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 the Predictive Potential of Complex Problem-Solving in Computing Education: A Case Study in the Introductory Programming Course
Mathematics 2024, 12(11), 1655; https://doi.org/10.3390/math12111655 - 24 May 2024
Abstract
Programming is acknowledged widely as a cornerstone skill in Computer Science education. Despite significant efforts to refine teaching methodologies, a segment of students is still at risk of failing programming courses. It is crucial to identify potentially struggling students at risk of underperforming
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Programming is acknowledged widely as a cornerstone skill in Computer Science education. Despite significant efforts to refine teaching methodologies, a segment of students is still at risk of failing programming courses. It is crucial to identify potentially struggling students at risk of underperforming or academic failure. This study explores the predictive potential of students’ problem-solving skills through dynamic, domain-independent, complex problem-solving assessment. To evaluate the predictive potential of complex problem-solving empirically, a case study with 122 participants was conducted in the undergraduate Introductory Programming Course at the University of Maribor, Slovenia. A latent variable approach was employed to examine the associations. The study results showed that complex problem-solving has a strong positive effect on performance in Introductory Programming Courses. According to the results of structural equation modeling, 64% of the variance in programming performance is explained by complex problem-solving ability. Our findings indicate that complex problem-solving performance could serve as a significant, cognitive, dynamic predictor, applicable to the Introductory Programming Course. Moreover, we present evidence that the demonstrated approach could also be used to predict success in the broader computing education community, including K-12, and the wider education landscape. Apart from predictive potential, our results suggest that valid and reliable instruments for assessing complex problem-solving could also be used for assessing general-purpose, domain-independent problem-solving skills in computing education. Likewise, the results confirmed the positive effect of previous programming experience on programming performance. On the other hand, there was no significant direct effect of performance in High School mathematics on Introductory Programming.
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(This article belongs to the Section Mathematics and Computer Science)
Open AccessArticle
A Study of Some Generalized Results of Neutral Stochastic Differential Equations in the Framework of Caputo–Katugampola Fractional Derivatives
by
Abdelhamid Mohammed Djaouti, Zareen A. Khan, Muhammad Imran Liaqat and Ashraf Al-Quran
Mathematics 2024, 12(11), 1654; https://doi.org/10.3390/math12111654 - 24 May 2024
Abstract
Inequalities serve as fundamental tools for analyzing various important concepts in stochastic differential problems. In this study, we present results on the existence, uniqueness, and averaging principle for fractional neutral stochastic differential equations. We utilize Jensen, Burkholder–Davis–Gundy, Grönwall–Bellman, Hölder, and Chebyshev–Markov inequalities. We
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Inequalities serve as fundamental tools for analyzing various important concepts in stochastic differential problems. In this study, we present results on the existence, uniqueness, and averaging principle for fractional neutral stochastic differential equations. We utilize Jensen, Burkholder–Davis–Gundy, Grönwall–Bellman, Hölder, and Chebyshev–Markov inequalities. We generalize results in two ways: first, by extending the existing result for to results in the space; second, by incorporating the Caputo–Katugampola fractional derivatives, we extend the results established with Caputo fractional derivatives. Additionally, we provide examples to enhance the understanding of the theoretical results we establish.
Full article
(This article belongs to the Special Issue Fractional Calculus and Mathematical Applications, 2nd Edition)
Open AccessArticle
Lp-Boundedness of a Class of Bi-Parameter Pseudo-Differential Operators
by
Jinhua Cheng
Mathematics 2024, 12(11), 1653; https://doi.org/10.3390/math12111653 - 24 May 2024
Abstract
In this paper, I explore a specific class of bi-parameter pseudo-differential operators characterized by symbols falling within the product-type Hörmander class . This classification
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In this paper, I explore a specific class of bi-parameter pseudo-differential operators characterized by symbols falling within the product-type Hörmander class . This classification imposes constraints on the behavior of partial derivatives of with respect to both spatial and frequency variables. Specifically, I demonstrate that for each multi-index , the inequality is satisfied. My investigation culminates in a rigorous analysis of the -boundedness of such pseudo-differential operators, thereby extending the seminal findings of C. Fefferman from 1973 concerning pseudo-differential operators within the Hörmander class.
Full article
(This article belongs to the Special Issue Recent Developments of Function Spaces and Their Applications II)
Open AccessArticle
Fuzzy Multi-Item Newsvendor Problem: An Application to Inventory Management
by
João M. C. Sousa, Rodrigo Luís, Rui Mirra Santos, Luís Mendonça and Susana M. Vieira
Mathematics 2024, 12(11), 1652; https://doi.org/10.3390/math12111652 - 24 May 2024
Abstract
This paper proposes a novel approach to the fuzzy newsvendor problem for inventory management applications. The main contributions of the paper are the following: a new credibility estimation is proposed, to explore the neighborhood around the most impactful demand scenarios; a simulation procedure
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This paper proposes a novel approach to the fuzzy newsvendor problem for inventory management applications. The main contributions of the paper are the following: a new credibility estimation is proposed, to explore the neighborhood around the most impactful demand scenarios; a simulation procedure was designed for the different demand scenarios, which allows comparison of the proposed approach with classical and fuzzy multi-item newsvendor problems; a modified genetic algorithm (GA) is introduced to ameliorate previous genetic algorithms in both the generation and evaluation of solutions. The new formulation of the fuzzy newsvendor problem, together with the modified GA, were shown to improve the average profit by up to 55% in problems with low-budget scenarios.
Full article
(This article belongs to the Special Issue Mathematical Methods and Operation Research in Logistics, Project Planning, and Scheduling, 2nd Edition)
Open AccessArticle
Dynamic Failure Characteristics of Sandstone Containing Different Angles of Pre-Existing Crack Defects
by
Hou-You Zhou, Dian-Shu Liu, Zheng-Hua Gao, En-An Chi, Jun-Ying Rao and Tao Hu
Mathematics 2024, 12(11), 1651; https://doi.org/10.3390/math12111651 - 24 May 2024
Abstract
Fracture within the rock is one of the main factors leading to rock destabilization and has a significant effect on the stability of the project. In this study, sandstone is used as a research target, specimens with crack inclination angles of 0°, 30°,
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Fracture within the rock is one of the main factors leading to rock destabilization and has a significant effect on the stability of the project. In this study, sandstone is used as a research target, specimens with crack inclination angles of 0°, 30°, 45°, 60°, and 90° are prefabricated, and the split Hopkinson pressure bar (SHPB) impact test of sandstone with cracks is carried out based on digital image recognition technology to explore the dynamic damage characteristics of the specimens with five angles. The basic mechanical parameters of sandstone are tested to determine the RHT model intrinsic parameters, and the numerical computational RHT model of sandstone containing crack defects is established, which is verified in comparison with the test to analyze the validity of the model. Finally, the failure characteristics of the numerical model under initial stress were carried out. The study shows the following: with the increase in the fracture angle, the dynamic compressive strength and deformation modulus are distributed in a slanting V-shape, and the inclination angle of 45° is the smallest. The strain rate and energy dissipation rate are distributed in a slanting N-shape, and the inclination angle of 45° is the largest. The transmittance shows a decreasing trend, which is the opposite of the reflectivity pattern. The crack angle determines the location and direction of the initial crack, which affects the failure mode. In addition, the parameters of the RHT constitutive model suitable for sandstone are obtained, and the damage and strength patterns of the established RHT model are highly consistent with the laboratory test results. The damage range of numerical models for crack defects with different inclination angles is negatively correlated with confining pressure values and positively correlated with axial pressure values. The damage zones are symmetrically distributed approximately perpendicular to the direction of cracks, and the confining pressure has a contributing role in the peak of the element stresses; however, the axial compression has no contribution in the peak of the element stresses.
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(This article belongs to the Special Issue Advances in Applied Mathematics, Mechanics and Engineering)
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Open AccessArticle
Reliability Estimation in Stress Strength for Generalized Rayleigh Distribution Using a Lower Record Ranked Set Sampling Scheme
by
Yinuo Dong and Wenhao Gui
Mathematics 2024, 12(11), 1650; https://doi.org/10.3390/math12111650 - 24 May 2024
Abstract
This paper explores the likelihood and Bayesian estimation of the stress–strength reliability parameter ( ) based on a lower record ranked set sampling scheme from the generalized Rayleigh distribution. Maximum likelihood and Bayesian estimators as well as confidence intervals of are
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This paper explores the likelihood and Bayesian estimation of the stress–strength reliability parameter ( ) based on a lower record ranked set sampling scheme from the generalized Rayleigh distribution. Maximum likelihood and Bayesian estimators as well as confidence intervals of are derived and their properties are studied. Furthermore, two parametric bootstrap confidence intervals are introduced in the paper. A comparative simulation study is conducted to assess the effectiveness of these four confidence interval methodologies in estimating . The application of the methods is demonstrated using real data on fiber strength to showcase their practicability and relevance in the industry.
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(This article belongs to the Section Probability and Statistics)
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A Modified Three-Term Conjugate Descent Derivative-Free Method for Constrained Nonlinear Monotone Equations and Signal Reconstruction Problems
by
Aliyu Yusuf, Nibron Haggai Manjak and Maggie Aphane
Mathematics 2024, 12(11), 1649; https://doi.org/10.3390/math12111649 - 24 May 2024
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Iterative methods for solving constraint nonlinear monotone equations have been developed and improved by many researchers. The aim of this research is to present a modified three-term conjugate descent (TTCD) derivative-free method for constrained nonlinear monotone equations. The proposed algorithm requires low storage
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Iterative methods for solving constraint nonlinear monotone equations have been developed and improved by many researchers. The aim of this research is to present a modified three-term conjugate descent (TTCD) derivative-free method for constrained nonlinear monotone equations. The proposed algorithm requires low storage memory; therefore, it has the capability to solve large-scale nonlinear equations. The algorithm generates a descent and bounded search direction at every iteration independent of the line search. The method is shown to be globally convergent under monotonicity and Lipschitz continuity conditions. Numerical results show that the suggested method can serve as an alternative to find the approximate solutions of nonlinear monotone equations. Furthermore, the method is promising for the reconstruction of sparse signal problems.
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Open AccessArticle
Multi-View and Multimodal Graph Convolutional Neural Network for Autism Spectrum Disorder Diagnosis
by
Tianming Song, Zhe Ren, Jian Zhang and Mingzhi Wang
Mathematics 2024, 12(11), 1648; https://doi.org/10.3390/math12111648 - 24 May 2024
Abstract
Autism Spectrum Disorder (ASD) presents significant diagnostic challenges due to its complex, heterogeneous nature. This study explores a novel approach to enhance the accuracy and reliability of ASD diagnosis by integrating resting-state functional magnetic resonance imaging with demographic data (age, gender, and IQ).
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Autism Spectrum Disorder (ASD) presents significant diagnostic challenges due to its complex, heterogeneous nature. This study explores a novel approach to enhance the accuracy and reliability of ASD diagnosis by integrating resting-state functional magnetic resonance imaging with demographic data (age, gender, and IQ). This study is based on improving the spectral graph convolutional neural network (GCN). It introduces a multi-view attention fusion module to extract useful information from different views. The graph’s edges are informed by demographic data, wherein an edge-building network computes weights grounded in demographic information, thereby bolstering inter-subject correlation. To tackle the challenges of oversmoothing and neighborhood explosion inherent in deep GCNs, this study introduces DropEdge regularization and residual connections, thus augmenting feature diversity and model generalization. The proposed method is trained and evaluated on the ABIDE-I and ABIDE-II datasets. The experimental results underscore the potential of integrating multi-view and multimodal data to advance the diagnostic capabilities of GCNs for ASD.
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(This article belongs to the Special Issue Network Biology and Machine Learning in Bioinformatics)
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Optimal Routing and Scheduling of Flag State Control Officers in Maritime Transportation
by
Xizi Qiao, Ying Yang, Yu Guo, Yong Jin and Shuaian Wang
Mathematics 2024, 12(11), 1647; https://doi.org/10.3390/math12111647 - 24 May 2024
Abstract
Maritime transportation plays a pivotal role in the global merchandise trade. To improve maritime safety and protect the environment, every state must effectively control ships flying its flag, which is called flag state control (FSC). However, the existing FSC system is so inefficient
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Maritime transportation plays a pivotal role in the global merchandise trade. To improve maritime safety and protect the environment, every state must effectively control ships flying its flag, which is called flag state control (FSC). However, the existing FSC system is so inefficient that it cannot perform its intended function. In this study, we adopt an optimization method to tackle this problem by constructing an integer programming (IP) model to solve the FSC officer routing and scheduling problem, which aims to maximize the total weight of inspected ships with limited budget and human resources. Then we prove that the IP model can be reformulated into a partially relaxed IP model with the guarantee of the result optimality. Finally, we perform a case study using the Hong Kong port as an example. The results show that our model can be solved to optimality within one second at different scales of the problem, with the ship number ranging from 20 to 1000. Furthermore, our study can be extended by considering the arrangement of working timetables with finer granularity and the fatigue level of personnel.
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(This article belongs to the Special Issue Applied Mathematics in Supply Chain and Logistics)
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A First Approach to Quantum Logical Shape Classification Framework
by
Alexander Köhler, Marvin Kahra and Michael Breuß
Mathematics 2024, 12(11), 1646; https://doi.org/10.3390/math12111646 - 24 May 2024
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Quantum logic is a well-structured theory, which has recently received some attention because of its fundamental relation to quantum computing. However, the complex foundation of quantum logic borrowing concepts from different branches of mathematics as well as its peculiar settings have made it
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Quantum logic is a well-structured theory, which has recently received some attention because of its fundamental relation to quantum computing. However, the complex foundation of quantum logic borrowing concepts from different branches of mathematics as well as its peculiar settings have made it a non-trivial task to devise suitable applications. This article aims to propose for the first time an approach using quantum logic in image processing for shape classification. We show how to make use of the principal component analysis to realize quantum logical propositions. In this way, we are able to assign a concrete meaning to the rather abstract quantum logical concepts, and we are able to compute a probability measure from the principal components. For shape classification, we consider encrypting given point clouds of different objects by making use of specific distance histograms. This enables us to initiate the principal component analysis. Through experiments, we explore the possibility of distinguishing between different geometrical objects and discuss the results in terms of quantum logical interpretation.
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Open AccessArticle
Dynamics of Hepatitis B Virus Transmission with a Lévy Process and Vaccination Effects
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Sayed Murad Ali Shah, Yufeng Nie, Anwarud Din and Abdulwasea Alkhazzan
Mathematics 2024, 12(11), 1645; https://doi.org/10.3390/math12111645 - 24 May 2024
Abstract
This work proposes a novel stochastic model describing the propagation dynamics of the hepatitis B virus. The model takes into account numerous disease characteristics, and environmental disturbances were collected using Lévy jumps and the conventional Brownian motions. Initially, the deterministic model is developed,
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This work proposes a novel stochastic model describing the propagation dynamics of the hepatitis B virus. The model takes into account numerous disease characteristics, and environmental disturbances were collected using Lévy jumps and the conventional Brownian motions. Initially, the deterministic model is developed, and the asymptotic behavior of the model’s solution near the equilibria is examined. The deterministic model is transformed into a stochastic model while retaining the Lévy jumps and conventional Brownian motions. Under specific assumptions, the stochastic system is shown to have a unique solution. The study further investigates the conditions that ensure the extinction and persistence of the infection. The numerical solutions to both stochastic and deterministic systems were obtained using the well-known Milstein and RK4 techniques, and the analytical findings are theoretically confirmed. The simulation suggests that the noise intensities have a direct relationship with the amplitudes of the stochastic curves around the equilibria of the deterministic system. Smaller values of the intensities imply negligible fluctuations of trajectories around the equilibria and, hence, better describe the extinction and persistence of the infection. It has also been found that both Brownian motions and the Lévy jump had a significant influence on the oscillations of these curves. A discussion of the findings of the study reveals other important aspects as well as some future research guidelines. In short, this study proposes a novel stochastic model to describe the propagation dynamics of the hepatitis B virus.
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(This article belongs to the Section Computational and Applied Mathematics)
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Methodology for Transient Stability Enhancement of Power Systems Based on Machine Learning Algorithms and Fast Valving in a Steam Turbine
by
Mihail Senyuk, Svetlana Beryozkina, Murodbek Safaraliev, Muhammad Nadeem, Ismoil Odinaev and Firuz Kamalov
Mathematics 2024, 12(11), 1644; https://doi.org/10.3390/math12111644 - 24 May 2024
Abstract
This study presents the results of the development and testing of a methodology for selecting parameters of the characteristics of fast valving in a steam turbine for emergency power system management to maintain dynamic stability based on machine learning algorithms. Modern power systems
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This study presents the results of the development and testing of a methodology for selecting parameters of the characteristics of fast valving in a steam turbine for emergency power system management to maintain dynamic stability based on machine learning algorithms. Modern power systems have reduced inertia and increased stochasticity due to the active integration of renewable energy sources. As a result, there is an increased likelihood of incorrect operation in traditional emergency automation devices, developed on the principles of deterministic analysis of transient processes. To date, it is possible to increase the adaptability and accuracy of emergency power system management through the application of machine learning algorithms. In this work, fast valving in a steam turbine was chosen as the considered device of emergency automation. To form the data sample, the IEEE39 mathematical model was used, for which benchmark laws of change in the position of the cutoff valve during the fast valving of a steam turbine were selected. The considered machine learning algorithms for classifying the law of change in the position of the steam turbine’s cutoff valve, k-nearest neighbors, support vector machine, decision tree, random forest, and extreme gradient boosting were used. The results show that the highest accuracy corresponds to extreme gradient boosting. For the selected eXtreme Gradient Boosting algorithm, the classification accuracy on the training set was 98.17%, and on the test set it was 97.14%. The work also proposes a methodology for forming synthetic data for the use of machine learning algorithms for emergency management of power systems and suggests directions for further research.
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(This article belongs to the Special Issue Artificial Intelligence Techniques Applications on Power Systems)
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Abnormal Traffic Detection System Based on Feature Fusion and Sparse Transformer
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Xinjian Zhao, Weiwei Miao, Guoquan Yuan, Yu Jiang, Song Zhang and Qianmu Li
Mathematics 2024, 12(11), 1643; https://doi.org/10.3390/math12111643 - 24 May 2024
Abstract
This paper presents a feature fusion and sparse transformer-based anomalous traffic detection system (FSTDS). FSTDS utilizes a feature fusion network to encode the traffic data sequences and extracting features, fusing them into coding vectors through shallow and deep convolutional networks, followed by deep
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This paper presents a feature fusion and sparse transformer-based anomalous traffic detection system (FSTDS). FSTDS utilizes a feature fusion network to encode the traffic data sequences and extracting features, fusing them into coding vectors through shallow and deep convolutional networks, followed by deep coding using a sparse transformer to capture the complex relationships between network flows; finally, a multilayer perceptron is used to classify the traffic and achieve anomaly traffic detection. The feature fusion network of FSTDS improves feature extraction from small sample data, the deep encoder enhances the understanding of complex traffic patterns, and the sparse transformer reduces the computational and storage overhead and improves the scalability of the model. Experiments demonstrate that the number of FSTDS parameters is reduced by up to nearly half compared to the baseline, and the success rate of anomalous flow detection is close to 100%.
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(This article belongs to the Special Issue Data Mining and Machine Learning in the Era of Big Knowledge and Large Models)
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Perfect Codes over Non-Prime Power Alphabets: An Approach Based on Diophantine Equations
by
Pedro-José Cazorla García
Mathematics 2024, 12(11), 1642; https://doi.org/10.3390/math12111642 - 23 May 2024
Abstract
Perfect error-correcting codes allow for an optimal transmission of information while guaranteeing error correction. For this reason, proving their existence has been a classical problem in both pure mathematics and information theory. Indeed, the classification of the parameters of e-error correcting perfect
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Perfect error-correcting codes allow for an optimal transmission of information while guaranteeing error correction. For this reason, proving their existence has been a classical problem in both pure mathematics and information theory. Indeed, the classification of the parameters of e-error correcting perfect codes over q-ary alphabets was a very active topic of research in the late 20th century. Consequently, all parameters of perfect e-error-correcting codes were found if , and it was conjectured that no perfect 2-error-correcting codes exist over any q-ary alphabet, where . In the 1970s, this was proved for q a prime power, for and for only seven other values of q. Almost 50 years later, it is surprising to note that there have been no new results in this regard and the classification of 2-error-correcting codes over non-prime power alphabets remains an open problem. In this paper, we use techniques from the resolution of the generalised Ramanujan–Nagell equation and from modern computational number theory to show that perfect 2-error-correcting codes do not exist for 172 new values of q which are not prime powers, substantially increasing the values of q which are now classified. In addition, we prove that, for any fixed value of q, there can be at most finitely many perfect 2-error-correcting codes over an alphabet of size q.
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(This article belongs to the Special Issue Codes, Designs, Cryptography and Optimization, 2nd Edition)
Open AccessArticle
A Software Reliability Model Considering a Scale Parameter of the Uncertainty and a New Criterion
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Kwang Yoon Song, Youn Su Kim, Hoang Pham and In Hong Chang
Mathematics 2024, 12(11), 1641; https://doi.org/10.3390/math12111641 - 23 May 2024
Abstract
It is becoming increasingly common for software to operate in various environments. However, even if the software performs well in the test phase, uncertain operating environments may cause new software failures. Traditional proposed software reliability models under uncertain operating environments suffer from the
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It is becoming increasingly common for software to operate in various environments. However, even if the software performs well in the test phase, uncertain operating environments may cause new software failures. Traditional proposed software reliability models under uncertain operating environments suffer from the problem of being well-suited to special cases due to the large number of assumptions involved. To improve these problems, this study proposes a new software reliability model that assumes an uncertain operating environment. The new software reliability model is a model that minimizes assumptions and minimizes the number of parameters that make up the model, so that the model can be applied to general situations better than the traditional proposed software reliability models. In addition, various criteria based on the difference between the predicted and estimated values have been used in the past to demonstrate the superiority of the software reliability models. Also, we propose a new multi-criteria decision method that can simultaneously consider multiple goodness-of-fit criteria. The multi-criteria decision method using ranking is useful for comprehensive evaluation because it does not rely on individual criteria alone by ranking and weighting multiple criteria for the model. Based on this, 21 existing models are compared with the proposed model using two datasets, and the proposed model is found to be superior for both datasets using 15 criteria and the multi-criteria decision method using ranking.
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(This article belongs to the Section Mathematics and Computer Science)
Open AccessArticle
Analyzing and Simulating Evolution of Subsidy–Operation Strategies for Multi-Type China Railway Express Operation Market
by
Fenling Feng, Ze Zhang, Mingxu Cai and Chengguang Liu
Mathematics 2024, 12(11), 1640; https://doi.org/10.3390/math12111640 - 23 May 2024
Abstract
The China Railway Express stands as a crucial facilitator of trade across the land routes of Eurasian countries. During its initial developmental phase, the China Railway Express heavily relied on subsidies to establish a market presence. This dependency hindered its independence and sustainability.
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The China Railway Express stands as a crucial facilitator of trade across the land routes of Eurasian countries. During its initial developmental phase, the China Railway Express heavily relied on subsidies to establish a market presence. This dependency hindered its independence and sustainability. Hence, there exists a paramount need to regulate the subsidy market and institute more rational operation strategies. This study focuses on the dynamics of the subsidies and operations in the market for the China Railway Express under different types of development models. It uses evolutionary game theory and the Activity-Based Costing (ABC) method to describe the dynamic evolution of four cases between local governments and operating-platform enterprises. Four corresponding lines were selected as instances: from Xiamen, Wuxi, Changsha, and Zhengzhou to Malaszewicze, Poland. The findings conclude that the optimal conditions for the development of the China Railway Express market exist when operating-platform enterprises possess higher assets and the local government’s supervision and punishment of the market are relatively weaker. This study offers valuable insights for guiding subsidy and operational decision-making processes for the China Railway Express.
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(This article belongs to the Special Issue Optimization and Big Data in Logistics and Supply Chain Management)
Open AccessArticle
Augmentation of Soft Partition with a Granular Prototype Based Fuzzy C-Means
by
Ruixin Wang, Kaijie Xu and Yixi Wang
Mathematics 2024, 12(11), 1639; https://doi.org/10.3390/math12111639 - 23 May 2024
Abstract
Clustering is a fundamental cornerstone in unsupervised learning, playing a pivotal role in various data mining techniques. The precise and efficient classification of data stands as a central focus for numerous researchers and practitioners alike. In this study, we design an effective soft
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Clustering is a fundamental cornerstone in unsupervised learning, playing a pivotal role in various data mining techniques. The precise and efficient classification of data stands as a central focus for numerous researchers and practitioners alike. In this study, we design an effective soft partition classification method which refines and extends the prototype of the well-known Fuzzy C-Means clustering algorithm. Specifically, the developed scheme employs membership function to extend the prototypes into a series of granular prototypes, thus achieving a deeper revelation of the structure of the data. This process softly divides the data into core and extended parts. The core part can be succinctly encapsulated through several information granules, whereas the extended part lacks discernible geometry and requires formal descriptors (such as membership formulas). Our objective is to develop information granules that shape the core structure within the dataset, delineate their characteristics, and explore the interaction among these granules that result in their deformation. The granular prototypes become the main component of the information granules and provide an optimization space for traditional prototypes. Subsequently, we apply quantum-behaved particle swarm optimization to identify the optimal partition matrix for the data. This optimized matrix significantly enhances the partition performance of the data. Experimental results provide substantial evidence of the effectiveness of the proposed approach.
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(This article belongs to the Special Issue New Advances in Data Analytics and Mining)
Open AccessArticle
Stability Analysis of Linear Time-Varying Delay Systems via a Novel Augmented Variable Approach
by
Wenqi Liao, Hongbing Zeng and Huichao Lin
Mathematics 2024, 12(11), 1638; https://doi.org/10.3390/math12111638 - 23 May 2024
Abstract
This paper investigates the stability issues of time-varying delay systems. Firstly, a novel augmented Lyapunov functional is constructed for a class of bounded time-varying delays by introducing new double integral terms. Subsequently, a time-varying matrix-dependent zero equation is introduced to relax the constraints
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This paper investigates the stability issues of time-varying delay systems. Firstly, a novel augmented Lyapunov functional is constructed for a class of bounded time-varying delays by introducing new double integral terms. Subsequently, a time-varying matrix-dependent zero equation is introduced to relax the constraints of traditional constant matrix-dependent zero equations. Secondly, for a class of periodic time-varying delays, considering the monotonicity of the delay and combining it with an augmented variable approach, Lyapunov functionals are constructed for monotonically increasing and monotonically decreasing delay intervals, respectively. Based on the constructed augmented Lyapunov functionals and the employed time-varying zero equation, less conservative stability criteria are obtained separately for bounded and periodic time-varying delays. Lastly, three examples are used to verify the superiority of the stability conditions obtained in this paper.
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(This article belongs to the Section Dynamical Systems)
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Open AccessArticle
Advancements in Korean Emotion Classification: A Comparative Approach Using Attention Mechanism
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Eojin Kang, Yunseok Choi and Juae Kim
Mathematics 2024, 12(11), 1637; https://doi.org/10.3390/math12111637 - 23 May 2024
Abstract
Recently, the analysis of emotions in social media has been considered a significant NLP task in digital and social-media-driven environments due to their pervasive influence on communication, culture, and consumer behavior. In particular, the task of Aspect-Based Emotion Analysis (ABEA), which involves analyzing
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Recently, the analysis of emotions in social media has been considered a significant NLP task in digital and social-media-driven environments due to their pervasive influence on communication, culture, and consumer behavior. In particular, the task of Aspect-Based Emotion Analysis (ABEA), which involves analyzing the emotions of various targets within a single sentence, has drawn attention to understanding complex and sophisticated human language. However, ABEA is a challenging task in languages with limited data and complex linguistic properties, such as Korean, which follows spiral thought patterns and has agglutinative characteristics. Therefore, we propose a Korean Target-Attention-Based Emotion Classifier (KOTAC) designed to utilize target information by unveiling emotions buried within intricate Korean language patterns. In the experiment section, we compare various methods of utilizing and representing vectors of target information for the attention mechanism. Specifically, our final model, KOTAC, shows a performance enhancement on the MTME (Multiple Targets Multiple Emotions) samples, which include multiple targets and distinct emotions within a single sentence, achieving a 0.72% increase in F1 score over a baseline model without effective target utilization. This research contributes to the development of Korean language models that better reflect syntactic features by innovating methods to not only obtain but also utilize target-focused representations.
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Open AccessArticle
On S-2-Prime Ideals of Commutative Rings
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Sanem Yavuz, Bayram Ali Ersoy, Ünsal Tekir and Ece Yetkin Çelikel
Mathematics 2024, 12(11), 1636; https://doi.org/10.3390/math12111636 - 23 May 2024
Abstract
Prime ideals and their generalizations are crucial in numerous research areas, particularly in commutative algebra. The concept of generalization of prime ideals begins with the study of weakly prime ideals. Since then, subsequent works aimed at expanding this concept into more generalized forms.
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Prime ideals and their generalizations are crucial in numerous research areas, particularly in commutative algebra. The concept of generalization of prime ideals begins with the study of weakly prime ideals. Since then, subsequent works aimed at expanding this concept into more generalized forms. Among these, S-prime ideals and 2-prime ideals have reaped attention recently. This paper aims to characterize S-2-prime ideals, which serve as a generalization encompassing both 2-prime ideals and S-prime ideals. To accomplish this objective, we construct an ideal which distinct from a multiplicatively closed subset with the help of commutative rings. We investigate the localization and the S-2-prime avoidance lemma in commutative rings. Furthermore, we explore the properties of this class of ideals in trivial ring extensions and amalgamated algebras along an ideal. We delve into S-properties for compactly packedness, compactly 2-packedness and coprimely packedness in trivial ring extentions. Moreover, this notion of ideals helps us to indicate that many results stated in S-prime ideals and 2-prime ideals can be readily expanded to the framework of S-2-prime ideals. Supporting examples also highlight a significant distinction between S-2-prime ideals and stated ideals.
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(This article belongs to the Section Algebra, Geometry and Topology)
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