I. K. Agwu, Umar Ishtiaq, N. Saleem, D. Igbokwe, F. Jarad
In this paper, a novel implicit IH-multistep fixed point algorithm and convergence result for a general class of contractive maps is introduced without any imposition of the "sum conditions" on the countably finite family of the iteration parameters. Furthermore, it is shown that the convergence of the proposed iteration scheme is equivalent to some other implicit IH-type iterative schemes (e.g., implicit IH-Noor, implicit IH-Ishikawa and implicit IH-Mann) for the same class of maps. Also, some numerical examples are given to illustrate that the equivalence is true. Our results complement, improve and unify several equivalent results recently announced in literature.
{"title":"Equivalence of novel IH-implicit fixed point algorithms for a general class of contractive maps","authors":"I. K. Agwu, Umar Ishtiaq, N. Saleem, D. Igbokwe, F. Jarad","doi":"10.3934/math.2023041","DOIUrl":"https://doi.org/10.3934/math.2023041","url":null,"abstract":"In this paper, a novel implicit IH-multistep fixed point algorithm and convergence result for a general class of contractive maps is introduced without any imposition of the \"sum conditions\" on the countably finite family of the iteration parameters. Furthermore, it is shown that the convergence of the proposed iteration scheme is equivalent to some other implicit IH-type iterative schemes (e.g., implicit IH-Noor, implicit IH-Ishikawa and implicit IH-Mann) for the same class of maps. Also, some numerical examples are given to illustrate that the equivalence is true. Our results complement, improve and unify several equivalent results recently announced in literature.","PeriodicalId":48562,"journal":{"name":"AIMS Mathematics","volume":"1 1","pages":""},"PeriodicalIF":2.2,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70149511","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Muhammad Akram, S. Shah, M. M. Al-Shamiri, S. Edalatpanah
Data envelopment analysis (DEA) is a linear programming approach used to determine the relative efficiencies of multiple decision-making units (DMUs). A transportation problem (TP) is a special type of linear programming problem (LPP) which is used to minimize the total transportation cost or maximize the total transportation profit of transporting a product from multiple sources to multiple destinations. Because of the connection between the multi-objective TP (MOTP) and DEA, DEA-based techniques are more often used to handle practical TPs. The objective of this work is to investigate the TP with Fermatean fuzzy costs in the presence of numerous conflicting objectives. In particular, a Fermatean fuzzy DEA (FFDEA) method is proposed to solve the Fermatean fuzzy MOTP (FFMOTP). In this regard, every arc in FFMOTP is considered a DMU. Additionally, those objective functions that should be maximized will be used to define the outputs of DMUs, while those that should be minimized will be used to define the inputs of DMUs. As a consequence, two different Fermatean fuzzy effciency scores (FFESs) will be obtained for every arc by solving the FFDEA models. Therefore, unique FFESs will be obtained for every arc by finding the mean of these FFESs. Finally, the FFMOTP will be transformed into a single objective Fermatean fuzzy TP (FFTP) that can be solved by applying standard algorithms. A numerical example is illustrated to support the proposed method, and the results obtained by using the proposed method are compared to those of existing techniques. Moreover, the advantages of the proposed method are also discussed.
数据包络分析(DEA)是一种用于确定多个决策单元(dmu)相对效率的线性规划方法。运输问题(TP)是一种特殊类型的线性规划问题(LPP)，用于将产品从多个来源运输到多个目的地的总运输成本最小化或总运输利润最大化。由于多目标目标决策(MOTP)与DEA之间的联系，基于DEA的技术更常用于处理实际的多目标目标决策。本工作的目的是研究在存在许多冲突目标的情况下，具有费尔马模糊成本的TP。针对fermatan fuzzy MOTP (FFMOTP)问题，提出了一种fermatan fuzzy DEA (FFDEA)方法。在这方面，《FFMOTP》中的每个弧都被视为DMU。此外，那些应该最大化的目标函数将被用来定义dmu的输出，而那些应该最小化的目标函数将被用来定义dmu的输入。因此，通过求解FFDEA模型，每条弧线将得到两个不同的Fermatean模糊效率分数(FFESs)。因此，通过求这些FFESs的均值，就可以得到每条弧唯一的FFESs。最后，将FFMOTP转化为可应用标准算法求解的单目标Fermatean fuzzy TP (FFTP)。数值算例验证了所提方法的正确性，并将所提方法的结果与现有方法的结果进行了比较。此外，还讨论了该方法的优点。
{"title":"Extended DEA method for solving multi-objective transportation problem with Fermatean fuzzy sets","authors":"Muhammad Akram, S. Shah, M. M. Al-Shamiri, S. Edalatpanah","doi":"10.3934/math.2023045","DOIUrl":"https://doi.org/10.3934/math.2023045","url":null,"abstract":"Data envelopment analysis (DEA) is a linear programming approach used to determine the relative efficiencies of multiple decision-making units (DMUs). A transportation problem (TP) is a special type of linear programming problem (LPP) which is used to minimize the total transportation cost or maximize the total transportation profit of transporting a product from multiple sources to multiple destinations. Because of the connection between the multi-objective TP (MOTP) and DEA, DEA-based techniques are more often used to handle practical TPs. The objective of this work is to investigate the TP with Fermatean fuzzy costs in the presence of numerous conflicting objectives. In particular, a Fermatean fuzzy DEA (FFDEA) method is proposed to solve the Fermatean fuzzy MOTP (FFMOTP). In this regard, every arc in FFMOTP is considered a DMU. Additionally, those objective functions that should be maximized will be used to define the outputs of DMUs, while those that should be minimized will be used to define the inputs of DMUs. As a consequence, two different Fermatean fuzzy effciency scores (FFESs) will be obtained for every arc by solving the FFDEA models. Therefore, unique FFESs will be obtained for every arc by finding the mean of these FFESs. Finally, the FFMOTP will be transformed into a single objective Fermatean fuzzy TP (FFTP) that can be solved by applying standard algorithms. A numerical example is illustrated to support the proposed method, and the results obtained by using the proposed method are compared to those of existing techniques. Moreover, the advantages of the proposed method are also discussed.","PeriodicalId":48562,"journal":{"name":"AIMS Mathematics","volume":"1 1","pages":""},"PeriodicalIF":2.2,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70149818","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
The singular value decomposition (SVD) is an important tool in matrix theory and numerical linear algebra. Research on the efficient numerical algorithms for computing the SVD of a matrix is extensive in the past decades. In this paper, we propose an alternating direction power-method for computing the largest singular value and singular vector of a matrix. The new method is similar to the well-known power method but needs fewer operations in the iterations. Convergence of the new method is proved under suitable conditions. Theoretical analysis and numerical experiments show both that the new method is feasible and is effective than the power method in some cases.
{"title":"An alternating direction power-method for computing the largest singular value and singular vectors of a matrix","authors":"Yonghong Duan, Ruiping Wen","doi":"10.3934/math.2023056","DOIUrl":"https://doi.org/10.3934/math.2023056","url":null,"abstract":"The singular value decomposition (SVD) is an important tool in matrix theory and numerical linear algebra. Research on the efficient numerical algorithms for computing the SVD of a matrix is extensive in the past decades. In this paper, we propose an alternating direction power-method for computing the largest singular value and singular vector of a matrix. The new method is similar to the well-known power method but needs fewer operations in the iterations. Convergence of the new method is proved under suitable conditions. Theoretical analysis and numerical experiments show both that the new method is feasible and is effective than the power method in some cases.","PeriodicalId":48562,"journal":{"name":"AIMS Mathematics","volume":"1 1","pages":""},"PeriodicalIF":2.2,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70149953","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In this paper we use the fixed point index theory to study the existence of positive radial solutions for a system of boundary value problems with semipositone second order elliptic equations. Some appropriate concave and convex functions are utilized to characterize coupling behaviors of our nonlinearities.
{"title":"Positive radial solutions for a boundary value problem associated to a system of elliptic equations with semipositone nonlinearities","authors":"Limin Guo, Jiafa Xu, D. O’Regan","doi":"10.3934/math.2023053","DOIUrl":"https://doi.org/10.3934/math.2023053","url":null,"abstract":"In this paper we use the fixed point index theory to study the existence of positive radial solutions for a system of boundary value problems with semipositone second order elliptic equations. Some appropriate concave and convex functions are utilized to characterize coupling behaviors of our nonlinearities.","PeriodicalId":48562,"journal":{"name":"AIMS Mathematics","volume":"1 1","pages":""},"PeriodicalIF":2.2,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70150124","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Xinna Mao, Hongwei Feng, M. Al-Towailb, H. Saberi-Nik
The dynamical behavior of a 5-dimensional Lorenz model (5DLM) is investigated. Bifurcation diagrams address the chaotic and periodic behaviors associated with the bifurcation parameter. The Hamilton energy and its dependence on the stability of the dynamical system are presented. The global exponential attractive set (GEAS) is estimated in different 3-dimensional projection planes. A more conservative bound for the system is determined, that can be applied in synchronization and chaos control of dynamical systems. Finally, the finite time synchronization of the 5DLM, indicating the role of the ultimate bound for each variable, is studied. Simulations illustrate the effectiveness of the achieved theoretical results.
{"title":"Dynamical analysis and boundedness for a generalized chaotic Lorenz model","authors":"Xinna Mao, Hongwei Feng, M. Al-Towailb, H. Saberi-Nik","doi":"10.3934/math.20231005","DOIUrl":"https://doi.org/10.3934/math.20231005","url":null,"abstract":"The dynamical behavior of a 5-dimensional Lorenz model (5DLM) is investigated. Bifurcation diagrams address the chaotic and periodic behaviors associated with the bifurcation parameter. The Hamilton energy and its dependence on the stability of the dynamical system are presented. The global exponential attractive set (GEAS) is estimated in different 3-dimensional projection planes. A more conservative bound for the system is determined, that can be applied in synchronization and chaos control of dynamical systems. Finally, the finite time synchronization of the 5DLM, indicating the role of the ultimate bound for each variable, is studied. Simulations illustrate the effectiveness of the achieved theoretical results.","PeriodicalId":48562,"journal":{"name":"AIMS Mathematics","volume":"1 1","pages":""},"PeriodicalIF":2.2,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70152785","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In recent years, it has been gradually recognized that efficient scheduling of automated guided vehicles (AGVs) can help companies find the balance between energy consumption and workstation satisfaction. Therefore, the energy consumption of AGVs for the manufacturing environment and the AGV energy efficient scheduling problem with customer satisfaction (AGVEESC) in a flexible manufacturing system are investigated. A new multi-objective non-linear programming model is developed to minimize energy consumption while maximizing workstation satisfaction by optimizing the pick-up and delivery processes of the AGV for material handling. Through the introduction of auxiliary variables, the model is linearized. Then, an interactive fuzzy programming approach is developed to obtain a compromise solution by constructing a membership function for two conflicting objectives. The experimental results show that a good level of energy consumption and workstation satisfaction can be achieved through the proposed model and algorithm.
{"title":"Multi-objective optimization for AGV energy efficient scheduling problem with customer satisfaction","authors":"Jiaxin Chen, Yuxuan Wu, Shuai Huang, Pei Wang","doi":"10.3934/math.20231024","DOIUrl":"https://doi.org/10.3934/math.20231024","url":null,"abstract":"In recent years, it has been gradually recognized that efficient scheduling of automated guided vehicles (AGVs) can help companies find the balance between energy consumption and workstation satisfaction. Therefore, the energy consumption of AGVs for the manufacturing environment and the AGV energy efficient scheduling problem with customer satisfaction (AGVEESC) in a flexible manufacturing system are investigated. A new multi-objective non-linear programming model is developed to minimize energy consumption while maximizing workstation satisfaction by optimizing the pick-up and delivery processes of the AGV for material handling. Through the introduction of auxiliary variables, the model is linearized. Then, an interactive fuzzy programming approach is developed to obtain a compromise solution by constructing a membership function for two conflicting objectives. The experimental results show that a good level of energy consumption and workstation satisfaction can be achieved through the proposed model and algorithm.","PeriodicalId":48562,"journal":{"name":"AIMS Mathematics","volume":"1 1","pages":""},"PeriodicalIF":2.2,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70153931","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In the value distribution theory of complex analysis, Petrenko's deviation is to describe more precisely the quantitative relationship between $ T (r, f) $ and $ log M (r, f) $ when the modulus of variable $ |z| = r $ is sufficiently large. In this paper we introduce Petrenko's deviations to the coefficients of three types of complex equations, which include difference equations, differential equations and differential-difference equations. Under different assumptions we study the lower bound of limiting directions of Julia sets of solutions of these equations, where Julia set is an important concept in complex dynamical systems. The results of this article show that the lower bound of limiting directions mentioned above is closely related to Petrenko's deviation, and our conclusions improve some known results.
在复分析的值分布理论中，Petrenko的偏差是在变量$ |z| = r $的模足够大时，更精确地描述$ T (r, f) $与$ log M (r, f) $之间的定量关系。本文介绍了差分方程、微分方程和微分-差分方程三种复方程系数的Petrenko偏差。在不同的假设条件下，研究了这些方程的Julia集解的极限方向的下界，其中Julia集是复杂动力系统中的一个重要概念。本文的结果表明，上述极限方向的下界与Petrenko偏差密切相关，我们的结论改进了一些已知的结果。
{"title":"The lower bound on the measure of sets consisting of Julia limiting directions of solutions to some complex equations associated with Petrenko's deviation","authors":"Guowei Zhang","doi":"10.3934/math.20231028","DOIUrl":"https://doi.org/10.3934/math.20231028","url":null,"abstract":"In the value distribution theory of complex analysis, Petrenko's deviation is to describe more precisely the quantitative relationship between $ T (r, f) $ and $ log M (r, f) $ when the modulus of variable $ |z| = r $ is sufficiently large. In this paper we introduce Petrenko's deviations to the coefficients of three types of complex equations, which include difference equations, differential equations and differential-difference equations. Under different assumptions we study the lower bound of limiting directions of Julia sets of solutions of these equations, where Julia set is an important concept in complex dynamical systems. The results of this article show that the lower bound of limiting directions mentioned above is closely related to Petrenko's deviation, and our conclusions improve some known results.","PeriodicalId":48562,"journal":{"name":"AIMS Mathematics","volume":"1 1","pages":""},"PeriodicalIF":2.2,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70155401","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
This article discusses the robustness of exponential synchronization (ESy) of complex dynamic networks (CDNs) with random perturbations. Using the Gronwall-Bellman lemma and partial inequality techniques, by solving the transcendental equation, the maximum perturbation intensity of the CDN is estimated. This implies that the disturbed system achieves ESy if the disturbance intensity is within the range of our estimation. We illustrate the theoretical results with two numerical examples.
{"title":"Robustness analysis of exponential synchronization in complex dynamic networks with random perturbations","authors":"Qike Zhang, Wenxiang Fang, Tao Xie","doi":"10.3934/math.20231044","DOIUrl":"https://doi.org/10.3934/math.20231044","url":null,"abstract":"This article discusses the robustness of exponential synchronization (ESy) of complex dynamic networks (CDNs) with random perturbations. Using the Gronwall-Bellman lemma and partial inequality techniques, by solving the transcendental equation, the maximum perturbation intensity of the CDN is estimated. This implies that the disturbed system achieves ESy if the disturbance intensity is within the range of our estimation. We illustrate the theoretical results with two numerical examples.","PeriodicalId":48562,"journal":{"name":"AIMS Mathematics","volume":"1 1","pages":""},"PeriodicalIF":2.2,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70155523","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
The main interest of this work is to construct surface family pair with the symmetry of Bertrand pair in Euclidean 3-space $ mathbb{E}^{3} $. Then, by employing the Serret-Frenet frame, we conclude the sufficient and necessary conditions of surface family pair interpolating Bertrand pair as mutual geodesic curves. Moreover, the conclusion to ruled surface family pair is also obtained. Meanwhile, this work is demonstrated through several examples.
{"title":"Surface family pair with Bertrand pair as mutual geodesic curves in Euclidean 3-space $ mathbb{E}^{3} $","authors":"Areej A. Almoneef, R. Abdel-Baky","doi":"10.3934/math.20231047","DOIUrl":"https://doi.org/10.3934/math.20231047","url":null,"abstract":"The main interest of this work is to construct surface family pair with the symmetry of Bertrand pair in Euclidean 3-space $ mathbb{E}^{3} $. Then, by employing the Serret-Frenet frame, we conclude the sufficient and necessary conditions of surface family pair interpolating Bertrand pair as mutual geodesic curves. Moreover, the conclusion to ruled surface family pair is also obtained. Meanwhile, this work is demonstrated through several examples.","PeriodicalId":48562,"journal":{"name":"AIMS Mathematics","volume":"1 1","pages":""},"PeriodicalIF":2.2,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70156092","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
This paper considers the local stabilization problem for a hyperchaotic finance system by using a time-delayed feedback controller based on discrete-time observations. The quadratic system theory is employed to represent the nonlinear finance system and a piecewise augmented discontinuous Lyapunov-Krasovskii functional is constructed to analyze the stability of the closed-loop system. By further incorporating some advanced integral inequalities, a stabilization criterion is proposed by means of the feasibility of a set of linear matrix inequalities under which the hyperchaotic finance system can be asymptotically stabilized for any initial condition satisfying certain constraint. As the by-product, a simplified criterion is also obtained for the case without time delay. Moreover, the optimization problems with respect to the domain of attraction are specially discussed, which are transformed into the minimization problems subject to linear matrix inequalities. Finally, numerical simulations are provided to illustrate the effectiveness of the derived results.
{"title":"Local stabilization for a hyperchaotic finance system via time-delayed feedback based on discrete-time observations","authors":"E. Xu, Wenxing Xiao, Yonggang Chen","doi":"10.3934/math.20231045","DOIUrl":"https://doi.org/10.3934/math.20231045","url":null,"abstract":"This paper considers the local stabilization problem for a hyperchaotic finance system by using a time-delayed feedback controller based on discrete-time observations. The quadratic system theory is employed to represent the nonlinear finance system and a piecewise augmented discontinuous Lyapunov-Krasovskii functional is constructed to analyze the stability of the closed-loop system. By further incorporating some advanced integral inequalities, a stabilization criterion is proposed by means of the feasibility of a set of linear matrix inequalities under which the hyperchaotic finance system can be asymptotically stabilized for any initial condition satisfying certain constraint. As the by-product, a simplified criterion is also obtained for the case without time delay. Moreover, the optimization problems with respect to the domain of attraction are specially discussed, which are transformed into the minimization problems subject to linear matrix inequalities. Finally, numerical simulations are provided to illustrate the effectiveness of the derived results.","PeriodicalId":48562,"journal":{"name":"AIMS Mathematics","volume":"1 1","pages":""},"PeriodicalIF":2.2,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70156393","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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