Вісник Київського національного університету імені Тараса Шевченка. Серія: фізико-математичні науки
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Comparing of educational programs in terms of achievement of competencies and learning outcomes of compulsory educational components
Get PDFThe most important elements of educational programs are the educational components (disciplines), as well as the competencies and learning outcomes they provide. The article presents a comparative analysis of some compulsory disciplines of the educational and professional program "Informatics" of the first (bachelor\u27s) level of higher education in the field of knowledge 12 "Information Technology", specialty 122 "Computer Science" with disciplines of educational and professional programs of the same level and specialties of other institutions of higher education. The work analyzes the educational and professional program "Computer Science" of the first (bachelor\u27s) level of higher education in the specialty 122 "Computer Science". It is implemented by the Faculty of Computer Science and Cybernetics of Taras Shevchenko National University of Kyiv in terms of comparing compulsory educational components educational-professional program "Informatics" and provided (achievable) standard learning outcomes and competencies with compulsory educational components of other educational programs.
Pages of the article in the issue: 129 - 136
Language of the article: Ukrainia
On the distribution of stresses near the crack in a toroidal shell with a flexible coating
Get PDFElastic equilibrium of shallow toroidal shell loaded by internal pressure and containing the cross-cutting crack located along equator or throat of the shell has been studied in the two-dimensional formulation. The shell is reinforced by coating on one of the face surfaces. The crack in the shell with a flexible coating is simulated by a cuts with eccentrically hinge joint edges. The boundary problem for equations of classical shell theory with interrelated conditions of tension and bending along the cutting line is formulated within the framework of such model. Singular integral equation for the unknown jump of normal displacement on the crack edges has been elaborated. Based on asymptotical solutions of integral equation obtained using the small parameter method forces and moments intensity factors in the vicinity of the defect tips are defined. Their dependences of on the parameters of shell curvature and form parameter are investigated. It is established that the reinforcement of the shell leads to a decrease in the force intensity factor and to the appearance of a non-zero moment intensity factor.
Pages of the article in the issue: 67 - 70
Language of the article: Ukrainia
Asymptotic behavior of the module of the characteristic Cantor distribution function
Get PDFThe asymptotic behavior of the modulus of a characteristic function of a random variable, the distribution function of which is the classical singular Cantor function, is investigated. The emphasis is on calculating the upper bound of the modulus of the characteristic Cantor distribution function. The probabilistic measure corresponding to Cantor\u27s distribution belongs to the class of Bernoulli\u27s symmetric convolutions, the interest in which is considerable today. Bernoulli\u27s symmetrical convolutions were actively studied by both domestic mathematicians: M. Pratsovyty, G. Turbin, G. Torbin, J. Honcharenko, O. Baranovsky and others, and foreign ones: Erdos P, Peres Y, Schlag W, Solomyak B, Albeverio, S and other. The value of the upper bound of the modulus of the characteristic function plays an important role in the problem of determining the Lebesgue structure of distributions of sums of probably convergent random series with independent discrete terms (random values of the Jessen-Winter type).
The exact value of the upper bound of the module of the characteristic Cantor distribution function is found in the article.
Pages of the article in the issue: 63 - 68
Language of the article: Ukrainia
On estimating exponential moment for the simultaneous renewal time for two random walks on a half line
Get PDFIn this paper, we consider conditions for existence and finitness for an exponential moment for the time of the simultaneous hitting of a given set by two random walks on a half-line. It is addmitted that random walks may be time-inhomogeneous. Obtained conditions that guarantee existence of the hitting time for individual chains and simultaneous hitting time for both chains. It is shown, how the estimates could be calculated in practical applications.
Pages of the article in the issue: 26 - 31
Language of the article: Ukrainia
Algorithm for determining the optimal flow in Supply Chains, considering multi-criteria conditions and stochastic processes
Get PDFOne of the main criteria for planning and evaluating supply chains is the indicator of the flow capacity, which affects the structure of the supply graph, terms of supply, risks, opportunities and the need to differentiate supply channels. The paper analyse an algorithm for calculating the optimal value of the flow in supply chains, taking into account the requirements and expectations of key stakeholders in the supply process. The algorithm provides for finding a balance between "requirements" and "expectations" by mathematical modelling of a multicriteria problem for each side of the supply process. It proposed to use the obtained parameters for calculating multicriteria problems as "input" data for an iterative algorithm for finding the optimal flow value. The proposed model allows one to take into account probabilistic fluctuations in processes by using stochastic programming. The model allows the parties to the procurement process to consider alternative proposals before the formation of contractual obligations, that is, based on residual capacity after choosing the best alternative.
Pages of the article in the issue: 109 - 116
Language of the article: Ukrainia
Non-stationary problem of elasticity for a quarter-plane
Get PDFThe plane problem for an elastic quarter-plane under the non-stationary loading is solved in the article. The method for solving was proposed in the previous authors’ papers, but it was used for the stationary case of the problem there. The initial problem is reduced to the one-dimensional problem by using the Laplace and Fourier integral transforms. The one-dimensional problem in transform space is written in vector form. Its solution is constructed as the superposition of the general solution for the homogeneous equation and the partial solution for the inhomogeneous equation. The general solution for the homogeneous vector equation is derived using the matrix differential calculations. The partial solution is found through Green’s matrix-function. The derived expressions for displacements and stresses are inverted by using of mutual inversion of Laplace-Fourier transforms. The solving of the initial problem is reduced to the solving of the singular integral equation regarding the displacement function at the one of the boundary of the quarter-plane. The time discretization is used, and the singular integral equation is solved using the orthogonal polynomials method at the fixed time moments. Based on numerical research some important mechanical characteristics depending on the time and loading types were derived.
Pages of the article in the issue: 28 - 33
Language of the article: Englis
Representation of solutions to the plane elasticity problems for a rectangular domain via Vihak’s functions
Get PDFThe paper presents the generalization of the direct integration method for the governing equations of the basic elasticity problems for the bounded domains with corner points. An important stage in the realization of the method is the representation of the unknown stress-tensor components via the key functions. The selection of these functions is motivated by some specific features of the problems and thus was regarded as a weakest part of the solution algorithm. Herein, we suggest an universal approach for the selection of the key functions, which we started to call the Vihak functions (to honor Prof. Vasyl M. Vihak, the founder and developer of the direct integration method) by using the integral relationships derived from the equilibrium equations. The approach is illustrated by the solution of a plane elasticity problem for an elastic rectangle. The relationship between Vihak’s function for the considered problem and the classical biharmonic Airy stress function is shown.
Pages of the article in the issue: 123 - 126
Language of the article: Ukrainia
Vortex dynamics of junction flows
Get PDFGroup constructions of bluff bodies are widely used in bridge construction practice. The junction flows of such structures are characterized by considerable complexity, nonstationarity and instability. In the vicinity of bluff bodies, systems of horseshoe vortex structures, shear layers, separated regions, jet flows, wake vortices and vortex Karman’s streets are formed. The study of the features of the generation and evolution of vortex and jet flows, the mechanisms of interaction of these flows with streamlined surfaces requires considerable effort during numerical and physical modeling. The purpose of the work is to determine the features of vortex and jet flow in the region of junction of three-row pile grillage with a rigid flat surface. Experimental studies were carried out in laboratory conditions in a hydrodynamic channel, where the three-row group of cylinders was installed on the hydraulically smooth rigid surface. Visual investigations and measurements of the velocity field were carried out inside and around the three-row grillage. The features of the formation and evolution of vortex and jet flows inside and near the cylindrical group were established. Integral and spectral characteristics of the velocity fluctuation field were obtained.
Pages of the article in the issue: 25 - 28
Language of the article: Ukrainia
The flow of a liquid in a cylindrical duct with diaphragms of a rectangular profile
Get PDFThe flow of a viscous incompressible liquid in a cylindrical duct with two serial diaphragms of a rectangular profile is studied by the numerical solution of the unsteady Navier-Stokes equations. The discretization procedure is based on the finite volume method using the TVD scheme for the discretization of the convective terms and second order accurate in both space and time difference schemes. The resulting system of non-linear algebraic equations is solved by the PISO algorithm. It is shown that the fluid flow in the region between the diaphragms is non-stationary and is characterized by the presence of an unstable shear layer under the certain parameters. A series of ring vortices is formed in the shear layer that causes quasi-periodic self-sustained oscillations of the velocity field in the vicinity of the orifice of the second diaphragm. In comparison with the case of rounded diaphragms, an increase in the maximum jet velocity is observed, which in turn leads to an increase in the frequency of self-sustained oscillations and a decrease in the Reynolds numbers at which quasi-periodic oscillations are excited.
Pages of the article in the issue: 76 - 81
Language of the article: Ukrainia
Determination of parameters of the primary mode of the tunung fork type solid-state gyroscope
Get PDFThe use of a tuning fork resonator as sensitive element of a gyroscopic sensor has some advantages in comparison with other types of the resonators. For instance, it allows to compensate lateral accelerations in the direction perpendicular to the axis of rotation. At the same time, the task of accurate determination of the carrying frequency of the primary mode of a non-moving tuning fork is of great importance. Thus, in [1] the analysis of vibrations of a gyroscope is built on the evaluation of the first frequency of flexure vibrations of Timoshenko\u27s beam with one rigidly fixed end [2]. As a result, the sensing frequencies of the Bryan\u27s splitting pair [3] of the fork lie below the frequency of Timoshenko\u27s beam, and the resonant frequency of the non-moving tuning fork remained uncertain. The purpose of a present paper is to establish this frequency. In the statement of a problem, concerning real geometric dimensions of the tuning fork elements, we assume that the length of the tuning fork rods l is much more then the radius of the base r: r/l << 1. Then, frequencies of the flexure vibrations of the half-ring lie much higher than the frequencies of the bending vibrations of the rods. It allows us to give a solution for the base in a quasi-static approximation, and to take into account the dynamics of the tuning fork in the solution for bimorph piezoceramic rods. Conditions of coupling between the rods and the half-ring are reduced to the conditions of elastic fixing of the rods, which take into account the geometric parameters r and l.
Pages of the article in the issue: 82 - 87
Language of the article: Ukrainia