Вісник Київського національного університету імені Тараса Шевченка. Серія: фізико-математичні науки
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Light source with variable wavelength based on acousto-optical deflector
Get PDFThe proposed work analyzes the design features of the acousto-optical de?ector and ?lter on paratelurite. It is shown that under certain conditions the acousto-optical de?ector can be used as an acousto-optical ?lter (as an element that performs spectral ?ltering of the incident light beam). The fundamental possibility of creating a monochromatic light source with a variable wavelength and a spectrum width of about 5 nm using an acousto-optical de?ector as an element that adjusts the original wavelength is shown experimentally. As a broadband light source in this system, a semiconductor laser operating in subthreshold mode was used. The dependence of the output wavelength on the acoustic frequency is obtained. The comparison of experimental data with the calculated ones is given, it is shown that they have small di?erences.
Pages of the article in the issue: 116 - 119
Language of the article: Ukrainia
About audience overlaps in the social media
Get PDFIn this paper we provided the definition of the Audience overlap network, as well as proposed a simple algorithm to compute overlap between two users on social media based on public data about their followers. There was proposed an alternative approach for computing overlaps based only on public data about users. This approach allows to include content overlap and activity patterns signals to be incorporated into more general statistical models featuring other covariates such as influencers’ direct engagement in shared conversations; relative influencer sizes and histories and links to similar third-party content to recover otherwise censored network structures and properties. For validate results there was designed a calibration process which utilizes Evolution Strategies algorithm to find a set of conditions which will make Audience overlap network built using similarity measures structurally equivalent to the Audience overlap network build on full information about followers.
Pages of the article in the issue: 69 - 73
Language of the article: Englis
Research of e-sports development world tendencies on the base of Data Mining methods
Get PDFThe article analyzes the current state and trends of e-sports in the world by studying the time series of the number of requests from Internet users, obtained through the use of Google Trends. The positive and negative consequences of e-sports development in the world have been identified. The forecasting of world tendencies of e-sports by means of methods of data mining is carried out. Using the application of multivariate adaptive regression splines (MARSplines), a model of the relationship between the predictor - a time indicator and the dependent variable - the time series of the number of requests of Internet users, which are non-monotonic in nature and provide the possibility of regression switching points. The adequacy of the constructed model is proved by means of regression statistics and histogram of correspondence of residuals to the normal distribution law. The expediency of using the method of multivariate adaptive regression splines (MARSplines) before other statistical methods is substantiated.
Pages of the article in the issue: 117 - 124
Language of the article: Ukrainia
Study of nanosized gold films by scanning tunneling microscopy
Get PDFIt was shown that despite the difference in the morphology of thin gold films obtained by different methods and on different substrates, the films mainly consist of spherical nanoparticles. The linear dimensions of individual surface objects were determined using the example of a gold film on mica. Analysis of the surface morphology showed that its structural formations are evenly distributed and have sizes from 250 nm to 500 nm. Upon receipt of gold nanofilms by magnetron sputtering on a glass substrate, the size of individual gold nanoparticles ranges from 20 nm to 80 nm. When ion spraying on a substrate of polished monocrystalline silicon, the size of individual gold nanoparticles ranges from 2 nm to 10 nm. The union of individual nanoparticles into large elongated nanoobjects up to 20-40 nm in size is observed. Thus, having the opportunity to compare data on the mode of vacuum deposition (substrate temperature, beam density, deposition time, etc.), as well as surface relief, you can develop technologies for obtaining a surface with a given set of properties, as well as develop new methods of gold deposition on different surfaces. The obtained results are very important for application in biology and medicine. They make it possible to create different types of sensors and diagnostic tests.
Pages of the article in the issue: 42 - 45
Language of the article: Ukrainia
Damped steady-state resonant sloshing in a container of circular cross-section for arbitrary periodic nonparametric forcing
Get PDFNonlinear modal Narimanov-Moiseev—type equations are investigated to study resonant sloshing in a vertical cylindrical tank. The tank moves periodically in the space with the forcing frequency close to the lowest natural sloshing frequency. We show that the considered sloshing problem can to within the higher-order asymptotic terms be reduced to the case of orbital tank motions in the horizontal plane. Analytical solutions of the secular system which couples the dominant amplitudes of the steady-state sloshing are analytically solved. Effect of viscous damping is accounted. The results are compared with experimental measurements conducted by diverse authors for longitudinal and circular orbital tank excitations. A parametric analysis of the amplitude curves is done to clarify how the steady-state wave regimes and their stability change versus the forcing frequency and the semi-axes ratio of the elliptic orbit. The main result consists of confirming the experimental disappearance of the counter-directed swirling wave mode (relative to the elliptic orbit direction) when passaging to the circular orbit.
Pages of the article in the issue: 97 - 100
Language of the article: Ukrainia
On the problem of calculating shear deformations in prismatic bars made of polymer materials under tension with torsion
Get PDFThe process of creep of prismatic rods made of linear-viscoelastic polymeric materials under combined loading is considered. Defining equations that determine the relationship between strains, stresses and time are given in the form of a superposition of shear and bulk strain. The object of study is prismatic bars made of fiberglass ST-1. The area of linearity of the model is substantiated on the basis of the hypothesis of the existence of the creep function, which is built on the yield curves, a single diagram of long-term deformation and the statistical value of the quantile of statistics. The region of linear-elastic deformation is recognized based on the fulfillment of the condition of existence of a single creep function. The defining equations of the model contain a set of functions and coefficients determined from the basic experiments. On the basis of the relations between the kernels of the one-dimensional stress state, the parameters of the kernels under the condition of a complex stress state are determined. The linearity of viscoelastic properties is given by the Boltzmann-Voltaire equations. The fractional-exponential kernels of heredity are chosen as the kernels of heredity. The obtained values of the core parameters are used to calculate the creep deformations of prismatic bars made of ST-1 fiberglass under conditions of simultaneous tensile tension.
Pages of the article in the issue: 115 - 118
Language of the article: Ukrainia
Numerical simulation of the thermo-stress-strain state of elements under 3D printing
Get PDFThe paper is devoted to the assessment of the thermo-stress-strain state of elements of structures obtained by 3D printing using FDM (Fusing Deposition Modeling) technology. Three stages of solving this problem are considered: (1) - mathematical formulation of the problem, that includes universal balance relations, constitutive equations of mechanical behavior of the material and is based on the model of growing bodies; (2) the technique of finite-element solution with increasing mesh due to the addition of new elements; (3) - study of a specific problem of growing plate-like element by polymer PLA (polylactide) with temperature-dependent physical properties. Options of deposed layers of different thickness are considered. The residual stress-strain state of the body has a two-scale structure, which reflects the change of state characteristics in the scale of body size, as well as the thickness of the layers. As the thickness of the layers increases, the average values of the residual stresses decrease, but the amplitude of the stress fluctuations along the thickness of the layer slightly increase.
Pages of the article in the issue: 70 - 75
Language of the article: Ukrainia
Stochastic models in artificial intelligence development
Get PDFIn this paper, we consider some properties of stochastic random matrices of large dimensions under conditions of independence of matrix elements or under conditions of independence of rows (columns). The main properties of stochastic random matrices spectrum are analyzed and the result of convergence to 0 is proved of almost all eigenvalues. Also, the application of these results to clustering problems and selection of the optimal number of clusters is considered. Note that the results obtained in this work are consistent with the Marchenko - Pastur theorem on the asymptotic distribution of eigenvalues of random matrices with independent elements. The results proved in this paper can be interpreted as a law of large numbers and will be used in the study of the asymptotic behavior of the maximum.
Pages of the article in the issue: 53 - 57
Language of the article: Ukrainia
Monte-Carlo method for option pricing in sub-diffusive arithmetic models
No full textThis paper focuses on applying the Monte Carlo approach to option pricing in markets with illiquid assets. Anomalous sub-diffusion is a well-known model for describing such markets when relatively long periods without any trading are observed. For constructing sub-diffusive models we need to replace a calendar time t with some stochastic processes S(t), which is called inverse subordinator. The inverse subordinator S(t) means first hitting time and is based on subordinator processes. In this paper, we propose to use the gamma process as a subordinator for Bashelie sub-diffusion model. Using well-known properties for gamma and inverse gamma processes we find the covariance structure of fractional Bachelier model with FBM time-changed by gamma process and then explore the asymptotic behavior of it. Then we apply the Monte-Carlo method and propose a procedure of option pricing for the Bashelie sub-diffusion model. For this aim, we use iterative schemes for simulating N scenarios of stock prices for our models. Finally, we demonstrate numerical results.
Pages of the article in the issue: 85 - 92
Language of the article: Englis
Optimization of power distribution of network channels based on Orlin\u27s algorithm
Get PDFThe article proposes an algorithm for solving the problem of optimal distribution of the capacity of data transmission channels between providers and Internet users. A mathematical model of the problem of distribution of a limited homogeneous resource with transport-type constraints is formulated. A solution method based on Orlin\u27s stream algorithm is considered. A practical application of the algorithm for solving a real distribution problem is proposed. The results of the capacity of the channels of the computer network are obtained with a perspective increase in the capacity of the connections represented by the intervals of the planned changes. An analysis of the solutions obtained with different number of switching servers was made, conclusions about the choice of the provider to meet the optimal information needs of users were made.
Pages of the article in the issue: 63 - 68
Language of the article: Ukrainia