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":null,"pages":null},"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":null,"pages":null},"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":null,"pages":null},"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":null,"pages":null},"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":null,"pages":null},"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":null,"pages":null},"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":null,"pages":null},"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":null,"pages":null},"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}
Amit Singh Nayal, B. Singh, Abhishek Tyagi, C. Chesneau
The subject matter described herein includes the analysis of the stress-strength reliability of the system, in which the discrete strength of the system is impacted by two random discrete stresses. The reliability function of such systems is denoted by $ R = P[Y < X < Z] $, where $ X $ is the strength of the system and $ Y $ and $ Z $ are the stresses. We look at how $ X $, $ Y $ and $ Z $ fit into a well-known discrete distribution known as the geometric distribution. The stress-strength reliability of this form is not widely studied in the current literature, and research in this area has only considered the scenario when the strength and stress variables follow a continuous distribution, although it is essentially nil in the case of discrete stress and strength. There are numerous applications wherein a system is exposed to external stress, and its functionality depends on whether its intrinsic physical strength falls within specific stress limits. Furthermore, the continuous measurement of stress and strength variables presents inherent difficulties and inconveniences in such scenarios. For the suggested distribution, we obtain the maximum likelihood estimate of the variable $ R $, as well as its asymptotic distribution and confidence interval. Additionally, in the classical setup, we find the boot-p and boot-t confidence intervals for $ R $. In the Bayesian setup, we utilize the widely recognized Markov Chain Monte Carlo technique and the Lindley approximation method to find the Bayes estimate of $ R $ under the squared error loss function. A Monte Carlo simulation study and real data analysis are demonstrated to show the applicability of the suggested model in the real world.
本文描述的主题包括系统的应力-强度可靠度分析，其中系统的离散强度受到两个随机的离散应力的影响。用R = P[Y < X < Z] $表示系统的可靠性函数，其中$ X $为系统的强度，$ Y $和$ Z $为应力。我们看看X $， Y $和Z $是如何符合一个众所周知的离散分布，即几何分布的。目前文献中对这种形式的应力-强度可靠度的研究并不广泛，而且该领域的研究只考虑了强度和应力变量服从连续分布的情况，而在应力和强度离散的情况下基本没有研究。在许多应用中，系统暴露于外部应力，其功能取决于其内在物理强度是否落在特定的应力范围内。此外，在这种情况下，连续测量应力和强度变量存在固有的困难和不便。对于建议的分布，我们得到了变量$ R $的极大似然估计，以及它的渐近分布和置信区间。此外，在经典设置中，我们找到了$ R $的启动-p和启动-t置信区间。在贝叶斯设置中，我们利用广泛认可的马尔可夫链蒙特卡罗技术和林德利近似方法来寻找平方误差损失函数下的R $的贝叶斯估计。通过蒙特卡罗仿真研究和实际数据分析，证明了该模型在现实世界中的适用性。
{"title":"Classical and Bayesian inferences on the stress-strength reliability $ {R = P[Y < X < Z]} $ in the geometric distribution setting","authors":"Amit Singh Nayal, B. Singh, Abhishek Tyagi, C. Chesneau","doi":"10.3934/math.20231054","DOIUrl":"https://doi.org/10.3934/math.20231054","url":null,"abstract":"The subject matter described herein includes the analysis of the stress-strength reliability of the system, in which the discrete strength of the system is impacted by two random discrete stresses. The reliability function of such systems is denoted by $ R = P[Y < X < Z] $, where $ X $ is the strength of the system and $ Y $ and $ Z $ are the stresses. We look at how $ X $, $ Y $ and $ Z $ fit into a well-known discrete distribution known as the geometric distribution. The stress-strength reliability of this form is not widely studied in the current literature, and research in this area has only considered the scenario when the strength and stress variables follow a continuous distribution, although it is essentially nil in the case of discrete stress and strength. There are numerous applications wherein a system is exposed to external stress, and its functionality depends on whether its intrinsic physical strength falls within specific stress limits. Furthermore, the continuous measurement of stress and strength variables presents inherent difficulties and inconveniences in such scenarios. For the suggested distribution, we obtain the maximum likelihood estimate of the variable $ R $, as well as its asymptotic distribution and confidence interval. Additionally, in the classical setup, we find the boot-p and boot-t confidence intervals for $ R $. In the Bayesian setup, we utilize the widely recognized Markov Chain Monte Carlo technique and the Lindley approximation method to find the Bayes estimate of $ R $ under the squared error loss function. A Monte Carlo simulation study and real data analysis are demonstrated to show the applicability of the suggested model in the real world.","PeriodicalId":48562,"journal":{"name":"AIMS Mathematics","volume":null,"pages":null},"PeriodicalIF":2.2,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70156586","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}
S. Jesic, N. Ćirović, R. Nikolić, Branislav M. Ranƌelović
The main motivation for this paper is to investigate the fixed point property for non-expansive mappings defined on $ b $-fuzzy metric spaces. First, following the idea of S. Ješić's result from 2009, we introduce convex, strictly convex and normal structures for sets in $ b $-fuzzy metric spaces. By using topological methods and these notions, we prove the existence of fixed points for self-mappings defined on $ b $-fuzzy metric spaces satisfying a nonlinear type condition. This result generalizes and improves many previously known results, such as W. Takahashi's result on metric spaces from 1970. A representative example illustrating the main result is provided.
本文的主要动机是研究定义在$ b $-模糊度量空间上的非扩展映射的不动点性质。首先，根据s. Ješić在2009年的结果，我们引入了$ b $-模糊度量空间集合的凸结构、严格凸结构和正规结构。利用拓扑方法和这些概念，证明了在满足非线性型条件的$ b $-模糊度量空间上定义的自映射不动点的存在性。这个结果推广并改进了许多先前已知的结果，例如W. Takahashi在1970年关于度量空间的结果。给出了一个代表性的例子来说明主要结果。
{"title":"A fixed point theorem in strictly convex $ b $-fuzzy metric spaces","authors":"S. Jesic, N. Ćirović, R. Nikolić, Branislav M. Ranƌelović","doi":"10.3934/math.20231068","DOIUrl":"https://doi.org/10.3934/math.20231068","url":null,"abstract":"The main motivation for this paper is to investigate the fixed point property for non-expansive mappings defined on $ b $-fuzzy metric spaces. First, following the idea of S. Ješić's result from 2009, we introduce convex, strictly convex and normal structures for sets in $ b $-fuzzy metric spaces. By using topological methods and these notions, we prove the existence of fixed points for self-mappings defined on $ b $-fuzzy metric spaces satisfying a nonlinear type condition. This result generalizes and improves many previously known results, such as W. Takahashi's result on metric spaces from 1970. A representative example illustrating the main result is provided.","PeriodicalId":48562,"journal":{"name":"AIMS Mathematics","volume":null,"pages":null},"PeriodicalIF":2.2,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70157647","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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