Institute of Mathematics and Mechanics
Azerbaijan National Academy of Science

Department of “Algebra and mathematical logic”


Head of the department: Ali Avaz oglu Babaev
phD in math.
Tel:  (+994 12) 5396960 , (050)303-03-10
E-mail: ,
Number of employees: 11
The basic scientific of the department: Investigation of wave propagation process in deformable solids. Impact and failure problems. Elaboration of new solution methods.
The obtained basic scientific results: On the first problem T.Evens problem on indecomposable in intersection of semigroup varietes is solved.
A. Salomaa problem on fundamental subgroups of symmetric groups is solved.
R.Knoebel problem for finite groupoid is solved.
With the help of method of proof theory coherence theorem in Cartesian closed, biclosed and symmetric monoidal categories is proved.
In special class of topological spaces in terms of right ideals semigroups of homeomorphic mappings of these spaces into itself dimension of these spaces is expressed.
Questions connected with semigroups of homeomorphic, local homeomorphic, open continuous and open mappings of topological spaces are studied.
The investigations in the field of non-classic logics. A few form of formalization of intuitionist negationlesse logic and their interpretations are proposed.
The deductive possibility of this system has been studied.
In the framework of the group-theoretic approach of the investigation of nonlinear classical and quantum dynamical systems it have been obtained the exact solutions of the four-dimensional self-duality Yang-Mills model (SDYM) for an arbitrary semisimple Lie algebra, and for a variety of symmetry reductions of the self-duality equations, such as the model of WZNW (Wess-Zumino -Novikov-Witten), the principal chiral field model with movable poles and others.
The second problem is the research on mathematcal and logical works of Nasir ad-din at-Tusi.
The manuscripts of Tusi:”The Collection of Arithmetic (Jami al-hisab bi-l-Takht wa-l-turab ), ”Tadjrid-al-mantic” and “The exporsition of  “The book of supposition” of Sabit ibn Kurra” were translated into Azerbaijani and Russian.This work are investigated. The translation of “Tahriri Oglidis” of Tusi was edited.This work is investigated.
In the study of the treatises we found facts previously unknown and changing the dating of some mathematical statments.There are:
the prinsiple of letter designation of degrees of Tusi and Outred (1574-1660) are the same.
-Ad-Tusi’s remark about “criterion” that is the concidence of “criterions” is necessary, but not sufficient In the history of mathematics the first indication of insufficiency of that condition dates back to the 15-th century.
It was thout that the first streometric axioms were formulated only 17-th century. N.Tusi in “Tahriri Oqlidis” formulated three stereometric axiom. The study of Tusi’s comment in terms of geometric concepts, terminology and demonstrations of  theorems leads us to the conclusion that at the time of writing the “ Tahrir”, the nature and conception of a geometry was changed.
The logical treatise “A’sas al ikchtibas” is translated and stadied.
Another interesting fact is the metod of finding a common denominator as the least common multiple. For the first time this method dates from the second half of the 16th century (Tartalia and Clavius).
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