Semicircles and circular sectors are both ubiquitous in the natural realm. However, mathematically speaking they have represented an enigma since antiquity. In recent years, the author has worked in integral equations with sections of spheres as related to radiative heat transfer and their associated form factors, to the point of defining new postulates. The main theorems thus far enunciated refer to the radiative exchange between circles and half disks, but recently the possibility to treat circular sectors has arrived, thanks to the research already conducted. As is known, to find the exact expression of the configuration factor by integration is complex. In the above mentioned problem of the circular sectors, the author reached the first two steps of the basic formulation for radiant exchange. Subsequently, the novelty of the procedure lies in introducing a finite differences approach for the third and fourth integrals which still remain unsolved, once we have been able to find the preliminary integrals. This possibility had not been identified by former research and the output provides us with an ample variety of unexpected scenarios. As a consequence, we are able to analyze with more precision the spatial transference of radiant heat for figures composed of circular sectors. We already know that spherical shapes cannot be discretized with any accuracy. Therefore, we would be able to reduce a considerable amount of hindrance in the progress of thermal radiation science. Important sequels will be derived for radiation in the entrance to tunnels, aircraft design and lighting as well.
{"title":"New Geometric Theorems Derived from Integral Equations Applied to Radiative Transfer in Spherical Sectors and Circular Segments","authors":"Joseph Cabeza-Lainez","doi":"10.3390/math12182875","DOIUrl":"https://doi.org/10.3390/math12182875","url":null,"abstract":"Semicircles and circular sectors are both ubiquitous in the natural realm. However, mathematically speaking they have represented an enigma since antiquity. In recent years, the author has worked in integral equations with sections of spheres as related to radiative heat transfer and their associated form factors, to the point of defining new postulates. The main theorems thus far enunciated refer to the radiative exchange between circles and half disks, but recently the possibility to treat circular sectors has arrived, thanks to the research already conducted. As is known, to find the exact expression of the configuration factor by integration is complex. In the above mentioned problem of the circular sectors, the author reached the first two steps of the basic formulation for radiant exchange. Subsequently, the novelty of the procedure lies in introducing a finite differences approach for the third and fourth integrals which still remain unsolved, once we have been able to find the preliminary integrals. This possibility had not been identified by former research and the output provides us with an ample variety of unexpected scenarios. As a consequence, we are able to analyze with more precision the spatial transference of radiant heat for figures composed of circular sectors. We already know that spherical shapes cannot be discretized with any accuracy. Therefore, we would be able to reduce a considerable amount of hindrance in the progress of thermal radiation science. Important sequels will be derived for radiation in the entrance to tunnels, aircraft design and lighting as well.","PeriodicalId":18303,"journal":{"name":"Mathematics","volume":"185 1","pages":""},"PeriodicalIF":2.4,"publicationDate":"2024-09-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142249193","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}
Mario Versaci, Filippo Laganà, Francesco Carlo Morabito, Annunziata Palumbo, Giovanni Angiulli
In this work, a known Eddy Current (EC) model is adapted to characterize subsurface defects in carbon fiber-reinforced polymer (CFRP) plates intended for the civil aerospace industry. The considered defects include delaminations, microcracks, porosity, fiber breakage, and the simultaneous presence of these defects. Each defect is modeled as an additive variation in the material’s electrical conductivity tensor, allowing for a detailed mathematical representation of the defect’s influence on the CFRP’s electromagnetic behavior. The additivity of the variations in the conductivity tensor is justified by the assumption that the defects are not visible to the naked eye, implying that the material does not require non-destructive testing. The adapted EC model admits a unique and stable solution by verifying that all analytical steps are satisfied. To reconstruct 2D maps of the magnetic flux density amplitude, a FEM formulation is adopted, based on the energy functional because it ensures a stable and consistent numerical formulation given its coercivity. Moreover, the numerical approach allows precise and reliable numerical solutions, enhancing the capability to detect and quantify defects. The numerical results show that the obtained 2D maps are entirely superimposable on those highlighting the distribution of mechanical stress states known in the literature, offering a clear advantage in terms of detection costs. This approach provides an effective and economical solution for the non-destructive inspection of CFRP, ensuring accurate and timely defect diagnosis for maintaining structural integrity.
{"title":"Adaptation of an Eddy Current Model for Characterizing Subsurface Defects in CFRP Plates Using FEM Analysis Based on Energy Functional","authors":"Mario Versaci, Filippo Laganà, Francesco Carlo Morabito, Annunziata Palumbo, Giovanni Angiulli","doi":"10.3390/math12182854","DOIUrl":"https://doi.org/10.3390/math12182854","url":null,"abstract":"In this work, a known Eddy Current (EC) model is adapted to characterize subsurface defects in carbon fiber-reinforced polymer (CFRP) plates intended for the civil aerospace industry. The considered defects include delaminations, microcracks, porosity, fiber breakage, and the simultaneous presence of these defects. Each defect is modeled as an additive variation in the material’s electrical conductivity tensor, allowing for a detailed mathematical representation of the defect’s influence on the CFRP’s electromagnetic behavior. The additivity of the variations in the conductivity tensor is justified by the assumption that the defects are not visible to the naked eye, implying that the material does not require non-destructive testing. The adapted EC model admits a unique and stable solution by verifying that all analytical steps are satisfied. To reconstruct 2D maps of the magnetic flux density amplitude, a FEM formulation is adopted, based on the energy functional because it ensures a stable and consistent numerical formulation given its coercivity. Moreover, the numerical approach allows precise and reliable numerical solutions, enhancing the capability to detect and quantify defects. The numerical results show that the obtained 2D maps are entirely superimposable on those highlighting the distribution of mechanical stress states known in the literature, offering a clear advantage in terms of detection costs. This approach provides an effective and economical solution for the non-destructive inspection of CFRP, ensuring accurate and timely defect diagnosis for maintaining structural integrity.","PeriodicalId":18303,"journal":{"name":"Mathematics","volume":"8 1","pages":""},"PeriodicalIF":2.4,"publicationDate":"2024-09-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142223523","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 study addresses the diagnostic challenges of Systemic Lupus Erythematosus (SLE), an autoimmune disease with a complex etiology and varied symptoms. The ANA (antinuclear antibody) test, currently the primary diagnostic tool for SLE, exhibits high sensitivity but low specificity, often leading to inaccurate diagnoses. To enhance diagnostic precision, we propose integrating machine learning algorithms with existing clinical classification guidelines to improve SLE diagnosis accuracy, potentially reducing diagnostic errors and healthcare costs. We analyzed real-world data from a cohort of 24,990 patients over a 10-year period at the hospitals, excluding those previously diagnosed with SLE. Patients were categorized into three groups: negative ANA, positive ANA with non-SLE, and positive ANA with SLE. Feature selection was conducted to identify key factors influencing SLE diagnosis, and machine learning algorithms were employed to develop the CDSS. Performance analysis of three machine learning algorithms—decision tree, random forest, and gradient boosting—based on feature sets of 10, 20, and all available features revealed accuracy rates of 70%, 88%, and 87%, respectively, for the 20-feature set. The proposed system, utilizing real-world medical data, demonstrated modest performance in SLE diagnosis, highlighting the potential of machine learning-based CDSS in real clinical settings.
系统性红斑狼疮（SLE）是一种病因复杂、症状多样的自身免疫性疾病。ANA（抗核抗体）检测是目前系统性红斑狼疮的主要诊断工具，但其灵敏度高而特异性低，常常导致诊断不准确。为了提高诊断的准确性，我们建议将机器学习算法与现有的临床分类指南相结合，以提高系统性红斑狼疮诊断的准确性，从而减少诊断错误和医疗成本。我们分析了各家医院 10 年间 24990 名患者的真实世界数据，其中不包括之前被诊断为系统性红斑狼疮的患者。患者被分为三组：ANA 阴性、非系统性红斑狼疮 ANA 阳性和系统性红斑狼疮 ANA 阳性。通过特征选择来确定影响系统性红斑狼疮诊断的关键因素，并采用机器学习算法来开发 CDSS。对基于 10、20 和所有可用特征集的三种机器学习算法（决策树、随机森林和梯度提升）进行的性能分析表明，20 个特征集的准确率分别为 70%、88% 和 87%。所提出的系统利用真实世界的医疗数据，在系统性红斑狼疮诊断中表现出了适度的性能，凸显了基于机器学习的 CDSS 在实际临床环境中的潜力。
{"title":"Improving the Diagnosis of Systemic Lupus Erythematosus with Machine Learning Algorithms Based on Real-World Data","authors":"Meeyoung Park","doi":"10.3390/math12182849","DOIUrl":"https://doi.org/10.3390/math12182849","url":null,"abstract":"This study addresses the diagnostic challenges of Systemic Lupus Erythematosus (SLE), an autoimmune disease with a complex etiology and varied symptoms. The ANA (antinuclear antibody) test, currently the primary diagnostic tool for SLE, exhibits high sensitivity but low specificity, often leading to inaccurate diagnoses. To enhance diagnostic precision, we propose integrating machine learning algorithms with existing clinical classification guidelines to improve SLE diagnosis accuracy, potentially reducing diagnostic errors and healthcare costs. We analyzed real-world data from a cohort of 24,990 patients over a 10-year period at the hospitals, excluding those previously diagnosed with SLE. Patients were categorized into three groups: negative ANA, positive ANA with non-SLE, and positive ANA with SLE. Feature selection was conducted to identify key factors influencing SLE diagnosis, and machine learning algorithms were employed to develop the CDSS. Performance analysis of three machine learning algorithms—decision tree, random forest, and gradient boosting—based on feature sets of 10, 20, and all available features revealed accuracy rates of 70%, 88%, and 87%, respectively, for the 20-feature set. The proposed system, utilizing real-world medical data, demonstrated modest performance in SLE diagnosis, highlighting the potential of machine learning-based CDSS in real clinical settings.","PeriodicalId":18303,"journal":{"name":"Mathematics","volume":"151 1","pages":""},"PeriodicalIF":2.4,"publicationDate":"2024-09-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142177052","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}
Aleksandar Senić, Momčilo Dobrodolac, Zoran Stojadinović
Road infrastructure plays a crucial role in the development of countries, significantly influencing economic growth, social progress, and environmental sustainability. Major infrastructure projects are frequently challenged by substantial risks and uncertainties, leading to delays, budget overruns, and compromised quality. These issues can undermine the economic viability and efficiency of projects, making effective risk management essential for minimizing negative impacts and ensuring project success. For these reasons, a study was conducted using a Sugeno fuzzy logic system applied to completed projects. The resulting model is based on 10 project characteristics and provides highly accurate predictions for Extension of Time (EoT) and Increasing Contract Price (ICP). By utilizing this model, project management can be significantly improved through more accurate forecasting of potential delays and cost overruns. The high precision of the Sugeno fuzzy logic system enables better risk assessment and proactive decision-making, allowing project managers to implement targeted strategies to mitigate risks and optimize project outcomes.
{"title":"Predicting Extension of Time and Increasing Contract Price in Road Infrastructure Projects Using a Sugeno Fuzzy Logic Model","authors":"Aleksandar Senić, Momčilo Dobrodolac, Zoran Stojadinović","doi":"10.3390/math12182852","DOIUrl":"https://doi.org/10.3390/math12182852","url":null,"abstract":"Road infrastructure plays a crucial role in the development of countries, significantly influencing economic growth, social progress, and environmental sustainability. Major infrastructure projects are frequently challenged by substantial risks and uncertainties, leading to delays, budget overruns, and compromised quality. These issues can undermine the economic viability and efficiency of projects, making effective risk management essential for minimizing negative impacts and ensuring project success. For these reasons, a study was conducted using a Sugeno fuzzy logic system applied to completed projects. The resulting model is based on 10 project characteristics and provides highly accurate predictions for Extension of Time (EoT) and Increasing Contract Price (ICP). By utilizing this model, project management can be significantly improved through more accurate forecasting of potential delays and cost overruns. The high precision of the Sugeno fuzzy logic system enables better risk assessment and proactive decision-making, allowing project managers to implement targeted strategies to mitigate risks and optimize project outcomes.","PeriodicalId":18303,"journal":{"name":"Mathematics","volume":"78 1","pages":""},"PeriodicalIF":2.4,"publicationDate":"2024-09-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142177056","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}
We consider the problem of finding the largest clique of a graph. This is an NP-hard problem and no exact algorithm to solve it exactly in polynomial time is known to exist. Several heuristic approaches have been proposed to find approximate solutions. Markov Chain Monte Carlo is one of these. In the context of Markov Chain Monte Carlo, we present a class of “parallel dynamics”, known as Probabilistic Cellular Automata, which can be used in place of the more standard choice of sequential “single spin flip” to sample from a probability distribution concentrated on the largest cliques of the graph. We perform a numerical comparison between the two classes of chains both in terms of the quality of the solution and in terms of computational time. We show that the parallel dynamics are considerably faster than the sequential ones while providing solutions of comparable quality.
{"title":"Probabilistic Cellular Automata Monte Carlo for the Maximum Clique Problem","authors":"Alessio Troiani","doi":"10.3390/math12182850","DOIUrl":"https://doi.org/10.3390/math12182850","url":null,"abstract":"We consider the problem of finding the largest clique of a graph. This is an NP-hard problem and no exact algorithm to solve it exactly in polynomial time is known to exist. Several heuristic approaches have been proposed to find approximate solutions. Markov Chain Monte Carlo is one of these. In the context of Markov Chain Monte Carlo, we present a class of “parallel dynamics”, known as Probabilistic Cellular Automata, which can be used in place of the more standard choice of sequential “single spin flip” to sample from a probability distribution concentrated on the largest cliques of the graph. We perform a numerical comparison between the two classes of chains both in terms of the quality of the solution and in terms of computational time. We show that the parallel dynamics are considerably faster than the sequential ones while providing solutions of comparable quality.","PeriodicalId":18303,"journal":{"name":"Mathematics","volume":"46 1","pages":""},"PeriodicalIF":2.4,"publicationDate":"2024-09-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142177053","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}
Malihe Niksirat, Mohsen Saffarian, Javad Tayyebi, Adrian Marius Deaconu, Delia Elena Spridon
This paper explores a multi-objective, multi-period integrated routing and scheduling problem under uncertain conditions for distributing relief to disaster areas. The goals are to minimize costs and maximize satisfaction levels. To achieve this, the proposed mathematical model aims to speed up the delivery of relief supplies to the most affected areas. Additionally, the demands and transportation times are represented using fuzzy numbers to more accurately reflect real-world conditions. The problem was formulated using a fuzzy multi-objective integer programming model. To solve it, a hybrid algorithm combining a multi-objective ant colony system and simulated annealing algorithm was proposed. This algorithm adopts two ant colonies to obtain a set of nondominated solutions (the Pareto set). Numerical analyses have been conducted to determine the optimal parameter values for the proposed algorithm and to evaluate the performance of both the model and the algorithm. Furthermore, the algorithm’s performance was compared with that of the multi-objective cat swarm optimization algorithm and multi-objective fitness-dependent optimizer algorithm. The numerical results demonstrate the computational efficiency of the proposed method.
{"title":"Fuzzy Multi-Objective, Multi-Period Integrated Routing–Scheduling Problem to Distribute Relief to Disaster Areas: A Hybrid Ant Colony Optimization Approach","authors":"Malihe Niksirat, Mohsen Saffarian, Javad Tayyebi, Adrian Marius Deaconu, Delia Elena Spridon","doi":"10.3390/math12182844","DOIUrl":"https://doi.org/10.3390/math12182844","url":null,"abstract":"This paper explores a multi-objective, multi-period integrated routing and scheduling problem under uncertain conditions for distributing relief to disaster areas. The goals are to minimize costs and maximize satisfaction levels. To achieve this, the proposed mathematical model aims to speed up the delivery of relief supplies to the most affected areas. Additionally, the demands and transportation times are represented using fuzzy numbers to more accurately reflect real-world conditions. The problem was formulated using a fuzzy multi-objective integer programming model. To solve it, a hybrid algorithm combining a multi-objective ant colony system and simulated annealing algorithm was proposed. This algorithm adopts two ant colonies to obtain a set of nondominated solutions (the Pareto set). Numerical analyses have been conducted to determine the optimal parameter values for the proposed algorithm and to evaluate the performance of both the model and the algorithm. Furthermore, the algorithm’s performance was compared with that of the multi-objective cat swarm optimization algorithm and multi-objective fitness-dependent optimizer algorithm. The numerical results demonstrate the computational efficiency of the proposed method.","PeriodicalId":18303,"journal":{"name":"Mathematics","volume":"88 1","pages":""},"PeriodicalIF":2.4,"publicationDate":"2024-09-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142177047","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 safety of chemical processes is of critical importance. However, traditional fault monitoring methods have insufficiently studied the monitoring accuracy of multi-channel data and have not adequately considered the impact of noise on industrial processes. To address this issue, this paper proposes a neural network-based model, DSCBAM-DenseNet, which integrates depthwise separable convolution and attention modules to fuse multi-channel data features and enhance the model’s noise resistance. We simulated a real environment by adding Gaussian noise with different signal-to-noise ratios to the Tennessee Eastman process dataset and trained the model using multi-channel data. The experimental results show that this model outperforms traditional models in both fault diagnosis accuracy and noise resistance. Further research on a compressor unit engineering instance validated the superiority of the model.
{"title":"Fault Monitoring Method for the Process Industry System Based on the Improved Dense Connection Network","authors":"Jiarula Yasenjiang, Zhigang Lan, Kai Wang, Luhui Lv, Chao He, Yingjun Zhao, Wenhao Wang, Tian Gao","doi":"10.3390/math12182843","DOIUrl":"https://doi.org/10.3390/math12182843","url":null,"abstract":"The safety of chemical processes is of critical importance. However, traditional fault monitoring methods have insufficiently studied the monitoring accuracy of multi-channel data and have not adequately considered the impact of noise on industrial processes. To address this issue, this paper proposes a neural network-based model, DSCBAM-DenseNet, which integrates depthwise separable convolution and attention modules to fuse multi-channel data features and enhance the model’s noise resistance. We simulated a real environment by adding Gaussian noise with different signal-to-noise ratios to the Tennessee Eastman process dataset and trained the model using multi-channel data. The experimental results show that this model outperforms traditional models in both fault diagnosis accuracy and noise resistance. Further research on a compressor unit engineering instance validated the superiority of the model.","PeriodicalId":18303,"journal":{"name":"Mathematics","volume":"107 1","pages":""},"PeriodicalIF":2.4,"publicationDate":"2024-09-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142177048","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}
Based on the principles of biomimicry, evolutionary algorithms (EAs) have been widely applied across diverse domains to tackle practical challenges. However, the inherent limitations of these algorithms call for further refinement to strike a delicate balance between global exploration and local exploitation. Thus, this paper introduces a novel multi-strategy enhanced hybrid algorithm called MHWACO, which integrates a Whale Optimization Algorithm (WOA) and Ant Colony Optimization (ACO). Initially, MHWACO employs Gaussian perturbation optimization for individual initialization. Subsequently, individuals selectively undertake either localized exploration based on the refined WOA or global prospecting anchored in the Golden Sine Algorithm (Golden-SA), determined by transition probabilities. Inspired by the collaborative behavior of ant colonies, a Flight Ant (FA) strategy is proposed to guide unoptimized individuals toward potential global optimal solutions. Finally, the Gaussian scatter search (GSS) strategy is activated during low population activity, striking a balance between global exploration and local exploitation capabilities. Moreover, the efficacy of Support Vector Regression (SVR) and random forest (RF) as regression models heavily depends on parameter selection. In response, we have devised the MHWACO-SVM and MHWACO-RF models to refine the selection of parameters, applying them to various real-world problems such as stock prediction, housing estimation, disease forecasting, fire prediction, and air quality monitoring. Experimental comparisons against 9 newly proposed intelligent optimization algorithms and 9 enhanced algorithms across 34 benchmark test functions and the CEC2022 benchmark suite, highlight the notable superiority and efficacy of MSWOA in addressing global optimization problems. Finally, the proposed MHWACO-SVM and MHWACO-RF models outperform other regression models across key metrics such as the Mean Bias Error (MBE), Coefficient of Determination (R2), Mean Absolute Error (MAE), Explained Variance Score (EVS), and Median Absolute Error (MEAE).
{"title":"A Multi-Strategy Enhanced Hybrid Ant–Whale Algorithm and Its Applications in Machine Learning","authors":"Chenyang Gao, Yahua He , Yuelin Gao","doi":"10.3390/math12182848","DOIUrl":"https://doi.org/10.3390/math12182848","url":null,"abstract":"Based on the principles of biomimicry, evolutionary algorithms (EAs) have been widely applied across diverse domains to tackle practical challenges. However, the inherent limitations of these algorithms call for further refinement to strike a delicate balance between global exploration and local exploitation. Thus, this paper introduces a novel multi-strategy enhanced hybrid algorithm called MHWACO, which integrates a Whale Optimization Algorithm (WOA) and Ant Colony Optimization (ACO). Initially, MHWACO employs Gaussian perturbation optimization for individual initialization. Subsequently, individuals selectively undertake either localized exploration based on the refined WOA or global prospecting anchored in the Golden Sine Algorithm (Golden-SA), determined by transition probabilities. Inspired by the collaborative behavior of ant colonies, a Flight Ant (FA) strategy is proposed to guide unoptimized individuals toward potential global optimal solutions. Finally, the Gaussian scatter search (GSS) strategy is activated during low population activity, striking a balance between global exploration and local exploitation capabilities. Moreover, the efficacy of Support Vector Regression (SVR) and random forest (RF) as regression models heavily depends on parameter selection. In response, we have devised the MHWACO-SVM and MHWACO-RF models to refine the selection of parameters, applying them to various real-world problems such as stock prediction, housing estimation, disease forecasting, fire prediction, and air quality monitoring. Experimental comparisons against 9 newly proposed intelligent optimization algorithms and 9 enhanced algorithms across 34 benchmark test functions and the CEC2022 benchmark suite, highlight the notable superiority and efficacy of MSWOA in addressing global optimization problems. Finally, the proposed MHWACO-SVM and MHWACO-RF models outperform other regression models across key metrics such as the Mean Bias Error (MBE), Coefficient of Determination (R2), Mean Absolute Error (MAE), Explained Variance Score (EVS), and Median Absolute Error (MEAE).","PeriodicalId":18303,"journal":{"name":"Mathematics","volume":"18 1","pages":""},"PeriodicalIF":2.4,"publicationDate":"2024-09-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142177050","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}
A sequence of n trials from a finite population with no replacement is described by the hypergeometric distribution as the number of successes. Calculating the likelihood that factory-produced items would be defective is one of the most popular uses of the hypergeometric distribution in industrial quality control. Very recently, several researchers have applied this distribution on certain families of analytic functions. In this study, we provide certain adequate criteria for the generalized hypergeometric distribution series to be in two families of analytic functions defined in the open unit disk. Furthermore, we consider an integral operator for the hypergeometric distribution. Some corollaries will be implied from our main results.
超几何分布用成功次数来描述从有限群体中进行的 n 次无替换试验序列。计算工厂生产的产品出现缺陷的可能性是超几何分布在工业质量控制中最常用的方法之一。最近，一些研究人员将该分布应用于某些分析函数族。在本研究中，我们为广义超几何分布序列进入定义在开放单位盘中的两个解析函数族提供了某些适当的标准。此外，我们还考虑了超几何分布的积分算子。我们的主要结果将隐含一些推论。
{"title":"Applications of Generalized Hypergeometric Distribution on Comprehensive Families of Analytic Functions","authors":"Tariq Al-Hawary, Basem Frasin, Ibtisam Aldawish","doi":"10.3390/math12182851","DOIUrl":"https://doi.org/10.3390/math12182851","url":null,"abstract":"A sequence of n trials from a finite population with no replacement is described by the hypergeometric distribution as the number of successes. Calculating the likelihood that factory-produced items would be defective is one of the most popular uses of the hypergeometric distribution in industrial quality control. Very recently, several researchers have applied this distribution on certain families of analytic functions. In this study, we provide certain adequate criteria for the generalized hypergeometric distribution series to be in two families of analytic functions defined in the open unit disk. Furthermore, we consider an integral operator for the hypergeometric distribution. Some corollaries will be implied from our main results.","PeriodicalId":18303,"journal":{"name":"Mathematics","volume":"42 1","pages":""},"PeriodicalIF":2.4,"publicationDate":"2024-09-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142177054","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}
Hui Chen, Jie Chen, Yangyang Lai, Xiaoqi Yu, Lijun Shang, Rui Peng, Baoliang Liu
With advanced digital technologies as the key support, many scholars and researchers have proposed various random warranty models by integrating mission cycles into the warranty stage. However, these existing warranty models are designed only from the manufacturer’s subjective perspective, ignoring certain consumer requirements. For instance, they overlook a wide range of warranty coverage, the pursuit of reliability improvement rather than mere minimal repair, and the need to limit the delay in repair. To address these consumer requirements, this paper proposes a novel random collaborative preventive maintenance warranty with repair-time threshold (RCPMW-RTT). This model incorporates terms that are jointly designed by manufacturers and consumers to meet specific consumer needs, thereby overcoming the limitations of existing warranty models. The introduction of a repair-time threshold aims to limit the time delay in repairing failures and to compensate for any losses incurred by consumers. Using probability theory, the RCPMW-RTT is evaluated in terms of cost and time, and relevant variants are derived by analyzing key parameters. As an exemplary representation of the RCPMW-RTT, two random replacement policies named the discrete random renewable back replacement (DRRBR) and the discrete random renewable front replacement (DRRFR) are proposed and modelled to ensure reliability after the expiration of the RCPMW-RTT. In both policies, product replacement is triggered either by the occurrence of the first extreme mission cycle or by reaching the limit on the number of non-extreme mission cycles, whichever comes first. Probability theory is used to present cost rates for both policies in order to determine optimal values for decision variables. Finally, numerical analysis is performed on the RCPMW-RTT to reveal hidden variation tendencies and mechanisms; numerical analysis is also performed on the DRRBR and the DRRFR. The numerical results show that the proposed random replacement policies are feasible and unique; the replacement time within the post-warranty coverage increases as the maintenance quality improves and the cost rate can be reduced by setting a smaller repair-time threshold.
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