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A mathematical model describing the dynamics of HIV-1 infection in a single lymph node during the initial period of infection development is presented. Within the framework of the model, the infection of an individual is set by a nonnegative finite function describing the rate of entry of the initial viral particles into the lymph node. The equations of the model are derived with consideration of two factors: 1) the interaction of viral particles with naive CD4+ T lymphocytes in various phases of the cell cycle; 2) contact interaction between multiplying naive CD4+ T lymphocytes and infected CD4+ T lymphocytes producing viral particles. The specific feature of intercellular contact interactions is the formation of complexes consisting of pairs of these cells. The duration of the complexes’ existence is determined by the distribution functions over finite time intervals. The model is presented as a high-dimensional system of nonlinear delay differential equations, including two equations with distributed delay, and is supplemented with non-negative initial data. In the absence of HIV-1 infection, the model is reduced to four delay differential equations describing the number of naive CD4+ T-lymphocytes in different phases of the cell cycle. The global solvability of the model (the existence and uniqueness of the solution on the semi-axis) is determined, and the non-negativity of the solution components is established. To carry out computational experiments with the model, an algorithm for numerically solving the used system of differential equations are developed based on the semi-implicit Euler scheme for the case of uniform distribution of durations of the complexes existence. The results of computational experiments aimed at approximation the numerical solution of the model to describing the kinetics of HIV-1 infection spread in its acute phase, including the eclipse phase, are presented. The variable used as the observable is the variable describing the number of viral particles per milliliter of blood on days 10–12 after the onset of acute infection. The dynamics of the observable variable is numerically studied depending on the variation of the model parameters reflecting the patterns of complex formation and the formation of cells producing viral particles. The possibility of attenuation of HIV-1 infection in the lymph node at certain values of some of the model parameters is shown.

For the three-axis stabilization of the spacecraft in the orbital coordinate system, including in the indirect equilibrium position, an electrodynamic control method is used based on the simultaneous use of two control torques that affect the dynamics of the spacecraft’s rotational motion in the Earth’s magnetic field (EMF), namely, the Lorentz torque and the torque of magnetic interaction. It is assumed that the spacecraft, equipped with an electric charge with a controlled vector of static moment of charge of the first order and a controlled intrinsic magnetic moment, moves in a Keplerian circular Earth orbit of arbitrary inclination. It was previously shown that combining two control systems, magnetic and Lorentz control, into a single electrodynamic control system (EDCS) makes it possible to successfully solve various problems of controlling the angular motion of spacecraft. Unlike many well-known studies performed for one or another approximate EMF model, this work does not impose restrictions on the accuracy of the EMF approximation. Previous studies have shown the limited capabilities of the EDCS for spacecraft moving in orbits close to the polar ones, due to the presence in this case of such points on the spacecraft trajectory in which it is possible for the lines of action of the geomagnetic induction vector and the spacecraft velocity vector relative to the EMF. Therefore, in this paper, the problem of overcoming these difficulties is posed and solved. A modification of the EDCS is proposed, based, firstly, on optimizing the control of the angular motion of the spacecraft and, secondly, on limiting the maximum value of the modulus of the vector of the center of charge relative to the center of mass of the spacecraft, which must be created during control. A method for selecting parameters for a modified EMF is recommended. The presented results of numerical experiments for spacecraft located in polar and circumpolar orbits not only demonstrate the operability of the proposed modification of the EDCS, but also indicate the possibility of technical implementation of the modified electrodynamic method of three-axis spacecraft stabilization.

X-ray diffraction experiment allows determining of magnitudes of complex coefficients in the decomposition of the studied electron density distribution into Fourier series. The determination of the lost in the experiment phase values poses the central problem of the method, namely the phase problem. Some methods for solving of the phase problem result in a set of feasible solutions. Cluster analysis method may be used to investigate the composition of this set and to extract one or several typical solutions. An essential feature of the approach is the estimation of the closeness of two solutions by the map correlation between two aligned Fourier syntheses calculated with the use of phase sets under comparison. An interactive computer program ClanGR was designed to perform this analysis.

The BES-III experiment at the IHEP CAS, Beijing, is running at the high-luminosity e+e- collider BEPC-II to study physics of charm quarks and tau leptons. The world largest samples of J/psi and psi' events are already collected, a number of unique data samples in the energy range 2.5–4.6 GeV have been taken. The data volume is expected to increase by an order of magnitude in the coming years. This requires to move from a centralized computing system to a distributed computing environment, thus allowing the use of computing resources from remote sites — members of the BES-III Collaboration. In this report the general information, latest results and development plans of the BES-III distributed computing system are presented.

The article presents the results of computer simulations aimed to assess the influence of tree spatial locations (planting schemes) on the productivity and the dynamics of soil fertility in forest plantations. The growth of aspen (Populus tremula L.) in plantations with short rotation (30 years) was simulated in the EFIMOD system of models with the soil and climatic data matching forested lands in the Mari El Republic. The outcome reveals that higher biomass rates, increase in soil organic matter stocks, and the minimal loss of soil nitrogen can be obtained when the distance between trees in the row equals 1–4 m and 4–6 м in aisles.

In this paper we consider a new modification of the discrete version of Mikhailov’s ‘power–society’ model, previously proposed by the author. This modification includes social-economical dynamics and corruption of the system similarly to continuous ‘power–society–economics–corruption’ model but is based on a stochastic cellular automaton describing the dynamics of power distribution in a hierarchy. This new version is founded on previously proposed ‘power–society’ system modeling cellular automaton, its cell state space enriched with variables corresponding to population, economic production, production assets volume and corruption level. The social-economical structure of the model is inherited from Solow and deterministic continuous ‘power–society–economics–corruption’ models. At the same time the new model is flexible, allowing to consider regional differentiation in all social and economical dynamics parameters, to use various production and demography models and to account for goods transit between the regions. A simulation system was built, including three power hierarchy levels, five regions and 100 municipalities. and a number of numerical experiments were carried out. This research yielded results showing specific changes of the dynamics in power distribution in hierarchy when corruption level increases. While corruption is zero (similar to the previous version of the model) the power distribution in hierarchy asymptotically tends to one of stationary states. If the corruption level increases substantially, volume of power in the system is subjected to irregular oscillations, and only much later tends to a stationary value. The meaning of these results can be interpreted as the fact that the stability of power hierarchy decreases when corruption level goes up.

Technical diagnosis’ current trends are connected to application of FEM computer simulation, which allows, to some extent, replace real experiments, reduce costs for investigation and minimize risks. Computer simulation, just at the stage of research and development, allows carrying out of diagnostics of equipment to detect permissible fluctuations of parameters of equipment’s work. Peculiarity of diagnosis of rolling equipment is that functioning of rolling equipment is directly tied with manufacturing of product with required quality, including accuracy. At that design of techniques of technical diagnosis and diagnostical modelling is very important. Computer simulation of cold rolling of strip was carried out. At that upper working roll was doing vibrations in horizontal direction according with published data of experiments on continuous 1700 rolling mill. Vibration of working roll in a stand appeared due to gap between roll’s craft and guide in a stand and led to periodical fluctuations of strip’s thickness. After computer simulation with the help of DEFORM software strip with longitudinal and transversal thickness variation was gotten. Visualization of strip’s geometrical parameters, according with simulation data, corresponded to type of inhomogeneity of surface of strip rolled in real. Further analysis of thickness variation was done in order to identify, on the basis of simulation, sources of periodical components of strip’s thickness, whose reasons are malfunctions of equipment. Advantage of computer simulation while searching the sources of forming of thickness variation is that different hypothesis concerning thickness formations may be tested without conducting real experiments and costs of different types may be reduced. Moreover, while simulation, initial strip’s thickness will not have fluctuations as opposed to industrial or laboratorial experiments. On the basis of spectral analysis of random process, it was established that frequency of changing of strip’s thickness after rolling in one stand coincides with frequency of working roll’s vibration. Results of computer simulation correlate with results of the researches for 1700 mill. Therefore, opportunity to apply computer simulation to find reasons of formation of thickness variation of strip on the industrial rolling mill is shown.

To study nonlinear effects of biological species interactions numerical-analytical approach is being developed. The approach is based on the cosymmetry theory accounting for the phenomenon of the emergence of a continuous family of solutions to differential equations where each solution can be obtained from the appropriate initial state. In problems of mathematical ecology the onset of cosymmetry is usually connected with a number of relationships between the parameters of the system. When the relationships collapse families vanish, we get a finite number of isolated solutions instead of a continuum of solutions and transient process can be long-term, dynamics taking place in a neighborhood of a family that has vanished due to cosymmetry collapse.

We consider a model for spatiotemporal competition of predators or prey with an account for directed migration, Holling type II functional response and nonlinear prey growth function permitting Alley effect. We found out the conditions on system parameters under which there is linear with respect to population densities cosymmetry. It is demonstated that cosymmetry exists for any resource function in case of heterogeneous habitat. Numerical experiment in MATLAB is applied to compute steady states and oscillatory regimes in case of spatial heterogeneity.

The dynamics of three population interactions (two predators and a prey, two prey and a predator) are considered. The onset of families of stationary distributions and limit cycle branching out of equlibria of a family that lose stability are investigated in case of homogeneous habitat. The study of the system for two prey and a predator gave a wonderful result of species coexistence. We have found out parameter regions where three families of stable solutions can be realized: coexistence of two prey in absence of a predator, stationary and oscillatory distributions of three coexisting species. Cosymmetry collapse is analyzed and long-term transient dynamics leading to solutions with the exclusion of one of prey or extinction of a predator is established in the numerical experiment.

In 2007 Kasman conducted a series of original computer experiments with sine-Gordon kinks moving along artificial DNA sequences. Two sequences were considered. Each consisted of two parts separated by a boundary. The left part of the first sequence contained repeating TTA triplets that encode leucines, and the right part contained repeating CGC triplets that encode arginines. In the second sequence, the left part contained repeating CTG triplets encoding leucines, and the right part contained repeating AGA triplets encoding arginines. When modeling the kink movement, an interesting effect was discovered. It turned out that the kink, moving in one of the sequences, stopped without reaching the end of the sequence, and then “bounced off” as if he had hit a wall. At the same time, the kink movement in the other sequence did not stop during the entire time of the experiment. In these computer experiments, however, a simple DNA model proposed by Salerno was used. It takes into account differences in the interactions of complementary bases within pairs, but does not take into account differences in the moments of inertia of nitrogenous bases and in the distances between the centers of mass of the bases and the sugar-phosphate chain. The question of whether the Kasman effect will continue with the use of more accurate DNA models is still open. In this paper, we investigate the Kasman effect on the basis of a more accurate DNA model that takes both of these differences into account. We obtained the energy profiles of Kasman's sequences and constructed the trajectories of the motion of kinks launched in these sequences with different initial values of the energy. The results of our investigations confirmed the existence of the Kasman effect, but only in a limited interval of initial values of the kink energy and with a certain direction of the kinks movement. In other cases, this effect did not observe. We discussed which of the studied sequences were energetically preferable for the excitation and propagation of kinks.

Problems of multiple covering ($k$-covering) of a bounded set $G$ with equal circles of a given radius are well known. They are thoroughly studied under the assumption that $G$ is a finite set. There are several papers concerned with studying this problem in the case where $G$ is a connected set. In this paper, we study the problem of minimizing the number of circles that form a $k$-covering, $k \geqslant 1$, provided that $G$ is a bounded convex plane domain.

For the above-mentioned problem, we state a 0-1 linear model, a general integer linear model, and a nonlinear model, imposing a constraint on the minimum distance between the centers of covering circles. The latter constraint is due to the fact that in practice one can place at most one device at each point. We establish necessary and sufficient solvability conditions for the linear models and describe one (easily realizable) variant of these conditions in the case where the covered set $G$ is a rectangle.

We propose some methods for finding an approximate number of circles of a given radius that provide the desired $k$-covering of the set $G$, both with and without constraints on distances between the circles’ centers. We treat the calculated values as approximate upper bounds for the number of circles. We also propose a technique that allows one to get approximate lower bounds for the number of circles that is necessary for providing a $k$-covering of the set $G$. In the general linear model, as distinct from the 0-1 linear model, we require no additional constraint. The difference between the upper and lower bounds for the number of circles characterizes the quality (acceptability) of the constructed $k$-covering.

We state a nonlinear mathematical model for the $k$-covering problem with the above-mentioned constraints imposed on distances between the centers of covering circles. For this model, we propose an algorithm which (in certain cases) allows one to find more exact solutions to covering problems than those calculated from linear models.

For implementing the proposed approach, we have developed computer programs and performed numerical experiments. Results of numerical experiments demonstrate the effectiveness of the method.