# diffusion

## A generalized diffusive IS-LM business cycle model with delays in gross product and capital stock

In this paper, we suggest a diffusive and delayed IS-LM business cycle model with interest rate, general investment and money supply under homogeneous Neumann boundary conditions.  The time delays are respectively incorporated into capital stock and gross product.  We first demonstrate the model's sound mathematical and economic posing.  By examining the corresponding characteristic equation, the local stability of the economic equilibrium and the existence of Hopf bifurcation are proved.

## Global stability of fractional partial differential equations applied to the biological system modeling a viral infection with Hattaf time-fractional derivative

In this article, we study the global stability of fractional partial differential equations applied to the biological system modeling a viral infection.  The reaction in the proposed biological system is described by the new generalized Hattaf fractional (GHF) derivative.  However, the diffusion is modeled by the Laplacian operator.

## Mathematical modeling of impurity diffusion process under given statistics of a point mass sources system. I

The model of the impurity diffusion process in the layer where a system of random point mass sources acts, is proposed.  Mass sources of various power are uniformly distributed in a certain internal interval of the body.  Statistics of random sources are given.  The solution of the initial-boundary value problem is constructed as a sum of the homogeneous problem solution and the convolution of the Green's function and the system of the random point mass sources.  The solution is averaged over both certain internal subinterval and the entire body region.  Simulation unit

## Mathematical analysis of a spatiotemporal dynamics of a delayed IS-LM model in economics

The purpose of this research is to suggest and analyze a spatiotemporal of an IS-LM model with two delays, interest rate, liquidity preference and general investment function.  The first delay into the proposed model refers to the time delay between the decision of investment and his implementation.  However, the second one represents the delay in investment production.  The well posedness of the model is proved.  The stability analysis and the existence of Hopf bifurcation are obtained.  Furthermore, numerical examples that confirm the analytical results are shown.

## USE OF MODIFIED ADSORBENTS TO REMOVE PESTICIDES FROM WASTEWATER

The migration of highly concentrated pesticide solutions in the soil has been experimentally studied. A mathematical model of the diffusion process in the soil environment has been developed. Based on the mathematical model, a system of equations for calculating the duration and intensity of the process depending on environmental parameters was obtained. The dependence of the process velocity on the direction of the diffusion front is determined, and the diffusion coefficients, kinetic coefficients of the diffusion process and the diffusion front velocity were calculated.

## Mathematical modeling and analysis of Phytoplankton–Zooplankton–Nanoparticle dynamics

In this paper, we investigate the population dynamics of phytoplankton–zooplankton–nanoparticle model with diffusion and density dependent death rate of predator.  The functional response of predator in this model is considered as Beddington–DeAngelis type.  The stability analysis of the equilibrium points is observed by applying the Routh–Hurwitz criterion.  Numerical simulations are given to illustrate the theoretical results.

## STUDY OF KINETIC PROCESSES DURING CANDIED FRUITS INDUSTRIAL SATURATION

The process of saturation of sucrose particles of pumpkin fruits is considered. An experimental setup for saturation of fruit particles with sugar under conditions of intensive pneumatic mixing was developed. The kinetic dependences of the saturation of candied fruits and changes in the concentration of sugar syrup under various temperatures were obtained. The saturation conditions are compared for various ratios of «candied fruit: syrup». A mathematical generalization confirms the ratio “candied fruit: syrup” selected by the authors of the article.

## Circular Model of Interaction of Enterprise Innovation Capacity and Exports

In the current conditions of globalization and European integration, the need for the development of innovative economy and activation of export activity, innovation capacity is one of the key drivers of export diversification towards science-intensive products. An important prerequisite for starting and developing export activity is not only the availability of sufficient innovation potential, but also the willingness, need and feasibility of introducing and commercializing innovative products in foreign markets.

## Modeling of internal diffusion mass transfer during filtration drying of capillary-porous material

The article presents the results of theoretical and experimental studies on the determination of the coefficients of internal diffusion of moisture from capillary-porous materials of plant origin during filtration drying, in particular, beet pulp, a by-product of sugar production.  A model based on the solution of the internal diffusion differential equation with the corresponding initial and boundary conditions were used to find the internal diffusion coefficient.

## Self-Assembly Processes of the Magnetic Polymer Nanocomposites in Magnetic Fields

Processes of self-assembly were studied in the magnetic polymer carbon nanocomposites doped with cobalt nanoclusters. These processes proceed due to the diffusion of magnetic nanoparticles stimulated by a combined effect of an outer steady magnetic fields and heating. The obtained polymer composites are promising for practical applications.