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
A Machine Learning-Based Framework with Enhanced Feature Selection and Resampling for Improved Intrusion Detection
Mathematics 2024, 12(12), 1799; https://doi.org/10.3390/math12121799 (registering DOI) - 9 Jun 2024
Abstract
Intrusion Detection Systems (IDSs) play a crucial role in safeguarding network infrastructures from cyber threats and ensuring the integrity of highly sensitive data. Conventional IDS technologies, although successful in achieving high levels of accuracy, frequently encounter substantial model bias. This bias is primarily
[...] Read more.
Intrusion Detection Systems (IDSs) play a crucial role in safeguarding network infrastructures from cyber threats and ensuring the integrity of highly sensitive data. Conventional IDS technologies, although successful in achieving high levels of accuracy, frequently encounter substantial model bias. This bias is primarily caused by imbalances in the data and the lack of relevance of certain features. This study aims to tackle these challenges by proposing an advanced machine learning (ML) based IDS that minimizes misclassification errors and corrects model bias. As a result, the predictive accuracy and generalizability of the IDS are significantly improved. The proposed system employs advanced feature selection techniques, such as Recursive Feature Elimination (RFE), sequential feature selection (SFS), and statistical feature selection, to refine the input feature set and minimize the impact of non-predictive attributes. In addition, this work incorporates data resampling methods such as Synthetic Minority Oversampling Technique and Edited Nearest Neighbor (SMOTE_ENN), Adaptive Synthetic Sampling (ADASYN), and Synthetic Minority Oversampling Technique–Tomek Links (SMOTE_Tomek) to address class imbalance and improve the accuracy of the model. The experimental results indicate that our proposed model, especially when utilizing the random forest (RF) algorithm, surpasses existing models regarding accuracy, precision, recall, and F Score across different data resampling methods. Using the ADASYN resampling method, the RF model achieves an accuracy of 99.9985% for botnet attacks and 99.9777% for Man-in-the-Middle (MITM) attacks, demonstrating the effectiveness of our approach in dealing with imbalanced data distributions. This research not only improves the abilities of IDS to identify botnet and MITM attacks but also provides a scalable and efficient solution that can be used in other areas where data imbalance is a recurring problem. This work has implications beyond IDS, offering valuable insights into using ML techniques in complex real-world scenarios.
Full article
(This article belongs to the Special Issue Artificial Intelligence and Data Science)
Open AccessArticle
Housing Developers’ Heterogeneous Decision-Making under Negative Shock after the High-Growth Era: Evidence from the Chinese Real Estate Economy
by
Dachen Sheng, Huijun Cheng and Minmin Yin
Mathematics 2024, 12(12), 1798; https://doi.org/10.3390/math12121798 (registering DOI) - 8 Jun 2024
Abstract
This research uses difference-in-difference (DID) and other empirical methods to analyze firm-level real estate data to discover how heterogeneous firm characteristics affect managers’ decision-making about development expansion when a firm faces a temporary negative sales shock in the Chinese housing market. The manager’s
[...] Read more.
This research uses difference-in-difference (DID) and other empirical methods to analyze firm-level real estate data to discover how heterogeneous firm characteristics affect managers’ decision-making about development expansion when a firm faces a temporary negative sales shock in the Chinese housing market. The manager’s decision is a utility maximization problem under uncertainty, determined by their risk aversion levels, which managers choose to optimize by considering other factors of interest, including career risk and personal wealth. Also, the advance payment rule encourages real estate developers to maintain high turnover, since new projects allow developers to collect cash first. The results show that state-owned enterprises (SOEs) are much more conservative than other types of developers. SOEs tend to focus on current developing projects. Firms with more concentrated management pursue expansion and seek to use new project sales to compensate for their slower growth. Larger developers with headquarters in large cities tend to slow their development speed when they observe negative signals, as they can quickly engage in new projects given these firms’ easy access to financial resources such as bank loans. This study makes a novel contribution to the literature since previous research has tended to focus on the macro market level rather than the firm level. The findings also have strong policy and regulation value. The results indicate that higher cashflow monitoring needs, especially to monitor family-owned developers, to prevent misuse and excessive project expansion.
Full article
(This article belongs to the Special Issue Advances in Mathematical Behavioural Finance and Decision Analysis)
Open AccessArticle
Dynamics of Infectious Diseases Incorporating a Testing Compartment
by
Chayu Yang and Bo Deng
Mathematics 2024, 12(12), 1797; https://doi.org/10.3390/math12121797 (registering DOI) - 8 Jun 2024
Abstract
In this paper, we construct an infectious disease model with a testing compartment and analyze the existence and stability of its endemic states. We obtain the basic reproduction number, , and demonstrate the existence of one endemic equilibrium without testing and
[...] Read more.
In this paper, we construct an infectious disease model with a testing compartment and analyze the existence and stability of its endemic states. We obtain the basic reproduction number, , and demonstrate the existence of one endemic equilibrium without testing and one endemic equilibrium with testing and prove their local and global stabilities based on the value of the basic reproduction number, . We then apply our model to the US COVID-19 pandemic and find that, for a large parameter set, including those relevant to the SARS-CoV-2 virus, our analytic and numerical results suggest that the trajectories will be trapped to the testing-free state when the testing number is small enough. This indicates that the pandemic may end with a testing-free endemic state through a novel and surprising mechanism called stochastic trapping.
Full article
(This article belongs to the Section Mathematical Biology)
Open AccessArticle
Dynamics of a Stochastic Predator–Prey Model with Smith Growth Rate and Cooperative Defense
by
Qiuyue Zhao and Xinglong Niu
Mathematics 2024, 12(12), 1796; https://doi.org/10.3390/math12121796 (registering DOI) - 8 Jun 2024
Abstract
The random changes in the environment play a crucial role in the sustainability of ecosystems. Usually, the construction of stochastic models does not take into account the non-linear growth of intrinsic growth rate. In addition, prey only considers the collective response of the
[...] Read more.
The random changes in the environment play a crucial role in the sustainability of ecosystems. Usually, the construction of stochastic models does not take into account the non-linear growth of intrinsic growth rate. In addition, prey only considers the collective response of the population when encountering predators and ignores the role of individual prey. To address this issue, we contemplate the dynamics of a stochastic prey–predator model with Smith growth rate and cooperative defense. The population density of prey is measured by mass, and the growth limitations are based on the proportion of unused available resources. Additionally, the grazing pattern of the predator incorporates cooperative characteristics into the functional response. We carry out existence and uniqueness analysis for the global positive solution. Then, we construct sufficient conditions for the existence of an ergodic stationary distribution of positive solutions for investigating whether prey and predator populations continue to survive. Numerical examples indicate that the Smith growth rate, cooperative defense and environmental disturbance play crucial roles in the coexistence of interacting populations.
Full article
Open AccessArticle
EDiffuRec: An Enhanced Diffusion Model for Sequential Recommendation
by
Hanbyul Lee and Junghyun Kim
Mathematics 2024, 12(12), 1795; https://doi.org/10.3390/math12121795 (registering DOI) - 8 Jun 2024
Abstract
Sequential recommender models should capture evolving user preferences over time, but there is a risk of obtaining biased results such as false positives and false negatives due to noisy interactions. Generative models effectively learn the underlying distribution and uncertainty of the given data
[...] Read more.
Sequential recommender models should capture evolving user preferences over time, but there is a risk of obtaining biased results such as false positives and false negatives due to noisy interactions. Generative models effectively learn the underlying distribution and uncertainty of the given data to generate new data, and they exhibit robustness against noise. In particular, utilizing the Diffusion model, which generates data through a multi-step process of adding and removing noise, enables stable and effective recommendations. The Diffusion model typically leverages a Gaussian distribution with a mean fixed at zero, but there is potential for performance improvement in generative models by employing distributions with higher degrees of freedom. Therefore, we propose a Diffusion model-based sequential recommender model that uses a new noise distribution. The proposed model improves performance through a Weibull distribution with two parameters determining shape and scale, a modified Transformer architecture based on Macaron Net, normalized loss, and a learning rate warmup strategy. Experimental results on four types of real-world e-commerce data show that the proposed model achieved performance gains ranging from a minimum of to a maximum of across HR@K and NDCG@K metrics compared to the existing Diffusion model-based sequential recommender model.
Full article
(This article belongs to the Special Issue Advances in Recommender Systems and Intelligent Agents)
Open AccessArticle
Covers of Finitely Generated Acts over Monoids
by
Xiaoqin Zhang and Tingting Zhao
Mathematics 2024, 12(12), 1794; https://doi.org/10.3390/math12121794 (registering DOI) - 8 Jun 2024
Abstract
This paper attempts to initiate the study of covers of finitely generated S-acts over monoids. We provide necessary and sufficient conditions for a monoid to ensure that n-generated S-acts have strongly flat covers, Condition covers, and projective
[...] Read more.
This paper attempts to initiate the study of covers of finitely generated S-acts over monoids. We provide necessary and sufficient conditions for a monoid to ensure that n-generated S-acts have strongly flat covers, Condition covers, and projective covers. The main conclusions extend some known results. We also show that Condition covers of finitely generated S-acts are not unique, unlike strongly flat covers. Additionally, we demonstrate the property of Enochs’ -precover of S-act A, where denotes a class of S-acts that are closed under isomorphisms.
Full article
(This article belongs to the Section Algebra, Geometry and Topology)
Open AccessArticle
Influence of the Effective Reproduction Number on the SIR Model with a Dynamic Transmission Rate
by
Fernando Córdova-Lepe, Juan Pablo Gutiérrez-Jara and Gerardo Chowell
Mathematics 2024, 12(12), 1793; https://doi.org/10.3390/math12121793 (registering DOI) - 8 Jun 2024
Abstract
In this paper, we examine the epidemiological model B-SIR, focusing on the dynamic law that governs the transmission rate . We define this dynamic law by the differential equation , where
[...] Read more.
In this paper, we examine the epidemiological model B-SIR, focusing on the dynamic law that governs the transmission rate . We define this dynamic law by the differential equation , where represents a reaction factor reflecting the stress proportional to the active group’s percentage variation. Conversely, is a factor proportional to the deviation of from its intrinsic value. We introduce the notion of contagion impulsef and explore its role within the model. Specifically, for the case where , we derive an autonomous differential system linking the effective reproductive number with f and subsequently analyze its dynamics. This analysis provides new insights into the model’s behavior and its implications for understanding disease transmission.
Full article
(This article belongs to the Special Issue Advances in Mathematical Biology and Applications)
Open AccessArticle
Enhancing Control Systems through Type-3 Fuzzy Logic Optimization
by
Patricia Ochoa, Cinthia Peraza, Patricia Melin, Oscar Castillo, Seungmin Park and Zong Woo Geem
Mathematics 2024, 12(12), 1792; https://doi.org/10.3390/math12121792 (registering DOI) - 8 Jun 2024
Abstract
The advancement of new tools in the field of control systems is a contemporary development. This work introduces the utilization of Type-3 fuzzy logic, a relatively recent concept that has been applied across various disciplines. In our case, a Type-3 fuzzy system is
[...] Read more.
The advancement of new tools in the field of control systems is a contemporary development. This work introduces the utilization of Type-3 fuzzy logic, a relatively recent concept that has been applied across various disciplines. In our case, a Type-3 fuzzy system is designed to enhance the optimization of parameters within the harmony search algorithm, specifically tailored for a control problem. Through a series of experiments, the efficacy of this novel Type-3 fuzzy logic tool is put to the test. Previous studies have primarily explored Type-1 and Type-2 fuzzy logic. To assess the performance of this new Type-3 fuzzy logic tool, a comparative analysis of results is conducted using statistical testing. The introduction of Type-3 fuzzy logic in the control domain represents a novel and innovative approach. This approach extends beyond the conventional Type-1 and Type-2 fuzzy logic, showcasing the dynamic evolution in the field. Results obtained through experimentation are analyzed, and statistical tests are employed to determine whether the Type-3 fuzzy logic tool yields superior outcomes compared to its predecessors. By doing so, this study contributes to the growing body of research that explores the potential benefits of Type-3 fuzzy logic and its application in control systems, offering new perspectives and opportunities for further advancements in the field. We have to mention that the utilization of Type-3 fuzzy logic in enhancing metaheuristics is a relatively new trend, and in this work, this research has extended this to the realm of harmony search. In addition, the application of the optimal design of the ball-and-beam fuzzy controllers has not been previously carried out with the Type-3 fuzzy harmony search algorithm, which is the novelty of this study.
Full article
(This article belongs to the Section Fuzzy Sets, Systems and Decision Making)
Open AccessArticle
Nodal Invulnerability Recovery Considering Power Generation Balance: A Bi-Objective Robust Optimization Framework
by
Xueyang Zhang, Shengjun Huang, Qingxia Li, Rui Wang, Tao Zhang and Bo Guo
Mathematics 2024, 12(12), 1791; https://doi.org/10.3390/math12121791 (registering DOI) - 8 Jun 2024
Abstract
Nodal invulnerability has broad application prospects because of its emphasis on the differences between buses. Due to their long-term exposure, transmission lines are inevitably susceptible to damage caused by physical attacks or extreme weather. Therefore, restoring nodal invulnerability through a remedial approach or
[...] Read more.
Nodal invulnerability has broad application prospects because of its emphasis on the differences between buses. Due to their long-term exposure, transmission lines are inevitably susceptible to damage caused by physical attacks or extreme weather. Therefore, restoring nodal invulnerability through a remedial approach or the introduction of mobile generators (MGs) is pivotal for resisting subsequent damage after a system is attacked. However, the research devoted to this field is limited. In order to fill the gap, this study conducts research on the configuration of MGs considering power generation balance to recover nodal invulnerability. First, a defender–attacker–defender (DAD) model is established, corresponding to the bi-objective robust optimization problem. The upper-level model is formulated to obtain the optimal compromise configuration scheme, the uncertainties of the attacked lines are elucidated in the middle level, and the nodal security criterion utilized for measuring nodal invulnerability cooperates in the lower level. Then, a modified column-and-constraint generation (C&CG) algorithm is developed to incorporate fuzzy mathematics into the solution framework. In addition, the nodal invulnerability settings are optimized under limited resources. Numerical experiments are executed on the IEEE 24-bus system to verify the effectiveness and rationality of the proposed method.
Full article
(This article belongs to the Topic Power System Modeling and Control, 2nd Volume)
Open AccessFeature PaperArticle
Differentiation of Solutions of Caputo Boundary Value Problems with Respect to Boundary Data
by
Jeffrey W. Lyons
Mathematics 2024, 12(12), 1790; https://doi.org/10.3390/math12121790 (registering DOI) - 8 Jun 2024
Abstract
Under suitable continuity and uniqueness conditions, solutions of an order Caputo fractional boundary value problem are differentiated with respect to boundary values and boundary points. This extends well-known results for nth order boundary value problems. The approach used applies a standard algorithm
[...] Read more.
Under suitable continuity and uniqueness conditions, solutions of an order Caputo fractional boundary value problem are differentiated with respect to boundary values and boundary points. This extends well-known results for nth order boundary value problems. The approach used applies a standard algorithm to achieve the result and makes heavy use of recent results for differentiation of solutions of Caputo fractional intial value problems with respect to initial conditions and continuous dependence for Caputo fractional boundary value problems.
Full article
(This article belongs to the Special Issue Advances in Differential and Difference Equations and Their Applications)
Open AccessArticle
Coupons versus Rebates: An Economic–Mathematical Comparative Analysis with Policy Implications
by
Tin-Chun Lin
Mathematics 2024, 12(12), 1789; https://doi.org/10.3390/math12121789 (registering DOI) - 8 Jun 2024
Abstract
It is very important to understand how promotions offered by sellers to consumers influence consumer and seller behaviors because it helps us study how consumers make their purchase decisions and how sellers determine their sale strategies. Unlike past studies which utilized the classical
[...] Read more.
It is very important to understand how promotions offered by sellers to consumers influence consumer and seller behaviors because it helps us study how consumers make their purchase decisions and how sellers determine their sale strategies. Unlike past studies which utilized the classical price discrimination dilemma and focused on sellers’ aspect to divide consumers into two types (higher/lower reservation prices), we focused on the consumers’ perspective and applied neoclassical consumer choice theory to develop a two-period mathematical utility-maximization model to study how different promotions influence consumer and seller behaviors. This mathematical study uncovered several key findings: (1) coupons offer consumers a greater discount compared to rebates with identical discount rates; (2) impatient consumers exhibit a preference for coupons over rebates; (3) coupons generate higher sales than rebates; and (4) sellers may adopt the coupon policy for low-ticket products and the rebate policy for high-ticket products.
Full article
Open AccessArticle
Supply Chain Elastic Strain
by
Zihui Yang, Qingchun Meng, Zheng Fang and Xiaona Zhang
Mathematics 2024, 12(12), 1788; https://doi.org/10.3390/math12121788 - 7 Jun 2024
Abstract
The introduction of the concepts of shear elastic strain ( ) and tensile elastic strain ( ) is a catalyst for new horizons of research into supply chain elasticity. Functional formulas encompassing the metrics of and
[...] Read more.
The introduction of the concepts of shear elastic strain ( ) and tensile elastic strain ( ) is a catalyst for new horizons of research into supply chain elasticity. Functional formulas encompassing the metrics of and , their critical point, maximum strain value, and similar parameters are established through rigorous mathematical derivations. The supply chain elasticity of agricultural commodities, including grains, apples, and wheat, are assessed by utilizing the derived formulas. The results show that the metrics of supply chain elastic strain serve as direct metrics of measuring the supply chain’s anti-interference capability, and they also facilitate an objective assessment of the supply chain’s safety and stability. The formula is succinctly derived, and it yields objective outcomes with general applicability, particularly suited for research and application for supply chain elasticity.
Full article
(This article belongs to the Special Issue Applications and Analysis of Statistics and Data Science)
Open AccessArticle
Enhancing Mobile Robot Navigation: Optimization of Trajectories through Machine Learning Techniques for Improved Path Planning Efficiency
by
Safa Jameel Al-Kamil and Róbert Szabolcsi
Mathematics 2024, 12(12), 1787; https://doi.org/10.3390/math12121787 - 7 Jun 2024
Abstract
Efficient navigation is crucial for intelligent mobile robots in complex environments. This paper introduces an innovative approach that seamlessly integrates advanced machine learning techniques to enhance mobile robot communication and path planning efficiency. Our method combines supervised and unsupervised learning, utilizing spline interpolation
[...] Read more.
Efficient navigation is crucial for intelligent mobile robots in complex environments. This paper introduces an innovative approach that seamlessly integrates advanced machine learning techniques to enhance mobile robot communication and path planning efficiency. Our method combines supervised and unsupervised learning, utilizing spline interpolation to generate smooth paths with minimal directional changes. Experimental validation with a differential drive mobile robot demonstrates exceptional trajectory control efficiency. We also explore Motion Planning Networks (MPNets), a neural planner that processes raw point-cloud data from depth sensors. Our tests demonstrate MPNet’s ability to create optimal paths using the Probabilistic Roadmap (PRM) method. We highlight the importance of correctly setting parameters for reliable path planning with MPNet and evaluate the algorithm on various path types. Our experiments confirm that the trajectory control algorithm works effectively, consistently providing precise and efficient trajectory control for the robot.
Full article
(This article belongs to the Special Issue Advances in Dynamical System Modelling and Computer-Aided Design)
Open AccessArticle
Influence of Incident Orientation on the Dynamic Response of Deep U-Shaped Cavern Subjected to Transient Loading
by
Lisha Liang, Xibing Li, Zhixiang Liu and Siyu Peng
Mathematics 2024, 12(12), 1786; https://doi.org/10.3390/math12121786 - 7 Jun 2024
Abstract
In deep rock engineering, caverns are often disturbed by engineering loads from different directions. To investigate the dynamic response of deep U-shaped caverns under different incident orientations, a theoretical solution of the dynamic stress concentration factor along the cavern boundary was derived based
[...] Read more.
In deep rock engineering, caverns are often disturbed by engineering loads from different directions. To investigate the dynamic response of deep U-shaped caverns under different incident orientations, a theoretical solution of the dynamic stress concentration factor along the cavern boundary was derived based on the wave function expansion and conformal mapping method, and the failure characteristics around the cavern were further investigated by PFC2D (Particle Flow Code in two dimensions). As the incident orientation increases from 0° to 90°, the dynamic compressive stress concentration area transforms from both the roof and the floor to the sidewalls, and the peak dynamic stress concentration factor of the roof decreases from 2.98 to −0.20. The failure of the floor converts from dynamic compression shear failure to dynamic tensile failure. Compared to a stress wave incident from the curved boundary, a stress wave incident from the flat boundary causes severer damage. When the stress wave is incident from the sidewall, the cavern with a larger height-to-width (h/w) ratio exhibits severer damage. Conversely, the cavern with a smaller h/w ratio tends to fail as the stress wave is incident from the floor. This paper provides a basic understanding of dynamic responses of the deep U-shaped cavern.
Full article
(This article belongs to the Topic Physical Monitoring and Healthy Controlling of Geotechnical Engineering)
Open AccessArticle
Fredholm Theory Relative to Any Algebra Homomorphisms
by
Yingying Kong, Yabo Wang and Jingen Yang
Mathematics 2024, 12(12), 1785; https://doi.org/10.3390/math12121785 - 7 Jun 2024
Abstract
In this paper, we give another definition of Ruston elements and almost Ruston elements, which is equivalent to the definitions given by Mouton and Raubenheimer in the case that the homomorphism has a closed range and Riesz property. For two homomorphisms, we consider
[...] Read more.
In this paper, we give another definition of Ruston elements and almost Ruston elements, which is equivalent to the definitions given by Mouton and Raubenheimer in the case that the homomorphism has a closed range and Riesz property. For two homomorphisms, we consider the preserver problems of Fredholm theory and Fredholm spectrum theory. In addition, we study the spectral mapping theorems of Fredholm (Weyl, Browder, Ruston, and almost Ruston) elements relative to a homomorphism. Last but not least, the dependence of Fredholm theory on three homomorphisms is considered, and meanwhile, the transitivity of Fredholm theory relative to three homomorphisms is illustrated. Furthermore, we consider the Fredholm theory relative to more homomorphisms.
Full article
Open AccessFeature PaperArticle
Hyers–Ulam Stability of Isometries on Bounded Domains–III
by
Ginkyu Choi and Soon-Mo Jung
Mathematics 2024, 12(12), 1784; https://doi.org/10.3390/math12121784 - 7 Jun 2024
Abstract
The question of whether there is a true isometry that approximates the -isometry defined on a bounded set has long interested mathematicians. The first paper on this topic was published by Fickett, whose result was subsequently greatly improved by Alestalo et al.,
[...] Read more.
The question of whether there is a true isometry that approximates the -isometry defined on a bounded set has long interested mathematicians. The first paper on this topic was published by Fickett, whose result was subsequently greatly improved by Alestalo et al., Väisälä and Vestfrid. Recently, the authors published some papers improving the previous results. The main purpose of this paper is to improve all of the abovementioned results by utilizing the properties of the norm and inner product for Euclidean space.
Full article
Open AccessArticle
Wafer Delay Minimization in Scheduling Single-Arm Cluster Tools with Two-Space Process Modules
by
Chengyu Zou, Siwei Zhang, Shan Zeng, Lei Gu and Jie Li
Mathematics 2024, 12(12), 1783; https://doi.org/10.3390/math12121783 - 7 Jun 2024
Abstract
In semiconductor manufacturing, multi-space process modules (PMs) are adopted in some cluster tools for wafer processing. With multi-space PMs, a PM can have multiple wafers concurrently. Also, the internal chamber in a PM should rotate to make the robot able to load/unload a
[...] Read more.
In semiconductor manufacturing, multi-space process modules (PMs) are adopted in some cluster tools for wafer processing. With multi-space PMs, a PM can have multiple wafers concurrently. Also, the internal chamber in a PM should rotate to make the robot able to load/unload a wafer into/from a space in the PM. This means that the wafer staying time in PMs is affected by both the rotation operations of the internal chambers of PMs and the robot tasks. Thus, minimizing the wafer delay time is quite challenging. In this work, for cluster tools with single-arm robots and two-space PMs, efforts are made for wafer delay minimization in scheduling the tools. Specifically, a two-wafer backward strategy is presented to operate the tools in a steady state. Then, the workloads of each processing step and the robot are analyzed. Further, to find optimal schedules with the objective of minimizing the total wafer delay time, efficient algorithms are established. Finally, case studies show that the wafer delay time at some steps can be totally eliminated by the proposed method. In the meantime, in all cases, the proposed method can work well in reducing the total wafer delay time at all steps.
Full article
(This article belongs to the Special Issue Discrete Event Dynamic Systems and Applications)
Open AccessArticle
Research on Quantile Regression Method for Longitudinal Interval-Censored Data Based on Bayesian Double Penalty
by
Ke Zhao, Ting Shu, Chaozhu Hu and Youxi Luo
Mathematics 2024, 12(12), 1782; https://doi.org/10.3390/math12121782 - 7 Jun 2024
Abstract
The increasing prominence of the problem of censored data in various fields has made studying how to perform parameter estimation and variable selection in censored mixed-effects models one of the hotspots of current research. In this paper, considering the situation that the response
[...] Read more.
The increasing prominence of the problem of censored data in various fields has made studying how to perform parameter estimation and variable selection in censored mixed-effects models one of the hotspots of current research. In this paper, considering the situation that the response variable is restricted by the bilateral limit, a double-penalty Bayesian Tobit quantile regression model was constructed to carry out parameter estimation and variable selection in the interval-censored mixed-effects model, and at the same time, the fixed-effects and random effects coefficients are compressed in Tobit’s mixed-effects model, so as to reduce the estimation error of the model at the same time as the variable selection of the model is carried out. The posterior distribution of each unknown parameter was derived using the conditional Laplace prior and the mixed truncated normal distribution of interval-censored data, and then the Gibbs sampling algorithm for unknown parameter estimation was constructed. Through Monte Carlo simulation, it was found that the new method is more advantageous than the classical method in terms of variable selection and parameter estimation accuracy in various situations, such as different model sparsity, different data censoring ratios and different random error distributions, and the model is able to realize automatic variable selection. Finally, the new method is used to analyze the correlation between the crime rate and various economic indicators in China.
Full article
Open AccessArticle
Monotonicity Results of Ratios Between Normalized Tails of Maclaurin Power Series Expansions of Sine and Cosine
by
Da-Wei Niu and Feng Qi
Mathematics 2024, 12(12), 1781; https://doi.org/10.3390/math12121781 - 7 Jun 2024
Abstract
In the paper, the authors establish the monotonicity results of the ratios between normalized tails of the Maclaurin power series expansions of the sine and cosine functions and restate them in terms of the generalized hypergeometric functions.
Full article
(This article belongs to the Section Computational and Applied Mathematics)
Open AccessArticle
Globally Exponentially Attracting Sets and Heteroclinic Orbits Revealed
by
Guiyao Ke
Mathematics 2024, 12(12), 1780; https://doi.org/10.3390/math12121780 - 7 Jun 2024
Abstract
Motivated by the open problems on the global dynamics of the generalized four-dimensional Lorenz-like system, this paper deals with the existence of globally exponentially attracting sets and heteroclinic orbits by constructing a series of Lyapunov functions. Specifically, not only is a family of
[...] Read more.
Motivated by the open problems on the global dynamics of the generalized four-dimensional Lorenz-like system, this paper deals with the existence of globally exponentially attracting sets and heteroclinic orbits by constructing a series of Lyapunov functions. Specifically, not only is a family of mathematical expressions of globally exponentially attracting sets derived, but the existence of a pair of orbits heteroclinic to and is also proven with the aid of a Lyapunov function and the definitions of both the -limit set and -limit set. Moreover, numerical examples are used to justify the theoretical analysis. Since the obtained results improve and complement the existing ones, they may provide support in chaos control, chaos synchronization, the Hausdorff and Lyapunov dimensions of strange attractors, etc.
Full article
(This article belongs to the Section Dynamical Systems)
Journal Menu
► ▼ Journal Menu-
- Mathematics Home
- Aims & Scope
- Editorial Board
- Reviewer Board
- Topical Advisory Panel
- Instructions for Authors
- Special Issues
- Topics
- Sections & Collections
- Article Processing Charge
- Indexing & Archiving
- Editor’s Choice Articles
- Most Cited & Viewed
- Journal Statistics
- Journal History
- Journal Awards
- Society Collaborations
- Conferences
- Editorial Office
Journal Browser
► ▼ Journal BrowserHighly Accessed Articles
Latest Books
E-Mail Alert
News
Topics
Topic in
Algorithms, Axioms, Fractal Fract, Mathematics, Symmetry
Fractal and Design of Multipoint Iterative Methods for Nonlinear Problems
Topic Editors: Xiaofeng Wang, Fazlollah SoleymaniDeadline: 30 June 2024
Topic in
Algorithms, Computation, Information, Mathematics
Complex Networks and Social Networks
Topic Editors: Jie Meng, Xiaowei Huang, Minghui Qian, Zhixuan XuDeadline: 31 July 2024
Topic in
Algorithms, Future Internet, Information, Mathematics, Symmetry
Research on Data Mining of Electronic Health Records Using Deep Learning Methods
Topic Editors: Dawei Yang, Yu Zhu, Hongyi XinDeadline: 31 August 2024
Topic in
Applied Sciences, Energies, Mathematics, Electronics, Designs
Distributed Optimization for Control
Topic Editors: Honglei Xu, Lingyun WangDeadline: 20 September 2024
Conferences
Special Issues
Special Issue in
Mathematics
Applications of Fuzzy Modeling in Risk Management
Guest Editors: Edit Toth-Laufer, László PokorádiDeadline: 20 June 2024
Special Issue in
Mathematics
Computational Statistical Methods and Extreme Value Theory
Guest Editor: Frederico CaeiroDeadline: 30 June 2024
Special Issue in
Mathematics
Dynamical System and Stochastic Analysis
Guest Editors: Jun Huang, Yueyuan ZhangDeadline: 20 July 2024
Special Issue in
Mathematics
Mathematical Structures and Their Applications
Guest Editor: Nelson Martins FerreiraDeadline: 31 July 2024
Topical Collections
Topical Collection in
Mathematics
Topology and Foundations
Collection Editors: Lorentz Jäntschi, Dušanka Janežič
Topical Collection in
Mathematics
Multiscale Computation and Machine Learning
Collection Editors: Yalchin Efendiev, Eric Chung
Topical Collection in
Mathematics
Theoretical and Mathematical Ecology
Collection Editor: Yuri V. Tyutyunov