Journal Description
Mathematics
Mathematics
is a peer-reviewed, open access journal which provides an advanced forum for studies related to mathematics, and is published semimonthly online by MDPI. The European Society for Fuzzy Logic and Technology (EUSFLAT) and International Society for the Study of Information (IS4SI) are affiliated with Mathematics and their members receive a discount on article processing charges.
- Open Access— free for readers, with article processing charges (APC) paid by authors or their institutions.
- High Visibility: indexed within Scopus, SCIE (Web of Science), RePEc, and other databases.
- Journal Rank: JCR - Q1 (Mathematics) / CiteScore - Q1 (General Mathematics)
- Rapid Publication: manuscripts are peer-reviewed and a first decision is provided to authors approximately 16.9 days after submission; acceptance to publication is undertaken in 2.6 days (median values for papers published in this journal in the second half of 2023).
- Recognition of Reviewers: reviewers who provide timely, thorough peer-review reports receive vouchers entitling them to a discount on the APC of their next publication in any MDPI journal, in appreciation of the work done.
- Sections: published in 13 topical sections.
- Companion journals for Mathematics include: Foundations, AppliedMath, Analytics, International Journal of Topology, Geometry and Logics.
Impact Factor:
2.4 (2022);
5-Year Impact Factor:
2.3 (2022)
Latest Articles
An Adaptive Cubature Kalman Filter Based on Resampling-Free Sigma-Point Update Framework and Improved Empirical Mode Decomposition for INS/CNS Navigation
Mathematics 2024, 12(10), 1607; https://doi.org/10.3390/math12101607 (registering DOI) - 20 May 2024
Abstract
For the degradation of the filtering performance of the INS/CNS navigation system under measurement noise uncertainty, an adaptive cubature Kalman filter (CKF) is proposed based on improved empirical mode decomposition (EMD) and a resampling-free sigma-point update framework (RSUF). The proposed algorithm innovatively integrates
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For the degradation of the filtering performance of the INS/CNS navigation system under measurement noise uncertainty, an adaptive cubature Kalman filter (CKF) is proposed based on improved empirical mode decomposition (EMD) and a resampling-free sigma-point update framework (RSUF). The proposed algorithm innovatively integrates improved EMD and RSUF into CKF to estimate measurement noise covariance in real-time. Specifically, the improved EMD is used to reconstruct measurement noise, and the exponential decay weighting method is introduced to emphasize the use of new measurement noise while gradually discarding older data to estimate the measurement noise covariance. The estimated measurement noise covariance is then imported into RSUF to directly construct the posterior cubature points without a resampling step. Since the measurement noise covariance is updated in real-time and the prediction cubature points error is directly transformed to the posterior cubature points error, the proposed algorithm is less sensitive to the measurement noise uncertainty. The proposed algorithm is verified by simulations conducted on the INS/CNS-integrated navigation system. The experimental results indicate that the proposed algorithm achieves better performance for attitude angle.
Full article
(This article belongs to the Special Issue Intelligent Robots Control and Navigation and Their Mathematical Methods and Insights)
Open AccessArticle
Data-Proximal Complementary ℓ1-TV Reconstruction for Limited Data Computed Tomography
by
Simon Göppel, Jürgen Frikel and Markus Haltmeier
Mathematics 2024, 12(10), 1606; https://doi.org/10.3390/math12101606 (registering DOI) - 20 May 2024
Abstract
In a number of tomographic applications, data cannot be fully acquired, resulting in severely underdetermined image reconstruction. Conventional methods in such cases lead to reconstructions with significant artifacts. To overcome these artifacts, regularization methods are applied that incorporate additional information. An important example
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In a number of tomographic applications, data cannot be fully acquired, resulting in severely underdetermined image reconstruction. Conventional methods in such cases lead to reconstructions with significant artifacts. To overcome these artifacts, regularization methods are applied that incorporate additional information. An important example is TV reconstruction, which is known to be efficient in compensating for missing data and reducing reconstruction artifacts. On the other hand, tomographic data are also contaminated by noise, which poses an additional challenge. The use of a single regularizer must therefore account for both the missing data and the noise. A particular regularizer may not be ideal for both tasks. For example, the TV regularizer is a poor choice for noise reduction over multiple scales, in which case curvelet regularization methods are well suited. To address this issue, in this paper, we present a novel variational regularization framework that combines the advantages of different regularizers. The basic idea of our framework is to perform reconstruction in two stages. The first stage is mainly aimed at accurate reconstruction in the presence of noise, and the second stage is aimed at artifact reduction. Both reconstruction stages are connected by a data proximity condition. The proposed method is implemented and tested for limited-view CT using a combined curvelet–TV approach. We define and implement a curvelet transform adapted to the limited-view problem and illustrate the advantages of our approach in numerical experiments.
Full article
(This article belongs to the Section Computational and Applied Mathematics)
Open AccessArticle
A Study on Optimizing the Maximal Product in Cubic Fuzzy Graphs for Multifaceted Applications
by
Annamalai Meenakshi, Obel Mythreyi, Robert Čep and Krishnasamy Karthik
Mathematics 2024, 12(10), 1605; https://doi.org/10.3390/math12101605 - 20 May 2024
Abstract
Graphs in the field of science and technology make considerable use of theoretical concepts. When dealing with numerous links and circumstances in which there are varying degrees of ambiguity or robustness in the connections between aspects, rather than purely binary interactions, cubic fuzzy
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Graphs in the field of science and technology make considerable use of theoretical concepts. When dealing with numerous links and circumstances in which there are varying degrees of ambiguity or robustness in the connections between aspects, rather than purely binary interactions, cubic fuzzy graphs ( are more adaptable and compatible than fuzzy graphs. To better represent the complexity of interactions or linkages in the real world, an emerging can be very helpful in achieving better problem-solving abilities that specialize in domains like network analysis, the social sciences, information retrieval, and decision support systems. This idea can be used for a variety of uncertainty-related issues and assist decision-makers in selecting the best course of action through the use of a . Enhancing the maximized network of three cubic fuzzy graphs’ decision-making efficiency was the ultimate objective of this study. We introduced the maximal product of three cubic fuzzy graphs to investigate how interval-valued fuzzy membership, fuzzy membership, and the miscellany of relations are all simultaneously supported through the aspect of degree and total degree of a vertex. Furthermore, the domination on the maximal product of three was illustrated to analyze the minimum domination number of the weighted , and the proposed approach is illustrated with applications.
Full article
Open AccessArticle
A Developed Model and Fuzzy Multi-Criteria Decision-Making Method to Evaluate Supply Chain Nervousness Strategies
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Ghazi M. Magableh, Mahmoud Z. Mistarihi, Taha Rababah, Ali Almajwal and Numan Al-Rayyan
Mathematics 2024, 12(10), 1604; https://doi.org/10.3390/math12101604 - 20 May 2024
Abstract
Nervousness is thought to be a source of confusion, instability, or uncertainty in SC systems due to disruptions and frequent changes in decisions. Nervousness persists even with consistent SCs, which arise from planning flexibility in response to changes, where responsiveness and customer satisfaction
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Nervousness is thought to be a source of confusion, instability, or uncertainty in SC systems due to disruptions and frequent changes in decisions. Nervousness persists even with consistent SCs, which arise from planning flexibility in response to changes, where responsiveness and customer satisfaction balance. Although the term “nervousness” is well known, to our knowledge no prior research has examined and explored supply chain nervousness strategies (SCNSs). This research explores supply chain nervousness strategies, factors, reduction methods, and recent trends in the supply chain’s relationship with nervousness. The main purpose of this research is to determine the comprehensive and relevant nervousness strategies in the supply chains, especially in light of the unprecedented development and change in business, economics, and technology and the fierce competition. SCN strategies are introduced in a developed model to designate SCN measurements and indicators, mitigation strategies and stages, and management strategies. The fuzzy PROMETHEE method is employed to rank the strategies based on their importance and order of implementation. The suggested method for managing nervousness is then presented with a numerical case, along with the results. The research outcomes indicate that the top five strategies for managing nervousness include planning continuity, utilizing technology, managing nervousness, improving the SC cyber system, and managing supplies. The findings assist decision makers, practitioners, and managers in focusing on SC improvement, resilience, and sustainability.
Full article
(This article belongs to the Section Fuzzy Sets, Systems and Decision Making)
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Open AccessArticle
A Sustainable Supply Chain Model with a Setup Cost Reduction Policy for Imperfect Items under Learning in a Cloudy Fuzzy Environment
by
Basim S. O. Alsaedi
Mathematics 2024, 12(10), 1603; https://doi.org/10.3390/math12101603 - 20 May 2024
Abstract
The present paper deals with an integrated sustainable supply chain model with the effect of learning for an imperfect production system under a cloudy fuzzy environment where the demand rate is treated as a cloudy triangular fuzzy (imprecise) number, which means that the
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The present paper deals with an integrated sustainable supply chain model with the effect of learning for an imperfect production system under a cloudy fuzzy environment where the demand rate is treated as a cloudy triangular fuzzy (imprecise) number, which means that the demand rate of the items is not constant, and shortages and a warranty policy are allowed. The vendor governs the manufacturing process to serve the demand of the buyer. When the vendor supplies the demanded lot after the production of items, it is also considered that the delivery lots have some defective items that follow an S-shape learning curve. After receiving the lot, the buyer inspects the whole lot, and the buyer classifies the whole lot into two categories: one is the defective-quality items and the other is the imperfect-quality items. The buyer returns the defective-quality items to the seller after a screening process, for which a warranty cost is included. During the transportation of the items, a lot of carbon units are emitted from the transportation, damaging the quality of the environment. The seller includes carbon emission costs to achieve sustainability as per considerations. A one-time discrete investment is also included for the minimizing of the setup cost of the seller for the next cycles. We developed models for the scenario of the separate decision and for the integrated decision of the players (seller/buyer) under the model’s consideration. Our aim is to jointly optimize the integrated total fuzzy cost under a cloudy fuzzy environment sustained by the seller and buyer. Numerical examples, sensitivity, analysis limitations, future scope and conclusions have been provided for the justification of the proposed model, and the impact of the input parameters on the decision variables and integrated total fuzzy cost for the supply chain are provided for the validity and robustness of this proposed model. The effect of learning in a cloudy fuzzy environment was positive for this proposed model.
Full article
(This article belongs to the Special Issue Advances and Applications on Fuzzy Logic for Decision Making Processes)
Open AccessArticle
Height Prediction of Water-Conducting Fracture Zone in Jurassic Coalfield of Ordos Basin Based on Improved Radial Movement Optimization Algorithm Back-Propagation Neural Network
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Zhiyong Gao, Liangxing Jin, Pingting Liu and Junjie Wei
Mathematics 2024, 12(10), 1602; https://doi.org/10.3390/math12101602 - 20 May 2024
Abstract
The development height of the water-conducting fracture zone (WCFZ) is crucial for the safe production of coal mines. The back-propagation neural network (BP-NN) can be utilized to forecast the WCFZ height, aiding coal mines in water hazard prevention and control efforts. However, the
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The development height of the water-conducting fracture zone (WCFZ) is crucial for the safe production of coal mines. The back-propagation neural network (BP-NN) can be utilized to forecast the WCFZ height, aiding coal mines in water hazard prevention and control efforts. However, the stochastic generation of initial weights and thresholds in BP-NN usually leads to local optima, which might reduce the prediction accuracy. This study thus invokes the excellent global optimization capability of the Improved Radial Movement Optimization (IRMO) algorithm to optimize BP-NN. The influences of mining thickness, coal seam depth, working width, and hard rock lithology proportion coefficient on the height of WCFZ are investigated through 75 groups of in situ data of WCFZ heights measured in the Jurassic coalfield of the Ordos Basin. Consequently, an IRMO-BP-NN model for predicting WCFZ height in the Jurassic coalfield of the Ordos Basin was constructed. The proposed IRMO-BP-NN model was validated through monitoring data from the 4−2216 working faces of Jianbei Coal Mine, followed by a comparative analysis with empirical formulas and conventional BP-NN models. The relative error of the IRMO-BP-NN prediction model is 4.93%, outperforming both the BP-NN prediction model, the SVR prediction model, and empirical formulas. The results demonstrate that the IRMO-BP-NN model enhances the accuracy of predicting WCFZ height, providing an application foundation for predicting such heights in the Jurassic coalfield of the Ordos Basin and protecting the ecological environment of Ordos Basin mining areas.
Full article
(This article belongs to the Topic Physical Monitoring and Healthy Controlling of Geotechnical Engineering)
Open AccessArticle
FedUB: Federated Learning Algorithm Based on Update Bias
by
Hesheng Zhang, Ping Zhang, Mingkai Hu, Muhua Liu and Jiechang Wang
Mathematics 2024, 12(10), 1601; https://doi.org/10.3390/math12101601 - 20 May 2024
Abstract
Federated learning, as a distributed machine learning framework, aims to protect data privacy while addressing the issue of data silos by collaboratively training models across multiple clients. However, a significant challenge to federated learning arises from the non-independent and identically distributed (non-iid) nature
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Federated learning, as a distributed machine learning framework, aims to protect data privacy while addressing the issue of data silos by collaboratively training models across multiple clients. However, a significant challenge to federated learning arises from the non-independent and identically distributed (non-iid) nature of data across different clients. non-iid data can lead to inconsistencies between the minimal loss experienced by individual clients and the global loss observed after the central server aggregates the local models, affecting the model’s convergence speed and generalization capability. To address this challenge, we propose a novel federated learning algorithm based on update bias (FedUB). Unlike traditional federated learning approaches such as FedAvg and FedProx, which independently update model parameters on each client before direct aggregation to form a global model, the FedUB algorithm incorporates an update bias in the loss function of local models—specifically, the difference between each round’s local model updates and the global model updates. This design aims to reduce discrepancies between local and global updates, thus aligning the parameters of locally updated models more closely with those of the globally aggregated model, thereby mitigating the fundamental conflict between local and global optima. Additionally, during the aggregation phase at the server side, we introduce a metric called the bias metric, which assesses the similarity between each client’s local model and the global model. This metric adaptively sets the weight of each client during aggregation after each training round to achieve a better global model. Extensive experiments conducted on multiple datasets have confirmed the effectiveness of the FedUB algorithm. The results indicate that FedUB generally outperforms methods such as FedDC, FedDyn, and Scaffold, especially in scenarios involving partial client participation and non-iid data distributions. It demonstrates superior performance and faster convergence in tasks such as image classification.
Full article
(This article belongs to the Special Issue Federated Learning Strategies for Machine Learning)
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Open AccessArticle
Assembly Theory of Binary Messages
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Szymon Łukaszyk and Wawrzyniec Bieniawski
Mathematics 2024, 12(10), 1600; https://doi.org/10.3390/math12101600 - 20 May 2024
Abstract
Using assembly theory, we investigate the assembly pathways of binary strings (bitstrings) of length N formed by joining bits present in the assembly pool and the bitstrings that entered the pool as a result of previous joining operations. We show that the bitstring
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Using assembly theory, we investigate the assembly pathways of binary strings (bitstrings) of length N formed by joining bits present in the assembly pool and the bitstrings that entered the pool as a result of previous joining operations. We show that the bitstring assembly index is bounded from below by the shortest addition chain for N, and we conjecture about the form of the upper bound. We define the degree of causation for the minimum assembly index and show that, for certain N values, it has regularities that can be used to determine the length of the shortest addition chain for N. We show that a bitstring with the smallest assembly index for N can be assembled via a binary program of a length equal to this index if the length of this bitstring is expressible as a product of Fibonacci numbers. Knowing that the problem of determining the assembly index is at least NP-complete, we conjecture that this problem is NP-complete, while the problem of creating the bitstring so that it would have a predetermined largest assembly index is NP-hard. The proof of this conjecture would imply since every computable problem and every computable solution can be encoded as a finite bitstring. The lower bound on the bitstring assembly index implies a creative path and an optimization path of the evolution of information, where only the latter is available to Turing machines (artificial intelligence). Furthermore, the upper bound hints at the role of dissipative structures and collective, in particular human, intelligence in this evolution.
Full article
(This article belongs to the Section Mathematical Physics)
Open AccessArticle
New and Efficient Estimators of Reliability Characteristics for a Family of Lifetime Distributions Under Progressive Censoring
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Syed Ejaz Ahmed, Reza Arabi Belaghi, Abdulkadir Hussein and Alireza Safariyan
Mathematics 2024, 12(10), 1599; https://doi.org/10.3390/math12101599 - 20 May 2024
Abstract
Estimation of reliability and stress–strength parameters is important in the manufacturing industry. In this paper, we develop shrinkage-type estimators for the reliability and stress–strength parameters based on progressively censored data from a rich class of distributions. These new estimators improve the performance of
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Estimation of reliability and stress–strength parameters is important in the manufacturing industry. In this paper, we develop shrinkage-type estimators for the reliability and stress–strength parameters based on progressively censored data from a rich class of distributions. These new estimators improve the performance of the commonly used Maximum Likelihood Estimators (MLEs) by reducing their mean squared errors. We provide analytical asymptotic and bootstrap confidence intervals for the targeted parameters. Through a detailed simulation study, we demonstrate that the new estimators have better performance than the MLEs. Finally, we illustrate the application of the new methods to two industrial data sets, showcasing their practical relevance and effectiveness.
Full article
(This article belongs to the Special Issue Reliability Estimation and Mathematical Statistics)
Open AccessArticle
Navigating Supply Chain Resilience: A Hybrid Approach to Agri-Food Supplier Selection
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Pasura Aungkulanon, Walailak Atthirawong, Pongchanun Luangpaiboon and Wirachchaya Chanpuypetch
Mathematics 2024, 12(10), 1598; https://doi.org/10.3390/math12101598 - 20 May 2024
Abstract
Globalization and multinational commerce have increased the dynamism and complexity of supply networks, thereby increasing their susceptibility to disruptions along interconnected supply chains. This study aims to tackle the significant concern of supplier selection disruptions in the Thai agri-food industry as a response
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Globalization and multinational commerce have increased the dynamism and complexity of supply networks, thereby increasing their susceptibility to disruptions along interconnected supply chains. This study aims to tackle the significant concern of supplier selection disruptions in the Thai agri-food industry as a response to the aforementioned challenges. A novel supplier evaluation system, PROMETHEE II, is suggested; it combines the Fuzzy Analytical Hierarchy Process (FAHP) with inferential statistical techniques. This investigation commences with the identification of critical indicators of risk in the sustainable supply chain via three phases of analysis and 315 surveys of management teams. Exploratory factor analysis (EFA) is utilized to ascertain six supply risk criteria and twenty-three sub-criteria. Following this, the parameters are prioritized by FAHP, whereas four prospective suppliers for an agricultural firm are assessed by PROMETHEE II. By integrating optimization techniques into sensitivity analysis, this hybrid approach improves supplier selection criteria by identifying dependable solutions that are customized to risk scenarios and business objectives. The iterative strategy enhances the resilience of the agri-food supply chain by enabling well-informed decision-making amidst evolving market dynamics and chain risks. In addition, this research helps agricultural and other sectors by providing a systematic approach to selecting low-risk suppliers and delineating critical supply chain risk factors. By bridging complexity and facilitating informed decision-making in supplier selection processes, the results of this study fill a significant void in the academic literature concerning sustainable supply chain risk management.
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Open AccessArticle
Secure Active Intelligent Reflecting Surface Communication against Colluding Eavesdroppers
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Jiaxin Xu, Yuyang Peng, Runlong Ye, Wei Gan, Fawaz AL-Hazemi and Mohammad Meraj Mirza
Mathematics 2024, 12(10), 1597; https://doi.org/10.3390/math12101597 - 20 May 2024
Abstract
An active intelligent reflecting surface (IRS)-assisted, secure, multiple-input–single-output communication method is proposed in this paper. In this proposed scheme, a practical and unfavorable propagation environment is considered by assuming that multiple colluding eavesdroppers (Eves) coexist. In this case, we jointly optimize the beamformers
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An active intelligent reflecting surface (IRS)-assisted, secure, multiple-input–single-output communication method is proposed in this paper. In this proposed scheme, a practical and unfavorable propagation environment is considered by assuming that multiple colluding eavesdroppers (Eves) coexist. In this case, we jointly optimize the beamformers of the base station (BS) and the active IRS for the formulated sum secrecy rate (SSR) maximization problem. Because the formulated problem is not convex, we apply the alternating optimization method to optimize the beamformers for maximizing the SSR. Specifically, we use the semi-definite relaxation method to solve the sub-problem of the beamforming vector of the BS, and we use the successive convex approximation method to solve the sub-problem of the power amplification matrix of the active IRS. Based on the solutions obtained using these stated methods, numerical results show that deploying an active IRS is superior compared to the cases of a passive IRS and a non-IRS for improving the physical layer security of wireless communication with multiple colluding Eves under different settings, such as the numbers of users, Eves, reflecting elements, and BS antennas as well as the maximum transmit power budget at the BS.
Full article
(This article belongs to the Special Issue Complexity in 6G: Measures, Advanced Models and Mathematical Algorithms to Face New Challenges in the New Communication Paradigm Development)
Open AccessArticle
Teaching–Learning-Based Optimization Algorithm with Stochastic Crossover Self-Learning and Blended Learning Model and Its Application
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Yindi Ma, Yanhai Li and Longquan Yong
Mathematics 2024, 12(10), 1596; https://doi.org/10.3390/math12101596 - 20 May 2024
Abstract
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This paper presents a novel variant of the teaching–learning-based optimization algorithm, termed BLTLBO, which draws inspiration from the blended learning model, specifically designed to tackle high-dimensional multimodal complex optimization problems. Firstly, the perturbation conditions in the “teaching” and “learning” stages of the original
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This paper presents a novel variant of the teaching–learning-based optimization algorithm, termed BLTLBO, which draws inspiration from the blended learning model, specifically designed to tackle high-dimensional multimodal complex optimization problems. Firstly, the perturbation conditions in the “teaching” and “learning” stages of the original TLBO algorithm are interpreted geometrically, based on which the search capability of the TLBO is enhanced by adjusting the range of values of random numbers. Second, a strategic restructuring has been ingeniously implemented, dividing the algorithm into three distinct phases: pre-course self-study, classroom blended learning, and post-course consolidation; this structural reorganization and the random crossover strategy in the self-learning phase effectively enhance the global optimization capability of TLBO. To evaluate its performance, the BLTLBO algorithm was tested alongside seven distinguished variants of the TLBO algorithm on thirteen multimodal functions from the CEC2014 suite. Furthermore, two excellent high-dimensional optimization algorithms were added to the comparison algorithm and tested in high-dimensional mode on five scalable multimodal functions from the CEC2008 suite. The empirical results illustrate the BLTLBO algorithm’s superior efficacy in handling high-dimensional multimodal challenges. Finally, a high-dimensional portfolio optimization problem was successfully addressed using the BLTLBO algorithm, thereby validating the practicality and effectiveness of the proposed method.
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Open AccessArticle
A Mathematical Analysis of Competitive Dynamics and Aggressive Treatment in the Evolution of Drug Resistance in Malaria Parasites
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Tianqi Song, Yishi Wang, Yang Li and Guoliang Fan
Mathematics 2024, 12(10), 1595; https://doi.org/10.3390/math12101595 - 20 May 2024
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Experimental evidence supports the counterintuitive notion that rapid eradication of pathogens within a host, infected with both drug-sensitive and -resistant malaria parasites, can actually accelerate the evolution of drug-resistant pathogens. This study aims to analyze the competitive dynamics between these two strains through
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Experimental evidence supports the counterintuitive notion that rapid eradication of pathogens within a host, infected with both drug-sensitive and -resistant malaria parasites, can actually accelerate the evolution of drug-resistant pathogens. This study aims to analyze the competitive dynamics between these two strains through a mathematical model and evaluate the impact of aggressive treatment on the spread of drug resistance. We conducted equilibrium, uncertainty, and sensitivity analyses to assess the model, identifying and measuring the influence of key factors on the outcome variable (the population of drug-resistant parasites). Both equilibrium and local sensitivity analyses concurred that the density of drug-resistant parasites is notably affected by genetic instability, the production rate of red blood cells, the number of merozoites, and competition factors. Conversely, there is a negative relationship between genetic instability and one of the competition coefficients. Global sensitivity analysis offers a comprehensive examination of the impact of each input parameter on the temporal propagation of drug resistance, effectively accounting for the interplay among parameters. Both local and global sensitivity analyses underscore the continuous impact of drug treatment on the progression of drug resistance over time. This paper anticipates exploring the underlying mechanisms of drug resistance and providing theoretical support for developing more effective drug treatment strategies.
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Open AccessArticle
A Class of Bi-Univalent Functions in a Leaf-Like Domain Defined through Subordination via
by
Abdullah Alsoboh and Georgia Irina Oros
Mathematics 2024, 12(10), 1594; https://doi.org/10.3390/math12101594 - 20 May 2024
Abstract
Bi-univalent functions associated with the leaf-like domain within open unit disks are investigated, and a new subclass is introduced and studied in the research presented here. This is achieved by applying the subordination principle for analytic functions in conjunction with -calculus. The
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Bi-univalent functions associated with the leaf-like domain within open unit disks are investigated, and a new subclass is introduced and studied in the research presented here. This is achieved by applying the subordination principle for analytic functions in conjunction with -calculus. The class is proved to not be empty. By proving its existence, generalizations can be given to other sets of functions. In addition, coefficient bounds are examined with a particular focus on and coefficients, and Fekete–Szegö inequalities are estimated for the functions in this new class. To support the conclusions, previous works are cited for confirmation.
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(This article belongs to the Special Issue Advanced Research in Complex Analysis Operators and Special Classes of Analytic Functions)
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Global Dynamics of a Social Hierarchy-Stratified Malaria Model: Insight from Fractional Calculus
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Sulaimon F. Abimbade, Furaha M. Chuma, Sunday O. Sangoniyi, Ramoshweu S. Lebelo, Kazeem O. Okosun and Samson Olaniyi
Mathematics 2024, 12(10), 1593; https://doi.org/10.3390/math12101593 - 20 May 2024
Abstract
In this study, a mathematical model for the transmission dynamics of malaria among different socioeconomic groups in the human population interacting with a susceptible-infectious vector population is presented and analysed using a fractional-order derivative of the Caputo type. The total human population is
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In this study, a mathematical model for the transmission dynamics of malaria among different socioeconomic groups in the human population interacting with a susceptible-infectious vector population is presented and analysed using a fractional-order derivative of the Caputo type. The total human population is stratified into two distinguished classes of lower and higher income individuals, with each class further subdivided into susceptible, infectious, and recovered populations. The socio hierachy-structured fractional-order malaria model is analyzed through the application of different dynamical system tools. The theory of positivity and boundedness based on the generalized mean value theorem is employed to investigate the basic properties of solutions of the model, while the Banach fixed point theory approach is used to prove the existence and uniqueness of the solution. Furthermore, unlike the existing related studies, comprehensive global asymptotic dynamics of the fractional-order malaria model around both disease-free and endemic equilibria are explored by generalizing the usual classical methods for establishing global asymptotic stability of the steady states. The asymptotic behavior of the trajectories of the system are graphically illustrated at different values of the fractional (noninteger) order.
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(This article belongs to the Special Issue Advances in Differential Dynamical Systems with Applications to Economics and Biology, 2nd Edition)
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Open AccessArticle
Efficient Image Details Preservation of Image Processing Pipeline Based on Two-Stage Tone Mapping
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Weijian Xu, Yuyang Cai, Feng Qian, Yuan Hu and Jingwen Yan
Mathematics 2024, 12(10), 1592; https://doi.org/10.3390/math12101592 - 20 May 2024
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Converting a camera’s RAW image to an RGB format for human perception involves utilizing an imaging pipeline, and a series of processing modules. Existing modules often result in varying degrees of original information loss, which can render the reverse imaging pipeline unable to
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Converting a camera’s RAW image to an RGB format for human perception involves utilizing an imaging pipeline, and a series of processing modules. Existing modules often result in varying degrees of original information loss, which can render the reverse imaging pipeline unable to recover the original RAW image information. To this end, this paper proposes a new, almost reversible image imaging pipeline. Thus, RGB images and RAW images can be effectively converted between each other. Considering the impact of original information loss, this paper introduces a two-stage tone mapping operation (TMO). In the first stage, the RAW image with a linear response is transformed into an RGB color image. In the second stage, color scale mapping corrects the dynamic range of the image suitable for human perception through linear stretching, and reduces the loss of sensitive information to the human eye during the integer process. effectively preserving the original image’s dynamic information. The DCRAW imaging pipeline addresses the problem of high light overflow by directly highlighting cuts. The proposed imaging pipeline constructs an independent highlight processing module, and preserves the highlighted information of the image. The experimental results demonstrate that the two-stage tone mapping operation embedded in the imaging processing pipeline provided in this article ensures that the image output is suitable for human visual system (HVS) perception and retains more original image information.
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Open AccessArticle
Uncertainty Analysis of Aircraft Center of Gravity Deviation and Passenger Seat Allocation Optimization
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Xiangling Zhao and Wenheng Xiao
Mathematics 2024, 12(10), 1591; https://doi.org/10.3390/math12101591 - 20 May 2024
Abstract
The traditional method of allocating passenger seats based on compartments does not effectively manage an aircraft’s center of gravity (CG), resulting in a notable divergence from the desired target CG (TCG). In this work, the Boeing B737-800 aircraft was employed as a case
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The traditional method of allocating passenger seats based on compartments does not effectively manage an aircraft’s center of gravity (CG), resulting in a notable divergence from the desired target CG (TCG). In this work, the Boeing B737-800 aircraft was employed as a case study, and row-based and compartment-based integer programming models for passenger allocation were examined and constructed with the aim of addressing the current situation. The accuracy of CG control was evaluated by comparing the row-based and compartment-based allocation techniques, taking into account different bodyweights and numbers of passengers. The key contribution of this research is to broaden the range of the mobilizable set for the aviation weight and balance (AWB) model, resulting in a significant reduction in the range of deviations in the center of gravity outcomes by a factor of around 6 to 16. The effectiveness of the row-based allocation approach and the impact of passenger weight randomness on the deviation of an airplane’s CG were also investigated in this study. The Monte Carlo method was utilized to quantify the uncertainty associated with passenger weight, resulting in the generation of the posterior distribution of the aircraft’s center of gravity (CG) deviation. The outcome of the row-based model test is the determination of the range of passenger numbers that can be effectively allocated under different TCG conditions.
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(This article belongs to the Section Engineering Mathematics)
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Performance Evaluation of Railway Infrastructure Managers: A Novel Hybrid Fuzzy MCDM Model
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Aida Kalem, Snežana Tadić, Mladen Krstić, Nermin Čabrić and Nedžad Branković
Mathematics 2024, 12(10), 1590; https://doi.org/10.3390/math12101590 - 19 May 2024
Abstract
Modern challenges such as the liberalization of the railway sector and growing demands for sustainability, high-quality services, and user satisfaction set new standards in railway operations. In this context, railway infrastructure managers (RIMs) play a crucial role in ensuring innovative approaches that will
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Modern challenges such as the liberalization of the railway sector and growing demands for sustainability, high-quality services, and user satisfaction set new standards in railway operations. In this context, railway infrastructure managers (RIMs) play a crucial role in ensuring innovative approaches that will strengthen the position of railways in the market by enhancing efficiency and competitiveness. Evaluating their performance is essential for assessing the achieved objectives, and it is conducted through a wide range of key performance indicators (KPIs), which encompass various dimensions of operations. Monitoring and analyzing KPIs are crucial for improving service quality, achieving sustainability, and establishing a foundation for research and development of new strategies in the railway sector. This paper provides a detailed overview and evaluation of KPIs for RIMs. This paper creates a framework for RIM evaluation using various scientific methods, from identifying KPIs to applying complex analysis methods. A novel hybrid model, which integrates the fuzzy Delphi method for aggregating expert opinions on the KPIs’ importance, the extended fuzzy analytic hierarchy process (AHP) method for determining the relative weights of these KPIs, and the ADAM method for ranking RIMs, has been developed in this paper. This approach enables a detailed analysis and comparison of RIMs and their performances, providing the basis for informed decision-making and the development of new strategies within the railway sector. The analysis results provide insight into the current state of railway infrastructure and encourage further efforts to improve the railway sector by identifying key areas for enhancement. The main contributions of the research include a detailed overview of KPIs for RIMs and the development of a hybrid multi-criteria decision making (MCDM) model. The hybrid model represents a significant step in RIM performance analysis, providing a basis for future research in this area. The model is universal and, as such, represents a valuable contribution to MCDM theory.
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(This article belongs to the Special Issue Multi-criteria Optimization Models and Methods for Smart Cities)
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Open AccessFeature PaperArticle
Micro-Grinding Parameter Control of Hard and Brittle Materials Based on Kinematic Analysis of Material Removal
by
Hisham Manea, Hong Lu, Qi Liu, Junbiao Xiao and Kefan Yang
Mathematics 2024, 12(10), 1589; https://doi.org/10.3390/math12101589 - 19 May 2024
Abstract
This article explores the intricacies of micro-grinding parameter control for hard and brittle materials, with a specific focus on Zirconia ceramics (ZrO2) and Optical Glass (BK7). Given the increasing demand and application of these materials in various high-precision industries, this study
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This article explores the intricacies of micro-grinding parameter control for hard and brittle materials, with a specific focus on Zirconia ceramics (ZrO2) and Optical Glass (BK7). Given the increasing demand and application of these materials in various high-precision industries, this study aims to provide a comprehensive kinematic analysis of material removal during the micro-grinding process. According to the grinding parameters selected to be analyzed in this study, the ac-max values are between (9.55 nm ~ 67.58 nm). Theoretical modeling of the grinding force considering the brittle and ductile removal phase, frictional effects, the possibility of grit to cut materials, and grinding conditions is very important in order to control and optimize the surface grinding process. This research introduces novel models for predicting and optimizing micro-grinding forces effectively. The primary objective is to establish a micro-grinding force model that facilitates the easy manipulation of micro-grinding parameters, thereby optimizing the machining process for these challenging materials. Through experimental investigations conducted on Zirconia ceramics, the paper evaluates a mathematical model of the grinding force, highlighting its significance in predicting and controlling the forces involved in micro-grinding. The suggested model underwent thorough testing to assess its validity, revealing an accuracy with average variances of 6.616% for the normal force and 5.752% for the tangential force. Additionally, the study delves into the coefficient of friction within the grinding process, suggesting a novel frictional force model. This model is assessed through a series of experiments on Optical Glass BK7, aiming to accurately characterize the frictional forces at play during grinding. The empirical results obtained from both sets of experiments—on Zirconia ceramics and Optical Glass BK7—substantiate the efficacy of the proposed models. These findings confirm the models’ capability to accurately describe the force dynamics in the micro-grinding of hard and brittle materials. The research not only contributes to the theoretical understanding of micro-grinding processes but also offers practical insights for enhancing the efficiency and effectiveness of machining operations involving hard and brittle materials.
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(This article belongs to the Special Issue Advanced Mathematical Modeling and Numerical Solutions in Applied Mechanics and Engineering, 2nd Edition)
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Open AccessArticle
Persistence and Stochastic Extinction in a Lotka–Volterra Predator–Prey Stochastically Perturbed Model
by
Leonid Shaikhet and Andrei Korobeinikov
Mathematics 2024, 12(10), 1588; https://doi.org/10.3390/math12101588 - 19 May 2024
Abstract
The classical Lotka–Volterra predator–prey model is globally stable and uniformly persistent. However, in real-life biosystems, the extinction of species due to stochastic effects is possible and may occur if the magnitudes of the stochastic effects are large enough. In this paper, we consider
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The classical Lotka–Volterra predator–prey model is globally stable and uniformly persistent. However, in real-life biosystems, the extinction of species due to stochastic effects is possible and may occur if the magnitudes of the stochastic effects are large enough. In this paper, we consider the classical Lotka–Volterra predator–prey model under stochastic perturbations. For this model, using an analytical technique based on the direct Lyapunov method and a development of the ideas of R.Z. Khasminskii, we find the precise sufficient conditions for the stochastic extinction of one and both species and, thus, the precise necessary conditions for the stochastic system’s persistence. The stochastic extinction occurs via a process known as the stabilization by noise of the Khasminskii type. Therefore, in order to establish the sufficient conditions for extinction, we found the conditions for this stabilization. The analytical results are illustrated by numerical simulations.
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(This article belongs to the Special Issue Stochastic Models in Mathematical Biology, 2nd Edition)
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