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
Enhancing Security and Efficiency: A Fine-Grained Searchable Scheme for Encryption of Big Data in Cloud-Based Smart Grids
Mathematics 2024, 12(10), 1512; https://doi.org/10.3390/math12101512 (registering DOI) - 13 May 2024
Abstract
The smart grid, as a crucial part of modern energy systems, handles extensive and diverse data, including inputs from various sensors, metering devices, and user interactions. Outsourcing data storage to remote cloud servers presents an economical solution for enhancing data management within the
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The smart grid, as a crucial part of modern energy systems, handles extensive and diverse data, including inputs from various sensors, metering devices, and user interactions. Outsourcing data storage to remote cloud servers presents an economical solution for enhancing data management within the smart grid ecosystem. However, ensuring data privacy before transmitting it to the cloud is a critical consideration. Therefore, it is common practice to encrypt the data before uploading them to the cloud. While encryption provides data confidentiality, it may also introduce potential issues such as limiting data owners’ ability to query their data. The searchable attribute-based encryption (SABE) not only enables fine-grained access control in a dynamic large-scale environment but also allows for data searches on the ciphertext domain, making it an effective tool for cloud data sharing. Although SABE has become a research hotspot, existing schemes often have limitations in terms of computing efficiency on the client side, weak security of the ciphertext and the trapdoor. To address these issues, we propose an efficient server-aided ciphertext-policy searchable attribute-based encryption scheme (SA-CP-SABE). In SA-CP-SABE, the user’s data access authority is consistent with the search authority. During the search process, calculations are performed not only to determine whether the ciphertext matches the keyword in the trapdoor, but also to assist subsequent user ciphertext decryption by reducing computational complexity. Our scheme has been proven under the random oracle model to achieve the indistinguishability of the ciphertext and the trapdoor and to resist keyword-guessing attacks. Finally, the performance analysis and simulation of the proposed scheme are provided, and the results show that it performs with high efficiency.
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(This article belongs to the Special Issue Artificial Intelligence and Data Science)
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Open AccessArticle
Leveraging Blockchain for Maritime Port Supply Chain Management through Multicriteria Decision Making
by
Claudia Durán, Amir Karbassi Yazdi, Iván Derpich and Yong Tan
Mathematics 2024, 12(10), 1511; https://doi.org/10.3390/math12101511 (registering DOI) - 13 May 2024
Abstract
This research investigates the optimal integration of Blockchain Technology (BT) in Supply Chain Management (SCM) within Chile’s maritime ports. Utilizing fuzzy Logarithmic Methodology of Additive Weights (LMAW) and Double Normalization-based Multiple Aggregation Methods (DNMA), the study systematically identifies, prioritizes, and ranks key factors
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This research investigates the optimal integration of Blockchain Technology (BT) in Supply Chain Management (SCM) within Chile’s maritime ports. Utilizing fuzzy Logarithmic Methodology of Additive Weights (LMAW) and Double Normalization-based Multiple Aggregation Methods (DNMA), the study systematically identifies, prioritizes, and ranks key factors influencing BT adoption in SCM. The study’s findings highlight crucial factors like enhanced transaction security, good supply chain practices, and risk management. Furthermore, it ranks the application of ports as prime candidates for BT integration. The research contributes theoretically by developing a hybrid model combining MCDA methods, and practically by guiding the strategic application of BT in the maritime logistics sector, aligning with the principles of Industry 5.0. This paper presents a novel approach that explores the utilization of BT in maritime supply chain management, incorporating MCDA in a vague environment. The research gap of this study lies in defining new contexts in both theoretical and practical literature reviews for extending the use of BT in SCM in the ports of Chile, according to Industry 5.0, to increase the efficiency and effectiveness of all aspects of operations in these places. The contribution of this research is applying hybrid MCDA methods in an uncertain environment to assist decision-makers (DMs) in better implementing BT in SCM in Chilean ports, according to Industry 5.0.
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(This article belongs to the Special Issue Advances and Application of Fuzzy Sets, Decision Making and Soft Computing)
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Open AccessArticle
A Blow-Up Criterion for the Density-Dependent Incompressible Magnetohydrodynamic System with Zero Viscosity
by
Kunlong Shi, Jishan Fan and Gen Nakamura
Mathematics 2024, 12(10), 1510; https://doi.org/10.3390/math12101510 (registering DOI) - 12 May 2024
Abstract
In this paper, we provide a blow-up criterion for the density-dependent incompressible magnetohydrodynamic system with zero viscosity. The proof uses the -method and the Kato–Ponce inequalities in the harmonic analysis. The novelty of our work lies in the fact that we
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In this paper, we provide a blow-up criterion for the density-dependent incompressible magnetohydrodynamic system with zero viscosity. The proof uses the -method and the Kato–Ponce inequalities in the harmonic analysis. The novelty of our work lies in the fact that we deal with the case in which the resistivity is positive.
Full article
Open AccessArticle
On the Number of Customer Classes in a Single-Period Inventory System
by
Mónica López-Campos, Pablo Escalona, Alejandro Angulo, Francisca Recabarren and Raúl Stegmaier
Mathematics 2024, 12(10), 1509; https://doi.org/10.3390/math12101509 (registering DOI) - 12 May 2024
Abstract
A common practice in inventory systems with several customers requiring differentiated service levels is to group them into two or three classes, where a customer class is a group of customers with the same preset service level in terms of product availability. However,
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A common practice in inventory systems with several customers requiring differentiated service levels is to group them into two or three classes, where a customer class is a group of customers with the same preset service level in terms of product availability. However, there is no evidence that grouping customers into two or three classes is optimal in terms of the ordering policy parameters. This paper studies the effect of the number of customer classes on the inventory level of a single-period inventory system with stochastic demand and individual service-level requirements from multiple customer classes. Using a Sample Average Approximation approach, we formulate computationally tractable multi-class service level models, under responsive and anticipative priority policies in cases of shortage, as mixed integer linear problems (MIPs). The effect of the number of classes on the inventory level is determined using a round-up aggregation scheme; i.e., given a sufficiently large initial number of classes, it is reduced by adding the lower service level classes to the next higher class. We analytically characterize the optimal inventory level under responsive and anticipative priority policies as a function of the initial number of classes and the number of classes grouped based on the round-up aggregation scheme. Under a responsive priority policy, we show that there is an optimal number of classes, while under an anticipative priority policy, the optimal number of classes is equal to the initial number of classes. The effect of free-riders resulting from the round-up aggregation scheme on the optimal inventory level is studied through numerical experiments.
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(This article belongs to the Special Issue Mathematical Approaches Applied in Operations Research, Logistics, and Inventory)
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Open AccessArticle
AARF: Autonomous Attack Response Framework for Honeypots to Enhance Interaction Based on Multi-Agent Dynamic Game
by
Le Wang, Jianyu Deng, Haonan Tan, Yinghui Xu, Junyi Zhu, Zhiqiang Zhang, Zhaohua Li, Rufeng Zhan and Zhaoquan Gu
Mathematics 2024, 12(10), 1508; https://doi.org/10.3390/math12101508 (registering DOI) - 11 May 2024
Abstract
Highly interactive honeypots can form reliable connections by responding to attackers to delay and capture intranet attacks. However, current research focuses on modeling the attacker as part of the environment and defining single-step attack actions by simulation to study the interaction of honeypots.
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Highly interactive honeypots can form reliable connections by responding to attackers to delay and capture intranet attacks. However, current research focuses on modeling the attacker as part of the environment and defining single-step attack actions by simulation to study the interaction of honeypots. It ignores the iterative nature of the attack and defense game, which is inconsistent with the correlative and sequential nature of actions in real attacks. These limitations lead to insufficient interaction of the honeypot response strategies generated by the study, making it difficult to support effective and continuous games with attack behaviors. In this paper, we propose an autonomous attack response framework (named AARF) to enhance interaction based on multi-agent dynamic games. AARF consists of three parts: a virtual honeynet environment, attack agents, and defense agents. Attack agents are modeled to generate multi-step attack chains based on a Hidden Markov Model (HMM) combined with the generic threat framework ATT&CK (Adversarial Tactics, Techniques, and Common Knowledge). The defense agents iteratively interact with the attack behavior chain based on reinforcement learning (RL) to learn to generate honeypot optimal response strategies. Aiming at the sample utilization inefficiency problem of random uniform sampling widely used in RL, we propose the dynamic value label sampling (DVLS) method in the dynamic environment. DVLS can effectively improve the sample utilization during the experience replay phase and thus improve the learning efficiency of honeypot agents under the RL framework. We further couple it with a classic DQN to replace the traditional random uniform sampling method. Based on AARF, we instantiate different functional honeypot models for deception in intranet scenarios. In the simulation environment, honeypots collaboratively respond to multi-step intranet attack chains to defend against these attacks, which demonstrates the effectiveness of AARF. The average cumulative reward of the DQN with DVLS is beyond eight percent, and the convergence speed is improved by five percent compared to a classic DQN.
Full article
(This article belongs to the Special Issue Advanced Research on Information System Security and Privacy)
Open AccessArticle
Optimizing Insulator Defect Detection with Improved DETR Models
by
Dong Li, Panfei Yang and Yuntao Zou
Mathematics 2024, 12(10), 1507; https://doi.org/10.3390/math12101507 (registering DOI) - 11 May 2024
Abstract
With the increasing demand for electricity, the power grid is undergoing significant advancements. Insulators, which serve as protective devices for transmission lines in outdoor high-altitude power systems, are widely employed. However, the detection of defects in insulators captured under challenging conditions, such as
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With the increasing demand for electricity, the power grid is undergoing significant advancements. Insulators, which serve as protective devices for transmission lines in outdoor high-altitude power systems, are widely employed. However, the detection of defects in insulators captured under challenging conditions, such as rain, snow, fog, sunlight, and fast-moving drones during long-distance photography, remains a major challenge. To address this issue and improve the accuracy of defect detection, this paper presents a novel approach: the Multi-Scale Insulator Defect Detection Approach using Detection Transformer (DETR). In this study, we propose a multi-scale backbone network that effectively captures the features of small objects, enhancing the detection performance. Additionally, we introduce a self-attention upsampling (SAU) module to replace the conventional attention module, enhancing contextual information extraction and facilitating the detection of small objects. Furthermore, we introduce the insulator defect (IDIoU) loss, which mitigates the instability in the matching process caused by small defects. Extensive experiments were conducted on an insulator defect dataset to evaluate the performance of our proposed method. The results demonstrate that our approach achieves outstanding performance, particularly in detecting small defects. Compared to existing methods, our approach exhibits a remarkable 7.47% increase in the average precision, emphasizing its efficacy in insulator defect detection. The proposed method not only enhances the accuracy of defect detection, which is crucial for maintaining the reliability and safety of power transmission systems but also has broader implications for the maintenance and inspection of high-voltage power infrastructure.
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(This article belongs to the Section Engineering Mathematics)
Open AccessArticle
An Improved Golden Jackal Optimization Algorithm Based on Mixed Strategies
by
Yancang Li, Qian Yu, Zhao Wang, Zunfeng Du and Zidong Jin
Mathematics 2024, 12(10), 1506; https://doi.org/10.3390/math12101506 (registering DOI) - 11 May 2024
Abstract
In an effort to overcome the problems with typical optimization algorithms’ slow convergence and tendency to settle on a local optimal solution, an improved golden jackal optimization technique is proposed. Initially, the development mechanism is enhanced to update the prey’s location, addressing the
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In an effort to overcome the problems with typical optimization algorithms’ slow convergence and tendency to settle on a local optimal solution, an improved golden jackal optimization technique is proposed. Initially, the development mechanism is enhanced to update the prey’s location, addressing the limitation of just relying on local search in the later stages of the algorithm. This ensures a more balanced approach to both algorithmic development and exploration. Furthermore, incorporating the instinct of evading natural predators enhances both the effectiveness and precision of the optimization process. Then, cross-mutation enhances population variety and facilitates escaping from local optima. Finally, the crossbar strategy is implemented to change both the individual and global optimal solutions of the population. This technique aims to decrease blind spots, enhance population variety, improve solution accuracy, and accelerate convergence speed. A total of 20 benchmark functions are employed for the purpose of comparing different techniques. The enhanced algorithm’s performance is evaluated using the CEC2017 test function, and the results are assessed using the rank-sum test. Ultimately, three conventional practical engineering simulation experiments are conducted to evaluate the suitability of IWKGJO for engineering issues. The results obtained demonstrate the beneficial effects of the altered methodology and illustrate that the expanded golden jackal optimization algorithm has superior convergence accuracy and a faster convergence rate.
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Open AccessFeature PaperArticle
Dupin Cyclides Passing through a Fixed Circle
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Jean Michel Menjanahary and Raimundas Vidunas
Mathematics 2024, 12(10), 1505; https://doi.org/10.3390/math12101505 (registering DOI) - 11 May 2024
Abstract
Dupin cyclides are classical algebraic surfaces of low degree. Recently, they have gained popularity in computer-aided geometric design (CAGD) and architecture owing to the fact that they contain many circles. We derive algebraic conditions that fully characterize the Dupin cyclides passing through a
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Dupin cyclides are classical algebraic surfaces of low degree. Recently, they have gained popularity in computer-aided geometric design (CAGD) and architecture owing to the fact that they contain many circles. We derive algebraic conditions that fully characterize the Dupin cyclides passing through a fixed circle. The results are applied to the basic problem in CAGD of the blending of Dupin cyclides along circles.
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(This article belongs to the Special Issue Geometry and Topology with Applications)
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Open AccessReview
Deep Time Series Forecasting Models: A Comprehensive Survey
by
Xinhe Liu and Wenmin Wang
Mathematics 2024, 12(10), 1504; https://doi.org/10.3390/math12101504 (registering DOI) - 11 May 2024
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Deep learning, a crucial technique for achieving artificial intelligence (AI), has been successfully applied in many fields. The gradual application of the latest architectures of deep learning in the field of time series forecasting (TSF), such as Transformers, has shown excellent performance and
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Deep learning, a crucial technique for achieving artificial intelligence (AI), has been successfully applied in many fields. The gradual application of the latest architectures of deep learning in the field of time series forecasting (TSF), such as Transformers, has shown excellent performance and results compared to traditional statistical methods. These applications are widely present in academia and in our daily lives, covering many areas including forecasting electricity consumption in power systems, meteorological rainfall, traffic flow, quantitative trading, risk control in finance, sales operations and price predictions for commercial companies, and pandemic prediction in the medical field. Deep learning-based TSF tasks stand out as one of the most valuable AI scenarios for research, playing an important role in explaining complex real-world phenomena. However, deep learning models still face challenges: they need to deal with the challenge of large-scale data in the information age, achieve longer forecasting ranges, reduce excessively high computational complexity, etc. Therefore, novel methods and more effective solutions are essential. In this paper, we review the latest developments in deep learning for TSF. We begin by introducing the recent development trends in the field of TSF and then propose a new taxonomy from the perspective of deep neural network models, comprehensively covering articles published over the past five years. We also organize commonly used experimental evaluation metrics and datasets. Finally, we point out current issues with the existing solutions and suggest promising future directions in the field of deep learning combined with TSF. This paper is the most comprehensive review related to TSF in recent years and will provide a detailed index for researchers in this field and those who are just starting out.
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The Maximal and Minimal Distributions of Wealth Processes in Black–Scholes Markets
by
Shuhui Liu
Mathematics 2024, 12(10), 1503; https://doi.org/10.3390/math12101503 (registering DOI) - 11 May 2024
Abstract
The Black–Scholes formula is an important formula for pricing a contingent claim in complete financial markets. This formula can be obtained under the assumption that the investor’s strategy is carried out according to a self-financing criterion; hence, there arise a set of self-financing
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The Black–Scholes formula is an important formula for pricing a contingent claim in complete financial markets. This formula can be obtained under the assumption that the investor’s strategy is carried out according to a self-financing criterion; hence, there arise a set of self-financing portfolios corresponding to different contingent claims. The natural questions are: If an investor invests according to self-financing portfolios in the financial market, what are the maximal and minimal distributions of the investor’s wealth on some specific interval at the terminal time? Furthermore, if such distributions exist, how can the corresponding optimal portfolios be constructed? The present study applies the theory of backward stochastic differential equations in order to obtain an affirmative answer to the above questions. That is, the explicit formulations for the maximal and minimal distributions of wealth when adopting self-financing strategies would be derived, and the corresponding optimal (self-financing) portfolios would be constructed. Furthermore, this would verify the benefits of diversified portfolios in financial markets: that is, do not put all your eggs in the same basket.
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(This article belongs to the Special Issue New Trends in Stochastic Processes, Probability and Statistics)
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Open AccessArticle
Multivariate Mittag-Leffler Solution for a Forced Fractional-Order Harmonic Oscillator
by
Jessica Mendiola-Fuentes, Eugenio Guerrero-Ruiz and Juan Rosales-García
Mathematics 2024, 12(10), 1502; https://doi.org/10.3390/math12101502 (registering DOI) - 11 May 2024
Abstract
The harmonic oscillator is a fundamental physical–mathematical system that allows for the description of a variety of models in many fields of physics. Utilizing fractional derivatives instead of traditional derivatives enables the modeling of a more diverse array of behaviors. Furthermore, if the
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The harmonic oscillator is a fundamental physical–mathematical system that allows for the description of a variety of models in many fields of physics. Utilizing fractional derivatives instead of traditional derivatives enables the modeling of a more diverse array of behaviors. Furthermore, if the effect of the fractional derivative is applied to each of the terms of the differential equation, this will involve greater complexity in the description of the analytical solutions of the fractional differential equation. In this work, by using the Laplace method, the solutions to the multiple-term forced fractional harmonic oscillator are presented, described through multivariate Mittag-Leffler functions. Additionally, the cases of damped and undamped free fractional harmonic oscillators are addressed. Finally, through simulations, the effect of the fractional non-integer derivative is demonstrated, and the consistency of the result is verified when recovering the integer case.
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(This article belongs to the Special Issue Fractional Calculus: Advances and Applications)
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An Examination of Mental Stress in College Students: Utilizing Intelligent Perception Data and the Mental Stress Scale
by
Zhixuan Liao, Xiaomao Fan, Wenjun Ma and Yingshan Shen
Mathematics 2024, 12(10), 1501; https://doi.org/10.3390/math12101501 (registering DOI) - 11 May 2024
Abstract
In order to solve the problems of traditional mental stress detection in college students that are time-consuming, random, and subjective, this paper proposes an intelligent perception-driven mental stress assessment method for college students. First, we analyze the factors in SRQ and SCL-90, which
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In order to solve the problems of traditional mental stress detection in college students that are time-consuming, random, and subjective, this paper proposes an intelligent perception-driven mental stress assessment method for college students. First, we analyze the factors in SRQ and SCL-90, which can be measured by intelligent sensing methods, including sleep, exercise, social interaction, and environment, and then perform feature extraction. Secondly, we use machine learning methods to build a mental stress assessment model. The Shapley additive explanations (SHAP) model is used to explain the training results. Experimental results show that the model proposed in this article can effectively assess the mental stress state of college students. This means that the collection of intelligent perception data based on the mental stress scale can effectively evaluate the mental stress state of college students and provide a new research idea for further developing a non-intrusive and real-time mental stress assessment for college students.
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(This article belongs to the Special Issue New Trends in Computer Vision, Deep Learning and Artificial Intelligence)
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Open AccessArticle
Analysis of a Two-Stage Tandem Queuing System with Priority and Clearing Service in the Second Stage
by
Jia Xu and Liwei Liu
Mathematics 2024, 12(10), 1500; https://doi.org/10.3390/math12101500 (registering DOI) - 11 May 2024
Abstract
This paper considers a two-stage tandem queuing system with ordinary customers and priority customers. Upon arrival, ordinary customers are individually served in the first stage, then move to the second stage and receive clearing service. Priority customers can bypass the first stage and
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This paper considers a two-stage tandem queuing system with ordinary customers and priority customers. Upon arrival, ordinary customers are individually served in the first stage, then move to the second stage and receive clearing service. Priority customers can bypass the first stage and proceed directly to the second stage for clearing service. The second stage has N service seats. All customers currently in the second stage are served simultaneously (i.e., clearing service). Once there are N customers in the second stage, the first stage will be blocked, and newly arriving priority customers will balk and leave without joining. We first formulate a two-dimensional Markov chain to analyze this queuing system and derive the stability condition. Subsequently, the stationary distribution of the system is derived using the matrix-analytic method and spectral expansion technique. Furthermore, analytical expressions for the mean queue length, mean sojourn time, and other performance measures are presented. Finally, some numerical examples are provided to illustrate the effects of various parameters, offering valuable insights for designing such two-stage tandem queuing systems.
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(This article belongs to the Special Issue Queueing Systems Models and Their Applications)
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Open AccessArticle
Numerical Reconstruction of Time-Dependent Boundary Conditions to 2D Heat Equation on Disjoint Rectangles at Integral Observations
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Miglena N. Koleva and Lubin G. Vulkov
Mathematics 2024, 12(10), 1499; https://doi.org/10.3390/math12101499 (registering DOI) - 11 May 2024
Abstract
In this paper, two-dimensional (2D) heat equations on disjoint rectangles are considered. The solutions are connected by interface Robin’s-type internal conditions. The problem has external Dirichlet boundary conditions that, in the forward (direct) formulation, are given functions. In the inverse problem formulation, the
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In this paper, two-dimensional (2D) heat equations on disjoint rectangles are considered. The solutions are connected by interface Robin’s-type internal conditions. The problem has external Dirichlet boundary conditions that, in the forward (direct) formulation, are given functions. In the inverse problem formulation, the Dirichlet conditions are unknown functions, and the aim is to be reconstructed upon integral observations. Well-posedness both for direct and inverse problems is established. Using the given 2D integrals of the unknown solution on each of the domains and the specific interface boundary conditions, we reduce the 2D inverse problem to a forward heat 1D one. The resulting 1D problem is solved using the explicit Saul’yev finite difference method. Numerical test examples are discussed to illustrate the efficiency of the approach.
Full article
(This article belongs to the Special Issue Computational Methods and Applications for Numerical Analysis, 2nd Edition)
Open AccessArticle
Thermostatistics, Information, Subjectivity: Why Is This Association So Disturbing?
by
Didier Lairez
Mathematics 2024, 12(10), 1498; https://doi.org/10.3390/math12101498 (registering DOI) - 11 May 2024
Abstract
Although information theory resolves the inconsistencies (known in the form of famous enigmas) of the traditional approach of thermostatistics, its place in the corresponding literature is not what it deserves. This article supports the idea that this is mainly due to epistemological rather
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Although information theory resolves the inconsistencies (known in the form of famous enigmas) of the traditional approach of thermostatistics, its place in the corresponding literature is not what it deserves. This article supports the idea that this is mainly due to epistemological rather than scientific reasons: the subjectivity introduced into physics is perceived as a problem. Here is an attempt to expose and clarify where exactly this subjectivity lies: in the representation of reality and in probabilistic inference, two aspects that have been integrated into the practice of science for a long time and which should no longer frighten anyone but have become explicit with information theory.
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(This article belongs to the Special Issue Advanced Computational Mechanics)
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Open AccessArticle
Exploring Zeros of Hermite-λ Matrix Polynomials: A Numerical Approach
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Maryam Salem Alatawi, Manoj Kumar, Nusrat Raza and Waseem Ahmad Khan
Mathematics 2024, 12(10), 1497; https://doi.org/10.3390/math12101497 (registering DOI) - 10 May 2024
Abstract
This article aims to introduce a set of hybrid matrix polynomials associated with -polynomials and explore their properties using a symbolic approach. The main outcomes of this study include the derivation of generating functions, series definitions, and differential equations for the newly
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This article aims to introduce a set of hybrid matrix polynomials associated with -polynomials and explore their properties using a symbolic approach. The main outcomes of this study include the derivation of generating functions, series definitions, and differential equations for the newly introduced two-variable Hermite -matrix polynomials. Furthermore, we establish the quasi-monomiality property of these polynomials, derive summation formulae and integral representations, and examine the graphical representation and symmetric structure of their approximate zeros using computer-aided programs. Finally, this article concludes by introducing the idea of 1-variable Hermite matrix polynomials and their structure of zeros using a computer-aided program.
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(This article belongs to the Section Computational and Applied Mathematics)
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Hub-and-Spoke Network Optimization with Flow Delay Cost: The Case of Goods Delivery on Urban Logistics Networks in Eastern China
by
Bangjun Wang, Guoqiang Shen, Xingshen Wang, Yunwen Dong and Ziyu Li
Mathematics 2024, 12(10), 1496; https://doi.org/10.3390/math12101496 (registering DOI) - 10 May 2024
Abstract
With respect to a traditional point-to-point (P-P) network, a hub-and-spoke (H-S) network not only uses a smaller number of links/paths but also utilizes the scale economy advantage on consolidated flows on hub–hub links and at hubs. However, the inevitable
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With respect to a traditional point-to-point (P-P) network, a hub-and-spoke (H-S) network not only uses a smaller number of links/paths but also utilizes the scale economy advantage on consolidated flows on hub–hub links and at hubs. However, the inevitable delays through hubs have always been a critical concern. Therefore, this paper develops an H-S model considering flow delay costs and applies the model to a logistics case in Eastern China. The integer quadratic term in the model’s objective function is linearized using the algebraic method. Our model is applied to develop an H-S network for its 13-node express package delivery operation, using the particle swarm optimization (PSO) algorithm. The results show using the H-S can save more than 14.1% of the total cost annually. The model also provides an applied case to the H-S configuration, especially for urban express delivery logistics in China.
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(This article belongs to the Topic Mathematical Modeling)
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Open AccessArticle
Chebyshev–Jensen-Type Inequalities Involving χ-Products and Their Applications in Probability Theory
by
Ru Liu, Jiajin Wen and Lingzhi Zhao
Mathematics 2024, 12(10), 1495; https://doi.org/10.3390/math12101495 (registering DOI) - 10 May 2024
Abstract
By means of the functional analysis theory, reorder method, mathematical induction and the dimension reduction method, the Chebyshev-Jensen-type inequalities involving the -products and are established, and we proved that our main results are the
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By means of the functional analysis theory, reorder method, mathematical induction and the dimension reduction method, the Chebyshev-Jensen-type inequalities involving the -products and are established, and we proved that our main results are the generalizations of the classical Chebyshev inequalities. As applications in probability theory, the discrete with continuous probability inequalities are obtained.
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Open AccessArticle
Baire 1 Functions and the Topology of Uniform Convergence on Compacta
by
Ľubica Holá and Dušan Holý
Mathematics 2024, 12(10), 1494; https://doi.org/10.3390/math12101494 (registering DOI) - 10 May 2024
Abstract
Let X be a Tychonoff topological space, be the space of real-valued Baire 1 functions on X and be the topology of uniform convergence on compacta. The main purpose of this paper is
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Let X be a Tychonoff topological space, be the space of real-valued Baire 1 functions on X and be the topology of uniform convergence on compacta. The main purpose of this paper is to study cardinal invariants of . We prove that the following conditions are equivalent: (1) is metrizable; (2) is completely metrizable; (3) is Čech-complete; and (4) X is hemicompact. It is also proven that if X is a separable metric space with a non isolated point, then the topology of uniform convergence on compacta on is seen to behave like a metric topology in the sense that the weight, netweight, density, Lindelof number and cellularity are all equal for this topology and they are equal to . We find further conditions on X under which these cardinal invariants coincide on .
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(This article belongs to the Section Algebra, Geometry and Topology)
Open AccessArticle
Adaptive Graph Convolutional Recurrent Network with Transformer and Whale Optimization Algorithm for Traffic Flow Prediction
by
Chen Zhang, Yue Wu, Ya Shen, Shengzhao Wang, Xuhui Zhu and Wei Shen
Mathematics 2024, 12(10), 1493; https://doi.org/10.3390/math12101493 (registering DOI) - 10 May 2024
Abstract
Accurate traffic flow prediction plays a crucial role in the development of intelligent traffic management. Despite numerous investigations into spatio-temporal methods, achieving high accuracy in traffic flow prediction remains challenging. This challenge arises from the complex dynamic spatio-temporal correlations within the traffic road
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Accurate traffic flow prediction plays a crucial role in the development of intelligent traffic management. Despite numerous investigations into spatio-temporal methods, achieving high accuracy in traffic flow prediction remains challenging. This challenge arises from the complex dynamic spatio-temporal correlations within the traffic road network and the limitations imposed by the selection of hyperparameters based on experiments and manual experience, which can affect the performance of the network architecture. This paper introduces a novel transformer-based adaptive graph convolutional recurrent network. The proposed network automatically infers the interdependencies among different traffic sequences and incorporates the capability to capture global spatio-temporal correlations. This enables the dynamic capture of long-range temporal correlations. Furthermore, the whale optimization algorithm is employed to efficiently design an optimal network structure that aligns with the requirements of the traffic domain and maximizes the utilization of limited computational resources. This design approach significantly enhances the model’s performance and improves the accuracy of traffic flow prediction. The experimental results on four real datasets demonstrate the efficacy of our approach. In PEMS03, it improves MAE by 2.6% and RMSE by 1.4%. In PEMS04, improvements are 1.6% in MAE and 1.4% in RMSE, with a similar MAPE score to the best baseline. For PEMS07, our approach shows a 4.1% improvement in MAE and 2.2% in RMSE. On PEMS08, it surpasses the current best baseline with a 3.4% improvement in MAE and 1.6% in RMSE. These results confirm the good performance of our model in traffic flow prediction across multiple datasets.
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