The paper covers stoichiometric ratios of nutrients for phytoplankton algae on the basis of which a limiting substance can be determined. Observational models describing the consumption, accumulation of nutrients by phytoplankton and the growth rate of phytoplankton are considered. Three-dimensional mathematical transformation model of phosphorus, nitrogen and silicon forms in the problem of phytoplankton dynamics for shallow waters is developed and researched. It takes into account the convective and diffusive transports; absorption and isolation of nutrients by phytoplankton; transformation cycles of phosphorus, nitrogen and silicon forms.

This paper is devoted to the study of the spatial-three-dimensional model of sedimentation of suspended particles in the coastal zone, taking into account changes in the bottom topography. The model takes into account the following processes: advective transfer due to movement of the aquatic environment, microturbulent diffusion and gravitational sedimentation of suspended particles, as well as changes in bottom geometry caused by sedimentation of suspended particles or rise of sediment particles. A change in the bottom relief leads to the need to solve an initial-boundary value problem for an equation of parabolic type with lower derivatives in a domain whose geometry depends on the desired solution function, which leads, in general, to a non-linear formulation of the problem. The model was linearized on a time grid due to the «freezing» of the bottom relief within one time step and the subsequent recalculation of the bottom surface function based on the changed function of suspended matter concentration, as well as a possible change in the velocity vector of the aquatic environment. For the linearized problem, a quadratic functional was constructed and the energy method proved the uniqueness of the solution of the corresponding initial-boundary problem within an arbitrary time step. Based on the transformation of the quadratic functional, an a priori estimate of the solution norm in the L2 functional space was obtained depending on the integral estimates for the right side and the initial condition, and, thus, the stability of the solution of the initial problem against the change of the initial and boundary conditions and functions of the right side. The model may be of value in predicting the spread of pollution and changes in the bottom topography, both under anthropogenic impact and due to naturally occurring natural processes in the coastal zone.

The aim of the work is to study the influence of forest plantations on the distribution of pollutants in the ground layer of the atmosphere. The model that takes into account a variety of factors: the presence of forest plantations, the variability of pressure, density and temperature, the presence of a multicomponent impurity, etc., was proposed for the numerical modeling of the process of transferring air pollutants to air. The scheme obtained as a result of a linear combination of the central difference scheme and the «CABARET» scheme was constructed to approximate the convection operator in this paper. The use of cabaret schemes allowed to develop the mathematical model that has the property of stability for a wider class of input parameters. The constructed algorithms are implemented in the form of the software complex that allows to determine the influence of the forest plantations on the distribution of pollutants under the influence of ascending air currents. The developed model, the algorithms that implement it, and the software complex constructed allowed to carry out the numerical experiments that simulate the distribution of pollutants in the surface layer of the atmosphere in the presence of forest plantations. The influence of the presence of vegetation on the distribution of pollutants under the action of ascending air currents is studied: pollutants under the influence of ascending air currents rise upwards in the area of forest plantations. The influence of the forest plantations area width on the air velocity and pollutants concentration fields is studied. An analysis of the results of numerical experiments allows to conclude that the distribution of pollutants in a multicomponent air environment is most significantly affected by the density of vegetation, and insignificantly influenced by the width of the forest plantations area.

The paper covers the calculation of aerodynamic processes in a steam turbine using modern information technology and computational methods for improving the calculation accuracy. The practical significance of the paper is the next: the model of aerodynamic processes in the steam turbine is developed and implemented; limits and prospects of the proposed mathematical model is defined. Aerodynamic processes in the turbine are characterized by uneven steam and heat flows, which significantly affect the reliability and efficiency of the turbine. The calculation was performed taking into account the complex geometry of the turbine and can be applied to any turbine of similar design with minor changes.

The paper covers the mathematical model of hydrodynamics of a deep water reservoir-the sea of Japan, taking into account the complex geometry of the shoreline and the bottom, friction on the bottom and wind currents, evaporation, deviation of the pressure field from the hydrostatic approximation, water density as a function of the spatial distribution of temperature and salinity, is proposed and investigated. The models of observations for the functions included in the model problem, including the dependence of the water density distribution on the spatial distribution of its temperature, salinity and ionic composition, are determined and investigated. The application of these models is based on electrical conductivity and temperature, which makes them as accurate as possible in different conditions.

Paper covers the researching the process of fluid flow in the reservoir in the fracture-porous reservoir based on mathematical modelling. The model of the dual porosity of Warren and Root was used. The model has two pore systems - a system of fractures and a system of matrices with different values of geometric dimensions and filtration-capacitive properties. The pressure distribution in the "system of fracture-matrix" system is described by the piezoconductivity equations. The paper presents a numerical solution of the problem under consideration. Рartial differential equations were approximated using an implicit difference scheme. The matrix sweep method was used for the calculation. Model pressure recovery curves were obtained. Analysis showed that the specific conductivity coefficient depends on the size of the matrix blocks and possible to evaluate the process of manifestation of the effect of dual porosity.

This article is devoted to the development of fast arithmetical encoding algorithm for compressing digital images. Subject of this paper is the research of arithmetical encoder complexity dependency on set of criteria beside the problem input size. The task of this article is to research those encoder compartments, which are the most computationally expensive and optimize their implementations. Aim of this research is the development of fast arithmetical encoder as a part of still image codec for compressing the images coming during distant aquatory objects scanning. New mean algorithm complexity estimation method is proposed as well as optimized arithmetical encoder algorithm based on mentioned method. Theoretical research is conducted, results of which are proved with numerical experiment. Actual set of satellite images of Azov sea aquatory was used. Performance of arithmetical encoder is improved by 7%. New method for mean algorithm complexity assessment is proposed which is based on partitioning of inputs array into equivalence classes. Obtained practical results allows increasing newest image compression techniques performance and using them on mobile computational platforms including those, which are installed on UAVs. Theoretical results of this article expands set of methods for assessing the mean algorithm complexity for those cases when number of steps doesn’t depend on problem’s input size but rather on non-measureable criteria such as memory access pattern to RAM from multiple ALUs.