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
Exploring Zeros of Hermite-λ Matrix Polynomials: A Numerical Approach
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.
Full article
(This article belongs to the Section Computational and Applied Mathematics)
Open AccessArticle
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.
Full article
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 .
Full article
(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.
Full article
Open AccessArticle
On V-Geometric Ergodicity Markov Chains of the Two-Inertia Systems
by
Feng-Rung Hu and Jia-Sheng Hu
Mathematics 2024, 12(10), 1492; https://doi.org/10.3390/math12101492 (registering DOI) - 10 May 2024
Abstract
This study employs the diffusion process to construct Markov chains for analyzing the common two-inertia systems used in industry. Two-inertia systems are prevalent in commonly used equipment, where the load is influenced by the coupling of external force and the drive shaft, leading
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This study employs the diffusion process to construct Markov chains for analyzing the common two-inertia systems used in industry. Two-inertia systems are prevalent in commonly used equipment, where the load is influenced by the coupling of external force and the drive shaft, leading to variations in the associated output states. Traditionally, the control of such systems is often guided by empirical rules. This paper examines the equilibrium distribution and convergence rate of the two-inertia system and develops a predictive model for its long-term operation. We explore the qualitative behavior of the load end at discrete time intervals. Our findings are applicable not only in control engineering, but also provide insights for small-scale models incorporating dual-system variables.
Full article
(This article belongs to the Special Issue Advances of Applied Probability and Statistics)
Open AccessArticle
Two-Dimensional System of Moment Equations and Macroscopic Boundary Conditions Depending on the Velocity of Movement and the Surface Temperature of a Body Moving in Fluid
by
Auzhan Sakabekov, Yerkanat Auzhani and Shinar Akimzhanova
Mathematics 2024, 12(10), 1491; https://doi.org/10.3390/math12101491 (registering DOI) - 10 May 2024
Abstract
This article is dedicated to the derivation of a two-dimensional system of moment equations depending on the velocity of movement and the surface temperature of a body submerged in fluid, and macroscopic boundary conditions for the system of moment equations approximating the Maxwell
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This article is dedicated to the derivation of a two-dimensional system of moment equations depending on the velocity of movement and the surface temperature of a body submerged in fluid, and macroscopic boundary conditions for the system of moment equations approximating the Maxwell microscopic boundary condition for the particle distribution function. The initial-boundary value problem for the Boltzmann equation with the Maxwell microscopic boundary condition is approximated by a corresponding problem for the system of moment equations with macroscopic boundary conditions. The number of moment equations and the number of macroscopic boundary conditions are interconnected and depend on the parity of the approximation of the system of moment equations. The setting of the initial-boundary value problem for a non-stationary, nonlinear two-dimensional system of moment equations in the first approximation with macroscopic boundary conditions is presented, and the solvability of the above-mentioned problem in the space of functions continuous in time and square-integrable in spatial variables is proven.
Full article
(This article belongs to the Special Issue Advances in Non-equilibrium Fluid Mechanics: Theory, Analysis, and Simulations)
Open AccessArticle
On the Structure of SO(3): Trace and Canonical Decompositions
by
Demeter Krupka and Ján Brajerčík
Mathematics 2024, 12(10), 1490; https://doi.org/10.3390/math12101490 (registering DOI) - 10 May 2024
Abstract
This paper is devoted to some selected topics of the theory of special orthogonal group SO(3). First, we discuss the trace of orthogonal matrices and its relation to the characteristic polynomial; on this basis, the partition of SO(3) formed by conjugation classes is
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This paper is devoted to some selected topics of the theory of special orthogonal group SO(3). First, we discuss the trace of orthogonal matrices and its relation to the characteristic polynomial; on this basis, the partition of SO(3) formed by conjugation classes is described by trace mapping. Second, we show that every special orthogonal matrix can be expressed as the product of three elementary special orthogonal matrices. Explicit formulas for the decomposition as needed for applications in differential geometry and physics as symmetry transformations are given.
Full article
(This article belongs to the Special Issue Differentiable Manifolds and Geometric Structures)
Open AccessArticle
Some New Results on Stochastic Comparisons of Spacings of Generalized Order Statistics from One and Two Samples
by
Maryam Esna-Ashari, Mahdi Alimohammadi, Elnaz Garousi and Antonio Di Crescenzo
Mathematics 2024, 12(10), 1489; https://doi.org/10.3390/math12101489 (registering DOI) - 10 May 2024
Abstract
Generalized order statistics (GOSs) are often adopted as a tool for providing a unified approach to several stochastic models dealing with ordered random variables. In this contribution, we first recall various useful results based on the notion of total positivity. Then, some stochastic
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Generalized order statistics (GOSs) are often adopted as a tool for providing a unified approach to several stochastic models dealing with ordered random variables. In this contribution, we first recall various useful results based on the notion of total positivity. Then, some stochastic comparisons between spacings of GOSs from one sample, as well as two samples, are developed under the more general assumptions on the parameters of the model. Specifically, the given results deal with the likelihood ratio order, the hazard rate order and the mean residual life order. Finally, an application is demonstrated for sequential systems.
Full article
(This article belongs to the Section Probability and Statistics)
Open AccessArticle
Investigating the Influence of Non-Uniform Characteristics of Layered Foundation on Ground Vibration Using an Efficient 2.5D Random Finite Element Method
by
Shaofeng Yao, Liang Yue, Wei Xie, Sen Zheng, Shuo Tang, Jinglong Liu and Wenkai Wang
Mathematics 2024, 12(10), 1488; https://doi.org/10.3390/math12101488 (registering DOI) - 10 May 2024
Abstract
High-speed train operation may cause vibration near track facilities and propagate far through the ground, affecting people’s lives, work, and normal use of precision instruments in an urban environment. An efficient numerical method is proposed to calculate the non-uniform ground vibration under a
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High-speed train operation may cause vibration near track facilities and propagate far through the ground, affecting people’s lives, work, and normal use of precision instruments in an urban environment. An efficient numerical method is proposed to calculate the non-uniform ground vibration under a moving high-speed railway load. The theory of stochastic variables is used to describe the soil spatial variability of the non-uniform layered elastic ground, and the coupled 2.5D random finite element method (FEM) is proposed to reduce the computational cost without losing accuracy. Vibration propagation and attenuation of the non-uniform layered ground are investigated and the effect of train speed and soil non-homogeneity are analyzed. Results show that (1) at cross speed and high speed, the homogeneity coefficient of the layered ground has the most important influence on the ground vibration amplitude; (2) the upward acceleration is much larger than the downward acceleration at most speeds, and at cross speed and high speed, the acceleration amplitude decreases with the increase in the homogeneity coefficient; (3) as train speed increases from 60 m/s to 130 m/s, the influencing range of the homogeneity coefficient increases to 10 m from 2 m; and (4) the phenomenon of an in increase in local rebound can be observed in the velocity and acceleration attenuation curve at cross speed when the ground soil has a weaker homogeneity.
Full article
(This article belongs to the Special Issue Applications of Advanced Mathematical Method for Modeling, Predicting, Controlling, and Optimizing the Dynamical System in Engineering)
Open AccessArticle
Investigating the Dynamics of Bayoud Disease in Date Palm Trees and Optimal Control Analysis
by
Alaa A. Alsaqer, Azhar Iqbal Kashif Butt and Muneerah Al Nuwairan
Mathematics 2024, 12(10), 1487; https://doi.org/10.3390/math12101487 (registering DOI) - 10 May 2024
Abstract
The fungus Fusarium oxysporum (f.sp. albedinis) causes Bayoud disease. It is one of the epiphytotic diseases that affects a wide range of palm species and has no known cure at present. However, preventive measures can be taken to reduce the effects of the
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The fungus Fusarium oxysporum (f.sp. albedinis) causes Bayoud disease. It is one of the epiphytotic diseases that affects a wide range of palm species and has no known cure at present. However, preventive measures can be taken to reduce the effects of the disease. Bayoud disease has caused enormous economic losses due to decreased crop yield and quality. Therefore, it is essential to develop a mathematical model for the dynamics of the disease to propose some affordable methods for disease management. In this study, we propose a novel mathematical model that describes the transmission dynamics of the disease in date palm trees. The model incorporates various factors such as the contact rate of the fungi with date palm trees, the utilization of fungicides, and the introduction of a quarantine compartment to prevent disease dissemination. We first prove a few key properties of the proposed model to ensure that the model is well-posed and suitable for numerical investigations. We establish that the model has a unique positive solution that is bounded and stable over time. We use sensitivity analysis to identify the parameters that have the greatest effect on the reproduction number and illustrate this effect graphically. We then formulate an optimal control problem to identify the most suitable and cost-effective disease control approaches. As a first approach, we solely focus on the application of fungicide to susceptible trees and determine the best spray rates for a greater decrease in exposed and infected trees. Secondly, we emphasize quarantining exposed and infected trees at optimal quarantine rates. Finally, we explore the combined effect of fungicide spraying and isolating infected trees on disease control. The findings of the last approach turn out to be the most rewarding and cost-effective for minimizing infections in date palm trees.
Full article
Open AccessArticle
A Multi-Objective Pigeon-Inspired Optimization Algorithm for Community Detection in Complex Networks
by
Lin Yu, Xiaodan Guo, Dongdong Zhou and Jie Zhang
Mathematics 2024, 12(10), 1486; https://doi.org/10.3390/math12101486 (registering DOI) - 10 May 2024
Abstract
Community structure is a very interesting attribute and feature in complex networks, which has attracted scholars’ attention and research on community detection. Many single-objective optimization algorithms have been migrated and modified to serve community detection problems. Due to the limitation of resolution, the
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Community structure is a very interesting attribute and feature in complex networks, which has attracted scholars’ attention and research on community detection. Many single-objective optimization algorithms have been migrated and modified to serve community detection problems. Due to the limitation of resolution, the final algorithm implementation effect is not ideal. In this paper, a multi-objective community detection method based on a pigeon-inspired optimization algorithm, MOPIO-Net, is proposed. Firstly, the PIO algorithm is discretized in terms of the solution space representation, position, and velocity-updating strategies to adapt to discrete community detection scenarios. Secondly, by minimizing the two objective functions of community score and community fitness at the same time, the community structure with a tight interior and sparse exterior is obtained. Finally, for the misclassification caused by boundary nodes, a mutation strategy is added to improve the accuracy of the final community recognition. Experiments on synthetic and real networks verify that the proposed algorithm is more accurate in community recognition compared to 11 benchmark algorithms, confirming the effectiveness of the proposed method.
Full article
(This article belongs to the Special Issue Complex Network Analysis and Time Series Application)
Open AccessArticle
Time-Optimal Motions of a Mechanical System with Viscous Friction
by
Dmitrii Kamzolkin and Vladimir Ternovski
Mathematics 2024, 12(10), 1485; https://doi.org/10.3390/math12101485 - 10 May 2024
Abstract
Optimal control is a critical tool for mechanical robotic systems, facilitating the precise manipulation of dynamic processes. These processes are described through differential equations governed by a control function, addressing a time-optimal problem with bilinear characteristics. Our study utilizes the classical approach complemented
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Optimal control is a critical tool for mechanical robotic systems, facilitating the precise manipulation of dynamic processes. These processes are described through differential equations governed by a control function, addressing a time-optimal problem with bilinear characteristics. Our study utilizes the classical approach complemented by Pontryagin’s Maximum Principle (PMP) to explore this inverse optimal problem. The objective is to develop an exact piecewise control function that effectively manages trajectory control while considering the effects of viscous friction. Our simulations demonstrate that the proposed control law markedly diminishes oscillations induced by boundary conditions. This research not only aims to delineate the reachability set but also strives to determine the minimal time required for the process. The findings include an exact analytical solution for the stated control problem.
Full article
(This article belongs to the Section Computational and Applied Mathematics)
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Open AccessArticle
Optimal Control for an Epidemic Model of COVID-19 with Time-Varying Parameters
by
Yiheng Li
Mathematics 2024, 12(10), 1484; https://doi.org/10.3390/math12101484 - 10 May 2024
Abstract
The coronavirus disease 2019 (COVID-19) pandemic disrupted public health and economies worldwide. In this paper, we investigate an optimal control problem to simultaneously minimize the epidemic size and control costs associated with intervention strategies based on official data. Considering people with undetected infections,
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The coronavirus disease 2019 (COVID-19) pandemic disrupted public health and economies worldwide. In this paper, we investigate an optimal control problem to simultaneously minimize the epidemic size and control costs associated with intervention strategies based on official data. Considering people with undetected infections, we establish a control system of COVID-19 with time-varying parameters. To estimate these parameters, a parameter identification scheme is adopted and a mixed algorithm is constructed. Moreover, we present an optimal control problem with two objectives that involve the newly increased number of infected individuals and the control costs. A numerical scheme is conducted, simulating the epidemic data pertaining to Shanghai during the period of 2022, caused by the Omicron variant. Coefficient combinations of the objectives are obtained, and the optimal control measures for different infection peaks are indicated. The numerical results suggest that the identification variables obtained by using the constructed mixed algorithm to solve the parameter identification problem are feasible. Optimal control measures for different epidemic peaks can serve as references for decision-makers.
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(This article belongs to the Topic Mathematical Modeling)
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Open AccessArticle
Streamlining Ocean Dynamics Modeling with Fourier Neural Operators: A Multiobjective Hyperparameter and Architecture Optimization Approach
by
Yixuan Sun, Ololade Sowunmi, Romain Egele, Sri Hari Krishna Narayanan, Luke Van Roekel and Prasanna Balaprakash
Mathematics 2024, 12(10), 1483; https://doi.org/10.3390/math12101483 - 10 May 2024
Abstract
Training an effective deep learning model to learn ocean processes involves careful choices of various hyperparameters. We leverage DeepHyper’s advanced search algorithms for multiobjective optimization, streamlining the development of neural networks tailored for ocean modeling. The focus is on optimizing Fourier neural operators
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Training an effective deep learning model to learn ocean processes involves careful choices of various hyperparameters. We leverage DeepHyper’s advanced search algorithms for multiobjective optimization, streamlining the development of neural networks tailored for ocean modeling. The focus is on optimizing Fourier neural operators (FNOs), a data-driven model capable of simulating complex ocean behaviors. Selecting the correct model and tuning the hyperparameters are challenging tasks, requiring much effort to ensure model accuracy. DeepHyper allows efficient exploration of hyperparameters associated with data preprocessing, FNO architecture-related hyperparameters, and various model training strategies. We aim to obtain an optimal set of hyperparameters leading to the most performant model. Moreover, on top of the commonly used mean squared error for model training, we propose adopting the negative anomaly correlation coefficient as the additional loss term to improve model performance and investigate the potential trade-off between the two terms. The numerical experiments show that the optimal set of hyperparameters enhanced model performance in single timestepping forecasting and greatly exceeded the baseline configuration in the autoregressive rollout for long-horizon forecasting up to 30 days. Utilizing DeepHyper, we demonstrate an approach to enhance the use of FNO in ocean dynamics forecasting, offering a scalable solution with improved precision.
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(This article belongs to the Special Issue Artificial Intelligence for Fluid Mechanics)
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Open AccessArticle
Almost Sure Central Limit Theorem for Error Variance Estimator in Pth-Order Nonlinear Autoregressive Processes
by
Kaiyu Liang and Yong Zhang
Mathematics 2024, 12(10), 1482; https://doi.org/10.3390/math12101482 - 10 May 2024
Abstract
In this paper, under some suitable assumptions, using the Taylor expansion, Borel–Cantelli lemma and the almost sure central limit theorem for independent random variables, the almost sure central limit theorem for error variance estimator in the pth-order nonlinear autoregressive processes with independent and
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In this paper, under some suitable assumptions, using the Taylor expansion, Borel–Cantelli lemma and the almost sure central limit theorem for independent random variables, the almost sure central limit theorem for error variance estimator in the pth-order nonlinear autoregressive processes with independent and identical distributed errors was established. Four examples, first-order autoregressive processes, self-exciting threshold autoregressive processes, threshold-exponential AR progresses and multilayer perceptrons progress, are given to verify the results.
Full article
(This article belongs to the Section Probability and Statistics)
Open AccessArticle
Enhancing Global Blockchain Privacy via a Digital Mutual Trust Mechanism
by
Sheng Peng, Linkai Zhu, Shanwen Hu, Zhiming Cai and Wenjian Liu
Mathematics 2024, 12(10), 1481; https://doi.org/10.3390/math12101481 - 10 May 2024
Abstract
Blockchain technology, initially developed as a decentralized and transparent mechanism for recording transactions, faces significant privacy challenges due to its inherent transparency, exposing sensitive transaction data to all network participants. This study proposes a blockchain privacy protection algorithm that employs a digital mutual
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Blockchain technology, initially developed as a decentralized and transparent mechanism for recording transactions, faces significant privacy challenges due to its inherent transparency, exposing sensitive transaction data to all network participants. This study proposes a blockchain privacy protection algorithm that employs a digital mutual trust mechanism integrated with advanced cryptographic techniques to enhance privacy and security in blockchain transactions. The contribution includes the development of a new dynamic Byzantine consensus algorithm within the Practical Byzantine Fault Tolerance framework, incorporating an authorization mechanism from the reputation model and a proof consensus algorithm for robust digital mutual trust. Additionally, the refinement of homomorphic cryptography using the approximate greatest common divisor technique optimizes the encryption process to support complex operations securely. The integration of a smart contract system facilitates automatic and private transaction execution across the blockchain network. Experimental evidence demonstrates the superior performance of the algorithm in handling privacy requests and transaction receipts with reduced delays and increased accuracy, marking a significant improvement over existing methods.
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(This article belongs to the Section Mathematics and Computer Science)
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ARS-Chain: A Blockchain-Based Anonymous Reputation-Sharing Framework for E-Commerce Platforms
by
Yungui Chen, Li Feng, Qinglin Zhao, Liwei Tian and Lei Yang
Mathematics 2024, 12(10), 1480; https://doi.org/10.3390/math12101480 - 10 May 2024
Abstract
E-commerce platforms incorporate reputation systems that allow buyers to rate sellers after transactions. However, existing reputation systems face challenges such as privacy leakage, linkability, and multiple rating attacks. The feedback data can inadvertently expose user information privacy because they reveal the buyers’ identities
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E-commerce platforms incorporate reputation systems that allow buyers to rate sellers after transactions. However, existing reputation systems face challenges such as privacy leakage, linkability, and multiple rating attacks. The feedback data can inadvertently expose user information privacy because they reveal the buyers’ identities and preferences, which deters a significant number of users from providing their ratings. Moreover, malicious actors can exploit data analysis and machine learning techniques to mine user privacy from the rating data, posing serious threats to user security and trust. This study introduces ARS-Chain, a pioneering and secure blockchain-driven anonymous reputation-sharing framework tailored for e-commerce platforms. The core of ARS-Chain is a dynamic ring addition mechanism with linkable ring signatures (LRS), where the number of LRS rings is dynamically added in alignment with the evolving purchase list, and LRS link tags are constructed with the LRS rings and item identifiers. Further, a consortium blockchain is introduced to store these anonymous ratings on e-commerce platforms. As a result, ARS-Chain ensures full anonymity while achieving cross-platform reputation sharing, making rating records unlinkable, and effectively countering multiple rating attacks. The experimental results confirm that ARS-Chain significantly enhances user information privacy protection while maintaining system performance, having an important impact on the construction of trust mechanisms for e-commerce platforms.
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(This article belongs to the Special Issue Hybrid Data Processing by Combining Machine Learning, Expert, Safety and Security)
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Open AccessArticle
Deformation Prediction Model of Existing Tunnel Structures with Equivalent Layered Method–Peck Coupled under Multiple Factors
by
Yifan Li, Changfu Huang, Hongjian Lu and Chao Mou
Mathematics 2024, 12(10), 1479; https://doi.org/10.3390/math12101479 - 9 May 2024
Abstract
The existing tunnel structure, the new underpass tunnel structure and the rock strata in the area of influence of the crossover tunnel are interacting systems that are affected by various factors, such as dynamic and static excavation loads and dynamic and static train
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The existing tunnel structure, the new underpass tunnel structure and the rock strata in the area of influence of the crossover tunnel are interacting systems that are affected by various factors, such as dynamic and static excavation loads and dynamic and static train loads. The existing theoretical models for the deformation prediction of existing tunnels lack the synergistic analysis of dynamic and static loads on both existing and new tunnels. Based on the theory of the current layer method and Peck’s empirical formula, this paper considers the stiffness of existing tunnels, the stiffness of new tunnels, the loads of excavation methods and the loads of existing tunnels. The results show that a theoretical model for the prediction of the deformation of double-lane highway tunnels underneath existing railroad tunnels with the coupling of the current layer method and Peck under multiple factors is constructed; a modified Peck settlement formula for the base plate of the existing tunnels is put forward; and, through numerical calculations and monitoring data for validation and optimization, it is proved that the theoretical model is applicable to the excavation of tunnels underneath mountainous areas mined by the blasting method.
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Open AccessArticle
Enhancing Robustness in Precast Modular Frame Optimization: Integrating NSGA-II, NSGA-III, and RVEA for Sustainable Infrastructure
by
Andrés Ruiz-Vélez , José García, Julián Alcalá and Víctor Yepes
Mathematics 2024, 12(10), 1478; https://doi.org/10.3390/math12101478 - 9 May 2024
Abstract
The advancement toward sustainable infrastructure presents complex multi-objective optimization (MOO) challenges. This paper expands the current understanding of design frameworks that balance cost, environmental impacts, social factors, and structural integrity. Integrating MOO with multi-criteria decision-making (MCDM), the study targets enhancements in life cycle
[...] Read more.
The advancement toward sustainable infrastructure presents complex multi-objective optimization (MOO) challenges. This paper expands the current understanding of design frameworks that balance cost, environmental impacts, social factors, and structural integrity. Integrating MOO with multi-criteria decision-making (MCDM), the study targets enhancements in life cycle sustainability for complex engineering projects using precast modular road frames. Three advanced evolutionary algorithms—NSGA-II, NSGA-III, and RVEA—are optimized and deployed to address sustainability objectives under performance constraints. The efficacy of these algorithms is gauged through a comparative analysis, and a robust MCDM approach is applied to nine non-dominated solutions, employing SAW, FUCA, TOPSIS, PROMETHEE, and VIKOR decision-making techniques. An entropy theory-based method ensures systematic, unbiased criteria weighting, augmenting the framework’s capacity to pinpoint designs balancing life cycle sustainability. The results reveal that NSGA-III is the algorithm converging towards the most cost-effective solutions, surpassing NSGA-II and RVEA by 21.11% and 10.07%, respectively, while maintaining balanced environmental and social impacts. The RVEA achieves up to 15.94% greater environmental efficiency than its counterparts. The analysis of non-dominated solutions identifies the design, utilizing 35 MPa concrete and B500S steel, as the most sustainable alternative across 80% of decision-making algorithms. The ranking correlation coefficients above 0.94 demonstrate consistency among decision-making techniques, underscoring the robustness of the integrated MOO and MCDM framework. The results in this paper expand the understanding of the applicability of novel techniques for enhancing engineering practices and advocate for a comprehensive strategy that employs advanced MOO algorithms and MCDM to enhance sustainable infrastructure development.
Full article
(This article belongs to the Special Issue Combinatorial Optimization and Applications)
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Mathematical Modeling
Topic Editors: Babak Shiri, Zahra AlijaniDeadline: 31 May 2024
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Algorithms, Axioms, Fractal Fract, Mathematics, Symmetry
Fractal and Design of Multipoint Iterative Methods for Nonlinear Problems
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Algorithms, Computation, Information, Mathematics
Complex Networks and Social Networks
Topic Editors: Jie Meng, Xiaowei Huang, Minghui Qian, Zhixuan XuDeadline: 31 July 2024
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Research on Data Mining of Electronic Health Records Using Deep Learning Methods
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Special Issues
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Mathematics
Advances in Linear Recurrence System
Guest Editors: Lorentz Jäntschi, Virginia NiculescuDeadline: 15 May 2024
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New Trends on Boundary Value Problems
Guest Editors: Miklós Rontó, András Rontó, Nino Partsvania, Bedřich Půža, Hriczó KrisztiánDeadline: 31 May 2024
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Mathematics
Applications of Fuzzy Modeling in Risk Management
Guest Editors: Edit Toth-Laufer, László PokorádiDeadline: 20 June 2024
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Mathematics
Computational Statistical Methods and Extreme Value Theory
Guest Editor: Frederico CaeiroDeadline: 30 June 2024
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Topology and Foundations
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Mathematics
Multiscale Computation and Machine Learning
Collection Editors: Yalchin Efendiev, Eric Chung
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Theoretical and Mathematical Ecology
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