Вісник Київського національного університету імені Тараса Шевченка. Серія: фізико-математичні науки
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Analysis and optimization of retrial systems and queue with variable rate of input flow
Get PDFThe paper is focused on in-depth study of the promising area of the stochastic systems theory related with scrutiny of queuing systems with repeated calls. We research Markov`s models of retrial systems with queue and variable rate of input flow controlled by threshold strategy with no restriction on the capacity of the orbit. We defined stationary regime existence conditions and investigated probability characteristics of process for two-dimension Markov process with continuous time which we took as a main model of the specified system. In stationary regime for probability characteristics of the service process were found explicit formulas. Research methods which we used are based on the initial process approximation by the process with bounded state space. Results of the research allow us to evaluate convergence rates of stationary distribution of finite systems with repeated calls to stationary distribution of infinite systems. Method of probability flow equating is used for obtain explicit expressions for stationary system probabilities through the closed path which are defined in a special way. For threshold control strategies the optimization problem of the total income of the system was stated and solved.Key words: queue, repeated calls, threshold strategies, stationary regime, optimization.Pages of the article in the issue: 130 - 134Language of the article: Ukrainia
Investigation by X-ray photoelectron spectroscopy of the process of TiC synthesis during annealing of ?i?2/?i?2/? in vacuum
Get PDFSmall dimensional transition metal carbides (MXenes) are promising materials for the development of photocatalysts and are highly efficient cocatalysts for industrial TiO_2 (P25). Thus, in the Ti_3C_2@TiO_2 nanocomposite obtained by layering Ti_3C_2 nanoplates, the ability to separate charge carriers increases due to the high electrical conductivity of TiC_{1-x}. The task of forming the TiC_{1-x}@TiO_{2-x} nanocomposite by direct synthesis with n-TiO_2 is promising, which allows to increase the quality of contact between the shell and the nanocomposite core and to reduce the number of intermediate stages of synthesis. In addition, highly dispersed TiC has high values of hardness, melting point, modulus of elasticity and shear and has the prospect of use in materials science in plasma spraying coatings. In work TiC was synthesized on the surface of TiO_2 - the shell of the modified micropowder TiH_2/TiO_2/C during reductive annealing in vacuum using TiH_2 as a source of atomic hydrogen. After a series of annealing at 535 ºC - 600 ºC, the Ti2p- C1s- and O1s- spectra of surface atoms were obtained. The main stages of TiC synthesis in the TiO_2/C conversion reaction were established by the XPS method. The use of TiH_2 as a source of atomic hydrogen in nanosystems of the «core/shell» type is proposed for local synthesis on the surface of nanoobjects in a vacuum or inert atmosphere.Key words: X-ray photoelectron spectroscopy, XPS, titanium carbide, TiC, TiO_2, nanopowders.Pages of the article in the issue: 85 - 94Language of the article: Ukrainia
The convergense rate of stationary distribution of retrial queueing system with queue
Get PDFThis paper describes a steady state behavior of the retrial system in the case of one server, one place in the queue and an infinity orbit. We research Markov`s models of retrial systems and variable rate of input flow controlled by threshold strategy. We defined stationary regime existence conditions and investigated probability characteristics of process for two-dimension Markov process with continuous time which we took as a main model of the specified system. In stationary regime for probability characteristics of the service process were found explicit formulas. Research methods which we used are based on the initial process approximation by the process with bounded state space. Results of the research allow us to evaluate convergence rates of stationary distribution of finite systems with repeated calls to stationary distribution of infinite systems. Method of probability flow equating is used for obtain explicit expressions for stationary system probabilities through the closed path which are defined in a special way. We considered model for one service devices and one place in the queue, which are controlled by threshold strategies.Key words: queue, repeated calls, threshold strategies, stationary regime, convergense rate.Pages of the article in the issue: 52 - 55Language of the article: Ukrainia
Asymptotics of the mild solution of awave equation in three-dimensional space driven by a general stochastic measure
Get PDFWe study the Cauchy problem for a wave equation in three-dimensional space driven by a general stochastic measure. Under some assumptions, we prove that the mild solution tends to zero almost surely as the absolute value of the spatial variable tends to infinity.Key words: asymptotic behavior, stochastic measure, stochastic wave equation, mild solution, Besov space.Pages of the article in the issue: 12 - 17Language of the article: Englis
Minimax-robust estimation problems for sequences with periodically stationary increments observed with noise
Get PDFThe problem of optimal estimation of linear functionals constructed from the unobserved values of a stochastic sequence with periodically stationary increments based on observations of the sequence with stationary noise is considered. For sequences with known spectral densities, we obtain formulas for calculating values of the mean square errors and the spectral characteristics of the optimal estimates of the functionals. Formulas that determine the least favorable spectral densities and the minimax-robust spectral characteristics of the optimal linear estimates of functionals are proposed in the case where spectral densities of the sequence are not exactly known while some sets of admissible spectral densities are specified.Key words: periodically stationary increments, minimax-robust estimate, least favorable spectral density, minimax-robust spectral characteristics.Pages of the article in the issue: 68 - 83Language of the article: Englis
Fast pattern matching method for a bitstream
Get PDFA family of algorithms for fast pattern matching in a bitstream is described. A bitstream is assumed to be stored in a memory and divided into bytes and machine words. The proposed algorithms are based on RZ-family of algorithms for fast pattern matching in a 256-ary text and inherit such their properties as ‘1.5-byte read’, double skip loop, right-to-left text processing as well as a special technique of multiple sliding windows. Beyond that, the new algorithms provide longer average shifts than the best known Binary Faro-Lecroq algorithm and more efficient technique of match checking. Applied to a text close to random, our algorithms outperform all known analogues for all pattern lengths from 20 up to 500.Key words: pattern matching, Faro-Lecroq, fast search, bitstream, search window.Pages of the article in the issue: 36 - 39Language of the article: Ukrainia
Metric dimension of a direct sum and direct product of metric spaces
Get PDFFor an arbitrary metric space (X, d) subset A \subset X is called resolving if for any two points x \ne y \in X there exists point a in subset A for which following inequality holds d(a, x) \ne d(a, y). Cardinality of the subset A with the least amount of points is called metric dimension.In general, the problem of finding metric dimension of a metric space is NP–hard [1]. In this paper metric dimension for particular constructs of metric spaces is provided. In particular, it is fully characterized metric dimension for the direct sum of metric spaces and shown some properties of the metric dimension of direct product.Key words: metric dimension, direct sum of metric spaces, direct product of metric spaces.Pages of the article in the issue: 41 - 46Language of the article: Ukrainia
Control and diagnosis methods for the information system of the enterprise on the principle of adaptive accumulation of diagnostic information
Get PDFThe paper proposes a methodology for building an effective system of self-diagnostics of information systems on the example of Ukrainian enterprises in the metallurgical, energy and chemical industries.The article shows that if the dependence of the probability of issuing information on the time of execution of the element of elementary checks is known, it is enough to carry out checks within a predetermined time, when a given probability value is given.It is investigated that in the information system of the enterprise the self-control organized by means of elementary checks occurs at arbitrary moments of time of functioning of modules on purpose and the relation of probability of delivery of the information which occurs by comparison of deviations from average values.Criteria for the adequacy of diagnostic information in the absence of restrictions on the implementation of basic tests and in the presence of restrictions on the implementation of basic tests.Key words: functional stability, diagnosis, adaptive diagnosis, sufficiency of diagnostic information.Pages of the article in the issue: 69 - 78Language of the article: Ukrainia
Modeling of blood microcirculation, heat and mass transfer in human tissues
Get PDFA mathematical model of the structure of the blood vessels system which provides blood microcirculation in the superficial tissues of human, namely the skin, to provide blood supply as a fluid, which heats / cools, and determines thermoregulation in changes of ambient temperature and overheating / supercooling is proposed. The model is based on data from current studies of the structure of microcirculatory beds based on microCT technologies. The microvascular system is modeled as a fractal binary tree optimized for uniform supply of a nutrient fluid (blood for biological tissues) due to the homogeneous distribution of capillaries, optimal values for diameters, lengths and branching angles in bifurcations of tubes that provide flow distribution with minimal energy costs. The model has been developed to use in computer-based monitoring systems for the planning of physiotherapy procedures for different diseases.Key words: optimal fluid transport systems, microcirculation, mathematical modeling. Pages of the article in the issue: 58-61Language of the article: UkrainianA mathematical model of the structure of the blood vessels system which provides blood microcirculation in the superficial tissues of human, namely the skin, to provide blood supply as a fluid, which heats / cools, and determines thermoregulation in changes of ambient temperature and overheating / supercooling is proposed. The model is based on data from current studies of the structure of microcirculatory beds based on microCT technologies. The microvascular system is modeled as a fractal binary tree optimized for uniform supply of a nutrient fluid (blood for biological tissues) due to the homogeneous distribution of capillaries, optimal values for diameters, lengths and branching angles in bifurcations of tubes that provide flow distribution with minimal energy costs. The model has been developed to use in computer-based monitoring systems for the planning of physiotherapy procedures for different diseases.Key words: optimal fluid transport systems, microcirculation, mathematical modeling.Pages of the article in the issue: 58 - 61Language of the article: Ukrainia
Residual analysis in regression mixture model
Get PDFWe consider data in which each observed subject belongs to one of different subpopulations (components). The true number of component which a subject belongs to is unknown, but the researcher knows the probabilities that a subject belongs to a given component (concentration of the component in the mixture). The concentrations are different for different observations. So the distribution of the observed data is a mixture of components’ distributions with varying concentrations. A set of variables is observed for each subject. Dependence between these variables is described by a nonlinear regression model. The coefficients of this model are different for different components. An estimator is proposed for these regression coefficients estimation based on the least squares and generalized estimating equations. Consistency of this estimator is demonstrated under general assumptions. A mixture of logistic regression models with continuous response is considered as an example. It is shown that the general consistency conditions are satisfied for this model under very mild assumptions. Performance of the estimator is assessed by simulations and applied for sociological data analysis. Q-Q diagrams are built for visual comparison of residuals’ distributions.Key words: asymptotic behavior, generalized estimation equations, mixture model, non-linear regression, minimax weights, variance estimator.Pages of the article in the issue: 8 - 16Language of the article: Ukrainia