Single-machine due-window assignment scheduling with delivery times and variable processing times is investigated, where the variable processing time of a job means that the processing time is a function of its position in a sequence and its resource allocation. Currently, there are multiple optimization objectives for the due-window assignment problem, and there is a small amount of research on optimization problems where the window starting time, the rejected cost and the optimal scheduling are jointly required. The goal of this paper is to minimize the weighed sum of scheduling cost, resource consumption cost and outsourcing measure under the optional job outsourcing (rejection). Under two resource allocation models (i.e., linear and convex resource allocation models), the scheduling cost is the weighted sum of the number of early–tardy jobs, earliness–tardiness penalties and due-window starting time and size, where the weights are positional-dependent. The main contributions of this paper include the study and data simulation of single-machine scheduling with learning effects, delivery times and outsourcing cost. For the weighed sum of scheduling cost, resource consumption cost and outsourcing measure, we prove the polynomial solvability of the problem. Under the common and slack due-window assignments, through the theoretical analysis of the optimal solution, we reveal that four problems can be solved in O(n6) time, where n is the number of jobs.
研究了具有交货时间和可变处理时间的单机到期窗口分配调度，其中作业的可变处理时间意味着处理时间是其在序列中的位置和资源分配的函数。目前，到期窗口分配问题有多个优化目标，而对窗口起始时间、拒绝成本和优化调度共同要求的优化问题的研究较少。本文的目标是在可选工作外包（拒绝）的情况下，使调度成本、资源消耗成本和外包措施的权重之和最小化。在两种资源分配模型（即线性资源分配模型和凸资源分配模型）下，调度成本是早迟到作业数量、早迟到惩罚和到期窗口开始时间及大小的加权和，其中权重与位置有关。本文的主要贡献包括对具有学习效应、交货时间和外包成本的单机调度进行了研究和数据模拟。对于调度成本、资源消耗成本和外包成本的权重和，我们证明了问题的多项式可解性。在普通和松弛的到期窗口分配下，通过最优解的理论分析，我们发现四个问题可以在 O(n6) 时间内求解，其中 n 为作业数。
{"title":"Study on Single-Machine Common/Slack Due-Window Assignment Scheduling with Delivery Times, Variable Processing Times and Outsourcing","authors":"Bing Bai, Cai-Min Wei, Hong-Yu He, Ji-Bo Wang","doi":"10.3390/math12182883","DOIUrl":"https://doi.org/10.3390/math12182883","url":null,"abstract":"Single-machine due-window assignment scheduling with delivery times and variable processing times is investigated, where the variable processing time of a job means that the processing time is a function of its position in a sequence and its resource allocation. Currently, there are multiple optimization objectives for the due-window assignment problem, and there is a small amount of research on optimization problems where the window starting time, the rejected cost and the optimal scheduling are jointly required. The goal of this paper is to minimize the weighed sum of scheduling cost, resource consumption cost and outsourcing measure under the optional job outsourcing (rejection). Under two resource allocation models (i.e., linear and convex resource allocation models), the scheduling cost is the weighted sum of the number of early–tardy jobs, earliness–tardiness penalties and due-window starting time and size, where the weights are positional-dependent. The main contributions of this paper include the study and data simulation of single-machine scheduling with learning effects, delivery times and outsourcing cost. For the weighed sum of scheduling cost, resource consumption cost and outsourcing measure, we prove the polynomial solvability of the problem. Under the common and slack due-window assignments, through the theoretical analysis of the optimal solution, we reveal that four problems can be solved in O(n6) time, where n is the number of jobs.","PeriodicalId":18303,"journal":{"name":"Mathematics","volume":"5 1","pages":""},"PeriodicalIF":2.4,"publicationDate":"2024-09-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142249143","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 investigates the impact of tariff escalation on multinational suppliers relocating their production capacity to tariff-preferential regions with unreliable supply caused by low-production technology. We build a game theory model to analyze this issue based on three decisions for supplier-capacity relocation: no relocation, partial relocation, and full relocation. Our analysis finds that when tariffs are low or the production technology of the base in a preferential tariff region is not advanced, the supplier tends to adopt a partial-relocation strategy, but this strategy may be hindered by a manufacturer’s order-allocation decision, leading to a no-relocation strategy as the supply chain’s equilibrium. This may result in greater losses for the supplier. When tariffs are high or the production technology of the base in the preferential tariff region is advanced, the equilibrium strategy for the supply chain shifts to a full-relocation strategy. Interestingly, in the partial-relocation strategy, the higher production technology in the preferential tariff region negatively impacts the manufacturer’s expected profits but benefits the supplier’s expected profits due to the increased double marginalization. Finally, we find that the supplier can reduce the impact of tariffs by relocating their production capacity, especially with the partial-relocation strategy, as the supplier is always motivated to improve the production technology of the base in the preferential tariff region, with a potential purpose of transferring tariff costs to the manufacturer and consumers.
{"title":"Should Multinational Suppliers Relocate Their Production Capacity to Preferential Tariff Regions with Unreliable Supply under the Impact of Tariffs?","authors":"Zongbao Zou, Yuxin Liang, Lihao Chen","doi":"10.3390/math12182876","DOIUrl":"https://doi.org/10.3390/math12182876","url":null,"abstract":"This paper investigates the impact of tariff escalation on multinational suppliers relocating their production capacity to tariff-preferential regions with unreliable supply caused by low-production technology. We build a game theory model to analyze this issue based on three decisions for supplier-capacity relocation: no relocation, partial relocation, and full relocation. Our analysis finds that when tariffs are low or the production technology of the base in a preferential tariff region is not advanced, the supplier tends to adopt a partial-relocation strategy, but this strategy may be hindered by a manufacturer’s order-allocation decision, leading to a no-relocation strategy as the supply chain’s equilibrium. This may result in greater losses for the supplier. When tariffs are high or the production technology of the base in the preferential tariff region is advanced, the equilibrium strategy for the supply chain shifts to a full-relocation strategy. Interestingly, in the partial-relocation strategy, the higher production technology in the preferential tariff region negatively impacts the manufacturer’s expected profits but benefits the supplier’s expected profits due to the increased double marginalization. Finally, we find that the supplier can reduce the impact of tariffs by relocating their production capacity, especially with the partial-relocation strategy, as the supplier is always motivated to improve the production technology of the base in the preferential tariff region, with a potential purpose of transferring tariff costs to the manufacturer and consumers.","PeriodicalId":18303,"journal":{"name":"Mathematics","volume":"3 1","pages":""},"PeriodicalIF":2.4,"publicationDate":"2024-09-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142249136","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}
Edgar D. Silva-Vera, Jesus E. Valdez-Resendiz, Gerardo Escobar, Daniel Guillen, Julio C. Rosas-Caro, Jose M. Sosa
This article presents a data-driven methodology for modeling lithium-ion batteries, which includes the estimation of the open-circuit voltage and state of charge. Using the proposed methodology, the dynamics of a battery cell can be captured without the need for explicit theoretical models. This approach only requires the acquisition of two easily measurable variables: the discharge current and the terminal voltage. The acquired data are used to build a linear differential system, which is algebraically manipulated to form a space-state representation of the battery cell. The resulting model was tested and compared against real discharging curves. Preliminary results showed that the battery’s state of charge can be computed with limited precision using a model that considers a constant open-circuit voltage. To improve the accuracy of the identified model, a modified recursive least-squares algorithm is implemented inside the data-driven method to estimate the battery’s open-circuit voltage. These last results showed a very precise tracking of the real battery discharging dynamics, including the terminal voltage and state of charge. The proposed data-driven methodology could simplify the implementation of adaptive control strategies in larger-scale solutions and battery management systems with the interconnection of multiple battery cells.
{"title":"Data-Driven Modeling and Open-Circuit Voltage Estimation of Lithium-Ion Batteries","authors":"Edgar D. Silva-Vera, Jesus E. Valdez-Resendiz, Gerardo Escobar, Daniel Guillen, Julio C. Rosas-Caro, Jose M. Sosa","doi":"10.3390/math12182880","DOIUrl":"https://doi.org/10.3390/math12182880","url":null,"abstract":"This article presents a data-driven methodology for modeling lithium-ion batteries, which includes the estimation of the open-circuit voltage and state of charge. Using the proposed methodology, the dynamics of a battery cell can be captured without the need for explicit theoretical models. This approach only requires the acquisition of two easily measurable variables: the discharge current and the terminal voltage. The acquired data are used to build a linear differential system, which is algebraically manipulated to form a space-state representation of the battery cell. The resulting model was tested and compared against real discharging curves. Preliminary results showed that the battery’s state of charge can be computed with limited precision using a model that considers a constant open-circuit voltage. To improve the accuracy of the identified model, a modified recursive least-squares algorithm is implemented inside the data-driven method to estimate the battery’s open-circuit voltage. These last results showed a very precise tracking of the real battery discharging dynamics, including the terminal voltage and state of charge. The proposed data-driven methodology could simplify the implementation of adaptive control strategies in larger-scale solutions and battery management systems with the interconnection of multiple battery cells.","PeriodicalId":18303,"journal":{"name":"Mathematics","volume":"25 1","pages":""},"PeriodicalIF":2.4,"publicationDate":"2024-09-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142249140","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}
Igor Fernández de Bustos, Haritz Uriarte, Gorka Urkullu, Ibai Coria
There are several common procedures used to numerically integrate second-order ordinary differential equations. The most common one is to reduce the equation’s order by duplicating the number of variables. This allows one to take advantage of the family of Runge–Kutta methods or the Adams family of multi-step methods. Another approach is the use of methods that have been developed to directly integrate an ordinary differential equation without increasing the number of variables. An important drawback when using Runge–Kutta methods is that when one tries to apply them to differential algebraic equations, they require a reduction in the index, leading to a need for stabilization methods to remove the drift. In this paper, a new family of methods for the direct integration of second-order ordinary differential equations is presented. These methods can be considered as a generalization of the central differences method. The methods are classified according to the number of derivatives they take into account (degree). They include some parameters that can be chosen to configure the equation’s behavior. Some sets of parameters were studied, and some examples belonging to structural dynamics and multibody dynamics are presented. An example of the application of the method to a differential algebraic equation is also included.
{"title":"A Family of Conditionally Explicit Methods for Second-Order ODEs and DAEs: Application in Multibody Dynamics","authors":"Igor Fernández de Bustos, Haritz Uriarte, Gorka Urkullu, Ibai Coria","doi":"10.3390/math12182862","DOIUrl":"https://doi.org/10.3390/math12182862","url":null,"abstract":"There are several common procedures used to numerically integrate second-order ordinary differential equations. The most common one is to reduce the equation’s order by duplicating the number of variables. This allows one to take advantage of the family of Runge–Kutta methods or the Adams family of multi-step methods. Another approach is the use of methods that have been developed to directly integrate an ordinary differential equation without increasing the number of variables. An important drawback when using Runge–Kutta methods is that when one tries to apply them to differential algebraic equations, they require a reduction in the index, leading to a need for stabilization methods to remove the drift. In this paper, a new family of methods for the direct integration of second-order ordinary differential equations is presented. These methods can be considered as a generalization of the central differences method. The methods are classified according to the number of derivatives they take into account (degree). They include some parameters that can be chosen to configure the equation’s behavior. Some sets of parameters were studied, and some examples belonging to structural dynamics and multibody dynamics are presented. An example of the application of the method to a differential algebraic equation is also included.","PeriodicalId":18303,"journal":{"name":"Mathematics","volume":"14 1","pages":""},"PeriodicalIF":2.4,"publicationDate":"2024-09-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142249183","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 Klein–-Gordon equation plays an important role in mathematical physics, such as plasma and, condensed matter physics. Exploring its exact solution helps us understand its complex nonlinear wave phenomena. In this paper, we first propose a new extended Jacobian elliptic function expansion method for constructing rich exact periodic wave solutions of the (2+1)-dimensional Klein–-Gordon equation. Then, we introduce a novel wave transformation for constructing nonlinear complex waves. To demonstrate the effectiveness of this method, we numerically simulated several sets of complex wave structures, which indicate new types of complex wave phenomena. The results show that this method is simple and effective for constructing rich exact solutions and complex nonlinear wave phenomena to nonlinear equations.
{"title":"Nonlinear Complex Wave Excitations in (2+1)-Dimensional Klein–Gordon Equation Investigated by New Wave Transformation","authors":"Guojiang Wu, Yong Guo, Yanlin Yu","doi":"10.3390/math12182867","DOIUrl":"https://doi.org/10.3390/math12182867","url":null,"abstract":"The Klein–-Gordon equation plays an important role in mathematical physics, such as plasma and, condensed matter physics. Exploring its exact solution helps us understand its complex nonlinear wave phenomena. In this paper, we first propose a new extended Jacobian elliptic function expansion method for constructing rich exact periodic wave solutions of the (2+1)-dimensional Klein–-Gordon equation. Then, we introduce a novel wave transformation for constructing nonlinear complex waves. To demonstrate the effectiveness of this method, we numerically simulated several sets of complex wave structures, which indicate new types of complex wave phenomena. The results show that this method is simple and effective for constructing rich exact solutions and complex nonlinear wave phenomena to nonlinear equations.","PeriodicalId":18303,"journal":{"name":"Mathematics","volume":"18 1","pages":""},"PeriodicalIF":2.4,"publicationDate":"2024-09-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142249186","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}
Milica Dragas, Slobodanka Galovic, Dejan Milicevic, Edin Suljovrujic, Katarina Djordjevic
The inverse photoacoustic problem is an ill-posed mathematical physics problem. There are many methods of solving the inverse photoacoustic problem, from parameter reduction to the development of complex regularization algorithms. The idea of this work is that semiconductor physical properties are determined from phase characteristic measurements because phase measurements are more sensitive than amplitude measurements. To solve the inverse photoacoustic problem, the thermoelastic properties and thickness of the sample are estimated using a neural network approach. The neural network was trained on a large database of photoacoustic phases calculated from a theoretical Si n-type model in the range of 20 Hz to 20 kHz, to which random Gaussian noise was applied. It is shown that in solving the inverse photoacoustic problem, high accuracy and precision can be achieved by applying phase measurement and neural network approaches. This study showed that a multi-parameter inverse problem can be solved using phase networks.
反向光声问题是一个难以解决的数学物理问题。解决反向光声问题的方法有很多，从减少参数到开发复杂的正则化算法。这项工作的思路是通过相位特性测量来确定半导体的物理特性，因为相位测量比振幅测量更灵敏。为了解决逆光声学问题，使用神经网络方法估算样品的热弹性特性和厚度。神经网络是在一个大型光声相位数据库上进行训练的，该数据库是根据 20 Hz 至 20 kHz 范围内的硅 n 型理论模型计算得出的，其中应用了随机高斯噪声。研究表明，在解决反向光声问题时，应用相位测量和神经网络方法可以实现高精度和高准确度。这项研究表明，利用相位网络可以解决多参数逆问题。
{"title":"Solution of Inverse Photoacoustic Problem for Semiconductors via Phase Neural Network","authors":"Milica Dragas, Slobodanka Galovic, Dejan Milicevic, Edin Suljovrujic, Katarina Djordjevic","doi":"10.3390/math12182858","DOIUrl":"https://doi.org/10.3390/math12182858","url":null,"abstract":"The inverse photoacoustic problem is an ill-posed mathematical physics problem. There are many methods of solving the inverse photoacoustic problem, from parameter reduction to the development of complex regularization algorithms. The idea of this work is that semiconductor physical properties are determined from phase characteristic measurements because phase measurements are more sensitive than amplitude measurements. To solve the inverse photoacoustic problem, the thermoelastic properties and thickness of the sample are estimated using a neural network approach. The neural network was trained on a large database of photoacoustic phases calculated from a theoretical Si n-type model in the range of 20 Hz to 20 kHz, to which random Gaussian noise was applied. It is shown that in solving the inverse photoacoustic problem, high accuracy and precision can be achieved by applying phase measurement and neural network approaches. This study showed that a multi-parameter inverse problem can be solved using phase networks.","PeriodicalId":18303,"journal":{"name":"Mathematics","volume":"11 1","pages":""},"PeriodicalIF":2.4,"publicationDate":"2024-09-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142249147","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 delves into the dynamics of a discrete-time predator–prey system. Initially, it presents the existence and stability conditions of the fixed points. Subsequently, by employing the center manifold theorem and bifurcation theory, the conditions for the occurrence of four types of codimension 1 bifurcations (transcritical bifurcation, fold bifurcation, flip bifurcation, and Neimark–Sacker bifurcation) are examined. Then, through several variable substitutions and the introduction of new parameters, the conditions for the existence of codimension 2 bifurcations (fold–flip bifurcation, 1:2 and 1:4 strong resonances) are derived. Finally, some numerical analyses of two-parameter planes are provided. The two-parameter plane plots showcase interesting dynamical behaviors of the discrete system as the integral step size and other parameters vary. These results unveil much richer dynamics of the discrete-time model in comparison to the continuous model.
{"title":"Some Bifurcations of Codimensions 1 and 2 in a Discrete Predator–Prey Model with Non-Linear Harvesting","authors":"Ming Liu, Linyi Ma, Dongpo Hu","doi":"10.3390/math12182872","DOIUrl":"https://doi.org/10.3390/math12182872","url":null,"abstract":"This paper delves into the dynamics of a discrete-time predator–prey system. Initially, it presents the existence and stability conditions of the fixed points. Subsequently, by employing the center manifold theorem and bifurcation theory, the conditions for the occurrence of four types of codimension 1 bifurcations (transcritical bifurcation, fold bifurcation, flip bifurcation, and Neimark–Sacker bifurcation) are examined. Then, through several variable substitutions and the introduction of new parameters, the conditions for the existence of codimension 2 bifurcations (fold–flip bifurcation, 1:2 and 1:4 strong resonances) are derived. Finally, some numerical analyses of two-parameter planes are provided. The two-parameter plane plots showcase interesting dynamical behaviors of the discrete system as the integral step size and other parameters vary. These results unveil much richer dynamics of the discrete-time model in comparison to the continuous model.","PeriodicalId":18303,"journal":{"name":"Mathematics","volume":"1 1","pages":""},"PeriodicalIF":2.4,"publicationDate":"2024-09-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142249189","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}
Cuiping Zhou, Shaobo Li, Cankun Xie, Panliang Yuan, Xiangfu Long
The snow ablation optimizer (SAO) is a meta-heuristic technique used to seek the best solution for sophisticated problems. In response to the defects in the SAO algorithm, which has poor search efficiency and is prone to getting trapped in local optima, this article suggests a multi-strategy improved (MISAO) snow ablation optimizer. It is employed in the unmanned aerial vehicle (UAV) path planning issue. To begin with, the tent chaos and elite reverse learning initialization strategies are merged to extend the diversity of the population; secondly, a greedy selection method is deployed to retain superior alternative solutions for the upcoming iteration; then, the Harris hawk (HHO) strategy is introduced to enhance the exploitation capability, which prevents trapping in partial ideals; finally, the red-tailed hawk (RTH) is adopted to perform the global exploration, which, enhances global optimization capability. To comprehensively evaluate MISAO’s optimization capability, a battery of digital optimization investigations is executed using 23 test functions, and the results of the comparative analysis show that the suggested algorithm has high solving accuracy and convergence velocity. Finally, the effectiveness and feasibility of the optimization path of the MISAO algorithm are demonstrated in the UAV path planning project.
{"title":"MISAO: A Multi-Strategy Improved Snow Ablation Optimizer for Unmanned Aerial Vehicle Path Planning","authors":"Cuiping Zhou, Shaobo Li, Cankun Xie, Panliang Yuan, Xiangfu Long","doi":"10.3390/math12182870","DOIUrl":"https://doi.org/10.3390/math12182870","url":null,"abstract":"The snow ablation optimizer (SAO) is a meta-heuristic technique used to seek the best solution for sophisticated problems. In response to the defects in the SAO algorithm, which has poor search efficiency and is prone to getting trapped in local optima, this article suggests a multi-strategy improved (MISAO) snow ablation optimizer. It is employed in the unmanned aerial vehicle (UAV) path planning issue. To begin with, the tent chaos and elite reverse learning initialization strategies are merged to extend the diversity of the population; secondly, a greedy selection method is deployed to retain superior alternative solutions for the upcoming iteration; then, the Harris hawk (HHO) strategy is introduced to enhance the exploitation capability, which prevents trapping in partial ideals; finally, the red-tailed hawk (RTH) is adopted to perform the global exploration, which, enhances global optimization capability. To comprehensively evaluate MISAO’s optimization capability, a battery of digital optimization investigations is executed using 23 test functions, and the results of the comparative analysis show that the suggested algorithm has high solving accuracy and convergence velocity. Finally, the effectiveness and feasibility of the optimization path of the MISAO algorithm are demonstrated in the UAV path planning project.","PeriodicalId":18303,"journal":{"name":"Mathematics","volume":"2 1","pages":""},"PeriodicalIF":2.4,"publicationDate":"2024-09-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142249192","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}
Lígia Henriques-Rodrigues, Frederico Caeiro, M. Ivette Gomes
The estimation of the extreme value index (EVI) is a crucial task in the field of statistics of extremes, as it provides valuable insights into the tail behavior of a distribution. For models with a Pareto-type tail, the Hill estimator is a popular choice. However, this estimator is susceptible to bias, which can lead to inaccurate estimations of the EVI, impacting the reliability of risk assessments and decision-making processes. This paper introduces a novel reduced-bias generalized Hill estimator, which aims to enhance the accuracy of EVI estimation by mitigating the bias.
{"title":"A New Class of Reduced-Bias Generalized Hill Estimators","authors":"Lígia Henriques-Rodrigues, Frederico Caeiro, M. Ivette Gomes","doi":"10.3390/math12182866","DOIUrl":"https://doi.org/10.3390/math12182866","url":null,"abstract":"The estimation of the extreme value index (EVI) is a crucial task in the field of statistics of extremes, as it provides valuable insights into the tail behavior of a distribution. For models with a Pareto-type tail, the Hill estimator is a popular choice. However, this estimator is susceptible to bias, which can lead to inaccurate estimations of the EVI, impacting the reliability of risk assessments and decision-making processes. This paper introduces a novel reduced-bias generalized Hill estimator, which aims to enhance the accuracy of EVI estimation by mitigating the bias.","PeriodicalId":18303,"journal":{"name":"Mathematics","volume":"11 1","pages":""},"PeriodicalIF":2.4,"publicationDate":"2024-09-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142249185","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 manuscript introduces a novel three-variable cubic functional equation and derives its general solution. Employing both the direct and fixed-point methods, we investigate the orthogonal stability of this equation within the frameworks of quasi-β-Banach spaces and multi-Banach spaces. Additionally, the study explores the stability of the equation in various extended Banach spaces and provides a specific example illustrating the absence of stability in certain cases.
{"title":"Orthogonal Stability and Solution of a Three-Variable Functional Equation in Extended Banach Spaces","authors":"Jagjeet Jakhar, Shalu Sharma, Jyotsana Jakhar, Majeed A. Yousif, Pshtiwan Othman Mohammed, Alina Alb Lupas, Nejmeddine Chorfi","doi":"10.3390/math12182868","DOIUrl":"https://doi.org/10.3390/math12182868","url":null,"abstract":"This manuscript introduces a novel three-variable cubic functional equation and derives its general solution. Employing both the direct and fixed-point methods, we investigate the orthogonal stability of this equation within the frameworks of quasi-β-Banach spaces and multi-Banach spaces. Additionally, the study explores the stability of the equation in various extended Banach spaces and provides a specific example illustrating the absence of stability in certain cases.","PeriodicalId":18303,"journal":{"name":"Mathematics","volume":"2 1","pages":""},"PeriodicalIF":2.4,"publicationDate":"2024-09-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142249188","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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