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 Extended Beta-Logarithmic Function: Matrix Arguments and Properties
Mathematics 2024, 12(11), 1674; https://doi.org/10.3390/math12111674 (registering DOI) - 27 May 2024
Abstract
The beta-logarithmic function substantially generalizes the standard beta function, which is widely recognized for its significance in many applications. This article is devoted to the study of a generalization of the classical beta-logarithmic function in a matrix setting called the extended beta-logarithmic matrix
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The beta-logarithmic function substantially generalizes the standard beta function, which is widely recognized for its significance in many applications. This article is devoted to the study of a generalization of the classical beta-logarithmic function in a matrix setting called the extended beta-logarithmic matrix function. The proofs of some essential properties of this extension, such as convergence, partial derivative formulas, functional relations, integral representations, inequalities, and finite and infinite sums, are established. Moreover, an application of the extended beta-logarithmic function in matrix arguments is proposed in probability theory. Further, numerical examples and graphical presentations of the new generalization are obtained.
Full article
(This article belongs to the Special Issue Analytical and Computational Methods in Differential Equations, Special Functions, Transmutations and Integral Transforms, 2nd Edition)
Open AccessArticle
Adaptive Iterative Learning Constrained Control for Linear Motor-Driven Gantry Stage with Fault-Tolerant Non-Repetitive Trajectory Tracking
by
Chaohai Yu
Mathematics 2024, 12(11), 1673; https://doi.org/10.3390/math12111673 (registering DOI) - 27 May 2024
Abstract
This article introduces an adaptive fault-tolerant control method for non-repetitive trajectory tracking of linear motor-driven gantry platforms under state constraints. It provides a comprehensive solution to real-world issues involving state constraints and actuator failures in gantry platforms, alleviating the challenges associated with precise
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This article introduces an adaptive fault-tolerant control method for non-repetitive trajectory tracking of linear motor-driven gantry platforms under state constraints. It provides a comprehensive solution to real-world issues involving state constraints and actuator failures in gantry platforms, alleviating the challenges associated with precise modeling. Through the integration of iterative learning and backstepping cooperative design, this method achieves system stability without requiring a priori knowledge of system dynamic models or parameters. Leveraging a barrier composite energy function, the proposed controller can effectively regulate the stability of the controlled system, even when operating under state constraints. Instability issues caused by actuator failures are properly addressed, thereby enhancing controller robustness. The design of a trajectory correction function further extends applicability. Experimental validation on a linear motor-driven gantry platform serves as empirical evidence of the effectiveness of the proposed method.
Full article
(This article belongs to the Special Issue Application of Mathematical Method in Robust and Nonlinear Control)
Open AccessArticle
DE-MKD: Decoupled Multi-Teacher Knowledge Distillation Based on Entropy
by
Xin Cheng, Zhiqiang Zhang, Wei Weng, Wenxin Yu and Jinjia Zhou
Mathematics 2024, 12(11), 1672; https://doi.org/10.3390/math12111672 - 27 May 2024
Abstract
The complexity of deep neural network models (DNNs) severely limits their application on devices with limited computing and storage resources. Knowledge distillation (KD) is an attractive model compression technology that can effectively alleviate this problem. Multi-teacher knowledge distillation (MKD) aims to leverage the
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The complexity of deep neural network models (DNNs) severely limits their application on devices with limited computing and storage resources. Knowledge distillation (KD) is an attractive model compression technology that can effectively alleviate this problem. Multi-teacher knowledge distillation (MKD) aims to leverage the valuable and diverse knowledge distilled by multiple teacher networks to improve the performance of the student network. Existing approaches typically rely on simple methods such as averaging the prediction logits or using sub-optimal weighting strategies to fuse distilled knowledge from multiple teachers. However, employing these techniques cannot fully reflect the importance of teachers and may even mislead student’s learning. To address this issue, we propose a novel Decoupled Multi-Teacher Knowledge Distillation based on Entropy (DE-MKD). DE-MKD decouples the vanilla knowledge distillation loss and assigns adaptive weights to each teacher to reflect its importance based on the entropy of their predictions. Furthermore, we extend the proposed approach to distill the intermediate features from multiple powerful but cumbersome teachers to improve the performance of the lightweight student network. Extensive experiments on the publicly available CIFAR-100 image classification benchmark dataset with various teacher-student network pairs demonstrated the effectiveness and flexibility of our approach. For instance, the VGG8|ShuffleNetV2 model trained by DE-MKD reached 75.25%|78.86% top-one accuracy when choosing VGG13|WRN40-2 as the teacher, setting new performance records. In addition, surprisingly, the distilled student model outperformed the teacher in both teacher-student network pairs.
Full article
(This article belongs to the Special Issue Data-Driven Algorithms for Optimal Decision Making in Logistics and Supply Chain Management)
Open AccessArticle
Rota–Baxter Operators on Skew Braces
by
Ximu Wang, Chongxia Zhang and Liangyun Zhang
Mathematics 2024, 12(11), 1671; https://doi.org/10.3390/math12111671 - 27 May 2024
Abstract
In this paper, we introduce the concept of Rota–Baxter skew braces, and provide classifications of Rota–Baxter operators on various skew braces, such as and .
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In this paper, we introduce the concept of Rota–Baxter skew braces, and provide classifications of Rota–Baxter operators on various skew braces, such as and . We also present a necessary and sufficient condition for a skew brace to be a co-inverse skew brace. Additionally, we describe some constructions of Rota–Baxter quasiskew braces, and demonstrate that every Rota–Baxter skew brace can induce a quasigroup and a Rota–Baxter quasiskew brace.
Full article
Open AccessArticle
Bifurcation Analysis in a Coffee Berry-Borer-and-Ants Prey–Predator Model
by
Carlos Andrés Trujillo-Salazar, Gerard Olivar-Tost and Deissy Milena Sotelo-Castelblanco
Mathematics 2024, 12(11), 1670; https://doi.org/10.3390/math12111670 - 27 May 2024
Abstract
One of the most important agricultural activities worldwide, coffee cultivation, is severely affected by the Coffee Berry Borer (CBB), Hypothenemus hampei, considered the primary coffee pest. The CBB is a tiny beetle that diminishes the quantity and quality of coffee beans by
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One of the most important agricultural activities worldwide, coffee cultivation, is severely affected by the Coffee Berry Borer (CBB), Hypothenemus hampei, considered the primary coffee pest. The CBB is a tiny beetle that diminishes the quantity and quality of coffee beans by penetrating them to feed on the endosperm and deposit its eggs, continuing its life cycle. One strategy to combat CBBs is using biological control agents, such as certain species of ants. Here, a mathematical model (consisting of a system of nonlinear ordinary differential equations) is formulated to describe the prey–predator interaction between CBBs and an unspecified species of ants. From this mathematical perspective, the model allows us to determine conditions for the existence and stability of extinction, persistence or co-existence equilibria. Transitions among those equilibrium states are investigated through the maximum per capita consumption rate of the predator as a bifurcation parameter, allowing us to determine the existence of transcritical and saddle-node bifurcations. Phase portraits of the system are presented for different values of bifurcation parameter, to illustrate stability outcomes and the occurrence of bifurcations. It is concluded that an increase in bifurcation parameters significantly reduces the CBB population, suggesting that ant predation is an effective control strategy, at least theoretically.
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(This article belongs to the Special Issue Dynamics and Differential Equations in Mathematical Biology)
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Utilizing Cross-Ratios for the Detection and Correction of Missing Digits in Instrument Digit Recognition
by
Jui-Hua Huang, Yong-Han Chen and Yen-Lung Tsai
Mathematics 2024, 12(11), 1669; https://doi.org/10.3390/math12111669 - 27 May 2024
Abstract
This paper aims to enhance the existing Automatic Meter Reading (AMR) technologies for utilities in the public services sector, such as water, electricity, and gas, by allowing users to regularly upload images of their meters, which are then automatically processed by machines for
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This paper aims to enhance the existing Automatic Meter Reading (AMR) technologies for utilities in the public services sector, such as water, electricity, and gas, by allowing users to regularly upload images of their meters, which are then automatically processed by machines for digit recognition. We propose an end-to-end AMR approach designed explicitly for unconstrained environments, offering practical solutions to common failures encountered during the automatic recognition process, such as image blur, perspective distortion, partial reflection, poor lighting, missing digits, and intermediate digit states, to reduce the failure rate of automatic meter readings. The system’s first stage involves checking the quality of the user-uploaded images through the SVM method and requesting re-uploads for images unsuitable for digit extraction and recognition. The second stage employs deep learning models for digit localization and recognition, automatically detecting and correcting issues such as missing and intermediate digits to enhance the accuracy of automatic meter readings. Our research established a gas meter training dataset comprising 52,000 images, extensively annotated across various degrees, to train the deep learning models for high-precision digit recognition. Experimental results demonstrate that, with the simple SVM model, an accuracy of 87.03% is achieved for the classification of blurry image types. In addition, meter digit recognition (including intermediate digit states) can reach 97.6% (mAP), and the detection and correction of missing digits can be as high as 63.64%, showcasing the practical application value of the system developed in this study.
Full article
(This article belongs to the Special Issue Advanced Methods and Applications with Deep Learning in Object Recognition)
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Open AccessArticle
The Shape Operator of Real Hypersurfaces in S6(1)
by
Djordje Kocić and Miroslava Antić
Mathematics 2024, 12(11), 1668; https://doi.org/10.3390/math12111668 - 27 May 2024
Abstract
The aim of the paper is to present two results concerning real hypersurfaces in the six-dimensional sphere . More precisely, we prove that real hypersurfaces with the Lie-parallel shape operator A must be totally geodesic hyperspheres. Additionally, we
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The aim of the paper is to present two results concerning real hypersurfaces in the six-dimensional sphere . More precisely, we prove that real hypersurfaces with the Lie-parallel shape operator A must be totally geodesic hyperspheres. Additionally, we classify real hypersurfaces in a nearly Kähler sphere whose Lie derivative of the shape operator coincides with its covariant derivative.
Full article
(This article belongs to the Special Issue Differential Geometry, Geometric Analysis and Their Related Applications)
Open AccessArticle
SSRES: A Student Academic Paper Social Recommendation Model Based on a Heterogeneous Graph Approach
by
Yiyang Guo and Zheyu Zhou
Mathematics 2024, 12(11), 1667; https://doi.org/10.3390/math12111667 - 27 May 2024
Abstract
In an era overwhelmed by academic big data, students grapple with identifying academic papers that resonate with their learning objectives and research interests, due to the sheer volume and complexity of available information. This study addresses the challenge by proposing a novel academic
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In an era overwhelmed by academic big data, students grapple with identifying academic papers that resonate with their learning objectives and research interests, due to the sheer volume and complexity of available information. This study addresses the challenge by proposing a novel academic paper recommendation system designed to enhance personalized learning through the nuanced understanding of academic social networks. Utilizing the theory of social homogeneity, the research first constructs a sophisticated academic social network, capturing high-order social relationships, such as co-authorship and advisor–advisee connections, through hypergraph modeling and advanced network representation learning techniques. The methodology encompasses the development and integration of a hypergraph convolutional neural network and a contrastive learning framework to accurately model and recommend academic papers, focusing on aligning with students’ unique preferences and reducing reliance on sparse interaction data. The findings, validated across multiple real-world datasets, demonstrate a significant improvement in recommendation accuracy, particularly in addressing the cold-start problem and effectively mapping advisor–advisee relationships. The study concludes that leveraging complex academic social networks can substantially enhance the personalization and precision of academic paper recommendations, offering a promising avenue for addressing the challenges of academic information overload and fostering more effective personalized learning environments.
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(This article belongs to the Section Mathematics and Computer Science)
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Open AccessArticle
On the Strong Secure Domination Number of a Graph
by
Turki Alsuraiheed, J. Annaal Mercy, L. Benedict Michael Raj and Thangaraj Asir
Mathematics 2024, 12(11), 1666; https://doi.org/10.3390/math12111666 - 27 May 2024
Abstract
In this paper, we characterize trees with a strong secure domination number less than or equal to 4 and compute this parameter for certain classes of graphs. Also, we investigate bounds for the strong secure domination number of vertex gluing of two graphs.
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In this paper, we characterize trees with a strong secure domination number less than or equal to 4 and compute this parameter for certain classes of graphs. Also, we investigate bounds for the strong secure domination number of vertex gluing of two graphs.
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(This article belongs to the Special Issue Graph Theory and Applications, 2nd Edition)
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Fault Distance Measurement in Distribution Networks Based on Markov Transition Field and Darknet-19
by
Haozhi Wang, Wei Guo and Yuntao Shi
Mathematics 2024, 12(11), 1665; https://doi.org/10.3390/math12111665 - 27 May 2024
Abstract
The modern distribution network system is gradually becoming more complex and diverse, and traditional fault location methods have difficulty in quickly and accurately locating the fault location after a single-phase ground fault occurs. Therefore, this study proposes a new solution based on the
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The modern distribution network system is gradually becoming more complex and diverse, and traditional fault location methods have difficulty in quickly and accurately locating the fault location after a single-phase ground fault occurs. Therefore, this study proposes a new solution based on the Markov transfer field and deep learning to predict the fault location, which can accurately predict the location of a single-phase ground fault in the distribution network. First, a new phase-mode transformation matrix is used to take the fault current of the distribution network as the modulus 1 component, avoiding complex calculations in the complex field; then, the extracted modulus 1 component of the current is transformed into a Markov transfer field and converted into an image using pseudo-color coding, thereby fully exploiting the fault signal characteristics; finally, the Darknet-19 network is used to automatically extract fault features and predict the distance of the fault occurrence. Through simulations on existing models and training and testing with a large amount of data, the experimental results show that this method has good stability, high accuracy, and strong anti-interference ability. This solution can effectively predict the distance of ground faults in distribution networks.
Full article
(This article belongs to the Special Issue Complex Process Modeling and Control Based on AI Technology)
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Stagewise Accelerated Stochastic Gradient Methods for Nonconvex Optimization
by
Cui Jia and Zhuoxu Cui
Mathematics 2024, 12(11), 1664; https://doi.org/10.3390/math12111664 - 27 May 2024
Abstract
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For large-scale optimization that covers a wide range of optimization problems encountered frequently in machine learning and deep neural networks, stochastic optimization has become one of the most used methods thanks to its low computational complexity. In machine learning and deep learning problems,
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For large-scale optimization that covers a wide range of optimization problems encountered frequently in machine learning and deep neural networks, stochastic optimization has become one of the most used methods thanks to its low computational complexity. In machine learning and deep learning problems, nonconvex problems are common, while convex problems are rare. How to find the global minimum for nonconvex optimization and reduce the computational complexity are challenges. Inspired by the phenomenon that the stagewise stepsize tuning strategy can empirically improve the convergence speed in deep neural networks, we incorporate the stagewise stepsize tuning strategy into the iterative framework of Nesterov’s acceleration- and variance reduction-based methods to reduce the computational complexity, i.e., the stagewise stepsize tuning strategy is incorporated into randomized stochastic accelerated gradient and stochastic variance-reduced gradient. The proposed methods are theoretically derived to reduce the complexity of the nonconvex and convex problems and improve the convergence rate of the frameworks, which have the complexity and , respectively, where is the PL modulus and L is the Lipschitz constant. In the end, numerical experiments on large benchmark datasets validate well the competitiveness of the proposed methods.
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Open AccessArticle
Implicit Stance Detection with Hashtag Semantic Enrichment
by
Li Dong, Zinao Su, Xianghua Fu, Bowen Zhang and Genan Dai
Mathematics 2024, 12(11), 1663; https://doi.org/10.3390/math12111663 - 26 May 2024
Abstract
Stance detection is a crucial task in natural language processing and social computing, focusing on classifying expressed attitudes towards specific targets based on the input text. Conventional methods predominantly view stance detection as a task of target-oriented, sentence-level text classification. On popular social
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Stance detection is a crucial task in natural language processing and social computing, focusing on classifying expressed attitudes towards specific targets based on the input text. Conventional methods predominantly view stance detection as a task of target-oriented, sentence-level text classification. On popular social media platforms like Twitter, users often express their opinions through hashtags in addition to textual content within tweets. However, current methods primarily treat hashtags as data retrieval labels, neglecting to effectively utilize the semantic information they carry. In this paper, we propose a large language model knowledge-enhanced stance detection framework (LKESD) for stance detection. LKESD contains three main components: an instruction-prompted background knowledge acquisition module (IPBKA) that retrieves background knowledge of hashtags by providing handcrafted prompts to large language models (LLMs); a graph convolutional feature-enhancement module (GCFEM) is designed to extract the semantic representations of words that frequently co-occur with hashtags in the dataset by leveraging textual associations; an a knowledge fusion network (KFN) is proposed to selectively integrate graph representations and LLM features using a prompt-tuning framework. Extensive experimental results on three benchmark datasets demonstrate that our LKESD method outperforms 2.7% on all setups over compared methods, validating its effectiveness in stance detection tasks.
Full article
(This article belongs to the Special Issue New Trends in Computer Vision, Deep Learning and Artificial Intelligence)
Open AccessArticle
Deterministic and Stochastic Nonlinear Model for Transmission Dynamics of COVID-19 with Vaccinations Following Bayesian-Type Procedure
by
Mohammadi Begum Jeelani, Rahim Ud Din, Ghaliah Alhamzi, Manel Hleili and Hussam Alrabaiah
Mathematics 2024, 12(11), 1662; https://doi.org/10.3390/math12111662 - 26 May 2024
Abstract
We develop a mathematical model for the SARAS-CoV-2 double variant transmission characteristics with variant 1 vaccination to address this novel aspect of the disease. The model is theoretically examined, and adequate requirements are derived for the stability of its equilibrium points. The model
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We develop a mathematical model for the SARAS-CoV-2 double variant transmission characteristics with variant 1 vaccination to address this novel aspect of the disease. The model is theoretically examined, and adequate requirements are derived for the stability of its equilibrium points. The model includes the single variant 1 and variant 2 endemic equilibria in addition to the endemic and disease-free equilibria. Various approaches are used for the global and local stability of the model. For both strains, we determine the basic reproductive numbers and . To investigate the occurrence of the layers (waves), we expand the model to include some analysis based on the second-order derivative. The model is then expanded to its stochastic form, and numerical outcomes are computed. For numerical purposes, we use the nonstandard finite difference method. Some error analysis is also recorded.
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Open AccessArticle
Convolutional Neural Networks for Local Component Number Estimation from Time–Frequency Distributions of Multicomponent Nonstationary Signals
by
Vedran Jurdana and Sandi Baressi Šegota
Mathematics 2024, 12(11), 1661; https://doi.org/10.3390/math12111661 - 26 May 2024
Abstract
Frequency-modulated (FM) signals, prevalent across various applied disciplines, exhibit time-dependent frequencies and a multicomponent nature necessitating the utilization of time-frequency methods. Accurately determining the number of components in such signals is crucial for various applications reliant on this metric. However, this poses a
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Frequency-modulated (FM) signals, prevalent across various applied disciplines, exhibit time-dependent frequencies and a multicomponent nature necessitating the utilization of time-frequency methods. Accurately determining the number of components in such signals is crucial for various applications reliant on this metric. However, this poses a challenge, particularly amidst interfering components of varying amplitudes in noisy environments. While the localized Rényi entropy (LRE) method is effective for component counting, its accuracy significantly diminishes when analyzing signals with intersecting components, components that deviate from the time axis, and components with different amplitudes. This paper addresses these limitations and proposes a convolutional neural network-based (CNN) approach for determining the local number of components using a time–frequency distribution of a signal as input. A comprehensive training set comprising single and multicomponent linear and quadratic FM components with diverse time and frequency supports has been constructed, emphasizing special cases of noisy signals with intersecting components and differing amplitudes. The results demonstrate that the estimated component numbers outperform those obtained using the LRE method for considered noisy multicomponent synthetic signals. Furthermore, we validate the efficacy of the proposed CNN approach on real-world gravitational and electroencephalogram signals, underscoring its robustness and applicability across different signal types and conditions.
Full article
(This article belongs to the Section Mathematics and Computer Science)
Open AccessArticle
Mathematical Logic Model for Analysing the Controllability of Mining Equipment
by
Pavel V. Shishkin, Boris V. Malozyomov, Nikita V. Martyushev, Svetlana N. Sorokova, Egor A. Efremenkov, Denis V. Valuev and Mengxu Qi
Mathematics 2024, 12(11), 1660; https://doi.org/10.3390/math12111660 - 26 May 2024
Abstract
The issues of the evaluation and prediction of the reliability and testability of mining machinery and equipment are becoming particularly relevant, since the safety of technological processes and human life is reaching a new level of realisation due to changes in mining technology.
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The issues of the evaluation and prediction of the reliability and testability of mining machinery and equipment are becoming particularly relevant, since the safety of technological processes and human life is reaching a new level of realisation due to changes in mining technology. The work is devoted to the development of a logical model for analysing the controllability of mining equipment. The paper presents a model of reliability of the operation of mining equipment on the example of a mine load and passenger hoist. This generalised model is made in the form of a graph of transitions and supplemented with a system of equations. The model allows for the estimation of the reliability of equipment elements and equipment as a whole. A mathematical and logical model for the calculation of the availability and downtime coefficients of various designs of mining equipment systems is proposed. This model became the basis for the methods to calculate the optimal values of diagnostic depth. At these calculated values, the maximum value of availability factor will be obtained. In this paper, an analytical study was carried out and dependences of the readiness factor of parameters of the investigated system such as the intensity of control of technical systems, intensity of failures, etc., were constructed. The paper proposes a mathematical model to assess the reliability of mine hoisting plants through its integration into the method of improving the reliability of mine hoisting plants.
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(This article belongs to the Special Issue Stochastic Processes, Models and Methods in Resilience Management and Reliability Optimization)
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A Novel Fuzzy Bi-Clustering Algorithm with Axiomatic Fuzzy Set for Identification of Co-Regulated Genes
by
Kaijie Xu and Yixi Wang
Mathematics 2024, 12(11), 1659; https://doi.org/10.3390/math12111659 - 26 May 2024
Abstract
The identification of co-regulated genes and their Transcription-Factor Binding Sites (TFBSs) are the key steps toward understanding transcription regulation. In addition to effective laboratory assays, various bi-clustering algorithms for the detection of the co-expressed genes have been developed. Bi-clustering methods are used to
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The identification of co-regulated genes and their Transcription-Factor Binding Sites (TFBSs) are the key steps toward understanding transcription regulation. In addition to effective laboratory assays, various bi-clustering algorithms for the detection of the co-expressed genes have been developed. Bi-clustering methods are used to discover subgroups of genes with similar expression patterns under to-be-identified subsets of experimental conditions when applied to gene expression data. By building two fuzzy partition matrices of the gene expression data with the Axiomatic Fuzzy Set (AFS) theory, this paper proposes a novel fuzzy bi-clustering algorithm for the identification of co-regulated genes. Specifically, the gene expression data are transformed into two fuzzy partition matrices via the sub-preference relations theory of AFS at first. One of the matrices considers the genes as the universe and the conditions as the concept, and the other one considers the genes as the concept and the conditions as the universe. The identification of the co-regulated genes (bi-clusters) is carried out on the two partition matrices at the same time. Then, a novel fuzzy-based similarity criterion is defined based on the partition matrices, and a cyclic optimization algorithm is designed to discover the significant bi-clusters at the expression level. The above procedures guarantee that the generated bi-clusters have more significant expression values than those extracted by the traditional bi-clustering methods. Finally, the performance of the proposed method is evaluated with the performance of the three well-known bi-clustering algorithms on publicly available real microarray datasets. The experimental results are in agreement with the theoretical analysis and show that the proposed algorithm can effectively detect the co-regulated genes without any prior knowledge of the gene expression data.
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(This article belongs to the Special Issue New Advances in Data Analytics and Mining)
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Partition Entropy as a Measure of Regularity of Music Scales
by
Rafael Cubarsi
Mathematics 2024, 12(11), 1658; https://doi.org/10.3390/math12111658 - 25 May 2024
Abstract
The entropy of the partition generated by an n-tone music scale is proposed to quantify its regularity. The normalized entropy relative to a regular partition and its complementary, here referred to as the bias, allow us to analyze various conditions of similarity
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The entropy of the partition generated by an n-tone music scale is proposed to quantify its regularity. The normalized entropy relative to a regular partition and its complementary, here referred to as the bias, allow us to analyze various conditions of similarity between an arbitrary scale and a regular scale. Interesting particular cases are scales with limited bias because their tones are distributed along specific interval fractions of a regular partition. The most typical case in music concerns partitions associated with well-formed scales generated by a single tone h. These scales are maximal even sets that combine two elementary intervals. Then, the normalized entropy depends on each number of intervals as well as their relative size. When well-formed scales are refined, several nested families stand out with increasing regularity. It is proven that a scale of minimal bias, i.e., with less bias than those with fewer tones, is always a best rational approximation of .
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(This article belongs to the Special Issue Computational Mathematics and Numerical Analysis)
Open AccessArticle
Navigating Uncharted Waters: The Transformation of the Bank of Korea’s Monetary Policy in Response to Global Economic Uncertainty
by
Yugang He and Zhuoqi Teng
Mathematics 2024, 12(11), 1657; https://doi.org/10.3390/math12111657 - 25 May 2024
Abstract
The evolving global economic landscape necessitates adaptive monetary policies, especially for economies like South Korea that are deeply integrated with global markets. This research explores the strategic recalibrations of the Bank of Korea’s monetary policy amid fluctuations in global economic uncertainty. Utilizing a
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The evolving global economic landscape necessitates adaptive monetary policies, especially for economies like South Korea that are deeply integrated with global markets. This research explores the strategic recalibrations of the Bank of Korea’s monetary policy amid fluctuations in global economic uncertainty. Utilizing a sophisticated microeconomic theoretical framework, this study employs Bayesian estimation techniques and impulse response analysis to dissect the dynamic effects of these global shocks on South Korea’s macroeconomic stability and policy direction. Our findings reveal that the Bank of Korea has adeptly navigated through turbulent economic conditions induced by external shocks through well-coordinated policy adaptations. These adaptations, which include both traditional and innovative monetary tools, have been crucial in stabilizing the financial environment and promoting economic growth. By detailing the tailored application of the Taylor rule within the Korean context and strategic foreign exchange interventions by the central bank, this study contributes significantly to the broader discourse on the efficacy of monetary policy in open economies and offers insights on integrating advanced analytical methods into economic policy analysis.
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(This article belongs to the Special Issue Statistical Methods of Analyzing Financial Equilibrium, Performance and Risk, 2nd Edition)
Open AccessArticle
On Summations of Generalized Hypergeometric Functions with Integral Parameter Differences
by
Kirill Bakhtin and Elena Prilepkina
Mathematics 2024, 12(11), 1656; https://doi.org/10.3390/math12111656 - 25 May 2024
Abstract
In this paper, we present an extension of the Karlsson–Minton summation formula for a generalized hypergeometric function with integral parameter differences. Namely, we extend one single negative difference in Karlsson–Minton formula to a finite number of integral negative differences, some of which will
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In this paper, we present an extension of the Karlsson–Minton summation formula for a generalized hypergeometric function with integral parameter differences. Namely, we extend one single negative difference in Karlsson–Minton formula to a finite number of integral negative differences, some of which will be repeated. Next, we continue our study of the generalized hypergeometric function evaluated at unity and with integral positive differences (IPD hypergeometric function at the unit argument). We obtain a recurrence relation that reduces the IPD hypergeometric function at the unit argument to . Finally, we note that Euler–Pfaff-type transformations are always based on summation formulas for finite hypergeometric functions, and we give a number of examples.
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(This article belongs to the Special Issue Analytical and Computational Methods in Differential Equations, Special Functions, Transmutations and Integral Transforms, 2nd Edition)
Open AccessArticle
Exploring the Predictive Potential of Complex Problem-Solving in Computing Education: A Case Study in the Introductory Programming Course
by
Bostjan Bubnic, Marjan Mernik and Tomaž Kosar
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)
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