logical views of N.Tousi).

The structures of clones of iterative algebras have been investigated comprehensively and profoundly, all permutational complete sub-clones of k-valued logics have been determined. Analogies of Birkhoff theorem have been obtained for nonstandard sub-Cartesian expansions. Evans problem has been solved for variety of semigroups not subjected to expansion in intersections. Absolute basis of algebra of holomorphic functions of non-commutative form has been established. Algebraic approach to solving the problem of self-duality of Young Mills domains has been elaborated.  The method of algebraic theory of perturbations known in references as Leznov-Mukhtarov method, the method of Riemanns problem and the method of discrete transformations allowed to get first new classes of exact solutions of self-duality equations for Lie arbitrary algebra. The work of N.Tousi "Collection in arithmetics by means of a board and dust" was translated from the Arabic language to the Azerbaijan language, edited and investigated. In the course of investigation it was established that N.Tousi first introduced the symbols for indices of powers and was the first mathematician that has noted that the rule of verification by means of "criterion" is not sufficient. It was also revealed that the first stereometrical axioms were formulated by N.Tousi in his work "Statement of Euclid". To present time, the first place in establishing these facts were ascribed to European mathematicians that have lived 3-4 centuries after N.Tousi.