Вісник Київського національного університету імені Тараса Шевченка. Серія: фізико-математичні науки
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The main structural components of the STEM-environment of the educational institution
Get PDFThe article deals with the creation of an educational STEM-environment of an educational institution. The definition of the concept of such an educational phenomenon as the STEM-environment of the institution is substantiated. The most important structural components of the STEM-environment of the educational institution and the main tasks of its functioning are identified. The interpretation of the concept of an educational STEM-environment of an educational institution is proposed as the combination of intellectual and material conditions for the implementation of researches, technologies, engineering, integrated knowledge that ensure self-development of a free and active person, realization of the child’s creative potential. The idea that the child\u27s personality is the most important element of the STEM-educational environment which is the complex and open system that is constantly self-developing is outlined.Key words: STEM-education, STEM-educational space, STEM-educational institution.Pages of the article in the issue: 80 - 84Language of the article: Ukrainia
Finding and analysis of the partial mutual diffusion coefficients for binary solutions with chloroform using the complex-associative model
Get PDFIn the article within the complex-associative model of liquid systems the nonlinear diffusion for a number of binary solutions, such as acetone-chloroform, tetrachlorethane-chloroform, diethyl ether-chloroform and benzene-chloroform, is considered: Real binary solutions are replaced by ideal three-component ones, which consist of averaged two associates of substance and solvent and an effective averaged complex, which is the result of quasi-chemical reactions of molecular solutions. The coefficient of mutual diffusion, which nonmonotonically depends on the concentration of the solvent, is represented as a matrix of partial coefficients of mutual diffusion, which are constant values and represent the material parameters of the considered solutions. The method of analytical calculation of numerical values of such quantities when considering the simplest type of one averaged complex is developed. It is shown that the partial coefficients are constant values and the analysis of their values for the considered solutions depending on the structure of the molecules of the substance, enthalpy and temperature is carried out. Based on the proposed approach, the deviation of the calculated «Fick’s» coefficient of mutual diffusion through the matrix of partial coefficients in comparison with experimental data is less than 2.5%.Key words: complex-associative model, nonlinear diffusion, binary solution, partial coefficients mutual diffusion coefficient.Pages of the article in the issue: 97 - 100Language of the article: Ukrainia
Properties of -sub-Gaussian stochastic processes related to the heat equation with random initial conditions
No full textIn this paper, there are studied sample paths properties of stochastic processes representing solutions (in sense) of the heat equation with random initial conditions given by -sub-Gaussian stationary processes. The main results are the bounds for the distributions of the suprema for such stochastic processes considered over bounded and unbounded domains.Key words: ?-sub-Gaussian processes, heat equation, random initial condition, distribution of supremum.Pages of the article in the issue: 17 - 24Language of the article: Englis
The conditions of existence with probability one of generalized solutions of Cauchy problem for the heat equation with a random right part
Get PDFThe subject of this work is at the intersection of two branches of mathematics: mathematical physics and stochastic processes. The influence of random factors should often be taken into account in solving problems of mathematical physics. The heat equation with random conditions is a classical problem of mathematical physics. In this paper we consider a Cauchy problem for the heat equations with a random right part. We study the inhomogeneous heat equation on a line with a random right part. We consider the right part as a random function of the space Sub?(?). The conditions of existence with probability one generalized solution of the problem are investigated.Using this results one can construct modeless, which approximate solutions of such equations with given accuracy and reliability in the uniform metric.Key words: Sub?(?) stochastic processes, heat equation, generalized solution. Pages of the article in the issue: 42-49Language of the article: EnglishThe subject of this work is at the intersection of two branches of mathematics: mathematical physics and stochastic processes. The influence of random factors should often be taken into account in solving problems of mathematical physics. The heat equation with random conditions is a classical problem of mathematical physics. In this paper we consider a Cauchy problem for the heat equations with a random right part. We study the inhomogeneous heat equation on a line with a random right part. We consider the right part as a random function of the space Sub?(?). The conditions of existence with probability one generalized solution of the problem are investigated.Using this results one can construct modeless, which approximate solutions of such equations with given accuracy and reliability in the uniform metric.Key words: Sub?(?) stochastic processes, heat equation, generalized solution.Pages of the article in the issue: 42 - 49Language of the article: Englis
Interferometry feedback in the laser resonator. Parametric model.
Get PDFThe article is devoted to an alternative view on the explanation of the mechanism of action of devices based on laser feedback interferometry (LFI-model), which is caused by contradictions between the theory of existing models and practical results. A view other than the Lang-Kobayashi model (LK model) and the parametric LFI model (P model) are proposed. Due to the theory, which is based on the parametric properties of the LFI-model, the level of advantage of LFI technology over traditional technologies is quantitatively substantiated. The article gives an example of calculating the useful signal power. It is calculated that at a distance of 500 meters, the signal according to the P-model is 34 dB higher than the signal calculated by traditional models. Thus, from the traditional models follows the inverse square dependence of the signal-to-noise ratio (S / N ratio, hereinafter - SNR) on the distance to the target l_t, viz.: SNR ~ l_t^{-2}. In practice, the SNR is much higher. Within the P-model, another dependence of SNR on l_t, is theoretically proved and experimentally confirmed, viz.: SNR ~ (l_t * ln l_t^2)^{-1/2}. Traditional models do not consider the presence of a useful signal in the pump current, while, in fact, its power is more than 10 times greater than the radiation power in the resonator. The P-model eliminates contradictions between theoretical models and practical results.Key words: interferometry, LFI model, pump current.Pages of the article in the issue: 62 - 69Language of the article: UkrainianThe article is devoted to an alternative view on the explanation of the mechanism of action of devices based on laser feedback interferometry (LFI-model), which is caused by contradictions between the theory of existing models and practical results. A view other than the Lang-Kobayashi model (LK model) and the parametric LFI model (P model) are proposed. Due to the theory, which is based on the parametric properties of the LFI-model, the level of advantage of LFI technology over traditional technologies is quantitatively substantiated. The article gives an example of calculating the useful signal power. It is calculated that at a distance of 500 meters, the signal according to the P-model is 34 dB higher than the signal calculated by traditional models. Thus, from the traditional models follows the inverse square dependence of the signal-to-noise ratio (S / N ratio, hereinafter - SNR) on the distance to the target l_t, viz.: SNR ~ l_t^{-2}. In practice, the SNR is much higher. Within the P-model, another dependence of SNR on l_t, is theoretically proved and experimentally confirmed, viz.: SNR ~ (l_t * ln l_t^2)^{-1/2}. Traditional models do not consider the presence of a useful signal in the pump current, while, in fact, its power is more than 10 times greater than the radiation power in the resonator. The P-model eliminates contradictions between theoretical models and practical results.Key words: interferometry, LFI model, pump current.Pages of the article in the issue: 62 - 69Language of the article: Ukrainia
Some properties and estimates for ?-sub-Gaussian stochastic processes
Get PDFIn this paper, there are studied properties of stochastic processes belonging to the spaces of ?-sub-Gaussian random variables Sub_? (?). For the processes defined on R, we obtain conditions for boundedness and continuity with probability 1, estimates for the distribution of the supremum are also derived.
Pages of the article in the issue: 18 - 22
Language of the article: Ukrainia
Asymptotic normality of the least squares estimate in trigonometric regression with strongly dependent noise
Get PDFThe least squares estimator asymptotic properties of the parameters of trigonometric regression model with strongly dependent noise 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 least squares estimator of regression model parameters are asymptotically normal. Trigonometric regression model with discrete observation time and open convex parametric set is research object. Asymptotic normality of trigonometric regression model parameters the least squares estimator is research subject. For obtaining the thesis 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, spectral measure of regression function, admissibility of singular spectral density of stationary time series in relation to this measure, expansions by Chebyshev-Hermite polynomials of the transformed Gaussian time series values and it’s covariances, central limit theorem for weighted vector sums of the values of such a local transformation and Brouwer fixed point theorem.Key words: trigonometric regression model, regression function, random noise, local transformation of Gaussian stationary time series, the least squares estimator, singular spectral density, spectral measure of regression function, -admissibility, expansions by Chebyshev-Hermite polynomials, Hermite rank, asymptotic normality.Pages of the article in the issue: 24 - 41Language of the article: Ukrainia
Applying information technologies to mathematical education of IT specialists in English-speaking academic groups
Get PDFKnowledge of the basic theoretical foundations and possession of the skills of applying Mathematical Analysis, Differential Equations, Linear Algebra, Analytic Geometry, Discrete Mathematics, Numerical Methods, Theory of Probability and Mathematical Statistics are important for the professional training of future specialists in the field of information technologies. Since future specialists in the field of information technology require a deep mathematical training, the curricula of IT specialties usually contain various mathematical disciplines from this list. A specialist of any IT profile must have specific professional features and competencies. These characteristics of future IT professionals should preferably be formed in the process of studying both special and general scientific disciplines. The result of the educational process is formation of both hard and soft skills of students.This article is devoted to the study of some features of the use of information technology in the process of teaching some questions of mathematical disciplines in English to students of IT profile who are not native speakers of this language.Key words: teaching mathematics to IT specialists, teaching mathematics in English, information technologies.Pages of the article in the issue: 70 - 75Language of the article: Englis
S-boson production in the reaction of Coulomb scattering of a nucleus by a proton or electron
Get PDFThe production cross-section of the beyond the standard model (BSM) scalar boson (S boson) have been considered it the article. Scalar boson produced via photon fusion reaction in the deep inelastic scattering of a charged particle (proton or electron) on heavy nucleus of the target. This process is one of the possible mechanisms of BSM boson production at the SHiP (Search for Hidden Particles) experiment at the CERN LHC and may be dominating among others processes due to large nuclear charge. Previously [1], the amplitude and the production cross-section of this reaction were found. The found cross-section was analyzed for the case of proton scattering on the lead nucleus and compared with the production cross-section in the decay of Ds meson. In this paper we make estimate of the process more accurate and consider also electron-nucleus scattering. It was found that the photon fusion reaction pZ \to S may be effective only in the case of massless S boson.Key words: SHiP, production cross-section, BSM scalar boson, photon fusion reaction.Pages of the article in the issue: 88 - 89Language of the article: Ukrainia
About one method of evaluating the effectiveness of advertising text
Get PDFThe article considers the method of evaluating the effectiveness of the textual content of the advertising message. The basis of the proposed method is the linguistic principles, in which the effectiveness of the text is analyzed from the view of the decoding of information by the target recipient of the message. Materials used for the study were the texts used in SEO promotion of information resources, the method is based on the approach of breaking the text into keywords and phrases. The method of evaluating the effectiveness of the text is based on an analogue of the method of mechanical verification of the relevance of the text by the search engine, which was expanded by the parameters of expert evaluation of the quality of text construction.Key words: advertising text; text effectiveness in advertising; verbal and non-verbal components; structure of the advertisment; relevance index.Pages of the article in the issue: 44 - 48Language of the article: Ukrainia