APPLICATION OF MATHEMATICS IN TECHNICAL AND NATURAL SCIENCES: 11th International Conference for Promoting the Application of Mathematics in Technical and Natural Sciences - AMiTaNS’19最新文献

{"title":"Enhancement of longitudinal EM waves in a graded Epsilon Near Zero (ENZ) materials","authors":"N. Kukhtarev, T. Kukhtareva, A. Fedoseyev, A. Glushchenko","doi":"10.1063/1.5130833","DOIUrl":"https://doi.org/10.1063/1.5130833","url":null,"abstract":"Low permittivity (low epsilon) materials are now attracting wide attention due to potential novel applications in optics and radio communications. Longitudinal electromagnetic waves play important ...","PeriodicalId":179088,"journal":{"name":"APPLICATION OF MATHEMATICS IN TECHNICAL AND NATURAL SCIENCES: 11th International Conference for Promoting the Application of Mathematics in Technical and Natural Sciences - AMiTaNS’19","volume":"15 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-10-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"133398089","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"On convexity of small-time reachable sets of nonlinear control systems","authors":"M. Gusev, I. O. Osipov","doi":"10.1063/1.5130809","DOIUrl":"https://doi.org/10.1063/1.5130809","url":null,"abstract":"The convexity of reachable sets plays an essential role in the development of algorithms for solving optimal control problems and problems of feedback control. For nonlinear control systems the reachable sets are generally not convex and may have a rather complicated structure. However, for systems with integral quadratic constraints on the control B. Polyak showed that the reachable sets are convex if the linearization of the system is controllable and control inputs are restricted from above in L2 norm by a sufficiently small number. In the present paper we use this result to prove sufficient conditions for the convexity of reachable sets of a nonlinear control-affine system on small time intervals, assuming that control resources are limited by a given (not necessarily small) value. These conditions are based on the asymptotics for the minimal eigenvalue of the controllability Gramian of system linearization as a function of the length of the time interval. We prove the asymptotics for a linear time-invariant system containing a small parameter that implies the convexity of small-time reachable sets for some classes of two-dimensional nonlinear control systems. The results of numerical simulations for illustrative examples are discussed.","PeriodicalId":179088,"journal":{"name":"APPLICATION OF MATHEMATICS IN TECHNICAL AND NATURAL SCIENCES: 11th International Conference for Promoting the Application of Mathematics in Technical and Natural Sciences - AMiTaNS’19","volume":"17 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-10-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129764220","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Dark broad-band solitons and opposite self-frequency shift","authors":"B. Nenova, A. Dakova, D. Dakova, V. Slavchev, L. Kovachev","doi":"10.1063/1.5130843","DOIUrl":"https://doi.org/10.1063/1.5130843","url":null,"abstract":"In the present paper the nonlinear propagation of ultra-short dark solitons in dispersive optical fibers, described in the frames of the nonparaxial nonlinear amplitude equation is investigated. The nonparaxial equation governs the evolution of narrow-band, as well as broad-band laser pulses with few oscillations under the envelope. We are looking for a solution of that equation, describing the propagation of broad-band laser pulses in single mode optical fibers with normal dispersion. Analytical solutions in the form of dark solitons are found.In the present paper the nonlinear propagation of ultra-short dark solitons in dispersive optical fibers, described in the frames of the nonparaxial nonlinear amplitude equation is investigated. The nonparaxial equation governs the evolution of narrow-band, as well as broad-band laser pulses with few oscillations under the envelope. We are looking for a solution of that equation, describing the propagation of broad-band laser pulses in single mode optical fibers with normal dispersion. Analytical solutions in the form of dark solitons are found.","PeriodicalId":179088,"journal":{"name":"APPLICATION OF MATHEMATICS IN TECHNICAL AND NATURAL SCIENCES: 11th International Conference for Promoting the Application of Mathematics in Technical and Natural Sciences - AMiTaNS’19","volume":"42 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-10-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127194770","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Risk estimation in the case of limited insurance liability","authors":"E. Raeva","doi":"10.1063/1.5130817","DOIUrl":"https://doi.org/10.1063/1.5130817","url":null,"abstract":"There are models, used for the insurance risk estimation. There are two directions of analysis called “Classical risk theory” and “Modern risk theory” in the practice. The modern risk theory includes additional conditions, typical for the insurance company business like taxes, different internal costs and many others. Unfortunately these peculiarities are usually not available for the “outside world”. That is why, it is very difficult to do analysis with such details. On the other hand, the classical risk theory is focused on the analytical models of stochastic processes which open a wide field for mathematical application.As a fundamental part of insurance risk theory, the model of Cramer-Lundberg is based on the balance between claims costs of the insurer and the premium payments from the side of the insured persons. The model also includes information about the retention and the initial capital necessary to meet the expected claims costs. The expected claims process is a compound stochastic process, which is usually modeled by continuous distributions. The approach often used for reducing the insurance risk is by using franchise value or just declaring a limit value for the insurer’s liability. Including such restriction in the models the claims cost distribution is continuous no more. This involves considering of appropriate approximations for the mixed discrete-continuous distributions of the claims cost. Also all estimations of the level of risk like the retention and the necessary free reserves are affected by the choice of approximate distribution.The influence of different transformations of the random variables, which describe the claims cost in the risk models is considered in the current work. The classical risk model of Cramer-Lundberg for one year fixed period of time was used for estimations of the retention and the free reserves. The experiment we provide is based on empirical distribution for simulating transformed random variables. Fourier approximation for the mixed discrete-continuous probability distributions was used. Finally, there is a comparison between the results for the estimated free reserves without limited insurance liability and after including the liability limitation. The considered approach uses simple methods for implementation and could find useful application in insurance practice.There are models, used for the insurance risk estimation. There are two directions of analysis called “Classical risk theory” and “Modern risk theory” in the practice. The modern risk theory includes additional conditions, typical for the insurance company business like taxes, different internal costs and many others. Unfortunately these peculiarities are usually not available for the “outside world”. That is why, it is very difficult to do analysis with such details. On the other hand, the classical risk theory is focused on the analytical models of stochastic processes which open a wide field for mathematical application.As a fund","PeriodicalId":179088,"journal":{"name":"APPLICATION OF MATHEMATICS IN TECHNICAL AND NATURAL SCIENCES: 11th International Conference for Promoting the Application of Mathematics in Technical and Natural Sciences - AMiTaNS’19","volume":"71 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-10-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129270844","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Two-dimensional trend analysis of time series of complex technical objects diagnostic parameters","authors":"V. Myrhorod, I. Hvozdeva, Y. Derenh","doi":"10.1063/1.5130815","DOIUrl":"https://doi.org/10.1063/1.5130815","url":null,"abstract":"An approach to assessing the relationship and differences of multidimensional trends is proposed and justified. The approach is based on construction of multidimensional arrays from time series of registration data of the diagnosed objects technical parameters. To identify the similarities and differences of time series trends, a pairwise joining of their samples with the same arguments is proposed. The unified time series has the counts in the form of complex numbers and is analysed by the proposed improved principal components method. The proposed method permits dividing the parameters of the object condition into groups that have trends of the same type, which allows localising faults and increasing the reliability of diagnostic conclusions about the technical condition of the object. The a priori statistical model of data generation adopted in the studies was chosen as a model of deviations of the diagnosed objects parameters from the nominal values.An approach to assessing the relationship and differences of multidimensional trends is proposed and justified. The approach is based on construction of multidimensional arrays from time series of registration data of the diagnosed objects technical parameters. To identify the similarities and differences of time series trends, a pairwise joining of their samples with the same arguments is proposed. The unified time series has the counts in the form of complex numbers and is analysed by the proposed improved principal components method. The proposed method permits dividing the parameters of the object condition into groups that have trends of the same type, which allows localising faults and increasing the reliability of diagnostic conclusions about the technical condition of the object. The a priori statistical model of data generation adopted in the studies was chosen as a model of deviations of the diagnosed objects parameters from the nominal values.","PeriodicalId":179088,"journal":{"name":"APPLICATION OF MATHEMATICS IN TECHNICAL AND NATURAL SCIENCES: 11th International Conference for Promoting the Application of Mathematics in Technical and Natural Sciences - AMiTaNS’19","volume":"310 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-10-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116338104","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Geodesic lines on the cyclic helical surfaces","authors":"O. Nikitenko, G. Kovalova","doi":"10.1063/1.5130795","DOIUrl":"https://doi.org/10.1063/1.5130795","url":null,"abstract":"At present, wind turbines with a vertical axis are widely used in engineering. Due to the twist of the blades, the rotation of the helicoid rotor is more uniform, which significantly reduces the dynamic load on the support nodes and, thus, increases their service life. But in the process of wind load there are cracks in the surface of blades, the development of which may eventually lead to their partial destruction or the entire structure, so their detection and elimination are an important part of design and manufacturing. It is known that trajectories of cracks coincide with families of geodesic surface lines, which ultimately leads to the idea that the voltages along the geodesics are larger in comparison with the stresses along the lines of curvature. The term “geodesic” was first used by P. Laplas in relation to the “shortest lines” on the earth’s surface. For a long time, the geodesic line existed only theoretically in differential geometry as a line of internal surface geometry. But at the present time families of geodetic lines find practical application in engineering and production. For example, in the formation of surfaces for laying out of fiberglass or strengthening the cylinders of composite materials with reinforced threads, in the calculation of the trajectory of mobile robot. The obstacle in finding geodesic surface lines is the problem of a computational nature. Only for a limited list of known surfaces (cylinder, cone, pseudosphere) can one find the equation of geodesic lines in explicit form. For all others, including the sphere, their retrieval is reduced to the integration of differential equations by numerical methods.In this paper, the equation of the geodesic lines on the cyclic helical surface is obtained by minimizing the curve length. Since all the formulas are rather cumbersome for calculations, we used Simpson’s formulas to calculate certain integrals. Several geodesics were built on such surfaces in a graphic editor to confirm the results.At present, wind turbines with a vertical axis are widely used in engineering. Due to the twist of the blades, the rotation of the helicoid rotor is more uniform, which significantly reduces the dynamic load on the support nodes and, thus, increases their service life. But in the process of wind load there are cracks in the surface of blades, the development of which may eventually lead to their partial destruction or the entire structure, so their detection and elimination are an important part of design and manufacturing. It is known that trajectories of cracks coincide with families of geodesic surface lines, which ultimately leads to the idea that the voltages along the geodesics are larger in comparison with the stresses along the lines of curvature. The term “geodesic” was first used by P. Laplas in relation to the “shortest lines” on the earth’s surface. For a long time, the geodesic line existed only theoretically in differential geometry as a line of internal surface geome","PeriodicalId":179088,"journal":{"name":"APPLICATION OF MATHEMATICS IN TECHNICAL AND NATURAL SCIENCES: 11th International Conference for Promoting the Application of Mathematics in Technical and Natural Sciences - AMiTaNS’19","volume":"19 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-10-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"117146714","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Invariant solutions of the two-dimensional shallow water equations with a particular class of bottoms","authors":"S. Meleshko, N. Samatova","doi":"10.1063/1.5130801","DOIUrl":"https://doi.org/10.1063/1.5130801","url":null,"abstract":"The two-dimensional shallow water equations with a particular bottom and the Coriolis's force $f=f_{0}+Omega y$ are studied in this paper. The main goal of the paper is to describe all invariant solutions for which the reduced system is a system of ordinary differential equations. For solving the systems of ordinary differential equations we use the sixth-order Runge-Kutta method.","PeriodicalId":179088,"journal":{"name":"APPLICATION OF MATHEMATICS IN TECHNICAL AND NATURAL SCIENCES: 11th International Conference for Promoting the Application of Mathematics in Technical and Natural Sciences - AMiTaNS’19","volume":"191 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-10-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121101783","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"A predator-prey model with SEIR and SEIRS epidemic in the prey","authors":"S.-M. Gurova","doi":"10.1063/1.5130826","DOIUrl":"https://doi.org/10.1063/1.5130826","url":null,"abstract":"In this paper, the author studies a predator-prey model based on epidemic disease. The epidemic disease is described by SEIR (Susceptible-Exposed-Infected-Recovered) and SEIRS (Susceptible-Exposed-Infected-Recovered-Susceptible) models with a logistic growth function only in the susceptible prey population. The function of response in the predator-prey model is given by a Lotka-Volterra type. Notice, all epidemic models are characterized by the basic reproduction number R0. This number gives information whether the epidemic can be controlled. In this work, the author introduces two systems of five nonlinear ordinary differential equations which describe the eco-epidemiological model above using the following functions: susceptible prey S (t), exposed prey E(t), infected prey I(t), recovered prey R(t) and predator P(t). The solutions of the systems are studied by proving their positivity and boundedness. A set of equilibrium points is presented and conditions for their existence and stability are analyzed. A formula for the basic reproduction number R0 is found. Biological interpretation for different equilibria depending on R0 is discussed. The numerical experiments presented show some differences in the dynamic of all populations when the SEIR and SEIRS epidemic models are used.","PeriodicalId":179088,"journal":{"name":"APPLICATION OF MATHEMATICS IN TECHNICAL AND NATURAL SCIENCES: 11th International Conference for Promoting the Application of Mathematics in Technical and Natural Sciences - AMiTaNS’19","volume":"5 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-10-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127052625","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Drag based vertical axis wind turbine numerical efficiency evaluation","authors":"I. Mălăel, I. Bucur, D. Preda","doi":"10.1063/1.5130852","DOIUrl":"https://doi.org/10.1063/1.5130852","url":null,"abstract":"Climate changes have led to a new approach of the energy situation of Europe, Asia and the Americas that face the effects of pollution. Thus, wind energy, considered clean energy - zero emissions of carbon and greenhouse gases, has become a viable option for increasing the life sustainability on Earth. Wind turbines convert the air currents kinetic energy into either electrical or mechanical energy. By using the CFD methods, it is possible to make quantifiable views of the flows associated with physical phenomena for which experimental tests would be very expensive if not impossible. In this paper a vertical axis wind turbine, Lenz type, axis was numerically analyzed. To determine the wind turbine efficiency, CFD methods were used with the Ansys Fluent software, analyzing two cases where the current velocity of 12 m/s and 14 m/s was varied. The unstructured meshes with quad elements were performed in Ansys meshing. In terms of numerical results obtained from unsteady analyzes, using the URANS method, emphasis was placed on observing the vortexes evolutions from a blade and their influence on the others with impact on the wind turbine efficiency. Thus, the variations of the torque coefficients and variations of the vorticity magnitude for different blade positions are presented. For future work, the numerical results will be validated using an experimental model which will be tested in the aerodynamic wind tunnel.Climate changes have led to a new approach of the energy situation of Europe, Asia and the Americas that face the effects of pollution. Thus, wind energy, considered clean energy - zero emissions of carbon and greenhouse gases, has become a viable option for increasing the life sustainability on Earth. Wind turbines convert the air currents kinetic energy into either electrical or mechanical energy. By using the CFD methods, it is possible to make quantifiable views of the flows associated with physical phenomena for which experimental tests would be very expensive if not impossible. In this paper a vertical axis wind turbine, Lenz type, axis was numerically analyzed. To determine the wind turbine efficiency, CFD methods were used with the Ansys Fluent software, analyzing two cases where the current velocity of 12 m/s and 14 m/s was varied. The unstructured meshes with quad elements were performed in Ansys meshing. In terms of numerical results obtained from unsteady analyzes, using the URANS method, emph...","PeriodicalId":179088,"journal":{"name":"APPLICATION OF MATHEMATICS IN TECHNICAL AND NATURAL SCIENCES: 11th International Conference for Promoting the Application of Mathematics in Technical and Natural Sciences - AMiTaNS’19","volume":"20 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-10-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126843479","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Infinitesimal conformal transformations in the Riemannian space of the second approximation for a space of non-zero constant curvature","authors":"S. Pokas, A. Krutoholova","doi":"10.1063/1.5130796","DOIUrl":"https://doi.org/10.1063/1.5130796","url":null,"abstract":"For the Riemannian space Vn, the invariantly associated with Vn space V˜n2 is constructed, which implements a second order approximation for Vn. We studied conformal transformations when the original space is a space of non-zero constant curvature.For the Riemannian space Vn, the invariantly associated with Vn space V˜n2 is constructed, which implements a second order approximation for Vn. We studied conformal transformations when the original space is a space of non-zero constant curvature.","PeriodicalId":179088,"journal":{"name":"APPLICATION OF MATHEMATICS IN TECHNICAL AND NATURAL SCIENCES: 11th International Conference for Promoting the Application of Mathematics in Technical and Natural Sciences - AMiTaNS’19","volume":"50 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-10-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124758030","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}