Вісник Київського національного університету імені Тараса Шевченка. Серія: фізико-математичні науки
Not a member yet
409 research outputs found
Sort by
Probabilistic models of water resources management on urbanized areas
Get PDFGradual global climate change poses new challenges to the mathematical sciences, which are related to forecasting of meteorological conditions, preparing the infrastructure for possible rains, storms, droughts, and other climatic disasters. One of the most common approaches is synthetic regression-probability models, which use the spatio-temporal probability density functions of precipitation level. This approach is applied to the statistics of precipitation in the Kharkiv region, which shows the tendency to a gradual increase in air temperature, high indices of basic water stress, indices of drought and riverside flood threats. Open data on temperature distributions and precipitation were processed using various probability statistics. It is shown that the lognormal distribution most accurately describes the measurement data and allows making more accurate prognoses. Estimates of drought and flood probabilities in Kharkiv region under different scenarios of climate change dynamics have been carried out. The results of the study can be used for management of water resources on urban territories at global climate warming.
Pages of the article in the issue: 22 - 27
Language of the article: Ukrainia
Two-dimensional generalized instantaneous images and approximations of the Pade type function of two variables
Get PDFGeneralized instantaneous image were introduced by V.K. Dzyaduk [1] in 1981 and proved to be a convenient tool for constructing and studying the Padé approximants and their generalizations (see [2]). The method of generalized instantaneous images proposed by Dzyadyk made it possible to construct and study rational Padé approximants and their generalizations for many classes of special functions from a single position. As an example, the Padé approximants is constructed for a class of basic hypergeometric series, which includes a q-analogue of the exponential function. In this paper the construction of the Pade approximants for the function of two variables is investigated. A two-dimensional functional sequence is constructed, which has a generalized instantaneous image, and rational approximants are determined, which will be generalizations of one-dimensional Padé approximants. The function of the two variables is entirely related to the basic hypergeometric series.Key words: Pade approximation, instantaneous image, hypergeometric series, rational approximation.Pages of the article in the issue: 75 - 80Language of the article: Ukrainia
The Cauchy problem for the heat equation on the plane with a random right part from the Orlicz space
Get PDFThe heat equation with random conditions is a classical problem of mathematical physics. Recently, a number of works appeared, which in many ways investigated this equation according to the type of random initial conditions. We consider a Cauchy problem for the heat equations with a random right part. We study the inhomogeneous heat equation on the plane with a random right part. We consider the right part as a random function of the Orlicz space. The conditions of existence with probability one classical solution of the problem are investigated. For such a problem has been got the estimation for the distribution of the supremum solution.Key words: stochastic processes of the Orlicz space, heat equation, estimation for the distribution of the supremum solution.Pages of the article in the issue: 103 - 109Language of the article: Ukrainia
Analytical properties of sample paths of some stochastic processes
Get PDFThe study of the analytical properties of random processes and their functionals, without a doubt, was and remains the relevant topic of the theory of random processes. The first result from which the study of the local properties of random processes began is Kolmogorov’s theorem on sample continuity with probability one. The classic result for Gaussian random processes is Dudley’s theorem. This paper is devoted to the study of local properties of sample paths of random processes that can be represented as a sum of squares of Gaussian random processes. Such processes are called square-Gaussian. We investigate the sufficient conditions of sample continuity with probability 1 for square-Gaussian processes based on the convergence of entropy Dudley type integrals. The estimation of the distribution of the continuity module is studied for square-Gaussian random processes. It is considered in detail an example with an estimator (correlogram) of the covariance function of a Gaussian stationary random process. The conditions on continuity of correlogram’s trajectories with probability one are found and the distribution of the continuity module is also estimated.Key words: Gaussian process, square-Gaussian process, correlogram, sample continuity.Pages of the article in the issue: 11 - 15Language of the article: Ukrainia
The optimal algorithm for dynamic support of the Voronoi Diagram for a set of points
Get PDFThe article is devoted to the development of a dynamic data structure for solving proximity problems based on the dynamic Voronoi Diagram. This data structure can be used as the core of the common algorithmic space model for solving a set of visualization and computer modeling problems.The data structure is based on the strategy of "divide and rule" for Voronoi diagram construction. Similar to the original algorithm, we store a binary tree that represents the Voronoi diagram, but define three new operations: insert, delete, and balance. To ensure the efficiency of operations, it is proposed to use red-black tree. In general, the proposed data structure shows much better results than the original static algorithm. Compared to existing algorithms, this data structure is both simple and efficient.Key words: dynamic data structures, algorithm, divide and conquer, Voronoi diagram, nearest neighbour, model of common algorithmic space.Pages of the article in the issue: 63 - 68Language of the article: Englis
Projective lattices of tiled orders
Get PDFTiled orders over discrete valuation ring have been studied since the 1970s by many mathematicians, in particular, by Yategaonkar V.A., Tarsy R.B., Roggenkamp K.W, Simson D., Drozd Y.A., Zavadsky A.G. and Kirichenko V.V. Yategaonkar V.A. proved that for every n > 2, there is, up to an isomorphism, a finite number of tiled orders over a discrete valuation ring O of finite global dimension which lie in where K is a field of fractions of a commutatively discrete valuation ring O. The articles by R.B. Tarsy, V.A. Yategaonkar, H. Fujita, W. Rump and others are devoted to the study of the global dimension of tiled orders. H. Fujita described the reduced tiled orders in Mn(D) of finite global dimension for n = 4; 5. V.M. Zhuravlev and D.V. Zhuravlev described reduced tiled orders in Mn(D) of finite global dimension for n = 6: This paper examines the necessary condition for the finiteness of the global dimension of the tile order. Let A be a tiled order. The kernel of the projective resolvent of an irreducible lattice has the form M1f1 +M2f2 + ::: +Msfs, where Mi is irreducible lattice, fi is some vector. If the tile order has a finite global dimension, then there is a projective lattice that is the intersection of projective lattices. This condition is the one explored in the paper.Key words: tiled order, exponent matrix, projective lattice.Pages of the article in the issue: 16-19Language of the article: UkrainianTiled orders over discrete valuation ring have been studied since the 1970s by many mathematicians, in particular, by Yategaonkar V.A., Tarsy R.B., Roggenkamp K.W, Simson D., Drozd Y.A., Zavadsky A.G. and Kirichenko V.V. Yategaonkar V.A. proved that for every n > 2, there is, up to an isomorphism, a finite number of tiled orders over a discrete valuation ring O of finite global dimension which lie in where K is a field of fractions of a commutatively discrete valuation ring O. The articles by R.B. Tarsy, V.A. Yategaonkar, H. Fujita, W. Rump and others are devoted to the study of the global dimension of tiled orders. H. Fujita described the reduced tiled orders in Mn(D) of finite global dimension for n = 4; 5. V.M. Zhuravlev and D.V. Zhuravlev described reduced tiled orders in Mn(D) of finite global dimension for n = 6: This paper examines the necessary condition for the finiteness of the global dimension of the tile order. Let A be a tiled order. The kernel of the projective resolvent of an irreducible lattice has the form M1f1 +M2f2 + ::: +Msfs, where Mi is irreducible lattice, fi is some vector. If the tile order has a finite global dimension, then there is a projective lattice that is the intersection of projective lattices. This condition is the one explored in the paper.Key words: tiled order, exponent matrix, projective lattice.Pages of the article in the issue: 16 - 19Language of the article: Ukrainia
Equivalence between tails, Grand Lebesgue Spaces and Orlicz norms for random variables without Kramer\u27s condition
Get PDFWe offer in this paper the non-asymptotical pairwise bilateral exact up to multiplicative constants interrelations between the tail behavior, moments (Grand Lebesgue Spaces) norm and Orlicz’s norm for random variables (r.v.), which does not satisfy in general case the Kramer’s condition.Key words: Random variable and random vector (r.v.), saddle-point method, tail of distribution, moments, Lebesgue-Riesz, Orlicz and Grand Lebesgue Spaces (GLS); slowly varying functions, Young-Fenchel transform, theorem and inequality of Fenchel-Moreau, Young-Orlicz function, Markov-Chernov’s estimate, non-asymptotical estimates, Kramer’s condition.Pages of the article in the issue: 20-29Language of the article: EnglishWe offer in this paper the non-asymptotical pairwise bilateral exact up to multiplicative constants interrelations between the tail behavior, moments (Grand Lebesgue Spaces) norm and Orlicz’s norm for random variables (r.v.), which does not satisfy in general case the Kramer’s condition.Key words: Random variable and random vector (r.v.), saddle-point method, tail of distribution, moments, Lebesgue-Riesz, Orlicz and Grand Lebesgue Spaces (GLS); slowly varying functions, Young-Fenchel transform, theorem and inequality of Fenchel-Moreau, Young-Orlicz function, Markov-Chernov’s estimate, non-asymptotical estimates, Kramer’s condition.Pages of the article in the issue: 20 - 29Language of the article: Englis
On measure preserving self-homeomorphisms of path spaces of simple stationary Bratteli diagrams
Get PDFBorel measures which are invariant under the tail equivalence relation on path spaces of Bratteli diagrams are considered. We study the following problem: Let Bratteli diagram is fixed. Do every selfhomeomorphisms that preserve such a measure can be approximated by homeomorphisms which are “close to finitary” homeomorphisms? We found some conditions on diagrams for which it is true.Key words: Borel measure, path space, Bratteli diagram, homeomorphism group. Pages of the article in the issue: 30-35Language of the article: EnglishBorel measures which are invariant under the tail equivalence relation on path spaces of Bratteli diagrams are considered. We study the following problem: Let Bratteli diagram is fixed. Do every selfhomeomorphisms that preserve such a measure can be approximated by homeomorphisms which are “close to finitary” homeomorphisms? We found some conditions on diagrams for which it is true.Key words: Borel measure, path space, Bratteli diagram, homeomorphism group.Pages of the article in the issue: 30 - 35Language of the article: Englis
Damping of unisothermal axisymmetric bending vibrations of viscoelastic plates
Get PDFA problem on the forced monoharmonic axisymmetric bending vibrations and dissipative heating of circular viscoelastic plate with the piezoelectric sensors and actuators is considered. Viscoelastic behavior of passive (without piezoeffect) and piezoactive materials is described using the concept of complex moduli which depend on temperature.The nonlinear coupled problem of electrothermoviscoelasticity is solved by numerical methods. The influence of the boundary conditions and temperature of disspative heating on active damping of harmonic vibrations of thin viscoelastic plates with the simultaneous use of sensors and actuators is investigated. For modeling viscoelastic properties of passive and piezoelectric materials, linear models of integral type viscoelasticity are used, which are most effective for simulating the dissipative properties of materials in the linear region. If the material characteristics depend on temperature, investigation of the influence of temperature of dissipative heating is reduced to solution of complicated nonlinear systems of differential equations.Key words: active damping, sensors, actuators. Pages of the article in the issue: 68-71Language of the article: UkrainianA problem on the forced monoharmonic axisymmetric bending vibrations and dissipative heating of circular viscoelastic plate with the piezoelectric sensors and actuators is considered. Viscoelastic behavior of passive (without piezoeffect) and piezoactive materials is described using the concept of complex moduli which depend on temperature.The nonlinear coupled problem of electrothermoviscoelasticity is solved by numerical methods. The influence of the boundary conditions and temperature of disspative heating on active damping of harmonic vibrations of thin viscoelastic plates with the simultaneous use of sensors and actuators is investigated. For modeling viscoelastic properties of passive and piezoelectric materials, linear models of integral type viscoelasticity are used, which are most effective for simulating the dissipative properties of materials in the linear region. If the material characteristics depend on temperature, investigation of the influence of temperature of dissipative heating is reduced to solution of complicated nonlinear systems of differential equations.Key words: active damping, sensors, actuators.Pages of the article in the issue: 68 - 71Language of the article: Ukrainia
Alternative estimate of curve exceeding probability of sub-Gaussian random process
Get PDFInvestigation of sub-gaussian random processes are of special interest since obtained results can be applied to Gaussian processes. In this article the properties of trajectories of a sub-Gaussian process drifted by a curve a studied. The following functionals of extremal type from stochastic process are studied: , and . An alternative estimate of exceeding by sub-Gaussian process a level, given by a continuous linear curve is obtained. The research is based on the results obtained in the work \cite{yamnenko_vasylyk_TSP_2007}. The results can be applied to such problems of queuing theory and financial mathematics as an estimation of buffer overflow probability and bankruptcy probability.Key words: sub-Gaussian process, metric entropy, supremum distribution, trajectory of random process.Pages of the article in the issue: 37 - 39Language of the article: Englis