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Basic directions of scientific researches of department:
Scientific activity
The scientific interests of the teachers of the department are quite diverse, both in the field of fundamental mathematics and in applied mathematics. Currently the main directions of scientific research of the department are:
• the problem of moments, the theory of interpolation problems for analytic matrix functions, and related analysis questions (Yu.M. Dyukarev, S.N. Zinenko, I.Yu. Serikova);
• almost periodic functions (N.D. Parfenova);
• mathematical modeling of heat conduction processes for areas of non-canonical form using variational and regionally structural methods (T.V. Butenko);
• mathematical modeling of the processes of superconductivity of single-domain crystals (Zavgorodnyaya N.N.);
• The theory of turbulent plasma (D.V. Chibisov).
• Distribution of ultra-widewave radio signals in near-Earth space, analysis and processing of ultra-widewave processes (O.V. Lazorenko)
In 2013-2014, 2 theses were defended by the teachers of the department: I.Yu. Serikova PhD thesis "Interpolation problems in the classes R [a, b] and S [a, b]" (2013) and D.V. Chibisov's doctoral thesis "The Instability and Turbulence of a Plasma with Inhomogeneous Ion Flows Along and Across a Magnetic Field" (2014)
Publications of the Department of Higher Mathematics:
1. Бутенко Т.В., Зарецька І.Т., Куланхіна О., Міхайленко Г. Consistency of UMC Design I.J. Information Technology and Computer Science, 2018, номер 9, стр. 47-56
2. Чібісов Д.В. Formation of cavities in the ionospheric plasma due to localized electrostatic
turbulence, Problems of atomic science and technology (PAST), 2018 №4(116) стр. 131-134
3. Чібісов Д.В., Азаренков М.О Anomalous diffusion of plasma in the lower hybrid cavities
observed in the terrestrial ionosphere, Problems of atomic science and technology (PAST), 2018 №6(118) стр. 117-120
4. Dyukarev, Yu.M. ENTROPY FUNCTIONALS AND THEIR EXTREMAL VALUES FOR SOLVING THE STIELTJES MATRIX MOMENT PROBLEM., Methods of Functional Analysis and Topology, 2020, 26(1), стр. 27–38
5. Dyukarev, Y.M. On conditions of complete indeterminacy for the matricial hamburger moment problem., Operator Theory: Advances and Applications, 2020, 280, стр. 327–353
6. Чібісов Д.В. Distribution function of plasma particles in axial magnetic and radial electric fieldsfor the transverse injection of neutral gas - Problems of atomic science and technology.2016,№ 6. Series: Plasma Physics (22)- p. 104-107.
7. N.M.Zavgorodnya, K.V.Tiutierieva, , Ya.V.Dovgopolova, O.O.Chernovol-Tkachenko, R.V.Vovk, A.Chroneos Effect of longitudinal magnetic field on the excess conductivity of monodomain YBa2Cu3O7-? single crystals - Funct. Mater. 2016;- 23 (2)- р. 170-173
8. Чібісов Д.В. , Міхайленко В.С. Response to “Comment on ‘The ion-kinetic D'Angelomode”" Phys. Plasmas >22, 044704 (2015) 3 22, 044704 (2015)3 стр
9. Сєрікова І.Ю. Покроковий розв'язок матричної задачі Каратеодорі в класі 
-Вісник Харківського національного університету, серія «Математика, прикладна математика і механіка» - 2014. № 1133. C. 76-94.
10. Чібісов Д.В. The distribution function of plasma particles in longitudinal magnetic and radial electric fields//International Conference-School on Plasma Physics and Controlled Fusion and The Adjoint Workshop "Nano- and micro-sized structures in plasmas" Kharkiv, Ukraine, September 15-18, 2014. Book of abstracts.
11. INDETERMINACY CONDITIONS FOR THE MATRIX NEVANLINNA-PICK PROBLEM AND RATIONAL MATRIX FUNCTIONS OF THE FIRST AND SECOND KIND
Dyukarev, Yu.M.
2022 Methods of Functional Analysis and Topology
28(1), с. 25-40
12. Movement of charged particles in magnetic and nonuniform stochastic electric fields. Problems of Atomic Science and Technology 2021. No 4 (134) Series: Plasma Electronics and New Methods of Acceleration, p. 112-117, N.A. Azarenkov, A.D..Chibisov https://doi.org/10.46813/2021-134-112
13. Positively charged macroparticles in low-temperature plasma. East European Journal of Physics 2022, № 1, p. 110-115 A.A. Bizyukov, A. D. Chibisov, O.A.Zhernovnykova, T. I. Deуnichenkob, N. N. Yunakov https://doi.org/10.26565/2312-4334-2022-1-15
14. Plasma density depletion caused by inhomogeneous stochastic electric fields. 48th EPS Conference on Plasma Physics June 27, 2022 to July 1, 2022 Online Europe/Amsterdam. N.A. Azarenkov, A.D..Chibisov https://indico.fusenet.eu/event/28/contributions/689/