Mathematics Research Laboratory

Updated 17.09.2015

Research Laboratory for Mathematics, Economics, mechanics and psychology

Chairperson - Dr. Shchogolev  S. A 
Research is conducted in several areas: mathematics, applied mathematics, mechanics, economics, psychology. 


The department of differential equations is working on the department scientific theme "Researching  of the behavior of solutions of differential equations by the asymptotic and qualitative methods" - the  scientific adviser professor Evtukhov VM. For differential and difference equations and systems of equations with properly and quickly varying nonlinearities the new methods of establishing asymptotic formulas for non-oscillating solutions are constructed, and Necessary and sufficient conditions for the existence of solutions satisfying the found asymptotic are obtained. 
The department of higher mathematics studies within the department scientific  theme "Researching of the asymptotic theory of differential equations, the theory of oscillations, the theory of singular integro-differential equations." The results on the asymptotic behavior of solutions of quasi-linear two-dimensional systems in cases not covered by previous results are obtained. An extension to more difficult  classes of signs of the existence of particular solutions of quasi-linear systems, represented by the Fourier series with slowly varying parameters are obtained. The signs of existence of the integral manifold of quasi-linear two-dimensional system, represented by this form, are obtained. The problem of Carleman for bands with analytic continuation into the upper half-plane, and for the Carleman problem for the ring. Investigated the application of theory intro-differential equations to solve some problems in the theory of risk. 
At the Department of Geometry and Topology studies within the state budget theme "Researching of deformations of the surfaces, the geometry of approximate second order Riemannian spaces  and reflections of Riemannian spaces" – the  scientific adviser associated professor Pokas S. M.

 Applied Mathematics. 

The department of computational mathematics research work carried out in the framework of implementation of the scientific theme № 229 "Researching of certain classes of boundary-value problems of differential equations, their approximations and image processing techniques," which is included in the plan of scientific researching of Odessa I.I. Mechnikov National University (number of state registration  0111U008971; scientific adviser prof. Vityuk A.N.). 
Main scientific achievements are: 
We construct the exact solution of axisymmetrical mixed problem of elasticity theory for jammed on the lateral surface of a cone with a ball attached segment. 
The problem of the tense state of indissoluble band-type plate, which weakened by the crack. 
The method of calculating continuous plate-type constructions with defects such as cracks or rigid inclusion based on the method of three points are developed. 
The existence and uniqueness of the solution to the problem of Darboux for differential equations with mixed derivative regularized fractional order. 
The stipulater for a system of linear algebraic equations with saddle matrix, based on generalized  expansions of Holetsky, are constructed. 
A temporal interpolation algorithm for image sequences based on generalized  series Whittaker - Kotelnikov - Shannon, making it possible to reduce the computation complexity of temporal interpolation of image sequences, and an algorithm to port applications to mobile devices in real time. 
The department of software of computation systems are working within the scientific-research state budget theme "Development of methods of intellectual analys of data and software information and Distributed Systems" (number of state 0106U006199), scientific adviser Ph.D. , associate professor Petrushina TI 
 The department of methods of mathematical physics is working on a scientific-research state budget theme "Researching of boundary value problems of elasticity in the presence of mixed boundary conditions and cracks appear in the surface, scientific adviser professor Vaysfeld N. D. 


The department of theoretical mechanics in 2013, is working on department  scientific theme "Researching of rotational motion of the satellite relative to the center of mass under the influence of disturbing moments" - the scientific adviser professor Aslanov S.K. The problem of rotational motions of dynamically asymmetric satellite under the influence of the gravitational moment in the medium with resistance are developed. The results of problems of motion of satellite relative of center of mass under the influence of light pressure and resistance are obtained. Researched a new approach to solving the problem of the motion of the satellite relative to the center of mass of a spherical cavity, it is filled with high viscosity fluid under the influence of gravitation moment and light pressure. A package of applications to illustrate the motion of the satellite with the help of 3D-graphics are developed. 


The department of management and mathematical modeling of market processes is working on the scientific theme of "Managing transformation processes at different levels of economic and ecological systems" - the scientific adviser professor Sadchenko O. V. The problems of innovative development of domestic enterprises in the conditions of transitive economics are determined. The main areas of governance transformation processes in business systems are determined. A methodology for strategy formation greening business and its components (innovation and marketing functions) are constructed. A theoretical and methodological framework of innovation development at the enterprise level of environmentally hazardous working conditions, as well as for businesses using hazardous materials or technology are constructed. In this regard, improved approaches to the greening of innovation in line with the concept of sustainable development. The composition of ecological and economic security and state are determined. The composition of environmental management and marketing at the company are determined. 
At the Department of World Economy and International Economic Relations research on "Sustainable development of national economies in terms of instability of the world financial system" is continues – scientific adviser professor Yakubovsky  S.A. The study is based on a new approach for national science assessment on the consequences of international investment for national stability of financial systems. It is based on a comparative analysis of the impact of foreign investment on the parameters that determine the international competitiveness of the country. Determine the stability of national financial systems is estimated investment position of countries, justified and implemented recommendations to improve the financial sustainability of the economy of Ukraine. The features of monetary policy in Russia and Ukraine, the parameters of stability of national financial systems in terms of global imbalances are determined. The proposed recommendations to improve the financial stability of the economy of Ukraine will allow the Government and the National Bank of Ukraine to optimize the portfolio of foreign borrowing to curb the rate of money creation, stimulate economic growth. 
The department of economic theory and history of economic thought within the scientific work on the Cathedral theme number 231 "Researching of the formation of institutional structures in a market transformation" - the scientific adviser professor Gornyak O.V.,  researching the interaction of institutions and individuals in terms of the institutionalization of economic structure, transactions and transaction costs of market transformation, including: the cost of detection, alternatives, cost measurement, cost negotiation and conclusion of the contract, the cost specification and human ownership costs of opportunistic behavior. 


The department of differential and special psychology is working on the scientific theme number 195 (scientific adviser professor Viskovatova T.P.). The data on the principles of construction and general characteristics of psychological treatment of people with mental and physical disabilities (for example, autism) are obtained. The main tasks of psycho-corrective and therapeutic work of psychologist with parents of children with mental and physical developmental disabilities are considered. A theoretical and methodological basis of providing psychological rehabilitation of local business leaders by developing their own efficiency are developed. A program of psychological training "Effective communication in business leaders" are constructed.
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