Vol 25, No 2 (2019)

As it is well known, the Gustavsson — Peetre construction, using the concept of unconditional convergence in Banach spaces, provides an important class of interpolation functors. In this paper, we define a new close construction, based on the use of the so-called random unconditional convergence. We find necessary and sufficient conditions, which being imposed on a generating function give us an interpolation functor defined on the category of Banach couples. It is shown that calculating the latter functor for a couple of Orlicz spaces results in the ”natural” interpolation theorem. Moreover, we obtain conditions that guarantee the coincidence of this functor with the corresponding Gustavsson — Peetre functor, as well as with the Calder´on — Lozanovskii method.

In the present paper the crack propagation direction angles on the basis of three different fracture criteria are found. The maximum tangential stress criterion, the minimum strain energy density criterion and the deformation criterion are used and analysed. The generalized forms of these criteria have been used. It implies that the crack propagation direction angles are obtained with the Williams series expansion in which the higher order terms are kept. The calculations are performed in Waterloo Maple computer algebra software. The analysis of the crack propagation direction angles show that the influence of the higher order terms can’t be ignored. The angles differ considerably when the higher order terms are taken into account.

The article is devoted to the digital processing interferograms (isochromatic fringe patterns) obtained by the photoelasticity method. An application to interpretate the isochromatic fringe patterns is developed. It allows us to automate this procedure, gets to avoid the routine and time-consuming work. The features of the developed software package are described in detail by means of the classic problem of a diametrically compressed disk. The application’s algorithm includes following main steps: image pre-processing, localization interference fringe, fringe tracing. The application creates a text file containing all the necessary data to further determine the stress-strain state (isochromatic fringe’s number and locus of fringes).

Our studies are devoted to various aspects of invasive processes in biosystems. When invading aggressive insects, the resistance of the biotic environment is significant, but the final time may be completely absent. Under conditions of high specific fecundity, there will be non-stationary regimes of changes in the abundance of individuals in the population. An outbreak with a phase of explosive growth is realized, so we modeled one particular variant of an outbreak of populations earlier. Outbreaks are associated with a number of changes in physiological regulation that are observed in ecodynamics under extreme conditions of the species and environment. A classic example of changes is the appearance of migratory winged forms in the locust and the usually flightless leaf beetle introduced in the Stavropol Territory Zygogramma suturalis during the formation of a population wave front with a huge density of individuals. Traditional mathematical models for describing the rates of average weight gain for individuals of a generation cannot consider situations of rapid invasions, where competition and survival factors at different stages of insect development are very different, since the density of generations varies by orders of magnitude. Effect on growth of local congestion value may not be constant in ontogenesis. The factor of the total number is reflected differently at different stages of life. The purpose of the simulation is to obtain a bistable and flexible dynamic system. The article proposes a model for a differentiated description of weight gain at three stages of development of insects with an incomplete cycle of transformations by three differential equations conjugated by initial conditions. As a result, a continuously discrete dynamic system with a hybrid representation of time on the life cycle interval is implemented. We will use the model when supplementing the hybrid computing structure for calculating the rate of decline of individuals of generations. Mortality changes dramatically with the launch and attenuation of an invasive outbreak. Here, the deviation of growth rates from optimal values plays a role. The idea of the work is that all processes: changes in numbers or growth for insects should be simulated by the stages of development of their ontogenesis.