Вісник Київського національного університету імені Тараса Шевченка. Серія: фізико-математичні науки
Not a member yet
409 research outputs found
Sort by
Two-dimensional generalized instantaneous images and approximations of the Pade type function of two variables, which is a generalization of hypergeometric series
Get PDFGeneralized instantaneous image were introduced by V.K. Dzyaduk in 1981 and proved to be aconvenient tool for constructing and studying the Padé approximants and their generalizations. The method of generalized instantaneous images proposed by Dzyadyk madeit possible to construct and studyrational 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, namely with the q-analog of the exponent e_q.
Pages of the article in the issue: 95 - 100
Language of the article: Ukrainia
Scene Change Localization in a Video
Get PDFMillions of videos are uploaded each day to Youtube and similar platforms. One of the many issues that these services face is the extraction of useful metadata. There are a lot of tasks that arise with the processing of videos. For example, putting an ad is better in the middle of a video, and as an advertiser, one would probably prefer to show the ad in between scene cuts, where it would be less intrusive. Another example is when one would like to watch only through the most interesting or important pieces of video recording. In many cases, it is better to have an automatic scene cut detection approach instead of manually labeling thousands of videos. The scene change detection can help to analyze video-stream automatically: which characters appear in which scenes, how they interact and for how long, their relations and importance, and also to track many other issues. The potential solution can rely on different facts: objects appearance, contrast or intensity changed, other colorization, background chang, and also sound changes.
In this work, we propose the method for effective scene change detection, which is based on thresholding, and also fade-in/fade-out scene analysis. It uses computer vision and image analysis approaches to identify the scene cuts. Experiments demonstrate the effectiveness of the proposed scene change detection approach.
Pages of the article in the issue: 57 - 62
Language of the article: Ukrainia
Investigation of structural features of SARS-CoV-2 S-protein interaction with lipid membranes by small-angle neutron scattering
Get PDFThe effect of SARS-CoV-2 coronavirus S-protein on the structural parameters of the model lipid membrane on dimyristoylphosphatidylcholine (DMPC) systems with cholesterol and melatonin impurities was studied by the method of small angle neutron scattering. It is shown that an increase in the concentration of melatonin in the lipid membrane leads to a decrease in the thickness of the lipid bilayer, and an increase in the concentration of cholesterol leads to an increase in it. It has been suggested that increasing the concentration of melatonin in the membrane prevents the interaction of coronaviral S-protein with the lipid membrane of the cell. In the presence of cholesterol impurities in the system, the interaction of the lipid membrane with the active part of the S-protein occurs depending on the phase state of the lipid. Thus, when the lipid is in the gel phase (at 10 ° C), the active part of the S-protein does not change the structural parameters of the lipid bilayer, i.e. the interaction between the lipid membrane and the active part of the S-protein does not occur. At 37 ° C, when the lipid is in the liquid crystalline phase, the addition of RBD SARS-CoV-2 in the system DMPC / 30% Cholesterol / D2O leads to a decrease in membrane thickness, indicating the interaction of S-protein with the membrane.
Pages of the article in the issue: 127 - 130
Language of the article: Ukrainia
Modeling and Control for Complicated Education Systems
Get PDFThe paper aims to investigate the model of a complicated educational system, built on the basis of general principles of mathematical modeling of complex hierarchical systems. The model consists of three components, the interaction between them is provided by certain conditions. This interaction is the basis for modeling the main parameter of the study - the level of funding required for higher education.
An important feature of the modeled system is its controllability, because in a real educational system the controlling influence can be performed as an external management of the system to ensure an average level of funding. For the initial problem of optimal control, which consists of a parabolic equation with a multivalued reaction function of the system, the approximate synthesis problem for a certain class of target functionals with control restrictions is solved.
The results of modeling can be used in the development of various models of complex systems, as well as for decision-making in public administration and higher education management.
Pages of the article in the issue: 110 - 115
Language of the article: Ukrainia
Real-Time Analysis and Processing of Cardiogram Signals
Get PDFAnalysis of Electrocardiogram (ECG) signals is an important task to save and enhance human life because a major cause of death is heart disease and the consequences. In many cases, early diagnostics of such problems can save and prolong life.
In this work, we develop and present an approach to the real-time detection of Atrial Fibrillation (AF) Arrhythmia, which is a common cardiac arrhythmia affecting a large number of people. Being undetected, it develops into chronic disability or even early mortality. At the same time, This disease is hard to diagnose, especially in its early stage. A real-time automatic and non-invasive effective detection is needed to help diagnose this kind of health problem early. In-time medical intervention can save human life. ECG as a record of the heart electrical activity is widely used for detecting different heart disabilities. At the same time, AF is hard to detect due to its non-regular nature, and also because the performance of detection models depends largely on the quality of data and careful feature engineering.
The research is based on the dataset from PhysioNet Computing in Cardiology Challenge 2017. It contains 8528 single-lead ECG recordings of short-term heart rhythms (9-61 sec.). Our method and the trained model reach the known state-of-the-art results in this field, but, at the same time, it is much less computationally intensive, and, thus, less power consumptive to be implemented in an embedded device.
Pages of the article in the issue: 108 - 113
Language of the article: Ukrainia
Influence of the internal dynamics of the interacting coherent vortex structures to the generated sound field
Get PDFThe article is dedicated to the glowing memory of the talented Ukrainian scientist-mechanic, professor, doctor of physical and mathematical sciences Vyacheslav Vladimirovich Meleshko. The sound fields of several coherent vortex structures interacting with each other were calculated using the moment model (MZS-model) of the first and second orders. In the first-order MZS-model, vortices are described by point vortices, in the second-order MZS-model--by Kirchhoff vortices. Sound fields as a result of vortex interaction are calculated using the Lighthill\u27s acoustic analogy under Powell\u27s formulation. The spectrum of the sound field in the description of coherent vortices by point vortices is characterized by a single frequency band, which reflects the motion of the vortex centers of vortices (large-scale vortex movements). Taking into account the inner vortex dynamics leads to the expansion of spectrum and level increasing of calculated sound: the lower band describes the motion of the vorticity centers of spots, the higher band describes the internal dynamics of the vorticity. It is shown that large-scale vortex movements can be modeled by point vortices, when the sound spectrum of distributed vortices is clearly divided into bands and the width of the lower frequency band is close to the width of the sound spectrum from point vortices. The presence of an upper frequency band in the sound field of interacting vortex spots does not allow us to describe the distributed vortices as point vortices when constructing a sound source, since such a simplification leads to a significant underestimation of the level of the calculated sound field.
Pages of the article in the issue: 51 - 54
Language of the article: Ukrainia
Justification of application of nonlinear viscoelasticity model of Rabotnov\u27s model type in creep problems
Get PDFThe relationship between the components of the strain tensor, stress tensor and time is given by the defining equations of the hereditary type, which are written based on the hypothesis of proportionality of the deviators. Thin-walled tubular low-pressure polyethylene elements are considered as the object of research. The scope of the model is substantiated based on the hypothesis of the existence of a single diagram of instantaneous deformation and a single diagram of long-term deformation. The invariance of the tensile and torsion diagrams with respect to the stress state is checked. The region of nonlinear elastic deformation is determined. The defining equations of the model contain a set of functions and coefficients determined from the basic experiments. A method for determining the parameters of heredity kernels of nonlinear viscoelastic materials under complex stress state has been developed. The nonlinearity of viscoelastic properties is given by equations of the Rabotnov\u27s model type. The method is based on the relations between the creep kernels obtained under conditions of complex stress state and the creep kernels under one-dimensional stress state. The method is tested experimentally on the problems of calculating creep deformations under combined loading of thin-walled tubular elements made of low-pressure polyethylene.
Pages of the article in the issue: 111 - 114
Language of the article: Ukrainia
Deterministic and stochastic methods combining while solving the problem of defectoscopy of an elastic rod
Get PDFThe paper considers the problem of natural harmonic oscillations of an elastic rod with stress-free ends in the presence of one or a set of defects. Defects are modeled by the inhomogeneity of the Young\u27s modulus. The location of the defects, their geometric size, which is considered small, and the change in elastic properties are the parameters of the defects. The analysis of natural frequency shifts caused by the defect of the rod is the subject of the study. The aim of the work is a mathematical substantiation for the construction of fast and stable algorithms for determining the defect parameters of elastic bodies by analyzing free oscillations. The paper uses and compares fundamentally different research methods. The first methods are classical mathematical methods of mechanics, applied to the analysis of deterministic systems and based on analytical studies combined with numerical implementation. In contrast, a composite machine learning meta-algorithm used in standard statistical classification and regression - Bootstrap-aggregated Regression Trees (BART) - is used to solve the inverse problem. When comparing the constructed algorithms, the statistical method Sampling was used, which allowed to quantify the accuracy and stability of the algorithms.
Pages of the article in the issue: 35 - 38
Language of the article: Ukrainia
Sequential resource allocation in a stochastic environment: an overview and numerical experiments
Get PDFIn this paper, we consider policies for the sequential resource allocation under the multi-armed bandit problem in a stochastic environment. In this model, an agent sequentially selects an action from a given set and an environment reveals a reward in return. In the stochastic setting, each action is associated with a probability distribution with parameters that are not known in advance. The agent makes a decision based on the history of the chosen actions and obtained rewards. The objective is to maximize the total cumulative reward, which is equivalent to the loss minimization. We provide a brief overview of the sequential analysis and an appearance of the multi-armed bandit problem as a formulation in the scope of the sequential resource allocation theory. Multi-armed bandit classification is given with an analysis of the existing policies for the stochastic setting. Two different approaches are shown to tackle the multi-armed bandit problem. In the frequentist view, the confidence interval is used to express the exploration-exploitation trade-off. In the Bayesian approach, the parameter that needs to be estimated is treated as a random variable. Shown, how this model can be modelled with help of the Markov decision process. In the end, we provide numerical experiments in order to study the effectiveness of these policies.
Pages of the article in the issue: 13 - 25
Language of the article: Ukrainia
Investigation of solutions to higher-order dispersive equations with ?-sub-Gaussian initial conditions
Get PDFIn this paper, there are studied sample paths properties of stochastic processes representing solutions of higher-order dispersive equations with random initial conditions given by ?-sub-Gaussian harmonizable processes. The main results are the bounds for the rate of growth of such stochastic processes considered over unbounded domains. The class of ?-sub-Gaussian processes with ?(x) = |x|^?/?, 1 < ? <= 2, is a natural generalization of Gaussian processes. For such initial conditions the bounds for the distribution of supremum of solutions can be calculated in rather simple form. The bounds for the rate of growth of solution to higher-order partial differential equations with random initial conditions in the case of general ? were obtained in [9], the derivation was based on the sults stated in [1]. Here we use another approach, which allows us, for the particular case ?(x) = |x|^?/?, ? ? (1, 2], to present the expressions for the bounds in the closed form.
Pages of the article in the issue: 78 - 84
Language of the article: EnglishIn this paper, there are studied sample paths properties of stochastic processes representing solutions of higher-order dispersive equations with random initial conditions given by ?-sub-Gaussian harmonizable processes. The main results are the bounds for the rate of growth of such stochastic processes considered over unbounded domains. The class of ?-sub-Gaussian processes with ?(x) = |x|^?/?, 1 < ? <= 2, is a natural generalization of Gaussian processes. For such initial conditions the bounds for the distribution of supremum of solutions can be calculated in rather simple form. The bounds for the rate of growth of solution to higher-order partial differential equations with random initial conditions in the case of general ? were obtained in [9], the derivation was based on the sults stated in [1]. Here we use another approach, which allows us, for the particular case ?(x) = |x|^?/?, ? ? (1, 2], to present the expressions for the bounds in the closed form