Mathematics

19 pages, 6448 KiB

Open AccessArticle

Optimal Control Design and Online Controller-Area-Network Bus Data Analysis for a Light Commercial Hybrid Electric Vehicle

by Aminu Babangida, Chiedozie Maduakolam Light Odazie and Péter Tamás Szemes

Mathematics 2023, 11(15), 3436; https://doi.org/10.3390/math11153436 - 7 Aug 2023

Cited by 7 | Viewed by 2812

Abstract

In this article, a hybrid powertrain for the Volkswagen (VW) Crafter is designed using the Model-In-The-Loop (MIL) method. An enhanced Proportional-Integral (PI) control technique based on integral cost functions is developed by carrying out a time-based simulation in MATLAB/Simulink software to realize the [...] Read more.

In this article, a hybrid powertrain for the Volkswagen (VW) Crafter is designed using the Model-In-The-Loop (MIL) method. An enhanced Proportional-Integral (PI) control technique based on integral cost functions is developed by carrying out a time-based simulation in MATLAB/Simulink software to realize the optimal fuel economy of the vehicle. Moreover, a comparative study is conducted between the vehicle’s hybrid and pure electric versions to assess the optimal battery energy consumption per unit distance traveled. Communication within our vehicles’ Electronic Control Units (ECUs) is facilitated by a message-based protocol called a Controller Area Network (CAN). Consequently, this paper presents an online CAN Bus data analysis using the Hardware-In-The-Loop (HIL) method. This method uses a standard frame, J1939 CAN protocol, implemented with Net CAN Plus 110 hardware. A graphical user interface is developed on a host Personal Computer (PC) using LabVIEW for decoding the acquired raw CAN data to physical values. The simulation results reveal that the proposed controller is promising and suitable for realizing optimal performance over the HIL method. Full article

(This article belongs to the Special Issue Dynamics and Control Theory with Applications)

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17 pages, 365 KiB

Open AccessArticle

Fixed Point Results in Controlled Fuzzy Metric Spaces with an Application to the Transformation of Solar Energy to Electric Power

by Umar Ishtiaq, Doha A. Kattan, Khaleel Ahmad, Salvatore Sessa and Farhan Ali

Mathematics 2023, 11(15), 3435; https://doi.org/10.3390/math11153435 - 7 Aug 2023

Cited by 3 | Viewed by 1004

Abstract

In this manuscript, we give sufficient conditions for a sequence to be Cauchy in the context of controlled fuzzy metric space. Furthermore, we generalize the concept of Banach’s contraction principle by utilizing several new contraction conditions and prove several fixed point results. Furthermore, [...] Read more.

In this manuscript, we give sufficient conditions for a sequence to be Cauchy in the context of controlled fuzzy metric space. Furthermore, we generalize the concept of Banach’s contraction principle by utilizing several new contraction conditions and prove several fixed point results. Furthermore, we provide a number of non-trivial examples to validate the superiority of main results in the existing literature. At the end, we discuss an important application to the transformation of solar energy to electric power by utilizing differential equations. Full article

(This article belongs to the Special Issue Fixed Point, Optimization, and Applications II)

28 pages, 1067 KiB

Open AccessArticle

Analysis of U-V2X Communications with Non-Clustered and Clustered Jamming in the Presence of Fluctuating UAV Beam Width

by Mohammad Arif and Wooseong Kim

Mathematics 2023, 11(15), 3434; https://doi.org/10.3390/math11153434 - 7 Aug 2023

Cited by 4 | Viewed by 1368

Abstract

Jammers emit strong intentional jamming signals aiming to limit or block legitimate communications. The distribution of jammers, whether in non-clustered or clustered form, significantly influences the performance of vehicle-to-everything (V2X) networks. In addition, the fluctuations in the three-dimensional (3D) antenna beam width of [...] Read more.

Jammers emit strong intentional jamming signals aiming to limit or block legitimate communications. The distribution of jammers, whether in non-clustered or clustered form, significantly influences the performance of vehicle-to-everything (V2X) networks. In addition, the fluctuations in the three-dimensional (3D) antenna beam width of unmanned aerial vehicles (UAVs) can exert a substantial impact on the network’s overall performance. This paper introduces a model for UAV-V2X (U-V2X) communications in mm-Wave bands, considering non-clustered and clustered jammers, as well as the varying 3D antenna beam width. The roads are modeled using a Poisson line process, vehicular nodes (VNs) are modeled using a 1D Poisson point process (PPP), and UAVs are modeled using a 3D PPP. The jammers are distributed in two ways: non-clustered and clustered distributions. Moreover, the fluctuations in the 3D antenna beam width follow a normal distribution. To this end, a typical node’s performance in U-V2X communications is evaluated for various network configurations, including the number of UAVs, VNs, roads, jammers, and jammer’s transmission power. The analytical expressions for the outage probability (OP) of VN to VN connection (i.e., V2V), VN to UAV connection (i.e., V2U2V), and an overall connection (i.e., U-V2X), under non-clustered and clustered jamming, along with the fluctuating antenna beam width, are derived. The results revealed that the performance of the U-V2X communications utilizing mm-Waves is significantly degraded with the non-clustered jamming in comparison with the clustered jamming. The fluctuations in the 3D beam width of the UAV antennas further compromise the network’s performance. Thus, accurate modeling of these fluctuations is crucial, particularly in the presence of non-clustered jammers. Furthermore, the system designers should focus on implementing additional anti-jamming countermeasures specifically targeting non-clustered jammers in U-V2X communications. Full article

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22 pages, 701 KiB

Open AccessFeature PaperArticle

Clustering Methods over the Tropical Projective Torus

by David Barnhill and Ruriko Yoshida

Mathematics 2023, 11(15), 3433; https://doi.org/10.3390/math11153433 - 7 Aug 2023

Cited by 2 | Viewed by 1416

Abstract

In this paper, we propose clustering methods for use on data described as tropically convex. Our approach is similar to clustering methods used in the Euclidean space, where we identify groupings of similar observations using tropical analogs of K-means and hierarchical clustering in [...] Read more.

In this paper, we propose clustering methods for use on data described as tropically convex. Our approach is similar to clustering methods used in the Euclidean space, where we identify groupings of similar observations using tropical analogs of K-means and hierarchical clustering in the Euclidean space. We provide results from computational experiments on generic simulated data as well as an application to phylogeny using ultrametrics, demonstrating the efficacy of these methods. Full article

(This article belongs to the Section Algebra, Geometry and Topology)

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14 pages, 312 KiB

Open AccessArticle

Inverse Problem for a Fourth-Order Hyperbolic Equation with a Complex-Valued Coefficient

by Asselkhan Imanbetova, Abdissalam Sarsenbi and Bolat Seilbekov

Mathematics 2023, 11(15), 3432; https://doi.org/10.3390/math11153432 - 7 Aug 2023

Cited by 3 | Viewed by 1041

Abstract

This paper studies the existence and uniqueness of the classical solution of inverse problems for a fourth-order hyperbolic equation with a complex-valued coefficient with Dirichlet and Neumann boundary conditions. Using the method of separation of variables, formal solutions are obtained in the form [...] Read more.

This paper studies the existence and uniqueness of the classical solution of inverse problems for a fourth-order hyperbolic equation with a complex-valued coefficient with Dirichlet and Neumann boundary conditions. Using the method of separation of variables, formal solutions are obtained in the form of a Fourier series in terms of the eigenfunctions of a non-self-adjoint fourth-order ordinary differential operator. The proofs of the uniform convergence of the Fourier series are based on estimates of the norms of the derivatives of the eigenfunctions of a fourth-order ordinary differential operator and the uniform boundedness of the Riesz bases of the eigenfunctions. Full article

(This article belongs to the Special Issue Mathematical Analysis and Functional Analysis and Their Applications)

17 pages, 1479 KiB

Open AccessArticle

Hybrid Attitude Saturation and Fault-Tolerant Control for Rigid Spacecraft without Unwinding

by Jun Ma, Zeng Wang and Chang Wang

Mathematics 2023, 11(15), 3431; https://doi.org/10.3390/math11153431 - 7 Aug 2023

Cited by 2 | Viewed by 1075

Abstract

This paper tackles the saturation and fault-tolerant attitude tracking problem without unwinding for rigid spacecraft with external disturbances and partial loss of actuator effectiveness faults. A hybrid saturation and fault-tolerant attitude control (HSFC) is proposed. The Lyapunov method is employed to prove that [...] Read more.

This paper tackles the saturation and fault-tolerant attitude tracking problem without unwinding for rigid spacecraft with external disturbances and partial loss of actuator effectiveness faults. A hybrid saturation and fault-tolerant attitude control (HSFC) is proposed. The Lyapunov method is employed to prove that the tracking errors of the spacecraft system tend to the equilibrium point asymptotically with HSFC. The advantages of the HSFC are that it is fault-tolerant, anti-unwinding and explicitly upper bounded a priori which means that both actuator saturation and the unwinding phenomenon can be avoided. Simulations verify the effectiveness of the proposed approach. Full article

(This article belongs to the Special Issue Advanced Guidance and Control of Flight Vehicle: Theory and Application)

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13 pages, 386 KiB

Open AccessArticle

Investigation of the Product of Random Matrices and Related Evolution Models

by Hirobumi Mineo, Vladimir Suvorov and David B. Saakian

Mathematics 2023, 11(15), 3430; https://doi.org/10.3390/math11153430 - 7 Aug 2023

Cited by 1 | Viewed by 1384

Abstract

In this paper, we study the phase structure of the product of D * D order matrices. In each round, we randomly choose a matrix from a finite set of d matrices and multiply it with the product from the previous round. Initially, [...] Read more.

In this paper, we study the phase structure of the product of D * D order matrices. In each round, we randomly choose a matrix from a finite set of d matrices and multiply it with the product from the previous round. Initially, we derived a functional equation for the case of matrices with real eigenvalues and correlated choice of matrices, which led to the identification of several phases. Subsequently, we explored the case of uncorrelated choice of matrices and derived a simpler functional equation, again identifying multiple phases. In our investigation, we observed a phase with a smooth distribution in steady-state and phases with singularities. For the general case of D-dimensional matrices, we derived a formula for the phase transition point. Additionally, we solved a related evolution model. Moreover, we examined the relaxation dynamics of the considered models. In both the smooth phase and the phase with singularities, the relaxation is exponential. The superiority of relaxation in the smooth phase depends on the specific case. Full article

(This article belongs to the Section Mathematical Biology)

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11 pages, 271 KiB

Open AccessArticle

On Effective Fine Functions for Inspection—Corruption Games (Evolutionary Approach)

by Vassili N. Kolokoltsov and Dmitri V. Vetchinnikov

Mathematics 2023, 11(15), 3429; https://doi.org/10.3390/math11153429 - 7 Aug 2023

Viewed by 1003

Abstract

In previous papers of the authors, a generalized evolutionary approach was developed for the analysis of popular inspection and corruption games. Namely, a two-level hierarchy was studied, where a local inspector I of a pool of agents (that may break the law) can [...] Read more.

In previous papers of the authors, a generalized evolutionary approach was developed for the analysis of popular inspection and corruption games. Namely, a two-level hierarchy was studied, where a local inspector I of a pool of agents (that may break the law) can be corrupted and is further controlled by the higher authority A. Here, we extend this two-level modeling by answering the following questions: (i) what levels of illegal profit r of violators and what level of bribes α (fraction of illegal profit asked as a bribe from a violator) of an inspector are feasible, that is, realizable in stable equilibria of generalized replicator dynamics; and (ii) what α can be optimal for a corrupted inspector that aims at maximizing the total profit. Concrete settings that we have in mind are illegal logging, the sales of products with substandard quality, and tax evasion. Full article

(This article belongs to the Special Issue Multi-Agent Systems of Competitive and Cooperative Interaction)

10 pages, 1256 KiB

Open AccessArticle

Anomaly Detection in the Molecular Structure of Gallium Arsenide Using Convolutional Neural Networks

by Timothy Roche, Aihua Wood, Philip Cho and Chancellor Johnstone

Mathematics 2023, 11(15), 3428; https://doi.org/10.3390/math11153428 - 7 Aug 2023

Viewed by 1134

Abstract

This paper concerns the development of a machine learning tool to detect anomalies in the molecular structure of Gallium Arsenide. We employ a combination of a CNN and a PCA reconstruction to create the model, using real images taken with an electron microscope [...] Read more.

This paper concerns the development of a machine learning tool to detect anomalies in the molecular structure of Gallium Arsenide. We employ a combination of a CNN and a PCA reconstruction to create the model, using real images taken with an electron microscope in training and testing. The methodology developed allows for the creation of a defect detection model, without any labeled images of defects being required for training. The model performed well on all tests under the established assumptions, allowing for reliable anomaly detection. To the best of our knowledge, such methods are not currently available in the open literature; thus, this work fills a gap in current capabilities. Full article

(This article belongs to the Special Issue Applied Mathematics and Machine Learning)

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12 pages, 329 KiB

Open AccessArticle

A Hypersurfaces of Revolution Family in the Five-Dimensional Pseudo-Euclidean Space

E_{2}^{5}

by Yanlin Li and Erhan Güler

Mathematics 2023, 11(15), 3427; https://doi.org/10.3390/math11153427 - 7 Aug 2023

Cited by 19 | Viewed by 1789

Abstract

We present a family of hypersurfaces of revolution distinguished by four parameters in the five-dimensional pseudo-Euclidean space

E_{2}^{5}

. The matrices corresponding to the fundamental form, Gauss map, and shape operator of this family are computed. By utilizing the Cayley–Hamilton theorem, [...] Read more.

We present a family of hypersurfaces of revolution distinguished by four parameters in the five-dimensional pseudo-Euclidean space

E_{2}^{5}

. The matrices corresponding to the fundamental form, Gauss map, and shape operator of this family are computed. By utilizing the Cayley–Hamilton theorem, we determine the curvatures of the specific family. Furthermore, we establish the criteria for maximality within this framework. Additionally, we reveal the relationship between the Laplace–Beltrami operator of the family and a

5 \times 5

matrix. Full article

(This article belongs to the Special Issue Advances in Differential Geometry and Its Applications)

16 pages, 6095 KiB

Open AccessArticle

Efficient Maximum Likelihood Algorithm for Estimating Carrier Frequency Offset of Generalized Frequency Division Multiplexing Systems

by Yung-Yi Wang, Bo-Rui Chen and Chih-Hsiang Hsu

Mathematics 2023, 11(15), 3426; https://doi.org/10.3390/math11153426 - 7 Aug 2023

Cited by 2 | Viewed by 1164

Abstract

This study presents a computationally efficient maximum likelihood (ML) algorithm for estimating the carrier frequency offset (CFO) of generalized frequency division multiplexing systems. The proposed algorithm uses repetitive subsymbols and virtual carriers to estimate the fractional and integer CFOs, respectively. Through the use [...] Read more.

This study presents a computationally efficient maximum likelihood (ML) algorithm for estimating the carrier frequency offset (CFO) of generalized frequency division multiplexing systems. The proposed algorithm uses repetitive subsymbols and virtual carriers to estimate the fractional and integer CFOs, respectively. Through the use of repetitive subsymbols, this study first calculates the ML estimate of the fractional CFO in the time domain and then, accordingly, compensates for it from the received signal. The integer CFO can then be estimated through a virtual-carrier-mapping process in the frequency domain. In addition to improving performance in terms of estimation accuracy and computational complexity, the proposed non-data-aided algorithm is spectrally efficient relative to traditional algorithms. Full article

(This article belongs to the Section Engineering Mathematics)

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22 pages, 410 KiB

Open AccessArticle

An Overview of Kriging and Cokriging Predictors for Functional Random Fields

by Ramón Giraldo, Víctor Leiva and Cecilia Castro

Mathematics 2023, 11(15), 3425; https://doi.org/10.3390/math11153425 - 7 Aug 2023

Cited by 2 | Viewed by 2006

Abstract

This article presents an overview of methodologies for spatial prediction of functional data, focusing on both stationary and non-stationary conditions. A significant aspect of the functional random fields analysis is evaluating stationarity to characterize the stability of statistical properties across the spatial domain. [...] Read more.

This article presents an overview of methodologies for spatial prediction of functional data, focusing on both stationary and non-stationary conditions. A significant aspect of the functional random fields analysis is evaluating stationarity to characterize the stability of statistical properties across the spatial domain. The article explores methodologies from the literature, providing insights into the challenges and advancements in functional geostatistics. This work is relevant from theoretical and practical perspectives, offering an integrated view of methodologies tailored to the specific stationarity conditions of the functional processes under study. The practical implications of our work span across fields like environmental monitoring, geosciences, and biomedical research. This overview encourages advancements in functional geostatistics, paving the way for the development of innovative techniques for analyzing and predicting spatially correlated functional data. It lays the groundwork for future research, enhancing our understanding of spatial statistics and its applications. Full article

3 pages, 183 KiB

Open AccessEditorial

Preface to the Special Issue on “Hypergroup Theory and Algebrization of Incidence Structures”

by Dario Fasino and Domenico Freni

Mathematics 2023, 11(15), 3424; https://doi.org/10.3390/math11153424 - 7 Aug 2023

Viewed by 786

Abstract

This work contains the accepted papers of a Special Issue of the MDPI journal Mathematics entitled “Hypergroup Theory and Algebrization of Incidence Structure” [...] Full article

(This article belongs to the Special Issue Hypergroup Theory and Algebrization of Incidence Structures)

18 pages, 303 KiB

Open AccessReview

Quantum Computing in Telecommunication—A Survey

by Frank Phillipson

Mathematics 2023, 11(15), 3423; https://doi.org/10.3390/math11153423 - 6 Aug 2023

Cited by 8 | Viewed by 4782

Abstract

Quantum computing, an emerging paradigm based on the principles of quantum mechanics, has the potential to revolutionise various industries, including Telecommunications. This paper explores the transformative impact of quantum computing on the telecommunication market, focusing on its applications in solving computationally intensive problems. [...] Read more.

Quantum computing, an emerging paradigm based on the principles of quantum mechanics, has the potential to revolutionise various industries, including Telecommunications. This paper explores the transformative impact of quantum computing on the telecommunication market, focusing on its applications in solving computationally intensive problems. By leveraging the inherent properties of quantum systems, such as superposition and entanglement, quantum computers offer the promise of exponential computational speedup and enhanced problem-solving capabilities. This paper provides an in-depth analysis of the current state of quantum computing in telecommunication, examining key algorithms and approaches, discussing potential use cases, and highlighting the challenges and future prospects of this disruptive technology. Full article

(This article belongs to the Special Issue Advances in Quantum Computing and Applications)

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17 pages, 636 KiB

Open AccessArticle

Semi-Analytical Methods in the Problem of Deformation of a Fluid Strip

by Evgenii Karabut and Elena Zhuravleva

Mathematics 2023, 11(15), 3422; https://doi.org/10.3390/math11153422 - 6 Aug 2023

Viewed by 985

Abstract

A problem from a class of unsteady plane potential flows with a free boundary is considered. The entire boundary occupied by the liquid is free, and a zero pressure is maintained. There are neither external nor capillary forces. The motion is driven by [...] Read more.

A problem from a class of unsteady plane potential flows with a free boundary is considered. The entire boundary occupied by the liquid is free, and a zero pressure is maintained. There are neither external nor capillary forces. The motion is driven by inertia. The parameters prescribed at the initial time are the velocity field and the domain occupied by the fluid. The task is to determine these parameters at subsequent time instants. The solution is sought in the form of power series, which are then summed up with the use of the Pade approximation. Full article

(This article belongs to the Special Issue Numerical and Analytical Study of Fluid Dynamics)

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16 pages, 427 KiB

Open AccessArticle

Controlled Invariant Sets of Discrete-Time Linear Systems with Bounded Disturbances

by Chengdan Wang, Hongli Yang and Ivan Ganchev Ivanov

Mathematics 2023, 11(15), 3421; https://doi.org/10.3390/math11153421 - 6 Aug 2023

Cited by 1 | Viewed by 1465

Abstract

This paper proposes two novel methods for computing the robustly controlled invariant set of linear discrete-time systems with additive bounded disturbances. In the proposed methods, the robustly controlled invariant set of discrete-time systems is obtained by solving the linear matrix inequality given by [...] Read more.

This paper proposes two novel methods for computing the robustly controlled invariant set of linear discrete-time systems with additive bounded disturbances. In the proposed methods, the robustly controlled invariant set of discrete-time systems is obtained by solving the linear matrix inequality given by logarithmic norm and difference inequality. Illustrative examples are presented to demonstrate the obtained methods. Full article

(This article belongs to the Section Difference and Differential Equations)

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20 pages, 383 KiB

Open AccessArticle

Differential Properties of Jacobi-Sobolev Polynomials and Electrostatic Interpretation

by Héctor Pijeira-Cabrera, Javier Quintero-Roba and Juan Toribio-Milane

Mathematics 2023, 11(15), 3420; https://doi.org/10.3390/math11153420 - 6 Aug 2023

Cited by 2 | Viewed by 2738

Abstract

We study the sequence of monic polynomials

{S_{n}}_{n ⩾ 0}

, orthogonal with respect to the Jacobi-Sobolev inner product [...] Read more.

We study the sequence of monic polynomials

{S_{n}}_{n ⩾ 0}

, orthogonal with respect to the Jacobi-Sobolev inner product

{⟨ f, g ⟩}_{s} = \int_{- 1}^{1} f (x) g (x) d μ^{α, β} (x) + \sum_{j = 1}^{N} \sum_{k = 0}^{d_{j}} λ_{j, k} f^{(k)} (c_{j}) g^{(k)} (c_{j}),

where

N, d_{j} \in Z_{+}

,

λ_{j, k} ⩾ 0

,

d μ^{α, β} (x) = {(1 - x)}^{α} {(1 + x)}^{β} d x

,

α, β > - 1

, and

c_{j} \in R ∖ (- 1, 1)

. A connection formula that relates the Sobolev polynomials

S_{n}

with the Jacobi polynomials is provided, as well as the ladder differential operators for the sequence

{S_{n}}_{n ⩾ 0}

and a second-order differential equation with a polynomial coefficient that they satisfied. We give sufficient conditions under which the zeros of a wide class of Jacobi-Sobolev polynomials can be interpreted as the solution of an electrostatic equilibrium problem of n unit charges moving in the presence of a logarithmic potential. Several examples are presented to illustrate this interpretation. Full article

(This article belongs to the Special Issue Orthogonal Polynomials and Special Functions: Recent Trends and Their Applications)

10 pages, 503 KiB

Open AccessArticle

Imputing Phylogenetic Trees Using Tropical Polytopes over the Space of Phylogenetic Trees

by Ruriko Yoshida

Mathematics 2023, 11(15), 3419; https://doi.org/10.3390/math11153419 - 6 Aug 2023

Cited by 2 | Viewed by 1221

Abstract

When we apply comparative phylogenetic analyses to genome data, it poses a significant problem and challenge that some of the given species (or taxa) often have missing genes (i.e., data). In such a case, we have to impute a missing part of a [...] Read more.

When we apply comparative phylogenetic analyses to genome data, it poses a significant problem and challenge that some of the given species (or taxa) often have missing genes (i.e., data). In such a case, we have to impute a missing part of a gene tree from a sample of gene trees. In this short paper, we propose a novel method to infer the missing part of a phylogenetic tree using an analogue of a classical linear regression in the setting of tropical geometry. In our approach, we consider a tropical polytope, a convex hull with respect to the tropical metric closest to the data points. We show a condition that we can guarantee that an estimated tree from the method has at most a Robinson–Foulds (RF) distance of four from the ground truth, and computational experiments with simulated data and empirical data from Clavicipitaceae, which contains more than 4000 genes, show the method works well. Full article

(This article belongs to the Special Issue Advanced Computational Biology and Bioinformatics)

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22 pages, 3558 KiB

Open AccessArticle

Spectral Salt-and-Pepper Patch Masking for Self-Supervised Speech Representation Learning

by June-Woo Kim, Hoon Chung and Ho-Young Jung

Mathematics 2023, 11(15), 3418; https://doi.org/10.3390/math11153418 - 5 Aug 2023

Viewed by 1834

Abstract

Recent advanced systems in the speech recognition domain use large Transformer neural networks that have been pretrained on massive speech data. General methods in the deep learning area have been frequently shared across various domains, and the Transformer model can also be used [...] Read more.

Recent advanced systems in the speech recognition domain use large Transformer neural networks that have been pretrained on massive speech data. General methods in the deep learning area have been frequently shared across various domains, and the Transformer model can also be used effectively across speech and image. In this paper, we introduce a novel masking method for self-supervised speech representation learning with salt-and-pepper (S&P) mask which is commonly used in computer vision. The proposed scheme includes consecutive quadrilateral-shaped S&P patches randomly contaminating the input speech spectrum. Furthermore, we modify the standard S&P mask to make it appropriate for the speech domain. In order to validate the effect of the proposed spectral S&P patch masking for the self-supervised representation learning approach, we conduct the pretraining and downstream experiments with two languages, English and Korean. To this end, we pretrain the speech representation model using each dataset and evaluate the pretrained models for feature extraction and fine-tuning performance on varying downstream tasks, respectively. The experimental outcomes clearly illustrate that the proposed spectral S&P patch masking is effective for various downstream tasks when combined with the conventional masking methods. Full article

(This article belongs to the Special Issue Computational Intelligence and Human–Computer Interaction: Modern Methods and Applications, 2nd Edition)

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24 pages, 457 KiB

Open AccessArticle

Cost-Effective Imperfect Production-Inventory System under Variable Production Rate and Remanufacturing

by Baishakhi Ganguly, Bikash Koli Dey, Sarla Pareek and Biswajit Sarkar

Mathematics 2023, 11(15), 3417; https://doi.org/10.3390/math11153417 - 5 Aug 2023

Cited by 1 | Viewed by 1861

Abstract

Several industries are facing many challenges in their production systems due to increasing customer demand. Customer demand is growing for products with innovative features that are flexible, good quality, and appealing. This paper presents a flexible production-inventory system that produces multiple parts of [...] Read more.

Several industries are facing many challenges in their production systems due to increasing customer demand. Customer demand is growing for products with innovative features that are flexible, good quality, and appealing. This paper presents a flexible production-inventory system that produces multiple parts of a product. Defective products may be produced during the production process. Those defective products are remanufactured immediately after inspection. Limited budget and space constraints are considered, along with product assembly. Based on different distribution functions, non-linear equations are calculated using the Kuhn–Tucker optimization technique. Numerical examples, a graphical representation, and sensitivity analysis are presented in this paper. The solution procedure evaluates the minimization of the total investment based on the

χ^{2}

distribution. This study examines electronic products those are more likely to be defective rather than perfect during production. Full article

(This article belongs to the Section Financial Mathematics)

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16 pages, 10872 KiB

Open AccessArticle

Understanding In-Line Connections Behavior from Experimental and Numerical Analyses on Rectangular and Circular Hollow Section Elements

by Calin-Ioan Birdean, Ioan Both, Ioan Mărginean and Anghel Cernescu

Mathematics 2023, 11(15), 3416; https://doi.org/10.3390/math11153416 - 5 Aug 2023

Viewed by 1050

Abstract

Depending on the connection type, especially semi-rigid connections, the analyses of building structures offer accurate results function of the rigidity and ductility. The present paper analyzes the in-line connection of rectangular and circular hollow sections, categorized as semi-rigid connections, suitable for an architectural [...] Read more.

Depending on the connection type, especially semi-rigid connections, the analyses of building structures offer accurate results function of the rigidity and ductility. The present paper analyzes the in-line connection of rectangular and circular hollow sections, categorized as semi-rigid connections, suitable for an architectural design of invisible joints. For such connection the standards do not cover an explicit design method. Experimental bending tests were performed on rectangular and circular hollow sections having the end plate fixed inside the profile and bolted by four and one high-strength bolts, respectively. The joint separation represents a serviceability criterion which was monitored using digital image correlation technique. Based on experimental results, a numerical model was validated using the finite element method. After the validation of the numerical model based on the experimental results, a parametric investigation was conducted to study the influence of the access hole, the preload level, the end plate thickness, and the axial force. The results show the small influence of the bolt preload, but the end plate thickness was of major importance. A reduction of the assembly rigidity was also caused by the manhole. The study shows the feasibility of the connection configuration with the end plate positioned inside the hollow profile. Full article

(This article belongs to the Special Issue Numerical and Computational Methods in Structural Engineering and Mechanics)

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18 pages, 439 KiB

Open AccessArticle

The Optimal Consumption, Investment and Life Insurance for Wage Earners under Inside Information and Inflation

by Rui Jiao, Wei Liu and Yijun Hu

Mathematics 2023, 11(15), 3415; https://doi.org/10.3390/math11153415 - 5 Aug 2023

Viewed by 1291

Abstract

This paper studies the dynamically optimal consumption, investment and life-insurance strategies for a wage earners under inside information and inflation. Assume that the wage earner can invest in a risk-free asset, a risky asset and an inflation-indexed bond and that the wage earner [...] Read more.

This paper studies the dynamically optimal consumption, investment and life-insurance strategies for a wage earners under inside information and inflation. Assume that the wage earner can invest in a risk-free asset, a risky asset and an inflation-indexed bond and that the wage earner can obtain some additional information on the risky asset from the financial market. By maximizing the expected utility of the wage earner’s consumption, inheritance and terminal wealth, we obtain the dynamically optimal consumption, investment and life-insurance strategies for the wage earner. The method of this paper is mainly based on (dynamical) stochastic control theory and the technique of enlargement of filtrations. Moreover, sensitivity analysis is carried out, which reveals that a wage earner with inside information tends to increase his/her consumption and investment, while reducing his/her purchase of life insurance. Full article

(This article belongs to the Special Issue Dynamic Modeling and Simulation for Control Systems, 2nd Edition)

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17 pages, 319 KiB

Open AccessArticle

Expansion Theory of Deng’s Metric in [0,1]-Topology

by Bin Meng, Peng Chen and Xiaohui Ba

Mathematics 2023, 11(15), 3414; https://doi.org/10.3390/math11153414 - 4 Aug 2023

Cited by 1 | Viewed by 1093

Abstract

The aim of this paper is to focus on a fuzzy metric called Deng’s metric in

[0, 1]

-topology. Firstly, we will extend the domain of this metric function from

M_{0} \times M_{0}

to

M \times M

, [...] Read more.

The aim of this paper is to focus on a fuzzy metric called Deng’s metric in

[0, 1]

-topology. Firstly, we will extend the domain of this metric function from

M_{0} \times M_{0}

to

M \times M

, where

M_{0}

and M are defined as the sets of all special fuzzy points and all standard fuzzy points, respectively. Secondly, we will further extend this metric to the completely distributive lattice

L^{X}

and, based on this extension result, we will compare this metric with the other two fuzzy metrics: Erceg’s metric and Yang-Shi’s metric, and then reveal some of its interesting properties, particularly including its quotient space. Thirdly, we will investigate the relationship between Deng’s metric and Yang-Shi’s metric and prove that a Deng’s metric must be a Yang-Shi’s metric on

I^{X}

, and consequently an Erceg’s metric. Finally, we will show that a Deng’s metric on

I^{X}

must be

Q - C_{1}

, and Deng’s metric topology and its uniform structure are Erceg’s metric topology and Hutton’s uniform structure, respectively. Full article

30 pages, 3307 KiB

Open AccessArticle

Dynamic Generation Method of Highway ETC Gantry Topology Based on LightGBM

by Fumin Zou, Weihai Wang, Qiqin Cai, Feng Guo and Rouyue Shi

Mathematics 2023, 11(15), 3413; https://doi.org/10.3390/math11153413 - 4 Aug 2023

Cited by 1 | Viewed by 1591

Abstract

In Electronic Toll Collection (ETC) systems, accurate gantry topology data are crucial for fair and efficient toll collection. Currently, inaccuracies in the topology data can cause tolls to be based on the shortest route rather than the actual distance travelled, contradicting the ETC [...] Read more.

In Electronic Toll Collection (ETC) systems, accurate gantry topology data are crucial for fair and efficient toll collection. Currently, inaccuracies in the topology data can cause tolls to be based on the shortest route rather than the actual distance travelled, contradicting the ETC system’s purpose. To address this, we adopt a novel Gradient Boosting Decision Tree (GBDT) algorithm, Light Gradient Boosting Machine (LightGBM), to dynamically update ETC gantry topology data on highways. We use ETC gantry and toll booth transaction data from a province in southeast China, where ETC usage is high at 72.8%. From this data, we generate a candidate topology set and extract five key characteristics. We then use Amap API and QGIS map analysis to annotate the candidate set, and, finally, apply LightGBM to train on these features, generating the dynamic topology. Our comparison of LightGBM with 14 other machine learning algorithms showed that LightGBM outperformed the others, achieving an impressive accuracy of 97.6%. This methodology can help transportation departments maintain accurate and up-to-date toll systems, reducing errors and improving efficiency. Full article

(This article belongs to the Special Issue Applied Statistical Modeling and Data Mining)

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26 pages, 424 KiB

Open AccessEditor’s ChoiceArticle

A New Instrumental-Type Estimator for Quantile Regression Models

by Li Tao, Lingnan Tai, Manling Qian and Maozai Tian

Mathematics 2023, 11(15), 3412; https://doi.org/10.3390/math11153412 - 4 Aug 2023

Cited by 1 | Viewed by 1319

Abstract

This paper proposes a new instrumental-type estimator of quantile regression models for panel data with fixed effects. The estimator is built upon the minimum distance, which is defined as the weighted average of the conventional individual instrumental variable quantile regression slope estimators. The [...] Read more.

This paper proposes a new instrumental-type estimator of quantile regression models for panel data with fixed effects. The estimator is built upon the minimum distance, which is defined as the weighted average of the conventional individual instrumental variable quantile regression slope estimators. The weights assigned to each estimator are determined by the inverses of their corresponding individual variance–covariance matrices. The implementation of the estimation has many advantages in terms of computational efforts and simplifies the asymptotic distribution. Furthermore, the paper shows consistency and asymptotic normality for sequential and simultaneous asymptotics. Additionally, it presents an empirical application that investigates the income elasticity of health expenditures. Full article

(This article belongs to the Special Issue Statistical Analysis: Theory, Methods and Applications)

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20 pages, 1514 KiB

Open AccessArticle

A Study on the Laney p′ Control Chart with Parameters Estimated from Phase I Data: Performance Evaluation and Applications

by Pei-Wen Chen, Chuen-Sheng Cheng and Ching-Wen Wang

Mathematics 2023, 11(15), 3411; https://doi.org/10.3390/math11153411 - 4 Aug 2023

Cited by 1 | Viewed by 1748

Abstract

The Laney p′ control chart is a new type of attribute control chart that can be applied in situations where the process exhibits either overdispersion or underdispersion. While it has gained acceptance in the industry, there is still limited knowledge about its effectiveness [...] Read more.

The Laney p′ control chart is a new type of attribute control chart that can be applied in situations where the process exhibits either overdispersion or underdispersion. While it has gained acceptance in the industry, there is still limited knowledge about its effectiveness in detecting process variation. It is well known that before applying a control chart, understanding its performance is crucial, especially when the parameters of the control chart need to be estimated from historical data. In this study, we used simulations to investigate the ability of the Laney p′ control chart to detect process variations when the parameters are estimated. We designed appropriate experiments to assess the impact of overdispersion on the average run length (ARL) performance. In this study, we assumed that the overdispersion comes from the variation in the mean fraction nonconforming of each sample. The mean value varies according to a uniform distribution. This study evaluated the performance of the Laney

p^{'}

control chart using the average of the ARL (AARL) and the standard deviation of the ARL (SDARL). Additionally, real-world data were utilized to illustrate the practical applications of the Laney

p^{'}

control chart in the PCB and IC substrate industries. The research findings can serve as valuable guidance for practical implementation. Full article

(This article belongs to the Special Issue Statistical Process Control and Application)

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26 pages, 1802 KiB

Open AccessArticle

The Financial Sustainability of Retail Food SMEs Based on Financial Equilibrium and Financial Performance

by Emilia Herman and Kinga-Emese Zsido

Mathematics 2023, 11(15), 3410; https://doi.org/10.3390/math11153410 - 4 Aug 2023

Cited by 6 | Viewed by 4261

Abstract

The aim of this study was to investigate the financial sustainability of retail food SMEs for the 2016–2021 period, in Romania, from the perspective of financial equilibrium and performance. A multivariate analysis was used, including a correlation analysis, a principal component analysis (PCA), [...] Read more.

The aim of this study was to investigate the financial sustainability of retail food SMEs for the 2016–2021 period, in Romania, from the perspective of financial equilibrium and performance. A multivariate analysis was used, including a correlation analysis, a principal component analysis (PCA), and a cluster analysis. The empirical results show a positive link between the financial performance and financial equilibrium indicators. We employed the PCA in order to build a composite financial index using financial equilibrium indicators (ratios of liquidity, solvency, collection, and payment period) and financial performance indicators (Return on Assets and Return on Equity). The results show that financial equilibrium and performance are the two main dimensions which the financial sustainability index (FSI) was constructed on. Taking into account the dimensions of financial sustainability, the analyzed SMEs were clustered in four homogeneous clusters. The research findings clearly demonstrated that the retail food SMEs with a good/acceptable financial sustainability also have a good/acceptable financial balance and performance situation. Furthermore, a significant part of the analyzed SMEs faces difficulties regarding financial sustainability, being characterized by the lowest values of FSI, determined by both an uncertain situation in terms of liquidity, leading to a financial disequilibrium, and a negative financial performance. Therefore, this research emphasizes some specific measures that need to be taken to boost financial sustainability of these businesses in the retail food sector. Full article

(This article belongs to the Special Issue Statistical Methods of Analyzing Financial Equilibrium, Performance and Risk)

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16 pages, 4798 KiB

Open AccessArticle

Numerical Investigation for Nonlinear Thermal Radiation in MHD Cu–Water Nanofluid Flow in a Channel with Convective Boundary Conditions

by Tunde Abdulkadir Yusuf, Adeshina Taofeeq Adeosun, Victor Olajide Akinsola, Ramoshweu Solomon Lebelo and Oluwadamilare Joseph Akinremi

Mathematics 2023, 11(15), 3409; https://doi.org/10.3390/math11153409 - 4 Aug 2023

Cited by 1 | Viewed by 945

Abstract

The implications of nonlinear thermal radiation on a Cu–water nanofluid flow with varying viscosity characteristics and convective boundary conditions are investigated numerically in this article. The nonlinear model takes the combined effects of Joule dissipation and Ohmic heating into consideration. The Spectral Local [...] Read more.

The implications of nonlinear thermal radiation on a Cu–water nanofluid flow with varying viscosity characteristics and convective boundary conditions are investigated numerically in this article. The nonlinear model takes the combined effects of Joule dissipation and Ohmic heating into consideration. The Spectral Local Linearization Method (SLLM) is used to address the nonlinear governing model. The numerical investigation’s findings were conducted and compared with the existing study. In Cu–water nanofluid flows with variable viscosity and convective boundary conditions, nonlinear thermal radiation plays an important role, as this work insightfully demonstrates. Pertinent results for velocity, temperature, skin friction, and heat transfer rate are displayed graphically and discussed quantitatively with respect to various parameters embedded in the model. The results revealed that the Cu–water thermal distribution lessens as the nanoparticle volume fraction upsurges. The outcomes of this study have potential applications in industrial systems such as power plants, cooling systems, and climate control systems. Full article

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11 pages, 305 KiB

Open AccessArticle

A Class of Relational Functional Contractions with Applications to Nonlinear Integral Equations

by Khursheed J. Ansari, Salvatore Sessa and Aftab Alam

Mathematics 2023, 11(15), 3408; https://doi.org/10.3390/math11153408 - 4 Aug 2023

Cited by 6 | Viewed by 920

Abstract

In this article, we investigate some fixed-point results under certain functional contractive mappings in a relation metric space. In the process, we utilize more general contraction condition which must be verified for comparative elements only. Our results enrich, modify, refine, unify and sharpen [...] Read more.

In this article, we investigate some fixed-point results under certain functional contractive mappings in a relation metric space. In the process, we utilize more general contraction condition which must be verified for comparative elements only. Our results enrich, modify, refine, unify and sharpen several existing fixed-point results. We construct some examples in support of our results. To attest to the applicability of our results, we establish the existence and uniqueness of theorems regarding the solutions of certain nonlinear integral equations. Full article

17 pages, 733 KiB

Open AccessArticle

Edge-Based Minimal k-Core Subgraph Search

by Ting Wang, Yu Jiang, Jianye Yang and Lei Xing

Mathematics 2023, 11(15), 3407; https://doi.org/10.3390/math11153407 - 4 Aug 2023

Cited by 1 | Viewed by 1512

Abstract

In social networks, k-core is commonly used to measure the stability of a network. When a user in a k-core leaves the network, other users may follow the user to leave. Hence, maintaining a key user is important to keep the [...] Read more.

In social networks, k-core is commonly used to measure the stability of a network. When a user in a k-core leaves the network, other users may follow the user to leave. Hence, maintaining a key user is important to keep the stability of a network. It is known that an edge between two users models the relationship between the two users. In some scenarios, maintaining a relationship comes at a cost. Therefore, selectively in maintaining the relationships between users is crucial. In this paper, we for the first time conceive the concept of an edge-based minimal k-core model. An edge-based minimal k-core is a k-core with a minimal number of edges. In other words, removing any edge in an edge-based minimal k-core would make it not be a k-core any more. Based on this model, we proposed two problems, namely, an edge-based minimal k-core subgraph search (EMK-SS) and an edge-based minimal k-core subgraph search with a query node q (EMK-q-SS). Given a graph G, an integer k, and a query node (a key user) q, the EMK-q-SS problem is to find all the edge-based minimal k-cores containing the query node q, and the EMK-SS problem is to find all the edge-based minimal k-cores. We also theoretically prove that the two problems are both NP-complete. To deal with the proposed problems, we design two novel algorithms, namely the edge deletion algorithm and edge extension algorithm. Further, a graph partitioning technique is employed to speed up the computation. Comprehensive experiments on synthetic and real networks are conducted to demonstrate the effect and efficiency of our proposed methods. Full article

(This article belongs to the Special Issue Graph Theory: Advanced Algorithms and Applications)

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Mathematics, Volume 11, Issue 15 (August-1 2023) – 179 articles

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