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Numerical simulation of hull flow, marine propellers and other basic problems of ship hydrodynamics using Cartesian adaptive locally-refined grids is advantageous with respect to numerical setup and makes an express analysis very convenient. However, when more accurate viscous phenomena are needed, they condition some problems including a sharp increase of cell number due to high levels of main grid adaptation needed to resolve boundary layers and time step decrease in simulations with a free surface due to decrease of transit time in adapted cells. To avoid those disadvantages, additional boundary layer grids are suggested for resolution of boundary layers. The boundary layer grids are one-dimensional adaptations of main grid layers nearest to a wall, which are built along a normal direction. The boundary layer grids are additional (or chimerical), their volumes are not subtracted from main grid volumes. Governing equations of flow are integrated in both grids simultaneously, and the solutions are merged according to a special algorithm. In simulations of ship hull flow boundary layer grids are able to provide sufficient conditions for low-Reynolds turbulence models and significantly improve flow structure in continues boundary layers along smooth surfaces. When there are flow separations or other complex phenomena on a hull surface, it can be subdivided into regions, and the boundary layer grids should be applied to the regions with simple flow only. This still provides a drastic decrease of computational efforts. In simulations of marine propellers, the boundary layer grids are able to provide refuse of wall functions on blade surfaces, what leads to significantly more accurate hydrodynamic forces. Altering number and configuration of boundary grid layers, it is possible to vary a boundary layer resolution without change of a main grid. This makes the boundary layer grids a suitable tool to investigate scale effects in both problems considered.

A mathematical model of tumor growth in tissue taking into account angiogenesis and antiangiogenic therapy is developed. In the model the convective flows in tissue are considered as well as individual motility of tumor cells. It is considered that a cell starts to migrate if the nutrient concentration falls lower than the critical level and returns into proliferation in the region with high nutrient concentration. Malignant cells in the state of metabolic stress produce vascular endothelial growth factor (VEGF), stimulating tumor angiogenesis, which increases the nutrient supply. In this work an antiangiogenic drug which bounds irreversibly to VEGF, converting it to inactive form, is modeled. Numerical analysis of influence of antiangiogenic drug concentration and efficiency on tumor rate of growth and structure is performed. It is shown that antiangiogenic therapy can decrease the growth of low-invasive tumor, but is not able to stop it completely.

The article dwells upon investigating the issue of the most adequate tools developing and justifying to forecast the interregional migration flows value and structure. Migration processes have a significant impact on the size and demographic structure of the population of territories, the state and balance of regional and local labor markets.

To analyze the migration processes and to assess their impact an economic-mathematical tool is required which would be instrumental in modelling the migration processes and flows for different areas with the desired precision. The current methods and approaches to the migration processes modelling, including the analysis of their advantages and disadvantages, were considered. It is noted that to implement many of these methods mass aggregated statistical data is required which is not always available and doesn’t characterize the migrants behavior at the local level where the decision to move to a new dwelling place is made. This has a significant impact on the ability to apply appropriate migration processes modelling techniques and on the projection accuracy of the migration flows magnitude and structure.

The cellular automata model for interregional migration flows modelling, implementing the integration of the households migration behavior model under the conditions of the Bounded Rationality into the general model of the area migration flow was developed and tested based on the Primorye Territory data. To implement the households migration behavior model under the conditions of the Bounded Rationality the integral attractiveness index of the regions with economic, social and ecological components was proposed in the work.

To evaluate the prognostic capacity of the developed model, it was compared with the available cellular automata models used to predict interregional migration flows. The out of sample prediction method which showed statistically significant superiority of the proposed model was applied for this purpose. The model allows obtaining the forecasts and quantitative characteristics of the areas migration flows based on the households real migration behaviour at the local level taking into consideration their living conditions and behavioural motives.

The technology of creating patterns from natural language words (concepts) based on text data in the bag of words model is considered. Patterns are used to reduce the dimension of the original space in the description of documents and search for semantically related words by topic. The process of dimensionality reduction is implemented through the formation of patterns of latent features. The variety of structures of document relations is investigated in order to divide them into themes in the latent space.

It is considered that a given set of documents (objects) is divided into two non-overlapping classes, for the analysis of which it is necessary to use a common dictionary. The belonging of words to a common vocabulary is initially unknown. Class objects are considered as opposition to each other. Quantitative parameters of oppositionality are determined through the values of the stability of each feature and generalized assessments of objects according to non-overlapping sets of features.

To calculate the stability, the feature values are divided into non-intersecting intervals, the optimal boundaries of which are determined by a special criterion. The maximum stability is achieved under the condition that the boundaries of each interval contain values of one of the two classes.

The composition of features in sets (patterns of words) is formed from a sequence ordered by stability values. The process of formation of patterns and latent features based on them is implemented according to the rules of hierarchical agglomerative grouping.

A set of latent features is used for cluster analysis of documents using metric grouping algorithms. The analysis applies the coefficient of content authenticity based on the data on the belonging of documents to classes. The coefficient is a numerical characteristic of the dominance of class representatives in groups.

To divide documents into topics, it is proposed to use the union of groups in relation to their centers. As patterns for each topic, a sequence of words ordered by frequency of occurrence from a common dictionary is considered.

The results of a computational experiment on collections of abstracts of scientific dissertations are presented. Sequences of words from the general dictionary on 4 topics are formed.

The paper outlines the approaches to mathematical modeling correlation adaptometry techniques widely used in biology and medicine. The analysis is based on models employed in descriptions of structured biological systems. It is assumed that the distribution density of the biological population numbers satisfies the equation of Kolmogorov-Fokker-Planck. Using this technique evaluated the effectiveness of treatment of patients with obesity. All patients depending on the obesity degree and the comorbidity nature were divided into three groups. Shows a decrease in weight of the correlation graph computed from the measured in the patients of the indicators that characterizes the effectiveness of the treatment for all studied groups. This technique was also used to assess the intensity of the training loads in academic rowing three age groups. It was shown that with the highest voltage worked with athletes for youth group. Also, using the technique of correlation adaptometry evaluated the effectiveness of the treatment of hormone replacement therapy in women. All the patients depending on the assigned drug were divided into four groups. In the standard analysis of the dynamics of mean values of indicators, it was shown that in the course of the treatment were observed normalization of the averages for all groups of patients. However, using the technique of correlation adaptometry it was found that during the first six months the weight of the correlation graph was decreasing and during the second six months the weight increased for all study groups. This indicates the excessive length of the annual course of hormone replacement therapy and the practicality of transition to a semiannual rate.

Modern power transportation systems are the complex engineering systems. Such systems include both point facilities (power producers, consumers, transformer substations, etc.) and the distributed elements (f.e. power lines). Such structures are presented in the form of the graphs with different types of nodes under creating the mathematical models. It is necessary to solve the system of partial differential equations of the hyperbolic type to study the dynamic effects in such systems.

An approach similar to one already applied in modeling similar problems earlier used in the work. New variant of the splitting method was used proposed by the authors. Unlike most known works, the splitting is not carried out according to physical processes (energy transport without dissipation, separately dissipative processes). We used splitting to the transport equations with the drain and the exchange between Reimann’s invariants. This splitting makes possible to construct the hybrid schemes for Riemann invariants with a high order of approximation and minimal dissipation error. An example of constructing such a hybrid differential scheme is described for a single-phase power line. The difference scheme proposed is based on the analysis of the properties of the schemes in the space of insufficient coefficients.

Examples of the model problem numerical solutions using the proposed splitting and the difference scheme are given. The results of the numerical calculations shows that the difference scheme allows to reproduce the arising regions of large gradients. It is shown that the difference schemes also allow detecting resonances in such the systems.

The paper proposes a set of fairly simple analysis algorithms that can be used to analyze a wide range of protein-protein interactions. In this work, we jointly use the methods of Brownian and molecular dynamics to describe the process of formation of a complex of plastocyanin and cytochrome f proteins in higher plants. In the diffusion-collision complex, two clusters of structures were revealed, the transition between which is possible with the preservation of the position of the center of mass of the molecules and is accompanied only by a rotation of plastocyanin by 134 degrees. The first and second clusters of structures of collisional complexes differ in that in the first cluster with a positively charged region near the small domain of cytochrome f, only the “lower” plastocyanin region contacts, while in the second cluster, both negatively charged regions. The “upper” negatively charged region of plastocyanin in the first cluster is in contact with the amino acid residue of lysine K122. When the final complex is formed, the plastocyanin molecule rotates by 69 degrees around an axis passing through both areas of electrostatic contact. With this rotation, water is displaced from the regions located near the cofactors of the molecules and formed by hydrophobic amino acid residues. This leads to the appearance of hydrophobic contacts, a decrease in the distance between the cofactors to a distance of less than 1.5 nm, and further stabilization of the complex in a position suitable for electron transfer. Characteristics such as contact matrices, rotation axes during the transition between states, and graphs of changes in the number of contacts during the modeling process make it possible to determine the key amino acid residues involved in the formation of the complex and to reveal the physicochemical mechanisms underlying this process.

Despite the widespread use of cancer chemotherapy drugs, the molecular mechanisms of action of many of them remain unclear. Some of these drugs, such as taxol, are known to affect the dynamics of microtubule assembly and stop the process of cell division in prophase-prometaphase. Recently, new spatial structures of microtubules and individual tubulin oligomers have emerged associated with various regulatory proteins and cancer chemotherapy drugs. However, knowledge of the spatial structure in itself does not provide information about the mechanism of action of drugs.

In this work, we applied the molecular dynamics method to study the behavior of taxol-bound tubulin oligomers and used our previously developed method for analyzing the conformation of tubulin protofilaments, based on the calculation of modified Euler angles. Recent structures of microtubule fragments have demonstrated that tubulin protofilaments bend not in the radial direction, as many researchers assume, but at an angle of approximately 45◦ from the radial direction. However, in the presence of taxol, the bending direction shifts closer to the radial direction. There was no significant difference between the mean bending and torsion angles of the studied tubulin structures when bound to the various natural regulatory ligands, guanosine triphosphate and guanosine diphosphate. The intra-dimer bending angle was found to be greater than the interdimer bending angle in all analyzed trajectories. This indicates that the bulk of the deformation energy is stored within the dimeric tubulin subunits and not between them. Analysis of the structures of the latest generation of tubulins indicated that the presence of taxol in the tubulin beta subunit pocket allosterically reduces the torsional rigidity of the tubulin oligomer, which could explain the underlying mechanism of taxol’s effect on microtubule dynamics. Indeed, a decrease in torsional rigidity makes it possible to maintain lateral connections between protofilaments, and therefore should lead to the stabilization of microtubules, which is what is observed in experiments. The results of the work shed light on the phenomenon of dynamic instability of microtubules and allow to come closer to understanding the molecular mechanisms of cell division.

The article examines the impact of non-market actions of participants in oligopolistic markets on the market structure. The following actions of one of the market participants aimed at increasing its market share are analyzed: 1) price manipulation; 2) blocking investments of stronger oligopolists; 3) destruction of produced products and capacities of competitors. Linear dynamic games with a quadratic criterion are used to model the strategies of oligopolists. The expediency of their use is due to the possibility of both an adequate description of the evolution of markets and the implementation of two mutually complementary approaches to determining the strategies of oligopolists: 1) based on the representation of models in the state space and the solution of generalized Riccati equations; 2) based on the application of operational calculus methods (in the frequency domain) which owns the visibility necessary for economic analysis.

The article shows the equivalence of approaches to solving the problem with maximin criteria of oligopolists in the state space and in the frequency domain. The results of calculations are considered in relation to a duopoly, with indicators close to one of the duopolies in the microelectronic industry of the world. The second duopolist is less effective from the standpoint of costs, though more mobile. Its goal is to increase its market share by implementing the non-market methods listed above.

Calculations carried out with help of the game model, made it possible to construct dependencies that characterize the relationship between the relative increase in production volumes over a 25-year period of weak and strong duopolists under price manipulation. Constructed dependencies show that an increase in the price for the accepted linear demand function leads to a very small increase in the production of a strong duopolist, but, simultaneously, to a significant increase in this indicator for a weak one.

Calculations carried out with use of the other variants of the model, show that blocking investments, as well as destroying the products of a strong duopolist, leads to more significant increase in the production of marketable products for a weak duopolist than to a decrease in this indicator for a strong one.

The article considers the problem of forecasting the number of employed and unemployed persons in a multisectoral labor market using a balance mathematical model of labor force intersectoral dynamics.

The balance mathematical model makes it possible to calculate the values of intersectoral dynamics indicators using only statistical data on sectoral employment and unemployment provided by the Federal State Statistics Service. Intersectoral dynamics indicators of labor force calculated for several years in a row are used to build trends for each of these indicators. The found trends are used to calculation of forecasted intersectoral dynamics indicators of labor force. The sectoral employment and unemployment of researched multisectoral labor market is forecasted based on values these forecasted indicators.

The proposed approach was applied to forecast the employed persons in the economic sectors of the Russian Federation in 2011–2016. The following types of trends were used to describe changes of intersectoral dynamics indicators values: linear, non-linear, constant. The procedure for selecting trends is clearly demonstrated by the example of indicators that determine the labor force movements from the “Transport and communications” sector to the “Healthcare and social services” sector, as well as from the “Public administration and military security, social security” sector to the “Education” sector.

Several approaches to forecasting was compared: a) naive forecast, within which the labor market indicators was forecasted only using a constant trend; b) forecasting based on a balance model using only a constant trend for all intersectoral dynamics indicators of labor force; c) forecasting directly by the number employed persons in economic sectors using the types of trends considered in the article; d) forecasting based on a balance model with the trends choice for each intersectoral dynamics indicators of labor force.

The article shows that the use of a balance model provides a better forecast quality compared to forecasting directly by the number of employed persons. The use of trends in intersectoral dynamics indicators improves the quality of the forecast. The article also provides analysis examples of the multisectoral labor market in the Russian Federation. Using the balance model, the following information was obtained: the labor force flows distribution outgoing from concrete sectors by sectors of the economy; the sectoral structure of the labor force flows ingoing in concrete sectors. This information is not directly contained in the data provided by the Federal State Statistics Service.