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The International Science and Technology journal was founded in 1997.

State registration certificate: KB № 18963-775 ПР of April 25 2012.

ISSN 1810-0546 (Print)

ISSN 2519-8890 (Online)


LCCN: 2016214741

The journal publishes only the new results of fundamental and applied scientific research on the subjects of the journal, which had not been previously published in other scientific publications in Ukraine or abroad.

The editorial board of the journal accepts overview and original research papers on the following topics: electronics, radio engineering and telecommunications; power engineering and energy generating technologies; Information technologies, system analysis and control; science of materials and mechanical engineering; instrument- making and information-measuring equipment; problems of biotechnology; energy saving problems; problems of chemistry and chemical technology; theoretical and applied problems of physics and mathematics.

According to the order of MES of Ukraine from 07.13.2015 no. 747, from 07.10.2015 no. 1021, and from 09.03.2016 no. 241 the journal specializes in the physical and mathematical, technical, chemical and biological sciences.

The periodicity of the journal is 6 times a year (no. 1, 2, 5, 6 – engineering sciences, no. 3 – chemical and biological sciences and technology, no. 4 – physical and mathematical sciences).

Languages: Ukrainian, Russian, English.

Founder: National Technical University of Ukraine “Igor Sikorsky Kyiv Polytechnic Institute”.

Mailing address of the editorial office: building 1, room 171-3 and 193-Б, Peremohy Str. 37, Kyiv 03056, Ukraine.

E-mail: n.visti@kpi.ua   and  n-visti@kpi.ua

Tel.: +38(044)204-91-23; +38(044)204-94-53

The journal is covered by following indexing services:

Index Copernicus

Адреса URL: http://bulletin.kpi.ua/
Оновлено: 15 хв 4 сек тому

The Optimization of the Data Packet Length in Adaptive Radio Networks

Втр, 10/31/2017 - 00:00

Background. Development of methods and means of the adaptive management of the radio networks bandwidth with competitive access to the radio channel.

Objective. The aim of the paper is to determine the packet length effect on the effective radio networks transmission rate with taking into account the parameters, formats, and procedures of the physical and link levels at using the MAC protocol with a rigid strategy of competitive access to the radio channel.

Methods. The goal is achieved by creating and analyzing the mathematical model of the effective transmission rate in radio networks. The model is described by the equation for the effective transmission rate, which is the function of both the probability of the conflict-free transmission of the MAC protocol and the coefficient of the data packet size deviation from the optimal for LLC protocol.

Results. It is proved that there is the optimal deviation of the data packet length for each MAC protocol traffic intensity value, which provides the most effective transfer rate. This makes the possibility for adaptive management of the radio bandwidth by applying a pre-calculated deviation of the data packet size in dependence on the traffic intensity.

Conclusions. The proposed mathematical model is the tool for calculation of both the radio bandwidth network capacity and the optimal deviation of the data packet length at adaptive management of competitive access to a radio channel with a rigid strategy at conditions of the significant fluctuation in traffic intensity.

Technology of Rock Destruction by Combined Explosion-Mechanical Load

Втр, 10/31/2017 - 00:00

Background. Rock drilling is characterized by an energy capacity of more than 120 kWh/m3. This is due to the fact that about 90 % of the energy is expended on the “preparation” of rocks for destruction. This study proposes to combine explosive and mechanical loads to reduce specific energy consumption of rock destruction.

Objective. The aim of the paper is energy effective technology development for rock destruction by combined explosive-mechanical loads.

Methods. Analytical studies; regression analysis; math modeling; experimental research; technical and economic analysis.

Results. Specific energy decreasing for explosive-mechanical rock drilling by 4–16 % was experimentally proved.

Conclusions. As a result of the implementation of explosive-mechanical rock drilling on the created full-sized experimental device, the efficiency coefficient increased from 77 to 80 %.

Statistics Based Models for the Dynamics of Chernivtsi Children Disease

Втр, 10/31/2017 - 00:00

Background. Simple mathematical models of contamination and SIR-model of spreading an infection were used to simulate the time dynamics of the unknown before children disease, which occurred in Chernivtsi (Ukraine). The cause of many cases of alopecia, which began in this city in August 1988 is still not fully clarified. According to the official report of the governmental commission, the last new cases occurred in the middle of November 1988, and the reason of the illness was reported as chemical exogenous intoxication. Later this illness became the name “Chernivtsi chemical disease”. Nevertheless, the significantly increased number of new cases of the local alopecia was registered almost three years and is still not clarified.

Objective. The comparison of two different versions of the disease: chemical exogenous intoxication and infection. Identification of the parameters of mathematical models and prediction of the disease development.

Methods. Analytical solutions of the contamination models and SIR-model for an epidemic are obtained. The optimal values of parameters with the use of linear regression were found.

Results. The optimal values of the models parameters with the use of statistical approach were identified. The calculations showed that the infectious version of the disease is more reliable in comparison with the popular contamination one. The possible date of the epidemic beginning was estimated.

Conclusions. The optimal parameters of SIR-model allow calculating the realistic number of victims and other characteristics of possible epidemic. They also show that increased number of cases of local alopecia could be a part of the same epidemic as “Chernivtsi chemical disease”.

Finding an Optimal Decisions’ Subset by Minimaximax Regret Criterion Regarding Instability of the Decision Function

Втр, 10/31/2017 - 00:00

Background. A generalization of the minimax regret criterion is represented as even the best-assurance minimax regret criterion comes inconsistent under instable evaluations of decision situations.

Objective. The goal is to formulate the minimaximax regret criterion.

Methods. Unlike the classic one, the generalized regret criterion is minimaximax which operates over generalized regrets. These regrets are found from a generalized decision function which is defined on a Cartesian product of a decisions’ set, a set of states, and a set of metastates. Metastate describes instability of the decision function whose values change through a set of metastates. The instability destroys assurance of minimaxed regrets found classically, so regrets are found over a generalized decision function. For this, utility evaluations are subtracted from the utility maximized across a decision set, or the loss/risk minimized across a decision set is subtracted from loss/risk evaluations. Then regrets are minimized under uncertainty across two dimensions of states and metastates, that is they are minimaximaxed.

Results. The suggested minimaximax regret criterion allows finding an optimal decisions’ subset with not only regarding instability of the decision function, but also with reducing the initial decisions’ set more, unlike the ultimate pes-simism criterion without regrets (minimaximax/maximinimin). This especially concerns nonnegative utility matrices with many zeros.

Conclusions. A ratio of a number of optimal decisions by the without-regret maximinimin/minimaximax to a number of optimal decisions by the minimaximax regret criterion decreased by 1 can be interpreted as a gain of applying the represented minimax regret criterion generalization. This gain fundamentally depends on whether sets of decisions, states, and metastates are finite or not. If they all are finite, then the gain depends on values in a three-dimensional regret matrix and its dimensions. It is surprising but the gain may be negative, that is finding regrets may come non-effective.

Effect of Fluid Viscosity on Noise of Bileaflet Prosthetic Heart Valve

Втр, 10/31/2017 - 00:00

Background. Numerical simulation and experimental research have been used as powerful tools to understand and predict the behavior and mechanics of the operation of natural heart valves and their prostheses in natural and patho­logical conditions. Such studies help to evaluate the effectiveness of the valves, their design and the results of surgical procedures, to diagnose healthy and impaired function of the heart valves. There is an actual problem in creating more reliable methods and tools for the operation diagnostics of mechanical heart valves.

Objective. The aim of the research is to investigate the effect of fluid viscosity on the hydroacoustic characteristics of jets that flow from a semi-closed and open mechanical bileaflet heart valve. To study the possibility of using hydro­acoustic measuring instruments as diagnostic equipment for determining the working conditions of the bileaflet pro­sthe­tic heart valve.

Methods. The experimental research was carried out by means of hydroacoustic measurements of the hydrodynamic noise in the near wake of the side and central jets of the glycerin solution and the pure water flow downstream of the prosthetic bileaflet heart valve.

Results. The effect of fluid viscosity on the hydroacoustic characteristics of the jets that flow from a semi-closed and open mechanical bileaflet heart valve has been experimentally determined. Integral and spectral characteristics of the hydrodynamic noise of jets of the glycerin solution and the pure water flow downstream of the bileaflet mitral heart valve for different fluid rate were detected.

Conclusions. In the stream conditions of pure water, the integral characteristics of the pressure field are lower than in stream conditions of the aqueous glycerin solution. As the glycerin concentration in the solution increases, increase average pressures and especially RMS pressure fluctuations. The spectral levels of the hydrodynamic noise in the near wake of the side jet of the glycerin solution are lower than for water flow in the frequency ranges from 1 to 7-8 Hz and from 100 to 1000 Hz for fluid rate 5 l/min. For higher fluid rates, the spectral components of the hydrodynamic noise in the near wake of the side jet of the glycerin solution of the semi-closed mitral valve are higher than that for the pure water. The greatest difference (1.5–1.8 times) in the spectral levels is observed in the frequency range from 10 to 100 Hz for the fluid rate 15 l/min.

Modeling Financial Risk in Telecommunication Field

Втр, 10/31/2017 - 00:00

Background. The telecommunication field in Ukraine is dynamically developing continuously renewing its proposals for the market and consumer requirements. That is why a timely estimation of financial risks and optimization of financial expenses regarding development of new components and possible losses of clients is especially urgent problem today.

Objective. The aim of the paper is to suggest an approach for estimation of financial risks and forecasting of the client loss and optimal service time utilization based on intellectual data analysis and behavior models.

Methods. To determine the probability of customer loss the neural networks theory, gradient busting, random forest and logistic regression are used. The survival analysis models for possible client transition time to another company are developed.

Results. The best model for forecasting the clients intending for transition to another telecommunication company turned out to be the one based on gradient busting.

Conclusions. It was shown that timely estimation of financial losses, provoked by possible loss of clients, is an urgent task for intellectual data analysis. A perspective approach for optimization of the company financial resources is determining the time period related to possible loss of clients.

Method of Encoding the Output Signal of Neural Networks Models

Втр, 10/31/2017 - 00:00

Background. A significant drawback of the technology of creating modern neural network models based on the multilayer perceptron is that when the parameters of the case studies are encoded, the expected output signal correlation with the similarity of the class standards to be recognized is not taken into account.

Objective. The aim of the paper is the development of the method for encoding the output of the case studies, which ensures the reflection of the similarity of the class standards to be recognized.

Methods. The encoding method is based on a probabilistic neural network, in which case studies the expected output signal is determined not by numerical form but by the class name to be recognized. At the same time, when recognizing, it is possible in the numerical form of the output signal of the network to show the similarity of the input image to each class that was laid in it during the training.

Results. The encoding method has been developed, which, due to the use of the probabilistic neural network, allows us to consider the similarity of the class standards to be recognized in the expected output signal of the case studies.

Conclusions. The proposed method allows reducing the number of training iterations 1.3–1.5 times to achieve a tolerable learning error within 1 %.

The Influence of Nanodispersed Modifiers on the Structure and Properties of Plasma-Sprayed Coatings

Втр, 10/31/2017 - 00:00

Background. Currently, plasma-sprayed coatings are widely used to protect machine parts operating under conditions of high loads and temperatures, abrasive wear and exposure to corrosive media.

Objective. The aim of the paper is to improve the physico-mechanical characteristics of plasma-sprayed coatings by modification of nano-sized particles of TiO2 oxides compounds.

Methods. Experimental studies of corrosion resistance, microhardness, adhesion strength and residual stresses of plasma-sprayed coatings based on the oxide aluminum ceramic powder with the addition of nanodisperse TiO2 powder were conducted.

Results. It is found that addition of TiO2 nanodisperse modifier to the oxide aluminum ceramic powder composition leads to corrosion resistance increase 2.8 times in a 10 % hydrochloric acid solution. The adhesive strength of ceramic nanomodified coatings is increased by 15–20 %.

Conclusions. The positive influence of nanodispersed powders on the physico-mechanical and tribological characteristics of plasma-sprayed coatings is established.

Elaboration of the Thermodynamic Model of Refining the Converter Bath when Blowing through Three-Tier Oxygen Lance

Втр, 10/31/2017 - 00:00

Background. In modern conditions, the BOP-process is the main method of mass use steel product production. At the same time, due to the shortage of high-quality charge materials, resource and energy-saving technologies are particularly relevant. To optimize the BOP-process under modern conditions, it is promising to use improved oxygen lances for top blowing in comparison with known designs.

Objective. An important stage in the development of advanced steel production technologies is obtaining information on the thermodynamic model of blowing a converter bath through a three-tier lance with the elaboration of the regularities of oxidation processes within the reaction zone of a 160-ton industrial converter.

Methods. The analysis that was carried out has a theoretical nature and is based on the definition of the influence of temperature and pressure on the regularities of oxidation processes within the reaction zones formed when oxygen jets are introduced into the volume of a metal bath, foamed slag-metallic emulsion and waste gases in the working space of the converter. As a thermodynamic parameter, the Gibbs energy was used to estimate the probability of chemical reactions. The pressure effect on the oxidation processes in the converter bath was evaluated in accordance with the Van’t Hoff formula.

Results. The thermodynamic features of oxidation processes in the 160-ton BOF bath using a three-tier lance are presented. Primary reaction zone is characterized by the occurrence of oxidation of manganese, silicon, carbon, and iron by gaseous oxygen. In the secondary reaction zone there are chemical reactions of the oxidation of silicon and carbon dissolved in the metal by oxygen, as well as the reduction of iron oxide by carbon. The presence or absence of a slag phase on the melt surface practically does not affect the occurrence probability of chemical transformations within the boundary of primary and secondary reaction zones. The additional secondary oxygen jets are characterized by oxidation of the oxide components of the slag and gas phases.

Conclusions. During the research it was clarified the thermodynamical model of the oxidation processes in primary and secondary reaction zones, that were formed due to the interaction of 160-ton BOF bath with the supersonic and sonic oxygen jets flowing out of the separate groups of nozzles (of Laval and cylindrical shapes) of top three-level oxygen lance.

Structure and Mechanical Properties of Powdered Quasicrystalline Al94Fe3Cr3 Alloy Consolidated by Quasi-Hydrostatic Compression

Втр, 10/31/2017 - 00:00

Background. Quasicrystalline Al-based alloys belong to the class of the state-of-the-art metal materials for the application in light engineering constructions, primarily in aviation and the motor transport industry. These materials are commonly made in the form of powders, which is due to the high productivity of powder metallurgy methods. Therefore, the powder consolidation methods are of great importance in the production of products, which is associated with certain difficulties, and consequently, they should be chosen considering not only the quasicrystals’ propensity to brittle fracture but also the metastable nature of the quasicrystalline phases. Certain possibilities in this direction are provided by the quasi-hydrostatic compression method, which can provide a non-trivial combination of strength and ductility properties of materials.

Objective. The aim of the paper is to investigate the effect of high pressure under quasi-hydrostatic compression on the formation of structure, phase composition and mechanical properties of the quasicrystalline Al94Fe3Cr3 alloy.

Methods. 40 μm Al94Fe3Cr3 alloy quasicrystalline powder was fabricated by water-atomisation technique. Consolidation of quasicrystalline powder was performed by quasi-hydrostatic compression technique in high-pressure cells at room temperature at a pressure of 2.5, 4, and 6 hPa. Structure, phase composition and mechanical characteristics of Al94Fe3Cr3 alloy were performed by scanning electron microscopy (SEM), X-ray diffraction andmicromechanical tests.

Results. Using the phase X-ray analysis and SEM, the content of the quasicrystalline icosahedral phase (i-phase) in the Al94Fe3Cr3 alloy structure was completely preserved after its consolidation at different pressures (2.5, 4, and 6 hPa) under quasi-hydrostatic compression at room temperature. Despite the high pressure applied in the consolidation process, the morphology of quasicrystalline phase particles located in the a-Al deformed matrix solid solution remains unchanged. The mechanical properties of the alloy exceed the similar characteristics of the alloy consolidated by warm extrusion.

Conclusions. Consolidation of the Al94Fe3Cr3 alloy powder under quasi-hydrostatic compression allows for the complete conservation of metastable quasicrystalline i-phase particles in the aluminum matrix, which provides the highest values of strength properties together with sufficient ductility for application in the engineering practice.

Oxidation Resistance of Medium-Carbon Heat-Resistant Cr-Al Steels in Extreme Conditions

Втр, 10/31/2017 - 00:00

Background. From the analysis of exploitation of heat-resistant details of thermal power and metallurgical equipment, it was found that the basic characteristic of metallic materials working under extreme conditions is oxidation resistance. However, the choice of materials for work in the conditions of high temperatures and aggressive environments should be made taking into account not only its oxidation resistance but also the possibility of this material to work long time in the conditions of thermal cycling without being damaged, thus thinking about its heat-resistance. Consequently, it is tremendously important to determine the oxidation resistance of iron-based alloys in extreme conditions depending on the presence of main elements – chrome and aluminium – in their content on the basis of study of formation processes on the item surface of high-quality protective oxides films.

Objective. The aim of the paper is to establish the selection rules of heat-resistant iron-based alloys for work in extreme conditions depending on temperatures and aggressive environments and to accumulate some information on their oxidation resistance for the creation of a database and development of methodology how to forecast special properties of alloys.

Methods. Models with 10 mm in diameter and 20 mm in length were tested in a tubular stove at the temperature of 1200 and 1250 °C during 100 hours. Oxidation resistance was determined by a weight method. Phase composition and structure were explored by modern X-ray structural and metallographic methods.

Results. Processes and mechanisms of formation of oxide scale in the conditions of exploitation of items under the temperature 1250 °C in different aggressive environments are established. The optimum boundaries of concentration of basic chemical elements – chrome and aluminium – in heat-resistant alloys for work in extreme conditions depending on temperatures and environments are determined. A database for development of methodology for forecasting of the special properties of Cr-Al steels depending on their chemical composition is created.

Conclusions. Optimal concentration of chrome in heat-resistant Cr steels for work of items at temperatures up to 1100 °C can be considered 25–30 %. To provide high oxidation resistance of items working at temperatures up to 1250 °C in aggressive gas environments, the concentration of Cr in a metal should be within the limits of 25–30 %, and aluminium – from 2.0 to 3.5 %, the relation [% Cr]/[% Al] = 7–10 must be executed. Various gas environments differently effect on oxidation resistance of steels. At the temperatures of 1200 °C items in the water steam environment oxidize faster, and slower in the carbon dioxide environment.

Minimum Temperature Difference Perceived for Undersampled Medical Thermal Imager

Втр, 10/31/2017 - 00:00

Background. Currently, thermal imagers with matrix radiation detectors (MRD) are widely used in medicine. A common feature of these thermal imagers is the ability to sample the signal in two directions: horizontal and vertical. Such thermal imagers are undersampled. That is why the question of evaluating the effectiveness of such thermal imagers is very relevant now.

Objective. The aim of the paper is to provide a physico-mathematical model of a thermal imager to calculate the minimum temperature difference perceived (MTDP).

Methods. It is proposed to determine MTDP based on the physico-mathematical model of the thermal imager for determining the minimum resolution temperature difference.

Results. The developed physico-mathematical model of a thermal imager with MRD allows calculating MTDP that enables determining the spatial resolution of a thermal imager outside the Nyquist frequency. It is proposed to consider the Average Modulation at Optimum Phase (AMOP) as the line scale average contrasts, which allow obtaining an equation for calculating the MTDP function.

Conclusions. The proposed physico-mathematical model provides an opportunity to determine the spatial resolution of the thermal imager outside the Nyquist frequency, which is an important factor in the effect on the thermal imaging quality.

Heat and Mass Transfer Remote Control in Bioreactors of Technological Lines

Втр, 10/31/2017 - 00:00

Background. The main problems that arise when using equipment for cultivation are to ensure the heat and mass transfer processes in devices, presence of turbulent and stagnant zones, high-energy consumption, low heat transfer coefficients when working with viscous fluids.

Objective. The aim of the paper is the experimental determination of the remote control heat transfer advantages in production line bioreactors using ultrasonic beam compared to contact methods.

Methods. An experimental study of the heat and mass transfer process in a bioreactor on the stand with UZP-6-1 immersion unit of the ultrasonic radiator with radiation frequency 42 kHz is carried out.

Results. Sound waves emitted into a liquid form a concentration zone of passable sound energy in the confocal vessel form of a cylindrical surface and force the liquid to move along the inner surface of the glass along the ascending cylindrical spiral, forming a motive flow throughout the volume, causing peripheral layers of liquid and bottom layers to move in a horizontal and vertical planes, without leaving stagnant zones. The closer to the coincidence angle  is the directed ultrasonic beam the greater is the effectiveness of the driving flow.

Conclusions. The use of sound waves allows obtaining a high-quality product in technological lines based on bioreactors with minimal risk for the technological process. Radiation parameters and working volume physic-mechanical properties change allow fully using the properties of resonant manifestations of the sound wave influence on the working liquid with minimal costs.

Effect of the Convection Processes in Liquid on Thermal Conductivity Measurement Error by Direct Heating Thermistor Method

Втр, 10/31/2017 - 00:00

Background. The problems of choosing the optimal utensil diameter for the test liquids on the basis of the investigation of the convection phenomenon effect on the error when measuring the thermal conductivity of liquids by the method of direct heating of a thermistor are considered.

Objective. The aim of the paper is to carry out experimental studies to determine the effect of the convection phenomenon on the error in measuring the thermal conductivity of liquids.

Methods. An estimation of the thermistor heating temperature measuring accuracy by the method of direct heating of the thermistor for the test liquid in utensils of different diameters in determining the coefficient of thermal conductivity is carried out. Series of experimental research was carried out with the help of a device for measuring the liquids TPC in order to determine the optimum design of the probe and the thermostat, to select the optimum volume of the material research and to choose the materials of construction.

Results. The results of experimental research with control liquids using the developed instrument based on the method of direct heating of the thermistor are presented, the thermistor heating temperature fluctuation values depending on the utensil diameter with the test liquid are determined.

Conclusions. It is substantiated that when designing devices for measuring the TPC of liquids, it is necessary to take into account the individual properties of the liquids under investigation and to create the greatest possible uniform heating or cooling of the utensil with the test material. Also, it is necessary to use the minimum diameter utensils. It is recommended to use utensils for the test liquid with a diameter of up to 10 mm to reduce the error in measuring the liquid thermal conductivity.

Obtaining of Peracetic Cellulose from Oat Straw for Paper Manufacturing

Втр, 10/31/2017 - 00:00

Background. Development of technology for obtaining peracetic pulp from oat straw and its use in the production of one of the paper mass types.

Objective. Determination of peracetic cooking technological parameters’ optimal values for oat straw peracetic cellulose quality indicators.

Methods. The oat straw cooking was carried out with peracetic acid at 95 ± 1 °C from 90 to 180 min for hydromodulus 8:1 and 7:1, using a sodium tungstate catalyst. To determine the oat straw peracetic cellulose mechanical indexes, laboratory samples of paper weighing 70 g/m2 were made.

Results. Technological parameters’ optimum values (temperature, cooking duration, hydromodulus, hydrogen peroxide and acetic acid concentration) for the oat straw delignification process were established. It is shown that the sodium tungstate catalyst addition to the cooking solution at a rate of up to 1 % of the plant raw material weight helps to reduce the lignin content in cellulose to 15 %. A diagram of the cellulose yield dependence on its residual lignin content for various methods of non-wood plant material species delignification is constructed. The high efficiency of the peracetic method for obtaining cellulose from non-wood plant raw materials, in particular from oat straw, has been confirmed. It is determined that the obtained peracetic cellulose from oat straw has high mechanical indexes.

Conclusions. Oat straw peracetic cellulose can be used for the production of paper and cardboard mass types, in particular wrapping paper.

Evaluation of the Influence of Amphoteric Synthetic Resins on the Degree of Fiber Holding and Contamination of Pit Water

Втр, 10/31/2017 - 00:00

Background. Waste paper recycling is characterized by deterioration in the content of fiber mass on the fourdrinier wire of a paper-making (cardboard-making) machine, which leads to the fiber content increase in the pit water and to an increase in losses of the source fiber raw material with waste water.

Objective. The aim of the paper is to evaluate the influence of amphoteric polymer resins (APR) on the fiber content effectiveness on the fourdrinier wire and the pit water contamination degree.

Methods. According to standard techniques, the degree of fiber content and water turbidity, which arises in the paper and cardboard production during the formation on the paper-making machine fourdrinier wire, is determined.

Results. The graphs of the dependence of the pit water turbidity on the APR consumption for different milling degree for MS-5B-2 and МС-8В-3 waste paper grades have been constructed. The high efficiency of the APR influence on the fiber content degree on the PPM wire is confirmed. The optimal values of technological parameters (milling degree and APR consumption) for the estimation of the APR impact on the pit water quality have been established. It is shown that the most effective APR among the investigated chemical auxiliaries is UltraRez 200, and the optimum consumption of all APR is 4 kg/ton of paper. The investigated APR are located by the effectiveness increasing of the APR influence on the degree of fiber content and the pit water turbidity reduction in the following series: Luresin KS – Eka WS 325 – Kymene 25X-Cel – UltraRez 200 – Fennostrengt PA21.

Conclusions. The use of APR allows achieving a high degree of fiber retention on the wire up to 97 % and reduces 50–85 % of the pit water turbidity, reduces the loss of the source fibrous raw material, reduces the fresh water consumption and increases the efficiency of paper and paperboard production from waste paper.

Boundedness of Lebesgue Constants and Interpolating Faber Bases

Пон, 09/18/2017 - 00:00

Background. We investigate the relationship between the boundedness of Lebesgue constants for the Lagrange polynomial interpolation on a compact subset of

\[\mathbb R\]

and the existence of a Faber basis in the space of continuous functions on this compact set.

Objective. The aim of the paper is to describe the conditions on the matrix of interpolation nodes under which the interpolation of any continuous function coincides with the decomposition of this function in a series on the Faber basis.

Methods. The methods of general theory of Schauder bases and the results which describe the convergence of interpolating Lagrange processes are used.

Results. The structure of matrices of interpolation nodes which generate the interpolating Faber bases is described.

Conclusions. Every interpolating Faber basis is generated by the interpolating Lagrange process with the interpolating matrix of a special kind and bounded Lebesgue constants.

Estimation of Accuracy and Reliability of Models of φ-sub-Gaussian Stochastic Processes in Spaces

Пон, 09/18/2017 - 00:00

Background. At present, in the theory of stochastic process modeling a problem of assessment of reliability and accuracy of stochastic process model in C(T) space wasn’t studied for the case of inexplicit decomposition of process in the form of a series with independent terms.

Objective. The goal is to study reliability and accuracy in C(T) of models of processes from Subφ(Ω) that cannot be decomposed in a series with independent elements explicitly.

Methods. Using previous research in the field of modeling of stochastic processes, assumption is considered about possibility of decomposition of a stochastic process in the series with independent elements that can be found using approximations.

Results. Impact of approximation error of process decomposition in series with independent elements on reliability and accuracy of modeling of stochastic process in C(T) is studied.

Conclusions. Theorems are proved that allow estimation of reliability and accuracy of a model in C(T) of a stochastic process from Subφ(Ω) in the case when decomposition of this process in a series with independent elements can be found only with some error, for example, using numerical approximations.

An Efficiency of Strategies in Models of Conflict Redistribution of Resource Space

Пон, 09/18/2017 - 00:00

Background. The model of conflict redistribution of resource space (territory) between a pair of opponents in the case of infinite fractal division of space is investigated.

ObjectiveThe aim of the paper is to consider the problem of conflict redistribution of resource space, if the opponent presence measures on the space are limited, but not necessarily probabilistic.

Methods. To specify the measures of the occupied territories and to find their limiting values a probabilistic approach was applied.

Results. The existence of limit values of measures of occupied territories with an infinite increase in the division step is established. The possible values are indicated. Using computer simulation graphs are obtained which show the behavior of the measures of the occupied territories with increasing of the division step.

Conclusions. It is shown that the limit values of measures of occupied territories depend only on the selected strategies (that is, the way of structured representation of measures that correspond to each of the opponents). 

The Main Properties of q-Functions

Пон, 09/18/2017 - 00:00

Background.  The new generalization of the function of complex variable (q-function) is considered, its main properties are investigated. Such distributions have a special place among the special functions due to their widespread use in many areas of applied mathematics.

Objective. The aim of the paper is to study the new generalization of the function of complex variable for application in applied sciences.

Methods. To obtain scientific results the general methods of the mathematical analysis, and the theory of special functions have been used.

Results. The article deals with new generalization of the function of complex variable – q-functions, its main properties are investigated. The theorem on integral representation of q = xk-analytical functions is proved, its inverse formula is constructed.

Conclusions. Considered in the article new generalization of the function of complex variable opens up opportunities for the use of q-functions in the theory of special functions, and in the applications of mathematical and physical problems. In the future we plan to use the results to solve the boundary value problems of mathematical physics, in the theory of elasticity, for solving of, the theory of integral equations, etc.