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GENERALIZED INFORMATION ABOUT THE SCIENTIFIC ACTIVITY OF THE DIVISION.

In 2019, 188 employees took part in research work, including 17 doctors of physical and mathematical sciences, 4 doctors of technical sciences, 103 candidates of physical and mathematical sciences, 10 candidates of technical sciences and 2 students with payment and 72 students without payment .

In the reporting year, 17 topics were performed, including 3 state budget, 14 - research work.

Published 6 monographs, 4 textbooks, 39 textbooks, published 242 works and received 18 patents for inventions, received 1 certificate of author's registration, submitted applications - 11. Published articles and abstracts of reports with the participation of students - 189. According to the results of research students defended 22 master's theses and 4 dissertations.

The main priority areas of scientific activity:

During the reporting year, the scientific work of the Department of General and Experimental Physics was focused on the implementation of the state budget "Interaction of spin waves and spin-polarized current with magnetic inhomogeneities in nanostructured ferromagnetic materials" (supervisor SO Reshetnyak), participation in international conferences articles, support of scientific cooperation with institutions of NASU, with scientific institutions of the People's Republic of China and work within the framework of the international program "Horizon 2020". In particular, several employees of the department underwent internships at the university - partners in this program.

The main direction of scientific work of the Department of Mathematical Analysis and Probability Theory is the study of boundary theorems of probability theory and the theory of random processes, in particular, the asymptotic behavior of generalized recovery sets and certain functionals from random fields. In this area, the asymptotic properties of random fields and functionals from generalized recovery sets, which arise in studies of excursions, extrema, solutions of stochastic differential equations and partial differential equations, statistical estimates of hidden periodicity parameters, are investigated. These studies are carried out in the priority area "fundamental research on the most important issues of scientific and technical, socio-economic, socio-political, human potential to ensure the competitiveness of Ukraine and sustainable development of society and the state" and are supported by the state budget № 2105F "Application of stochastic, statistical and functional methods for the analysis of asymptotic behavior of random fields ". The department also performs two initiative topics: "Statistical evaluation of characteristics and construction of mathematical models of random processes and fields" and "Statistical analysis of the quality of tests in higher mathematics."

Another area of ​​scientific work of the department is the spectral theory of operators and its application to differential equations of mathematical physics.

In addition, the teachers of the department prepared and certified three distance courses "Mathematics for engineers and economists. Differential equations for bachelors majoring in 073 Management "," Methods of Mathematical Economics" and "Higher and Applied Mathematics. Part 1. Elements of linear algebra and analytical geometry and their application to the problems of management, business, economics", which are posted on the website of NMK "IPO"KPI. Igor Sikorsky.

Scientific work at the Department of General Physics and Solid State Physics is associated with joint research with a number of scientific centers around the world. They are mainly based on computer simulations of physical processes in a wide range of research objects.

In collaboration with the London Imperial Collage, methods have been developed to create acoustic metamaterials with desirable properties for use. Such materials are artificially created media with a complex elastic structure in local resonators (so-called “mass-in-mass” constructions with a multilevel hierarchy are used). Similar to optical metamaterials, acoustic metamaterials can have a negative effective mass density and a negative modulus of elasticity. Used to create mechanical filters, vibration isolators and acoustic waveguides. This year, an article was published on the dispersion properties of pseudo-fractal hyperstructures.

Cooperation with Los Alamos National Laboratory USA is carried out in the field of quantum chemistry. The development of methods for calculating nonadiabatic states of polyatomic molecules continues. The main joint work in this direction (Nature Communications), which is based on non-traditional quasiclassical approximations in quantum mechanics, is intensively cited in the world literature. Joint research on quantum states of intergalactic dark matter has also begun. The first published work (Modern Physics Letters A. Vol. 34 (2019) 1950361) was the beginning of the study of the features of hypothetical two-component axion systems, the results of which are being prepared for publication.
Collaboration with the University of Liverpool (London)

Employees of the Department of Differential Equations work in the following areas:

There are two scientific groups at the Department of Mathematical Physics

The scientific work of the department covers basic research in the following areas:

Research at the Department of General and Experimental Physics is performed within the scientific school "Physics of Magnetic Phenomena".
Members of the staff of the Department of General and Experimental Physics are working on current and promising research in the field of magnetism. Together with foreign colleagues from the leading ones world scientific institutions not only solve modern problems of the industry, but also the plan of development of directions of research is planned. In particular, in recent years fruitful international cooperation of the team with the University. Adam Mickiewicz (Poland, Poznan), University of Exeter (UK, Exeter) and the University of the Basque Country (Spain) developed under the European program "Horizon - 2020". The scientific school, whose followers are members of the team, was formed in mid-twentieth century. Its founders can be considered such well-known theoretical physicists as LD Landau, IM Lifshitz, E.M. Lifshitz and their closest colleagues.
The team members have made a significant contribution to solving the problems description of static and dynamic states in magnetic media, problems propagation of linear and nonlinear perturbations of magnetization waves in magnetic ones materials, study of magnetochemical and thermomagnetic characteristics of solids bodies and magnetic fluids, etc.