Klaipėdos universitetas

This paper proposes methodology for companies’ assessment. There is suggesting assessing the company’s prospect, not only according to share price, forecasts of the analysts, but also on the basis of position of each company in two-dimensional space in respect of the other companies. Seeking to describe the share prices of a company during the year, the parameters of skew t distribution are calculated. Then they are used in the inputs of random forest algorithm. Proximity matrices are stored during classification, and they are displayed in two-dimensional space. Thus, two clusters are obtained: one of the companies with upgrade trend, another one – with downgrade trend. This method may be useful those investors who are important to choose the most promising companies of all industry without wasting a lot of time.

The article deals with interaction of tumour cells and leucocytes in the cylindrical cavities. This type of interaction is typical in the cases of development of a tumour in the intestine, blood vessel or in a bone cavity. Two cases are separated: the case of soft and hard tumour. In the case of a solid tumour, leucocytes can interact only with the surface cells of the tumour. This type of interaction is described by the system of two nonlinear first degree differential equations. The expressions of stationary points are obtained and analysis of their stability is performed. In the case of a soft tumour the system of two partial differential equations with first order derivatives and initial and boundary conditions is proposed. An algorithm for computing the numeric solution of the mathematical model is applied. In this case the diffusion of leucocytes and their ability to reach the tumour cells in the whole volume of the tumour is included. The algorithm is constructed and the system is solved numerically. Bifurcation curve is obtained. It separates two qualitatively different areas on the two parameter plane. Under the same initial parameters in the first area development of the tumour cells cannot be stopped, whereas in the second area leukocytes defeat the tumour cells.