Pub Date : 2021-06-16DOI: 10.33842/22195203/2021/22/96/103
O. Mostovenko, S. Kovalov, A. Zolotova
Resolving energy saving tasks is an urgent problem of our time. Geometric modelling of energy processes makes it possible for the designer or architect to solve such problems and to consider the energy costs of a project in advance. It is important for practice to solve a number of optimization tasks, in which it is possible to choose the best solution from a set of criteria. The way of solving one of such tasks is proposed in this study. In a mathematical model of an energy field, which is represented in the form of an equation, some of the specified parameters can be set, and the rest are free. If the number of free parameters exceeds the number of given parameters by one, the mathematical model of the energy field will be underdetermined, and it will be possible to find its optimal solution from the one-parameter set of possible parameters. A mathematical model can be represented by a single equation, if the parameters of energy sources are given. If the parameters of the energy field points are set, but the parameters of the energy sources are unknown, the mathematical model of the field is represented by a system of equations. If the unknowns are the coordinates of the given points of the field, the specified system of equations is non-linear. Most of practical tasks of energy field optimization are connected with energy saving. Optimization criterion in this case is minimization of power of energy sources under fulfillment of given task conditions. Dependence between parameters of a target function is described by a single equation or a system of such equations. The optimization problem in this case becomes single-criteria. Variable parameters of an equation or system of such equations are optimization parameters. In this publication one of several problems of energy field parameters optimization connected with practice of architectural design of interiors and exteriors is solved - minimization of energy source powers to provide given potentials in given points of field or minimization of power of given number of identical energy sources as for artificial illumination of rooms.
{"title":"OPTIMIZATION OF ENERGY FIELD PARAMETERS","authors":"O. Mostovenko, S. Kovalov, A. Zolotova","doi":"10.33842/22195203/2021/22/96/103","DOIUrl":"https://doi.org/10.33842/22195203/2021/22/96/103","url":null,"abstract":"Resolving energy saving tasks is an urgent problem of our time. Geometric modelling of energy processes makes it possible for the designer or architect to solve such problems and to consider the energy costs of a project in advance. It is important for practice to solve a number of optimization tasks, in which it is possible to choose the best solution from a set of criteria. The way of solving one of such tasks is proposed in this study. In a mathematical model of an energy field, which is represented in the form of an equation, some of the specified parameters can be set, and the rest are free. If the number of free parameters exceeds the number of given parameters by one, the mathematical model of the energy field will be underdetermined, and it will be possible to find its optimal solution from the one-parameter set of possible parameters. A mathematical model can be represented by a single equation, if the parameters of energy sources are given. If the parameters of the energy field points are set, but the parameters of the energy sources are unknown, the mathematical model of the field is represented by a system of equations. If the unknowns are the coordinates of the given points of the field, the specified system of equations is non-linear. Most of practical tasks of energy field optimization are connected with energy saving. Optimization criterion in this case is minimization of power of energy sources under fulfillment of given task conditions. Dependence between parameters of a target function is described by a single equation or a system of such equations. The optimization problem in this case becomes single-criteria. Variable parameters of an equation or system of such equations are optimization parameters. In this publication one of several problems of energy field parameters optimization connected with practice of architectural design of interiors and exteriors is solved - minimization of energy source powers to provide given potentials in given points of field or minimization of power of given number of identical energy sources as for artificial illumination of rooms.","PeriodicalId":188754,"journal":{"name":"Modern problems of modeling","volume":"66 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-06-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127122280","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 : 2021-06-16DOI: 10.33842/22195203/2021/21/583/90
Y. Kholodniak, Y. Havrylenko, I. Pykhtieieva, O. Dereza, O. Ivzhenko
{"title":"MODELING THE WORKING SURFACES OF INDUSTRIAL PRODUCTS BASED ON AN ARRAY OF POINTS","authors":"Y. Kholodniak, Y. Havrylenko, I. Pykhtieieva, O. Dereza, O. Ivzhenko","doi":"10.33842/22195203/2021/21/583/90","DOIUrl":"https://doi.org/10.33842/22195203/2021/21/583/90","url":null,"abstract":"","PeriodicalId":188754,"journal":{"name":"Modern problems of modeling","volume":"124 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-06-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114472155","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 : 2021-06-16DOI: 10.33842/22195203/2021/21/54/65
V. Vereshchaha, Y. Adoniev, O. Pavlenko, M. Rubtsov
The article shows the sequence of parameterization, along the coordinate axis, of the original discretely presented line (DPL) and is presented in general form by a point polynomial. Possible options for the appearance of multiple points are considered and the values of the parameters for these options are presented. It is indicated that with the appearance of multiple points on the DPL in the constituent elements of a point polynomial, uncertainties arise. It is proved that all these uncertainties are revealed, the limits of which, at the nodal points, are zero or one. It is shown that the uncertainties that arise with the appearance of multiple points on the DPC are not an obstacle to global interpolation modeling resources will increase, and the efficiency and quality of modeling will decrease.
{"title":"GLOBAL INTERPOLATION OF THE POINTING POLYNOMIAL OF THE GEOMETRIC COMPOSITION WITH MULTIPLE POINTS","authors":"V. Vereshchaha, Y. Adoniev, O. Pavlenko, M. Rubtsov","doi":"10.33842/22195203/2021/21/54/65","DOIUrl":"https://doi.org/10.33842/22195203/2021/21/54/65","url":null,"abstract":"The article shows the sequence of parameterization, along the coordinate axis, of the original discretely presented line (DPL) and is presented in general form by a point polynomial. Possible options for the appearance of multiple points are considered and the values of the parameters for these options are presented. It is indicated that with the appearance of multiple points on the DPL in the constituent elements of a point polynomial, uncertainties arise. It is proved that all these uncertainties are revealed, the limits of which, at the nodal points, are zero or one. It is shown that the uncertainties that arise with the appearance of multiple points on the DPC are not an obstacle to global interpolation modeling resources will increase, and the efficiency and quality of modeling will decrease.","PeriodicalId":188754,"journal":{"name":"Modern problems of modeling","volume":"9 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-06-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114888280","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 : 2021-06-16DOI: 10.33842/22195203/2021/21/144/153
A. Kalinovsky
The proposed geometric container model for a new way to deliver a fire extinguishing agent into a fire zone located at a considerable distance. The shipping idea is based on a mechanical process of throwing. For this, the substance (for example, the fire extinguishing powder) is placed in a solid shell a special container. After delivery to the place of fire, the container should be collapsed and released a substance that will assist when steaming a fire. In the known method of remote delivery of the fire extinguishing agent, a pneumatic gun with a cylindrical container is used. In the process of delivery, the cylinder should rotate around its axis to ensure the stability of the movement. At the same time, the difficulty of regulating the distribution of compressed air flows in the dule of cannons. In a new delivery method, a container is used, which consists of two spherical tanks connected by a rod (like dumbbells). The initiation of the rotational and progressive movement dumbbells is carried out by simultaneously exposure to explosive pulses aimed at each cargo in advance. The proposed method of remote delivery of a fire extinguishing agent, packed into the shell of a dumbbell-like form, requires studies of the design of the elements of the dumbbells. It is necessary to combine solutions of several tasks with contradictory conditions. First, the design of the dumbbells should be strong and withstand the starting force created by explosive pulses of sickness. Secondly, the design should provide its instant destruction after delivery to the fire zone. And, thirdly, the design of the dumbbells should provide a convenient technology of filling the containers with fire extinguishes. To solve this problem, it is proposed to use one of the multifaceted bodies of Archimedes. The possibility of separate delivery of two fire extinguishing substances due to the presence of two spherical tanks dumbbells allows you to develop a new fire extinguishing technology. It is based on the fact that in order to increase the effect of quenching, some chemicals should be combined and mixed directly in the fire zone.
{"title":"DEVELOPMENT OF A CONTAINER MODEL FOR A NEW METHOD OF DELIVERY OF FIRE EXTINGUISHES","authors":"A. Kalinovsky","doi":"10.33842/22195203/2021/21/144/153","DOIUrl":"https://doi.org/10.33842/22195203/2021/21/144/153","url":null,"abstract":"The proposed geometric container model for a new way to deliver a fire extinguishing agent into a fire zone located at a considerable distance. The shipping idea is based on a mechanical process of throwing. For this, the substance (for example, the fire extinguishing powder) is placed in a solid shell a special container. After delivery to the place of fire, the container should be collapsed and released a substance that will assist when steaming a fire. In the known method of remote delivery of the fire extinguishing agent, a pneumatic gun with a cylindrical container is used. In the process of delivery, the cylinder should rotate around its axis to ensure the stability of the movement. At the same time, the difficulty of regulating the distribution of compressed air flows in the dule of cannons. In a new delivery method, a container is used, which consists of two spherical tanks connected by a rod (like dumbbells). The initiation of the rotational and progressive movement dumbbells is carried out by simultaneously exposure to explosive pulses aimed at each cargo in advance. The proposed method of remote delivery of a fire extinguishing agent, packed into the shell of a dumbbell-like form, requires studies of the design of the elements of the dumbbells. It is necessary to combine solutions of several tasks with contradictory conditions. First, the design of the dumbbells should be strong and withstand the starting force created by explosive pulses of sickness. Secondly, the design should provide its instant destruction after delivery to the fire zone. And, thirdly, the design of the dumbbells should provide a convenient technology of filling the containers with fire extinguishes. To solve this problem, it is proposed to use one of the multifaceted bodies of Archimedes. The possibility of separate delivery of two fire extinguishing substances due to the presence of two spherical tanks dumbbells allows you to develop a new fire extinguishing technology. It is based on the fact that in order to increase the effect of quenching, some chemicals should be combined and mixed directly in the fire zone.","PeriodicalId":188754,"journal":{"name":"Modern problems of modeling","volume":"179 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-06-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116604456","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 : 2021-06-16DOI: 10.33842/22195203/2021/22/39/47
O. Zelevska, O. Finogenov, I. Ibnukhsein, V. Suvorova
{"title":"USE OF ONLINE TECHNOLOGIES TO BUILD THREE-DIMENSIONAL CELLULAR AUTOMATA","authors":"O. Zelevska, O. Finogenov, I. Ibnukhsein, V. Suvorova","doi":"10.33842/22195203/2021/22/39/47","DOIUrl":"https://doi.org/10.33842/22195203/2021/22/39/47","url":null,"abstract":"","PeriodicalId":188754,"journal":{"name":"Modern problems of modeling","volume":"93 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-06-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115302747","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 : 2021-06-16DOI: 10.33842/22195203/2021/22/163/172
O. Sobol, V. Sobol, S. Bordiuzhenko, O. Liashevska
{"title":"METHOD FOR DETERMINING RATIONAL NUMBER OF CITIZEN SECURITY CENTERS FOR PROTECTING POPULATION AND RURAL AREAS","authors":"O. Sobol, V. Sobol, S. Bordiuzhenko, O. Liashevska","doi":"10.33842/22195203/2021/22/163/172","DOIUrl":"https://doi.org/10.33842/22195203/2021/22/163/172","url":null,"abstract":"","PeriodicalId":188754,"journal":{"name":"Modern problems of modeling","volume":"47 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-06-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"131457001","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 : 2021-06-16DOI: 10.33842/22195203/2021/22/22/31
V. Vereshchaha, A. Naidysh, A. Pavlenko, I. Chyzhykov
{"title":"ANALYSIS OF COMPOSITE GEOMETRIC MODELING","authors":"V. Vereshchaha, A. Naidysh, A. Pavlenko, I. Chyzhykov","doi":"10.33842/22195203/2021/22/22/31","DOIUrl":"https://doi.org/10.33842/22195203/2021/22/22/31","url":null,"abstract":"","PeriodicalId":188754,"journal":{"name":"Modern problems of modeling","volume":"9 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-06-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122727190","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 : 2021-06-16DOI: 10.33842/22195203/2021/22/104/110
O. Nazarko, V. Ragulin, I. Zaitsev
{"title":"USE OF THE COMPUTER SIMULATION METHOD IN THE STUDY OF THE CAR FLOW EQUIPPED WITH AERODYNAMIC ELEMENTS","authors":"O. Nazarko, V. Ragulin, I. Zaitsev","doi":"10.33842/22195203/2021/22/104/110","DOIUrl":"https://doi.org/10.33842/22195203/2021/22/104/110","url":null,"abstract":"","PeriodicalId":188754,"journal":{"name":"Modern problems of modeling","volume":"118 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-06-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116351651","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 : 2021-06-16DOI: 10.33842/22195203/2021/22/32/38
A. Demchyshyn, N. Ausheva, B. Rassamakin
{"title":"METHOD OF PRIMARY PROCESSING OF MULTISSPECTRAL IMAGES OF THE EMBEDDED SYSTEM OF A NANOSATELLITE","authors":"A. Demchyshyn, N. Ausheva, B. Rassamakin","doi":"10.33842/22195203/2021/22/32/38","DOIUrl":"https://doi.org/10.33842/22195203/2021/22/32/38","url":null,"abstract":"","PeriodicalId":188754,"journal":{"name":"Modern problems of modeling","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-06-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128926659","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 : 2021-06-16DOI: 10.33842/22195203/2021/22/111/117
V. Nesvidomin, S. Pylypaka, A. Nesvidomina
Abstract. The article reveals an analytical description of the formation of families of orthogonal flat curved lines in the implicit form based on the analysis of the parametric equation of a flat isometric grid constructed by separating the real and imaginary parts of the function of a complex variable. This problem is due to the fact that flat isometric grids, as two families of orthogonal coordinate lines with square cells, are used in conformal mappings, for example, when drawing images on curved surfaces with the least distortion. At the same time, families of flat parallel lines are widely used in geometric modeling of heat transfer, electric fields, fluid flow, etc. There is a connection between these geometric images, which is explained by specific examples. Analytical calculations of deriving the parametric equation of an isometric grid are quite time-consuming, so they are performed in the environment of symbolic algebra Maple. For this purpose, the corresponding software of the interactive model of derivation of parametric equations of isometric grids for any initial function of a complex variable with the subsequent separation of its real and imaginary parts was created. It was found that the values of the abscissa and ordinates of the parametric equation of a flat isometric grid can be represented as explicit surface equations. For integer values of the power of the exponential function of the complex variable, the values of the abscissa and the ordinate will be represented by algebraic surfaces in the explicit form. The projections of the cross sections of the abscissa and ordinate surfaces by horizontal cutting planes on the horizontal plane form two families of curved lines, the equations of which can be obtained only implicitly. By the example of the quadratic function of a complex variable, it is proved that these families of lines are mutually perpendicular. The practical application of building a family of lines for geometric modeling of fluid flow lines that flow around the barrier in the form of a semicircle is shown.
{"title":"CONSTRUCTION OF A FAMILY OF FLAT CURVES ACCORDING TO THE EQUATIONS OF ISOMETRIC GRIDS","authors":"V. Nesvidomin, S. Pylypaka, A. Nesvidomina","doi":"10.33842/22195203/2021/22/111/117","DOIUrl":"https://doi.org/10.33842/22195203/2021/22/111/117","url":null,"abstract":"Abstract. The article reveals an analytical description of the formation of families of orthogonal flat curved lines in the implicit form based on the analysis of the parametric equation of a flat isometric grid constructed by separating the real and imaginary parts of the function of a complex variable. This problem is due to the fact that flat isometric grids, as two families of orthogonal coordinate lines with square cells, are used in conformal mappings, for example, when drawing images on curved surfaces with the least distortion. At the same time, families of flat parallel lines are widely used in geometric modeling of heat transfer, electric fields, fluid flow, etc. There is a connection between these geometric images, which is explained by specific examples. Analytical calculations of deriving the parametric equation of an isometric grid are quite time-consuming, so they are performed in the environment of symbolic algebra Maple. For this purpose, the corresponding software of the interactive model of derivation of parametric equations of isometric grids for any initial function of a complex variable with the subsequent separation of its real and imaginary parts was created. It was found that the values of the abscissa and ordinates of the parametric equation of a flat isometric grid can be represented as explicit surface equations. For integer values of the power of the exponential function of the complex variable, the values of the abscissa and the ordinate will be represented by algebraic surfaces in the explicit form. The projections of the cross sections of the abscissa and ordinate surfaces by horizontal cutting planes on the horizontal plane form two families of curved lines, the equations of which can be obtained only implicitly. By the example of the quadratic function of a complex variable, it is proved that these families of lines are mutually perpendicular. The practical application of building a family of lines for geometric modeling of fluid flow lines that flow around the barrier in the form of a semicircle is shown.","PeriodicalId":188754,"journal":{"name":"Modern problems of modeling","volume":"17 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-06-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114903297","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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