Mathematics

7 pages, 248 KiB

Open AccessArticle

Nonlinear Volterra Integrodifferential Equations from above on Unbounded Time Scales

by Andrejs Reinfelds and Shraddha Christian

Mathematics 2023, 11(7), 1760; https://doi.org/10.3390/math11071760 - 6 Apr 2023

Cited by 2 | Viewed by 1557

The paper is devoted to studying the existence, uniqueness and certain growth rates of solutions with certain implicit Volterra-type integrodifferential equations on unbounded from above time scales. We consider the case where the integrand is estimated by the Lipschitz type function with respect [...] Read more.

The paper is devoted to studying the existence, uniqueness and certain growth rates of solutions with certain implicit Volterra-type integrodifferential equations on unbounded from above time scales. We consider the case where the integrand is estimated by the Lipschitz type function with respect to the unknown variable. Lipschitz coefficient is an unbounded rd-function and the Banach fixed-point theorem at a functional space endowed with a suitable Bielecki-type norm. Full article

(This article belongs to the Special Issue Differential and Integro–Differential Equations: Theory and Applications)

19 pages, 352 KiB

Open AccessReview

The Askey–Wilson Integral and Extensions

by Wenchang Chu

Mathematics 2023, 11(7), 1759; https://doi.org/10.3390/math11071759 - 6 Apr 2023

Viewed by 1149

Abstract

By means of the q-derivative operator method, we review the q-beta integrals of Askey–Wilson and Nassrallah–Rahman. More integrals are evaluated by the author, making use of Bailey’s identity of well-poised bilateral

_{6} ψ_{6}

-series as well as the extended identity [...] Read more.

By means of the q-derivative operator method, we review the q-beta integrals of Askey–Wilson and Nassrallah–Rahman. More integrals are evaluated by the author, making use of Bailey’s identity of well-poised bilateral

_{6} ψ_{6}

-series as well as the extended identity of Karlsson–Minton type for parameterized well-poised bilateral q-series. Full article

16 pages, 410 KiB

Open AccessArticle

Modelling Heavy Tailed Phenomena Using a LogNormal Distribution Having a Numerically Verifiable Infinite Variance

by Marco Cococcioni, Francesco Fiorini and Michele Pagano

Mathematics 2023, 11(7), 1758; https://doi.org/10.3390/math11071758 - 6 Apr 2023

Cited by 3 | Viewed by 4922

Abstract

One-sided heavy tailed distributions have been used in many engineering applications, ranging from teletraffic modelling to financial engineering. In practice, the most interesting heavy tailed distributions are those having a finite mean and a diverging variance. The LogNormal distribution is sometimes discarded from [...] Read more.

One-sided heavy tailed distributions have been used in many engineering applications, ranging from teletraffic modelling to financial engineering. In practice, the most interesting heavy tailed distributions are those having a finite mean and a diverging variance. The LogNormal distribution is sometimes discarded from modelling heavy tailed phenomena because it has a finite variance, even when it seems the most appropriate one to fit the data. In this work we provide for the first time a LogNormal distribution having a finite mean and a variance which converges to a well-defined infinite value. This is possible thanks to the use of Non-Standard Analysis. In particular, we have been able to obtain a Non-Standard LogNormal distribution, for which it is possible to numerically and experimentally verify whether the expected mean and variance of a set of generated pseudo-random numbers agree with the theoretical ones. Moreover, such a check would be much more cumbersome (and sometimes even impossible) when considering heavy tailed distributions in the traditional framework of standard analysis. Full article

(This article belongs to the Section Engineering Mathematics)

23 pages, 9572 KiB

Open AccessArticle

Design of Continuous Finite-Time Controller Based on Adaptive Tuning Approach for Disturbed Boost Converters

by Hammad Alnuman, Kuo-Hsien Hsia, Mohammadreza Askari Sepestanaki, Emad M. Ahmed, Saleh Mobayen and Ammar Armghan

Mathematics 2023, 11(7), 1757; https://doi.org/10.3390/math11071757 - 6 Apr 2023

Cited by 1 | Viewed by 1482

Abstract

This research study proposes a continuous finite-time controller based on the adaptive tuning approach for the boost converters with unknown disturbances. A Lyapunov candidate function which contains an absolute function based on the fractional power of the sliding surface is employed to attain [...] Read more.

This research study proposes a continuous finite-time controller based on the adaptive tuning approach for the boost converters with unknown disturbances. A Lyapunov candidate function which contains an absolute function based on the fractional power of the sliding surface is employed to attain a smooth continuous control input. The recommended technique can eliminate the chattering phenomenon made by the sliding mode control signal and improve the control performance. Furthermore, the continuous adaptive-tuning control law is given to estimate the unknown bounds of exterior disturbances. The performance of the adaptive-tuned terminal sliding mode control law to the load variations and parametric uncertainties, and the input voltage, are studied in the MATLAB-Simulink environment. The obtained simulation results confirm the effectiveness of the suggested technique. Full article

► Show Figures

Figure 1

19 pages, 358 KiB

Open AccessArticle

Generalized Čebyšev and Grüss Type Results in Weighted Lebesgue Spaces

by Saad Ihsan Butt, Josip Pečarić and Sanja Tipurić-Spužević

Mathematics 2023, 11(7), 1756; https://doi.org/10.3390/math11071756 - 6 Apr 2023

Cited by 1 | Viewed by 919

Abstract

The classical Grüss and related inequalities have spurred a range of improvements, refinements, generalizations, and extensions. In the present article, we provide generalizations of Sokolov’s inequality in weighted Lebesgue

L_{ω} (Ω, A, μ)

spaces by employing the weighted Sonin’s identity [...] Read more.

The classical Grüss and related inequalities have spurred a range of improvements, refinements, generalizations, and extensions. In the present article, we provide generalizations of Sokolov’s inequality in weighted Lebesgue

L_{ω} (Ω, A, μ)

spaces by employing the weighted Sonin’s identity and Čebyšev functional. As a result, we provide a generalized Grüss inequality in which the bounding constants are improved with bounding functions in

L_{ω}^{p} (Ω, A, μ)

spaces. As an application, we provide several new bounds for Jensen–Grüss type differences. Full article

18 pages, 4475 KiB

Open AccessArticle

Breathers, Transformation Mechanisms and Their Molecular State of a (3+1)-Dimensional Generalized Yu–Toda–Sasa–Fukuyama Equation

by Jian Zhang, Juan Yue, Zhonglong Zhao and Yufeng Zhang

Mathematics 2023, 11(7), 1755; https://doi.org/10.3390/math11071755 - 6 Apr 2023

Viewed by 1313

Abstract

A (3+1)-dimensional generalized Yu–Toda–Sasa–Fukuyama equation is considered systematically. N-soliton solutions are obtained using Hirota’s bilinear method. The employment of the complex conjugate condition of parameters of N-soliton solutions leads to the construction of breather solutions. Then, the lump solution is obtained [...] Read more.

A (3+1)-dimensional generalized Yu–Toda–Sasa–Fukuyama equation is considered systematically. N-soliton solutions are obtained using Hirota’s bilinear method. The employment of the complex conjugate condition of parameters of N-soliton solutions leads to the construction of breather solutions. Then, the lump solution is obtained with the aid of the long-wave limit method. Based on the transformation mechanism of nonlinear waves, a series of nonlinear localized waves can be transformed from breathers, which include the quasi-kink soliton, M-shaped kink soliton, oscillation M-shaped kink soliton, multi-peak kink soliton, and quasi-periodic wave by analyzing the characteristic lines. Furthermore, the molecular state of the transformed two-breather is studied using velocity resonance, which is divided into three aspects, namely the modes of non-, semi-, and full transformation. The analytical method discussed in this paper can be further applied to the investigation of other complex high-dimensional nonlinear integrable systems. Full article

(This article belongs to the Section Mathematical Physics)

► Show Figures

Figure 1

10 pages, 265 KiB

Open AccessArticle

Spectrum of Zariski Topology in Multiplication Krasner Hypermodules

by Ergül Türkmen, Burcu Nişancı Türkmen and Öznur Kulak

Mathematics 2023, 11(7), 1754; https://doi.org/10.3390/math11071754 - 6 Apr 2023

Viewed by 1034

Abstract

In this paper, we define the concept of pseudo-prime subhypermodules of hypermodules as a generalization of the prime hyperideal of commutative hyperrings. In particular, we examine the spectrum of the Zariski topology, which we built on the element of the pseudo-prime subhypermodules of [...] Read more.

In this paper, we define the concept of pseudo-prime subhypermodules of hypermodules as a generalization of the prime hyperideal of commutative hyperrings. In particular, we examine the spectrum of the Zariski topology, which we built on the element of the pseudo-prime subhypermodules of a class of hypermodules. Moreover, we provide some relevant properties of the hypermodule in this topological hyperspace. Full article

(This article belongs to the Special Issue Topological Space and Its Applications)

29 pages, 12246 KiB

Open AccessArticle

Genesis Analysis of Special Deformation Characteristics for Super-High Arch Dams in the Alpine and Gorge Regions of Southwest China

by Chenfei Shao, Erfeng Zhao, Yanxin Xu, Sen Zheng and Shiguang Tian

Mathematics 2023, 11(7), 1753; https://doi.org/10.3390/math11071753 - 6 Apr 2023

Cited by 6 | Viewed by 1569

Abstract

During the operational period, unexpected upstream deformation has been observed in several super-high arch dams located in the alpine and gorge regions. In addition, the phenomenon of the downstream dam deformation monitoring values being apparently smaller than the numerical simulation results appears in [...] Read more.

During the operational period, unexpected upstream deformation has been observed in several super-high arch dams located in the alpine and gorge regions. In addition, the phenomenon of the downstream dam deformation monitoring values being apparently smaller than the numerical simulation results appears in some super-high arch dams. This paper focuses on the genetic mechanism of a super-high arch dam’s special deformation characteristics. The finite element method (FEM) was used to analyze the effects of solar radiation, valley contraction, and overhanging on super-high arch dam’s deformation behavior. First, the influences of solar radiation on the temperature field and deformation characteristics of the super-high arch dam under the shading effects of the mountain and the dam body were investigated. Second, the impacts of valley contraction on the deformation characteristics of the super-high arch dam during the storage period were studied. Subsequently, the impact of the overhanging effect on the super-high arch dam’s deformation was explored. Finally, a case study was conducted on the basis of the Jinping I super-high arch dam to evaluate the effectiveness of the proposed analytical method. It is indicated that the dam’s special deformation can be explained reasonably. Above all, in order to accurately analyze and predict the deformation characteristics of super high-arch dams in the alpine and gorge regions of Southwest China, solar radiation, valley contraction, and the dam-overhanging effect need to be considered as influencing factors of dam deformation. Full article

(This article belongs to the Special Issue Mathematical Modeling and Numerical Analysis for Applied Sciences)

► Show Figures

Figure 1

12 pages, 1444 KiB

Open AccessArticle

Extension of Divisible-Load Theory from Scheduling Fine-Grained to Coarse-Grained Divisible Workloads on Networked Computing Systems

by Xiaoli Wang, Bharadwaj Veeravalli, Kangjian Wu and Xiaobo Song

Mathematics 2023, 11(7), 1752; https://doi.org/10.3390/math11071752 - 6 Apr 2023

Cited by 1 | Viewed by 1624

Abstract

The big data explosion has sparked a strong demand for high-performance data processing. Meanwhile, the rapid development of networked computing systems, coupled with the growth of Divisible-Load Theory (DLT) as an innovative technology with competent scheduling strategies, provides a practical way of conducting [...] Read more.

The big data explosion has sparked a strong demand for high-performance data processing. Meanwhile, the rapid development of networked computing systems, coupled with the growth of Divisible-Load Theory (DLT) as an innovative technology with competent scheduling strategies, provides a practical way of conducting parallel processing with big data. Existing studies in the area of DLT usually consider the scheduling problem with regard to fine-grained divisible workloads. However, numerous big data loads nowadays can only be abstracted as coarse-grained workloads, such as large-scale image classification, context-dependent emotional analysis and so on. In view of this, this paper extends DLT from fine-grained to coarse-grained divisible loads by establishing a new multi-installment scheduling model. With this model, a subtle heuristic algorithm was proposed to find a feasible load partitioning scheme that minimizes the makespan of the entire workload. Simulation results show that the proposed algorithm is superior to the up-to-date multi-installment scheduling strategy in terms of achieving a shorter makespan of workloads when dealing with coarse-grained divisible loads. Full article

(This article belongs to the Special Issue Emerging Topics in Machine Learning, Image Processing and Pattern Recognition for AI-Related Applications)

► Show Figures

Figure 1

15 pages, 1108 KiB

Open AccessArticle

A Comparative Study of the Fractional-Order Belousov–Zhabotinsky System

by Samir A. El-Tantawy, Rasool Shah, Albandari W. Alrowaily, Nehad Ali Shah, Jae Dong Chung and Sherif. M. E. Ismaeel

Mathematics 2023, 11(7), 1751; https://doi.org/10.3390/math11071751 - 6 Apr 2023

Cited by 10 | Viewed by 1511

Abstract

In this article, we present a modified strategy that combines the residual power series method with the Laplace transformation and a novel iterative technique for generating a series solution to the fractional nonlinear Belousov–Zhabotinsky (BZ) system. The proposed techniques use the Laurent series [...] Read more.

In this article, we present a modified strategy that combines the residual power series method with the Laplace transformation and a novel iterative technique for generating a series solution to the fractional nonlinear Belousov–Zhabotinsky (BZ) system. The proposed techniques use the Laurent series in their development. The new procedures’ advantages include the accuracy and speed in obtaining exact/approximate solutions. The suggested approach examines the fractional nonlinear BZ system that describes flow motion in a pipe. Full article

(This article belongs to the Special Issue Numerical Methods for Fractional Differential Equations and Applications)

► Show Figures

Figure 1

19 pages, 4271 KiB

Open AccessArticle

Synergistic Mechanism of Designing Information Granules with the Use of the Principle of Justifiable Granularity

by Dan Wang, Yukang Liu and Zhenhua Yu

Mathematics 2023, 11(7), 1750; https://doi.org/10.3390/math11071750 - 6 Apr 2023

Viewed by 1371

Abstract

The construction of information granules is a significant and interesting topic of Granular Computing (GrC) in which information granules play a vital role in representing and describing data, and it has become one of the most effective frameworks for solving complex problems. In [...] Read more.

The construction of information granules is a significant and interesting topic of Granular Computing (GrC) in which information granules play a vital role in representing and describing data, and it has become one of the most effective frameworks for solving complex problems. In this study, we are interested in the collaborative impacts of several different characteristics on constructing information granules, and a novel synergistic mechanism of the principle of justifiable granularity is utilized in developing information granules. The synergistic mechanism is finalized with a two-phase process—to start with, the principle of justifiable granularity and Fuzzy C-Means Clustering method are combined to develop a collection of information granules. First, the available experimental data is transformed (normalized) into fuzzy sets following the standard Fuzzy C-Means Clustering method. Then, information granules are developed based on the elements located in different clusters with the use of the principle of justifiable granularity. In the sequel, the positions of information granules are updated by considering the collaborative impacts of the other information granules with the parameters of specifying the level of influence. Experimental studies are conducted to illustrate the nature and feasibility of the proposed framework based on the synthetic data as well as a series of publicly available datasets coming from KEEL machine learning repositories. Full article

(This article belongs to the Special Issue Systems Engineering, Control, and Automation)

► Show Figures

Figure 1

18 pages, 17280 KiB

Open AccessArticle

Analysis of the Characteristics and Speed of Spread of the “FUNA” on Twitter

by Sebastián Moreno, Danilo Bórquez-Paredes and Valentina Martínez

Mathematics 2023, 11(7), 1749; https://doi.org/10.3390/math11071749 - 6 Apr 2023

Viewed by 1719

Abstract

The funa is a prevalent concept in Chile that aims to expose a person’s bad behavior, punish the aggressor publicly, and warn the community about it. Despite its massive use on the social networks of Chilean society, the real dissemination of funas among [...] Read more.

The funa is a prevalent concept in Chile that aims to expose a person’s bad behavior, punish the aggressor publicly, and warn the community about it. Despite its massive use on the social networks of Chilean society, the real dissemination of funas among communities is unknown. In this paper, we extract, generate, analyze, and compare the Twitter social network’s spread of three tweets related to “funas” against three other trending topics, through the analysis of global network characteristics over time (degree distribution, clustering coefficient, hop plot, and betweenness centrality). As observed, funas have a specific behavior, and they disseminate as quickly as a common tweet or more quickly; however, they spread thanks to several network users, generating a cohesive group. Full article

(This article belongs to the Special Issue Feature Papers in Complex Networks and Their Applications)

► Show Figures

Figure 1

17 pages, 2434 KiB

Open AccessArticle

An Unfitted Method with Elastic Bed Boundary Conditions for the Analysis of Heterogeneous Arterial Sections

by Stephan Gahima, Pedro Díez, Marco Stefanati, José Félix Rodríguez Matas and Alberto García-González

Mathematics 2023, 11(7), 1748; https://doi.org/10.3390/math11071748 - 6 Apr 2023

Viewed by 1449

Abstract

This manuscript presents a novel formulation for a linear elastic model of a heterogeneous arterial section undergoing uniform pressure in a quasi-static regime. The novelties are twofold. First, an elastic bed support on the external boundary (elastic bed boundary condition) replaces the classical [...] Read more.

This manuscript presents a novel formulation for a linear elastic model of a heterogeneous arterial section undergoing uniform pressure in a quasi-static regime. The novelties are twofold. First, an elastic bed support on the external boundary (elastic bed boundary condition) replaces the classical Dirichlet boundary condition (i.e., blocking displacements at arbitrarily selected nodes) for elastic solids to ensure a solvable problem. In addition, this modeling approach can be used to effectively account for the effect of the surrounding material on the vessel. Secondly, to study many geometrical configurations corresponding to different patients, we devise an unfitted strategy based on the Immersed Boundary (IB) framework. It allows using the same (background) mesh for all possible configurations both to describe the geometrical features of the cross-section (using level sets) and to compute the solution of the mechanical problem. Results on coronary arterial sections from realistic segmented images demonstrate that the proposed unfitted IB-based approach provides results equivalent to the standard finite elements (FE) for the same number of active degrees of freedom with an average difference in the displacement field of less than 0.5%. However, the proposed methodology does not require the use of a different mesh for every configuration. Thus, it is paving the way for dimensionality reduction. Full article

(This article belongs to the Special Issue Numerical Simulation in Biomechanics and Biomedical Engineering-II)

► Show Figures

Figure 1

14 pages, 839 KiB

Open AccessArticle

On Mathematical and Logical Realism and Contingency

by Jovan M. Tadić

Mathematics 2023, 11(7), 1747; https://doi.org/10.3390/math11071747 - 6 Apr 2023

Viewed by 2048

Abstract

This study presents the claim that mathematics and logic are merely highly formalized reflections, grounded in the physical laws of conservation. The claim generally correlates with John Stuart Mill’s known stance, but unlike his general view, it specifies which elements of the natural [...] Read more.

This study presents the claim that mathematics and logic are merely highly formalized reflections, grounded in the physical laws of conservation. The claim generally correlates with John Stuart Mill’s known stance, but unlike his general view, it specifies which elements of the natural kingdom are reflected by mathematical objects and statements. As the study claims one version of physicalism, it raises the question of the necessity vs. contingency of mathematics and concludes that the necessity of mathematical judgments depends on the necessity of the conservation laws themselves. Since the conservation laws are only certain, it follows that there is no basis to claim the necessity of mathematical statements themselves, and that it is only possible to speak of a conditional necessity in the sense that mathematics is necessarily such as it is only in a world governed by conservation laws. Such conditional necessity does not possess the being of absolute necessity. Mathematics can only be considered necessary to the extent that the reflected world described by it is necessary, which further implies the claim that mathematics is necessarily a posteriori and synthetic. The entire series of mathematical proof types, including the most commonly utilized reduction ad absurdum, ultimately derives its strength from experience. Full article

► Show Figures

Figure 1

21 pages, 13364 KiB

Open AccessArticle

Reinforcement-Learning-Based Level Controller for Separator Drum Unit in Refinery System

by Anwer Abdulkareem Ali, Mofeed Turky Rashid, Bilal Naji Alhasnawi, Vladimír Bureš and Peter Mikulecký

Mathematics 2023, 11(7), 1746; https://doi.org/10.3390/math11071746 - 6 Apr 2023

Cited by 5 | Viewed by 2327

Abstract

The Basrah Refinery, Iraq, similarly to other refineries, is subject to several industrial constraints. Therefore, the main challenge is to optimize the parameters of the level controller of the process unit tanks. In this paper, a PI controller is designed for these important [...] Read more.

The Basrah Refinery, Iraq, similarly to other refineries, is subject to several industrial constraints. Therefore, the main challenge is to optimize the parameters of the level controller of the process unit tanks. In this paper, a PI controller is designed for these important processes in the Basrah Refinery, which is a separator drum (D5204). Furthermore, the improvement of the PI controller is achieved under several constraints, such as the inlet liquid flow rate to tank (m2) and valve opening in yi%, by using two different techniques: the first one is conducted using a closed-Loop PID auto-tuner that is based on a frequency system estimator, and the other one is via the reinforcement learning approach (RL). RL is employed through two approaches: the first is calculating the optimal PI parameters as an offline tuner, and the second is using RL as an online tuner to optimize the PI parameters. In this case, the RL system works as a PI-like controller of RD5204. The mathematical model of the RD5204 system is derived and simulated using MATLAB. Several experiments are designed to validate the proposed controller. Further, the performance of the proposed system is evaluated under several industrial constraints, such as disturbances and noise, in which the results indict that RL as a tuner for the parameters of the PI controller is superior to other methods. Furthermore, using RL as a PI-like controller increases the controller’s robustness against uncertainty and perturbations. Full article

(This article belongs to the Special Issue New Trends in Mathematical Modeling, Analysis and Optimization for Engineering and Mechanics)

► Show Figures

Figure 1

31 pages, 40502 KiB

Open AccessArticle

Levy Flight-Based Improved Grey Wolf Optimization: A Solution for Various Engineering Problems

by Bhargav Bhatt, Himanshu Sharma, Krishan Arora, Gyanendra Prasad Joshi and Bhanu Shrestha

Mathematics 2023, 11(7), 1745; https://doi.org/10.3390/math11071745 - 5 Apr 2023

Cited by 7 | Viewed by 3145

Abstract

Optimization is a broad field for researchers to develop new algorithms for solving various types of problems. There are various popular techniques being worked on for improvement. Grey wolf optimization (GWO) is one such algorithm because it is efficient, simple to use, and [...] Read more.

Optimization is a broad field for researchers to develop new algorithms for solving various types of problems. There are various popular techniques being worked on for improvement. Grey wolf optimization (GWO) is one such algorithm because it is efficient, simple to use, and easy to implement. However, GWO has several drawbacks as it is stuck in local optima, has a low convergence rate, and has poor exploration. Several attempts have been made recently to overcome these drawbacks. This paper discusses some strategies that can be applied to GWO to overcome its drawbacks. This article proposes a novel algorithm to enhance the convergence rate, which was poor in GWO, and it is also compared with the other optimization algorithms. GWO also has the limitation of becoming stuck in local optima when used in complex functions or in a large search space, so these issues are further addressed. The most remarkable factor is that GWO purely depends on the initialization constraints such as population size and wolf initial positions. This study demonstrates the improved position of the wolf by applying strategies with the same population size. As a result, this novel algorithm has enhanced its exploration capability compared to other algorithms presented, and statistical results are also presented to demonstrate its superiority. Full article

(This article belongs to the Special Issue Advances in Machine Learning, Optimization, and Control Applications)

► Show Figures

Figure 1

13 pages, 2138 KiB

Open AccessArticle

A Comparative Evaluation of Self-Attention Mechanism with ConvLSTM Model for Global Aerosol Time Series Forecasting

by Dušan S. Radivojević, Ivan M. Lazović, Nikola S. Mirkov, Uzahir R. Ramadani and Dušan P. Nikezić

Mathematics 2023, 11(7), 1744; https://doi.org/10.3390/math11071744 - 5 Apr 2023

Cited by 4 | Viewed by 1734

Abstract

The attention mechanism in natural language processing and self-attention mechanism in vision transformers improved many deep learning models. An implementation of the self-attention mechanism with the previously developed ConvLSTM sequence-to-one model was done in order to make a comparative evaluation with statistical testing. [...] Read more.

The attention mechanism in natural language processing and self-attention mechanism in vision transformers improved many deep learning models. An implementation of the self-attention mechanism with the previously developed ConvLSTM sequence-to-one model was done in order to make a comparative evaluation with statistical testing. First, the new ConvLSTM sequence-to-one model with a self-attention mechanism was developed and then the self-attention layer was removed in order to make comparison. The hyperparameters optimization process was conducted by grid search for integer and string type parameters, and with particle swarm optimization for float type parameters. A cross validation technique was used for better evaluating models with a predefined ratio of train-validation-test subsets. Both models with and without a self-attention layer passed defined evaluation criteria that means that models are able to generate the image of the global aerosol thickness and able to find patterns for changes in the time domain. The model obtained by an ablation study on the self-attention layer achieved better outcomes for Root Mean Square Error and Euclidean Distance in regards to developed ConvLSTM-SA model. As part of the statistical test, a Kruskal–Wallis H Test was done since it was determined that the data did not belong to the normal distribution and the obtained results showed that both models, with and without the SA layer, predict similar images with patterns at the pixel level to the original dataset. However, the model without the SA layer was more similar to the original dataset especially in the time domain at the pixel level. Based on the comparative evaluation with statistical testing, it was concluded that the developed ConvLSTM-SA model better predicts without an SA layer. Full article

(This article belongs to the Section Mathematics and Computer Science)

► Show Figures

Figure 1

14 pages, 91023 KiB

Open AccessArticle

Traffic Accident Detection Method Using Trajectory Tracking and Influence Maps

by Yihang Zhang and Yunsick Sung

Mathematics 2023, 11(7), 1743; https://doi.org/10.3390/math11071743 - 5 Apr 2023

Cited by 3 | Viewed by 4148

Abstract

With the development of artificial intelligence, techniques such as machine learning, object detection, and trajectory tracking have been applied to various traffic fields to detect accidents and analyze their causes. However, detecting traffic accidents using closed-circuit television (CCTV) as an emerging subject in [...] Read more.

With the development of artificial intelligence, techniques such as machine learning, object detection, and trajectory tracking have been applied to various traffic fields to detect accidents and analyze their causes. However, detecting traffic accidents using closed-circuit television (CCTV) as an emerging subject in machine learning remains challenging because of complex traffic environments and limited vision. Traditional research has limitations in deducing the trajectories of accident-related objects and extracting the spatiotemporal relationships among objects. This paper proposes a traffic accident detection method that helps to determine whether each frame shows accidents by generating and considering object trajectories using influence maps and a convolutional neural network (CNN). The influence maps with spatiotemporal relationships were enhanced to improve the detection of traffic accidents. A CNN is utilized to extract latent representations from the influence maps produced by object trajectories. Car Accident Detection and Prediction (CADP) was utilized in the experiments to train our model, which achieved a traffic accident detection accuracy of approximately 95%. Thus, the proposed method attained remarkable results in terms of performance improvement compared to methods that only rely on CNN-based detection. Full article

(This article belongs to the Special Issue Emerging Topics in Machine Learning, Image Processing and Pattern Recognition for AI-Related Applications)

► Show Figures

Figure 1

13 pages, 308 KiB

Open AccessArticle

Subclasses of p-Valent Functions Associated with Linear q-Differential Borel Operator

by Adriana Cătaş, Emilia-Rodica Borşa and Sheza M. El-Deeb

Mathematics 2023, 11(7), 1742; https://doi.org/10.3390/math11071742 - 5 Apr 2023

Viewed by 1086

Abstract

The aim of the present paper is to introduce and study some new subclasses of p-valent functions by making use of a linear q-differential Borel operator.We also deduce some properties, such as inclusion relationships of the newly introduced classes and the [...] Read more.

The aim of the present paper is to introduce and study some new subclasses of p-valent functions by making use of a linear q-differential Borel operator.We also deduce some properties, such as inclusion relationships of the newly introduced classes and the integral operator

J_{μ, p}

. Full article

(This article belongs to the Special Issue Fractional Calculus and Mathematical Applications)

31 pages, 8781 KiB

Open AccessArticle

Comprehensive Analysis of Multi-Objective Optimization Algorithms for Sustainable Hybrid Electric Vehicle Charging Systems

by Nahar F. Alshammari, Mohamed Mahmoud Samy and Shimaa Barakat

Mathematics 2023, 11(7), 1741; https://doi.org/10.3390/math11071741 - 5 Apr 2023

Cited by 23 | Viewed by 3608

Abstract

This study presents a multi-objective optimization approach for designing hybrid renewable energy systems for electric vehicle (EV) charging stations that considers both economic and reliability factors as well as seasonal variations in energy production and consumption. Four algorithms, MOPSO, NSGA-II, NSGA-III, and MOEA/D, [...] Read more.

This study presents a multi-objective optimization approach for designing hybrid renewable energy systems for electric vehicle (EV) charging stations that considers both economic and reliability factors as well as seasonal variations in energy production and consumption. Four algorithms, MOPSO, NSGA-II, NSGA-III, and MOEA/D, were evaluated in terms of their convergence, diversity, efficiency, and robustness. Unlike previous studies that focused on single-objective optimization or ignored seasonal variations, our approach results in a more comprehensive and sustainable design for EV charging systems. The proposed system includes a 223-kW photovoltaic system, an 80-kW wind turbine, and seven Lithium-Ion battery banks, achieving a total net present cost of USD 564,846, a levelized cost of electricity of 0.2521 USD/kWh, and a loss of power supply probability of 1.21%. NSGA-II outperforms the other algorithms in terms of convergence and diversity, while NSGA-III is the most efficient, and MOEA/D has the highest robustness. The findings contribute to the development of efficient and reliable renewable energy systems for urban areas, emphasizing the importance of considering both economic and reliability factors in the design process. Our study represents a significant advance in the field of hybrid renewable energy systems for EV charging stations. Full article

(This article belongs to the Special Issue Multi-Objective Optimization and Decision Support Systems)

► Show Figures

Figure 1

23 pages, 4086 KiB

Open AccessFeature PaperArticle

Machine Downtime Effect on the Warm-Up Period in an Economic Production Quantity Problem

by Erfan Nobil, Leopoldo Eduardo Cárdenas-Barrón, Dagoberto Garza-Núñez, Gerardo Treviño-Garza, Armando Céspedes-Mota, Imelda de Jesús Loera-Hernández, Neale R. Smith and Amir Hossein Nobil

Mathematics 2023, 11(7), 1740; https://doi.org/10.3390/math11071740 - 5 Apr 2023

Cited by 4 | Viewed by 2743

Abstract

Success in the industrial sector is compromised by diverse conditions such as imperfect product production, manufacturing line interruptions, and unscheduled maintenance. The precise use of common practices in production environments is an available solution to eliminate some of these issues. Applying a warm-up [...] Read more.

Success in the industrial sector is compromised by diverse conditions such as imperfect product production, manufacturing line interruptions, and unscheduled maintenance. The precise use of common practices in production environments is an available solution to eliminate some of these issues. Applying a warm-up period in a manufacturing process is adequate and cost-effective for almost all companies. It improves the equipment’s productivity and helps the manufacturing line generate fewer defective products. Even though several inventory management studies have included a warm-up phase in their models, its use in economic production quantity (EPQ) models remains largely unexplored. Adding a warm-up phase to the production cycle minimizes maintenance expenses and defective products and increases the machine’s performance. In this study, the dependency between the machine downtime and the warm-up length is examined for the first time. The warm-up time depends on the machine’s off-state period: if the machine has a longer operation timeout, then a longer warm-up period is needed. The model includes a function to model the warm-up time relative to the machine downtime and two types of defective products: scrapping and reworking items. The study is concluded with some numerical examples, a sensitivity analysis, and some management insights related to the EPQ. Full article

(This article belongs to the Special Issue Mathematical Programming, Optimization and Operations Research)

► Show Figures

Figure 1

17 pages, 1994 KiB

Open AccessArticle

An Investigation into Thermal Vibrations Caused by a Moving Heat Supply on a Spinning Functionally Graded Isotropic Piezoelectric Bounded Rod

by Ahmed E. Abouelregal, Marin Marin and Sahar M. Abusalim

Mathematics 2023, 11(7), 1739; https://doi.org/10.3390/math11071739 - 5 Apr 2023

Cited by 8 | Viewed by 1519

Abstract

By laminating piezoelectric and flexible materials, we can increase their performance. Therefore, the electrical and mechanical properties of layered piezoelectric materials subjected to electromechanical loads and heat sources must be analyzed theoretically and mechanically. Since the problem of infinite wave propagation cannot be [...] Read more.

By laminating piezoelectric and flexible materials, we can increase their performance. Therefore, the electrical and mechanical properties of layered piezoelectric materials subjected to electromechanical loads and heat sources must be analyzed theoretically and mechanically. Since the problem of infinite wave propagation cannot be addressed using classical thermoelasticity, extended thermoelasticity models have been derived. The thermo-mechanical response of a piezoelectric functionally graded (FG) rod due to a moveable axial heat source is considered in this paper, utilizing the dual-phase-lag (DPL) heat transfer model. It was supposed that the physical characteristics of the FG rod varied exponentially along the axis of the body. Both ends hold the rod, and there is no voltage across them. The Laplace transform and decoupling techniques were used to obtain the physical fields that have been analyzed. A range of heterogeneity, rotation, and heat source velocity measures were used to compare the results presented here and those in the previous literature. Full article

(This article belongs to the Special Issue Finite Element Modeling in Mechanical Systems)

► Show Figures

Figure 1

21 pages, 1216 KiB

Open AccessArticle

Elucidating the Effects of Ionizing Radiation on Immune Cell Populations: A Mathematical Modeling Approach with Special Emphasis on Fractional Derivatives

by Dalal Yahya Alzahrani, Fuaada Mohd Siam and Farah A. Abdullah

Mathematics 2023, 11(7), 1738; https://doi.org/10.3390/math11071738 - 5 Apr 2023

Viewed by 1459

Abstract

Despite recent advances in the mathematical modeling of biological processes and real-world situations raised in the day-to-day life phase, some phenomena such as immune cell populations remain poorly understood. The mathematical modeling of complex phenomena such as immune cell populations using nonlinear differential [...] Read more.

Despite recent advances in the mathematical modeling of biological processes and real-world situations raised in the day-to-day life phase, some phenomena such as immune cell populations remain poorly understood. The mathematical modeling of complex phenomena such as immune cell populations using nonlinear differential equations seems to be a quite promising and appropriate tool to model such complex and nonlinear phenomena. Fractional differential equations have recently gained a significant deal of attention and demonstrated their relevance in modeling real phenomena rather than their counterpart, classical (integer) derivative differential equations. We report in this paper a mathematical approach susceptible to answering some relevant questions regarding the side effects of ionizing radiation (IR) on DNA with a particular focus on double-strand breaks (DSBs), leading to the destruction of the cell population. A theoretical elucidation of the population memory was carried out within the framework of fractional differential equations (FODEs). Using FODEs, the mathematical approach presented herein ensures connections between fractional calculus and the nonlocal feature of the fractional order of immune cell populations by taking into account the memory trace and genetic qualities that are capable of integrating all previous actions and considering the system’s long-term history. An illustration of both fractional modeling, which provides an excellent framework for the description of memory and hereditary properties of immune cell populations, is elucidated. The mathematics presented in this research hold promise for modeling real-life phenomena and paves the way for obtaining accurate model parameters resulting from the mathematical modeling. Finally, the numerical simulations are conducted for the analytical approach presented herein to elucidate the effect of various parameters that govern the influence of ionizing irradiation on DNA in immune cell populations as well as the evolution of cell population dynamics, and the results are presented using plots and contrasted with previous theoretical findings. Full article

(This article belongs to the Special Issue Numerical Methods for Fractional Differential Equations and Applications)

► Show Figures

Figure 1

17 pages, 2930 KiB

Open AccessArticle

Threshold Analysis of a Stochastic SIRS Epidemic Model with Logistic Birth and Nonlinear Incidence

by Huyi Wang, Ge Zhang, Tao Chen and Zhiming Li

Mathematics 2023, 11(7), 1737; https://doi.org/10.3390/math11071737 - 5 Apr 2023

Cited by 3 | Viewed by 1373

Abstract

The paper mainly investigates a stochastic SIRS epidemic model with Logistic birth and nonlinear incidence. We obtain a new threshold value (

R_{0}^{m}

) through the Stratonovich stochastic differential equation, different from the usual basic reproduction number. If [...] Read more.

The paper mainly investigates a stochastic SIRS epidemic model with Logistic birth and nonlinear incidence. We obtain a new threshold value (

R_{0}^{m}

) through the Stratonovich stochastic differential equation, different from the usual basic reproduction number. If

R_{0}^{m} < 1

, the disease-free equilibrium of the illness is globally asymptotically stable in probability one. If

R_{0}^{m} > 1

, the disease is permanent in the mean with probability one and has an endemic stationary distribution. Numerical simulations are given to illustrate the theoretical results. Interestingly, we discovered that random fluctuations can suppress outbreaks and control the disease. Full article

► Show Figures

Figure 1

15 pages, 367 KiB

Open AccessArticle

A Study of Assessment of Casinos’ Risk of Ruin in Casino Games with Poisson Distribution

by Ka-Meng Siu, Ka-Hou Chan and Sio-Kei Im

Mathematics 2023, 11(7), 1736; https://doi.org/10.3390/math11071736 - 5 Apr 2023

Viewed by 3338

Abstract

Gambling, as an uncertain business involving risks confronting casinos, is commonly analysed using the risk of ruin (ROR) formula. However, due to its brevity, the ROR does not provide any implication of nuances in terms of the distribution of wins/losses, thus causing the [...] Read more.

Gambling, as an uncertain business involving risks confronting casinos, is commonly analysed using the risk of ruin (ROR) formula. However, due to its brevity, the ROR does not provide any implication of nuances in terms of the distribution of wins/losses, thus causing the potential failure of unravelling exceptional and extreme cases. This paper discusses the mathematical model of ROR using Poisson distribution theory with the consideration of house advantage (a) and the law of large numbers in order to compensate for the insufficiency mentioned above. In this discussion, we explore the relationship between cash flow and max bet limits in the model and examine how these factors interact in influencing the risk of casino bankruptcy. In their business nature, casinos operate gambling businesses and capitalize on the house advantage favouring them. The house advantage of the games signifies casinos’ profitability, and in addition, the uncertainty inevitably poses a certain risk of bankruptcy to them even though the house advantage favours them. In this paper, the house advantage is incorporated into our model for a few popular casino games. Furthermore, a set of full-range scales is defined to facilitate effective judgment on the levels of risk confronted by casinos in certain settings. Some wagers of popular casino games are also exemplified with our proposed model. Full article

(This article belongs to the Special Issue Advances in Applied Probability and Statistical Inference)

► Show Figures

Figure 1

14 pages, 6073 KiB

Open AccessArticle

An In-Phase Unit Slot-Opening Shift Method for Cogging Torque Reduction in Interior Permanent Magnet Machine

by Linwei Wang, Shuai Lu, Yangming Chen and Shiya Wang

Mathematics 2023, 11(7), 1735; https://doi.org/10.3390/math11071735 - 5 Apr 2023

Cited by 3 | Viewed by 1378

Abstract

The cogging torque reduction methods in permanent magnet (PM) machines are more or less FEA trial and error-based and cause undesirable side effects, such as distorted back EMF, new harmonic components, and structure asymmetry. A slot-opening grouping method can address these issues. However, [...] Read more.

The cogging torque reduction methods in permanent magnet (PM) machines are more or less FEA trial and error-based and cause undesirable side effects, such as distorted back EMF, new harmonic components, and structure asymmetry. A slot-opening grouping method can address these issues. However, it needs to model all slots in FEA design validation during practical cogging torque optimization iterations, and also leads to back-EMF reduction. In this paper, a new grouping strategy, termed in-phase unit (IPU), is introduced, together with the slot-opening angle-shift method. The slot openings with the same cogging torque distribution pattern are grouped into an IPU, and the cogging torque peaks of the slot openings within an IPU can now be interleaved. Thereby, the major harmonic components of the cogging torque are cancelled out, instead of being summed up. The IPU grouping principle, the slot-opening shift angle computation, and the selection of the harmonic order to cancel are analyzed in detail. By comparison, the proposed method not only simplifies cogging torque optimization iterations by only modeling the slots in one IPU in FEA, but also compensates for the back-EMF constant reduction. The effectiveness of the proposed methods is validated by two typical interior PM machine design cases. Full article

(This article belongs to the Special Issue Mathematical Approaches to Modeling, Optimally Designing, and Controlling Electric Machine and Power Converters)

► Show Figures

Figure 1

11 pages, 312 KiB

Open AccessArticle

Nonlinear Stability of the Monotone Traveling Wave for the Isothermal Fluid Equations with Viscous and Capillary Terms

by Xiang Li, Weiguo Zhang and Haipeng Jin

Mathematics 2023, 11(7), 1734; https://doi.org/10.3390/math11071734 - 5 Apr 2023

Cited by 2 | Viewed by 1183

Abstract

We prove the existence of the monotone traveling wave for the isothermal fluid equations with viscous and capillary terms by the planar dynamical system method. We obtain that the monotone traveling wave is asymptotically stable under the suitable perturbation. In the process of [...] Read more.

We prove the existence of the monotone traveling wave for the isothermal fluid equations with viscous and capillary terms by the planar dynamical system method. We obtain that the monotone traveling wave is asymptotically stable under the suitable perturbation. In the process of establishing the uniform a priori estimate, we dispose the capillary term reasonably according to the feature of the equations, and find the appropriate weighted function to overcome the difficulty caused by the non-convex pressure function. Full article

(This article belongs to the Special Issue Applications of Partial Differential Equations in Mathematical Physics, 1st Edition)

► Show Figures

Figure 1

16 pages, 2398 KiB

Open AccessArticle

Research on Robust Audio-Visual Speech Recognition Algorithms

by Wenfeng Yang, Pengyi Li, Wei Yang, Yuxing Liu, Yulong He, Ovanes Petrosian and Aleksandr Davydenko

Mathematics 2023, 11(7), 1733; https://doi.org/10.3390/math11071733 - 5 Apr 2023

Cited by 4 | Viewed by 3251

Abstract

Automatic speech recognition (ASR) that relies on audio input suffers from significant degradation in noisy conditions and is particularly vulnerable to speech interference. However, video recordings of speech capture both visual and audio signals, providing a potent source of information for training speech [...] Read more.

Automatic speech recognition (ASR) that relies on audio input suffers from significant degradation in noisy conditions and is particularly vulnerable to speech interference. However, video recordings of speech capture both visual and audio signals, providing a potent source of information for training speech models. Audiovisual speech recognition (AVSR) systems enhance the robustness of ASR by incorporating visual information from lip movements and associated sound production in addition to the auditory input. There are many audiovisual speech recognition models and systems for speech transcription, but most of them have been tested based in a single experimental setting and with a limited dataset. However, a good model should be applicable to any scenario. Our main contributions are: (i) Reproducing the three best-performing audiovisual speech recognition models in the current AVSR research area using the most famous audiovisual databases, LSR2 (Lip Reading Sentences 2) LSR3 (Lip Reading Sentences 3), and comparing and analyzing their performances under various noise conditions. (ii) Based on our experimental and research experiences, we analyzed the problems currently encountered in the AVSR domain, which are summarized as the feature-extraction problem and the domain-generalization problem. (iii) According to the experimental results, the Moco (momentum contrast) + word2vec (word to vector) model has the best AVSR effect on the LRS datasets regardless of whether there is noise or not. Additionally, the model also produced the best experimental results in the experiments of audio recognition and video recognition. Our research lays the foundation for further improving the performance of AVSR models. Full article

(This article belongs to the Special Issue Application of Mathematical Methods in Artificial Intelligence)

► Show Figures

Figure 1

18 pages, 326 KiB

Open AccessArticle

Minimal Rank Properties of Outer Inverses with Prescribed Range and Null Space

by Dijana Mosić, Predrag S. Stanimirović and Spyridon D. Mourtas

Mathematics 2023, 11(7), 1732; https://doi.org/10.3390/math11071732 - 5 Apr 2023

Cited by 2 | Viewed by 1338

Abstract

The purpose of this paper is to investigate solvability of systems of constrained matrix equations in the form of constrained minimization problems. The main novelty of this paper is the unification of solutions of considered matrix equations with corresponding minimization problems. For a [...] Read more.

The purpose of this paper is to investigate solvability of systems of constrained matrix equations in the form of constrained minimization problems. The main novelty of this paper is the unification of solutions of considered matrix equations with corresponding minimization problems. For a particular case we extend some well-known results and give several new results for the weak Drazin inverse. The main characterizations of the Drazin inverse, group inverse and Moore–Penrose inverse are obtained as consequences. Full article

(This article belongs to the Special Issue Numerical Analysis: Inverse Problems – Theory and Applications)

22 pages, 2120 KiB

Open AccessArticle

Managing Disruptions in a Flow-Shop Manufacturing System

by Ajay Surendrarao Bhongade, Prakash Manohar Khodke, Ateekh Ur Rehman, Manoj Dattatray Nikam, Prathamesh Dattatray Patil and Pramod Suryavanshi

Mathematics 2023, 11(7), 1731; https://doi.org/10.3390/math11071731 - 4 Apr 2023

Cited by 5 | Viewed by 1965

Abstract

There is a manufacturing system where several parts are processed through machining workstations and later assembled to form final products. In the event of disruptions such as machine failure, the original flow-shop schedule needs to be revised and/or rescheduled. In such a scenario, [...] Read more.

There is a manufacturing system where several parts are processed through machining workstations and later assembled to form final products. In the event of disruptions such as machine failure, the original flow-shop schedule needs to be revised and/or rescheduled. In such a scenario, rescheduling methods based on right-shift rescheduling and affected operations rescheduling work very well. Here in this study, the deviation of the make-span of the revised schedule from the original schedule is used as a performance measure. We have proposed three rescheduling methods. There are multiple factors that influence the performance of the rescheduling methodology. One of them is the make-span deviation of the schedule, and the factors influencing it are optimality of the initial solution, failure duration, deviation of make-span, rescheduling method, size, and instant of failure. The initial schedule and problem size depend on the flow-shop manufacturing system for which scheduling is performed, but the method of rescheduling depends on the decision as to which rescheduling methodology is to be selected. Computations are performed using full factorial experimentation. We also observed that right-shift rescheduling is the preferred rescheduling method in the majority of situations. In contrast, the affected operation rescheduling method is also equally suitable when the initial solution is created using modified bottleneck minimum idleness. Full article

(This article belongs to the Special Issue Mathematical Models and Methods of Scheduling Theory)

► Show Figures

Figure 1

Journal Menu

Journal Browser

Mathematics, Volume 11, Issue 7 (April-1 2023) – 200 articles

Further Information

Guidelines

MDPI Initiatives

Follow MDPI