Pub Date : 2021-01-01DOI: 10.17721/2706-9699.2021.1.09
G. Voropaiev, V. I. Korobov, N. Dimitrieva
The results of physical and numerical modeling of a ventilated air cavity behind a streamlined body are presented. The results of laboratory experiments to determine the amount of gas flowing from the ventilated cavity are presented. It is formed behind the cavitator depending on a number of geometric and dynamic parameters. Numerical simulation of non-stationary 3D two-phase flow was performed on the basis of open source software OpenFOAM. The influence of gas blowing parameters on the formation of an air cavity, size, shape and stability has been investigated. Good qualitative agreement with experimental data was obtained. It is shown that the thickness of the ventilated cavity is determined by the diameter of the cavitator regardless of the diameter of the blow hole, and the increase in velocity or gas flow rate has a positive effect on the length and stability of the formed cavity.
{"title":"MODELING OF A VENTILATED CAVITY BEHIND A STREAMLINED BODY","authors":"G. Voropaiev, V. I. Korobov, N. Dimitrieva","doi":"10.17721/2706-9699.2021.1.09","DOIUrl":"https://doi.org/10.17721/2706-9699.2021.1.09","url":null,"abstract":"The results of physical and numerical modeling of a ventilated air cavity behind a streamlined body are presented. The results of laboratory experiments to determine the amount of gas flowing from the ventilated cavity are presented. It is formed behind the cavitator depending on a number of geometric and dynamic parameters. Numerical simulation of non-stationary 3D two-phase flow was performed on the basis of open source software OpenFOAM. The influence of gas blowing parameters on the formation of an air cavity, size, shape and stability has been investigated. Good qualitative agreement with experimental data was obtained. It is shown that the thickness of the ventilated cavity is determined by the diameter of the cavitator regardless of the diameter of the blow hole, and the increase in velocity or gas flow rate has a positive effect on the length and stability of the formed cavity.","PeriodicalId":40347,"journal":{"name":"Journal of Numerical and Applied Mathematics","volume":"124 1","pages":""},"PeriodicalIF":0.1,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"81712030","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}
Pub Date : 2021-01-01DOI: 10.17721/2706-9699.2021.1.04
V. Vanin, M. Kruhol
The work is devoted to the study of thermal power plants auxiliary energy efficiency. The main mechanisms in the auxiliary systems are centrifugal mechanisms that work in complex hydraulic networks with variable productivity. The main ways to adjust the parameters of the centrifugal mechanisms are to change the speed of rotor rotation, change the guide vane angle and throttle. The operation mode of a complex hydraulic network which includes a group of centrifugal mechanisms with a mixed connection scheme is analyzed. The system of equations which characterize the hydraulic system has been obtained on the basis of Kirchhoff's laws. The centrifugal mechanisms' operating characteristics are given by approximation dependences obtained with the method of least squares and similarity laws. To analyze efficiency of different methods of centrifugal mechanisms parameters regulation, optimal control problems were set and solved. The constraints for the problems are a system of equations that describe the hydraulic system operation and technical constraints that depend on the control method. Through solving the problems, values of the optimal parameters and weighted average efficiency of the group mechanisms were obtained. Studies have shown that the most effective way to regulate the centrifugal mechanisms parameters is to use an individual frequency drive, the least effective is to use only changing angle of centrifugal mechanism's guide vane. Utilization of group control is highly efficient and not inferior to individual frequency drive. However, this statement is correct under condition of the operating characteristics agreement with the centrifugal mechanisms’ operating modes similarity.
{"title":"HYDRAULIC MODELS IN THE PROBLEMS OF THERMAL POWER PLANT AUXILIARY ENERGY EFFICIENCY IMPROVEMENT","authors":"V. Vanin, M. Kruhol","doi":"10.17721/2706-9699.2021.1.04","DOIUrl":"https://doi.org/10.17721/2706-9699.2021.1.04","url":null,"abstract":"The work is devoted to the study of thermal power plants auxiliary energy efficiency. The main mechanisms in the auxiliary systems are centrifugal mechanisms that work in complex hydraulic networks with variable productivity. The main ways to adjust the parameters of the centrifugal mechanisms are to change the speed of rotor rotation, change the guide vane angle and throttle. The operation mode of a complex hydraulic network which includes a group of centrifugal mechanisms with a mixed connection scheme is analyzed. The system of equations which characterize the hydraulic system has been obtained on the basis of Kirchhoff's laws. The centrifugal mechanisms' operating characteristics are given by approximation dependences obtained with the method of least squares and similarity laws. To analyze efficiency of different methods of centrifugal mechanisms parameters regulation, optimal control problems were set and solved. The constraints for the problems are a system of equations that describe the hydraulic system operation and technical constraints that depend on the control method. Through solving the problems, values of the optimal parameters and weighted average efficiency of the group mechanisms were obtained. Studies have shown that the most effective way to regulate the centrifugal mechanisms parameters is to use an individual frequency drive, the least effective is to use only changing angle of centrifugal mechanism's guide vane. Utilization of group control is highly efficient and not inferior to individual frequency drive. However, this statement is correct under condition of the operating characteristics agreement with the centrifugal mechanisms’ operating modes similarity.","PeriodicalId":40347,"journal":{"name":"Journal of Numerical and Applied Mathematics","volume":"1 1","pages":""},"PeriodicalIF":0.1,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"85094124","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}
Pub Date : 2021-01-01DOI: 10.17721/2706-9699.2021.1.13
N. Gorodetskaya, I. Starovoit, T. Shcherbak
The work is devoted to the analysis of the wave field, which is excited by the reflection of the first normal propagation Rayleigh-Lamb wave from the edge of an elastic semi-infinite strip, part of which is rigidly clamped, and part is free from stresses. The boundary value problem belongs to the class of mixed boundary value problems, the characteristic feature of which is the presence of a local feature of stresses at the point of change of the type of boundary conditions. To solve this boundary value problem, the paper proposes a method of superposition, which allows to take into account the feature of stresses due to the asymptotic properties of the unknown coefficients. Asymptotic dependences for coefficients are determined by the nature of the feature, which is known from the solution of the static problem. The criterion for the correctness of the obtained results was the control of the accuracy of the law of conservation of energy, the error of which did not exceed 2% of the energy of the incident wave for the entire considered frequency range. The paper evaluates the accuracy of the boundary conditions. It is shown that the boundary conditions are fulfilled with graphical accuracy along the entire end of the semi-infinite strip, except around a special point ($epsilon$). In this case, along the clamped end of the semi-infinite strip in the vicinity of a special point of stress remain limited. The presence of the region $epsilon$ and the limited stresses are due to the fact that the calculations took into account the $N$ members of the series that describe the wave field, and starting from the $N+1$ member of the series moved to asymptotic values of unknown coefficients, the number of which was also limited to $2N$. As the value $N$ increased, the accuracy of the boundary conditions increased, the region $epsilon$ decreased, and the magnitude of the stresses near the singular point increased.
{"title":"PARTICULARS OF A WAVE FIELD IN A SEMI-INFINITE WAVEGUIDE WITH MIXED BOUNDARY CONDITIONS AT ITS EDGE","authors":"N. Gorodetskaya, I. Starovoit, T. Shcherbak","doi":"10.17721/2706-9699.2021.1.13","DOIUrl":"https://doi.org/10.17721/2706-9699.2021.1.13","url":null,"abstract":"The work is devoted to the analysis of the wave field, which is excited by the reflection of the first normal propagation Rayleigh-Lamb wave from the edge of an elastic semi-infinite strip, part of which is rigidly clamped, and part is free from stresses. The boundary value problem belongs to the class of mixed boundary value problems, the characteristic feature of which is the presence of a local feature of stresses at the point of change of the type of boundary conditions. To solve this boundary value problem, the paper proposes a method of superposition, which allows to take into account the feature of stresses due to the asymptotic properties of the unknown coefficients. Asymptotic dependences for coefficients are determined by the nature of the feature, which is known from the solution of the static problem. The criterion for the correctness of the obtained results was the control of the accuracy of the law of conservation of energy, the error of which did not exceed 2% of the energy of the incident wave for the entire considered frequency range. The paper evaluates the accuracy of the boundary conditions. It is shown that the boundary conditions are fulfilled with graphical accuracy along the entire end of the semi-infinite strip, except around a special point ($epsilon$). In this case, along the clamped end of the semi-infinite strip in the vicinity of a special point of stress remain limited. The presence of the region $epsilon$ and the limited stresses are due to the fact that the calculations took into account the $N$ members of the series that describe the wave field, and starting from the $N+1$ member of the series moved to asymptotic values of unknown coefficients, the number of which was also limited to $2N$. As the value $N$ increased, the accuracy of the boundary conditions increased, the region $epsilon$ decreased, and the magnitude of the stresses near the singular point increased.","PeriodicalId":40347,"journal":{"name":"Journal of Numerical and Applied Mathematics","volume":"135 1","pages":""},"PeriodicalIF":0.1,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86825720","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}
Pub Date : 2021-01-01DOI: 10.17721/2706-9699.2021.1.01
Technical University, Kherson State, академия, Украина
We received normal distribution parameters that approximates the distribution of numbers in the n-th row of Pascal's triangle. We calculated the values for normalized moments of even orders and shown their asymptotic tendency towards values corresponding to a normal distribution. We have received highly accurate approximations for central elements of even rows of Pascal's triangle, which allows for calculation of binomial, as well as trinomial (or, in general cases, multinomial) coefficients. A hypothesis is proposed, according to which it is possible that physical and physics-chemical processes function according to Pascal's distribution, but due to how slight its deviation is from a normal distribution, it is difficult to notice. It is also possible that as technology and experimental methodology improves, this difference will become noticeable where it is traditionally considered that a normal distribution is taking place.
{"title":"GAUSS APPROXIMATION FOR NUMBER DISTRIBUTION IN OF A PASCAL’S TRIANGLE","authors":"Technical University, Kherson State, академия, Украина","doi":"10.17721/2706-9699.2021.1.01","DOIUrl":"https://doi.org/10.17721/2706-9699.2021.1.01","url":null,"abstract":"We received normal distribution parameters that approximates the distribution of numbers in the n-th row of Pascal's triangle. We calculated the values for normalized moments of even orders and shown their asymptotic tendency towards values corresponding to a normal distribution. We have received highly accurate approximations for central elements of even rows of Pascal's triangle, which allows for calculation of binomial, as well as trinomial (or, in general cases, multinomial) coefficients. A hypothesis is proposed, according to which it is possible that physical and physics-chemical processes function according to Pascal's distribution, but due to how slight its deviation is from a normal distribution, it is difficult to notice. It is also possible that as technology and experimental methodology improves, this difference will become noticeable where it is traditionally considered that a normal distribution is taking place.","PeriodicalId":40347,"journal":{"name":"Journal of Numerical and Applied Mathematics","volume":"60 1","pages":""},"PeriodicalIF":0.1,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"78887022","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}
Pub Date : 2021-01-01DOI: 10.17721/2706-9699.2021.1.20
V. Matvienko, V. V. Pichkur, D. Cherniy
The paper considers methods of parametric optimization of a dynamical system, which is described by a parametric system of differential equations. The gradient of the functional in the form of Boltz is found, which is the basis of methods such as gradient descent. Another method is based on the application of the sensitivity function.
{"title":"METHODS OF OPTIMIZATION OF PARAMETRIC SYSTEMS","authors":"V. Matvienko, V. V. Pichkur, D. Cherniy","doi":"10.17721/2706-9699.2021.1.20","DOIUrl":"https://doi.org/10.17721/2706-9699.2021.1.20","url":null,"abstract":"The paper considers methods of parametric optimization of a dynamical system, which is described by a parametric system of differential equations. The gradient of the functional in the form of Boltz is found, which is the basis of methods such as gradient descent. Another method is based on the application of the sensitivity function.","PeriodicalId":40347,"journal":{"name":"Journal of Numerical and Applied Mathematics","volume":"9 1","pages":""},"PeriodicalIF":0.1,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"85439958","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}
Pub Date : 2021-01-01DOI: 10.17721/2706-9699.2021.1.03
A. Bomba, I. P. Moroz
With prolonged transmission of an electric current through the semiconductor devices, in a particular p-i-n diodes, an electron-hole plasma of their active region is heated. This paper presents the theoretical studies results of the plasma heating effect by the Joule heat release in the p-i-n diode volume and the charge carriers recombination energy release on the plasma concentration distribution in the p-i-n diodes active region. The mathematical model is proposed for predicting the electron-hole plasma stationary concentration distribution and the temperature field in the i-region of the bulk p-i-n diodes in the form of a nonlinear boundary value problem in a given area for the equations system, which consist of the charge carrier current continuity equations, the Poisson and the thermal conductivity. It is shown that the differential equations of the model contain a small parameter in such a way that the Poisson equation is singularly perturbed and the heat conduction equation is regularly perturbed. An approximate solution of the problem posed is obtained in the form of the corresponding asymptotic series in powers of the small parameter. The asymptotic serieses, which describes the behavior of the plasma concentration and potential in the investigated region, containing near-boundary corrections to ensure the fulfillment of the boundary conditions. The terms of these series are found as a result of solving a sequence of boundary value problems, obtained as a result of splitting the original problem, for systems of linear differential equations. The boundary value problem for a nonlinear heat equation is reduced to a sequence of problems for the corresponding linear inhomogeneous equations. The process of refining solutions is iterative. The stabilization of the process is ensured by the existence of negative feedback in the system (as the temperature rises, the mobility of charge carriers decreases).
{"title":"THE DIFFUSION-DRIFT PROCESS WITH ACCOUNT HEATING AND RECOMBINATION IN THE p-i-n DIODES ACTIVE REGION MATHEMATICAL MODELING BY THE PERTURBATION THEORY METHODS","authors":"A. Bomba, I. P. Moroz","doi":"10.17721/2706-9699.2021.1.03","DOIUrl":"https://doi.org/10.17721/2706-9699.2021.1.03","url":null,"abstract":"With prolonged transmission of an electric current through the semiconductor devices, in a particular p-i-n diodes, an electron-hole plasma of their active region is heated. This paper presents the theoretical studies results of the plasma heating effect by the Joule heat release in the p-i-n diode volume and the charge carriers recombination energy release on the plasma concentration distribution in the p-i-n diodes active region. The mathematical model is proposed for predicting the electron-hole plasma stationary concentration distribution and the temperature field in the i-region of the bulk p-i-n diodes in the form of a nonlinear boundary value problem in a given area for the equations system, which consist of the charge carrier current continuity equations, the Poisson and the thermal conductivity. It is shown that the differential equations of the model contain a small parameter in such a way that the Poisson equation is singularly perturbed and the heat conduction equation is regularly perturbed. An approximate solution of the problem posed is obtained in the form of the corresponding asymptotic series in powers of the small parameter. The asymptotic serieses, which describes the behavior of the plasma concentration and potential in the investigated region, containing near-boundary corrections to ensure the fulfillment of the boundary conditions. The terms of these series are found as a result of solving a sequence of boundary value problems, obtained as a result of splitting the original problem, for systems of linear differential equations. The boundary value problem for a nonlinear heat equation is reduced to a sequence of problems for the corresponding linear inhomogeneous equations. The process of refining solutions is iterative. The stabilization of the process is ensured by the existence of negative feedback in the system (as the temperature rises, the mobility of charge carriers decreases).","PeriodicalId":40347,"journal":{"name":"Journal of Numerical and Applied Mathematics","volume":"25 1","pages":""},"PeriodicalIF":0.1,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"84708659","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}
Pub Date : 2021-01-01DOI: 10.17721/2706-9699.2021.2.02
V. Zorkaltsev
The problem of minimizing weighted Chebyshev norm on a convex polyhedron defined as the set of solutions to a system of linear inequalities may have a non-unique solution. Moreover, among the solutions to this problem, there may be clearly not suitable points of the polyhedron for the role of the closest points to the zero vector. It complicates, in particular, the Chebyshev approximation. In order to overcome the problems arising from this, the Haar condition is used, which means the requirement for the uniqueness of the solution of the indicated problem. This requirement is not always easy to verify and it is not clear what to do if it is not true. An algorithm is presented that always generates a unique solution to the indicated problem, based on the search with respect to interior points for optimal solutions of a finite sequence of linear programming problems. The solution developed is called the Chebyshev projection of the origin onto the polyhedron. It is proved that this solution is a vector of a polyhedron with Pareto-minimal absolute values of the components. It is proved that the sets of Chebyshev (according to the introduced algorithm) and Euclidean projections of the origin of coordinates onto the polyhedron, formed by varying the positive weight coefficients in the minimized Euclidean and Chebyshev norms, coincide.
{"title":"THE CHEBYSHEV PROJECTIONS ON POLYHEDRON","authors":"V. Zorkaltsev","doi":"10.17721/2706-9699.2021.2.02","DOIUrl":"https://doi.org/10.17721/2706-9699.2021.2.02","url":null,"abstract":"The problem of minimizing weighted Chebyshev norm on a convex polyhedron defined as the set of solutions to a system of linear inequalities may have a non-unique solution. Moreover, among the solutions to this problem, there may be clearly not suitable points of the polyhedron for the role of the closest points to the zero vector. It complicates, in particular, the Chebyshev approximation. In order to overcome the problems arising from this, the Haar condition is used, which means the requirement for the uniqueness of the solution of the indicated problem. This requirement is not always easy to verify and it is not clear what to do if it is not true. An algorithm is presented that always generates a unique solution to the indicated problem, based on the search with respect to interior points for optimal solutions of a finite sequence of linear programming problems. The solution developed is called the Chebyshev projection of the origin onto the polyhedron. It is proved that this solution is a vector of a polyhedron with Pareto-minimal absolute values of the components. It is proved that the sets of Chebyshev (according to the introduced algorithm) and Euclidean projections of the origin of coordinates onto the polyhedron, formed by varying the positive weight coefficients in the minimized Euclidean and Chebyshev norms, coincide.","PeriodicalId":40347,"journal":{"name":"Journal of Numerical and Applied Mathematics","volume":"9 1","pages":""},"PeriodicalIF":0.1,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"87777114","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}
Pub Date : 2021-01-01DOI: 10.17721/2706-9699.2021.1.26
A. G. Kharchenko, L. P. Abramova, I. A. K. I.B, Kudybyn, Institute of Hydromechanics, Academy of, Sciences of, Kyiv Ukraine
This paper presents the results of mathematical and physical modeling of the interaction of waves with the wave chamber on cylindrical supports and the upper part in the form of a permeable waterfront. On the basis of the diffraction model the mathematical modeling of refraction and transformation of waves near the structure is carried out. In the presence of a structure, the transformation of waves is co-accompanied by the phenomena of wave destruction at the edges of the structure and the partial reflection of residual waves from the walls of the protective front. Reflection phenomena cause changes in wave heights along the front of the structure. The results of experimental data are given, which showed that the structure with such a construction is resistant to waves, large soil erosion was not observed.
{"title":"PHYSICAL AND MATHEMATICAL MODELING OF THE WAVE QUENCHING CHAMBER WITH THE UPPER PART IN THE FORM OF A PERMEABLE WATERFRONT","authors":"A. G. Kharchenko, L. P. Abramova, I. A. K. I.B, Kudybyn, Institute of Hydromechanics, Academy of, Sciences of, Kyiv Ukraine","doi":"10.17721/2706-9699.2021.1.26","DOIUrl":"https://doi.org/10.17721/2706-9699.2021.1.26","url":null,"abstract":"This paper presents the results of mathematical and physical modeling of the interaction of waves with the wave chamber on cylindrical supports and the upper part in the form of a permeable waterfront. On the basis of the diffraction model the mathematical modeling of refraction and transformation of waves near the structure is carried out. In the presence of a structure, the transformation of waves is co-accompanied by the phenomena of wave destruction at the edges of the structure and the partial reflection of residual waves from the walls of the protective front. Reflection phenomena cause changes in wave heights along the front of the structure. The results of experimental data are given, which showed that the structure with such a construction is resistant to waves, large soil erosion was not observed.","PeriodicalId":40347,"journal":{"name":"Journal of Numerical and Applied Mathematics","volume":"70 1","pages":""},"PeriodicalIF":0.1,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82126567","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}
Pub Date : 2021-01-01DOI: 10.17721/2706-9699.2021.1.23
V. V. Pichkur, D. A. Mazur, V. Sobchuk
The paper proposes an analysis of controllability of a linear discrete system with change of the state vector dimension. We offer necessary and sufficient conditions of controllability and design the control that guarantees the decision of a problem of moving of such system to an arbitrary final state. It provides functional stability of technological processes described by a linear discrete system with change of the state vector dimension.
{"title":"CONTROLLABILITY OF A LINEAR DISCRETE SYSTEM WITH CHANGE OF THE STATE VECTOR DIMENSION","authors":"V. V. Pichkur, D. A. Mazur, V. Sobchuk","doi":"10.17721/2706-9699.2021.1.23","DOIUrl":"https://doi.org/10.17721/2706-9699.2021.1.23","url":null,"abstract":"The paper proposes an analysis of controllability of a linear discrete system with change of the state vector dimension. We offer necessary and sufficient conditions of controllability and design the control that guarantees the decision of a problem of moving of such system to an arbitrary final state. It provides functional stability of technological processes described by a linear discrete system with change of the state vector dimension.","PeriodicalId":40347,"journal":{"name":"Journal of Numerical and Applied Mathematics","volume":"155 1","pages":""},"PeriodicalIF":0.1,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"78524822","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}
Pub Date : 2021-01-01DOI: 10.17721/2706-9699.2021.2.07
V. Semenov, Yana Vedel, S. Denisov
In this paper, a two-level problem is considered: a variational inequality on the set of solutions to the equilibrium problem. An example of such a problem is the search for the normal Nash equilibrium. To solve this problem, two algorithms are proposed. The first combines the ideas of a two-step proximal method and iterative regularization. And the second algorithm is an adaptive version of the first with a parameter update rule that does not use the values of the Lipschitz constants of the bifunction. Theorems on strong convergence of algorithms are proved for monotone bifunctions of Lipschitz type and strongly monotone Lipschitz operators. It is shown that the proposed algorithms can be applied to monotone two-level variational inequalities in Hilbert spaces.
{"title":"TWO-LEVEL PROBLEMS AND TWO-STAGE PROXIMAL ALGORITHM","authors":"V. Semenov, Yana Vedel, S. Denisov","doi":"10.17721/2706-9699.2021.2.07","DOIUrl":"https://doi.org/10.17721/2706-9699.2021.2.07","url":null,"abstract":"In this paper, a two-level problem is considered: a variational inequality on the set of solutions to the equilibrium problem. An example of such a problem is the search for the normal Nash equilibrium. To solve this problem, two algorithms are proposed. The first combines the ideas of a two-step proximal method and iterative regularization. And the second algorithm is an adaptive version of the first with a parameter update rule that does not use the values of the Lipschitz constants of the bifunction. Theorems on strong convergence of algorithms are proved for monotone bifunctions of Lipschitz type and strongly monotone Lipschitz operators. It is shown that the proposed algorithms can be applied to monotone two-level variational inequalities in Hilbert spaces.","PeriodicalId":40347,"journal":{"name":"Journal of Numerical and Applied Mathematics","volume":"29 1","pages":""},"PeriodicalIF":0.1,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"81477284","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}
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