### Browsing by Author "Solomonovich, Mark"

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Item Didactic potential of modern information technologies in training a chemistry graduate(2018) Beresneva, E. V.; Zaitsev, M. A.; Selezenev, R. V.; Darovskikh, L. V.; Solomonovich, MarkThe article deals with maintaining the quality of teaching during curtailment of academic hours in curriculum. A university teacher should motivate students to use modern information technology training. The authors of the article describe the optimal didactic capabilities of modern information technologies to be used to improve the preparedness of a chemistry graduate. The aim of the article is to highlight the problem of finding the optimal didactic capabilities of modern information technologies used for improving the system of training specialists in the field of chemistry and to discuss the results of current studies in this direction.Item A dynamical model of the coral-algae competition in a coral reef ecosystem(2020) Bica, Ion; Solomonovich, MarkA coral reef system is a biodiverse ecosystem in which coral is in mutual competitive partnership with algae. The survival of coral in this competition with algae is vital for the well-being of any coral reef ecosystem. In ideal conditions, the coral mass concentration and algae mass concentration are in a stable equilibrium. However, in practice, it is not always the case due to numerous factors of natural and anthropogenic origin. It is not easy to take into account all these factors when studying the question of survival of the reef ecosystem. We propose a dynamical system that describes the competition between coral and algae and contains terms that describe two major features inherent in this competition. The first one is the accelerated growth of algae when the amount of the turf algae exceeds a certain threshold, and it transforms into macroalgae, which grows much faster and has a detrimental effect on the corals. The second feature is associated with the grazing of the herbivory and other marine life on corals and algae. We apply both analytical and numerical techniques to study the system to find out what kind of equilibria such a system may exhibit. The results of our analysis show that although the boost in the growth of algae may devastate the corals, the latter may still survive if the algae are also subject to sufficiently intense grazing.Item Modelling the Southwestern Alberta grizzly bear population using ordinary differential equations(2019) Bica, Ion; Solomonovich, Mark; Burak, K.; Deutscher, K.; Garrett, A.; Peacock, H.The Alberta grizzly bear population was listed as “threatened” by the Alberta Wildlife Association in 2010. This particular species is important, as it is an umbrella species for a variety of other animals. Our goal in this project was to create a model using ordinary differential equations, based on the logistic growth model, to determine whether the Southern Alberta grizzly bear population is recoverable. We aimed to calculate the rate at which the population was growing and its carrying capacity.Item Moving limit cycles model of an economic system(2017) Kryuchkov, Vladimir; Solomonovich, Mark; Anton, CristinaWe consider a model explaining the dependence between the productivity of labor (PL) and the fixed capital per worker (FC) in an economic system. The core of the model is a nonlinear oscillator with a limit cycle as an attractor. We run numerical simulations of the dynamics specific to this non-autonomous model to compare with the actual data recorded for the years 1987–2001 for the enterprise Omsk Bacon. Based on the numerical analysis we can conclude that the interior dynamics is not affected by exterior perturbations. The numerical simulations can help the managers of the enterprise to take the right steps to avoid stagnation.Item Ursus arctos horribilis: dynamic modeling of Canadian population(2019) Bica, Ion; Solomonovich, Mark; Deutscher, K.; Garrett, A.; Burak, K.; Peacock, H.The grizzly bears are K-strategists and their innate tendency is to reach homeostasis. In the First Nations folklore grizzly bears are viewed as “spirits” that bring balance in their untamed habitat where they roam, this being an indication that they do not overpopulate their habitat and their gene flow is “designed” to reach homeostasis without surpassing it. In the present article we study the dynamics of the grizzly bear population in the Southwest Alberta, Canada. Based on the dynamical model with three parameters, we obtain estimates for the carrying capacity and the minimum viable population of the grizzly bear population in their dynamical habitat. The article starts with the discussion of the rationale for choosing the Logistic Growth Model as the most appropriate for describing the dynamics of grizzly population. In addition to the usual for this kind of models parameters of the growth rate and the carrying capacity, in the current model we consider the parameters of Minimum Viable Population (MVP) and Safe Harbour (SH) – a measurement introduced by the Alberta Grizzly Bear Recovery Plan. The first of these parameters (MVP) is determined by the essential number of the individuals that would allow the survival of the species. The latter measurement (SH) is related to the so-called Grizzly Bear Priority Areas, where the risk of mortality is low. Then, based on Verhulst model and Statistical data, the carrying capacity and growth rate for the female grizzly bears in Alberta have been obtained. Mathematical analysis of the model has shown that the equilibria at K (carrying capacity) and MVP·SH are, respectively, stable and unstable. The time of possible extinction for the populations with the initial conditions below the threshold MVP·SH has been numerically estimated. The correlation between the system parameters and its influence on the survival of the population has been analyzed and the recommendations on ensuring the survival have been given.Item Use of LaTeX and other software for illustrating mathematical concepts(2024) Jagal, Tyler; Solomonovich, MarkThe work is focused on the use of Latex and related graphical software for illustrating some mathematical concepts. Those concepts include graphical presentations related to some notions of analysis in the extended complex plane. In particular, special considerations will be given to the stereographic projection, which often provides a natural setting for interpreting transformations in the complex plane.