The paper studies a mathematical model of a function that can be restored by integrals. In order to reduce image distortion during reconstruction, the representation of the desired function in the form of a sum of Gauss functions is proposed. A software package has been developed to study the model. The parameters and type of the grid giving the smallest error in this model are determined.

Keywords: mathematical modeling, inverse problem, Radon transform, image reconstruction, Gauss function, computed tomography

The paper proposes a mathematical model for evaluating the effectiveness of measures aimed at anticipating competitors in the market. The model is based on the theory of Markov random processes. It allows you to assess the probability of pre-emption in the implementation of commercial projects by one party over the other in a competitive environment. The dependences of probabilities of pre-emption of the parties from time to time. It is shown that these probabilities depend on the average project execution time of each competitor and have a maximum characterizing the most effective lead time. The obtained theoretical dependences allow us to analyze the possible outcomes of competition in market conditions.

Keywords: competition, market relations, advance, efficiency, commercial project, mathematical modeling, conflict of parties, random process, probability of state, time dependence