In this paper, we discuss a discrete mathematical model of Islamic polygamy and the social position of Muslims. In eleven compartments we explain the social situation and give an explanation of the marital status of each Males and females in Islamic societies that allow polygamy. In order to controlling and reducing the number of virgins men and women, divorced men and women we implement two control variables. The first control characterizes the benefits of an awareness campaign to educate virgin men and women about the benefits marriage to the individual and society, and the second control is about the legal procedures, administrative complexities and the grave financial and social implications of divorce. After that, we applied the optimal control theory to describe such an optimal strategies and finally a numerical simulation was performed to verify the theoretical analysis using a progressive-regressive discrete schema that converges following a convenient test related to the Forward–Backward Sweep Method (FBSM).
{"title":"Discrete mathematical modeling and optimal control of the marital status: Islamic polygamous marriage model case","authors":"A. Sakkoum, M. Lhous, M. Rachik, A. Tridane","doi":"10.23939/mmc2023.03.748","DOIUrl":"https://doi.org/10.23939/mmc2023.03.748","url":null,"abstract":"In this paper, we discuss a discrete mathematical model of Islamic polygamy and the social position of Muslims. In eleven compartments we explain the social situation and give an explanation of the marital status of each Males and females in Islamic societies that allow polygamy. In order to controlling and reducing the number of virgins men and women, divorced men and women we implement two control variables. The first control characterizes the benefits of an awareness campaign to educate virgin men and women about the benefits marriage to the individual and society, and the second control is about the legal procedures, administrative complexities and the grave financial and social implications of divorce. After that, we applied the optimal control theory to describe such an optimal strategies and finally a numerical simulation was performed to verify the theoretical analysis using a progressive-regressive discrete schema that converges following a convenient test related to the Forward–Backward Sweep Method (FBSM).","PeriodicalId":37156,"journal":{"name":"Mathematical Modeling and Computing","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"68769050","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}
M. Meftah, S. Ounacer, S. Ardchir, M. El Ghazouani, M. Azzouazi
The use of association rule mining techniques has become a focal point for many researchers seeking a better understanding of consumer behavior. By analyzing the relationships between products and their placement in aisles, valuable insights can be gained into the factors that influence product preservation in large-scale distribution environments. This approach has the potential to inform better decision-making processes and optimize product preservation outcomes, despite some limitations in the quality of the data available. Additionally, a hybridization approach was adopted by incorporating transactions from clients participating in a loyalty program to encourage large-scale distributions to gain a better understanding of customer behavior and improve their purchasing strategies. The goal of this research is to promote consistency between the real-world and virtual representations of customer behavior, ultimately leading to improved purchasing outcomes for large-scale distributions.
{"title":"Revolutionizing supermarket services with hierarchical association rule mining","authors":"M. Meftah, S. Ounacer, S. Ardchir, M. El Ghazouani, M. Azzouazi","doi":"10.23939/mmc2023.02.547","DOIUrl":"https://doi.org/10.23939/mmc2023.02.547","url":null,"abstract":"The use of association rule mining techniques has become a focal point for many researchers seeking a better understanding of consumer behavior. By analyzing the relationships between products and their placement in aisles, valuable insights can be gained into the factors that influence product preservation in large-scale distribution environments. This approach has the potential to inform better decision-making processes and optimize product preservation outcomes, despite some limitations in the quality of the data available. Additionally, a hybridization approach was adopted by incorporating transactions from clients participating in a loyalty program to encourage large-scale distributions to gain a better understanding of customer behavior and improve their purchasing strategies. The goal of this research is to promote consistency between the real-world and virtual representations of customer behavior, ultimately leading to improved purchasing outcomes for large-scale distributions.","PeriodicalId":37156,"journal":{"name":"Mathematical Modeling and Computing","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"68769085","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}
Simulated annealing algorithm is one of the most popular metaheuristics that has been successfully applied to many optimization problems. The main advantage of SA is its ability to escape from local optima by allowing hill-climbing moves and exploring new solutions at the beginning of the search process. One of its drawbacks is its slow convergence, requiring high computational time with a good set of parameter values to find a reasonable solution. In this work, a new improved SA is proposed to solve the well-known travelling salesman problem. In order to improve SA performance, a population-based improvement procedure is incorporated after the acceptance phase of SA, allowing the algorithm to take advantage of the social behavior of some solutions from the search space. Numerical results were carried out using known TSP instances from TSPLIB and preliminary results show that the proposed algorithm outperforms in terms of solution quality, the other comparison algorithms.
{"title":"A new improved simulated annealing for traveling salesman problem","authors":"N. Adil, H. Lakhbab","doi":"10.23939/mmc2023.03.764","DOIUrl":"https://doi.org/10.23939/mmc2023.03.764","url":null,"abstract":"Simulated annealing algorithm is one of the most popular metaheuristics that has been successfully applied to many optimization problems. The main advantage of SA is its ability to escape from local optima by allowing hill-climbing moves and exploring new solutions at the beginning of the search process. One of its drawbacks is its slow convergence, requiring high computational time with a good set of parameter values to find a reasonable solution. In this work, a new improved SA is proposed to solve the well-known travelling salesman problem. In order to improve SA performance, a population-based improvement procedure is incorporated after the acceptance phase of SA, allowing the algorithm to take advantage of the social behavior of some solutions from the search space. Numerical results were carried out using known TSP instances from TSPLIB and preliminary results show that the proposed algorithm outperforms in terms of solution quality, the other comparison algorithms.","PeriodicalId":37156,"journal":{"name":"Mathematical Modeling and Computing","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"68769100","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}
In this work, we numerically consider a swelling porous thermoelastic system with a heat flux given by the Maxwell–Cattaneo law. We study the numerical energy and the exponential decay of the thermoelastic problem. First, we give a variational formulation written in terms of the transformed derivatives corresponding to a coupled linear system composed of four first-order variational equations. A fully discrete algorithm is introduced and a discrete stability property is proven. A priori error estimates are also provided. Finally, some numerical results are given to demonstrate the behavior of the solution.
{"title":"A numerical study of swelling porous thermoelastic media with second sound","authors":"A. Smouk, A. Radid, A. Soufyane","doi":"10.23939/mmc2023.03.772","DOIUrl":"https://doi.org/10.23939/mmc2023.03.772","url":null,"abstract":"In this work, we numerically consider a swelling porous thermoelastic system with a heat flux given by the Maxwell–Cattaneo law. We study the numerical energy and the exponential decay of the thermoelastic problem. First, we give a variational formulation written in terms of the transformed derivatives corresponding to a coupled linear system composed of four first-order variational equations. A fully discrete algorithm is introduced and a discrete stability property is proven. A priori error estimates are also provided. Finally, some numerical results are given to demonstrate the behavior of the solution.","PeriodicalId":37156,"journal":{"name":"Mathematical Modeling and Computing","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"68769118","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}
In this paper, we are interested in solving the Toeplitz linear systems. By exploiting the special Toeplitz structure, we give a new decomposition form of the coefficient matrix. Based on this matrix decomposition form and combined with the Sherman–Morrison formula, we propose an efficient algorithm for solving the considered problem. A typical example is presented to illustrate the different steps of the proposed algorithm. In addition, numerical tests are given showing the efficiency of our algorithm.
{"title":"A new algorithm for solving Toeplitz linear systems","authors":"O. F. Aoulad, C. Tajani","doi":"10.23939/mmc2023.03.807","DOIUrl":"https://doi.org/10.23939/mmc2023.03.807","url":null,"abstract":"In this paper, we are interested in solving the Toeplitz linear systems. By exploiting the special Toeplitz structure, we give a new decomposition form of the coefficient matrix. Based on this matrix decomposition form and combined with the Sherman–Morrison formula, we propose an efficient algorithm for solving the considered problem. A typical example is presented to illustrate the different steps of the proposed algorithm. In addition, numerical tests are given showing the efficiency of our algorithm.","PeriodicalId":37156,"journal":{"name":"Mathematical Modeling and Computing","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"68769197","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}
We propose a homogenization method based on a matched asymptotic expansion technique to obtain the effective behavior of a periodic array of linear viscoelastic inclusions embedded in a linear viscoelastic matrix. The problem is considered for shear waves and the wave equation in the harmonic regime is considered. The obtained effective behavior is that of an equivalent interface associated to jump conditions, for the displacement and the normal stress at the interface. The transmission coefficients and the displacement fields are obtained in closed forms and their validity is inspected by comparison with direct numerics in the case of a rectangular inclusions.
{"title":"Homogenization of the Helmholtz problem in the presence of a row of viscoelastic inclusions","authors":"R. Belemou, A. Sbitti, M. Jaouahri, J. Marigo","doi":"10.23939/mmc2023.03.899","DOIUrl":"https://doi.org/10.23939/mmc2023.03.899","url":null,"abstract":"We propose a homogenization method based on a matched asymptotic expansion technique to obtain the effective behavior of a periodic array of linear viscoelastic inclusions embedded in a linear viscoelastic matrix. The problem is considered for shear waves and the wave equation in the harmonic regime is considered. The obtained effective behavior is that of an equivalent interface associated to jump conditions, for the displacement and the normal stress at the interface. The transmission coefficients and the displacement fields are obtained in closed forms and their validity is inspected by comparison with direct numerics in the case of a rectangular inclusions.","PeriodicalId":37156,"journal":{"name":"Mathematical Modeling and Computing","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"68769573","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}
Motion segmentation in real-world scenes is a fundamental component in computer vision. There exists a variety of motion recognition algorithms, each with varying degrees of accuracy and computational complexity. The most widely used techniques, in the case of static cameras, are those based on frame difference. Those methods have a significant weakness when it comes to detect slow moving objects. Therefore, we introduce in this paper a novel approach that aims to improve motion segmentation by proposing an accumulative wavelet based frame differencing technique. Moreover, in the proposed approach we exploit a combination of several techniques to efficiently enhance the quality of motion segmentation results. The approach's performance on real-world video sequences shows that comparing frames using the 2D wavelet transform increases motion segmentation quality.
{"title":"An adaptive wavelet shrinkage based accumulative frame differencing model for motion segmentation","authors":"M. J. Lahgazi, A. Hakim, P. Argoul","doi":"10.23939/mmc2023.01.159","DOIUrl":"https://doi.org/10.23939/mmc2023.01.159","url":null,"abstract":"Motion segmentation in real-world scenes is a fundamental component in computer vision. There exists a variety of motion recognition algorithms, each with varying degrees of accuracy and computational complexity. The most widely used techniques, in the case of static cameras, are those based on frame difference. Those methods have a significant weakness when it comes to detect slow moving objects. Therefore, we introduce in this paper a novel approach that aims to improve motion segmentation by proposing an accumulative wavelet based frame differencing technique. Moreover, in the proposed approach we exploit a combination of several techniques to efficiently enhance the quality of motion segmentation results. The approach's performance on real-world video sequences shows that comparing frames using the 2D wavelet transform increases motion segmentation quality.","PeriodicalId":37156,"journal":{"name":"Mathematical Modeling and Computing","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135534552","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}
I. Khaloufi, M. Lafif, Y. Benfatah, H. Laarabi, J. Bouyaghroumni, M. Rachik
A mathematical model of infectious disease contagion that accounts for population stratification based on immunity criteria is proposed. Our goal is to demonstrate the effectiveness of this idea in preventing different epidemics and to lessen the significant financial and human costs these diseases cause. We determined the fundamental reproduction rate, and with the help of this rate, we were able to examine the stability of the free equilibrium point and then proposed two control measures. The Pontryagin's maximum principle is used to describe the optimal controls, and an iterative approach is used to solve the optimality system. Finally, numerical simulations are carried out in MATLAB to verify the theoretical analysis.
{"title":"A continuous SIR mathematical model of the spread of infectious illnesses that takes human immunity into account","authors":"I. Khaloufi, M. Lafif, Y. Benfatah, H. Laarabi, J. Bouyaghroumni, M. Rachik","doi":"10.23939/mmc2023.01.053","DOIUrl":"https://doi.org/10.23939/mmc2023.01.053","url":null,"abstract":"A mathematical model of infectious disease contagion that accounts for population stratification based on immunity criteria is proposed. Our goal is to demonstrate the effectiveness of this idea in preventing different epidemics and to lessen the significant financial and human costs these diseases cause. We determined the fundamental reproduction rate, and with the help of this rate, we were able to examine the stability of the free equilibrium point and then proposed two control measures. The Pontryagin's maximum principle is used to describe the optimal controls, and an iterative approach is used to solve the optimality system. Finally, numerical simulations are carried out in MATLAB to verify the theoretical analysis.","PeriodicalId":37156,"journal":{"name":"Mathematical Modeling and Computing","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136092271","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}
Scale insects are parasitic insects that attack many indoor and outdoor plants, including cacti and succulents. These insects are among the frequent causes of diseases in cacti: for the reason that they are tough, multiply in record time and could be destructive to these plants, although they are considered resistant. Mealybugs feed on the sap of plants, drying them out and discoloring them. In this research, we propose and investigate a fractional model for the transmission of the Cochineal. In the first place, we prove the positivity and boundedness of solutions in order to ensure the well-posedness of the proposed model. The local stability of the disease-free equilibrium and the chronic infection equilibrium is established. Numerical simulations are presented in order to validate our theoretical results.
{"title":"Stability analysis of a fractional model for the transmission of the cochineal","authors":"O. El Baz, M. Ait Ichou, H. Laarabi, M. Rachik","doi":"10.23939/mmc2023.02.379","DOIUrl":"https://doi.org/10.23939/mmc2023.02.379","url":null,"abstract":"Scale insects are parasitic insects that attack many indoor and outdoor plants, including cacti and succulents. These insects are among the frequent causes of diseases in cacti: for the reason that they are tough, multiply in record time and could be destructive to these plants, although they are considered resistant. Mealybugs feed on the sap of plants, drying them out and discoloring them. In this research, we propose and investigate a fractional model for the transmission of the Cochineal. In the first place, we prove the positivity and boundedness of solutions in order to ensure the well-posedness of the proposed model. The local stability of the disease-free equilibrium and the chronic infection equilibrium is established. Numerical simulations are presented in order to validate our theoretical results.","PeriodicalId":37156,"journal":{"name":"Mathematical Modeling and Computing","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"68768499","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}
An analysis for the numerical computing of the temperature around a solidification point of liquid steel or melt contained in a mould is performed via the interaction of the conservation equations of mass, momentum and heat transfer. A cooling process of liquid steel due to the extraction of heat through the walls of the mould is analyzed using asymptotic methods and an ordinary differential equation that describes the temperature of interface melt-air is obtained. Also, the temperature of the melt in the mould around the solidification point is computed numerically using the OpenFOAM software.
{"title":"A numerical evaluation of the temperature of a solidification point in ingot casting processes","authors":"M. Zambrano","doi":"10.23939/mmc2023.02.410","DOIUrl":"https://doi.org/10.23939/mmc2023.02.410","url":null,"abstract":"An analysis for the numerical computing of the temperature around a solidification point of liquid steel or melt contained in a mould is performed via the interaction of the conservation equations of mass, momentum and heat transfer. A cooling process of liquid steel due to the extraction of heat through the walls of the mould is analyzed using asymptotic methods and an ordinary differential equation that describes the temperature of interface melt-air is obtained. Also, the temperature of the melt in the mould around the solidification point is computed numerically using the OpenFOAM software.","PeriodicalId":37156,"journal":{"name":"Mathematical Modeling and Computing","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"68768604","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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