Pub Date : 2023-09-01DOI: 10.26577/jmmcs2023v119i3a8
K. Bagitova
The scientific research is devoted to solving the important scientific and practical problem of recognizing calls for political extremism in online social networks, which today, due to their high popularity, are one of the main ways of spreading such calls. It is shown that modern means of detecting calls for political extremism in online social networks are mainly focused on the semantic analysis of text messages contained in them. At the same time, in modern online social networks, graphic resources have become widespread, which provide ample opportunities for the implementation of such calls. The possibility of detecting destructive content in images and video materials using neural network analysis is considered. The possibility of increasing the efficiency of neural network recognition has been determined due to the developed image pre-processing model, which makes it possible to adjust the brightness and contrast of images, as well as eliminate typical interference during video recording. The originality of the model lies in the use of a wavelet transform apparatus for filtering typical noise, as well as in the developed mathematical apparatus for adaptive contrast correction based on the local contrast of the neighborhood. It is shows that the use of the developed model for pre-processing images makes it possible to increase the accuracy of neural network recognition of calls for extremism in images and videos posted on online social networks by approximately 12 percent. It is advisable to correlate the paths for further research with the development of a neural network model adapted to the wide variation in the sizes of images and videos in online social networks.
{"title":"MODEL FOR PROCESSING IMAGES OF ONLINE SOCIAL NETWORKS USED TO RECOGNIZE POLITICAL EXTREMISM","authors":"K. Bagitova","doi":"10.26577/jmmcs2023v119i3a8","DOIUrl":"https://doi.org/10.26577/jmmcs2023v119i3a8","url":null,"abstract":"The scientific research is devoted to solving the important scientific and practical problem of recognizing calls for political extremism in online social networks, which today, due to their high popularity, are one of the main ways of spreading such calls. It is shown that modern means of detecting calls for political extremism in online social networks are mainly focused on the semantic analysis of text messages contained in them. At the same time, in modern online social networks, graphic resources have become widespread, which provide ample opportunities for the implementation of such calls. The possibility of detecting destructive content in images and video materials using neural network analysis is considered. The possibility of increasing the efficiency of neural network recognition has been determined due to the developed image pre-processing model, which makes it possible to adjust the brightness and contrast of images, as well as eliminate typical interference during video recording. The originality of the model lies in the use of a wavelet transform apparatus for filtering typical noise, as well as in the developed mathematical apparatus for adaptive contrast correction based on the local contrast of the neighborhood. It is shows that the use of the developed model for pre-processing images makes it possible to increase the accuracy of neural network recognition of calls for extremism in images and videos posted on online social networks by approximately 12 percent. It is advisable to correlate the paths for further research with the development of a neural network model adapted to the wide variation in the sizes of images and videos in online social networks.","PeriodicalId":53167,"journal":{"name":"Vestnik KazNU Seriia matematika mekhanika informatika","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135735252","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 : 2023-09-01DOI: 10.26577/jmmcs2023v119i3a7
O. Khabidolda
In this paper, there are studied the dynamic processes (free and forced oscillations) of isotropiccantilever plates in the form of an isosceles (wedge-shaped) triangle. In the study, the finitedifference method has been applied using a regular one-dimensional (linear) grid. The finite-difference equations developed by the authors for point-distributed masses along the length ofthe wedge are presented, taking into account the linearly variable bending stiffness. On this basis,the results of studies in the form of amplitude-frequency characteristics (frequencies, dynamicforces and deflections) in the resonant and near-resonant regions have been obtained. The contentof theoretical provisions and applied results can be widely used in the scientific and engineeringfields and in the field of mechanics of structures.
{"title":"STUDYING DYNAMICS OF A CANTILEVER BAR WITH VARIABLE BENDING STIFFNESS","authors":"O. Khabidolda","doi":"10.26577/jmmcs2023v119i3a7","DOIUrl":"https://doi.org/10.26577/jmmcs2023v119i3a7","url":null,"abstract":"In this paper, there are studied the dynamic processes (free and forced oscillations) of isotropiccantilever plates in the form of an isosceles (wedge-shaped) triangle. In the study, the finitedifference method has been applied using a regular one-dimensional (linear) grid. The finite-difference equations developed by the authors for point-distributed masses along the length ofthe wedge are presented, taking into account the linearly variable bending stiffness. On this basis,the results of studies in the form of amplitude-frequency characteristics (frequencies, dynamicforces and deflections) in the resonant and near-resonant regions have been obtained. The contentof theoretical provisions and applied results can be widely used in the scientific and engineeringfields and in the field of mechanics of structures.","PeriodicalId":53167,"journal":{"name":"Vestnik KazNU Seriia matematika mekhanika informatika","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135735013","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 : 2023-09-01DOI: 10.26577/jmmcs2023v119i3a4
Z. Nugayeva
Among recurrent functions the most sophisticated are Poisson stable functions. For discontinuous functions, there are very few results, for the stability. Discontinuous compartmental Poisson stable functions are in the focus of this research. As the discontinuity points of the functions, a special time sequences, Poisson sequences, are considered. It the first time, the discontinuous functions of two compartments, periodic and Poisson stable, are investigated. To combine periodicity and Poisson stability, in the case of continuous functions, a convergence sequence with a special kappa property was used [1,2]. For discontinuous functions, this property is not enough, because we also should consider the discontinuity points of the function. For this reason, we need a new concept known as Poisson couple, that is, a couple of a sequence of discontinuity points and convergence sequence that has the kappa property. Moreover, we meet the challenges for the stability by considering functions on diagonals in the space of arguments. Examples of Poisson stable functions are given to illustrate the theoretical results. The method and results can be effectively used in the study of different types of functional differential equations, impulsive differential equations and differential equations generalized piecewise constant argument, as well as their application.
{"title":"Discontinuous compartmental periodic Poisson stable functions","authors":"Z. Nugayeva","doi":"10.26577/jmmcs2023v119i3a4","DOIUrl":"https://doi.org/10.26577/jmmcs2023v119i3a4","url":null,"abstract":"Among recurrent functions the most sophisticated are Poisson stable functions. For discontinuous functions, there are very few results, for the stability. Discontinuous compartmental Poisson stable functions are in the focus of this research. As the discontinuity points of the functions, a special time sequences, Poisson sequences, are considered. It the first time, the discontinuous functions of two compartments, periodic and Poisson stable, are investigated. To combine periodicity and Poisson stability, in the case of continuous functions, a convergence sequence with a special kappa property was used [1,2]. For discontinuous functions, this property is not enough, because we also should consider the discontinuity points of the function. For this reason, we need a new concept known as Poisson couple, that is, a couple of a sequence of discontinuity points and convergence sequence that has the kappa property. Moreover, we meet the challenges for the stability by considering functions on diagonals in the space of arguments. Examples of Poisson stable functions are given to illustrate the theoretical results. The method and results can be effectively used in the study of different types of functional differential equations, impulsive differential equations and differential equations generalized piecewise constant argument, as well as their application.","PeriodicalId":53167,"journal":{"name":"Vestnik KazNU Seriia matematika mekhanika informatika","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135735263","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 : 2023-09-01DOI: 10.26577/jmmcs2023v119i3a2
E. Bakirova
In this paper, a linear boundary value problem under impulse effects for the system of Fredholm integro-differential equations with a parameter is investigated. The purpose of this research is to provide a method for solving the studied problem numerically. The ideas of the Dzhumabaev parameterisation method, classical numerical methods of solving Cauchy problems and numerical integration techniques were used as a basis for achieving the goal. When applying the method of parameterisation by points of impulse effects, the interval on which the boundary value problem is considered is divided, additional parameters and new unknown functions are introduced. As a consequence, a problem with parameters equivalent to the original problem is obtained. According to the data of the matrices of the integral term of the equation, boundary conditions and impulse conditions, the SLAE with respect to the introduced parameters is compiled. And the unknown functions are found as solutions of the initial-special problem for the system of integro-differential equations. A numerical algorithm for finding a solution to the boundary value problem for impulse integro-differential equations with a parameter is constructed. Numerical methods for solving Cauchy problems for ODE and calculating definite integrals are used for numerical implementation of the constructed algorithm. Numerical calculations are verified on test problem.
{"title":"NUMERICAL IMPLEMENTATION FOR SOLVING THE BOUNDARY VALUE PROBLEM FOR IMPULSIVE INTEGRO-DIFFERENTIAL EQUATIONS WITH PARAMETER","authors":"E. Bakirova","doi":"10.26577/jmmcs2023v119i3a2","DOIUrl":"https://doi.org/10.26577/jmmcs2023v119i3a2","url":null,"abstract":"In this paper, a linear boundary value problem under impulse effects for the system of Fredholm integro-differential equations with a parameter is investigated. The purpose of this research is to provide a method for solving the studied problem numerically. The ideas of the Dzhumabaev parameterisation method, classical numerical methods of solving Cauchy problems and numerical integration techniques were used as a basis for achieving the goal. When applying the method of parameterisation by points of impulse effects, the interval on which the boundary value problem is considered is divided, additional parameters and new unknown functions are introduced. As a consequence, a problem with parameters equivalent to the original problem is obtained. According to the data of the matrices of the integral term of the equation, boundary conditions and impulse conditions, the SLAE with respect to the introduced parameters is compiled. And the unknown functions are found as solutions of the initial-special problem for the system of integro-differential equations. A numerical algorithm for finding a solution to the boundary value problem for impulse integro-differential equations with a parameter is constructed. Numerical methods for solving Cauchy problems for ODE and calculating definite integrals are used for numerical implementation of the constructed algorithm. Numerical calculations are verified on test problem.","PeriodicalId":53167,"journal":{"name":"Vestnik KazNU Seriia matematika mekhanika informatika","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135735255","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 : 2023-09-01DOI: 10.26577/jmmcs2023v119i3a6
А. Adilkhan
Today, construction machines are widely used, which can be used in hazardous and toxic working environments, in other adverse environments, and in places where it is very difficult for a human operator to control the machine. At the same time, in the current difficult economic situation, it is important to increase the productivity of these construction machines in the mining, construction, and manufacturing sectors. Due to the versatility and convenience of hydraulically driven manipulators among construction machines, they occupy the majority of equipment used in mining or construction work. Vibration machines are used in many technological processes for the removal of hard rocks and other materials in the work performed by hydraulic excavators. This paper considers a hydraulically driven drilling robot with four degrees of freedom. These are machines and equipment based on lever mechanisms of variable structures, which have a number of advantages over analogs. The use of mechanisms of variable structures significantly increases the reliability of vibration shocks, their design is simple and does not require imported materials and components. This is especially important for machines operating in difficult mountain conditions. Under the above operating conditions, semi-automatic or fully computer-controlled machines can work successfully and efficiently. To do this, it is important to understand the kinematics of this machine. therefore, the article describes the sequence of actions required to solve the direct problem of kinematics directed at a drilling robot with four degrees of freedom.
{"title":"EFFECTIVE SOLUTION OF THE PROBLEM OF DIRECT KINEMATICS FOR DRILLING ROBOT-MANIPULATOR WITH FOUR DEGREES OF FREEDOM IN THE MAPLE PROGRAM","authors":"А. Adilkhan","doi":"10.26577/jmmcs2023v119i3a6","DOIUrl":"https://doi.org/10.26577/jmmcs2023v119i3a6","url":null,"abstract":"Today, construction machines are widely used, which can be used in hazardous and toxic working environments, in other adverse environments, and in places where it is very difficult for a human operator to control the machine. At the same time, in the current difficult economic situation, it is important to increase the productivity of these construction machines in the mining, construction, and manufacturing sectors. Due to the versatility and convenience of hydraulically driven manipulators among construction machines, they occupy the majority of equipment used in mining or construction work. Vibration machines are used in many technological processes for the removal of hard rocks and other materials in the work performed by hydraulic excavators. This paper considers a hydraulically driven drilling robot with four degrees of freedom. These are machines and equipment based on lever mechanisms of variable structures, which have a number of advantages over analogs. The use of mechanisms of variable structures significantly increases the reliability of vibration shocks, their design is simple and does not require imported materials and components. This is especially important for machines operating in difficult mountain conditions. Under the above operating conditions, semi-automatic or fully computer-controlled machines can work successfully and efficiently. To do this, it is important to understand the kinematics of this machine. therefore, the article describes the sequence of actions required to solve the direct problem of kinematics directed at a drilling robot with four degrees of freedom.","PeriodicalId":53167,"journal":{"name":"Vestnik KazNU Seriia matematika mekhanika informatika","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135735254","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 : 2023-09-01DOI: 10.26577/jmmcs2023v119i3a5
K. Bakhiyeva
In this article, a model is proposed for determining the parameters of the structural elements of a novel pincer robot for transporting plant microsprouts from a transport container in vitro to a working container with soil at the stage of their adaptation in soil during microclonal propagation. Scientific and practical result of the research is the creation of an innovative robotic complex of a manipulation device with a phalanx gripper for the transfer of plant microsprouts from a transport container in vitro to a working container with soil at the stage of their adaptation in soil during microclonal propagation, and the testing of its physical prototype in the adaptation of 3000 pieces of woody microsprouts. Plants with roots in the soil. The obtained research results will affect the scientific and technical potential and competitiveness of scientists in the Republic of Kazakhstan. In the Republic of Kazakhstan there are no studies on automation of the technology of microclonal propagation of plants for their mass production, the application of which would allow obtaining a large number of plants and reducing the cost of planting materials. Besides, the practical results of research on an innovative robotic complex will reduce the import of planting material of woody plants from other countries for the design of settlements in the Republic of Kazakhstan. In this regard, the need for native, high-quality planting material for woody plants will increase. One of the main solutions to the problem of landscaping in the settlement areas of the Republic of Kazakhstan is to obtain native high-quality planting material for woody plants by microclonal propagation.
{"title":"MODEL OF GRIPPER OF ROBOT MANIPULATOR WHEN OVERLOADING PLANT MICROSHOOTS FROM THE TRANSPORT CONTAINER TO THE WORKING CONTAINER","authors":"K. Bakhiyeva","doi":"10.26577/jmmcs2023v119i3a5","DOIUrl":"https://doi.org/10.26577/jmmcs2023v119i3a5","url":null,"abstract":"In this article, a model is proposed for determining the parameters of the structural elements of a novel pincer robot for transporting plant microsprouts from a transport container in vitro to a working container with soil at the stage of their adaptation in soil during microclonal propagation. Scientific and practical result of the research is the creation of an innovative robotic complex of a manipulation device with a phalanx gripper for the transfer of plant microsprouts from a transport container in vitro to a working container with soil at the stage of their adaptation in soil during microclonal propagation, and the testing of its physical prototype in the adaptation of 3000 pieces of woody microsprouts. Plants with roots in the soil. The obtained research results will affect the scientific and technical potential and competitiveness of scientists in the Republic of Kazakhstan. In the Republic of Kazakhstan there are no studies on automation of the technology of microclonal propagation of plants for their mass production, the application of which would allow obtaining a large number of plants and reducing the cost of planting materials. Besides, the practical results of research on an innovative robotic complex will reduce the import of planting material of woody plants from other countries for the design of settlements in the Republic of Kazakhstan. In this regard, the need for native, high-quality planting material for woody plants will increase. One of the main solutions to the problem of landscaping in the settlement areas of the Republic of Kazakhstan is to obtain native high-quality planting material for woody plants by microclonal propagation.","PeriodicalId":53167,"journal":{"name":"Vestnik KazNU Seriia matematika mekhanika informatika","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135735259","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 : 2023-09-01DOI: 10.26577/jmmcs2023v119i3a10
Askar Kudaibergenov
In this work, a software module for calculating drill string displacements taking into account the effect of a drilling fluid flow, external loads and the intermittent contact of the drill string with the borehole wall is developed. A generalized nonlinear mathematical model of the drill string spatial lateral vibrations underlies the module. The V.V. Novozhilov nonlinear elasticity theory and the Ostrogradsky-Hamilton variation principle were used to derive the mathematical model. To create the software module, the universal Wolfram Language with integrated computational intelligence is utilized. The functions for performing 2D visualization of the drill string spatial displacements, constructing phase portraits of the solution and conducting the comparative analysis of the obtained numerical results are included into the module. The developed module allows predicting the dynamics of the drill string before the beginning of well drilling due to the possibility of pre-setting the parameters of the drilling system and accounting for the environmental factors in the process of modeling for ensuring quick, safe and efficient exploration and production of natural resources.
{"title":"Development of a software module for modeling drill string displacements","authors":"Askar Kudaibergenov","doi":"10.26577/jmmcs2023v119i3a10","DOIUrl":"https://doi.org/10.26577/jmmcs2023v119i3a10","url":null,"abstract":"In this work, a software module for calculating drill string displacements taking into account the effect of a drilling fluid flow, external loads and the intermittent contact of the drill string with the borehole wall is developed. A generalized nonlinear mathematical model of the drill string spatial lateral vibrations underlies the module. The V.V. Novozhilov nonlinear elasticity theory and the Ostrogradsky-Hamilton variation principle were used to derive the mathematical model. To create the software module, the universal Wolfram Language with integrated computational intelligence is utilized. The functions for performing 2D visualization of the drill string spatial displacements, constructing phase portraits of the solution and conducting the comparative analysis of the obtained numerical results are included into the module. The developed module allows predicting the dynamics of the drill string before the beginning of well drilling due to the possibility of pre-setting the parameters of the drilling system and accounting for the environmental factors in the process of modeling for ensuring quick, safe and efficient exploration and production of natural resources.","PeriodicalId":53167,"journal":{"name":"Vestnik KazNU Seriia matematika mekhanika informatika","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135735253","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 : 2023-09-01DOI: 10.26577/jmmcs2023v119i3a3
S. Kabdrakhova
Boundary value problems for hyperbolic equations are an important area of mathematical physics and science in nature. They arise in various physical and engineering contexts and have a wide range of applications, including wave propagation in elastic media, electromagnetic waves, as well as problems related to fluid and gas motion. In this article, we will focus on one of the significant subclasses of hyperbolic equations, namely, semi-linear loaded hyperbolic equations, and examine the conditions for the existence of isolated solutions to boundary value problems for such equations.Semi-linear loaded hyperbolic equations are equations in which nonlinear terms depend on the solutions themselves. This makes their study more complex and mathematically intriguing. Our task is to find conditions under which such equations have isolated solutions, meaning solutions that exist in a bounded region of space and time and remain bounded themselves.Studying the conditions for the existence of isolated solutions for semi-linear loaded hyperbolic equations is of significant importance both in theory and practical applications. In this article, we will explore various approaches and methods used to analyze. In [1], issues related to loaded equations and their applications are investigated. The computational method for solving boundary value problems for loaded integro-differential equations and the correct solvability of boundary value problems for loaded differential equations were studied in works [2],[3]. Various problems for loaded differential equations and methods for finding their solutions are considered in [4-9].
{"title":"Conditions for the existence of an \"isolated\" solution of a boundary value problem for a semilinear loaded hyperbolic equation","authors":"S. Kabdrakhova","doi":"10.26577/jmmcs2023v119i3a3","DOIUrl":"https://doi.org/10.26577/jmmcs2023v119i3a3","url":null,"abstract":"Boundary value problems for hyperbolic equations are an important area of mathematical physics and science in nature. They arise in various physical and engineering contexts and have a wide range of applications, including wave propagation in elastic media, electromagnetic waves, as well as problems related to fluid and gas motion. In this article, we will focus on one of the significant subclasses of hyperbolic equations, namely, semi-linear loaded hyperbolic equations, and examine the conditions for the existence of isolated solutions to boundary value problems for such equations.Semi-linear loaded hyperbolic equations are equations in which nonlinear terms depend on the solutions themselves. This makes their study more complex and mathematically intriguing. Our task is to find conditions under which such equations have isolated solutions, meaning solutions that exist in a bounded region of space and time and remain bounded themselves.Studying the conditions for the existence of isolated solutions for semi-linear loaded hyperbolic equations is of significant importance both in theory and practical applications. In this article, we will explore various approaches and methods used to analyze. In [1], issues related to loaded equations and their applications are investigated. The computational method for solving boundary value problems for loaded integro-differential equations and the correct solvability of boundary value problems for loaded differential equations were studied in works [2],[3]. Various problems for loaded differential equations and methods for finding their solutions are considered in [4-9].","PeriodicalId":53167,"journal":{"name":"Vestnik KazNU Seriia matematika mekhanika informatika","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135735257","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 : 2023-09-01DOI: 10.26577/jmmcs2023v119i3a11
K. Shiyapov
The processes of immiscible liquids in porous media are one of the current topics in the modern world, where advanced technologies are used to obtain the most comprehensive information about the geological and geophysical properties of reservoirs. The process of separating two immiscible liquids at a contact surface without surface tension describes the phenomenon when two different types of liquids are in direct contact with each other without the formation of an interface boundary or surface tension between them. This phenomenon can be observed when certain conditions are met, and it is important in various scientific and engineering fields. It is well-known that all hydrodynamic processes are described by mathematical tools and models, and solving such problems allows for obtaining numerical solutions for practical applications in the future. The authors of the article present the problem statement of two immiscible liquids separated by a contact surface without surface tension. For the adequacy of this problem, the presence and singularity of a classical solution have been proven, which depend on the location of the unfixed boundary. The solution demonstrates the existence of a continuous boundary that divides the region into sections containing by two different liquids, where the initial density distribution is a smooth function.
{"title":"ON THE PROCESS OF TWO IMMISCIBLE LIQUIDS SEPARATED BY A CONTACT SURFACE WITHOUT SURFACE TENSION","authors":"K. Shiyapov","doi":"10.26577/jmmcs2023v119i3a11","DOIUrl":"https://doi.org/10.26577/jmmcs2023v119i3a11","url":null,"abstract":"The processes of immiscible liquids in porous media are one of the current topics in the modern world, where advanced technologies are used to obtain the most comprehensive information about the geological and geophysical properties of reservoirs. The process of separating two immiscible liquids at a contact surface without surface tension describes the phenomenon when two different types of liquids are in direct contact with each other without the formation of an interface boundary or surface tension between them. This phenomenon can be observed when certain conditions are met, and it is important in various scientific and engineering fields. It is well-known that all hydrodynamic processes are described by mathematical tools and models, and solving such problems allows for obtaining numerical solutions for practical applications in the future. The authors of the article present the problem statement of two immiscible liquids separated by a contact surface without surface tension. For the adequacy of this problem, the presence and singularity of a classical solution have been proven, which depend on the location of the unfixed boundary. The solution demonstrates the existence of a continuous boundary that divides the region into sections containing by two different liquids, where the initial density distribution is a smooth function.","PeriodicalId":53167,"journal":{"name":"Vestnik KazNU Seriia matematika mekhanika informatika","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135735262","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 : 2023-09-01DOI: 10.26577/jmmcs2023v119i3a1
Serik Aitzhanov
In this paper, we consider the coefficient inverse problem for a third-order pseudoparabolic equation, which represents mathematical model for the movement of moisture and salts in soils. Such non-classical equations are also called Sobolev-type equations. At present, the study of direct and inverse problems for a pseudoparabolic equation is readily developing due to the needs of modeling and controlling processes in hydrodynamics, mechanics, thermal physics and continuum mechanics. At the same time, the investigation of coefficient inverse problems is also important, since they are used in solving problems of planning the development of oil fields, in particular, in determining the filtration parameters of fields, in creating new types of measuring equipment, in solving environmental monitoring problems, etc. Thus both trend directions such as pseudoparabolic equations and coefficient inverse problems are relevant due to the abundance of various applications where such non-classical objects arise. In this work, the Galerkin method is used to prove the existence of the solution for the inverse coefficient problem and obtained sufficient conditions for the blow up of its solution in a finite time in a bounded domain. Moreover, authors developed the algorithm for the numerical solution of the given problem by using the finite difference method. In addition, computational experiments were carried out illustrating the theoretical calculations obtained in the work.
{"title":"The coefficient inverse problem for a pseudoparabolic equation of the third order","authors":"Serik Aitzhanov","doi":"10.26577/jmmcs2023v119i3a1","DOIUrl":"https://doi.org/10.26577/jmmcs2023v119i3a1","url":null,"abstract":"In this paper, we consider the coefficient inverse problem for a third-order pseudoparabolic equation, which represents mathematical model for the movement of moisture and salts in soils. Such non-classical equations are also called Sobolev-type equations. At present, the study of direct and inverse problems for a pseudoparabolic equation is readily developing due to the needs of modeling and controlling processes in hydrodynamics, mechanics, thermal physics and continuum mechanics. At the same time, the investigation of coefficient inverse problems is also important, since they are used in solving problems of planning the development of oil fields, in particular, in determining the filtration parameters of fields, in creating new types of measuring equipment, in solving environmental monitoring problems, etc. Thus both trend directions such as pseudoparabolic equations and coefficient inverse problems are relevant due to the abundance of various applications where such non-classical objects arise. In this work, the Galerkin method is used to prove the existence of the solution for the inverse coefficient problem and obtained sufficient conditions for the blow up of its solution in a finite time in a bounded domain. Moreover, authors developed the algorithm for the numerical solution of the given problem by using the finite difference method. In addition, computational experiments were carried out illustrating the theoretical calculations obtained in the work.","PeriodicalId":53167,"journal":{"name":"Vestnik KazNU Seriia matematika mekhanika informatika","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135735256","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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