Mathematics

30 pages, 14308 KiB

Open AccessArticle

Nonlinear Oscillations of a Composite Stepped Piezoelectric Cantilever Plate with Aerodynamic Force and External Excitation

by Yan Liu and Wensai Ma

Mathematics 2023, 11(13), 3034; https://doi.org/10.3390/math11133034 - 07 Jul 2023

Cited by 1 | Viewed by 852

Abstract

Axially moving wing aircraft can better adapt to the flight environment, improve flight performance, reduce flight resistance, and improve flight distance. This paper simplifies the fully unfolded axially moving wing into a stepped cantilever plate model, analyzes the structural nonlinearity of the system, [...] Read more.

Axially moving wing aircraft can better adapt to the flight environment, improve flight performance, reduce flight resistance, and improve flight distance. This paper simplifies the fully unfolded axially moving wing into a stepped cantilever plate model, analyzes the structural nonlinearity of the system, and studies the influence of aerodynamic nonlinearity on system vibration. The model is affected by aerodynamic forces, piezoelectric excitation, and in-plane excitation. Due to Hamilton’s principle of least action, the mathematical model is established based on Reddy’s higher-order shear deformation theory, and using Galerkin’s method, the governing dimensionless partial differential equations of the system are simplified to two nonlinear ordinary differential equations, and then a study of the influence of the various engineering parameters on the nonlinear oscillations and frequency responses of this model is conducted by the method of multiple scales. It was found that the different values of

a_{5}

,

a_{6}

,

b_{6}

and

b_{8}

can change the shape of the amplitude–frequency response curve and size of the plate, while different symbols

a_{7}

and

b_{7}

can change the rigidity of the model. The excitations greatly impact the nonlinear dynamic responses of the plate. Full article

(This article belongs to the Special Issue Modeling and Analysis in Dynamical Systems and Bistability)

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17 pages, 1268 KiB

Open AccessArticle

A Fuzzy Multi-Criteria Evaluation System for Share Price Prediction: A Tesla Case Study

by Simona Hašková, Petr Šuleř and Róbert Kuchár

Mathematics 2023, 11(13), 3033; https://doi.org/10.3390/math11133033 - 07 Jul 2023

Cited by 1 | Viewed by 1390

Abstract

The article presents the predictive capabilities of a fuzzy multi-criteria evaluation system that operates on the basis of a non-fuzzy neural approach, but also one that is capable of implementing a learning paradigm and working with vague concepts. Within this context, the necessary [...] Read more.

The article presents the predictive capabilities of a fuzzy multi-criteria evaluation system that operates on the basis of a non-fuzzy neural approach, but also one that is capable of implementing a learning paradigm and working with vague concepts. Within this context, the necessary elements of fuzzy logic are identified and the algebraic formulation of the fuzzy system is presented. It is with the help of the aforementioned that the task of predicting the short-term trend and price of the Tesla share is solved. The functioning of a fuzzy system and fuzzy neural network in the field of time series value prediction is discussed. The authors are inclined to the opinion that, despite the fact that a fuzzy neural network reacts in terms of applicability and effectiveness when solving prediction problems in relation to input data with a faster output than a fuzzy system, and is more “user friendly”, a sufficiently knowledgeable and experienced solver/expert could, by using a fuzzy system, achieve a higher speed of convergence in the learning process than a fuzzy neural network using the minimum range of input data carrying the necessary information. A fuzzy system could therefore be a possible alternative to a fuzzy neural network from the point of view of prediction. Full article

(This article belongs to the Special Issue Advances in Fuzzy Logic and Artificial Neural Networks)

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30 pages, 9208 KiB

Open AccessArticle

Mathematical Models of the Phase Voltages of High-, Medium- and Low-Voltage Busbars in a Substation during a Phase-to-Ground Fault on High-Voltage Busbars

by Dumitru Toader and Maria Vintan

Mathematics 2023, 11(13), 3032; https://doi.org/10.3390/math11133032 - 07 Jul 2023

Viewed by 744

Abstract

The electrical energy supply of industrial equipment is provided by electrical power stations with high- (HT), medium- (MV) and low-voltage (LV) busbars. Consumers are connected to either MV or LV busbars. In this paper, a real power station was considered, through which the [...] Read more.

The electrical energy supply of industrial equipment is provided by electrical power stations with high- (HT), medium- (MV) and low-voltage (LV) busbars. Consumers are connected to either MV or LV busbars. In this paper, a real power station was considered, through which the gasoline extraction from the well gas installation is powered. Electric consumers (electric motors) supplied by a MV busbar have active power of 13.54 MW, and those fed by a LV busbar have active power of 6.4 MW. Since electrical consumers operate in explosive environments, the design and operating conditions are more severe than in the case of electrical installations operating in non-explosive environments. The case of a single phase-to-ground fault occurring on the HV transmission lines feeding the power station has been analysed. First, the mathematical models for the calculation of the phase voltages, the dissymmetry and asymmetry coefficients, the reduction coefficient of the plus sequence component, and the effective values of the phase voltages were established. The influence of the source impedance (the equivalent impedance of the HV transmission lines) and of the neutral point configuration of the HV/MV medium-voltage transformer on the calculated quantities was analysed. Then, the results obtained using the established mathematical models were compared with those obtained experimentally by provoking a single-phase-to-ground fault near the HV busbars of the real power station. This study has shown that the de-symmetrisation of the phase voltages of the MV and LV busbars is lower when using the Y/Δ connection for the HV/MV transformer. As a result, it is recommended the Y/Δ connection be used for this transformer, instead of the Y₀/Δ connection. Full article

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18 pages, 4302 KiB

Open AccessArticle

A Cubic Class of Iterative Procedures for Finding the Generalized Inverses

by Munish Kansal, Manpreet Kaur, Litika Rani and Lorentz Jäntschi

Mathematics 2023, 11(13), 3031; https://doi.org/10.3390/math11133031 - 07 Jul 2023

Viewed by 707

Abstract

This article considers the iterative approach for finding the Moore–Penrose inverse of a matrix. A convergence analysis is presented under certain conditions, demonstrating that the scheme attains third-order convergence. Moreover, theoretical discussions suggest that selecting a particular parameter could further improve the convergence [...] Read more.

This article considers the iterative approach for finding the Moore–Penrose inverse of a matrix. A convergence analysis is presented under certain conditions, demonstrating that the scheme attains third-order convergence. Moreover, theoretical discussions suggest that selecting a particular parameter could further improve the convergence order. The proposed scheme defines the special cases of third-order methods for

β = 0, 1 / 2,

and

1 / 4

. Various large sparse, ill-conditioned, and rectangular matrices obtained from real-life problems were included from the Matrix-Market Library to test the presented scheme. The scheme’s performance was measured on randomly generated complex and real matrices, to verify the theoretical results and demonstrate its superiority over the existing methods. Furthermore, a large number of distinct approaches derived using the proposed family were tested numerically, to determine the optimal parametric value, leading to a successful conclusion. Full article

(This article belongs to the Special Issue Advances in Linear Recurrence System)

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18 pages, 6175 KiB

Open AccessArticle

Light Pollution Index System Model Based on Markov Random Field

by Liangkun Fang, Zhangjie Wu, Yuan Tao and Jinfeng Gao

Mathematics 2023, 11(13), 3030; https://doi.org/10.3390/math11133030 - 07 Jul 2023

Cited by 1 | Viewed by 1066

Abstract

Light pollution is one of the environmental pollution problems facing the world. The research on the measurement standard of light pollution is not perfect at present. In this paper, we proposed a Markov random field model to determine the light pollution risk level [...] Read more.

Light pollution is one of the environmental pollution problems facing the world. The research on the measurement standard of light pollution is not perfect at present. In this paper, we proposed a Markov random field model to determine the light pollution risk level of a site. Firstly, the specific data of 12 indicators of 5 typical cities were collected, and 10-factor indicators were screened using the R-type clustering algorithm. Then, the entropy weight method was used to determine the weight, and the light pollution measurement method of the Markov random field was established. The model was tested by five different data sets, and the test results show that the model is very effective. Three kinds of potential effects were proposed, and the relationship between the factor index and potential effects was established by using the partial least square method. Three possible intervention strategies for solving the problem of light pollution are pointed out: road lighting system planning, increasing vegetation coverage, and building system planning. Finally, a simulated annealing algorithm was used to determine the best intervention strategy, concluding that using strategy 1 in urban neighborhood 2 was the most effective measure, reducing the risk level of light pollution by 17.2%. Full article

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16 pages, 1781 KiB

Open AccessArticle

Direct Method for Identification of Two Coefficients of Acoustic Equation

by Nikita Novikov and Maxim Shishlenin

Mathematics 2023, 11(13), 3029; https://doi.org/10.3390/math11133029 - 07 Jul 2023

Cited by 1 | Viewed by 700

Abstract

We consider the coefficient inverse problem for the 2D acoustic equation. The problem is recovering the speed of sound in the medium (which depends only on the depth) and the density (function of both variables). We describe the method, based on the Gelfand–Levitan–Krein [...] Read more.

We consider the coefficient inverse problem for the 2D acoustic equation. The problem is recovering the speed of sound in the medium (which depends only on the depth) and the density (function of both variables). We describe the method, based on the Gelfand–Levitan–Krein approach, which allows us to obtain both functions by solving two sets of integral equations. The main advantage of the proposed approach is that the method does not use the multiple solution of direct problems, and thus has quite low CPU time requirements. We also consider the variation of the method for the 1D case, where the variation of the wave equation is considered. We illustrate the results with numerical experiments in the 1D and 2D case and study the efficiency and stability of the approach. Full article

(This article belongs to the Special Issue Direct and Inverse Spectral Problems for Ordinary Differential and Functional-Differential Operators)

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4 pages, 172 KiB

Open AccessEditorial

Preface to the Special Issue on “Differential Games and Its Applications”

by Bruno Antonio Pansera, Massimiliano Ferrara, Luca Guerrini and Tiziana Ciano

Mathematics 2023, 11(13), 3028; https://doi.org/10.3390/math11133028 - 07 Jul 2023

Viewed by 662

Abstract

The study of differential games has practical applications in the analysis and resolution of conflict issues by the use of differential equations [...] Full article

(This article belongs to the Special Issue Differential Games and Its Applications)

23 pages, 3845 KiB

Open AccessArticle

Epidemiological Investigation: Important Measures for the Prevention and Control of COVID-19 Epidemic in China

by Cheng-Cheng Zhu, Jiang Zhu and Jie Shao

Mathematics 2023, 11(13), 3027; https://doi.org/10.3390/math11133027 - 07 Jul 2023

Cited by 1 | Viewed by 941

Abstract

Based on China’s summary of three years of experience and measures in the prevention and control of the COVID-19 epidemic, we have built a COVID-19 prevention and control model integrating health and medical detection, big data information technology to track the trend of [...] Read more.

Based on China’s summary of three years of experience and measures in the prevention and control of the COVID-19 epidemic, we have built a COVID-19 prevention and control model integrating health and medical detection, big data information technology to track the trend of the epidemic throughout the whole process, isolation of key epidemic areas, and dynamic prevention and control management throughout the whole process. This model provides a simple, feasible, and theoretically reliable prevention and control model for future large-scale infectious disease prevention and control. The Lyapnov functional method is replaced by the global exponential attractor theory, which provides a new mathematical method for studying the global stability of the multi parameter, multi variable infectious disease prevention and control system. We extracted mathematical methods and models suitable for non-mathematical infectious disease researchers from profound and difficult to understand mathematical theories. Using the results of the global exponential Attractor theory obtained in this paper, we studied the global dynamics of the COVID-19 model with an epidemiological investigation. The results demonstrated that the non-constant disease-free equilibrium is globally asymptotically stable when

λ^{*} < 0

, and the COVID-19 epidemic is persisting uniformly when

λ^{*} > 0

. In order to understand the impact of the epidemiological investigation under different prevention and control stages in China, we compare the control effects of COVID-19 under different levels of epidemiological investigation policies. We visually demonstrate the global stability and global exponential attractiveness of the COVID-19 model with transferors between regions and epidemiological investigation in a temporal-spatial heterogeneous environment with the help of numerical simulations. We find that the epidemiological investigation really has a significant effect on the prevention and control of the epidemic situation, and we can also intuitively observe the relationship between the flow of people (including tourism, shopping, work and so on) and epidemiological investigation policies. Our model is adapted to different stages of prevention and control; the emergency “circuit breaker” mechanism of the model is also consistent with actual prevention and control. Full article

(This article belongs to the Special Issue Mathematical Modeling and Data Science for Biology and Medicine)

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26 pages, 4383 KiB

Open AccessArticle

Early Identification of Risk Factors in Non-Alcoholic Fatty Liver Disease (NAFLD) Using Machine Learning

by Luis Rolando Guarneros-Nolasco, Giner Alor-Hernández, Guillermo Prieto-Avalos and José Luis Sánchez-Cervantes

Mathematics 2023, 11(13), 3026; https://doi.org/10.3390/math11133026 - 07 Jul 2023

Viewed by 2117

Abstract

Liver diseases are a widespread and severe health concern, affecting millions worldwide. Non-alcoholic fatty liver disease (NAFLD) alone affects one-third of the global population, with some Latin American countries seeing rates exceeding 50%. This alarming trend has prompted researchers to explore new methods [...] Read more.

Liver diseases are a widespread and severe health concern, affecting millions worldwide. Non-alcoholic fatty liver disease (NAFLD) alone affects one-third of the global population, with some Latin American countries seeing rates exceeding 50%. This alarming trend has prompted researchers to explore new methods for identifying those at risk. One promising approach is using Machine Learning Algorithms (MLAs), which can help predict critical factors contributing to liver disease development. Our study examined nine different MLAs across four datasets to determine their effectiveness in predicting this condition. We analyzed each algorithm’s performance using five important metrics: accuracy, precision, recall, f1-score, and roc_auc. Our results showed that these algorithms were highly effective when used individually and as part of an ensemble modeling technique such as bagging or boosting. We identified alanine aminotransferase (ALT), aspartate aminotransferase (AST), alkaline phosphatase (ALP), and albumin as the top four attributes most strongly associated with non-alcoholic fatty liver disease risk across all datasets. Gamma-glutamyl transpeptidase (GGT), hemoglobin, age, and prothrombin time also played significant roles. In conclusion, this research provides valuable insights into how we can better detect and prevent non-alcoholic fatty liver diseases by leveraging advanced machine learning techniques. As such, it represents an exciting opportunity for healthcare professionals seeking more accurate diagnostic tools while improving patient outcomes globally. Full article

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

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20 pages, 325 KiB

Open AccessArticle

Development of a New Zeta Formula and Its Role in Riemann Hypothesis and Quantum Physics

by Saadeldin Abdelaziz, Ahmed Shaker and Mostafa M. Salah

Mathematics 2023, 11(13), 3025; https://doi.org/10.3390/math11133025 - 07 Jul 2023

Viewed by 1388

Abstract

In this study, we investigated a new zeta formula in which the zeta function can be expressed as the sum of an infinite series of delta and cosine functions. Our findings demonstrate that this formula possesses duality characteristics and we established a direct [...] Read more.

In this study, we investigated a new zeta formula in which the zeta function can be expressed as the sum of an infinite series of delta and cosine functions. Our findings demonstrate that this formula possesses duality characteristics and we established a direct connection between the Riemann hypothesis and this new formula. Additionally, we explored the behavior of energy or particles in quantum physics within the proposed mathematical model framework based on the new formula. Our model provides a valuable understanding of several important physics inquiries, including the collapse of the wave function during measurement and quantum entanglement, as well as the double slits experiment. Full article

(This article belongs to the Special Issue New Trends in Special Functions and Applications)

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10 pages, 347 KiB

Open AccessArticle

SOS Approach for Practical Stabilization of Tempered Fractional-Order Power System

by Hamdi Gassara, Dhouha Kharrat, Abdellatif Ben Makhlouf, Lassaad Mchiri and Mohamed Rhaima

Mathematics 2023, 11(13), 3024; https://doi.org/10.3390/math11133024 - 07 Jul 2023

Cited by 2 | Viewed by 689

Abstract

Fractional systems have been widely utilized in various fields, such as mathematics, physics and finance, providing a versatile framework for precise measurements and calculations involving partial quantities. This paper aims to develop a novel polynomial controller for a power system (PS) with fractional-order [...] Read more.

Fractional systems have been widely utilized in various fields, such as mathematics, physics and finance, providing a versatile framework for precise measurements and calculations involving partial quantities. This paper aims to develop a novel polynomial controller for a power system (PS) with fractional-order (FO) dynamics. It begins by studying the practical stability of a general class of tempered fractional-order (TFO) nonlinear systems, with broad applicability and potential for expanding its applications. Afterward, a polynomial controller is designed to guarantee the practical stability of the PS, encompassing the standard constant controller as a specific instance. The design conditions for this controller are resolved using the sum of squares (SOS) approach, a powerful technique for guaranteeing stability and control design. To showcase the practical value of the analytical findings, simulations of the PS are conducted utilizing SOSTOOLS. Full article

(This article belongs to the Special Issue Mathematical Modeling and Optimization of Energy Systems)

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19 pages, 1096 KiB

Open AccessArticle

Link Prediction Based on Heterogeneous Social Intimacy and Its Application in Social Influencer Integrated Marketing

by Shugang Li, He Zhu, Zhifang Wen, Jiayi Li, Yuning Zang, Jiayi Zhang, Ziqian Yan and Yanfang Wei

Mathematics 2023, 11(13), 3023; https://doi.org/10.3390/math11133023 - 07 Jul 2023

Cited by 1 | Viewed by 798

Abstract

The social influencer integrated marketing strategy, which builds social influencers through potential users, has gained widespread attention in the industry. Traditional Scoring Link Prediction Algorithms (SLPA) mainly rely on homogeneous network indicators to predict friend relationships, which cannot provide accurate link prediction results [...] Read more.

The social influencer integrated marketing strategy, which builds social influencers through potential users, has gained widespread attention in the industry. Traditional Scoring Link Prediction Algorithms (SLPA) mainly rely on homogeneous network indicators to predict friend relationships, which cannot provide accurate link prediction results in cold-start situations. To overcome these limitations, the Closeness Heterogeneous Link Prediction Algorithm (CHLPA) is proposed, which uses node closeness centrality to describe the social intimacy of nodes and provides a heterogeneous measure of a network based on this. Three types of heterogeneous indicators of social intimacy were proposed based on the principle of three-degree influence. Due to scarce overlapping node sample data, CHLPA uses gradient boosting trees to select the most suitable index, the second most suitable index, and the third most suitable index from Social Intimacy Heterogeneous Indexes (SIHIs) and SLPAs. Then, these indicators are weighted and combined to predict the likelihood of other node users in the two product circles in an online brand community becoming friends with overlapping node users. Finally, a hill-climbing algorithm is designed based on this to build integrated marketing social influencers, and the effectiveness and robustness of the algorithm are validated. Full article

(This article belongs to the Special Issue Big Data and Complex Networks)

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14 pages, 6015 KiB

Open AccessArticle

Mathematical Modelling of Fused Deposition Modeling (FDM) 3D Printing of Poly Vinyl Alcohol Parts through Statistical Design of Experiments Approach

by Mahmoud Moradi, Mojtaba Karamimoghadam, Saleh Meiabadi, Giuseppe Casalino, Mohammad Ghaleeh, Bobymon Baby, Harikrishna Ganapathi, Jomal Jose, Muhammed Shahzad Abdulla, Paul Tallon, Mahmoud Shamsborhan, Mohammad Rezayat, Satyam Paul and Davood Khodadad

Mathematics 2023, 11(13), 3022; https://doi.org/10.3390/math11133022 - 07 Jul 2023

Cited by 6 | Viewed by 1587

Abstract

This paper explores the 3D printing of poly vinyl alcohol (PVA) using the fused deposition modeling (FDM) process by conducting statistical modeling and optimization. This study focuses on varying the infill percentage (10–50%) and patterns (Cubic, Gyroid, tri-hexagon and triangle, Grid) as input [...] Read more.

This paper explores the 3D printing of poly vinyl alcohol (PVA) using the fused deposition modeling (FDM) process by conducting statistical modeling and optimization. This study focuses on varying the infill percentage (10–50%) and patterns (Cubic, Gyroid, tri-hexagon and triangle, Grid) as input parameters for the response surface methodology (DOE) while measuring modulus, elongation at break, and weight as experimental responses. To determine the optimal parameters, a regression equation analysis was conducted to identify the most significant parameters. The results indicate that both input parameters significantly impact the output responses. The Design Expert software was utilized to create surface and residual plots, and the interaction between the two input parameters shows that increasing the infill percentage (IP) leads to printing heavier samples, while the patterns do not affect the weight of the parts due to close printing structures. On the contrary, the discrepancy between the predicted and actual responses for the optimal samples is below 15%. This level of error is deemed acceptable for the DOE experiments. Full article

(This article belongs to the Special Issue Advances in Control Systems and Automatic Control)

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20 pages, 3552 KiB

Open AccessArticle

Contextual Augmentation Based on Metric-Guided Features for Ocular Axial Length Prediction

by Yeonwoo Jeong, Jae-Ho Han and Jaeryung Oh

Mathematics 2023, 11(13), 3021; https://doi.org/10.3390/math11133021 - 07 Jul 2023

Viewed by 716

Abstract

Ocular axial length (AL) measurement is important in ophthalmology because it should be considered prior to operations, such as strabismus surgery or cataract surgery, and the automation of AL measurement with easily obtained retinal fundus images has been studied. However, the performance of [...] Read more.

Ocular axial length (AL) measurement is important in ophthalmology because it should be considered prior to operations, such as strabismus surgery or cataract surgery, and the automation of AL measurement with easily obtained retinal fundus images has been studied. However, the performance of deep learning methods inevitably depends on distribution of the data set used, and the lack of data is an issue that needs to be addressed. In this study, we propose a framework for generating pairs of fundus images and their corresponding ALs to improve the AL inference. The generator’s encoder was trained independently using metric learning based on the AL information. A random vector and zero padding were incorporated into the generator to increase data creation flexibility, after which AL information was inserted as conditional information. We verified the effectiveness of this framework by evaluating the performance of AL inference models after training them on a combined data set comprising privately collected actual data and data generated by the proposed method. Compared to using only the actual data set, the mean absolute error and standard deviation of the proposed method decreased from 10.23 and 2.56 to 3.96 and 0.23, respectively, even with a smaller number of layers in the AL prediction models. Full article

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18 pages, 1406 KiB

Open AccessArticle

Performance of an Adaptive Optimization Paradigm for Optimal Operation of a Mono-Switch Class E Induction Heating Application

by Saddam Aziz, Cheung-Ming Lai and Ka Hong Loo

Mathematics 2023, 11(13), 3020; https://doi.org/10.3390/math11133020 - 07 Jul 2023

Viewed by 785

Abstract

The progress of technology involves the continuous improvement of current machines to attain higher levels of energy efficiency, operational dependability, and effectiveness. Induction heating is a thermal process that involves the heating of materials that possess electrical conductivity, such as metals. This technique [...] Read more.

The progress of technology involves the continuous improvement of current machines to attain higher levels of energy efficiency, operational dependability, and effectiveness. Induction heating is a thermal process that involves the heating of materials that possess electrical conductivity, such as metals. This technique finds diverse applications, including induction welding and induction cooking pots. The optimization of the operating point of the inverter discussed in this study necessitated the resolution of a pair of non-convex mathematical models to enhance the energy efficiency of the inverters and mitigate switching losses. In order to determine the most advantageous operational location, a sophisticated surface optimization was conducted, requiring the implementation of a sophisticated optimization methodology, such as the adaptive black widow optimization algorithm. The methodology draws inspiration from the resourceful behavior of female black widow spiders in their quest for nourishment. Its straightforward control variable design and limited computational complexity make it a feasible option for addressing multi-dimensional engineering problems within confined constraints. The primary objective of utilizing the adaptive black widow optimization algorithm in the context of induction heating is to optimize the pertinent process parameters, including power level, frequency, coil design, and material properties, with the ultimate goal of efficiently achieving the desired heating outcomes. The utilization of the adaptive black widow optimization algorithm presents a versatile and robust methodology for addressing optimization problems in the field of induction heating. This is due to its capacity to effectively manage intricate, non-linear, and multi-faceted optimization predicaments. The adaptive black widow optimization algorithm has been modified in order to enhance the optimization process and guarantee the identification of the global optimum. The empirical findings derived from an authentic inverter setup were compared with the hypothetical results. Full article

(This article belongs to the Special Issue Evolutionary Computation 2022)

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17 pages, 728 KiB

Open AccessArticle

Assessing the Risk of APOE-ϵ4 on Alzheimer’s Disease Using Bayesian Additive Regression Trees

by Yifan Xia and Baosheng Liang

Mathematics 2023, 11(13), 3019; https://doi.org/10.3390/math11133019 - 07 Jul 2023

Viewed by 761

Abstract

Alzheimer’s disease (AD) affects about a tenth of the population aged over 65 and nearly half of those over 85, and the number of AD patients continues to grow. Several studies have shown that the

ϵ 4

variant of the apolipoprotein E ( [...] Read more.

Alzheimer’s disease (AD) affects about a tenth of the population aged over 65 and nearly half of those over 85, and the number of AD patients continues to grow. Several studies have shown that the

ϵ 4

variant of the apolipoprotein E (

A P O E

) gene is potentially associated with an increased risk of AD. In this study, we aimed to investigate the causal effect of

A P O E

-

ϵ 4

on Alzheimer’s disease under the potential outcome framework and evaluate the individualized risk of disease onset for

A P O E

-

ϵ 4

carriers. A total of 1705 Hispanic individuals from the Washington Heights-Inwood Columbia Aging Project (WHICAP) were included in this study, comprising 453

A P O E

-

ϵ 4

carriers and 1252 non-carriers. Among them, 265 subjects had developed AD (23.2%). The non-parametric Bayesian additive regression trees (BART) approach was applied to model the individualized causal effects of

A P O E

-

ϵ 4

on disease onset in the presence of right-censored outcomes. The heterogeneous risk of

A P O E

-

ϵ 4

on AD was examined through the individualized posterior survival probability and posterior causal effects. The results showed that, on average, patients carrying

A P O E

-

ϵ 4

were

0.968

years younger at onset than those with non-carrying status, and the disease risk associated with

A P O E

-

ϵ 4

carrying status was

3.9 %

higher than that for non-carrying status; however, it should be noted that neither result was statistically significant. The posterior causal effects of

A P O E

-

ϵ 4

for individualized subjects indicate that 14.41% of carriers presented strong evidence of AD risk and approximately 38.65% presented mild evidence, while around 13.71% of non-carriers presented strong evidence of AD risk and 40.89% presented mild evidence. Furthermore, 79.26% of carriers exhibited a posterior probability of disease risk greater than 0.5. In conclusion, no significant causal effect of the

A P O E

-

ϵ 4

gene on AD was observed at the population level, but strong evidence of AD risk was identified in a sub-group of

A P O E

-

ϵ 4

carriers. Full article

(This article belongs to the Special Issue Application of the Bayesian Method in Statistical Modeling)

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15 pages, 363 KiB

Open AccessArticle

A New Family of Modified Slash Distributions with Applications

by Jimmy Reyes and Yuri A. Iriarte

Mathematics 2023, 11(13), 3018; https://doi.org/10.3390/math11133018 - 07 Jul 2023

Cited by 2 | Viewed by 805

Abstract

This article presents a new family of symmetric heavy-tailed distributions. This model is based on the ratio of two independent random variables; one with a normal distribution in the numerator and another with a Birnbaum–Saunders distribution in the denominator. The result is a [...] Read more.

This article presents a new family of symmetric heavy-tailed distributions. This model is based on the ratio of two independent random variables; one with a normal distribution in the numerator and another with a Birnbaum–Saunders distribution in the denominator. The result is a new slash-like distribution capable of modeling high levels of kurtosis, so it can be considered as a viable alternative to other heavy-tailed distributions in the literature. Fundamental properties such as density and raw moments are derived. Parameter estimation is performed using the moment and maximum likelihood methods. A simulation study to evaluate the behavior of the estimators is carried out. Finally, the utility of the new distribution is illustrated by fitting two real datasets. Full article

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19 pages, 2813 KiB

Open AccessArticle

Cluster-Based Vehicle-to-Everything Model with a Shared Cache

by Andrei Vladyko, Gleb Tambovtsev, Elena Podgornaya, Samia Allaoua Chelloug, Reem Alkanhel and Pavel Plotnikov

Mathematics 2023, 11(13), 3017; https://doi.org/10.3390/math11133017 - 07 Jul 2023

Cited by 1 | Viewed by 979

Abstract

This paper presents an analysis of the effectiveness of the element interaction model in a vehicular ad hoc network (VANET). An analysis of the mathematical model and its numerical solution for the system of boundary device interactions in the traditional configuration of roadside [...] Read more.

This paper presents an analysis of the effectiveness of the element interaction model in a vehicular ad hoc network (VANET). An analysis of the mathematical model and its numerical solution for the system of boundary device interactions in the traditional configuration of roadside unit (RSU) placement using single- and dual-channel connection between on-board units (OBU) and RSU is given. In addition, the model efficiency is improved using a clustering approach. The efficiency evaluation is based on calculating the percentage of unprocessed requests generated by OBUs during their mobility, the average power consumption and the magnitude of the delay in transmitting and processing the generated requests in the OBU–RSU system. The traditional and cluster models are compared. The results obtained in this paper show that each of the proposed models can be effectively implemented in mobile nodes and will significantly reduce the overall expected query processing time to improve the organization and algorithmic support of VANET. Along with this, it is shown that the developed approach allows for efficient power consumption when combining RSUs into clusters with a shared cache. The novelty of solving the problems is due to the lack of a comprehensive model that allows the distribution and prediction of the parameters and resources of the system for different computational tasks, which is essential when implementing and using V2X technology to solve the problems of complex management of VANET elements. Full article

(This article belongs to the Special Issue Network Planning and Internet of Things: Mathematical Modeling, Connectivity Problems, and Applications)

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10 pages, 263 KiB

Open AccessArticle

Novel Contributions to the System of Fractional Hamiltonian Equations

by Tayeb Mahrouz, Abdelaziz Mennouni, Abdelkader Moumen and Tariq Alraqad

Mathematics 2023, 11(13), 3016; https://doi.org/10.3390/math11133016 - 07 Jul 2023

Viewed by 672

Abstract

This work aims to analyze a new system of two fractional Hamiltonian equations. We propose an effective method for transforming the established model into a system of two distinct equations. Two functionals that are connected to the converted system of fractional Hamiltonian systems [...] Read more.

This work aims to analyze a new system of two fractional Hamiltonian equations. We propose an effective method for transforming the established model into a system of two distinct equations. Two functionals that are connected to the converted system of fractional Hamiltonian systems are introduced together with a new space, and it is demonstrated that these functionals are bounded below on this space. The hypotheses presented here differ from those provided in the literature. Full article

(This article belongs to the Special Issue Advances in Fractional Operators and Their Applications in Physical Sciences)

22 pages, 7566 KiB

Open AccessArticle

Probability-Distribution-Guided Adversarial Sample Attacks for Boosting Transferability and Interpretability

by Hongying Li, Miaomiao Yu, Xiaofei Li, Jun Zhang, Shuohao Li, Jun Lei and Hairong Huang

Mathematics 2023, 11(13), 3015; https://doi.org/10.3390/math11133015 - 06 Jul 2023

Viewed by 1007

Abstract

In recent years, with the rapid development of technology, artificial intelligence (AI) security issues represented by adversarial sample attack have aroused widespread concern in society. Adversarial samples are often generated by surrogate models and then transfer to attack the target model, and most [...] Read more.

In recent years, with the rapid development of technology, artificial intelligence (AI) security issues represented by adversarial sample attack have aroused widespread concern in society. Adversarial samples are often generated by surrogate models and then transfer to attack the target model, and most AI models in real-world scenarios belong to black boxes; thus, transferability becomes a key factor to measure the quality of adversarial samples. The traditional method relies on the decision boundary of the classifier and takes the boundary crossing as the only judgment metric without considering the probability distribution of the sample itself, which results in an irregular way of adding perturbations to the adversarial sample, an unclear path of generation, and a lack of transferability and interpretability. In the probabilistic generative model, after learning the probability distribution of the samples, a random term can be added to the sampling to gradually transform the noise into a new independent and identically distributed sample. Inspired by this idea, we believe that by removing the random term, the adversarial sample generation process can be regarded as the static sampling of the probabilistic generative model, which guides the adversarial samples out of the original probability distribution and into the target probability distribution and helps to boost transferability and interpretability. Therefore, we proposed a score-matching-based attack (SMBA) method to perform adversarial sample attacks by manipulating the probability distribution of the samples, which showed good transferability in the face of different datasets and models and provided reasonable explanations from the perspective of mathematical theory and feature space. Compared with the current best methods based on the decision boundary of the classifier, our method increased the attack success rate by 51.36% and 30.54% to the maximum extent in non-targeted and targeted attack scenarios, respectively. In conclusion, our research established a bridge between probabilistic generative models and adversarial samples, provided a new entry angle for the study of adversarial samples, and brought new thinking to AI security. Full article

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25 pages, 1181 KiB

Open AccessArticle

Compact Integer Programs for Depot-Free Multiple Traveling Salesperson Problems

by José Alejandro Cornejo-Acosta, Jesús García-Díaz, Julio César Pérez-Sansalvador and Carlos Segura

Mathematics 2023, 11(13), 3014; https://doi.org/10.3390/math11133014 - 06 Jul 2023

Cited by 2 | Viewed by 1448

Abstract

Multiple traveling salesperson problems (mTSP) are a collection of problems that generalize the classical traveling salesperson problem (TSP). In a nutshell, an mTSP variant seeks a minimum cost collection of m paths that visit all vertices of a given weighted [...] Read more.

Multiple traveling salesperson problems (mTSP) are a collection of problems that generalize the classical traveling salesperson problem (TSP). In a nutshell, an mTSP variant seeks a minimum cost collection of m paths that visit all vertices of a given weighted complete graph. This paper introduces novel compact integer programs for the depot-free mTSP (DFmTSP). This fundamental variant models real scenarios where depots are unknown or unnecessary. The proposed integer programs are adapted to the main variants of the DFmTSP, such as closed paths, open paths, bounding constraints (also known as load balance), and the minsum and minmax objective functions. Some of these integer programs have

O (n^{2} m)

binary variables and

O (n^{2})

constraints, where m is the number of salespersons and

n = | V (G) |

. Furthermore, we introduce more compact integer programs with

O (n^{2})

binary variables and

O (n^{2})

constraints for the same problem and most of its main variants. Without losing their compactness, all the proposed programs are adapted to fixed-destination multiple-depots mTSP (FD-MmTSP) and a combination of FD-MmTSP and DFmTSP, where fewer than m depots are part of the input, but the solution still consists of m paths. We used off-the-shelf optimization software to empirically test the proposed integer programs over a classical benchmark dataset; these tests show that the proposed programs meet desirable theoretical properties and have practical advantages over the state of the art. Full article

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

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14 pages, 331 KiB

Open AccessArticle

Decomposition Integrals of Set-Valued Functions Based on Fuzzy Measures

by Leifan Yan, Tong Kang and Huai Zhang

Mathematics 2023, 11(13), 3013; https://doi.org/10.3390/math11133013 - 06 Jul 2023

Cited by 1 | Viewed by 808

Abstract

The decomposition integrals of set-valued functions with regards to fuzzy measures are introduced in a natural way. These integrals are an extension of the decomposition integral for real-valued functions and include several types of set-valued integrals, such as the Aumann integral based on [...] Read more.

The decomposition integrals of set-valued functions with regards to fuzzy measures are introduced in a natural way. These integrals are an extension of the decomposition integral for real-valued functions and include several types of set-valued integrals, such as the Aumann integral based on the classical Lebesgue integral, the set-valued Choquet, pan-, concave and Shilkret integrals of set-valued functions with regard to capacity, etc. Some basic properties are presented and the monotonicity of the integrals in the sense of different types of the preorder relations are shown. By means of the monotonicity, the Chebyshev inequalities of decomposition integrals for set-valued functions are established. As a special case, we show the linearity of concave integrals of set-valued functions in terms of the equivalence relation based on a kind of preorder. The coincidences among the set-valued Choquet, the set-valued pan-integral and the set-valued concave integral are presented. Full article

(This article belongs to the Special Issue Set-Valued Analysis, 3rd Edition)

18 pages, 2881 KiB

Open AccessArticle

Enhancing IoT Connectivity in Massive MIMO Networks through Systematic Scheduling and Power Control Strategies

by Byung Moo Lee

Mathematics 2023, 11(13), 3012; https://doi.org/10.3390/math11133012 - 06 Jul 2023

Cited by 2 | Viewed by 792

Abstract

Massive MIMO systems can support a large number of Internet of Things (IoT) devices, even if the number of IoT devices exceeds the number of service antennas in a single base station (BS) located at the data center. In order to improve the [...] Read more.

Massive MIMO systems can support a large number of Internet of Things (IoT) devices, even if the number of IoT devices exceeds the number of service antennas in a single base station (BS) located at the data center. In order to improve the performance of Massive MIMO with massive IoT connectivity in a BS, simple scheduling and power control schemes can be of great help, but typically, they require high power consumption in the situation of serious shadow fading. In this paper, we try to improve the performance of Massive MIMO with massive IoT connectivity by using the dropping technique that drops the IoT devices that require high power consumption. Several scheduling and power control schemes have been proposed to increase the spectral efficiency (SE) and the energy efficiency (EE) of Massive MIMO systems. By the combination of these schemes with the dropping technique, we show that the performance can be even further increased under some circumstances. There is a dropping coefficient factor (DCF) to determine the IoT devices that should be dropped. This technique gives more benefits to the power control schemes that require higher power consumption. Simulation results and relevant analyses are provided to verify the effectiveness of the proposed technique. Full article

(This article belongs to the Section Engineering Mathematics)

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37 pages, 5758 KiB

Open AccessArticle

Stability Analysis of Plankton–Fish Dynamics with Cannibalism Effect and Proportionate Harvesting on Fish

by Sk Golam Mortoja, Prabir Panja and Shyamal Kumar Mondal

Mathematics 2023, 11(13), 3011; https://doi.org/10.3390/math11133011 - 06 Jul 2023

Cited by 4 | Viewed by 2204

Abstract

Plankton occupy a vital place in the marine ecosystem due to their essential role. However small or microscopic, their absence can bring the entire life process to a standstill. In this work, we have proposed a prey–predator ecological model consisting of phytoplankton, zooplankton, [...] Read more.

Plankton occupy a vital place in the marine ecosystem due to their essential role. However small or microscopic, their absence can bring the entire life process to a standstill. In this work, we have proposed a prey–predator ecological model consisting of phytoplankton, zooplankton, and fish, incorporating the cannibalistic nature of zooplankton harvesting the fish population. Due to differences in their feeding habits, zooplankton are divided into two sub-classes: herbivorous and carnivorous. The dynamic behavior of the model is examined for each of the possible steady states. The stability criteria of the model have been analyzed from both local and global perspectives. Hopf bifurcation analysis has been accomplished with the growth rate of carnivorous zooplankton using cannibalism as a bifurcation parameter. To characterize the optimal control, we have used Pontryagin’s maximum principle. Subsequently, the optimal system has been derived and solved numerically using an iterative method with Runge–Kutta fourth-order scheme. Finally, to facilitate the interpretation of our mathematical results, we have proceeded to investigate it using numerical simulations. Full article

(This article belongs to the Special Issue Complex Biological Systems and Mathematical Biology)

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34 pages, 1583 KiB

Open AccessArticle

A Study to Identify Long-Term Care Insurance Using Advanced Intelligent RST Hybrid Models with Two-Stage Performance Evaluation

by You-Shyang Chen, Ying-Hsun Hung and Yu-Sheng Lin

Mathematics 2023, 11(13), 3010; https://doi.org/10.3390/math11133010 - 06 Jul 2023

Cited by 1 | Viewed by 1038

Abstract

With the motivation of long-term care 2.0 plans, forecasting models to identify potential customers of long-term care insurance (LTCI) are an important and interesting issue. From the limited literature, most past researchers emphasize traditional statistics techniques to address this issue; however, these are [...] Read more.

With the motivation of long-term care 2.0 plans, forecasting models to identify potential customers of long-term care insurance (LTCI) are an important and interesting issue. From the limited literature, most past researchers emphasize traditional statistics techniques to address this issue; however, these are lacking in some areas. For example, intelligent hybrid models for LTCI are lacking, performance measurement of components for hybrid models is lacking, and research results for interpretative capacities are lacking, resulting in a black box scenario and difficulty in making decisions, and the gap between identifying potential customers and constructing hybrid models is unbridged. To solve the shortcomings mentioned above, this study proposes some advanced intelligent single and hybrid models; the study object is LTCI customers. The proposed hybrid models were used on the experimental dataset collected from real insurance data and possess the following advantages: (1) The feature selection technique was used to simplify variables for the purpose of improving model performance. (2) The performance of hybrid models was evaluated against some machine learning methods, including rough set theory, decision trees, multilayer perceptron, support vector machine, genetic algorithm, random forest, logistic regression, and naive Bayes, and sensitivity analysis was performed in terms of accuracy, coverage, rules number, and standard deviation. (3) We used the C4.5 algorithm of decision trees and the LEM2 algorithm of rough sets to extract and provide valuably comprehensible decisional rules as decision-making references for the interested parties for their varied benefits. (4) We used post hoc testing to verify the significant difference in groups. Conclusively, this study effectively identifies potential customers for their key attributes and creates a decision rule set of knowledge for use as a reference when solving practical problems by forming a structured solution. This study is a new trial in the LTCI application field and realizes novel creative application values. Such a hybrid model is rarely seen in identifying LTCI potential customers; thus, the study has sufficient application contribution and managerial benefits to attract much concern from the interested parties. Full article

(This article belongs to the Special Issue Industrial Mathematics in Management and Engineering)

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19 pages, 4540 KiB

Open AccessArticle

Numerical Solution of Thermal Phenomena in Welding Problems

by Mario Freire-Torres, Manuel Colera and Jaime Carpio

Mathematics 2023, 11(13), 3009; https://doi.org/10.3390/math11133009 - 06 Jul 2023

Viewed by 996

Abstract

We present a novel finite element method to solve the thermal variables in welding problems. The mathematical model is based on the enthalpy formulation of the energy conservation law, which is simultaneously valid for the solid, liquid, and mushy regions. Both isothermal and [...] Read more.

We present a novel finite element method to solve the thermal variables in welding problems. The mathematical model is based on the enthalpy formulation of the energy conservation law, which is simultaneously valid for the solid, liquid, and mushy regions. Both isothermal and non-isothermal melting models are considered to relate the enthalpy with the temperature. Quadratic triangular elements with local anisotropic mesh adaptation are employed for the space discretization of the governing equation, and a second-order backward differentiation formula is employed for the time discretization. The resulting non-linear discretized system is solved with a simple Newton algorithm with two versions: the

θ

-Newton algorithm, which considers the temperature as the main unknown variable, as in most works in the literature, and the h-Newton algorithm, which considers the enthalpy, which is the main novelty of the present work. Then, we show via numerical experiments that the h-Newton method is robust and converges well to the solution, both for isothermal and non-isothermal melting. However, the

θ

-method can only be applied to the case of non-isothermal melting and converges only for a sufficiently large melting temperature range or sufficiently small time step. Numerical experiments also confirm that the method is able to adequately capture the discontinuities or sharp variations in the solution without the need for any kind of numerical dissipation. Full article

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37 pages, 6691 KiB

Open AccessFeature PaperReview

Prognostics and Health Management of Rotating Machinery of Industrial Robot with Deep Learning Applications—A Review

by Prashant Kumar, Salman Khalid and Heung Soo Kim

Mathematics 2023, 11(13), 3008; https://doi.org/10.3390/math11133008 - 06 Jul 2023

Cited by 7 | Viewed by 2995

Abstract

The availability of computational power in the domain of Prognostics and Health Management (PHM) with deep learning (DL) applications has attracted researchers worldwide. Industrial robots are the prime mover of modern industry. Industrial robots comprise multiple forms of rotating machinery, like servo motors [...] Read more.

The availability of computational power in the domain of Prognostics and Health Management (PHM) with deep learning (DL) applications has attracted researchers worldwide. Industrial robots are the prime mover of modern industry. Industrial robots comprise multiple forms of rotating machinery, like servo motors and numerous gears. Thus, the PHM of the rotating components of industrial robots is crucial to minimize the downtime in the industries. In recent times, deep learning has proved its mettle in different areas, like bio-medical, image recognition, speech recognition, and many more. PHM with DL applications is a rapidly growing field. It has helped achieve a better understanding of the different condition monitoring signals, like vibration, current, temperature, acoustic emission, partial discharge, and pressure. Most current review articles are component- (or system-)specific and have not been updated to reflect the new deep learning approaches. Also, a unified review paper for PHM strategies for industrial robots and their rotating machinery with DL applications has not previously been presented. This paper presents a review of the PHM strategies with various DL algorithms for industrial robots and rotating machinery, along with brief theoretical aspects of the algorithms. This paper presents a trend of the up-to-date advancements in PHM approaches using DL algorithms. Also, the restrictions and challenges associated with the available PHM approaches are discussed, paving the way for future studies. Full article

(This article belongs to the Special Issue Recent Advances in Machine learning and Deep Learning Theories: Towards Intelligent Fault Diagnosis)

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16 pages, 384 KiB

Open AccessArticle

Assessing Multinomial Distributions with a Bayesian Approach

by Luai Al-Labadi, Petru Ciur, Milutin Dimovic and Kyuson Lim

Mathematics 2023, 11(13), 3007; https://doi.org/10.3390/math11133007 - 06 Jul 2023

Viewed by 1130

Abstract

This paper introduces a unified Bayesian approach for testing various hypotheses related to multinomial distributions. The method calculates the Kullback–Leibler divergence between two specified multinomial distributions, followed by comparing the change in distance from the prior to the posterior through the relative belief [...] Read more.

This paper introduces a unified Bayesian approach for testing various hypotheses related to multinomial distributions. The method calculates the Kullback–Leibler divergence between two specified multinomial distributions, followed by comparing the change in distance from the prior to the posterior through the relative belief ratio. A prior elicitation algorithm is used to specify the prior distributions. To demonstrate the effectiveness and practical application of this approach, it has been applied to several examples. Full article

(This article belongs to the Special Issue Research Progress and Application of Bayesian Statistics)

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24 pages, 5988 KiB

Open AccessArticle

Multi-Agent Evolutionary Game Analysis of Group Panic Buying in China during the COVID-19 Pandemic

by Xunqing Wang, Nan Zhang, Hang Zhou, Xinpeng Huang and Rundong Luo

Mathematics 2023, 11(13), 3006; https://doi.org/10.3390/math11133006 - 06 Jul 2023

Cited by 2 | Viewed by 1080

Abstract

With the global outbreak of COVID-19, the panic-buying incidents triggered by the variants of the Omicron strain have severely affected the normal social order. This paper considers the complex interest game and interactive relationship among multiple subjects in the mass-panic buying event caused [...] Read more.

With the global outbreak of COVID-19, the panic-buying incidents triggered by the variants of the Omicron strain have severely affected the normal social order. This paper considers the complex interest game and interactive relationship among multiple subjects in the mass-panic buying event caused by rumors and constructs a three-party evolution game model of local government, rumor-monger, and public. The strategy-selection process of each subject based on evolutionary game theory is studied, and the strategy selection of three game subjects in different situations and related influencing factors are analyzed. Taking the example of the montmorillonite powder panic buying caused by the XBB virus strain rumor in China, the evolutionary game model constructed in this study is simulated and analyzed. The study shows that the evolutionary process of the mass panic-buying event is characterized by six stages: the initial stage; the outbreak stage; the spread stage; the climax stage; the relief stage; and the recovery stage. There are four stable points in the evolutionary game of the three game subjects, namely (no intervention, no rumor, no panic buying), (no intervention, rumor, no panic buying), (intervention, no rumor, no panic buying), and (intervention, rumor, no panic buying). The strategy of government intervention will be adjusted according to the strategy selection of the public and the rumor-monger. Under the mechanism of reward and punishment of the higher-level government, increasing the punishment and reward intensity of the higher-level government will promote the local government to intervene in the rumor-mongering event faster, but increasing the reward intensity has a more significant impact on the intervention behavior of the local government than punishment, and increasing punishment intensity has a more significant impact on the non-rumor-mongering behavior of the rumor-monger than reward. The parameters of social risk-bearing cost, risk transmission coefficient, rumor-mongering income and cost, and public drug purchase cost have different degrees of influence on the evolutionary behavior of game subjects. Therefore, this study provides new ideas for effectively responding to mass panic buying events in the context of public emergencies. Full article

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11 pages, 902 KiB

Open AccessArticle

Efficiency Evaluation of China’s Provincial Digital Economy Based on a DEA Cross-Efficiency Model

by Yaqiao Xu, Jiayi Hu and Liusan Wu

Mathematics 2023, 11(13), 3005; https://doi.org/10.3390/math11133005 - 06 Jul 2023

Cited by 2 | Viewed by 821

Abstract

The Chinese government clearly put forward a strategy to speed up the development of the digital economy in “the 14th Five-Year” Plan, which will become the booster of China’s development. China has a vast territory and the state of development of the digital [...] Read more.

The Chinese government clearly put forward a strategy to speed up the development of the digital economy in “the 14th Five-Year” Plan, which will become the booster of China’s development. China has a vast territory and the state of development of the digital economy varies greatly across different regions. It is crucial to clarify the reasons for these differences and take measures to narrow them. Therefore, the evaluation and analysis of the current situation are conducive to the further development of the digital economy. Taking 30 provinces (excluding Tibet, Hong Kong, Macao and Taiwan) of China as the research objects, this paper constructs an index system taking digital infrastructure, digital technology and digital talent as input variables and taking digital industrialization and industrial digitization as output variables. The data envelopment analysis (DEA) cross-efficiency model is constructed to calculate and compare the cross-efficiency of the digital economies in each province. The results show the following: (1) The development efficiency of China’s digital economy has generally been low, and there is a large “digital divide” between provinces. (2) The input of digital talents is crucial for the digital economy in order to achieve high output and high efficiency, and high output is often accompanied by high efficiency. Based on the above conclusions, this paper puts forward some suggestions to promote the development of China’s digital economy. Full article

(This article belongs to the Special Issue Data-Driven Decision Making: Models, Methods and Applications)

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