Vol 29, No 2 (2018)

The article investigates the inverse sounding problem for a nonhomogeneous thin layer given the field on the surface of the half-space. A uniqueness theorem is proved for the solution of the inverse problem.

The article generalizes Germeier’s attack-defense model to allow for integer-valued and nonhomogeneous opponent resources and echeloned defense. It performs target allocation by solving the classical transportation problem on each level, which leads to discrete minimax problems for the best guaranteed defense outcome. These minimax problems can be solved by a coordinatewise-descent method based on a discrete analogue of Germeier’s equalization principle.

In this article, we have considered a simple food-consumer dynamic model in which the supply of food and the death of consumer species play the major role. The parameters representing these factors are allowed to vary with respect to time. It is established that by proper selection of these parameter functions, the system may be made to approach a desired state. It is noticed that these parameters define a space of equilibria for the given system in the limiting case. In case of different consumer species surviving on the same food, when there is no interference in consumption of one by the other, the growth is as desired. Growth is not as desired when one of the species is interfering with the food consumption of the other and the growth of the larger consumer is dominating. By simple variations in the death/removal of dominating species, the situation may be reversed in favor of the other species. The growth is as desired when the parameters are fixed constants. Examples are provided to understand the results and to illustrate various situations. The approach is tried on a popular mathematical model of biology to draw some useful conclusions. The study opens interesting problems for further research.

Numerical integration of one class of quasi-singular integrals appearing in the convenient formulas of electromagnetic field components and potential functions of linear source distributions is considered. Some comments to a recent paper by S.R. Jena, D. Nayak, and M.M. Acharya [Comput. Math. Modeling, 28, 267–276 (2017)] on this subject are given, as well as some illustrative numerical examples.

We consider the probability of ruin of a pension fund on a finite time interval. The basis is provided by the standard Cramer–Lundberg model, which is modified by specifying enrolment and contribution parameters in the form of random variables. A number of factors may be treated as random variables in the model: the date of member’s death, members’ wages, the number of fund members, financial indicators (discounting and return rates, inflation, wage growth rates). Each of these factors specified as a random variable affects the nondeterministic behavior of the fund’s receipts and payouts. In this article, the random factors include the number of members joining the pension fund in the relevant year and random mortality.

The article investigates the dynamics of various interactions between two partners described by a system of two nonlinear ordinary differential equations. The partners may be various social subjects, ranging from individuals and social groups to states and nations. The models are an extension of the Murray–Gottman model originally proposed to describe relationships between married people. New functions are introduced describing the own behavior of the actors in the absence of interactions as well as functions modeling the mutual influence of the partners. Phase portraits are constructed for systems with excitable, self-sufficient, and some other types of actors that do not strive to attain a neutral state, as in the Murray–Gottman model. New types of dynamic behavior are discovered. In particular, two nonlinear conservative models are proposed that demonstrate an oscillatory dynamic about the center. The models examined in this article demonstrate a rich set of phase portraits and may be applied to model various social interactions between two partners.

We consider the design of a transport network in a multinode market assuming time-dependent nonstationary demand. A gradient algorithm is proposed for capacity optimization of transport lines in the network. Numerical results are reported.