Вісник Київського національного університету імені Тараса Шевченка. Серія: фізико-математичні науки
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Numerical analysis of free vibrations of open cylindrical shells with elliptical cross section
Get PDFThe natural frequencies and the corresponding vibration modes of open cylindrical shells with an elliptical cross-section and variable thickness are analyzed. Various opening angle of the shell along both the minor and major axes are allowed and various boundary conditions are considered. The numerical solutions are obtained using the finite element package FEMAP with the NASTRAN solver. A number of lowfrequency vibrations are investigated in terms of their dependence on the opening angle along major and minor axes of the shell. The vibration forms for the first ten frequencies with different boundary conditions at the same opening angles are shown.Key words: open cylindrical shells, elliptical cross-section, opening angle, frequency, vibration forms, finite element method.Pages of the article in the issue: 52 - 59Language of the article: Ukrainia
Scheduling as a part of School Management System
Get PDFLearning Management Systems are very popular nowadays. They have many functions to support the learning process, classes home assignments, communications, and progress tracking. However, it lacks the functionality for the management staff like scheduling (planning) and reporting. Here we propose the software solution, which solves this issue and provides the scheduling for the classes in a school or university, considering requirements, limitations, and wishes. An innovative approach was applied to the scheduling problem. This solution is based on the workforce management techniques known previously. The first positive feedbacks from Iraq schools, where we implemented this solution, support us for the next development and improvements of the system.The focus of the paper is the scheduling module of the system developed, the context of the task (the scope), and arguing why it is important. The method from the area of workforce management systems was taken, adopted, and applied to the new task of school scheduling construction. This is the novelty of the presented work.Key words: ---Pages of the article in the issue: 77 - 81Language of the article: Ukrainia
Recurrent algorithm for non-stationary parameter estimation by least squares method with least deviations from ‘attraction’ points for bilinear discrete dynamic systems
Get PDFThe estimation problem of slowly time-varying parameter matrices is considered for bilinear discrete dynamic system in the presence of disturbances. The least squares estimate with variable forgetting factor is investigated for this object in non-classical situation when this estimate may be not unique and additionally ‘attraction’ points for unknown parameter matrices are given at any moment. The set of all above-mentioned estimates of these unknown matrices is defined through the Moore-Penrose pseudo-inverse operator. The least squares estimate with variable forgetting factor and least deviation norm from given ‘attraction’ point at any moment is proposed as unique estimate on this set of all estimates. The explicit form of representation is obtained for this unique estimate of the parameter matrices by the least squares method with variable forgetting factor and least deviation norm from given ‘attraction’ points under non-classical assumptions. The recurrent algorithm for this estimate is also derived which does not require the usage of the matrix pseudo-inverse operator.Key words: recurrent non-stationary parameter estimation, pseudo-inverse operator, bilinear system, least squares method with variable forgetting factor, ‘attraction’ points.Pages of the article in the issue: 71 - 74Language of the article: Ukrainia
One counterexample for convex approximation of function with fractional derivatives, r>4
Get PDFWe discuss whether on not it is possible to have interpolatory estimates in the approximation of a function f \in W^r [0,1] by polynomials. The problem of positive approximation is to estimate the pointwise degree of approximation of a function f \in C^r [0,1] \Wedge \Delta^0, where \Delta^0 is the set of positive functions on [0,1]. Estimates of the form (1) for positive approximation are known ([1],[2]). The problem of monotone approximation is that of estimating the degree of approximation of a monotone nondecreasing function by monotone nondecreasing polynomials. Estimates of the form (1) for monotone approximation were proved in [3],[4],[8]. In [3],[4] is consider r \in N, r>2. In [8] is consider r \in R, r>2. It was proved that for monotone approximation estimates of the form (1) are fails for r \in R, r>2. The problem of convex approximation is that of estimating the degree of approximation of a convex function by convex polynomials. The problem of convex approximation is that of estimating the degree of approximation of a convex function by convex polynomials. The problem of convex approximation is consider in ([5],[6],[11]). In [5] is consider r \in N, r>2. It was proved that for convex approximation estimates of the form (1) are fails for r \in N, r>2. In [6] is consider r \in R, r\in(2;3). It was proved that for convex approximation estimates of the form (1) are fails for r \in R, r\in(2;3). In [11] is consider r \in R, r\in(3;4). It was proved that for convex approximation estimates of the form (1) are fails for r \in R, r\in(3;4). In [9] is consider r \in R, r>4. It was proved that for f \in W^r [0,1] \Wedge \Delta^2, r>4 estimate (1) is not true. In this paper the question ofapproximation of function f \in W^r [0,1] \Wedge \Delta^2, r>4 by algebraic polynomial p_n \in \Pi_n \Wedge \Delta^2 is consider. It is proved, that for f \in W^r [0,1] \Wedge \Delta^2, r>4, estimate (1) can be improved, generally speaking.Key words: approximation of function, Sobolev space, algebraic polynomial, monotone function, convex function.Pages of the article in the issue: 53 - 56Language of the article: Ukrainia
Nonlinear optical properties of metal-alkanoate liquid crystalline media
Get PDFThis work presents the analysis of experimental data on studies of optical and nonlinear optical properties of lyotropic ionic liquid crystals of potassium caprylate doped with electrochromic viologen admixtures, and smectic glasses of thermotropic ionic liquid crystals of cobalt alkanoates homologous series (number of carbon atoms in alkanoate chain n = 7, 9, 11) and their multicomponent mixtures. Prior to performing nonlinear optical experiment the optical absorption spectra for all samples were investigated. Laser induced dynamic grating recording under the action of nanosecond laser pulses was realized, observed and analyzed for the proposed absorptive media. It was discovered that studied materials are characterized by cubic optical nonlinearity and have values of cubic nonlinear susceptibility ?(3) and hyperpolarizability ? comparable with the best characteristics of organic dyes. The possible mechanism of nonlinear response in studied systems was considered on the base of obtained data. The nonlinear response mechanism is connected with nonlinear polarization of ?-electrons in the field of laser radiation.Key words: ionic liquid crystal, viologen, optical spectroscopy, optical nonlinearity.Pages of the article in the issue: 89 - 94Language of the article: Ukrainia
Peculiarities of interaction of Physical vacuum and light waves
Get PDFBased on established representations, reliable facts and phenomena, the proposed model of the interaction of electromagnetic waves with a physical vacuum is studied. It is shown that from the assumption of a physical vacuum as a dielectric medium, the postulate of the constancy of speed of light follows in all inertial reference systems. The explanation of the partial capture of light by a moving medium (the effect of Fizeau), the effect of a gravitational lens, displacement of the spectrum of an electromagnetic wave in a gravitational field is given. The redshift of the spectrum of galaxies may have an alternative explanation not related to their expansion. As a result of this explanation there is no need to use the idea of dark energy.Key words: light, physical vacuum, virtual particles, gravitational lens, red shift, dark energy.Pages of the article in the issue: 95 - 98Language of the article: Ukrainia
Estimation of diffusion parameter for stochastic heat equation with white noise
Get PDFThis paper deals with stochastic differential heat equation which is the typical example of stochastic partial differential equations (SPDE). In particular, paper is devoted to the estimation of diffusion parameter for the random field which is the solution of stochastic differential heat equation for R^d, d = 1, 2, 3. The estimtion of diffusion parameter was constructed in accordance with observations on the grid. It was shown that the constructed estimate is strictly consistent and asymptotically normal, the asymptotic variance was calculated.Key words: stochastic partial differential equations, stochastic differential heat equation, estimate, asymptotical normality, consistency.Pages of the article in the issue: 9 - 16Language of the article: Englis
Consistency of Konker-Bassett estimators in linear regression model
Get PDFAsymptotic properties of Koenker - Bassett estimators of linear regression model parameters with discrete observation time and random noise being nonlinear local transformation of Gaussian stationary time series with singular spectrum are studied. The goal of the work lies in obtaining the requirements to regression function and time series that simulates the random noise, under which the Koenker - Bassett estimators of regression model parameters are consistent. Linear regression model with discrete observation time and bounded open convex parametric set is the object of the studying. For the first time in linear regression model with described stationary time series as noise having singular spectrum, the weak consistency of unknown parameters Koenker - Bassett estimators are obtained. For getting these results complicated concepts of time series theory and time series statistics have been used, namely: local transformation of Gaussian stationary time series, stationary time series with singular spectral density, expansions by Chebyshev - Hermite polynomials of the transformed Gaussian time series values.Key words: linear regression model, regression function, local transformation of Gaussian stationary time series, Koenker - Bassett estimators, consistency.Pages of the article in the issue: 17 - 24Language of the article: Ukrainia
Generalized least squares estimates for mixture of nonlinear regressions
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.Key words: asymptotic behavior, generalized estimation equations, mixture model, non-linear regression, minimax weights.Pages of the article in the issue: 25 - 29Language of the article: Ukrainia
On irreducibility of monomial 7 × 7?matrix over local ring
Get PDFWe consider a monomial n × n-matrix, which corresponds to a cyclic permutation of the length n, over a commutative local principle ideals ring. Non-zero elements of a non-empty set of first columns of the matrix are identity element of the ring and non-zero elements of non-empty set of the rest columns are a fixed non-zero generator element of the Jacobson radical of the ring. It is known if number of identities or number of generator elements is exact 1 or if n < 7 and number of identities is relatively prime to n, then the matrix is irreducible. If the number of identities is not relatively prime to n, then the matrix is reducible. If the Jacobson radical of the ring is nilpotent of degree 2, then the 7 × 7-matrix of considered form with 3 or 4 identities is reducible. It has been shown that the 7 × 7-matrix is irreducible if the degree of nilpotency of the Jacobson radical of the ring is higher than 2. Some necessary conditions of reducibility of this square matrix of arbitrary size are also established.Key words: monomial matrix, irreducible matrix, 7 × 7-matrix, local ring, principle ideal ring, Jacobson radical.Pages of the article in the issue: 37 - 44Language of the article: Ukrainia