The work is devoted to the laboratory experiment analysis and numerical modeling of perforation tunnel formation in a combined barrier under the action of a cumulative jet, which occurs during the detonation of an explosive (explosive substances). This process is typical for secondary and subsequent formation exposing process by using jet perforator, where the creation of high-quality hydrodynamic connection “well – reservoir” helps maintain a stable flow of oil and gas to the well.

The position of the harmonic series sum on infinity scales is found. These sums are defined by the generalized bit grid and number hyper axis. A representation for the Euler's constant C [1, 2, 3] is obtained, which differs from its direct definition: C = lim_n→∞ (1 + ½ + ⅓ + … + ⅟n – ln n).

The used approach allows extending the range of applicability of computing devices up to infinitely large numbers. This is shown by the example of calculations carried out by the shift automaton.

The article describes issues of interpretation of pressure transient analyses with a variable production rate of horizontal wells and wells with hydraulic fractures using the best-match method. New empirical interpretation models are proposed. These models allow prompt interpretation without specialized software. Models are tested at a specified range of parameters. The simulated examples are used to estimate the accuracy of parameter determination with the help of empirical models in comparison with the exact solution. It is around 21% for different parameters.

The article considers the problem of real time dynamic simulation of one-dimensional inextensible elastic objects (ropes, cables, etc.) in virtual environment systems. To solve this problem, the fundamentals of the Cosserat theory of elasticity for bending and twisting of the rope are used. An approach in which the rope is discretized by a set of points to define its position and a set of elements between points that determine its orientation is proposed. To specify the orientation of the rope elements, quaternions are involved. With this approach, the inextensibility of the rope is realized using the method of Lagrange multipliers, which leads to a system of linear equations with a tridiagonal matrix solved by the tridiagonal matrix algorithm. In turn, the bending and twisting of the rope are based on the finite element method, which is used to integrate the potential energy of rope deformation. In addition, the implementation of constraints respect to coordinates of the rope position and orientation is performed by the sequential impulses method. Approbation of proposed methods was carried out in a training complex, developed in the System Research Institute, Russian Academy of Sciences, and showed their applicability in virtual environment systems.

Many properties of Bessel functions with integer indices are related to the group of motions of the Euclidean plane. The replacement of the compact subgroup of Euclidean rotations by a noncompact subgroup of hyperbolic rotations and the proposed construction of representations lead to the study of the group properties of Bessel functions with arbitrary indices. The connections of Bessel functions with other special functions, most frequently encountered in applications: Hankel, MacDonald, Neumann, Euler Γ-functions and Β-functions, are found.

The article considers a mathematical model of two-phase immiscible filtration of oil and water at reservoir pressure above saturation. Model is calculated by implicit numerical scheme (by pressure and saturation) using the Voronoi diagram. The sensitivity of the mathematical model of two-phase filtration to some initial data is analyzed by the example of the field model of Western Siberia in the simulator Rubis (KAPPA Engineering).

The paper considers two classes of growing random graphs. The first class is the preferential attachment graphs with a linear weight function, and the second class is the hybrid Jackson – Rogers graphs. Exact formulas for the final vertex degree distributions and final edge/arc endpoints of two-dimensional distributions are derived. It is proved that each hybrid graph corresponds with the definite linear preferential attachment graph by vertex degree distribution and edge/arc endpoints distribution. A stronger assertion is also proved that every hybrid graph is equivalent to a definite graph with a linear weight function. A formula that allows the calibration of a linear function for growing graphs with the required asymptotic power-law vertex degree distribution is deduced. The reliability of the results is confirmed by numerical calculations and simulation modeling. The practical value of the results is demonstrated by successful graph calibration of the network model by autonomous Internet systems.

The article considers specific examples for elliptic orbits. It is shown that the solution for determination of the time of satellites falling can be unstable.

The paper considers the problem of collision response simulation of 3D objects in virtual environment systems. To solve this problem, we propose a block solver in which objects are resolved in pairs with simultaneous processing of clipping contact or impact. It leads to formulation of the LCP (Linear Complementarity Problem) with linear complements with respect to unknown values of impulses (impacts or contact forces). The solution of LCP is performed analytically by the search of all possible options, depending on the count of contact points that are received on the collision detection of virtual objects. Using the proposed approach, the collision response of objects system is based on the sequential impulses method developed earlier. Iterations of this method are performed for each pair of system objects until at least one of the convergence criteria is fulfilled, ensuring necessary accuracy and real time simulation. Approbation of the proposed methods and algorithms was carried out in the dynamic subsystem of training complex, developed in SRISA RAS and showed their applicability in virtual environment systems.

An effective method for loss probabilities calculation in queuing systems is developed. An analysis of accuracy and acceleration achieved in comparison with direct simulation is made. The method is used to analyze the queueing systems with power-series distributions which are widely used as models of network devices of modern computer networks. A dependence of loss probability on a buffer capacity in considered systems is established. The influence on this dependence by the heaviness of tails of power-series distributions and by the channel number is investigated. The obtained results can be used for solving engineering problems of analysis and design of modern computer networks operating under the fractal traffic.

The characteristics of the scattering and light radiation of radio-optical reflectors are considered. The results of full-scale tests of radio-optical direct and spherical reflectors are presented. The advanced constructions of artificial radar reflectors with polarization-anisotropic characteristics, and that are suitable for deployment as navigating marks of the shipping environment are described. The technical implementation of a polarimeter capable of selecting radar objects using a group of polarization properties is considered. Examples of construction of radar images of a river and coastal navigating marks using polarization signal processing are given.

The article describes the two-phase fluid filtration calculation for non-mixing fluids based on the Black-oil model with an application of structured and unstructured prismatic grids. Equations solution is conducted through a fully implicit finite volume method. The described approach is tested on the SPE8 algorithm. Quantitative and quality parameters correlate with the commercial software package Rubis (Kappa Engineering).

The article describes the applicability of the results of pressure transient analyses of the reservoir with the method of well interference testing to clarify the hydrodynamic models of fractured carbonaceous oil-saturated reservoirs. A description of the well interference testing in fractured carbonaceous oil-saturated reservoirs is given. The results of the research are presented.

The article considers the methods of obtaining sparse solutions based on the LS-SVM method. The training samples generated according to the D-optimal experiment design are used for obtaining a sparse solution. An algorithm for forming a test sample using the regularity criterion is also presented. A computational experiment is conducted to check the efficiency of the proposed methods of forming a training sample. The artificial data is used for this purpose. The improvement of the generalizing properties of the models obtained by LS-SVM is carried out through the selection of the Gaussian kernel function parameter while minimizing the prediction error. The kernel function parameter is chosen according to the minimum of external criteria. The criteria of cross-validation and regularity are used as external criteria for assessing the quality of models. The effectiveness of the obtained solutions is estimated by mean square error. The noise variance (noise level) is set as a percentage of the signal power during the data modeling. According to the results, conclusions are made that to receive a sparse solution it is possible to use a training sample, obtained with the use of D-optimal split. The additional optimization of the composition of points (exchange algorithm) is possible to use as well, which in some cases allows getting the best solutions.

A mathematical model of a roof slab of made of a different-modulus composite material is presented, analytical formulas for stresses and displacements are obtained for the case of bending a slab for a different-modulus material. An example of calculating a roof slab is considered.

Collisions are one of the most common types of object interaction with each other. This paper proposes distributed methods and algorithms for collision point calculation under simulation of particle system interaction with objects of virtual environment. Considered solutions are based on spatial subdivision of three-dimensional scene by means of regular grid, which is built in real time on a modern multicore graphics processor supporting the parallel computing architecture CUDA. Collision point search for each particle is performed on GPU as well. In this regard, possible intersections of particle's movement trajectory with polygons in grid cells are analyzed. Moreover this particle passed the grid at the time interval between rendering of the last and current frames of a virtual scene image. Based on proposed methods and algorithms, software modules for visualization systems of three-dimensional virtual scenes are created. They provide distributed simulation and visualization of particle system collisions with virtual environment objects on the CUDA-supported graphics processor in real time. The modules have been successfully tested and demonstrated their applicability in simulation-training complexes and virtual environment systems.

The article is devoted to the optimization of the algorithm execution time in the STF-ElectronMod software. The software is intended to design and model the temperature fields of electronic modules in both deterministic conditions and under uncertainty. The uncertainty of the input data is modeled by the stochastic interval model, and optimization is achieved by parallelizing matrix calculations on PC with multi-core processors. Optimization method is provided and results are presented. A comparison between the speed of the library written in C++ and the speed of the function of the STF-ElectronMod software package written in Pascal is made. It is shown that the function performance of C++ library compared to Pascal function is not less than 30 % using the original nonoptimized algorithm of the STF-ElectronMod software package. This performance is primarily due to the ability of the C++ compiler to use loops unrolling, which is practically not used in the Pascal compiler. The test results showed that performance of the new algorithm may be 6 times higher on the quad-core processor. The algorithm has been developed as a library and included in STF-ElectronMod software package.

New methods of data processing are needed to assess the objective differences between voluntary and involuntary human movements. In this regard, a method for calculating the parameters of quasiattractors in the evaluation of the human neuromuscular system is proposed. As part of the study for 15 samples of tremorogram and tappingramms are obtained from the same subject in a calm state (relaxation). For these samples, the matrices of paired comparisons are built and the parameters of quasi-attractors are calculated. As it turned out, the number of pairs of “matches” k is extremely low, but there is a stable pattern: for tappings the number of identical pairs of k is 2–3 times higher compared to the matrices obtained for tremorograms. In turn, the calculation of the parameters of quasi-attractors has allowed us to establish differences between voluntary and involuntary movements (the volume V_G2 for tappingramms is always much larger than V_G1 for tremorograms).

The article analyzes and specifies existing definitions for the concepts “data”, “information” and “intelligence” using foreign and domestic sources. Currently the problem of information processing is especially relevant, resulting from the increase of amount of information that economic entities and state organizations are working with. The issues of the interrelationship of the concepts “data”, “information” and “knowledge” are considered. A semantic analysis of the definitions and the most frequently used terms is carried out. Many researchers have reached a consensus with the meaning of the term “data”, in contrast to the terms “information”, “knowledge” and “intelligence”. The complexities associated with the evaluation of intelligence in computer programs and systems are examined, and the criteria of intelligence are analyzed. The metrological aspect of evaluating intelligence during the information processing is considered and criteria for such an evaluation are established. The problems arising during the practical implementation of tools for the intelligent information processing are analyzed.

The paper proposes distributed methods for realistic rendering of three-dimensional virtual objects using computing abilities of modern graphics processors (GPU). The idea of the considered solutions is to simulate a light reflected from surfaces of virtual environment objects with approximate imitation of their materials’ physical properties. Specifying of such properties is done by means of several textures with special format. Data from these textures are used in pixel shader when reflected light is calculated on GPU by own illumination model. The proposed model is the modification of the Cook-Torrance BRDF model and allows simulating in virtual environment both different light source types and shadows cast by objects. Created methods and algorithms are based on using of distributed computing on modern multi-core GPUs and support real-time visualization of complicated high polygonal virtual scenes. This provides their applicability in virtual environment systems and simulation-training complexes. Based on proposed solutions, software modules for 3D scene visualization systems are created. The modules allow performing realistic rendering of virtual environment objects.

The article considers the development of multiversion information system for managing software changes in information projects (IT-projects) and management of working time using the UML and Petri nets. This model of interaction between users and information system for managing software changes of an IT-project is implemented using UML diagrams. The interpretation of UML diagrams in Petri network is shown. Petri networks analysis using the reachability tree is made.

The statistical instability for consecutive samples of any biomechanical parameters is proved from the perspective of the new theory of chaos-self-organization. First of all, these parameters include tremor, tapping and electromyogram samples which are within a new Eskov – Zinchenko effect. However, it raises the question about the mechanics of such stability. It is proved that the primary statistical chaos occurs at the level of the central nervous system. The chaos parameters of the electroencephalograms are proved. Then there is a natural two-cluster cybernetic scheme of regulation of movements: chaos in the 1st cluster management generates and summed the chaos in the end organ – the neuromuscular system. As a result, muscles have the chaos of a higher order: if in the electroencephalograms the number of k pairs of matching samples is large (k₁ ≥ 25), then in matrices of tremorogram and electromyogram it is k₂ ≤ 10, i.e. 2–3 times less. The difference between the upper (electroencephalogram) and lower (effector) levels of motion regulation is proved from the perspective of the new theory of chaos-self-organization.

At the present stage of development of computer systems, users of software products are representatives of virtually all ages and all professions, unlike the middle of the last century, when communications with computers were exclusively handled by specialists who possessed all the necessary knowledge for this complicated process. Such a global change in the target audience is due not least to the development of user interaction technologies; the appearance of the graphic interface in its time revolutionized the availability of the computing system to a wide range of consumers. To date, there is an approach to the development of software, where the central object at all stages of work is not the functionality and technical characteristics of the system, but the user.

The paper provides an overview of the basic concepts associated with the development of an ergonomic user interface for application programs; considers the main indicators of the suitability of the use of the software product: effectiveness, efficiency and satisfaction. Possible ways of estimating these indicators, including the method of the semantic differential, which was not previously used for these purposes, are listed. The main types of design activities are presented in the human-oriented development approach in accordance with the existing standard documentation.

The article considers the terms of the same and homogeneous group within the framework of three approaches in science: determinism, stochastics and the theory of chaos-self-organization. The traditional approach requires a certain equality (functions, trajectories, etc.), but this is impossible for biosystems. It is proved that determinism (exact coincidence of the trajectories of the motion of the vector x(t) in the phase space of states), where the apparatus is a functional analysis, and stochastics (two samples of the parameters of the two groups belong to the same population) are not applicable to the medical and biological sciences. It is impossible to obtain exact equality of functions for biosystems (including static ones) because of their ultrastability. From the perspective of the new theory of homeostasis, special criteria for the homogeneity of the group are introduced. For each sample, the parameters of quasi-attractors are calculated and inequalities are introduced on the variation of the phase coordinates. Then the quasi-attractors of the parameters of two (or more) groups can be found in the same general quasi-attractors. A homogeneity criterion is introduced for the coordinates of the centers of these quasi-attractors. Similar criteria are used for the term “the same” when the centers of any quasi-attractor do not show the parameters (limits) of any quasi-attractors from a homogeneous group of subjects. The article presents an algorithm for calculating homogeneity, based on calculations of centers and boundaries of quasi-attractors.

The article considers existing and currently under development domestic technological solutions which allow enhancing oil recovery from the Bazhenov Formation. These solutions include thermal-gas treatment and intrastratal catalytical retorting concept. Brief characteristic of the Bazhenov Formation rock types and some parameters of oil and hydrocarbon saturated agents are discussed. Effective reserve recovery, including extraction of synthetic hydrocarbons, is possible with enhanced oil recovery methods (EOR). For conditions of deposits of the Bazhenov Formation, the need for implementation of process continuous control during thermal-gas treatment and other EOR methods is shown.

The paper proposes a technology for implementation of a multitasking graphical shell of a visualization system for digital model of the core material, based on development of widget subsystems using the open source cross-platform Qt library. The study provides a method to split the graphical interface of the visualization system between executive kernel and task modules, as well as a model to connect task modules to the kernel. Based on the developed technology, methods and algorithms a program complex implementing the graphical shell of the visualization system for digital model of the core material is created. The created complex is successfully tested through studies of digital models of the core materials of the Bazhenov Formation and Sandstone and showed adequacy of the proposed solution to the problem. The solution, developed in the System Research Institute, Russian Academy of Sciences, is aimed at the development of the “digital oilfield” technology and can be used in researches by specialists from oil and gas industry, virtual laboratories and educational applications.