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Mathematics, Volume 11, Issue 22 (November-2 2023) – 146 articles

Cover Story (view full-size image): New families of direct serendipity and direct mixed finite elements on general planar, strictly convex polygons were recently defined by the authors. The finite elements of index r are H1 and H(div) conforming, respectively, and approximate optimally to order r+1 while using the minimal number of degrees of freedom. The shape function space consists of the full set of polynomials defined directly on the element and augmented with a space of supplemental functions. In this work, we propose alternative ways to construct the supplemental functions on the element as continuous piecewise polynomials. One approach results in supplemental functions that are in Hp for any p≥1. We prove the optimal approximation property for these new finite elements. View this paper
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29 pages, 3855 KiB  
Article
Inferring Complementary and Substitutable Products Based on Knowledge Graph Reasoning
Mathematics 2023, 11(22), 4709; https://doi.org/10.3390/math11224709 - 20 Nov 2023
Viewed by 628
Abstract
Complementarity and substitutability between products are essential concepts in retail and marketing. To achieve this, existing approaches take advantage of knowledge graphs to learn more evidence for inference. However, they often omit the knowledge that lies in the unstructured data. In this research, [...] Read more.
Complementarity and substitutability between products are essential concepts in retail and marketing. To achieve this, existing approaches take advantage of knowledge graphs to learn more evidence for inference. However, they often omit the knowledge that lies in the unstructured data. In this research, we concentrate on inferring complementary and substitutable products in e-commerce from mass structured and unstructured data. An improved knowledge-graph-based reasoning model has been proposed which cannot only derive related products but also provide interpretable paths to explain the relationship. The methodology employed in our study unfolds through several stages. First, a knowledge graph refining entities and relationships from data was constructed. Second, we developed a two-stage knowledge representation learning method to better represent the structured and unstructured knowledge based on TransE and SBERT. Then, the relationship inferring problem was converted into a path reasoning problem under the Markov decision process environment by learning a dynamic policy network. We also applied a soft pruning strategy and a modified reward function to improve the effectiveness of the policy network training. We demonstrate the effectiveness of the proposed method on standard Amazon datasets, and it gives about 5–15% relative improvement over the state-of-the-art models in terms of NDCG@10, Recall@10, Precision @10, and HR@10. Full article
(This article belongs to the Special Issue Advances in Business Intelligence: Theoretical and Empirical Issues)
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27 pages, 2341 KiB  
Article
An Algorithm That Adjusts the Stepsize to Be Self-Adaptive with an Inertial Term Aimed for Solving Split Variational Inclusion and Common Fixed Point Problems
Mathematics 2023, 11(22), 4708; https://doi.org/10.3390/math11224708 - 20 Nov 2023
Viewed by 465
Abstract
In this research paper, we present a new inertial method with a self-adaptive technique for solving the split variational inclusion and fixed point problems in real Hilbert spaces. The algorithm is designed to choose the optimal choice of the inertial term at every [...] Read more.
In this research paper, we present a new inertial method with a self-adaptive technique for solving the split variational inclusion and fixed point problems in real Hilbert spaces. The algorithm is designed to choose the optimal choice of the inertial term at every iteration, and the stepsize is defined self-adaptively without a prior estimate of the Lipschitz constant. A convergence theorem is demonstrated to be strong even under lenient conditions and to showcase the suggested method’s efficiency and precision. Some numerical tests are given. Moreover, the significance of the proposed method is demonstrated through its application to an image reconstruction issue. Full article
(This article belongs to the Special Issue Advances in Fixed Point Theory and Its Applications)
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18 pages, 332 KiB  
Article
Noisy Tree Data Structures and Quantum Applications
Mathematics 2023, 11(22), 4707; https://doi.org/10.3390/math11224707 - 20 Nov 2023
Viewed by 630
Abstract
We suggest a new technique for developing noisy tree data structures. We call it a “walking tree”. As applications of the technique we present a noisy Self-Balanced Binary Search Tree (we use a Red–Black tree as an implementation) and a noisy segment tree. [...] Read more.
We suggest a new technique for developing noisy tree data structures. We call it a “walking tree”. As applications of the technique we present a noisy Self-Balanced Binary Search Tree (we use a Red–Black tree as an implementation) and a noisy segment tree. The asymptotic complexity of the main operations for the tree data structures does not change compared to the case without noise. We apply the data structures in quantum algorithms for several problems on strings like the string-sorting problem and auto-complete problem. For both problems, we obtain quantum speed-up. Moreover, for the string-sorting problem, we show a quantum lower bound. Full article
(This article belongs to the Special Issue Quantum Algorithms and Quantum Computing)
24 pages, 930 KiB  
Article
Analysis of Fluctuating Antenna Beamwidth in UAV-Assisted Cellular Networks
Mathematics 2023, 11(22), 4706; https://doi.org/10.3390/math11224706 - 20 Nov 2023
Viewed by 497
Abstract
This paper investigates a cellular network assisted by unmanned aerial vehicles (UAVs) in the presence of a fluctuating 3-dimensional (3D) antenna beamwidth. The primary objective is to perform an analysis of typical user equipment (T-UE) performance with a specific focus on coverage probability [...] Read more.
This paper investigates a cellular network assisted by unmanned aerial vehicles (UAVs) in the presence of a fluctuating 3-dimensional (3D) antenna beamwidth. The primary objective is to perform an analysis of typical user equipment (T-UE) performance with a specific focus on coverage probability and spectral efficiency (SE) in the presence of fluctuations of 3D antenna beamwidth. Within this analytical framework, the macro base stations (MBSs) are meticulously characterized through the application of an independent 2D homogeneous Poisson point process (PPP), while the low-altitude platforms (LAPs) are described using an independent 3D PPP. The study entails the derivation of association probabilities, determining the likelihood of the T-UE associating with MBSs, line-of-sight LAPs, and non-line-of-sight LAPs. Through rigorous mathematical analysis, the paper formulates precise analytical expressions that encapsulate the association and coverage probabilities, taking into account the inherent variability in the UAV antenna beamwidth. This research focuses on a thorough performance evaluation of the T-UE across diverse network configurations, encompassing LAP density, the transmission power of LAPs, and the critical signal-to-interference ratio threshold. The outcomes of this study distinctly underscore the substantial disruptive impact resulting from fluctuating beamwidth on the performance of the T-UE within the UAV-assisted cellular network. Additionally, this performance is further impacted by larger densities and transmission power of the LAP. Hence, it is imperative to take into account the influence of these fluctuations on network association, coverage, and SE whenever contemplating a UAV-assisted cellular network. Full article
(This article belongs to the Section Mathematics and Computer Science)
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17 pages, 327 KiB  
Article
Scheduling of Software Test to Minimize the Total Completion Time
Mathematics 2023, 11(22), 4705; https://doi.org/10.3390/math11224705 - 20 Nov 2023
Viewed by 476
Abstract
This paper investigates a single-machine scheduling problem of a software test with shared common setup operations. Each job has a corresponding set of setup operations, and the job cannot be executed unless its setups are completed. If two jobs have the same supporting [...] Read more.
This paper investigates a single-machine scheduling problem of a software test with shared common setup operations. Each job has a corresponding set of setup operations, and the job cannot be executed unless its setups are completed. If two jobs have the same supporting setups, the common setups are performed only once. No preemption of any processing is allowed. This problem is known to be computationally intractable. In this study, we propose sequence-based and position-based integer programming models and a branch-and-bound algorithm for finding optimal solutions. We also propose an ant colony optimization algorithm for finding approximate solutions, which will be used as the initial upper bound of the branch-and-bound algorithm. The computational experiments are designed and conducted to numerically appraise all of the proposed methods. Full article
(This article belongs to the Special Issue Recent Advances of Disсrete Optimization and Scheduling)
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16 pages, 659 KiB  
Article
Improving the Performance of Optimization Algorithms Using the Adaptive Fixed-Time Scheme and Reset Scheme
Mathematics 2023, 11(22), 4704; https://doi.org/10.3390/math11224704 - 20 Nov 2023
Viewed by 500
Abstract
Optimization algorithms have now played an important role in many fields, and the issue of how to design high-efficiency algorithms has gained increasing attention, for which it has been shown that advanced control theories could be helpful. In this paper, the fixed-time scheme [...] Read more.
Optimization algorithms have now played an important role in many fields, and the issue of how to design high-efficiency algorithms has gained increasing attention, for which it has been shown that advanced control theories could be helpful. In this paper, the fixed-time scheme and reset scheme are introduced to design high-efficiency gradient descent methods for unconstrained convex optimization problems. At first, a general reset framework for existing accelerated gradient descent methods is given based on the systematic representation, with which both convergence speed and stability are significantly improved. Then, the design of a novel adaptive fixed-time gradient descent, which has fewer tuning parameters and maintains better robustness to initial conditions, is presented. However, its discrete form introduces undesirable overshoot and easily leads to instability, and the reset scheme is then applied to overcome the drawbacks. The linear convergence and better stability of the proposed algorithms are theoretically proven, and several dedicated simulation examples are finally given to validate the effectiveness. Full article
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21 pages, 14317 KiB  
Review
Exploring the Contributions to Mathematical Economics: A Bibliometric Analysis Using Bibliometrix and VOSviewer
Mathematics 2023, 11(22), 4703; https://doi.org/10.3390/math11224703 - 20 Nov 2023
Viewed by 716
Abstract
From Cournot, Walras, and Pareto’s research to what followed in the form of marginalist economics, chaos theory, agent-based modeling, game theory, and econophysics, the interpretation and analysis of economic systems have been carried out using a broad range of higher mathematics methods. The [...] Read more.
From Cournot, Walras, and Pareto’s research to what followed in the form of marginalist economics, chaos theory, agent-based modeling, game theory, and econophysics, the interpretation and analysis of economic systems have been carried out using a broad range of higher mathematics methods. The evolution of mathematical economics is associated with the most productive and influential authors, sources, and countries, as well as the identification of interactions between the authors and research topics. Bibliometric analysis provides journal-, author-, document-, and country-level metrics. In the present study, a bibliometric overview of mathematical economics came from a screening performed in September 2023, covering the timespan 1898–2023. About 6477 documents on mathematical economics were retrieved and extracted from the Scopus academic database for analysis. The Bibliometrix package in the statistical programming language R was employed to perform a bibliometric analysis of scientific literature and citation data indexed in the Scopus database. VOSviewer (version 1.6.19) was used for the visualization of similarities using several bibliometric techniques, including bibliographic coupling, co-citation, and co-occurrence of keywords. The analysis traced the most influential papers, keywords, countries, and journals among high-quality studies in mathematical economics. Full article
(This article belongs to the Special Issue Latest Advances in Mathematical Economics)
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14 pages, 337 KiB  
Article
Terracini Loci: Dimension and Description of Its Components
Mathematics 2023, 11(22), 4702; https://doi.org/10.3390/math11224702 - 20 Nov 2023
Viewed by 420
Abstract
We study the Terracini loci of an irreducible variety X embedded in a projective space: non-emptiness, dimensions and the geometry of their maximal dimension’s irreducible components. These loci were studied because they describe where the differential of an important geometric map drops rank. [...] Read more.
We study the Terracini loci of an irreducible variety X embedded in a projective space: non-emptiness, dimensions and the geometry of their maximal dimension’s irreducible components. These loci were studied because they describe where the differential of an important geometric map drops rank. Our best results are if X is either a Veronese embedding of a projective space of arbitrary dimension (the set-up for the additive decomposition of homogeneous polynomials) or a Segre–Veronese embedding of a multiprojective space (the set-up for partially symmetric tensors). For an arbitrary X, we give several examples in which all Terracini loci are empty, several criteria for non-emptiness and examples with the maximal defect possible a priori of an element of a minimal Terracini locus. We raise a few open questions. Full article
14 pages, 300 KiB  
Article
A New Class of Leonardo Hybrid Numbers and Some Remarks on Leonardo Quaternions over Finite Fields
Mathematics 2023, 11(22), 4701; https://doi.org/10.3390/math11224701 - 20 Nov 2023
Cited by 3 | Viewed by 613
Abstract
In this paper, we present a new class of Leonardo hybrid numbers that incorporate quantum integers into their components. This advancement presents a broader generalization of the q-Leonardo hybrid numbers. We explore some fundamental properties associated with these numbers. Moreover, we study [...] Read more.
In this paper, we present a new class of Leonardo hybrid numbers that incorporate quantum integers into their components. This advancement presents a broader generalization of the q-Leonardo hybrid numbers. We explore some fundamental properties associated with these numbers. Moreover, we study special Leonardo quaternions over finite fields. In particular, we determine the Leonardo quaternions that are zero divisors or invertible elements in the quaternion algebra over the finite field Zp for special values of prime integer p. Full article
17 pages, 2094 KiB  
Article
Improved Self-Learning Genetic Algorithm for Solving Flexible Job Shop Scheduling
Mathematics 2023, 11(22), 4700; https://doi.org/10.3390/math11224700 - 20 Nov 2023
Viewed by 783
Abstract
The flexible job shop scheduling problem (FJSP), one of the core problems in the field of generative manufacturing process planning, has become a hotspot and a challenge in manufacturing production research. In this study, an improved self-learning genetic algorithm is proposed. The single [...] Read more.
The flexible job shop scheduling problem (FJSP), one of the core problems in the field of generative manufacturing process planning, has become a hotspot and a challenge in manufacturing production research. In this study, an improved self-learning genetic algorithm is proposed. The single mutation approach of the genetic algorithm was improved, while four mutation operators were designed on the basis of process coding and machine coding; their weights were updated and their selection mutation operators were adjusted according to the performance in the iterative process. Combined with the improved population initialization method and the optimized crossover strategy, the local search capability was enhanced, and the convergence speed was accelerated. The effectiveness and feasibility of the algorithm were verified by testing the benchmark arithmetic examples and numerical experiments. Full article
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13 pages, 1465 KiB  
Article
A Reduced-Dimension Extrapolating Method of Finite Element Solution Coefficient Vectors for Fractional Tricomi-Type Equation
Mathematics 2023, 11(22), 4699; https://doi.org/10.3390/math11224699 - 20 Nov 2023
Viewed by 420
Abstract
We here employ a proper orthogonal decomposition (POD) to reduce the dimensionality of unknown coefficient vectors of finite element (FE) solutions for the fractional Tricomi-type equation and develop a reduced-dimension extrapolating FE (RDEFE) method for the fractional Tricomi-type equation. For this purpose, we [...] Read more.
We here employ a proper orthogonal decomposition (POD) to reduce the dimensionality of unknown coefficient vectors of finite element (FE) solutions for the fractional Tricomi-type equation and develop a reduced-dimension extrapolating FE (RDEFE) method for the fractional Tricomi-type equation. For this purpose, we first develop an FE method for the fractional Tricomi-type equation and provide the existence, unconditional stability, and error analysis for the FE solutions. We then develop the RDEFE method for the fractional Tricomi-type equation by means of the POD technique and analyze the existence, unconditional stability, and errors for the RDEFE solutions by using the matrix analysis. Lastly, we provide two numerical examples to verify our theoretical results and to explain the advantages of the RDEFE method. Full article
(This article belongs to the Section Computational and Applied Mathematics)
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31 pages, 7299 KiB  
Article
Developing System-Based Artificial Intelligence Models for Detecting the Attention Deficit Hyperactivity Disorder
Mathematics 2023, 11(22), 4698; https://doi.org/10.3390/math11224698 - 20 Nov 2023
Viewed by 890
Abstract
This study presents a novel methodology for automating the classification of pediatric ADHD using electroencephalogram (EEG) biomarkers through machine learning and deep learning techniques. The primary objective is to develop accurate EEG-based screening tools to aid clinical diagnosis and enable early intervention for [...] Read more.
This study presents a novel methodology for automating the classification of pediatric ADHD using electroencephalogram (EEG) biomarkers through machine learning and deep learning techniques. The primary objective is to develop accurate EEG-based screening tools to aid clinical diagnosis and enable early intervention for ADHD. The proposed system utilizes a publicly available dataset consisting of raw EEG recordings from 61 individuals with ADHD and 60 control subjects during a visual attention task. The methodology involves meticulous preprocessing of raw EEG recordings to isolate brain signals and extract informative features, including time, frequency, and entropy signal characteristics. The feature selection techniques, including least absolute shrinkage and selection operator (LASSO) regularization and recursive elimination, were applied to identify relevant variables and enhance generalization. The obtained features are processed by employing various machine learning and deep learning algorithms, namely CatBoost, Random Forest Decision Trees, Convolutional Neural Networks (CNNs), and Long Short-Term Memory Networks (LSTMs). The empirical results of the proposed algorithms highlight the effectiveness of feature selection approaches in matching informative biomarkers with optimal model classes. The convolutional neural network model achieves superior testing accuracy of 97.75% using LASSO-regularized biomarkers, underscoring the strengths of deep learning and customized feature optimization. The proposed framework advances EEG analysis to uncover discriminative patterns, significantly contributing to the field of ADHD screening and diagnosis. The suggested methodology achieved high performance compared with different existing systems based on AI approaches for diagnosing ADHD. Full article
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10 pages, 278 KiB  
Article
Hyperconnectedness and Resolvability of Soft Ideal Topological Spaces
Mathematics 2023, 11(22), 4697; https://doi.org/10.3390/math11224697 - 19 Nov 2023
Cited by 2 | Viewed by 742
Abstract
This paper introduces and explores the concept of soft ideal dense sets, utilizing soft open sets and soft local functions, to examine their fundamental characteristics under some conditions for the following notions: soft ideal hyperconnectedness, soft ideal resolvability, soft ideal irresolvability, and soft [...] Read more.
This paper introduces and explores the concept of soft ideal dense sets, utilizing soft open sets and soft local functions, to examine their fundamental characteristics under some conditions for the following notions: soft ideal hyperconnectedness, soft ideal resolvability, soft ideal irresolvability, and soft ideal semi-irresolvability in soft ideal topological spaces. Moreover, it explores the relationship between these notions if τI¯=ϕE is obtained in the soft set environment. Full article
(This article belongs to the Special Issue Advances and Applications of Soft Computing)
19 pages, 3109 KiB  
Article
On the State-Feedback Controller Design for Polynomial Linear Parameter-Varying Systems with Pole Placement within Linear Matrix Inequality Regions
Mathematics 2023, 11(22), 4696; https://doi.org/10.3390/math11224696 - 19 Nov 2023
Viewed by 616
Abstract
The present paper addresses linear parameter-varying systems with high-order time-varying parameter dependency known as polynomial LPV systems and their controller design. Throughout this work, a procedure ensuring a state-feedback controller from a parameterized linear matrix inequality (PLMI) solution is presented. As the main [...] Read more.
The present paper addresses linear parameter-varying systems with high-order time-varying parameter dependency known as polynomial LPV systems and their controller design. Throughout this work, a procedure ensuring a state-feedback controller from a parameterized linear matrix inequality (PLMI) solution is presented. As the main contribution of this paper, the controller is designed by considering the time-varying parameter rate as a tuning parameter with a continuous control gain in such a way that the closed-loop eigenvalues lie in a complex plane subset, with high-order time-varying parameters defining the system dynamics. Simulation results are presented, aiming to show the effectiveness of the proposed controller design. Full article
(This article belongs to the Special Issue Mathematical Modeling and Simulation in Automatic Control)
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18 pages, 10242 KiB  
Article
Gaussian Process-Based Transfer Kernel Learning for Unsupervised Domain Adaptation
Mathematics 2023, 11(22), 4695; https://doi.org/10.3390/math11224695 - 19 Nov 2023
Cited by 1 | Viewed by 644
Abstract
The discriminability and transferability of models are two important factors for the success of domain adaptation methods. Recently, some domain adaptation methods have improved models by adding a discriminant information extraction module. However, these methods need to carefully balance the discriminability and transferability [...] Read more.
The discriminability and transferability of models are two important factors for the success of domain adaptation methods. Recently, some domain adaptation methods have improved models by adding a discriminant information extraction module. However, these methods need to carefully balance the discriminability and transferability of a model. To address this problem, we propose a new deep domain adaptation method, Gaussian Process-based Transfer Kernel Learning (GPTKL), which can perform domain knowledge transfer and improve the discrimination ability of the model simultaneously. GPTKL uses the kernel similarity between all samples in the source and target domains as a priori information to establish a cross-domain Gaussian process. By maximizing its likelihood function, GPTKL reduces the domain discrepancy between the source and target domains, thereby enhancing generalization across domains. At the same time, GPTKL introduces the deep kernel learning strategy into the cross-domain Gaussian process to learn a transfer kernel function based on deep features. Through transfer kernel learning, GPTKL learns a deep feature space with both discriminability and transferability. In addition, GPTKL uses cross-entropy and mutual information to learn a classification model shared by the source and target domains. Experiments on four benchmarks show that GPTKL achieves superior classification performance over state-of-the-art methods. Full article
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11 pages, 287 KiB  
Article
Applications to Solving Variational Inequality Problems via MR-Kannan Type Interpolative Contractions
Mathematics 2023, 11(22), 4694; https://doi.org/10.3390/math11224694 - 19 Nov 2023
Viewed by 509
Abstract
The aim of this paper is manifold. We first define the new class of operators called MR-Kannan interpolative type contractions, which includes the Kannan, enriched Kannan, interpolative Kannan type, and enriched interpolative Kannan type operators. Secondly, we prove the existence of a unique [...] Read more.
The aim of this paper is manifold. We first define the new class of operators called MR-Kannan interpolative type contractions, which includes the Kannan, enriched Kannan, interpolative Kannan type, and enriched interpolative Kannan type operators. Secondly, we prove the existence of a unique fixed point for this class of operators. Thirdly, we study Ulam-Hyers stability, well-posedness, and periodic point properties. Finally, an application of the main results to the variational inequality problem is given. Full article
33 pages, 6791 KiB  
Article
Power Transformer Fault Diagnosis Using Neural Network Optimization Techniques
Mathematics 2023, 11(22), 4693; https://doi.org/10.3390/math11224693 - 19 Nov 2023
Viewed by 695
Abstract
Artificial Intelligence (AI) techniques are considered the most advanced approaches for diagnosing faults in power transformers. Dissolved Gas Analysis (DGA) is the conventional approach widely adopted for diagnosing incipient faults in power transformers. The IEC-599 standard Ratio Method is an accurate method that [...] Read more.
Artificial Intelligence (AI) techniques are considered the most advanced approaches for diagnosing faults in power transformers. Dissolved Gas Analysis (DGA) is the conventional approach widely adopted for diagnosing incipient faults in power transformers. The IEC-599 standard Ratio Method is an accurate method that evaluates the DGA. All the classical approaches have limitations because they cannot diagnose all faults accurately. Precisely diagnosing defects in power transformers is a significant challenge due to their extensive quantity and dispersed placement within the power network. To deal with this concern and to improve the reliability and precision of fault diagnosis, different Artificial Intelligence techniques are presented. In this manuscript, an artificial neural network (ANN) is implemented to enhance the accuracy of the Rogers Ratio Method. On the other hand, it should be noted that the complexity of an ANN demands a large amount of storage and computing power. In order to address this issue, an optimization technique is implemented with the objective of maximizing the accuracy and minimizing the architectural complexity of an ANN. All the procedures are simulated using the MATLAB R2023a software. Firstly, the authors choose the most effective classification model by automatically training five classifiers in the Classification Learner app (CLA). After selecting the artificial neural network (ANN) as the sufficient classification model, we trained 30 ANNs with different parameters and determined the 5 models with the best accuracy. We then tested these five ANNs using the Experiment Manager app and ultimately selected the ANN with the best performance. The network structure is determined to consist of three layers, taking into consideration both diagnostic accuracy and computing efficiency. Ultimately, a (100-50-5) layered ANN was selected to optimize its hyperparameters. As a result, following the implementation of the optimization techniques, the suggested ANN exhibited a high level of accuracy, up to 90.7%. The conclusion of the proposed model indicates that the optimization of hyperparameters and the increase in the number of data samples enhance the accuracy while minimizing the complexity of the ANN. The optimized ANN is simulated and tested in MATLAB R2023a—Deep Network Designer, resulting in an accuracy of almost 90%. Moreover, compared to the Rogers Ratio Method, which exhibits an accuracy rate of just 63.3%, this approach successfully addresses the constraints associated with the conventional Rogers Ratio Method. So, the ANN has evolved a supremacy diagnostic method in the realm of power transformer fault diagnosis. Full article
(This article belongs to the Special Issue Artificial Intelligence Techniques Applications on Power Systems)
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25 pages, 316 KiB  
Article
A Two-Server Queue with Interdependence between Arrival and Service Processes
Mathematics 2023, 11(22), 4692; https://doi.org/10.3390/math11224692 - 18 Nov 2023
Viewed by 1413
Abstract
In this paper, we analyse a queueing system with two servers where the arrival and service processes are interdependent. The evolution of these processes is governed by transitions on the product space of three Markov chains, which are descriptors of the arrival and [...] Read more.
In this paper, we analyse a queueing system with two servers where the arrival and service processes are interdependent. The evolution of these processes is governed by transitions on the product space of three Markov chains, which are descriptors of the arrival and service processes. The transitions in this Markov chain follow a semi-Markov rule and the exponential distribution governs the sojourn times in the states. The stability condition of the system is derived and the stationary distribution is calculated for the system in equilibrium. Several important performance measures are provided, and numerical illustrations of the model are presented. Full article
23 pages, 675 KiB  
Article
Fourier Transform of the Lippmann-Schwinger Equation: Solving Vectorial Electromagnetic Scattering by Arbitrary Shapes
Mathematics 2023, 11(22), 4691; https://doi.org/10.3390/math11224691 - 18 Nov 2023
Viewed by 742
Abstract
In Electromagnetics, the field scattered by an ensemble of particles—of arbitrary size, shape, and material—can be obtained by solving the Lippmann–Schwinger equation. This singular vectorial integral equation is generally formulated in the direct space Rn (typically n=2 or [...] Read more.
In Electromagnetics, the field scattered by an ensemble of particles—of arbitrary size, shape, and material—can be obtained by solving the Lippmann–Schwinger equation. This singular vectorial integral equation is generally formulated in the direct space Rn (typically n=2 or n=3). In the article, we rigorously computed the Fourier transform of the vectorial Lippmann–Schwinger equation in the space of tempered distributions, S(R3), splitting it in a singular and a regular contribution. One eventually obtains a simple equation for the scattered field in the Fourier space. This permits to draw an explicit link between the shape of the scatterer and the field through the Fourier Transform of the body indicator function. We compare our results with accurate calculations based on the T-matrix method and find a good agreement. Full article
(This article belongs to the Special Issue Analytical Methods in Wave Scattering and Diffraction, 2nd Edition)
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15 pages, 2176 KiB  
Article
Improving Numerical Accuracy of the Localized Oscillatory Radial Basis Functions Collocation Method for Solving Elliptic Partial Differential Equations in 2D
Mathematics 2023, 11(22), 4690; https://doi.org/10.3390/math11224690 - 18 Nov 2023
Viewed by 537
Abstract
Recently, the localized oscillatory radial basis functions collocation method (L-ORBFs) has been introduced to solve elliptic partial differential equations in 2D with a large number of computational nodes. The research clearly shows that the L-ORBFs is very convenient and useful for solving large-scale [...] Read more.
Recently, the localized oscillatory radial basis functions collocation method (L-ORBFs) has been introduced to solve elliptic partial differential equations in 2D with a large number of computational nodes. The research clearly shows that the L-ORBFs is very convenient and useful for solving large-scale problems, but this method is numerically less accurate. In this paper, we propose a numerical scheme to improve the accuracy of the L-ORBFs by adding low-degree polynomials in the localized collocation process. The numerical results validate that the proposed numerical scheme is highly accurate and clearly outperforms the results of the L-ORBFs. Full article
(This article belongs to the Section Computational and Applied Mathematics)
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13 pages, 4333 KiB  
Article
Projection and Contraction Method for Pricing American Bond Options
Mathematics 2023, 11(22), 4689; https://doi.org/10.3390/math11224689 - 18 Nov 2023
Viewed by 533
Abstract
In this paper, an effective numerical method is proposed for a linear complementarity problem (LCP) arising in the valuation of American bond options under the Cox–Ingersoll–Ross (CIR) model. Firstly, a variable substitution is used to simplify the linear complementary model. Secondly, the finite [...] Read more.
In this paper, an effective numerical method is proposed for a linear complementarity problem (LCP) arising in the valuation of American bond options under the Cox–Ingersoll–Ross (CIR) model. Firstly, a variable substitution is used to simplify the linear complementary model. Secondly, the finite difference method is adopted to discretize the simplified model, and an equivalent variational form is obtained. Based on the positive definiteness of the discretized matrix, a projection and contraction method (PCM) is adopted for the resulting discretized variational problem. Finally, numerical experiments highlight the effectiveness and performance of the proposed algorithm. Full article
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18 pages, 410 KiB  
Article
Updating Utility Functions on Preordered Sets
Mathematics 2023, 11(22), 4688; https://doi.org/10.3390/math11224688 - 17 Nov 2023
Viewed by 590
Abstract
We consider the problem of extending a function fP defined on a subset P of an arbitrary set X to X strictly monotonically with respect to a preorder ≽ defined on X , without imposing continuity constraints. We show that whenever ≽ [...] Read more.
We consider the problem of extending a function fP defined on a subset P of an arbitrary set X to X strictly monotonically with respect to a preorder ≽ defined on X , without imposing continuity constraints. We show that whenever ≽ has a utility representation, fP is extendable if and only if it is gap-safe increasing. This property means that whenever xx, the infimum of fP on the upper contour of x exceeds the supremum of fP on the lower contour of x, where x, xX˜ and X˜ is X completed with two absolute ≽-extrema and, moreover, fP is weakly increasing. The completion of X makes the condition sufficient. The proposed method of extension is flexible in the sense that for any bounded utility representation u of ≽, it provides an extension of fP that coincides with u on a region of X that includes the set of P-neutral elements of X . An analysis of related topological theorems shows that the results obtained are not their consequences. The necessary and sufficient condition of extendability and the form of the extension are simplified when P is a Pareto set. Full article
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20 pages, 4473 KiB  
Article
Determination of Reservoir Oxidation Zone Formation in Uranium Wells Using Ensemble Machine Learning Methods
Mathematics 2023, 11(22), 4687; https://doi.org/10.3390/math11224687 - 17 Nov 2023
Viewed by 678
Abstract
Approximately 50% of the world’s uranium is mined in a closed way using underground well leaching. In the process of uranium mining at formation-infiltration deposits, an important role is played by the correct identification of the formation of reservoir oxidation zones (ROZs), within [...] Read more.
Approximately 50% of the world’s uranium is mined in a closed way using underground well leaching. In the process of uranium mining at formation-infiltration deposits, an important role is played by the correct identification of the formation of reservoir oxidation zones (ROZs), within which the uranium content is extremely low and which affect the determination of ore reserves and subsequent mining processes. The currently used methodology for identifying ROZs requires the use of highly skilled labor and resource-intensive studies using neutron fission logging; therefore, it is not always performed. At the same time, the available electrical logging measurements data collected in the process of geophysical well surveys and exploration well data can be effectively used to identify ROZs using machine learning models. This study presents a solution to the problem of detecting ROZs in uranium deposits using ensemble machine learning methods. This method provides an index of weighted harmonic measure (f1_weighted) in the range from 0.72 to 0.93 (XGB classifier), and sufficient stability at different ratios of objects in the input dataset. The obtained results demonstrate the potential for practical use of this method for detecting ROZs in formation-infiltration uranium deposits using ensemble machine learning. Full article
(This article belongs to the Special Issue Advances in Machine Learning and Applications)
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16 pages, 2878 KiB  
Article
Optimal Transport and Seismic Rays
Mathematics 2023, 11(22), 4686; https://doi.org/10.3390/math11224686 - 17 Nov 2023
Viewed by 749
Abstract
We present a theoretical framework that links Fermat’s principle of least time to optimal transport theory via a cost function that enforces local transport. The proposed cost function captures the physical constraints inherent in wave propagation; when paired with specific mass distributions, it [...] Read more.
We present a theoretical framework that links Fermat’s principle of least time to optimal transport theory via a cost function that enforces local transport. The proposed cost function captures the physical constraints inherent in wave propagation; when paired with specific mass distributions, it yields shortest paths in the considered media through the optimal transport plans. In the discrete setting, our formulation results in physically significant optimal couplings, whose off-diagonal entries identify shortest paths in both directed and undirected graphs. For undirected graphs with positive edge weights, commonly used to parameterize seismic media, our method provides solutions to the Eikonal equation consistent with those from the Dijkstra algorithm. For directed negative-weight graphs, corresponding to transportation cost matrices with negative entries, our approach aligns with the Bellman–Ford algorithm but offers considerable computational advantages. We also highlight potential research directions. These include the use of sparse cost matrices to reduce the number of unknowns and constraints in the considered transportation problem, and solving specific classes of optimal transport problems through the Dijkstra algorithm to enhance computational efficiency. Full article
(This article belongs to the Special Issue Mathematical Modeling in Geophysics: Concepts and Practices)
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19 pages, 392 KiB  
Article
Optimal Non-Asymptotic Bounds for the Sparse β Model
Mathematics 2023, 11(22), 4685; https://doi.org/10.3390/math11224685 - 17 Nov 2023
Viewed by 429
Abstract
This paper investigates the sparse β model with 𝓁1 penalty in the field of network data models, which is a hot topic in both statistical and social network research. We present a refined algorithm designed for parameter estimation in the proposed model. [...] Read more.
This paper investigates the sparse β model with 𝓁1 penalty in the field of network data models, which is a hot topic in both statistical and social network research. We present a refined algorithm designed for parameter estimation in the proposed model. Its effectiveness is highlighted through its alignment with the proximal gradient descent method, stemming from the convexity of the loss function. We study the estimation consistency and establish an optimal bound for the proposed estimator. Empirical validations facilitated through meticulously designed simulation studies corroborate the efficacy of our methodology. These assessments highlight the prospective contributions of our methodology to the advanced field of network data analysis. Full article
(This article belongs to the Special Issue New Advances in High-Dimensional and Non-asymptotic Statistics)
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14 pages, 339 KiB  
Article
Convergence of the Euler Method for Impulsive Neutral Delay Differential Equations
Mathematics 2023, 11(22), 4684; https://doi.org/10.3390/math11224684 - 17 Nov 2023
Viewed by 432
Abstract
In this paper, we are concerned with a fixed stepsize Euler method for a class of linear impulsive neutral delay differential equations. By taking the partition nodes for the Euler scheme and employing the linear interpolation, we strictly prove the method is convergent [...] Read more.
In this paper, we are concerned with a fixed stepsize Euler method for a class of linear impulsive neutral delay differential equations. By taking the partition nodes for the Euler scheme and employing the linear interpolation, we strictly prove the method is convergent of order one. Two examples illustrating the efficiency results are also presented. Full article
(This article belongs to the Special Issue Computational Mathematics and Numerical Analysis)
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16 pages, 323 KiB  
Article
Metallic Structures for Tangent Bundles over Almost Quadratic ϕ-Manifolds
Mathematics 2023, 11(22), 4683; https://doi.org/10.3390/math11224683 - 17 Nov 2023
Viewed by 565
Abstract
This paper aims to explore the metallic structure J2=pJ+qI, where p and q are natural numbers, using complete and horizontal lifts on the tangent bundle TM over almost quadratic ϕ-structures (briefly, [...] Read more.
This paper aims to explore the metallic structure J2=pJ+qI, where p and q are natural numbers, using complete and horizontal lifts on the tangent bundle TM over almost quadratic ϕ-structures (briefly, (ϕ,ξ,η)). Tensor fields F˜ and F* are defined on TM, and it is shown that they are metallic structures over (ϕ,ξ,η). Next, the fundamental 2-form Ω and its derivative dΩ, with the help of complete lift on TM over (ϕ,ξ,η), are evaluated. Furthermore, the integrability conditions and expressions of the Lie derivative of metallic structures F˜ and F* are determined using complete and horizontal lifts on TM over (ϕ,ξ,η), respectively. Finally, we prove the existence of almost quadratic ϕ-structures on TM with non-trivial examples. Full article
(This article belongs to the Special Issue Differential Geometry: Structures on Manifolds and Submanifolds)
12 pages, 1848 KiB  
Article
Causality-Driven Efficient Feature Selection for Deep-Learning-Based Surface Roughness Prediction in Milling Machines
Mathematics 2023, 11(22), 4682; https://doi.org/10.3390/math11224682 - 17 Nov 2023
Cited by 1 | Viewed by 507
Abstract
This paper studies the application of artificial intelligence to milling machines, focusing specifically on identifying the inputs (features) required for predicting surface roughness. Previous studies have extensively reviewed and presented useful features for surface roughness prediction. However, applying research findings to actual operational [...] Read more.
This paper studies the application of artificial intelligence to milling machines, focusing specifically on identifying the inputs (features) required for predicting surface roughness. Previous studies have extensively reviewed and presented useful features for surface roughness prediction. However, applying research findings to actual operational factories can be challenging due to the additional costs of sensor installations and the diverse environments present in each factory setting. To address these issues, in this paper, we introduced effective features for predicting surface roughness in situations where additional sensors are not installed in the existing environment. These features include feed per tooth, Fz; material removal rate, Q; and the load information. These features are suitable for use in highly constrained environments where separate sensor installation is not required, making it possible to apply the research findings in various factory environments. Additionally, to efficiently select the optimal subset for surface roughness prediction among subsets formed by available features, we apply causality to the feature selection method, proposing an approach called causality-driven efficient feature selection. The experimental results demonstrate that the features introduced in this paper are quite suitable for predicting surface roughness and that the proposed feature selection approach is more effective and efficient compared to existing selection methods. Full article
(This article belongs to the Special Issue Industrial Big Data and Process Modelling for Smart Manufacturing)
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15 pages, 4026 KiB  
Article
WT-CNN: A Hybrid Machine Learning Model for Heart Disease Prediction
Mathematics 2023, 11(22), 4681; https://doi.org/10.3390/math11224681 - 17 Nov 2023
Cited by 1 | Viewed by 967
Abstract
Heart disease remains a predominant health challenge, being the leading cause of death worldwide. According to the World Health Organization (WHO), cardiovascular diseases (CVDs) take an estimated 17.9 million lives each year, accounting for 32% of all global deaths. Thus, there is a [...] Read more.
Heart disease remains a predominant health challenge, being the leading cause of death worldwide. According to the World Health Organization (WHO), cardiovascular diseases (CVDs) take an estimated 17.9 million lives each year, accounting for 32% of all global deaths. Thus, there is a global health concern necessitating accurate prediction models for timely intervention. Several data mining techniques are used by researchers to help healthcare professionals to predict heart disease. However, the traditional machine learning models for predicting heart disease often struggle with handling imbalanced datasets. Moreover, when prediction is on the bases of complex data like ECG, feature extraction and selecting the most pertinent features that accurately represent the underlying pathophysiological conditions without succumbing to overfitting is also a challenge. In this paper, a continuous wavelet transformation and convolutional neural network-based hybrid model abbreviated as WT-CNN is proposed. The key phases of WT-CNN are ECG data collection, preprocessing, RUSBoost-based data balancing, CWT-based feature extraction, and CNN-based final prediction. Through extensive experimentation and evaluation, the proposed model achieves an exceptional accuracy of 97.2% in predicting heart disease. The experimental results show that the approach improves classification accuracy compared to other classification approaches and that the presented model can be successfully used by healthcare professionals for predicting heart disease. Furthermore, this work can have a potential impact on improving heart disease prediction and ultimately enhancing patient lifestyle. Full article
(This article belongs to the Section Fuzzy Sets, Systems and Decision Making)
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11 pages, 284 KiB  
Article
An Application for Bi-Concave Functions Associated with q-Convolution
Mathematics 2023, 11(22), 4680; https://doi.org/10.3390/math11224680 - 17 Nov 2023
Viewed by 462
Abstract
The aim of this paper is to introduce and investigate some new subclasses of bi-concave functions using q-convolution and some applications. These special cases are obtaining by making use of a q- derivative linear operator. For the new introduced subclasses, the [...] Read more.
The aim of this paper is to introduce and investigate some new subclasses of bi-concave functions using q-convolution and some applications. These special cases are obtaining by making use of a q- derivative linear operator. For the new introduced subclasses, the authors obtain the first two initial Taylor–Maclaurin coefficients |c2| and |c3| of bi-concave functions. For certain values of the parameters, the authors deduce interesting corollaries for coefficient bounds which imply special cases of the new introduced operator. Also, we develop two examples for coefficients |c2| and |c3| for certain functions. Full article
(This article belongs to the Special Issue Current Topics in Geometric Function Theory)
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