MATHEMATICAL MODEL OF DYNAMICS OF SMALL ENTERPRISES WITH ACCOUNT OF MEMORY EFFECTS

The paper proposes a new mathematical model of the dynamics of small enterprises with the participation of foreign investment, which takes into account the memory effect and affects the rate of change in the value of production assets. This memory effect can be considered as a property of the economic environment, for example, the influence on the production of external factors, in which the cost of production assets will depend on its previous values. This non-local effect can be written in terms of a fractional order derivative. In this paper, we will assume that the order of the fractional derivative is a function of time. Therefore, we will solve the initial model equation using numerical methods of the theory of finite difference schemes. Further, in the work, visualization and interpretation of the calculation result was carried out

Gd–LIII EXAFS study of structural and dynamic properties of Gd@C82\mathrm{Gd@C_{82}} between 10 and 300 K

The location of endohedral Gd ions in Gd@C82 is studied by Gd–LIII X-ray absorption spectroscopy in the temperature range 10–300 K. The near-edge data point to a covalent bond of trivalent Gd ions with the carbon cage. The EXAFS data can be well fitted with a Gd position above a carbon hexagon with two neighbour shells of carbon at distances R1,2=2.49(3) and 2.95(5) Å, corresponding to a large off-center position of about 1.8 Å from the center of the C82 cage. The second cumulants of these distances are relatively large and weakly depending on temperature. This points to a considerable distribution in Gd–C1 and Gd–C2 distances and confirms the relatively strong binding of the Gd ion to the C82 cage. These results will be discussed together with previous EXAFS studies and theoretical calculations of Y@C82 and La@C82