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Editor’s Choice Articles

Editor’s Choice articles are based on recommendations by the scientific editors of MDPI journals from around the world. Editors select a small number of articles recently published in the journal that they believe will be particularly interesting to readers, or important in the respective research area. The aim is to provide a snapshot of some of the most exciting work published in the various research areas of the journal.

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20 pages, 294 KiB  
Article
Qualitative Analyses of Differential Systems with Time-Varying Delays via Lyapunov–Krasovskiĭ Approach
by Cemil Tunç, Osman Tunç, Yuanheng Wang and Jen-Chih Yao
Mathematics 2021, 9(11), 1196; https://doi.org/10.3390/math9111196 - 25 May 2021
Cited by 22 | Viewed by 1780
Abstract
In this paper, a class of systems of linear and non-linear delay differential equations (DDEs) of first order with time-varying delay is considered. We obtain new sufficient conditions for uniform asymptotic stability of zero solution, integrability of solutions of an unperturbed system and [...] Read more.
In this paper, a class of systems of linear and non-linear delay differential equations (DDEs) of first order with time-varying delay is considered. We obtain new sufficient conditions for uniform asymptotic stability of zero solution, integrability of solutions of an unperturbed system and boundedness of solutions of a perturbed system. We construct two appropriate Lyapunov–Krasovskiĭ functionals (LKFs) as the main tools in proofs. The technique of the proofs depends upon the Lyapunov–Krasovskiĭ method. For illustration, two examples are provided in particular cases. An advantage of the new LKFs used here is that they allow to eliminate using Gronwall’s inequality. When we compare our results with recent results in the literature, the established conditions are more general, less restrictive and optimal for applications. Full article
(This article belongs to the Special Issue Mathematical Analysis and Analytic Number Theory 2020)
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22 pages, 3520 KiB  
Article
Maximizing the Chaotic Behavior of Fractional Order Chen System by Evolutionary Algorithms
by Jose-Cruz Nuñez-Perez, Vincent-Ademola Adeyemi, Yuma Sandoval-Ibarra, Francisco-Javier Perez-Pinal and Esteban Tlelo-Cuautle
Mathematics 2021, 9(11), 1194; https://doi.org/10.3390/math9111194 - 25 May 2021
Cited by 12 | Viewed by 2821
Abstract
This paper presents the application of three optimization algorithms to increase the chaotic behavior of the fractional order chaotic Chen system. This is achieved by optimizing the maximum Lyapunov exponent (MLE). The applied optimization techniques are evolutionary algorithms (EAs), namely: differential evolution (DE), [...] Read more.
This paper presents the application of three optimization algorithms to increase the chaotic behavior of the fractional order chaotic Chen system. This is achieved by optimizing the maximum Lyapunov exponent (MLE). The applied optimization techniques are evolutionary algorithms (EAs), namely: differential evolution (DE), particle swarm optimization (PSO), and invasive weed optimization (IWO). In each algorithm, the optimization process is performed using 100 individuals and generations from 50 to 500, with a step of 50, which makes a total of ten independent runs. The results show that the optimized fractional order chaotic Chen systems have higher maximum Lyapunov exponents than the non-optimized system, with the DE giving the highest MLE. Additionally, the results indicate that the chaotic behavior of the fractional order Chen system is multifaceted with respect to the parameter and fractional order values. The dynamical behavior and complexity of the optimized systems are verified using properties, such as bifurcation, LE spectrum, equilibrium point, eigenvalue, and sample entropy. Moreover, the optimized systems are compared with a hyper-chaotic Chen system on the basis of their prediction times. The results show that the optimized systems have a shorter prediction time than the hyper-chaotic system. The optimized results are suitable for developing a secure communication system and a random number generator. Finally, the Halstead parameters measure the complexity of the three optimization algorithms that were implemented in MATLAB. The results reveal that the invasive weed optimization has the simplest implementation. Full article
(This article belongs to the Special Issue Optimization Theory and Applications)
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14 pages, 517 KiB  
Review
A Survey on Software Defect Prediction Using Deep Learning
by Elena N. Akimova, Alexander Yu. Bersenev, Artem A. Deikov, Konstantin S. Kobylkin, Anton V. Konygin, Ilya P. Mezentsev and Vladimir E. Misilov
Mathematics 2021, 9(11), 1180; https://doi.org/10.3390/math9111180 - 24 May 2021
Cited by 38 | Viewed by 7182
Abstract
Defect prediction is one of the key challenges in software development and programming language research for improving software quality and reliability. The problem in this area is to properly identify the defective source code with high accuracy. Developing a fault prediction model is [...] Read more.
Defect prediction is one of the key challenges in software development and programming language research for improving software quality and reliability. The problem in this area is to properly identify the defective source code with high accuracy. Developing a fault prediction model is a challenging problem, and many approaches have been proposed throughout history. The recent breakthrough in machine learning technologies, especially the development of deep learning techniques, has led to many problems being solved by these methods. Our survey focuses on the deep learning techniques for defect prediction. We analyse the recent works on the topic, study the methods for automatic learning of the semantic and structural features from the code, discuss the open problems and present the recent trends in the field. Full article
(This article belongs to the Special Issue Numerical Analysis and Scientific Computing)
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15 pages, 283 KiB  
Article
A General Family of q-Hypergeometric Polynomials and Associated Generating Functions
by Hari Mohan Srivastava and Sama Arjika
Mathematics 2021, 9(11), 1161; https://doi.org/10.3390/math9111161 - 21 May 2021
Cited by 16 | Viewed by 1626
Abstract
Basic (or q-) series and basic (or q-) polynomials, especially the basic (or q-) hypergeometric functions and the basic (or q-) hypergeometric polynomials are studied extensively and widely due mainly to their potential for applications in many areas of [...] Read more.
Basic (or q-) series and basic (or q-) polynomials, especially the basic (or q-) hypergeometric functions and the basic (or q-) hypergeometric polynomials are studied extensively and widely due mainly to their potential for applications in many areas of mathematical and physical sciences. Here, in this paper, we introduce a general family of q-hypergeometric polynomials and investigate several q-series identities such as an extended generating function and a Srivastava-Agarwal type bilinear generating function for this family of q-hypergeometric polynomials. We give a transformational identity involving generating functions for the generalized q-hypergeometric polynomials which we have introduced here. We also point out relevant connections of the various q-results, which we investigate here, with those in several related earlier works on this subject. We conclude this paper by remarking that it will be a rather trivial and inconsequential exercise to give the so-called (p,q)-variations of the q-results, which we have investigated here, because the additional parameter p is obviously redundant. Full article
(This article belongs to the Special Issue Orthogonal Polynomials and Special Functions)
16 pages, 269 KiB  
Article
On the Boundary Value Problems of Hadamard Fractional Differential Equations of Variable Order via Kuratowski MNC Technique
by Ahmed Refice, Mohammed Said Souid and Ivanka Stamova
Mathematics 2021, 9(10), 1134; https://doi.org/10.3390/math9101134 - 17 May 2021
Cited by 26 | Viewed by 2157
Abstract
In this manuscript, we examine both the existence and the stability of solutions of the boundary value problems of Hadamard-type fractional differential equations of variable order. New outcomes are obtained in this paper based on the Darbo’s fixed point theorem (DFPT) combined with [...] Read more.
In this manuscript, we examine both the existence and the stability of solutions of the boundary value problems of Hadamard-type fractional differential equations of variable order. New outcomes are obtained in this paper based on the Darbo’s fixed point theorem (DFPT) combined with Kuratowski measure of noncompactness (KMNC). We construct an example to illustrate the validity of the observed results. Full article
(This article belongs to the Section Mathematical Physics)
11 pages, 243 KiB  
Article
New Oscillation Theorems for Second-Order Differential Equations with Canonical and Non-Canonical Operator via Riccati Transformation
by Shyam Sundar Santra, Abhay Kumar Sethi, Osama Moaaz, Khaled Mohamed Khedher and Shao-Wen Yao
Mathematics 2021, 9(10), 1111; https://doi.org/10.3390/math9101111 - 14 May 2021
Cited by 14 | Viewed by 1813
Abstract
In this work, we prove some new oscillation theorems for second-order neutral delay differential equations of the form [...] Read more.
In this work, we prove some new oscillation theorems for second-order neutral delay differential equations of the form (a(ξ)((v(ξ)+b(ξ)v(ϑ(ξ)))′))′+c(ξ)G1(v(κ(ξ)))+d(ξ)G2(v(ς(ξ)))=0 under canonical and non-canonical operators, that is, ∫ξ0∞dξa(ξ)=∞ and ∫ξ0∞dξa(ξ)<∞. We use the Riccati transformation to prove our main results. Furthermore, some examples are provided to show the effectiveness and feasibility of the main results. Full article
(This article belongs to the Special Issue Advances in Differential and Difference Equations with Applications 2023)
11 pages, 711 KiB  
Article
Developing a Novel Fuzzy Evaluation Model by One-Sided Specification Capability Indices
by Wei Lo, Chun-Ming Yang, Kuei-Kuei Lai, Shao-Yu Li and Chi-Han Chen
Mathematics 2021, 9(10), 1076; https://doi.org/10.3390/math9101076 - 11 May 2021
Cited by 9 | Viewed by 1538
Abstract
When all of the one-sided specification indices of each quality characteristic reach the requirements of the process quality level, they can ensure that the process capability of the product meets the requirements of the process quality level. This study constructs a fuzzy membership [...] Read more.
When all of the one-sided specification indices of each quality characteristic reach the requirements of the process quality level, they can ensure that the process capability of the product meets the requirements of the process quality level. This study constructs a fuzzy membership function based on the upper confidence limit of the index, derives the fuzzy critical value, and then labels the fuzzy critical value on the axis of the visualized radar chart as well as connects adjacent critical points to shape a regular polygonal critical region. Next, this study calculates the observed value of the index to estimate and mark it on the axis for forming a visualized fuzzy radar evaluation chart. Obviously, this fuzzy evaluation model not only reduces the testing cost but also makes the quality level quickly meet the requirements of the specifications. Further, the radar chart can reduce the risk of misjudgment attributable to sampling errors and help improve the accuracy of evaluation by a confidence-upper-limit-based fuzzy evaluation model. Therefore, this easy-to-use visualized fuzzy radar evaluation chart is used as an evaluation interface, which has good and convenient management performance to identify and improve critical-to-quality quickly. Improving the quality of the process before the product is completed will also have the advantage of reducing social losses and environmental damage costs. Full article
(This article belongs to the Special Issue Fuzzy Applications in Industrial Engineering)
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9 pages, 260 KiB  
Article
Philos-Type Oscillation Results for Third-Order Differential Equation with Mixed Neutral Terms
by Marappan Sathish Kumar, Omar Bazighifan, Alanoud Almutairi and Dimplekumar N. Chalishajar
Mathematics 2021, 9(9), 1021; https://doi.org/10.3390/math9091021 - 30 Apr 2021
Cited by 9 | Viewed by 1570
Abstract
The motivation for this paper is to create new Philos-type oscillation criteria that are established for third-order mixed neutral differential equations with distributed deviating arguments. The key idea of our approach is to use the triple of the Riccati transformation techniques and the [...] Read more.
The motivation for this paper is to create new Philos-type oscillation criteria that are established for third-order mixed neutral differential equations with distributed deviating arguments. The key idea of our approach is to use the triple of the Riccati transformation techniques and the integral averaging technique. The established criteria improve, simplify and complement results that have been published recently in the literature. An example is also given to demonstrate the applicability of the obtained conditions. Full article
32 pages, 2447 KiB  
Article
Carbon Futures Trading and Short-Term Price Prediction: An Analysis Using the Fractal Market Hypothesis and Evolutionary Computing
by Marc Lamphiere, Jonathan Blackledge and Derek Kearney
Mathematics 2021, 9(9), 1005; https://doi.org/10.3390/math9091005 - 29 Apr 2021
Cited by 11 | Viewed by 2855
Abstract
This paper presents trend prediction results based on backtesting of the European Union Emissions Trading Scheme futures market. This is based on the Intercontinental Exchange from 2005 to 2019. An alternative trend prediction strategy is taken that is predicated on an application of [...] Read more.
This paper presents trend prediction results based on backtesting of the European Union Emissions Trading Scheme futures market. This is based on the Intercontinental Exchange from 2005 to 2019. An alternative trend prediction strategy is taken that is predicated on an application of the Fractal Market Hypothesis (FMH) in order to develop an indicator that is predictive of short term future behaviour. To achieve this, we consider that a change in the polarity of the Lyapunov-to-Volatility Ratio precedes an associated change in the trend of the European Union Allowances (EUAs) price signal. The application of the FMH in this case is demonstrated to provide a useful tool in order to assess the likelihood of the market becoming bear or bull dominant, thereby helping to inform carbon trading investment decisions. Under specific conditions, Evolutionary Computing methods are utilised in order to optimise specific trading execution points within a trend and improve the potential profitability of trading returns. Although the approach may well be of value for general energy commodity futures trading (and indeed the wider financial and commodity derivative markets), this paper presents the application of an investment indicator for EUA carbon futures risk modelling and investment trend analysis only. Full article
(This article belongs to the Special Issue Fractal Market Hypothesis, Trend Analysis and Future Price Prediction)
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20 pages, 1966 KiB  
Article
Interdependence between Green Financial Instruments and Major Conventional Assets: A Wavelet-Based Network Analysis
by Román Ferrer, Rafael Benítez and Vicente J. Bolós
Mathematics 2021, 9(8), 900; https://doi.org/10.3390/math9080900 - 19 Apr 2021
Cited by 27 | Viewed by 5047
Abstract
This paper examines the interdependence between green financial instruments, represented by green bonds and green stocks, and a set of major conventional assets, such as Treasury, investment-grade and high-yield corporate bonds, general stocks, crude oil, and gold. To that end, a novel wavelet-based [...] Read more.
This paper examines the interdependence between green financial instruments, represented by green bonds and green stocks, and a set of major conventional assets, such as Treasury, investment-grade and high-yield corporate bonds, general stocks, crude oil, and gold. To that end, a novel wavelet-based network approach that allows for assessing the degree of interconnection between green financial products and traditional asset classes across different investment horizons is applied. The empirical results show that green bonds are tightly linked to Treasury and investment-grade corporate bonds, while green stocks are strongly tied to general stocks, regardless of the specific time period and investment horizon considered. However, despite their common climate-friendly nature, there is no a remarkable association between green bonds and green stocks. This means that these green investments constitute basically two independent asset classes, with a distinct risk-return profile and aimed at a different type of investor. Furthermore, green financial products have a weak connection with high-yield corporate bonds and crude oil. These findings can have important implications for investors and policy makers in terms of investment decision, hedging strategies, and sustainability and energy policies. Full article
(This article belongs to the Special Issue Application of Mathematical Methods in Financial Economics)
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27 pages, 2828 KiB  
Article
A Compromised Decision-Making Approach to Third-Party Logistics Selection in Sustainable Supply Chain Using Fuzzy AHP and Fuzzy VIKOR Methods
by Chia-Nan Wang, Ngoc-Ai-Thy Nguyen, Thanh-Tuan Dang and Chen-Ming Lu
Mathematics 2021, 9(8), 886; https://doi.org/10.3390/math9080886 - 16 Apr 2021
Cited by 87 | Viewed by 7685
Abstract
With the effects of the COVID-19 pandemic, the e-commerce trend is driving faster, significantly impacting supply chains around the world. Thus, the importance of logistics and supply chain functions has been amplified in almost every business that ships physical goods. In Vietnam, the [...] Read more.
With the effects of the COVID-19 pandemic, the e-commerce trend is driving faster, significantly impacting supply chains around the world. Thus, the importance of logistics and supply chain functions has been amplified in almost every business that ships physical goods. In Vietnam, the logistics service sector has seen rapid expansion. Since more and more businesses are seeking third-party logistics (3PL) providers to outsource the logistics functions, this article aims to offer decision-makers an integrated and consistent model for evaluating and selecting the most efficient 3PLs. To this end, the authors exploit a hybrid multi-criteria method which is fuzzy analytic hierarchy process (FAHP) and fuzzy vlsekriterijumska optimizacija i kompromisno resenje (FVIKOR) while examining the most influential and conflicting criteria regarding economic, service level, environmental, social, and risk aspects. Fuzzy information in the natural decision-making process is considered, linguistic variables are used to mitigate the uncertain levels in the criteria weights. First, FAHP (the weighting method) is adopted to evaluate and calculate each criterion’s relative significant fuzzy weight. FVIKOR (the compromised ranking method) is then used to rank the alternatives. The combination of FAHP and FVIKOR methods provides more accurate ranking results. As a result, reliability and delivery time, voice of customer, logistics cost, network management, and quality of service are the most impactful factors to the logistics outsourcing problem. Eventually, the optimized 3PLs were determined that fully meet the criteria of sustainable development. The developed integrated model offers the complete and robust 3PLs evaluation and selection process and can also be a powerful decision support tool for other industries. Full article
(This article belongs to the Special Issue Advances in Multiple Criteria Decision Analysis)
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16 pages, 6779 KiB  
Article
Deep Learning for Wave Energy Converter Modeling Using Long Short-Term Memory
by Seyed Milad Mousavi, Majid Ghasemi, Mahsa Dehghan Manshadi and Amir Mosavi
Mathematics 2021, 9(8), 871; https://doi.org/10.3390/math9080871 - 15 Apr 2021
Cited by 61 | Viewed by 4200
Abstract
Accurate forecasts of ocean waves energy can not only reduce costs for investment, but it is also essential for the management and operation of electrical power. This paper presents an innovative approach based on long short-term memory (LSTM) to predict the power generation [...] Read more.
Accurate forecasts of ocean waves energy can not only reduce costs for investment, but it is also essential for the management and operation of electrical power. This paper presents an innovative approach based on long short-term memory (LSTM) to predict the power generation of an economical wave energy converter named “Searaser”. The data for analysis is provided by collecting the experimental data from another study and the exerted data from a numerical simulation of Searaser. The simulation is performed with Flow-3D software, which has high capability in analyzing fluid–solid interactions. The lack of relation between wind speed and output power in previous studies needs to be investigated in this field. Therefore, in this study, wind speed and output power are related with an LSTM method. Moreover, it can be inferred that the LSTM network is able to predict power in terms of height more accurately and faster than the numerical solution in a field of predicting. The network output figures show a great agreement, and the root mean square is 0.49 in the mean value related to the accuracy of the LSTM method. Furthermore, the mathematical relation between the generated power and wave height was introduced by curve fitting of the power function to the result of the LSTM method. Full article
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20 pages, 2097 KiB  
Article
An Exhaustive Power Comparison of Normality Tests
by Jurgita Arnastauskaitė, Tomas Ruzgas and Mindaugas Bražėnas
Mathematics 2021, 9(7), 788; https://doi.org/10.3390/math9070788 - 06 Apr 2021
Cited by 22 | Viewed by 5053
Abstract
A goodness-of-fit test is a frequently used modern statistics tool. However, it is still unclear what the most reliable approach is to check assumptions about data set normality. A particular data set (especially with a small number of observations) only partly describes the [...] Read more.
A goodness-of-fit test is a frequently used modern statistics tool. However, it is still unclear what the most reliable approach is to check assumptions about data set normality. A particular data set (especially with a small number of observations) only partly describes the process, which leaves many options for the interpretation of its true distribution. As a consequence, many goodness-of-fit statistical tests have been developed, the power of which depends on particular circumstances (i.e., sample size, outlets, etc.). With the aim of developing a more universal goodness-of-fit test, we propose an approach based on an N-metric with our chosen kernel function. To compare the power of 40 normality tests, the goodness-of-fit hypothesis was tested for 15 data distributions with 6 different sample sizes. Based on exhaustive comparative research results, we recommend the use of our test for samples of size n≥118. Full article
(This article belongs to the Special Issue Probability, Statistics and Their Applications 2021)
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27 pages, 884 KiB  
Article
A Continuous Review Production-Inventory System with a Variable Preparation Time in a Fuzzy Random Environment
by Amalendu Singha Mahapatra, Hardik N Soni, Maheswar Singha Mahapatra, Biswajit Sarkar and Sanat Majumder
Mathematics 2021, 9(7), 747; https://doi.org/10.3390/math9070747 - 31 Mar 2021
Cited by 33 | Viewed by 2647
Abstract
With the increase in the varieties products and the increasing uncertainty about product demand, the production preparation time is a significant factor in addressing these issues. The trade-off between the reduction of the production preparation time and the associated cost remains a critical [...] Read more.
With the increase in the varieties products and the increasing uncertainty about product demand, the production preparation time is a significant factor in addressing these issues. The trade-off between the reduction of the production preparation time and the associated cost remains a critical decision. With this backdrop, this study presents a continuous review production-inventory model with a variable production preparation time and a time-dependent setup cost. The demand during the preparation time is captured through a min-max distribution-free approach. In a stochastic framework, the order quantity, reorder point, and setup time are optimized by minimizing the expected cost considering the time-value effect. Further, a fuzzy model is formulated to tackle the imprecise nature of the production setup time and demand. Two algorithms are developed using an analytical approach to obtain the optimal solution. A numerical illustration is given to present the key insights of the model for effective inventory management. It is observed that order quantity and total cost are more sensitive at the lower side of the optimal setup time rather than at the higher side. The discount rate is also found to be a sensitive factor while minimizing the total expected cost. Full article
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31 pages, 1777 KiB  
Article
Unified CACSD Toolbox for Hybrid Simulation and Robust Controller Synthesis with Applications in DC-to-DC Power Converter Control
by Mircea Şuşcă, Vlad Mihaly, Mihai Stănese, Dora Morar and Petru Dobra
Mathematics 2021, 9(7), 731; https://doi.org/10.3390/math9070731 - 28 Mar 2021
Cited by 15 | Viewed by 3004
Abstract
The current article presents the design, implementation, validation, and use of a Computer-Aided Control System Design (CACSD) toolbox for nonlinear and hybrid system uncertainty modeling, simulation, and control using μ synthesis. Remarkable features include generalization of classical system interconnection operations to nonlinear and [...] Read more.
The current article presents the design, implementation, validation, and use of a Computer-Aided Control System Design (CACSD) toolbox for nonlinear and hybrid system uncertainty modeling, simulation, and control using μ synthesis. Remarkable features include generalization of classical system interconnection operations to nonlinear and hybrid systems, automatic computation of equilibrium points for nonlinear systems, and optimization of least conservative uncertainty bounds, with direct applicability for μ synthesis. A unified approach is presented for the step-down (buck), step-up (boost), and single-ended primary-inductor (SEPIC) converters to showcase the use and flexibility of the toolbox. Robust controllers were computed by minimization of the H∞ norm of the augmented performance systems, encompassing a wide range of uncertainty types, and have been designed using the well-known mixed-sensitivity closed loop shaping μ synthesis method. Full article
(This article belongs to the Special Issue Applications of Mathematical Models in Engineering)
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13 pages, 488 KiB  
Article
Nonlinearities and Chaos: A New Analysis of CEE Stock Markets
by Claudiu Tiberiu Albulescu, Aviral Kumar Tiwari and Phouphet Kyophilavong
Mathematics 2021, 9(7), 707; https://doi.org/10.3390/math9070707 - 25 Mar 2021
Cited by 13 | Viewed by 2260
Abstract
After a long transition period, the Central and Eastern European (CEE) capital markets have consolidated their place in the financial systems. However, little is known about the price behavior and efficiency of these markets. In this context, using a battery of tests for [...] Read more.
After a long transition period, the Central and Eastern European (CEE) capital markets have consolidated their place in the financial systems. However, little is known about the price behavior and efficiency of these markets. In this context, using a battery of tests for nonlinear and chaotic behavior, we look for the presence of nonlinearities and chaos in five CEE stock markets. We document, in general, the presence of nonlinearities and chaos which questions the efficient market hypothesis. However, if all tests highlight a chaotic behavior for the analyzed index returns, there are noteworthy differences between the analyzed stock markets underlined by nonlinearity tests, which question, thus, their level of significance. Moreover, the results of nonlinearity tests partially contrast the previous findings reported in the literature on the same group of stock markets, showing, thus, a change in their recent behavior, compared with the 1990s. Full article
(This article belongs to the Special Issue Advanced Methods in the Mathematical Modeling of Financial Markets)
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19 pages, 334 KiB  
Article
On Hermite-Hadamard Type Inequalities for Coordinated Convex Functions via (p,q)-Calculus
by Fongchan Wannalookkhee, Kamsing Nonlaopon, Jessada Tariboon and Sotiris K. Ntouyas
Mathematics 2021, 9(7), 698; https://doi.org/10.3390/math9070698 - 24 Mar 2021
Cited by 12 | Viewed by 2097
Abstract
In this paper, we define (p,q)-integrals for continuous functions of two variables. Then, we prove the Hermite-Hadamard type inequalities for coordinated convex functions by using (p,q)-integrals. Many results obtained in this paper provide [...] Read more.
In this paper, we define (p,q)-integrals for continuous functions of two variables. Then, we prove the Hermite-Hadamard type inequalities for coordinated convex functions by using (p,q)-integrals. Many results obtained in this paper provide significant extensions of other related results given in the literature. Finally, we give some examples of our results. Full article
18 pages, 4599 KiB  
Article
Numerical Computation of Dusty Hybrid Nanofluid Flow and Heat Transfer over a Deformable Sheet with Slip Effect
by Nur Syazana Anuar, Norfifah Bachok and Ioan Pop
Mathematics 2021, 9(6), 643; https://doi.org/10.3390/math9060643 - 18 Mar 2021
Cited by 20 | Viewed by 2664
Abstract
The mathematical modeling of dusty Cu-Al2O3/water nanofluid flow driven by a permeable deformable sheet was explored numerically. Rather than no–slip conditions at the boundary, velocity slip and thermal slip were considered. To achieve the system of nonlinear ordinary differential [...] Read more.
The mathematical modeling of dusty Cu-Al2O3/water nanofluid flow driven by a permeable deformable sheet was explored numerically. Rather than no–slip conditions at the boundary, velocity slip and thermal slip were considered. To achieve the system of nonlinear ordinary differential equations (ODEs), we employed some appropriate transformations and solved them numerically using MATLAB software (built–in solver called bvp4c). The influences of relevant parameters on fluid flow and heat transfer characteristics are discussed and presented in graphs. The findings showed that double solutions appeared in the case of stretching and shrinking sheets which contributed to the analysis of stability. The stability analysis, therefore, confirmed that merely the first solution was a stable solution. The addition of nanometer-sized particles (Cu) was found to significantly strengthen the heat transfer rate of the dusty nanofluid. Meanwhile, an upsurge in the velocity and thermal slip was shown to decrease the local Nusselt number. The result also revealed that an increment of fluid particle interaction decreased the boundary layer thickness. Full article
(This article belongs to the Section Engineering Mathematics)
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16 pages, 1448 KiB  
Article
An Extended SEIR Model with Vaccination for Forecasting the COVID-19 Pandemic in Saudi Arabia Using an Ensemble Kalman Filter
by Rabih Ghostine, Mohamad Gharamti, Sally Hassrouny and Ibrahim Hoteit
Mathematics 2021, 9(6), 636; https://doi.org/10.3390/math9060636 - 17 Mar 2021
Cited by 95 | Viewed by 10934
Abstract
In this paper, an extended SEIR model with a vaccination compartment is proposed to simulate the novel coronavirus disease (COVID-19) spread in Saudi Arabia. The model considers seven stages of infection: susceptible (S), exposed (E), infectious (I), quarantined (Q), recovered (R), deaths (D), [...] Read more.
In this paper, an extended SEIR model with a vaccination compartment is proposed to simulate the novel coronavirus disease (COVID-19) spread in Saudi Arabia. The model considers seven stages of infection: susceptible (S), exposed (E), infectious (I), quarantined (Q), recovered (R), deaths (D), and vaccinated (V). Initially, a mathematical analysis is carried out to illustrate the non-negativity, boundedness, epidemic equilibrium, existence, and uniqueness of the endemic equilibrium, and the basic reproduction number of the proposed model. Such numerical models can be, however, subject to various sources of uncertainties, due to an imperfect description of the biological processes governing the disease spread, which may strongly limit their forecasting skills. A data assimilation method, mainly, the ensemble Kalman filter (EnKF), is then used to constrain the model outputs and its parameters with available data. We conduct joint state-parameters estimation experiments assimilating daily data into the proposed model using the EnKF in order to enhance the model’s forecasting skills. Starting from the estimated set of model parameters, we then conduct short-term predictions in order to assess the predicability range of the model. We apply the proposed assimilation system on real data sets from Saudi Arabia. The numerical results demonstrate the capability of the proposed model in achieving accurate prediction of the epidemic development up to two-week time scales. Finally, we investigate the effect of vaccination on the spread of the pandemic. Full article
(This article belongs to the Special Issue Mathematical and Computational Methods against the COVID-19 Pandemics)
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17 pages, 311 KiB  
Article
General Fractional Integrals and Derivatives with the Sonine Kernels
by Yuri Luchko
Mathematics 2021, 9(6), 594; https://doi.org/10.3390/math9060594 - 10 Mar 2021
Cited by 76 | Viewed by 4785
Abstract
In this paper, we address the general fractional integrals and derivatives with the Sonine kernels on the spaces of functions with an integrable singularity at the point zero. First, the Sonine kernels and their important special classes and particular cases are discussed. In [...] Read more.
In this paper, we address the general fractional integrals and derivatives with the Sonine kernels on the spaces of functions with an integrable singularity at the point zero. First, the Sonine kernels and their important special classes and particular cases are discussed. In particular, we introduce a class of the Sonine kernels that possess an integrable singularity of power function type at the point zero. For the general fractional integrals and derivatives with the Sonine kernels from this class, two fundamental theorems of fractional calculus are proved. Then, we construct the n-fold general fractional integrals and derivatives and study their properties. Full article
(This article belongs to the Special Issue Fractional Integrals and Derivatives: “True” versus “False” II)
22 pages, 3723 KiB  
Article
Stochastic Chebyshev Goal Programming Mixed Integer Linear Model for Sustainable Global Production Planning
by Chia-Nan Wang, Nhat-Luong Nhieu and Trang Thi Thu Tran
Mathematics 2021, 9(5), 483; https://doi.org/10.3390/math9050483 - 26 Feb 2021
Cited by 20 | Viewed by 2789
Abstract
Production planning is a necessary process that directly affects the efficiency of production systems in most industries. The complexity of the current production planning problem depends on increased options in production, uncertainties in demand and production resources. In this study, a stochastic multi-objective [...] Read more.
Production planning is a necessary process that directly affects the efficiency of production systems in most industries. The complexity of the current production planning problem depends on increased options in production, uncertainties in demand and production resources. In this study, a stochastic multi-objective mixed-integer optimization model is developed to ensure production efficiency in uncertainty conditions and satisfy the requirements of sustainable development. The efficiency of the production system is ensured through objective functions that optimize backorder quantity, machine uptime and customer satisfaction. The other three objective functions of the proposed model are related to optimization of profits, emissions, and employment changing. The objective functions respectively represent the three elements of sustainable development: economy, environment, and sociality. The proposed model also assures the production manager’s discretion over whether or not to adopt production options such as backorder, overtime, and employment of temporary workers. At the same time, the resource limits of the above options can also be adjusted according to the situation of each production facility via the model’s parameters. The solutions that compromise the above objective functions are determined with the Chebyshev goal programming approach together with the weights of the goals. The model is applied to the multinational production system of a Southeast Asian supplier in the textile industry. The goal programming solution of the model shows an improvement in many aspects compared to this supplier’s manufacturing practices under the same production conditions. Last but not least, the study develops different scenarios based on different random distributions of uncertainty demand and different weights between the objective functions. The analysis and evaluation of these scenarios provide a reference basis for managers to adjust the production system in different situations. Analysis of uncertain demand with more complex random distributions as well as making predictions about the effectiveness of scenarios through the advantages of machine learning can be considered in future studies. Full article
(This article belongs to the Special Issue Statistical Methods in Economics)
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17 pages, 491 KiB  
Article
On Laplacian Eigenvalues of the Zero-Divisor Graph Associated to the Ring of Integers Modulo n
by Bilal A. Rather, Shariefuddin Pirzada, Tariq A. Naikoo and Yilun Shang
Mathematics 2021, 9(5), 482; https://doi.org/10.3390/math9050482 - 26 Feb 2021
Cited by 36 | Viewed by 2571
Abstract
Given a commutative ring R with identity 1≠0, let the set Z(R) denote the set of zero-divisors and let Z*(R)=Z(R)∖{0} be the set of [...] Read more.
Given a commutative ring R with identity 1≠0, let the set Z(R) denote the set of zero-divisors and let Z*(R)=Z(R)∖{0} be the set of non-zero zero-divisors of R. The zero-divisor graph of R, denoted by Γ(R), is a simple graph whose vertex set is Z*(R) and each pair of vertices in Z*(R) are adjacent when their product is 0. In this article, we find the structure and Laplacian spectrum of the zero-divisor graphs Γ(Zn) for n=pN1qN2, where p<q are primes and N1,N2 are positive integers. Full article
(This article belongs to the Special Issue New Insights in Algebra, Discrete Mathematics, and Number Theory)
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12 pages, 297 KiB  
Article
Canonical Almost Geodesic Mappings of the First Type of Spaces with Affine Connections onto Generalized m-Ricci-Symmetric Spaces
by Volodymyr Berezovski, Yevhen Cherevko, Josef Mikeš and Lenka Rýparová
Mathematics 2021, 9(4), 437; https://doi.org/10.3390/math9040437 - 22 Feb 2021
Cited by 10 | Viewed by 1725
Abstract
In the paper we consider almost geodesic mappings of the first type of spaces with affine connections onto generalized 2-Ricci-symmetric spaces, generalized 3-Ricci-symmetric spaces, and generalized m-Ricci-symmetric spaces. In either case the main equations for the mappings are obtained as a closed [...] Read more.
In the paper we consider almost geodesic mappings of the first type of spaces with affine connections onto generalized 2-Ricci-symmetric spaces, generalized 3-Ricci-symmetric spaces, and generalized m-Ricci-symmetric spaces. In either case the main equations for the mappings are obtained as a closed system of linear differential equations of Cauchy type in the covariant derivatives. The obtained results extend an amount of research produced by N.S. Sinyukov, V.E. Berezovski, J. Mikeš. Full article
(This article belongs to the Special Issue Differential Geometry: Structures on Manifolds and Their Applications)
25 pages, 2582 KiB  
Article
Comprehensive Assessment of Distance Learning Modules by Fuzzy AHP-TOPSIS Method
by Svajone Bekesiene, Aidas Vasilis Vasiliauskas, Šárka Hošková-Mayerová and Virgilija Vasilienė-Vasiliauskienė
Mathematics 2021, 9(4), 409; https://doi.org/10.3390/math9040409 - 19 Feb 2021
Cited by 20 | Viewed by 4122
Abstract
This survey is focussed on distance learning studies, where there can be met a lot of technical obstacles, which creates complications in decision making. To get an ideal solution for these kinds of problems, the Fuzzy TOPSIS (Technique for Order Preference by Similarities [...] Read more.
This survey is focussed on distance learning studies, where there can be met a lot of technical obstacles, which creates complications in decision making. To get an ideal solution for these kinds of problems, the Fuzzy TOPSIS (Technique for Order Preference by Similarities to Ideal Solution) is one of the best solutions. Therefore, this paper presents the distance learning quality assessment surveys when the Fuzzy AHP (Analytic Hierarchy Process) and TOPSIS methods are used. Research results describe the application of the Fuzzy AHP—TOPSIS hybrid method. MCDM (Multi-Criteria Decision Making) programs with MATLAB (R2020b) mathematical package were written to calculate the evaluation results for three distance learning courses. In the practical implementation of the proposed distance learning module evaluation methodology, the experts’ evaluation method was applied. Thirty-four judges were chosen with specific knowledge and skills and with very different competencies to assess three alternatives by fourteen criteria. Following the experts’ evaluation, a statistical analysis method was used to process the data. After applying the complex evaluation, the comparative analysis method was used to summarize the obtained results. This work further provides useful guidelines for the development of an easily understandable hierarchy of criteria model that reflects the main goal of study quality assessment. Full article
(This article belongs to the Special Issue Recent Advances in Applications of Fuzzy Logic and Soft Computing)
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27 pages, 6191 KiB  
Article
Application of Hexagonal Fuzzy MCDM Methodology for Site Selection of Electric Vehicle Charging Station
by Arijit Ghosh, Neha Ghorui, Sankar Prasad Mondal, Suchitra Kumari, Biraj Kanti Mondal, Aditya Das and Mahananda Sen Gupta
Mathematics 2021, 9(4), 393; https://doi.org/10.3390/math9040393 - 16 Feb 2021
Cited by 34 | Viewed by 4081
Abstract
In this paper, the application of hexagonal fuzzy multiple-criteria decision-making (MCDM) methodology for the site selection of electric vehicle charging stations is considered. In this regard, four factors and thirteen sub-factors have been taken into consideration for E-vehicle charging site selection. In this [...] Read more.
In this paper, the application of hexagonal fuzzy multiple-criteria decision-making (MCDM) methodology for the site selection of electric vehicle charging stations is considered. In this regard, four factors and thirteen sub-factors have been taken into consideration for E-vehicle charging site selection. In this research, the geographic information system (GIS) has been incorporated with MCDM techniques. The fuzzy analytic hierarchy process (FAHP) is used to obtain a fuzzy weight of factors and sub-factors. MCDM tools fuzzy technique for order of preference by similarity to ideal solution (FTOPSIS) and fuzzy complex proportional assessment (FCOPRAS) have been used to rank the selected sites. A centroid-based method for defuzzification and distance measure between two hexagonal fuzzy numbers (HFN) has been developed for this paper. A practical example in Howrah, India, is considered to show the applicability and usefulness of the model. The results depict the suitability of the proposed research. Comparative and sensitivity analyses have been demonstrated to check the reliability, robustness and effectiveness of the proposed method. Full article
(This article belongs to the Special Issue Fuzzy Sets, Fuzzy Logic and Their Applications 2020)
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12 pages, 566 KiB  
Article
Inverse Problem of Recovering the Initial Condition for a Nonlinear Equation of the Reaction–Diffusion–Advection Type by Data Given on the Position of a Reaction Front with a Time Delay
by Dmitry Lukyanenko, Tatyana Yeleskina, Igor Prigorniy, Temur Isaev, Andrey Borzunov and Maxim Shishlenin
Mathematics 2021, 9(4), 342; https://doi.org/10.3390/math9040342 - 09 Feb 2021
Cited by 13 | Viewed by 2740
Abstract
In this paper, approaches to the numerical recovering of the initial condition in the inverse problem for a nonlinear singularly perturbed reaction–diffusion–advection equation are considered. The feature of the formulation of the inverse problem is the use of additional information about the value [...] Read more.
In this paper, approaches to the numerical recovering of the initial condition in the inverse problem for a nonlinear singularly perturbed reaction–diffusion–advection equation are considered. The feature of the formulation of the inverse problem is the use of additional information about the value of the solution of the equation at the known position of a reaction front, measured experimentally with a delay relative to the initial moment of time. In this case, for the numerical solution of the inverse problem, the gradient method of minimizing the cost functional is applied. In the case when only the position of the reaction front is known, the method of deep machine learning is applied. Numerical experiments demonstrated the possibility of solving such kinds of considered inverse problems. Full article
(This article belongs to the Section Computational and Applied Mathematics)
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14 pages, 3399 KiB  
Article
A Clustering Perspective of the Collatz Conjecture
by José A. Tenreiro Machado, Alexandra Galhano and Daniel Cao Labora
Mathematics 2021, 9(4), 314; https://doi.org/10.3390/math9040314 - 05 Feb 2021
Cited by 10 | Viewed by 6383
Abstract
This manuscript focuses on one of the most famous open problems in mathematics, namely the Collatz conjecture. The first part of the paper is devoted to describe the problem, providing a historical introduction to it, as well as giving some intuitive arguments of [...] Read more.
This manuscript focuses on one of the most famous open problems in mathematics, namely the Collatz conjecture. The first part of the paper is devoted to describe the problem, providing a historical introduction to it, as well as giving some intuitive arguments of why is it hard from the mathematical point of view. The second part is dedicated to the visualization of behaviors of the Collatz iteration function and the analysis of the results. Full article
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16 pages, 757 KiB  
Article
Modeling of the Bitcoin Volatility through Key Financial Environment Variables: An Application of Conditional Correlation MGARCH Models
by Ángeles Cebrián-Hernández and Enrique Jiménez-Rodríguez
Mathematics 2021, 9(3), 267; https://doi.org/10.3390/math9030267 - 29 Jan 2021
Cited by 13 | Viewed by 3529
Abstract
Since the launch of Bitcoin, there has been a lot of controversy surrounding what asset class it is. Several authors recognize the potential of cryptocurrencies but also certain deviations with respect to the functions of a conventional currency. Instead, Bitcoin’s diversifying factor and [...] Read more.
Since the launch of Bitcoin, there has been a lot of controversy surrounding what asset class it is. Several authors recognize the potential of cryptocurrencies but also certain deviations with respect to the functions of a conventional currency. Instead, Bitcoin’s diversifying factor and its high return potential have generated the attention of portfolio managers. In this context, understanding how its volatility is explained is a critical element of investor decision-making. By modeling the volatility of classic assets, nonlinear models such as Generalized Autoregressive Conditional Heteroskedasticity (GARCH) offer suitable results. Therefore, taking GARCH(1,1) as a reference point, the main aim of this study is to model and assess the relationship between the Bitcoin volatility and key financial environment variables through a Conditional Correlation (CC) Multivariate GARCH (MGARCH) approach. For this, several commodities, exchange rates, stock market indices, and company stocks linked to cryptocurrencies have been tested. The results obtained show certain heterogeneity in the fit of the different variables, highlighting the uncorrelation with respect to traditional safe haven assets such as gold and oil. Focusing on the CC-MGARCH model, a better behavior of the dynamic conditional correlation is found compared to the constant. Full article
(This article belongs to the Special Issue Application of Mathematical Analysis and Models to Financial Economics)
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23 pages, 881 KiB  
Article
A Simple and Effective Approach for Tackling the Permutation Flow Shop Scheduling Problem
by Mohamed Abdel-Basset, Reda Mohamed, Mohamed Abouhawwash, Ripon K. Chakrabortty and Michael J. Ryan
Mathematics 2021, 9(3), 270; https://doi.org/10.3390/math9030270 - 29 Jan 2021
Cited by 22 | Viewed by 2529
Abstract
In this research, a new approach for tackling the permutation flow shop scheduling problem (PFSSP) is proposed. This algorithm is based on the steps of the elitism continuous genetic algorithm improved by two strategies and used the largest rank value (LRV) rule to [...] Read more.
In this research, a new approach for tackling the permutation flow shop scheduling problem (PFSSP) is proposed. This algorithm is based on the steps of the elitism continuous genetic algorithm improved by two strategies and used the largest rank value (LRV) rule to transform the continuous values into discrete ones for enabling of solving the combinatorial PFSSP. The first strategy is combining the arithmetic crossover with the uniform crossover to give the algorithm a high capability on exploitation in addition to reducing stuck into local minima. The second one is re-initializing an individual selected randomly from the population to increase the exploration for avoiding stuck into local minima. Afterward, those two strategies are combined with the proposed algorithm to produce an improved one known as the improved efficient genetic algorithm (IEGA). To increase the exploitation capability of the IEGA, it is hybridized a local search strategy in a version abbreviated as HIEGA. HIEGA and IEGA are validated on three common benchmarks and compared with a number of well-known robust evolutionary and meta-heuristic algorithms to check their efficacy. The experimental results show that HIEGA and IEGA are competitive with others for the datasets incorporated in the comparison, such as Carlier, Reeves, and Heller. Full article
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16 pages, 5839 KiB  
Article
Design of Constrained Robust Controller for Active Suspension of In-Wheel-Drive Electric Vehicles
by Xianjian Jin, Jiadong Wang, Shaoze Sun, Shaohua Li, Junpeng Yang and Zeyuan Yan
Mathematics 2021, 9(3), 249; https://doi.org/10.3390/math9030249 - 27 Jan 2021
Cited by 26 | Viewed by 3322
Abstract
This paper presents a constrained robust H∞ controller design of active suspension system for in-wheel-independent-drive electric vehicles considering control constraint and parameter variation. In the active suspension system model, parameter uncertainties of sprung mass are analyzed via linear fraction transformation, and the [...] Read more.
This paper presents a constrained robust H∞ controller design of active suspension system for in-wheel-independent-drive electric vehicles considering control constraint and parameter variation. In the active suspension system model, parameter uncertainties of sprung mass are analyzed via linear fraction transformation, and the perturbation bounds can be also limited, then the uncertain quarter-vehicle active suspension model where the in-wheel motor is suspended as a dynamic vibration absorber is built. The constrained robust H∞ feedback controller of the closed-loop active suspension system is designed using the concept of reachable sets and ellipsoids, in which the dynamic tire displacements and the suspension working spaces are constrained, and a comprehensive solution is finally derived from H∞ performance and robust stability. Simulations on frequency responses and road excitations are implemented to verify and evaluate the performance of the designed controller; results show that the active suspension with a developed H∞ controller can effectively achieve better ride comfort and road-holding ability compared with passive suspension despite the existence of control constraints and parameter variations. Full article
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16 pages, 1270 KiB  
Article
A Bayesian Model of COVID-19 Cases Based on the Gompertz Curve
by Ángel Berihuete, Marta Sánchez-Sánchez and Alfonso Suárez-Llorens
Mathematics 2021, 9(3), 228; https://doi.org/10.3390/math9030228 - 25 Jan 2021
Cited by 13 | Viewed by 3331
Abstract
The COVID-19 pandemic has highlighted the need for finding mathematical models to forecast the evolution of the contagious disease and evaluate the success of particular policies in reducing infections. In this work, we perform Bayesian inference for a non-homogeneous Poisson process with an [...] Read more.
The COVID-19 pandemic has highlighted the need for finding mathematical models to forecast the evolution of the contagious disease and evaluate the success of particular policies in reducing infections. In this work, we perform Bayesian inference for a non-homogeneous Poisson process with an intensity function based on the Gompertz curve. We discuss the prior distribution of the parameter and we generate samples from the posterior distribution by using Markov Chain Monte Carlo (MCMC) methods. Finally, we illustrate our method analyzing real data associated with COVID-19 in a specific region located at the south of Spain. Full article
(This article belongs to the Special Issue Stochastic Models with Applications)
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24 pages, 596 KiB  
Article
Diffusion–Advection Equations on a Comb: Resetting and Random Search
by Trifce Sandev, Viktor Domazetoski, Alexander Iomin and Ljupco Kocarev
Mathematics 2021, 9(3), 221; https://doi.org/10.3390/math9030221 - 22 Jan 2021
Cited by 15 | Viewed by 2459
Abstract
This review addresses issues of various drift–diffusion and inhomogeneous advection problems with and without resetting on comblike structures. Both a Brownian diffusion search with drift and an inhomogeneous advection search on the comb structures are analyzed. The analytical results are verified by numerical [...] Read more.
This review addresses issues of various drift–diffusion and inhomogeneous advection problems with and without resetting on comblike structures. Both a Brownian diffusion search with drift and an inhomogeneous advection search on the comb structures are analyzed. The analytical results are verified by numerical simulations in terms of coupled Langevin equations for the comb structure. The subordination approach is one of the main technical methods used here, and we demonstrated how it can be effective in the study of various random search problems with and without resetting. Full article
(This article belongs to the Special Issue Fractional Calculus in Anomalous Transport Theory)
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10 pages, 263 KiB  
Article
New General Variants of Chebyshev Type Inequalities via Generalized Fractional Integral Operators
by Ahmet Ocak Akdemir, Saad Ihsan Butt, Muhammad Nadeem and Maria Alessandra Ragusa
Mathematics 2021, 9(2), 122; https://doi.org/10.3390/math9020122 - 07 Jan 2021
Cited by 86 | Viewed by 3310
Abstract
In this study, new and general variants have been obtained on Chebyshev’s inequality, which is quite old in inequality theory but also a useful and effective type of inequality. The main findings obtained by using integrable functions and generalized fractional integral operators have [...] Read more.
In this study, new and general variants have been obtained on Chebyshev’s inequality, which is quite old in inequality theory but also a useful and effective type of inequality. The main findings obtained by using integrable functions and generalized fractional integral operators have generalized many existing results as well as iterating the Chebyshev inequality in special cases. Full article
(This article belongs to the Section Difference and Differential Equations)
17 pages, 4208 KiB  
Article
Intelligent Agents in Co-Evolving Knowledge Networks
by Evangelos Ioannidis, Nikos Varsakelis and Ioannis Antoniou
Mathematics 2021, 9(1), 103; https://doi.org/10.3390/math9010103 - 05 Jan 2021
Cited by 6 | Viewed by 3227
Abstract
We extend the agent-based models for knowledge diffusion in networks, restricted to random mindless interactions and to “frozen” (static) networks, in order to take into account intelligent agents and network co-evolution. Intelligent agents make decisions under bounded rationality. This is the [...] Read more.
We extend the agent-based models for knowledge diffusion in networks, restricted to random mindless interactions and to “frozen” (static) networks, in order to take into account intelligent agents and network co-evolution. Intelligent agents make decisions under bounded rationality. This is the key distinction of intelligent interacting agents compared to mindless colliding molecules, involved in the usual diffusion mechanism resulting from accidental collisions. The co-evolution of link weights and knowledge levels is modeled at the local microscopic level of “agent-to-agent” interaction. Our network co-evolution model is actually a “learning mechanism”, where weight updates depend on the previous values of both weights and knowledge levels. The goal of our work is to explore the impact of (a) the intelligence of the agents, modeled by the selection-decision rule for knowledge acquisition, (b) the innovation rate of the agents, (c) the number of “top innovators” and (d) the network size. We find that rational intelligent agents transform the network into a “centralized world”, reducing the entropy of their selections-decisions for knowledge acquisition. In addition, we find that the average knowledge, as well as the “knowledge inequality”, grow exponentially. Full article
(This article belongs to the Section Network Science)
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13 pages, 1202 KiB  
Article
Mathematical Analysis of Maxwell Fluid Flow through a Porous Plate Channel Induced by a Constantly Accelerating or Oscillating Wall
by Constantin Fetecau, Rahmat Ellahi and Sadiq M. Sait
Mathematics 2021, 9(1), 90; https://doi.org/10.3390/math9010090 - 04 Jan 2021
Cited by 24 | Viewed by 2902
Abstract
Exact expressions for dimensionless velocity and shear stress fields corresponding to two unsteady motions of incompressible upper-convected Maxwell (UCM) fluids through a plate channel are analytically established. The porous effects are taken into consideration. The fluid motion is generated by one of the [...] Read more.
Exact expressions for dimensionless velocity and shear stress fields corresponding to two unsteady motions of incompressible upper-convected Maxwell (UCM) fluids through a plate channel are analytically established. The porous effects are taken into consideration. The fluid motion is generated by one of the plates which is moving in its plane and the obtained solutions satisfy all imposed initial and boundary conditions. The starting solutions corresponding to the oscillatory motion are presented as sum of their steady-state and transient components. They can be useful for those who want to eliminate the transients from their experiments. For a check of the obtained results, their steady-state components are presented in different forms whose equivalence is graphically illustrated. Analytical solutions for the incompressible Newtonian fluids performing the same motions are recovered as limiting cases of the presented results. The influence of physical parameters on the fluid motion is graphically shown and discussed. It is found that the Maxwell fluids flow slower as compared to Newtonian fluids. The required time to reach the steady-state is also presented. It is found that the presence of porous medium delays the appearance of the steady-state. Full article
(This article belongs to the Special Issue Mathematics in Fluid Mechanics: Theory, Modelling and Analytical Methods)
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27 pages, 391 KiB  
Article
Weak Dependence Notions and Their Mutual Relationships
by Jorge Navarro, Franco Pellerey and Miguel A. Sordo
Mathematics 2021, 9(1), 81; https://doi.org/10.3390/math9010081 - 31 Dec 2020
Cited by 8 | Viewed by 1977
Abstract
New weak notions of positive dependence between the components X and Y of a random pair (X,Y) have been considered in recent papers that deal with the effects of dependence on conditional residual lifetimes and conditional inactivity times. The [...] Read more.
New weak notions of positive dependence between the components X and Y of a random pair (X,Y) have been considered in recent papers that deal with the effects of dependence on conditional residual lifetimes and conditional inactivity times. The purpose of this paper is to provide a structured framework for the definition and description of these notions, and other new ones, and to describe their mutual relationships. An exhaustive review of some well-know notions of dependence, with a complete description of the equivalent definitions and reciprocal relationships, some of them expressed in terms of the properties of the copula or survival copula of (X,Y), is also provided. Full article
(This article belongs to the Section Probability and Statistics)
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27 pages, 354 KiB  
Article
Non-Homogeneous Semi-Markov and Markov Renewal Processes and Change of Measure in Credit Risk
by P.-C.G. Vassiliou
Mathematics 2021, 9(1), 55; https://doi.org/10.3390/math9010055 - 29 Dec 2020
Cited by 7 | Viewed by 1819
Abstract
For a G-inhomogeneous semi-Markov chain and G-inhomogeneous Markov renewal processes, we study the change from real probability measure into a forward probability measure. We find the values of risky bonds using the forward probabilities that the bond will not default up [...] Read more.
For a G-inhomogeneous semi-Markov chain and G-inhomogeneous Markov renewal processes, we study the change from real probability measure into a forward probability measure. We find the values of risky bonds using the forward probabilities that the bond will not default up to maturity time for both processes. It is established in the form of a theorem that the forward probability measure does not alter the semi Markov structure. In addition, foundation of a G-inhohomogeneous Markov renewal process is done and a theorem is provided where it is proved that the Markov renewal process is maintained under the forward probability measure. We show that for an inhomogeneous semi-Markov there are martingales that characterize it. We show that the same is true for a Markov renewal processes. We discuss in depth the calibration of the G-inhomogeneous semi-Markov chain model and propose an algorithm for it. We conclude with an application for risky bonds. Full article
(This article belongs to the Special Issue Stochastic Modeling and Applied Probability)
19 pages, 515 KiB  
Article
Bonferroni Prioritized Aggregation Operators Applied to Government Transparency
by Luis A. Perez-Arellano, Fabio Blanco-Mesa, Ernesto Leon-Castro and Victor Alfaro-Garcia
Mathematics 2021, 9(1), 24; https://doi.org/10.3390/math9010024 - 24 Dec 2020
Cited by 14 | Viewed by 2045
Abstract
This article applies the Bonferroni prioritized induced heavy ordered weighted average (OWA) to analyze a series of data and focuses on the Bonferroni average and heavy induced prioritized aggregation operators. The objective of the present work is to present a new aggregation operator [...] Read more.
This article applies the Bonferroni prioritized induced heavy ordered weighted average (OWA) to analyze a series of data and focuses on the Bonferroni average and heavy induced prioritized aggregation operators. The objective of the present work is to present a new aggregation operator that combines the heavy induced prioritized Bonferroni and its formulations and represents the Bonferroni mean with variables that induce an order with vectors that are greater than one. This work develops some extensions using prioritization. The main advantage is that different types of information provided by a group of decision makers to compare real situations are included in this formulation. Finally, an example using the operators to calculate the transparency of the websites of the 32 states of Mexico was performed. The main idea was to visualize how the ranking can change depending on the importance of the five components of the methodology. The main results show that it is possible to detect some important changes depending on the operator and the experts considered. Full article
(This article belongs to the Special Issue Fuzzy Sets in Business Management, Finance, and Economics)
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18 pages, 1783 KiB  
Article
Finite Element Study for Magnetohydrodynamic (MHD) Tangent Hyperbolic Nanofluid Flow over a Faster/Slower Stretching Wedge with Activation Energy
by Bagh Ali, Rizwan Ali Naqvi, Amna Mariam, Liaqat Ali and Omar M. Aldossary
Mathematics 2021, 9(1), 25; https://doi.org/10.3390/math9010025 - 24 Dec 2020
Cited by 40 | Viewed by 2230
Abstract
The below work comprises the unsteady flow and enhanced thermal transportation for Carreau nanofluids across a stretching wedge. In addition, heat source, magnetic field, thermal radiation, activation energy, and convective boundary conditions are considered. Suitable similarity functions use to transmuted partial differential formulation [...] Read more.
The below work comprises the unsteady flow and enhanced thermal transportation for Carreau nanofluids across a stretching wedge. In addition, heat source, magnetic field, thermal radiation, activation energy, and convective boundary conditions are considered. Suitable similarity functions use to transmuted partial differential formulation into the ordinary differential form, which is solved numerically by the finite element method and coded in Matlab script. Parametric computations are made for faster stretch and slowly stretch to the surface of the wedge. The progressing value of parameter A (unsteadiness), material law index ϵ, and wedge angle reduce the flow velocity. The temperature in the boundary layer region rises directly with exceeding values of thermophoresis parameter Nt, Hartman number, Brownian motion parameter Nb, ϵ, Biot number Bi and radiation parameter Rd. The volume fraction of nanoparticles rises with activation energy parameter EE, but it receded against chemical reaction parameter Ω, and Lewis number Le. The reliability and validity of the current numerical solution are ascertained by establishing convergence criteria and agreement with existing specific solutions. Full article
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14 pages, 1311 KiB  
Article
Positive Solutions of the Fractional SDEs with Non-Lipschitz Diffusion Coefficient
by Kęstutis Kubilius and Aidas Medžiūnas
Mathematics 2021, 9(1), 18; https://doi.org/10.3390/math9010018 - 23 Dec 2020
Cited by 8 | Viewed by 2114
Abstract
We study a class of fractional stochastic differential equations (FSDEs) with coefficients that may not satisfy the linear growth condition and non-Lipschitz diffusion coefficient. Using the Lamperti transform, we obtain conditions for positivity of solutions of such equations. We show that the trajectories [...] Read more.
We study a class of fractional stochastic differential equations (FSDEs) with coefficients that may not satisfy the linear growth condition and non-Lipschitz diffusion coefficient. Using the Lamperti transform, we obtain conditions for positivity of solutions of such equations. We show that the trajectories of the fractional CKLS model with β>1 are not necessarily positive. We obtain the almost sure convergence rate of the backward Euler approximation scheme for solutions of the considered SDEs. We also obtain a strongly consistent and asymptotically normal estimator of the Hurst index H>1/2 for positive solutions of FSDEs. Full article
(This article belongs to the Special Issue Applied Probability)
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14 pages, 4366 KiB  
Article
Analytical Methods for Nonlinear Evolution Equations in Mathematical Physics
by Khaled A. Gepreel
Mathematics 2020, 8(12), 2211; https://doi.org/10.3390/math8122211 - 13 Dec 2020
Cited by 15 | Viewed by 2464
Abstract
In this article, we will apply some of the algebraic methods to find great moving solutions to some nonlinear physical and engineering questions, such as a nonlinear (1 + 1) Ito integral differential equation and (1 + 1) nonlinear Schrödinger equation. To analyze [...] Read more.
In this article, we will apply some of the algebraic methods to find great moving solutions to some nonlinear physical and engineering questions, such as a nonlinear (1 + 1) Ito integral differential equation and (1 + 1) nonlinear Schrödinger equation. To analyze practical solutions to these problems, we essentially use the generalized expansion approach. After various W and G options, we get several clear means of estimating the plentiful nonlinear physics solutions. We present a process like-direct expansion process-method of expansion. In the particular case of W′=λG, G′=μW in which λ and μ are arbitrary constants, we use the expansion process to build some new exact solutions for nonlinear equations of growth if it fulfills the decoupled differential equations. Full article
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24 pages, 3671 KiB  
Article
A New Decision-Making Approach Based on Fermatean Fuzzy Sets and WASPAS for Green Construction Supplier Evaluation
by Mehdi Keshavarz-Ghorabaee, Maghsoud Amiri, Mohammad Hashemi-Tabatabaei, Edmundas Kazimieras Zavadskas and Arturas Kaklauskas
Mathematics 2020, 8(12), 2202; https://doi.org/10.3390/math8122202 - 10 Dec 2020
Cited by 94 | Viewed by 5035
Abstract
The construction industry is an important industry because of its effects on different aspects of human life experiences and circumstances. Environmental concerns have been considered in designing and planning processes of construction supply chains in the recent past. One of the most crucial [...] Read more.
The construction industry is an important industry because of its effects on different aspects of human life experiences and circumstances. Environmental concerns have been considered in designing and planning processes of construction supply chains in the recent past. One of the most crucial problems in managing supply chains is the process of evaluation and selection of green suppliers. This process can be categorized as a multi-criteria decision-making (MCDM) problem. The aim of this study is to propose a novel and efficient methodology for evaluation of green construction suppliers with uncertain information. The framework of the proposed methodology is based on weighted aggregated sum product assessment (WASPAS) and the simple multi-attribute rating technique (SMART), and Fermatean fuzzy sets (FFSs) are used to deal with uncertainty of information. The methodology was applied to a green supplier evaluation and selection in the construction industry. Fifteen suppliers were chosen to be evaluated with respect to seven criteria including “estimated cost”, “delivery efficiency”, “product flexibility”, “reputation and management level”, “eco-design”, and “green image pollution”. Sensitivity and comparative analyses were also conducted to assess the efficiency and validity of the proposed methodology. The analyses showed that the results of the proposed methodology were stable and also congruent with those of some existing methods. Full article
(This article belongs to the Special Issue Fuzzy Applications in Industrial Engineering)
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23 pages, 3708 KiB  
Article
PM2.5 Prediction Model Based on Combinational Hammerstein Recurrent Neural Networks
by Yi-Chung Chen, Tsu-Chiang Lei, Shun Yao and Hsin-Ping Wang
Mathematics 2020, 8(12), 2178; https://doi.org/10.3390/math8122178 - 06 Dec 2020
Cited by 15 | Viewed by 2417
Abstract
Airborne particulate matter 2.5 (PM2.5) can have a profound effect on the health of the population. Many researchers have been reporting highly accurate numerical predictions based on raw PM2.5 data imported directly into deep learning models; however, there is still considerable room for [...] Read more.
Airborne particulate matter 2.5 (PM2.5) can have a profound effect on the health of the population. Many researchers have been reporting highly accurate numerical predictions based on raw PM2.5 data imported directly into deep learning models; however, there is still considerable room for improvement in terms of implementation costs due to heavy computational overhead. From the perspective of environmental science, PM2.5 values in a given location can be attributed to local sources as well as external sources. Local sources tend to have a dramatic short-term impact on PM2.5 values, whereas external sources tend to have more subtle but longer-lasting effects. In the presence of PM2.5 from both sources at the same time, this combination of effects can undermine the predictive accuracy of the model. This paper presents a novel combinational Hammerstein recurrent neural network (CHRNN) to enhance predictive accuracy and overcome the heavy computational and monetary burden imposed by deep learning models. The CHRNN comprises a based-neural network tasked with learning gradual (long-term) fluctuations in conjunction with add-on neural networks to deal with dramatic (short-term) fluctuations. The CHRNN can be coupled with a random forest model to determine the degree to which short-term effects influence long-term outcomes. We also developed novel feature selection and normalization methods to enhance prediction accuracy. Using real-world measurement data of air quality and PM2.5 datasets from Taiwan, the precision of the proposed system in the numerical prediction of PM2.5 levels was comparable to that of state-of-the-art deep learning models, such as deep recurrent neural networks and long short-term memory, despite far lower implementation costs and computational overhead. Full article
(This article belongs to the Special Issue Applied Data Analytics)
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15 pages, 2279 KiB  
Article
Robust Control Design to the Furuta System under Time Delay Measurement Feedback and Exogenous-Based Perturbation
by Gisela Pujol-Vazquez, Saleh Mobayen and Leonardo Acho
Mathematics 2020, 8(12), 2131; https://doi.org/10.3390/math8122131 - 29 Nov 2020
Cited by 18 | Viewed by 2386
Abstract
When dealing with real control experimentation, the designer has to take into account several uncertainties, such as: time variation of the system parameters, exogenous perturbation and the presence of time delay in the feedback line. In the later case, this time delay behaviour [...] Read more.
When dealing with real control experimentation, the designer has to take into account several uncertainties, such as: time variation of the system parameters, exogenous perturbation and the presence of time delay in the feedback line. In the later case, this time delay behaviour may be random, or chaotic. Hence, the control block has to be robust. In this work, a robust delay-dependent controller based on H∞ theory is presented by employing the linear matrix inequalities techniques to design an efficient output feedback control. This approach is carefully tuned to face with random time-varying measurement feedback and applied to the Furuta pendulum subject to an exogenous ground perturbation. Therefore, a recent experimental platform is described. Here, the ground perturbation is realised using an Hexapod robotic system. According to experimental data, the proposed control approach is robust and the control objective is completely satisfied. Full article
(This article belongs to the Section Engineering Mathematics)
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20 pages, 300 KiB  
Review
The General Fractional Derivative and Related Fractional Differential Equations
by Yuri Luchko and Masahiro Yamamoto
Mathematics 2020, 8(12), 2115; https://doi.org/10.3390/math8122115 - 26 Nov 2020
Cited by 43 | Viewed by 3123
Abstract
In this survey paper, we start with a discussion of the general fractional derivative (GFD) introduced by A. Kochubei in his recent publications. In particular, a connection of this derivative to the corresponding fractional integral and the Sonine relation for their kernels are [...] Read more.
In this survey paper, we start with a discussion of the general fractional derivative (GFD) introduced by A. Kochubei in his recent publications. In particular, a connection of this derivative to the corresponding fractional integral and the Sonine relation for their kernels are presented. Then we consider some fractional ordinary differential equations (ODEs) with the GFD including the relaxation equation and the growth equation. The main part of the paper is devoted to the fractional partial differential equations (PDEs) with the GFD. We discuss both the Cauchy problems and the initial-boundary-value problems for the time-fractional diffusion equations with the GFD. In the final part of the paper, some results regarding the inverse problems for the differential equations with the GFD are presented. Full article
(This article belongs to the Special Issue Fractional Integrals and Derivatives: “True” versus “False”)
21 pages, 3443 KiB  
Article
A Sustainable Inventory Model with Imperfect Products, Deterioration, and Controllable Emissions
by Abu Hashan Md Mashud, Dipa Roy, Yosef Daryanto and Mohd Helmi Ali
Mathematics 2020, 8(11), 2049; https://doi.org/10.3390/math8112049 - 17 Nov 2020
Cited by 37 | Viewed by 3075
Abstract
Maintaining product quality and environmental performance are emerging concerns in modern competitive and transparent businesses. Many retailers separate perfect products from imperfect ones to ensure product quality and endeavor to achieve carbon dioxide (CO2) reduction through green technology investments and sustainable [...] Read more.
Maintaining product quality and environmental performance are emerging concerns in modern competitive and transparent businesses. Many retailers separate perfect products from imperfect ones to ensure product quality and endeavor to achieve carbon dioxide (CO2) reduction through green technology investments and sustainable inventory planning. Product deterioration often badly hampers the retailing business; hence, suitable preservation technologies are used. In this study, we examined the optimization model of the selling price, investment, and replenishment planning to maximize the total profit. The proposed model considered the effect of a greater deterioration rate and discount price of imperfect products. Due to the high uncertainty in demand, a realistic holding cost was deliberated with a variable and constant part. Every time the retailer transports purchased items, greenhouse gases (GHGs), including CO2, are produced. Government regulations on CO2 minimization and customer awareness for greener products stimulate retailers to invest in energy-efficient green technology. This study simultaneously showed a harmonious relationship among the attributes of preservation technology, green technology investment, and discounts on defective items. Theoretical derivations were performed with numerical analysis. Full article
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23 pages, 1368 KiB  
Article
Towards a Generalised Metaheuristic Model for Continuous Optimisation Problems
by Jorge M. Cruz-Duarte, José C. Ortiz-Bayliss, Iván Amaya, Yong Shi, Hugo Terashima-Marín and Nelishia Pillay
Mathematics 2020, 8(11), 2046; https://doi.org/10.3390/math8112046 - 17 Nov 2020
Cited by 29 | Viewed by 2144
Abstract
Metaheuristics have become a widely used approach for solving a variety of practical problems. The literature is full of diverse metaheuristics based on outstanding ideas and with proven excellent capabilities. Nonetheless, oftentimes metaheuristics claim novelty when they are just recombining elements from other [...] Read more.
Metaheuristics have become a widely used approach for solving a variety of practical problems. The literature is full of diverse metaheuristics based on outstanding ideas and with proven excellent capabilities. Nonetheless, oftentimes metaheuristics claim novelty when they are just recombining elements from other methods. Hence, the need for a standard metaheuristic model is vital to stop the current frenetic tendency of proposing methods chiefly based on their inspirational source. This work introduces a first step to a generalised and mathematically formal metaheuristic model, which can be used for studying and improving them. This model is based on a scheme of simple heuristics, which perform as building blocks that can be modified depending on the application. For this purpose, we define and detail all components and concepts of a metaheuristic (i.e., its search operators), such as heuristics. Furthermore, we also provide some ideas to take into account for exploring other search operator configurations in the future. To illustrate the proposed model, we analyse search operators from four well-known metaheuristics employed in continuous optimisation problems as a proof-of-concept. From them, we derive 20 different approaches and use them for solving some benchmark functions with different landscapes. Data show the remarkable capability of our methodology for building metaheuristics and detecting which operator to choose depending on the problem to solve. Moreover, we outline and discuss several future extensions of this model to various problem and solver domains. Full article
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15 pages, 4407 KiB  
Article
Experimental Validation of a Sliding Mode Control for a Stewart Platform Used in Aerospace Inspection Applications
by Javier Velasco, Isidro Calvo, Oscar Barambones, Pablo Venegas and Cristian Napole
Mathematics 2020, 8(11), 2051; https://doi.org/10.3390/math8112051 - 17 Nov 2020
Cited by 24 | Viewed by 3218
Abstract
The authors introduce a new controller, aimed at industrial domains, that improves the performance and accuracy of positioning systems based on Stewart platforms. More specifically, this paper presents, and validates experimentally, a sliding mode control for precisely positioning a Stewart platform used as [...] Read more.
The authors introduce a new controller, aimed at industrial domains, that improves the performance and accuracy of positioning systems based on Stewart platforms. More specifically, this paper presents, and validates experimentally, a sliding mode control for precisely positioning a Stewart platform used as a mobile platform in non-destructive inspection (NDI) applications. The NDI application involves exploring the specimen surface of aeronautical coupons at different heights. In order to avoid defocusing and blurred images, the platform must be positioned accurately to keep a uniform distance between the camera and the surface of the specimen. This operation requires the coordinated control of the six electro mechanic actuators (EMAs). The platform trajectory and the EMA lengths can be calculated by means of the forward and inverse kinematics of the Stewart platform. Typically, a proportional integral (PI) control approach is used for this purpose but unfortunately this control scheme is unable to position the platform accurately enough. For this reason, a sliding mode control (SMC) strategy is proposed. The SMC requires: (1) a priori knowledge of the bounds on system uncertainties, and (2) the analysis of the system stability in order to ensure that the strategy executes adequately. The results of this work show a higher performance of the SMC when compared with the PI control strategy: the average absolute error is reduced from 3.45 mm in PI to 0.78 mm in the SMC. Additionally, the duty cycle analysis shows that although PI control demands a smoother actuator response, the power consumption is similar. Full article
(This article belongs to the Special Issue Applications of Mathematical Models in Engineering)
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20 pages, 810 KiB  
Article
Multiple Solutions for Partial Discrete Dirichlet Problems Involving the p-Laplacian
by Sijia Du and Zhan Zhou
Mathematics 2020, 8(11), 2030; https://doi.org/10.3390/math8112030 - 14 Nov 2020
Cited by 17 | Viewed by 1511
Abstract
Due to the applications in many fields, there is great interest in studying partial difference equations involving functions with two or more discrete variables. In this paper, we deal with the existence of infinitely many solutions for a partial discrete Dirichlet boundary value [...] Read more.
Due to the applications in many fields, there is great interest in studying partial difference equations involving functions with two or more discrete variables. In this paper, we deal with the existence of infinitely many solutions for a partial discrete Dirichlet boundary value problem with the p-Laplacian by using critical point theory. Moreover, under appropriate assumptions on the nonlinear term, we determine open intervals of the parameter such that at least two positive solutions and an unbounded sequence of positive solutions are obtained by using the maximum principle. We also show two examples to illustrate our results. Full article
(This article belongs to the Special Issue Advances in Nonlinear Spectral Theory)
18 pages, 1341 KiB  
Article
Optimal Replenishment Policy for Deteriorating Products in a Newsboy Problem with Multiple Just-in-Time Deliveries
by Abu Hashan Md Mashud, Hui-Ming Wee, Chiao-Ven Huang and Jei-Zheng Wu
Mathematics 2020, 8(11), 1981; https://doi.org/10.3390/math8111981 - 06 Nov 2020
Cited by 16 | Viewed by 2307
Abstract
Product deterioration is a common phenomenon and is overlooked in most contemporary research on the newsboy problem. In this study, we have considered product deterioration in a production–inventory newsboy model based on multiple just-in-time (JIT) deliveries. This model is solved by a classical [...] Read more.
Product deterioration is a common phenomenon and is overlooked in most contemporary research on the newsboy problem. In this study, we have considered product deterioration in a production–inventory newsboy model based on multiple just-in-time (JIT) deliveries. This model is solved by a classical optimization technique for the manufacturer production size, wholesale price, replenishment plan, and retailer order policy using a distribution-free approach. Moreover, in order to improve business and entice more customers, a return policy and a post-sale warranty policy is adopted in the model. Theoretical development and numerical examples are provided to demonstrate the validity of this approach. Full article
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