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| Departments |
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| Department of "Differential equations" | ||
| Head of the department: |
Bala Agahuseyn oglu Iskenderov corr.-member of NASA, doctor of physico-mathematical sciences, professor |
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| Tel: | 510-14-91 | |
| E-mail: | balaiskenderov07@rambler.ru | |
| Basic scientific directions of the department: | Solvability and quality properties of solutions of partial differential equations. Investigation of solutions and spectral properties of differential-operator equations. | |
| Basic scientific results obtained in the department: | Sufficient condition for decrease of solutions of the Cauchy problem of correct by Petrovskiy equations and system is given. Principles of radiation in unbounded cylindrical domain are grounded. While grounding ultimate amplitude principle, the resonance phenomenon effect was revealed. In the bounded and unbounded cylindrical domains the solutions of the Cauchy problem, the mixed problems were investigated and their asymptotic expansions under large values of time were obtained for Sobolev equations. The trace of a boundary value problem for Sturm-Liouville operator with operator coefficient was calculated. Solvability, Fredholm property and spectrum were investigated for an operator differential equation of second order with a spectral parameter in the boundary condition. | |
| Department of "Functional analysis" | ||
Head of the department: |
Nizameddin Shirin oglu Iskenderov doctor of physico-mathematical sciences, professor | |
| Tel: | (050) 612-14-51; 438-81-51 | |
| E-mail: | nizameddin@hotbox.ru | |
| Amount of employees: | 20 | |
| Basic scientific directions of the department: | Theory of operators; Banach algebra; functional algebra and investigation of random processes; investigation of spectral theory of differential operators and inverse problems. | |
| Basic scientific results obtained in the department: | Algebra of Lie operators and invariant subspaces of semi groups; structure and spectral properties of operators of weight composition type operators; structure and spectrum of number domains of operators in Banach spaces; direct and inverse scattering problems for first order hyperbolic equations on a semi-axis and on the axis; basicity of eigen functions of differential operators with discontinuous coefficients; multiple completeness of eigen and adjoint functions for irregular boundary value problems; construction of tensor radicals in normalized algebras; limit theorems for Halton-Watson branching processes; direct problem for Sturm-Lioville operator with discontinuous boundary conditions; Green functions of differential equations with normal operator coefficients; solvability of boundary value problems for elliptic differential operators. | |
| Department of "Mathematical analysis" | ||
Head of the department: |
Rahim Mikail oglu Rzayev |
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| Tel: | (050) 579-10-56; 438-72-50 | |
| E-mail: | rrzaev@rambler.ru | |
| Amount of employees: | 19 | |
| Basic scientific directions of the department: | Boundedness of integral operators in different spaces. Application of harmonic analysis means to solving some problems of mathematical physics. Imbedding theorems for functional spaces. | |
| Basic scientific results obtained in the department: | Two-weight inequalities for some integral operators and imbedding theorems for Sobolev weight spaces. Different inequalities for integral operators generated by Besssel differential operators and some of their applications. Different properties of Lebesgue and Morrey spaces with variable exponent. Boundedness of maximal operator integral operator of potential and singular integral operator type in Lebesgue and Morrey spaces with variable exponent. Boundedness of some operators of harmonic analysis in mean oscillation spaces. Estimation of the modulus of smoothness of convolution of periodic functions in the terms of best approximations. | |
| Department of "Equations of mathematical physics" | ||
Head of the department: |
Rauf Veli oglu Guseynov corr.-member of NASA, doctor of physico-mathematical sciences, professor |
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| Tel: | (050) 682-04-30; 498-72-75 | |
| E-mail: | raufvh@yahoo.com | |
| Amount of employees: | 15 | |
| Basic scientific directions of the department: | Investigation of quality solutions, spectral analysis, direct and inverse problems, unique solvability of different boundary and initial boundary value problems for linear and nonlinear quasielliptic equations of divergent and non-divergent structure and nonstationary equations with a quasi elliptic part. | |
| Basic scientific results obtained in the department: | Global solvability criterion of Fijita type has been obtained for semi-linear pseudohyperbolic equations. The well-posedness of the Cauchy problem has been studied for hyperbolic equations when a part of coefficients are smooth and a part of coefficients are not smooth. The well-posedness of many-dimensional inverse problem has been investigated for a class of a system of parabolic equations. Quality properties of solutions of different boundary value problems have been obtained for elliptic and parabolic equations. Spectrum of equations with operator coefficients and partial equations have been studied. Negative spectra of quasielliptic operators have been investigated, appropriate quality estimates have been obtained. | |
| Department of "Theory functions" | ||
Head of the department: |
Melik-Bakish Ali-Ikram oglu Babayev doctor of physico-mathematical sciences, professor Honoured scientist |
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| Tel: | 438-62-17 | |
| E-mail: | melikbaxish@mail.ru | |
| Amount of employees: | 9 | |
| Basic scientific directions of the department: | Approximation of functions of many variables by linear and nonlinear superpositions of functions of fewer number of variables. Investigation of boundary properties of functions. Imbedding theorems in functional spaces. | |
| Basic scientific results obtained in the department: | New linear and nonlinear superpositions of functions have been constructed. Important problems of the best approximation have been investigated. The problems of exact estimation of the best approximation have been studied. The imbedding theorems were obtained for different functional spaces. Boundary extremal properties of special subclasses of generalized analytic functions in Vekua sense have been investigated. | |
| Department of "Algebra and logic" | ||
Head of the department: |
Ali Avaz oglu Babayev candidate of physico-mathematical sciences, docent |
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| Tel: | (050)303-03-10 | |
| E-mail: | a.babayev49@gmail.com | |
| Amount of employees: | 10 | |
| Basic scientific directions of the department: | Structural problem of functional algebras and many valued logics; history of science and engineering (investigation of mathematical and logical views of N.Tousi) | |
| Basic scientific results obtained in the department: | 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. | |
| Department of "Theory of elasticity" | ||
Head of the department: |
Isakh Salam oglu Mamedov candidate of physico-mathematical sciences, docent |
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| Tel: | 438-65-13 | |
| Amount of employees: | 10 | |
| Basic scientific directions of the department: | Investigation of problems of free and forced ascillations of inhomogeneous bars, plates and cylindrical shells interacting with medium, direct and inverse problems of great (or order unit or greater) axi-symmetric deformations of plane flaments, circular membranes and shells of rotation of open and cilosed profiles, the problems on strength, free and forced oscillations of plates and shells damaged in deformation process, solution of direct and inverse nonlinear problems of hydroelectricity of structural element and problems on oscillation of structural elements contacting with self-regulated medium. | |
| Basic scientific results obtained in the department: | The problems on stability and free oscillations of in- homogeneous rectangular and annular plates interacting with external medium, driect and inverse problems of great (of order unit or greater) axisymmetric deformations of plane filaments, isotropic and anisotropic annular membranes, momentless rotation shell of open profile, the problems on forced oscillations of felled cylindrical shells situated in magnetic field, the problems on free oscillations stiffened by rigidity bars of cylindrical shells and the problems of forced oscillations of elastic damaged bars, the direct and inverse problems of large deformations of annular membranes and momentless shells of open profile under the action of liquid and normal forced and under the action of liquid and parallel forces have been solved | |
| Department of "Wave dynamics" | ||
Head of the department: |
Jafar Gasan oglu Agalarov doctor of physico-mathematical sciences, professor |
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| Tel: | 498 87 08, (055) 306 91 21 | |
| E-mail: | Agalarov_Jafar@rambler.ru | |
| Amount of employees: | 16 | |
| Basic scientific directions of the department: | Investigation of wave propagation process in deformable solids. Impact and failure problems. Elaboration of new solution methods. | |
| Basic scientific results obtained in the department: | Theory of filament of membranes and nets has been created. Methods of experimental investigations of wave processes of flexible binders and the methods of definition of dynamical characteristics of materials have been worked out. Some one and multi – dimensional problems of impact and failure of structural element including for composite structural materials, have been solved. In the practice of world science the wave propagation process of nonstationary waves in a right prismatic body from the position of three-dimensional exact theory has been first investigated and appropriate analytic solutions have been obtained. Problems of dynamical failure were first investigated theoretically and experimentally for a set of different direction cracks and real results have been obtained. Stationary and nonstationary motions of shells have been investigated in liquid and elastic medium-filled continuum. | |
Department of "Theory of creeping" |
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Head of the department: |
Latif Khalil oglu Talybly doctor of physico-mathematical sciences, professor |
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| Tel: | (050) 281-29-92; 439-02-21 | |
| E-mail: | ltalybly@yahoo.com | |
| Amount of employees: | 15 | |
| Basic scientific directions of the department: | Construction of mathematical model with different mechanical properties; Statement of problem on definition of stress-strain state and elaboration of effective methods of their solution; elaboration of mechanical and thermal strength criteria. | |
| Basic scientific results obtained in the department: | A solution method of general problem of theory of linear isotropic viscoelasticity, where traditional use of integral transformations is excluded, has been suggested; effective nonlinear theories of deformation and fracture of visco-elastic and viscoelasticoplastic bodies under the action of arbitrary in time force and temperature factors have been elaborated. Equation on wear of surface layers of elastico-plastic bodies has been derived; a process on destruction of rapture constructions by means of model ones has been modeled; experimental-theoretical method for definition of time to corrosive failure of bodies of arbitrary geometry has been worked out; formula for characteristical durability of constructions with regard to influence of history of acting random loads has been derived. | |
Department of "Non-harmonic analysis" |
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Head of the department: |
Bilal Telman oglu Bilalov doctor of physico-mathematical sciences, professor |
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| Tel: | (012) 438-72-50 | |
| E-mail: | bilalov.bilal@gmail.com | |
| Amount of employees: | 24 | |
| Basic scientific directions of the department: | Study of spectral properties of not self-adjoint differential operators, basis properties of appropriate systems of eigen and adjoint functions and problems related with matters of theory of bases of Banach spaces; investigation of some inverse and quality problems for linear and nonlinear differential equations. | |
| Basic scientific results obtained in the department: | Sine and cosine analogy of "1/4 -Kadets" theorem have been found, banach generalization of Paley-Wiener classic theorems for close bases have been givani final results on basicity of the systems of exponents with complex coefficients in Lebesque spaces have been obtained; a complex generalization of Stone-Weierstrass classic theorem has been given; final result on basicity of A.G.Kostyuchenko system has been obtained; basicities of some perturbed systems of exponents, sines, and cosines in Lebesque spaces with variable summability index have been studied; important results on basic properties of the systems of root elements of ordinary differential operators have been obtained; quality problems for some classes of elliptic and parabolic equations have been studied; Sufficient in some sense exact results on well-posed solvability of some classes of operator-differential equations have been obtained. | |
Department of "Applied mathematics" |
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Head of the department: |
Gabil Garibkhan oglu Aliyev doctor of physico-mathematical sciences, professsor |
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| Tel: | (055) 767-74-34; (ev) 494-61-73 | |
| E-mail: | bilalov.bilal@gmail.com | |
| Amount of employees: | 6 | |
| Basic scientific directions of the department: | Study of mechanism of change of electromagnetic properties in physical chemical variable media. Creation of mathematical theory of electrodynamics of physical chemical variable media. Investigation of mechanism of adhesive strength of composite materials and creation of mathematical theory of adhesive strength of structural elements made of composite materials | |
| Basic scientific results obtained in the department: | Mathematical dependence of electromagnetic characteristics (ε, µ, λ) on character of chemical variability of two-component liquid has been established. Their dependence on temperature factor is also established. A physico-mathematical model of deformation of a polymerized bundle made of fibers at the neck zone is suggested. |
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| Department of "Computing mathematics and information science" | ||
Head of the department: |
Fariz Beykas oglu Imranov candidate of physico-mathematical sciences |
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| Tel: | 439-50-97 | |
| E-mail: | fariz@science.az | |
| Amount of employees: | 16 | |
| Basic scientific directions of the department: | Elaboration of mathematical-information technologies of the problems of calculating hydrodynamics control of dynamic systems and medical diagnostics. | |
| Basic scientific results obtained in the department: | A mathematical model of the flow formation process in Caspean sea under the influence of global vector of winds has been constructed. The soft ware has been worked out, the results of series of calculating experiments compared with the results of instrumental measurement have been visualized, satisfactory on-line animations of 2D schemes of flows have been obtained. Algorithm and software of technology of predicative –correct control of a closed dynamic thermal system of catalytic reaction and regeneratiron have been worked out, the results of series of calculation experiments have been visualized, satisfactory on-line animations of 3D phase portraits of mathematical model of dynamic system have been obtained. | |
Department of "Mechanics of liquid, gas, and theory of plasticity" Laboratory "Physico-mechanical processes under liquid and gas flow" |
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Head of the department: |
Vagif Jamal oglu Hajiyev doctor of physico-mathematical sciences, professor |
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| Head of the laboratory: | Geylani Minhaj oglu Panahov doctor of technical sciences, acad. of Russian Academy of Sciences | |
| Tel: | 439-02-21 | |
| E-mail: | pan_vniineft@rambler.ru | |
| Amount of employees: | 23 | |
| Basic scientific directions of the department: | Elaboration of solution methods of problem on strength stability and oscillation of thick-walled anisotropic and isotropic constructions. Oil industry mechanics, elaboration of energy and resource-saving engineerings on the base of mathematical simulation of hydrogasdynamics problems, investigations in the field of mathematical statistics, laboratory and industrial experiments. Investigation of not equilibrium gelation and electro kinetic properties while filtrating heterogeneous systems in fractal inhomogeneous porous media. Investigation of influence of transfer processes on non-stationary state in liquids and gas. | |
| Basic scientific results obtained in the department: | A mathematical model of the flow formation process in Caspean sea under the influence of global vector of winds has been constructed. The soft ware has been worked out, the results of series of calculating experiments compared with the results of instrumental measurement have been visualized, satisfactory on-line animations of 2D schemes of flows have been obtained. Algorithm and software of technology of predicative –correct control of a closed dynamic thermal system of catalytic reaction and regeneratiron have been worked out, the results of series of calculation experiments have been visualized, satisfactory on-line animations of 3D phase portraits of mathematical model of dynamic system have been obtained. | |
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