Mathematics

10 pages, 933 KiB

Open AccessArticle

Non-Relativistic Treatment of the 2D Electron System Interacting via Varshni–Shukla Potential Using the Asymptotic Iteration Method

by Collins Okon Edet, Salman Mahmoud, Etido P. Inyang, Norshamsuri Ali, Syed Alwee Aljunid, Rosdisham Endut, Akpan Ndem Ikot and Muhammad Asjad

Mathematics 2022, 10(15), 2824; https://doi.org/10.3390/math10152824 - 08 Aug 2022

Cited by 24 | Viewed by 1781

Abstract

The nonrelativistic treatment of the Varshni–Shukla potential (V–SP) in the presence of magnetic and Aharanov–Bohm fields is carried out using the asymptotic iteration method (AIM). The energy equation and wave function are derived analytically. The energy levels are summed to obtain the partition [...] Read more.

The nonrelativistic treatment of the Varshni–Shukla potential (V–SP) in the presence of magnetic and Aharanov–Bohm fields is carried out using the asymptotic iteration method (AIM). The energy equation and wave function are derived analytically. The energy levels are summed to obtain the partition function, which is employed to derive the expressions for the thermomagnetic properties of the V–SP. These properties are analyzed extensively using graphical representations. It is observed that in the various settings of the analysis, the system shows a diamagnetic characteristic, and the specific heat capacity behavior agrees with the recognized Dulong–Petit law, although some slight anomaly is observed. This irregular behavior could be attributed to a Schottky anomaly. Our findings will be valuable in a variety of fields of physics, including chemical, molecular and condensed matter physics, where our derived models could be applied to study other diatomic molecules and quantum dots, respectively. 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, 2738 KiB

Open AccessArticle

Negative Feedback Punishment Approach Helps Sanctioning Institutions Achieve Stable, Time-Saving and Low-Cost Performances

by Jun Qian, Xiao Sun, Ziyang Wang and Yueting Chai

Mathematics 2022, 10(15), 2823; https://doi.org/10.3390/math10152823 - 08 Aug 2022

Viewed by 1214

Abstract

Sanctioning institutions widely exist in human society. Although these institutions play an important role in the management of social affairs, sanctions are often seen to be costly in terms of both time and money. To enable sanctioning institutions to develop effective sanctions, we [...] Read more.

Sanctioning institutions widely exist in human society. Although these institutions play an important role in the management of social affairs, sanctions are often seen to be costly in terms of both time and money. To enable sanctioning institutions to develop effective sanctions, we propose a negative feedback punishment approach for these institutions that combines the feedback control principle and the negative correlation principle. In the negative feedback punishment approach, the punishment intensity imposed on the group is negatively correlated with the current group cooperation proportion. Through evolutionary simulation and theoretical analysis, we found that the negative feedback punishment approach facilitates more stable, time-saving and low-cost performance by sanctioning institutions than other punishment methods. This work offers a feasible solution for sanctioning institutions to solve social dilemmas and provides a possible theoretical starting point for investigating effective pool punishment measures. Full article

(This article belongs to the Special Issue Uncertain System Optimization and Games)

► Show Figures

Figure 1

14 pages, 291 KiB

Open AccessArticle

The Fuzzy Complex Linear Systems Based on a New Representation of Fuzzy Complex Numbers

by Zhiyong Xiao and Zengtai Gong

Mathematics 2022, 10(15), 2822; https://doi.org/10.3390/math10152822 - 08 Aug 2022

Cited by 1 | Viewed by 1182

Abstract

Since the product of complex numbers and rectangular fuzzy complex numbers (RFCN) is not necessarily a RFCN in the former fuzzy complex linear system (FCLS), the scalar multiplication and addition operations of complex numbers and fuzzy complex numbers (FCN) based on a new [...] Read more.

Since the product of complex numbers and rectangular fuzzy complex numbers (RFCN) is not necessarily a RFCN in the former fuzzy complex linear system (FCLS), the scalar multiplication and addition operations of complex numbers and fuzzy complex numbers (FCN) based on a new representation of FCN are proposed. We also introduce a new method for solving FCLS, which can convert FCLS into two distinct linear systems. One is an

n \times n

complex linear system, and the other is an

(m n) \times (m n)

real linear system, where n is the number of unknown variables, and m is the number of substitutional cyclic sets composed of coefficients of FCLS. In particular, using this method to solve one-dimensional fuzzy linear systems, a

(2 n) \times (2 n)

RLS is obtained, which is consistent with Friedman’s method. Finally, FCLS based on the RFCN as a special case are also investigated. Full article

(This article belongs to the Special Issue Fuzzy Group Decision Making)

11 pages, 346 KiB

Open AccessArticle

Mathematical Model of Hepatitis B Virus Treatment with Support of Immune System

by Irina Volinsky

Mathematics 2022, 10(15), 2821; https://doi.org/10.3390/math10152821 - 08 Aug 2022

Cited by 3 | Viewed by 1603

Abstract

In the current paper, the classification of the equilibrium points of an HBV mathematical model with combined therapy is presented. The influence of right-hand side changes on solution behavior is estimated, and regulation with delays in upper- and lower-bound integral limits that presents [...] Read more.

In the current paper, the classification of the equilibrium points of an HBV mathematical model with combined therapy is presented. The influence of right-hand side changes on solution behavior is estimated, and regulation with delays in upper- and lower-bound integral limits that presents a time period with IL-2 support therapy are researched. Full article

(This article belongs to the Special Issue Mathematical and Computational Methods in Systems Biology)

► Show Figures

Figure 1

21 pages, 2942 KiB

Open AccessArticle

Inference and Local Influence Assessment in a Multifactor Skew-Normal Linear Mixed Model

by Zeinolabedin Najafi, Karim Zare, Mohammad Reza Mahmoudi, Soheil Shokri and Amir Mosavi

Mathematics 2022, 10(15), 2820; https://doi.org/10.3390/math10152820 - 08 Aug 2022

Cited by 3 | Viewed by 1261

Abstract

This work considers a multifactor linear mixed model under heteroscedasticity in random-effect factors and the skew-normal errors for modeling the correlated datasets. We implement an expectation–maximization (EM) algorithm to achieve the maximum likelihood estimates using conditional distributions of the skew-normal distribution. The EM [...] Read more.

This work considers a multifactor linear mixed model under heteroscedasticity in random-effect factors and the skew-normal errors for modeling the correlated datasets. We implement an expectation–maximization (EM) algorithm to achieve the maximum likelihood estimates using conditional distributions of the skew-normal distribution. The EM algorithm is also implemented to extend the local influence approach under three model perturbation schemes in this model. Furthermore, a Monte Carlo simulation is conducted to evaluate the efficiency of the estimators. Finally, a real data set is used to make an illustrative comparison among the following four scenarios: normal/skew-normal errors and heteroscedasticity/homoscedasticity in random-effect factors. The empirical studies show our methodology can improve the estimates when the model errors follow from a skew-normal distribution. In addition, the local influence analysis indicates that our model can decrease the effects of anomalous observations in comparison to normal ones. Full article

(This article belongs to the Special Issue Mathematical and Computational Statistics and Their Applications)

► Show Figures

Figure 1

25 pages, 3776 KiB

Open AccessArticle

Explainable Machine Learning Methods for Classification of Brain States during Visual Perception

by Robiul Islam, Andrey V. Andreev, Natalia N. Shusharina and Alexander E. Hramov

Mathematics 2022, 10(15), 2819; https://doi.org/10.3390/math10152819 - 08 Aug 2022

Cited by 6 | Viewed by 2084

Abstract

The aim of this work is to find a good mathematical model for the classification of brain states during visual perception with a focus on the interpretability of the results. To achieve it, we use the deep learning models with different activation functions [...] Read more.

The aim of this work is to find a good mathematical model for the classification of brain states during visual perception with a focus on the interpretability of the results. To achieve it, we use the deep learning models with different activation functions and optimization methods for their comparison and find the best model for the considered dataset of 31 EEG channels trials. To estimate the influence of different features on the classification process and make the method more interpretable, we use the SHAP library technique. We find that the best optimization method is Adagrad and the worst one is FTRL. In addition, we find that only Adagrad works well for both linear and tangent models. The results could be useful for EEG-based brain–computer interfaces (BCIs) in part for choosing the appropriate machine learning methods and features for the correct training of the BCI intelligent system. Full article

(This article belongs to the Special Issue Dynamics and Bifurcations in Mathematical Neuroscience: Analysis, Modeling and Applications)

► Show Figures

Figure 1

19 pages, 7040 KiB

Open AccessArticle

Performance Comparison of Numerical Methods in a Predictive Controller for an AC–DC Power Converter

by Jazmin Ramirez-Hernandez, Oswaldo Ulises Juarez-Sandoval, Leobardo Hernandez-Gonzalez, Domingo Cortes, Juan C. Sanchez-Garcia and Pedro Guevara-Lopez

Mathematics 2022, 10(15), 2818; https://doi.org/10.3390/math10152818 - 08 Aug 2022

Cited by 1 | Viewed by 1737

Abstract

The use of model-based predictive control in power converters has substantially increased in recent years. This control technique always needs a discrete system model to be implemented. There are several methods to obtain a discrete model; in this paper, all common methods are [...] Read more.

The use of model-based predictive control in power converters has substantially increased in recent years. This control technique always needs a discrete system model to be implemented. There are several methods to obtain a discrete model; in this paper, all common methods are examined from a practical point of view. Their precision, simplicity, and implementation requirements are analyzed to establish their advantages and disadvantages. From this analysis, it is shown that different discretization methods result in different closed-loop converter performance. A model-based predictive control AC–DC converter is used to show that different discretization procedures result in different total harmonic distortion. For this evaluation, a simulation of a 1 kW three-phase active rectifier was performed in Matlab-Simulink. Full article

(This article belongs to the Special Issue Mathematical Modelling, Nonlinear Optimization, Nondimensionalization and Engineering Applications)

► Show Figures

Figure 1

17 pages, 1642 KiB

Open AccessArticle

Complex Noise-Resistant Zeroing Neural Network for Computing Complex Time-Dependent Lyapunov Equation

by Bolin Liao, Cheng Hua, Xinwei Cao, Vasilios N. Katsikis and Shuai Li

Mathematics 2022, 10(15), 2817; https://doi.org/10.3390/math10152817 - 08 Aug 2022

Cited by 9 | Viewed by 1877

Abstract

Complex time-dependent Lyapunov equation (CTDLE), as an important means of stability analysis of control systems, has been extensively employed in mathematics and engineering application fields. Recursive neural networks (RNNs) have been reported as an effective method for solving CTDLE. In the previous work, [...] Read more.

Complex time-dependent Lyapunov equation (CTDLE), as an important means of stability analysis of control systems, has been extensively employed in mathematics and engineering application fields. Recursive neural networks (RNNs) have been reported as an effective method for solving CTDLE. In the previous work, zeroing neural networks (ZNNs) have been established to find the accurate solution of time-dependent Lyapunov equation (TDLE) in the noise-free conditions. However, noises are inevitable in the actual implementation process. In order to suppress the interference of various noises in practical applications, in this paper, a complex noise-resistant ZNN (CNRZNN) model is proposed and employed for the CTDLE solution. Additionally, the convergence and robustness of the CNRZNN model are analyzed and proved theoretically. For verification and comparison, three experiments and the existing noise-tolerant ZNN (NTZNN) model are introduced to investigate the effectiveness, convergence and robustness of the CNRZNN model. Compared with the NTZNN model, the CNRZNN model has more generality and stronger robustness. Specifically, the NTZNN model is a special form of the CNRZNN model, and the residual error of CNRZNN can converge rapidly and stably to order

10^{- 5}

when solving CTDLE under complex linear noises, which is much lower than order

10^{- 1}

of the NTZNN model. Analogously, under complex quadratic noises, the residual error of the CNRZNN model can converge to

{2 ∥ A ∥}_{F} / ζ^{3}

quickly and stably, while the residual error of the NTZNN model is divergent. Full article

► Show Figures

Figure 1

17 pages, 417 KiB

Open AccessArticle

New Criterias of Synchronization for Discrete-Time Recurrent Neural Networks with Time-Varying Delay via Event-Triggered Control

by Lei Yu, Guici Chen, Feng Jiang and Zhi Wang

Mathematics 2022, 10(15), 2816; https://doi.org/10.3390/math10152816 - 08 Aug 2022

Cited by 1 | Viewed by 1158

Abstract

This paper mainly researches the synchronization issue of discrete-time recurrent neural networks (DTRNNs) with time-varying delay based on event-triggered control (ETC). ETC can effectively decrease the quantity of controller updates performed and the utilization of communication resources. By using Lyapunov–Krasovskii functional (LKF), Schur [...] Read more.

This paper mainly researches the synchronization issue of discrete-time recurrent neural networks (DTRNNs) with time-varying delay based on event-triggered control (ETC). ETC can effectively decrease the quantity of controller updates performed and the utilization of communication resources. By using Lyapunov–Krasovskii functional (LKF), Schur complement lemma, discrete time free weight matrix method, linear matrix inequalities (LMIs) and other analytical methods, the stability conditions of the error system are deduced. Accordingly, a class of event-triggered state feedback controllers is designed. Finally, through two numerical examples with simulations, the effectiveness of the controller is verified. Full article

(This article belongs to the Section Computational and Applied Mathematics)

► Show Figures

Figure 1

15 pages, 313 KiB

Open AccessArticle

Medical Diagnosis and Pattern Recognition Based on Generalized Dice Similarity Measures for Managing Intuitionistic Hesitant Fuzzy Information

by Majed Albaity and Tahir Mahmood

Mathematics 2022, 10(15), 2815; https://doi.org/10.3390/math10152815 - 08 Aug 2022

Cited by 5 | Viewed by 1106

Abstract

Pattern recognition is the computerized identification of shapes, designs, and reliabilities in information. It has applications in information compression, machine learning, statistical information analysis, signal processing, image analysis, information retrieval, bioinformatics, and computer graphics. Similarly, a medical diagnosis is a procedure to illustrate [...] Read more.

Pattern recognition is the computerized identification of shapes, designs, and reliabilities in information. It has applications in information compression, machine learning, statistical information analysis, signal processing, image analysis, information retrieval, bioinformatics, and computer graphics. Similarly, a medical diagnosis is a procedure to illustrate or identify diseases or disorders, which would account for a person’s symptoms and signs. Moreover, to illustrate the relationship between any two pieces of intuitionistic hesitant fuzzy (IHF) information, the theory of generalized dice similarity (GDS) measures played an important and valuable role in the field of genuine life dilemmas. The main influence of GDS measures is that we can easily obtain a lot of measures by using different values of parameters, which is the main part of every measure, called DGS measures. The major influence of this theory is to utilize the well-known and valuable theory of dice similarity measures (DSMs) (four different types of DSMs) under the assumption of the IHF set (IHFS), because the IHFS covers the membership grade (MG) and non-membership grade (NMG) in the form of a finite subset of [0, 1], with the rule that the sum of the supremum of the duplet is limited to [0, 1]. Furthermore, we pioneered the main theory of generalized DSMs (GDSMs) computed based on IHFS, called the IHF dice similarity measure, IHF weighted dice similarity measure, IHF GDS measure, and IHF weighted GDS measure, and computed their special cases with the help of parameters. Additionally, to evaluate the proficiency and capability of pioneered measures, we analyzed two different types of applications based on constructed measures, called medical diagnosis and pattern recognition problems, to determine the supremacy and consistency of the presented approaches. Finally, based on practical application, we enhanced the worth of the evaluated measures with the help of a comparative analysis of proposed and existing measures. Full article

(This article belongs to the Special Issue Advances in Fuzzy Decision Theory and Applications)

15 pages, 7196 KiB

Open AccessArticle

Study on Dynamic Characteristics of a Rotating Sandwich Porous Pre-Twist Blade with a Setting Angle Reinforced by Graphene Nanoplatelets

by Jiapei Peng, Lefa Zhao and Tianyu Zhao

Mathematics 2022, 10(15), 2814; https://doi.org/10.3390/math10152814 - 08 Aug 2022

Cited by 3 | Viewed by 1205

Abstract

Lightweight blades with high strength are urgently needed in practical rotor engineering. Sandwich structures with porous core and reinforced surfaces are commonly applied to achieve these mechanical performances. Moreover, blades with large aspect ratios are established by the elastic plate models in theory. [...] Read more.

Lightweight blades with high strength are urgently needed in practical rotor engineering. Sandwich structures with porous core and reinforced surfaces are commonly applied to achieve these mechanical performances. Moreover, blades with large aspect ratios are established by the elastic plate models in theory. This paper studies the vibration of a rotating sandwich pre-twist plate with a setting angle reinforced by graphene nanoplatelets (GPLs). Its core is made of foam metal, and GPLs are added into the surface layers. Supposing that nanofillers are perfectly connected with matrix material, the effective mechanical parameters of the surface layers are calculated by the mixing law and the Halpin–Tsai model, while those of the core layers are determined by the open-cell scheme. The governing equation of the rotating plate is derived by employing the Hamilton principle. By comparing with the finite element method obtained by ANSYS, the present model and vibration analysis are verified. The material and structural parameters of the blade, including graphene nanoplatelet (GPL) weight faction, GPL distribution pattern, porosity coefficient, porosity distribution pattern, length-to-thickness ratio, length-to-width ratio, setting angle and pre-twist angle of the plate are discussed in detail. The finds provide important inspiration in the designing of a rotating sandwich blade. Full article

(This article belongs to the Special Issue Applied Computing and Artificial Intelligence)

► Show Figures

Figure 1

26 pages, 13226 KiB

Open AccessArticle

New Analytical Results and Comparison of 14 Numerical Schemes for the Diffusion Equation with Space-Dependent Diffusion Coefficient

by Mahmoud Saleh, Endre Kovács, Imre Ferenc Barna and László Mátyás

Mathematics 2022, 10(15), 2813; https://doi.org/10.3390/math10152813 - 08 Aug 2022

Cited by 9 | Viewed by 1489

Abstract

We examine the one-dimensional transient diffusion equation with a space-dependent diffusion coefficient. Such equations can be derived from the Fokker–Planck equation and are essential for understanding the diffusion mechanisms, e.g., in carbon nanotubes. First, we construct new, nontrivial analytical solutions with the classical [...] Read more.

We examine the one-dimensional transient diffusion equation with a space-dependent diffusion coefficient. Such equations can be derived from the Fokker–Planck equation and are essential for understanding the diffusion mechanisms, e.g., in carbon nanotubes. First, we construct new, nontrivial analytical solutions with the classical self-similar Ansatz in one space dimension. Then we apply 14 different explicit numerical time integration methods, most of which are recently introduced unconditionally stable schemes, to reproduce the analytical solution. The test results show that the best algorithms, especially the leapfrog-hopscotch, are very efficient and severely outperform the conventional Runge–Kutta methods. Our results may attract attention in the community who develops multi-physics engineering software. Full article

► Show Figures

Figure 1

26 pages, 6946 KiB

Open AccessArticle

Dynamic Connectedness among Vaccine Companies’ Stock Prices: Before and after Vaccines Released

by Kazi Sohag, Anna Gainetdinova, Shawkat Hammoudeh and Riad Shams

Mathematics 2022, 10(15), 2812; https://doi.org/10.3390/math10152812 - 08 Aug 2022

Cited by 2 | Viewed by 1966

Abstract

This study investigates the interconnectedness among the stocks of the publicly listed vaccine-producing companies before and after vaccine releases in 2020/21. In doing so, the study utilizes the daily frequency equity returns of the major vaccine producers, including Moderna, Pfizer, Johnson & Johnson, [...] Read more.

This study investigates the interconnectedness among the stocks of the publicly listed vaccine-producing companies before and after vaccine releases in 2020/21. In doing so, the study utilizes the daily frequency equity returns of the major vaccine producers, including Moderna, Pfizer, Johnson & Johnson, Sinopharm and AstraZeneca. First, the investigation applies the TVP-VAR Dynamic Connectedness approach to explore the time–frequency connectedness between the stocks of those vaccine producers. The empirical findings demonstrate that Moderna performs as the most prominent net volatility contributor, whereas Sinopharm is the highest net volatility receiver. Interestingly, the vaccine release significantly increases the stock market connectedness among our sampled vaccine companies. Second, the cross-quantile dependency framework allows for the observation of the interconnectedness under the bearish and bullish stock market conditions by splitting any paired variables into 19 quantiles when considering short-, medium- and long-memories. The results also show that a high level of connectivity among the vaccine producers exists under bullish stock market conditions. Notably, Moderna transmits significant volatility spillovers to Sinopharm, Johnson & Johnson and AstraZeneca under both the bearish and bullish conditions, though the volatility transmission from Moderna to Pfizer is less pronounced. The policy implication proposes that the vaccine release allows companies to increase their stock returns and induce substantial volatility spillovers from company to company. Full article

(This article belongs to the Special Issue Complex Network Analysis of Nonlinear Time Series)

► Show Figures

Figure 1

14 pages, 300 KiB

Open AccessArticle

Solving Nonlinear Second-Order Differential Equations through the Attached Flow Method

by Carmen Ionescu and Radu Constantinescu

Mathematics 2022, 10(15), 2811; https://doi.org/10.3390/math10152811 - 08 Aug 2022

Cited by 4 | Viewed by 3204

Abstract

The paper considers a simple and well-known method for reducing the differentiability order of an ordinary differential equation, defining the first derivative as a function that will become the new variable. Practically, we attach to the initial equation a supplementary one, very similar [...] Read more.

The paper considers a simple and well-known method for reducing the differentiability order of an ordinary differential equation, defining the first derivative as a function that will become the new variable. Practically, we attach to the initial equation a supplementary one, very similar to the flow equation from the dynamical systems. This is why we name it as the “attached flow equation”. Despite its apparent simplicity, the approach asks for a closer investigation because the reduced equation in the flow variable could be difficult to integrate. To overcome this difficulty, the paper considers a class of second-order differential equations, proposing a decomposition of the free term in two parts and formulating rules, based on a specific balancing procedure, on how to choose the flow. These are the main novelties of the approach that will be illustrated by solving important equations from the theory of solitons as those arising in the Chafee–Infante, Fisher, or Benjamin–Bona–Mahony models. Full article

(This article belongs to the Special Issue Computational Methods in Nonlinear Analysis and Their Applications)

15 pages, 3771 KiB

Open AccessArticle

The Algorithm That Maximizes the Accuracy of k-Classification on the Set of Representatives of the k Equivalence Classes

by Alexandra Bernadotte

Mathematics 2022, 10(15), 2810; https://doi.org/10.3390/math10152810 - 08 Aug 2022

Cited by 5 | Viewed by 1948

Abstract

The article formulates the Dictionary Recognition problem, which is relevant for a wide range of applied problems: word recognition in a noisy audio signal for natural language processing tasks or in a noisy electromagnetic signal, recognition of visual patterns in limited visibility, and [...] Read more.

The article formulates the Dictionary Recognition problem, which is relevant for a wide range of applied problems: word recognition in a noisy audio signal for natural language processing tasks or in a noisy electromagnetic signal, recognition of visual patterns in limited visibility, and much more. A Dictionary Recognition problem is finding a set of words from a given set to maximize the classification accuracy of the words in the dictionary without losing semantic representation. The idea of solving the problem is to represent a set of objects (encoded as a sequence of symbols or visual sequences) in the form of a k-partite graph, where each partite of the graph corresponds to a group of objects with a certain common feature (equivalence class). The task is to find such a set of representatives of the k equivalence classes on which the k-classification accuracy by the classifier H meets certain criteria: (1) maximum classification accuracy; (2) maximin accuracy—the binary classification accuracy of every two objects is not lower than a certain value. The proposed Maximin Algorithm provides k-partite cliques with a maximin worst-case classification accuracy and belongs to the P-class. The Maximal Algorithm provides k-partite cliques with the maximum total weight (the problem belongs to the NP-hard class). The presented algorithms select a set of representatives optimally in terms of classification accuracy for the certain classifier and runtime. The algorithms increase classification accuracy when using classical classification methods without additional optimization of the classifiers themselves. We tested the algorithms on simulated data and provide an open-source project on GitHub. The results of the Maximin and Maximal Algorithms give 4-, 8- and 16-classification accuracy close to the best accuracy (obtained by brute-force enumeration) and better than the median accuracy by more than 20% for the support vector machine classifiers. Furthermore, the algorithms increase the selection speed of representatives by five orders of magnitude compared to the brute-force algorithm with a slight loss of accuracy. Full article

(This article belongs to the Section Computational and Applied Mathematics)

► Show Figures

Figure 1

17 pages, 4040 KiB

Open AccessArticle

Statistical Tables in Spanish Primary School Textbooks

by María M. Gea, Jocelyn D. Pallauta, Carmen Batanero and Silvia M. Valenzuela-Ruiz

Mathematics 2022, 10(15), 2809; https://doi.org/10.3390/math10152809 - 08 Aug 2022

Cited by 2 | Viewed by 1499

Abstract

Statistics is introduced in primary education in Spain, and its teaching is largely supported by textbooks, which are freely provided to the children. In this research, we analyse the activities based on statistical tables included in two complete collections of primary education mathematics [...] Read more.

Statistics is introduced in primary education in Spain, and its teaching is largely supported by textbooks, which are freely provided to the children. In this research, we analyse the activities based on statistical tables included in two complete collections of primary education mathematics textbooks. These activities are classified according to the type of table, the data presented in them, the activity requested from the student in relation to the table, and the data context, according to those suggested in the PISA studies. Using content analysis, we found that tables of distribution of a variable predominate, mainly with frequencies. The most frequent activity is the reading of information from the table, while the personal context appears in the majority of the activities. This analysis serves to highlight how the teaching of statistical tables is developed throughout primary education and inform the teachers about relevant variables that should be considered in their teaching. Full article

(This article belongs to the Special Issue Future of Education and Mathematics 2030: Challenges, Answers and New Strategies)

► Show Figures

Figure 1

26 pages, 621 KiB

Open AccessArticle

Portfolio Selection Problem Using CVaR Risk Measures Equipped with DEA, PSO, and ICA Algorithms

by Abdelouahed Hamdi, Arezou Karimi, Farshid Mehrdoust and Samir Brahim Belhaouari

Mathematics 2022, 10(15), 2808; https://doi.org/10.3390/math10152808 - 08 Aug 2022

Cited by 6 | Viewed by 2079

Abstract

Investors always pay attention to the two factors of return and risk in portfolio optimization. There are different metrics for the calculation of the risk factor, among which the most important one is the Conditional Value at Risk (CVaR). On the other hand, [...] Read more.

Investors always pay attention to the two factors of return and risk in portfolio optimization. There are different metrics for the calculation of the risk factor, among which the most important one is the Conditional Value at Risk (CVaR). On the other hand, Data Envelopment Analysis (DEA) can be used to form the optimal portfolio and evaluate its efficiency. In these models, the optimal portfolio is created by stocks or companies with high efficiency. Since the search space is vast in actual markets and there are limitations such as the number of assets and their weight, the optimization problem becomes difficult. Evolutionary algorithms are a powerful tool to deal with these difficulties. The automotive industry in Iran involves international automotive manufacturers. Hence, it is essential to investigate the market related to this industry and invest in it. Therefore, in this study we examined this market based on the price index of the automotive group, then optimized a portfolio of automotive companies using two methods. In the first method, the CVaR measurement was modeled by means of DEA, then Particle Swarm Optimization (PSO) and the Imperial Competitive Algorithm (ICA) were used to solve the proposed model. In the second method, PSO and ICA were applied to solve the CVaR model, and the efficiency of the portfolios of the automotive companies was analyzed. Then, these methods were compared with the classic Mean-CVaR model. The results showed that the automotive price index was skewed to the right, and there was a possibility of an increase in return. Most companies showed favorable efficiency. This was displayed the return of the portfolio produced using the DEA-Mean-CVaR model increased because the investment proposal was basedon the stock with the highest expected return and was effective at three risk levels. It was found that when solving the Mean-CVaR model with evolutionary algorithms, the risk decreased. The efficient boundary of the PSO algorithm was higher than that of the ICA algorithm, and it displayed more efficient portfolios.Therefore, this algorithm was more successful in optimizing the portfolio. Full article

(This article belongs to the Special Issue Stochastic Processes Applied to Modelling in Finance: Latest Advances and Prospects)

► Show Figures

Figure 1

30 pages, 5851 KiB

Open AccessArticle

Exhaustive Exploitation of Local Seeding Algorithms for Community Detection in a Unified Manner

by Yanmei Hu, Bo Yang, Bin Duo and Xing Zhu

Mathematics 2022, 10(15), 2807; https://doi.org/10.3390/math10152807 - 08 Aug 2022

Cited by 2 | Viewed by 1353

Abstract

Community detection is an essential task in network analysis and is challenging due to the rapid growth of network scales. Recently, discovering communities from the local perspective of some specified nodes called seeds, rather than requiring the global information of the entire network, [...] Read more.

Community detection is an essential task in network analysis and is challenging due to the rapid growth of network scales. Recently, discovering communities from the local perspective of some specified nodes called seeds, rather than requiring the global information of the entire network, has become an alternative approach to addressing this challenge. Some seeding algorithms have been proposed in the literature for finding seeds, but many of them require an excessive amount of effort because of the global information or intensive computation involved. In our study, we formally summarize a unified framework for local seeding by considering only the local information of each node. In particular, both popular local seeding algorithms and new ones are instantiated from this unified framework by adopting different centrality metrics. We categorize these local seeding algorithms into three classes and compare them experimentally on a number of networks. The experiments demonstrate that the degree-based algorithms usually select the fewest seeds, while the denseness-based algorithms, except the one with node mass as the centrality metric, select the most seeds; using the conductance of the egonet as the centrality metric performs best in discovering communities with good quality; the core-based algorithms perform best overall considering all the evaluation metrics; and among the core-based algorithms, the one with the Jaccard index works best. The experimental results also reveal that all the seeding algorithms perform poorly in large networks, which indicates that discovering communities in large networks is still an open problem that urgently needs to be addressed. Full article

(This article belongs to the Special Issue Soft Computing for Social Media Data Analytics)

► Show Figures

Figure 1

18 pages, 9439 KiB

Open AccessArticle

DL-Aided Underground Cavity Morphology Recognition Based on 3D GPR Data

by Feifei Hou, Xu Liu, Xinyu Fan and Ying Guo

Mathematics 2022, 10(15), 2806; https://doi.org/10.3390/math10152806 - 08 Aug 2022

Cited by 7 | Viewed by 1851

Abstract

Cavity under urban roads has increasingly become a huge threat to traffic safety. This paper aims to study cavity morphology characteristics and proposes a deep learning (DL)-based morphology classification method using the 3D ground-penetrating radar (GPR) data. Fine-tuning technology in DL can be [...] Read more.

Cavity under urban roads has increasingly become a huge threat to traffic safety. This paper aims to study cavity morphology characteristics and proposes a deep learning (DL)-based morphology classification method using the 3D ground-penetrating radar (GPR) data. Fine-tuning technology in DL can be used in some cases with relatively few samples, but in the case of only one or very few samples, there will still be overfitting problems. To address this issue, a simple and general framework, few-shot learning (FSL), is first employed for the cavity classification tasks, based on which a classifier learns to identify new classes given only very few examples. We adopt a relation network (RelationNet) as the FSL framework, which consists of an embedding module and a relation module. Furthermore, the proposed method is simpler and faster because it does not require pre-training or fine-tuning. The experimental results are validated using the 3D GPR road modeling data obtained from the gprMax3D system. The proposed method is compared with other FSL networks such as ProtoNet, R2D2, and BaseLine relative to different benchmarks. The experimental results demonstrate that this method outperforms other prior approaches, and its average accuracy reaches 97.328% in a four-way five-shot problem using few support samples. Full article

(This article belongs to the Special Issue Recent Advances in Swarm Intelligence Algorithms and Their Applications)

► Show Figures

Figure 1

10 pages, 503 KiB

Open AccessArticle

Lump Collision Phenomena to a Nonlinear Physical Model in Coastal Engineering

by Tukur Abdulkadir Sulaiman, Abdullahi Yusuf, Ali Saleh Alshomrani and Dumitru Baleanu

Mathematics 2022, 10(15), 2805; https://doi.org/10.3390/math10152805 - 08 Aug 2022

Cited by 19 | Viewed by 1414

Abstract

In this study, a dimensionally nonlinear evolution equation, which is the integrable shallow water wave-like equation, is investigated utilizing the Hirota bilinear approach. Lump solutions are achieved by its bilinear form and are essential solutions to various kind of nonlinear equations. It has [...] Read more.

In this study, a dimensionally nonlinear evolution equation, which is the integrable shallow water wave-like equation, is investigated utilizing the Hirota bilinear approach. Lump solutions are achieved by its bilinear form and are essential solutions to various kind of nonlinear equations. It has not yet been explored due to its vital physical significant in various field of nonlinear science. In order to establish some more interaction solutions with some novel physical features, we establish collision aspects between lumps and other solutions by using trigonometric, hyperbolic, and exponential functions. The obtained novel types of results for the governing equation includes lump-periodic, two wave, and breather wave solutions. Meanwhile, the figures for these results are graphed. The propagation features of the derived results are depicted. The results reveal that the appropriate physical quantities and attributes of nonlinear waves are related to the parameter values. Full article

► Show Figures

Figure 1

15 pages, 1165 KiB

Open AccessArticle

Efficient Reversible Data Hiding Based on Connected Component Construction and Prediction Error Adjustment

by Limengnan Zhou, Chongfu Zhang, Asad Malik and Hanzhou Wu

Mathematics 2022, 10(15), 2804; https://doi.org/10.3390/math10152804 - 07 Aug 2022

Cited by 2 | Viewed by 1295

Abstract

To achieve a good trade-off between the data-embedding payload and the data-embedding distortion, mainstream reversible data hiding (RDH) algorithms perform data embedding on a well-built prediction error histogram. This requires us to design a good predictor to determine the prediction errors of cover [...] Read more.

To achieve a good trade-off between the data-embedding payload and the data-embedding distortion, mainstream reversible data hiding (RDH) algorithms perform data embedding on a well-built prediction error histogram. This requires us to design a good predictor to determine the prediction errors of cover elements and find a good strategy to construct an ordered prediction error sequence to be embedded. However, many existing RDH algorithms use a fixed predictor throughout the prediction process, which does not take into account the statistical characteristics of local context. Moreover, during the construction of the prediction error sequence, these algorithms ignore the fact that adjacent cover elements may have the identical priority of data embedding. As a result, there is still room for improving the payload-distortion performance. Motivated by this insight, in this article, we propose a new content prediction and selection strategy for efficient RDH in digital images to provide better payload-distortion performance. The core idea is to construct multiple connected components for a given cover image so that the prediction errors of the cover pixels within a connected component are close to each other. Accordingly, the most suitable connected components can be preferentially used for data embedding. Moreover, the prediction errors of the cover pixels are adaptively adjusted according to their local context, allowing a relatively sharp prediction error histogram to be constructed. Experimental results validate that the proposed method is significantly superior to some advanced works regarding payload-distortion performance, demonstrating the practicality of our method. Full article

(This article belongs to the Special Issue Advanced Mathematical Methods in Intelligent Multimedia: Security and Applications)

► Show Figures

Figure 1

9 pages, 272 KiB

Open AccessArticle

An Axiomatization of the Value α for Games Restricted by Augmenting Systems

by Guangming Wang, Zeguang Cui and Erfang Shan

Mathematics 2022, 10(15), 2803; https://doi.org/10.3390/math10152803 - 07 Aug 2022

Cited by 1 | Viewed by 773

Abstract

The value

α

for augmenting structures was introduced and axiomatically characterized by Algaba, Bilbao and Slikker. In this paper, we provide a new axiomatization of the value

α

for augmenting structures by using marginality for augmenting structures and the standard axioms of component [...] Read more.

The value

α

for augmenting structures was introduced and axiomatically characterized by Algaba, Bilbao and Slikker. In this paper, we provide a new axiomatization of the value

α

for augmenting structures by using marginality for augmenting structures and the standard axioms of component efficiency, equal treatment of necessary players and loop-null. Full article

(This article belongs to the Special Issue Cooperative Game Theory and Mathematical Structures)

15 pages, 1932 KiB

Open AccessArticle

Multigrid Method for Solving Inverse Problems for Heat Equation

by Hassan K. Ibrahim Al-Mahdawi, Mostafa Abotaleb, Hussein Alkattan, Al-Mahdawi Zena Tareq, Amr Badr and Ammar Kadi

Mathematics 2022, 10(15), 2802; https://doi.org/10.3390/math10152802 - 07 Aug 2022

Cited by 8 | Viewed by 1375

Abstract

In this paper, the inverse problems for the boundary value and initial value in a heat equation are posed and solved. It is well known that those problems are ill posed. The problems are reformulated as integral equations of the first kind by [...] Read more.

In this paper, the inverse problems for the boundary value and initial value in a heat equation are posed and solved. It is well known that those problems are ill posed. The problems are reformulated as integral equations of the first kind by using the separation-of-variables method. The discretization of the integral equation allowed us to reduce the integral equation to a system of linear algebraic equations or a linear operator equation of the first kind on Hilbert spaces. The Landweber-type iterative method was used in order to find an approximation solution. The V-cycle multigrid method is used to obtain more frequent and fast convergence for iteration. The numerical computation examples are presented to verify the accuracy and fast computing of the approximation solution. Full article

(This article belongs to the Section Computational and Applied Mathematics)

► Show Figures

Figure 1

26 pages, 21806 KiB

Open AccessEditor’s ChoiceArticle

Chaotification of One-Dimensional Maps Based on Remainder Operator Addition

by Lazaros Moysis, Ioannis Kafetzis, Murilo S. Baptista and Christos Volos

Mathematics 2022, 10(15), 2801; https://doi.org/10.3390/math10152801 - 07 Aug 2022

Cited by 6 | Viewed by 1506

Abstract

In this work, a chaotification technique is proposed that can be used to enhance the complexity of any one-dimensional map by adding the remainder operator to it. It is shown that by an appropriate parameter choice, the resulting map can achieve a higher [...] Read more.

In this work, a chaotification technique is proposed that can be used to enhance the complexity of any one-dimensional map by adding the remainder operator to it. It is shown that by an appropriate parameter choice, the resulting map can achieve a higher Lyapunov exponent compared to its seed map, and all periodic orbits of any period will be unstable, leading to robust chaos. The technique is tested on several maps from the literature, yielding increased chaotic behavior in all cases, as indicated by comparison of the bifurcation and Lyapunov exponent diagrams of the original and resulting maps. Moreover, the effect of the proposed technique in the problem of pseudo-random bit generation is studied. Using a standard bit generation technique, it is shown that the proposed maps demonstrate increased statistical randomness compared to their seed ones, when used as a source for the bit generator. This study illustrates that the proposed method is an efficient chaotification technique for maps that can be used in chaos-based encryption and other relevant applications. Full article

(This article belongs to the Special Issue Chaos-Based Secure Communication and Cryptography)

► Show Figures

Figure 1

26 pages, 1847 KiB

Open AccessArticle

Statistical Inference on a Finite Mixture of Exponentiated Kumaraswamy-G Distributions with Progressive Type II Censoring Using Bladder Cancer Data

by Refah Alotaibi, Lamya A. Baharith, Ehab M. Almetwally, Mervat Khalifa, Indranil Ghosh and Hoda Rezk

Mathematics 2022, 10(15), 2800; https://doi.org/10.3390/math10152800 - 07 Aug 2022

Cited by 1 | Viewed by 1116

Abstract

A new family of distributions called the mixture of the exponentiated Kumaraswamy-G (henceforth, in short, ExpKum-G) class is developed. We consider Weibull distribution as the baseline (G) distribution to propose and study this special sub-model, which we call the exponentiated Kumaraswamy Weibull distribution. [...] Read more.

A new family of distributions called the mixture of the exponentiated Kumaraswamy-G (henceforth, in short, ExpKum-G) class is developed. We consider Weibull distribution as the baseline (G) distribution to propose and study this special sub-model, which we call the exponentiated Kumaraswamy Weibull distribution. Several useful statistical properties of the proposed ExpKum-G distribution are derived. Under the classical paradigm, we consider the maximum likelihood estimation under progressive type II censoring to estimate the model parameters. Under the Bayesian paradigm, independent gamma priors are proposed to estimate the model parameters under progressive type II censored samples, assuming several loss functions. A simulation study is carried out to illustrate the efficiency of the proposed estimation strategies under both classical and Bayesian paradigms, based on progressively type II censoring models. For illustrative purposes, a real data set is considered that exhibits that the proposed model in the new class provides a better fit than other types of finite mixtures of exponentiated Kumaraswamy-type models. Full article

(This article belongs to the Special Issue New Advances in Distribution Theory and Its Applications)

► Show Figures

Figure 1

13 pages, 329 KiB

Open AccessArticle

Tail Asymptotics for a Retrial Queue with Bernoulli Schedule

by Bin Liu and Yiqiang Q. Zhao

Mathematics 2022, 10(15), 2799; https://doi.org/10.3390/math10152799 - 07 Aug 2022

Cited by 3 | Viewed by 1016

Abstract

In this paper, we study the asymptotic behaviour of the tail probability of the number of customers in the steady-state

M / G / 1

retrial queue with Bernoulli schedule, under the assumption that the service time distribution has a regularly varying tail. [...] Read more.

In this paper, we study the asymptotic behaviour of the tail probability of the number of customers in the steady-state

M / G / 1

retrial queue with Bernoulli schedule, under the assumption that the service time distribution has a regularly varying tail. Detailed tail asymptotic properties are obtained for the conditional probability of the number of customers in the (priority) queue and orbit, respectively, in terms of the recently proposed exhaustive stochastic decomposition approach. Numerical examples are presented to show the impacts of system parameters on the tail asymptotic probabilities. Full article

(This article belongs to the Special Issue Advances in Queueing Theory)

► Show Figures

Figure 1

13 pages, 1524 KiB

Open AccessArticle

Updating the Landweber Iteration Method for Solving Inverse Problems

by Hassan K. Ibrahim Al-Mahdawi, Hussein Alkattan, Mostafa Abotaleb, Ammar Kadi and El-Sayed M. El-kenawy

Mathematics 2022, 10(15), 2798; https://doi.org/10.3390/math10152798 - 07 Aug 2022

Cited by 8 | Viewed by 2125

Abstract

The Landweber iteration method is one of the most popular methods for the solution of linear discrete ill-posed problems. The diversity of physical problems and the diversity of operators that result from them leads us to think about updating the main methods and [...] Read more.

The Landweber iteration method is one of the most popular methods for the solution of linear discrete ill-posed problems. The diversity of physical problems and the diversity of operators that result from them leads us to think about updating the main methods and algorithms to achieve the best results. We considered in this work the linear operator equation and the use of a new version of the Landweber iterative method as an iterative solver. The main goal of updating the Landweber iteration method is to make the iteration process fast and more accurate. We used a polar decomposition to achieve a symmetric positive definite operator instead of an identity operator in the classical Landweber method. We carried out the convergence and other necessary analyses to prove the usability of the new iteration method. The residual method was used as an analysis method to rate the convergence of the iteration. The modified iterative method was compared to the classical Landweber method. A numerical experiment illustrates the effectiveness of this method by applying it to solve the inverse boundary value problem of the heat equation (IBVP). Full article

(This article belongs to the Section Computational and Applied Mathematics)

► Show Figures

Figure 1

18 pages, 1300 KiB

Open AccessArticle

A Novel Multi-Source Domain Adaptation Method with Dempster–Shafer Evidence Theory for Cross-Domain Classification

by Min Huang and Chang Zhang

Mathematics 2022, 10(15), 2797; https://doi.org/10.3390/math10152797 - 06 Aug 2022

Cited by 2 | Viewed by 1669

Abstract

In this era of big data, Multi-source Domain Adaptation (MDA) becomes more and more popular and is employed to make full use of available source data collected from several different, but related domains. Although multiple source domains provide much information, the processing of [...] Read more.

In this era of big data, Multi-source Domain Adaptation (MDA) becomes more and more popular and is employed to make full use of available source data collected from several different, but related domains. Although multiple source domains provide much information, the processing of domain shifts becomes more challenging, especially in learning a common domain-invariant representation for all domains. Moreover, it is counter-intuitive to treat multiple source domains equally as most existing MDA algorithms do. Therefore, the domain-specific distribution for each source–target domain pair is aligned, respectively. Nevertheless, it is hard to combine adaptation outputs from different domain-specific classifiers effectively, because of ambiguity on the category boundary. Subjective Logic (SL) is introduced to measure the uncertainty (credibility) of each domain-specific classifier, so that MDA could be bridged with DST. Due to the advantage of information fusion, Dempster–Shafer evidence Theory (DST) is utilized to reduce the category boundary ambiguity and output reasonable decisions by combining adaptation outputs based on uncertainty. Finally, extensive comparative experiments on three popular benchmark datasets for cross-domain image classification are conducted to evaluate the performance of the proposed method via various aspects. Full article

(This article belongs to the Special Issue Advancement of Mathematical Methods in Feature Representation Learning for Artificial Intelligence, Data Mining and Robotics)

► Show Figures

Figure 1

24 pages, 7283 KiB

Open AccessArticle

SMoCo: A Powerful and Efficient Method Based on Self-Supervised Learning for Fault Diagnosis of Aero-Engine Bearing under Limited Data

by Zitong Yan and Hongmei Liu

Mathematics 2022, 10(15), 2796; https://doi.org/10.3390/math10152796 - 06 Aug 2022

Cited by 15 | Viewed by 2390

Abstract

Vibration signals collected in real industrial environments are usually limited and unlabeled. In this case, fault diagnosis methods based on deep learning tend to perform poorly. Previous work mainly used the unlabeled data of the same diagnostic object to improve the diagnostic accuracy, [...] Read more.

Vibration signals collected in real industrial environments are usually limited and unlabeled. In this case, fault diagnosis methods based on deep learning tend to perform poorly. Previous work mainly used the unlabeled data of the same diagnostic object to improve the diagnostic accuracy, but it did not make full use of the easily available unlabeled signals from different sources. In this study, a signal momentum contrast for unsupervised representation learning (SMoCo) based on the contrastive learning algorithm—momentum contrast for unsupervised visual representation Learning (MoCo)—is proposed. It can learn how to automatically extract fault features from unlabeled data collected from different diagnostic objects and then transfer this ability to target diagnostic tasks. On the structure, SMoCo increases the stability by adding batch normalization to the multilayer perceptron (MLP) layer of MoCo and increases the flexibility by adding a predictor to the query network. Using the data augmentation method, SMoCo performs feature extraction on vibration signals from both time and frequency domains, which is called signal multimodal learning (SML). It has been proved by experiments that after pre-training with artificially injected fault bearing data, SMoCo can learn a powerful and robust feature extractor, which can greatly improve the accuracy no matter the target diagnostic data with different working conditions, different failure modes, or even different types of equipment from the pre-training dataset. When faced with the target diagnosis task, SMoCo can achieve accuracy far better than other representative methods in only a very short time, and its excellent robustness regarding the amount of data in both the unlabeled pre-training dataset and the target diagnosis dataset as well as the strong noise demonstrates its great potential and superiority in fault diagnosis. Full article

(This article belongs to the Special Issue Mathematical Problems in Aerospace)

► Show Figures

Figure 1

20 pages, 331 KiB

Open AccessArticle

On the Residual Lifetime and Inactivity Time in Mixtures

by Francisco Germán Badía and María Dolores Berrade

Mathematics 2022, 10(15), 2795; https://doi.org/10.3390/math10152795 - 06 Aug 2022

Cited by 1 | Viewed by 1371

Abstract

In this paper we study the aging characteristics in mixtures of distributions, providing characterizations for their derivatives that explain the smooth behavior of the mixture. The classical preservation results for the reversed hazard rate, mean residual life and mean inactivity time are derived [...] Read more.

In this paper we study the aging characteristics in mixtures of distributions, providing characterizations for their derivatives that explain the smooth behavior of the mixture. The classical preservation results for the reversed hazard rate, mean residual life and mean inactivity time are derived under a different approach than in previous studies. We focus on the variance of both the residual life and inactivity time in mixtures, obtaining some preservation properties. We also state conditions for weak and strong bending properties for the variance of the residual life and the inactivity time in mixtures. Full article

(This article belongs to the Special Issue Probability Theory and Stochastic Modeling with Applications)

► Show Figures

Figure 1

Journal Menu

Journal Browser

Mathematics, Volume 10, Issue 15 (August-1 2022) – 277 articles

Further Information

Guidelines

MDPI Initiatives

Follow MDPI