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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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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 - 5 Jan 2021
Cited by 6 | Viewed by 4035
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 E: Applied Mathematics)
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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 10 | Viewed by 2734
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 D1: 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 9 | Viewed by 2588
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)
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 9 | Viewed by 2794
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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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 - 6 Dec 2020
Cited by 25 | Viewed by 3301
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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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 66 | Viewed by 4315
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”)
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 42 | Viewed by 2968
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 26 | Viewed by 4121
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 18 | Viewed by 2155
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 - 6 Nov 2020
Cited by 20 | Viewed by 3014
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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11 pages, 287 KiB  
Article
Boundary Value Problems for Hilfer Fractional Differential Inclusions with Nonlocal Integral Boundary Conditions
by Athasit Wongcharoen, Sotiris K. Ntouyas and Jessada Tariboon
Mathematics 2020, 8(11), 1905; https://doi.org/10.3390/math8111905 - 31 Oct 2020
Cited by 21 | Viewed by 2031
Abstract
In this paper, we study boundary value problems for differential inclusions, involving Hilfer fractional derivatives and nonlocal integral boundary conditions. New existence results are obtained by using standard fixed point theorems for multivalued analysis. Examples illustrating our results are also presented. Full article
(This article belongs to the Special Issue Nonlinear Equations: Theory, Methods, and Applications)
34 pages, 1562 KiB  
Article
On Semi-Analytical Solutions for Linearized Dispersive KdV Equations
by Appanah Rao Appadu and Abey Sherif Kelil
Mathematics 2020, 8(10), 1769; https://doi.org/10.3390/math8101769 - 14 Oct 2020
Cited by 19 | Viewed by 2660
Abstract
The most well-known equations both in the theory of nonlinearity and dispersion, KdV equations, have received tremendous attention over the years and have been used as model equations for the advancement of the theory of solitons. In this paper, some semi-analytic methods are [...] Read more.
The most well-known equations both in the theory of nonlinearity and dispersion, KdV equations, have received tremendous attention over the years and have been used as model equations for the advancement of the theory of solitons. In this paper, some semi-analytic methods are applied to solve linearized dispersive KdV equations with homogeneous and inhomogeneous source terms. These methods are the Laplace-Adomian decomposition method (LADM), Homotopy perturbation method (HPM), Bernstein-Laplace-Adomian Method (BALDM), and Reduced Differential Transform Method (RDTM). Three numerical experiments are considered. As the main contribution, we proposed a new scheme, known as BALDM, which involves Bernstein polynomials, Laplace transform and Adomian decomposition method to solve inhomogeneous linearized dispersive KdV equations. Besides, some modifications of HPM are also considered to solve certain inhomogeneous KdV equations by first constructing a newly modified homotopy on the source term and secondly by modifying Laplace’s transform with HPM to build HPTM. Both modifications of HPM numerically confirm the efficiency and validity of the methods for some test problems of dispersive KdV-like equations. We also applied LADM and RDTM to both homogeneous as well as inhomogeneous KdV equations to compare the obtained results and extended to higher dimensions. As a result, RDTM is applied to a 3D-dispersive KdV equation. The proposed iterative schemes determined the approximate solution without any discretization, linearization, or restrictive assumptions. The performance of the four methods is gauged over short and long propagation times and we compute absolute and relative errors at a given time for some spatial nodes. Full article
(This article belongs to the Special Issue Numerical Modeling and Analysis)
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19 pages, 2454 KiB  
Article
A Comparative Performance Assessment of Ensemble Learning for Credit Scoring
by Yiheng Li and Weidong Chen
Mathematics 2020, 8(10), 1756; https://doi.org/10.3390/math8101756 - 13 Oct 2020
Cited by 96 | Viewed by 10803
Abstract
Extensive research has been performed by organizations and academics on models for credit scoring, an important financial management activity. With novel machine learning models continue to be proposed, ensemble learning has been introduced into the application of credit scoring, several researches have addressed [...] Read more.
Extensive research has been performed by organizations and academics on models for credit scoring, an important financial management activity. With novel machine learning models continue to be proposed, ensemble learning has been introduced into the application of credit scoring, several researches have addressed the supremacy of ensemble learning. In this research, we provide a comparative performance evaluation of ensemble algorithms, i.e., random forest, AdaBoost, XGBoost, LightGBM and Stacking, in terms of accuracy (ACC), area under the curve (AUC), Kolmogorov–Smirnov statistic (KS), Brier score (BS), and model operating time in terms of credit scoring. Moreover, five popular baseline classifiers, i.e., neural network (NN), decision tree (DT), logistic regression (LR), Naïve Bayes (NB), and support vector machine (SVM) are considered to be benchmarks. Experimental findings reveal that the performance of ensemble learning is better than individual learners, except for AdaBoost. In addition, random forest has the best performance in terms of five metrics, XGBoost and LightGBM are close challengers. Among five baseline classifiers, logistic regression outperforms the other classifiers over the most of evaluation metrics. Finally, this study also analyzes reasons for the poor performance of some algorithms and give some suggestions on the choice of credit scoring models for financial institutions. Full article
(This article belongs to the Special Issue Mathematical Analysis in Economics and Management)
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17 pages, 2054 KiB  
Article
Capital City as a Factor of Multi-Criteria Decision Analysis—Application on Transport Companies in the Czech Republic
by Roman Vavrek and Jiří Bečica
Mathematics 2020, 8(10), 1765; https://doi.org/10.3390/math8101765 - 13 Oct 2020
Cited by 18 | Viewed by 2694
Abstract
The manuscript applied multi-criteria analysis using several indicators to evaluate 18 transport companies established on the level of the Czech statutory towns during period of 2001–2016 that provided for a mass commuting system. Transport companies were chosen for evaluation in the towns being [...] Read more.
The manuscript applied multi-criteria analysis using several indicators to evaluate 18 transport companies established on the level of the Czech statutory towns during period of 2001–2016 that provided for a mass commuting system. Transport companies were chosen for evaluation in the towns being company establishers in the area of mass commuting systems. Based on the prepared analysis outcomes, we suppose that transport companies in big Czech cities and towns using combination of various transport means within the mass commuting system reached lower effectiveness. The Transport Company of the Czech capital city Prague only one operates subway, i.e., it works with specific requirements laid on assurance of this public transport type. Nevertheless, its inclusion in the analysis didn’t affect total results, thus we are able to work with a complete group of transport companies in the Czech Republic when evaluating their economic effectiveness. Full article
(This article belongs to the Special Issue Advances in Multiple Criteria Decision Analysis)
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13 pages, 2192 KiB  
Article
Modeling Soil Water Redistribution under Gravity Irrigation with the Richards Equation
by Sebastián Fuentes, Josué Trejo-Alonso, Antonio Quevedo, Carlos Fuentes and Carlos Chávez
Mathematics 2020, 8(9), 1581; https://doi.org/10.3390/math8091581 - 13 Sep 2020
Cited by 12 | Viewed by 4604
Abstract
Soil water movement is important in fields such as soil mechanics, irrigation, drainage, hydrology, and agriculture. The Richards equation describes the flow of water in an unsaturated porous medium, and analytical solutions exist only for simplified cases. However, numerous practical situations require a [...] Read more.
Soil water movement is important in fields such as soil mechanics, irrigation, drainage, hydrology, and agriculture. The Richards equation describes the flow of water in an unsaturated porous medium, and analytical solutions exist only for simplified cases. However, numerous practical situations require a numerical solution (1D, 2D, or 3D) depending on the complexity of the studied problem. In this paper, numerical solution of the equation describing water infiltration into soil using the finite difference method is studied. The finite difference solution is made via iterative schemes of local balance, including explicit, implicit, and intermediate methods; as a special case, the Laasonen method is shown. The found solution is applied to water transfer problems during and after gravity irrigation to observe phenomena of infiltration, evaporation, transpiration, and percolation. Full article
(This article belongs to the Special Issue Mathematical Modelling in Applied Sciences)
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36 pages, 12863 KiB  
Review
Fourier-Spectral Method for the Phase-Field Equations
by Sungha Yoon, Darae Jeong, Chaeyoung Lee, Hyundong Kim, Sangkwon Kim, Hyun Geun Lee and Junseok Kim
Mathematics 2020, 8(8), 1385; https://doi.org/10.3390/math8081385 - 18 Aug 2020
Cited by 39 | Viewed by 8543
Abstract
In this paper, we review the Fourier-spectral method for some phase-field models: Allen–Cahn (AC), Cahn–Hilliard (CH), Swift–Hohenberg (SH), phase-field crystal (PFC), and molecular beam epitaxy (MBE) growth. These equations are very important parabolic partial differential equations and are applicable to many interesting scientific [...] Read more.
In this paper, we review the Fourier-spectral method for some phase-field models: Allen–Cahn (AC), Cahn–Hilliard (CH), Swift–Hohenberg (SH), phase-field crystal (PFC), and molecular beam epitaxy (MBE) growth. These equations are very important parabolic partial differential equations and are applicable to many interesting scientific problems. The AC equation is a reaction-diffusion equation modeling anti-phase domain coarsening dynamics. The CH equation models phase segregation of binary mixtures. The SH equation is a popular model for generating patterns in spatially extended dissipative systems. A classical PFC model is originally derived to investigate the dynamics of atomic-scale crystal growth. An isotropic symmetry MBE growth model is originally devised as a method for directly growing high purity epitaxial thin film of molecular beams evaporating on a heated substrate. The Fourier-spectral method is highly accurate and simple to implement. We present a detailed description of the method and explain its connection to MATLAB usage so that the interested readers can use the Fourier-spectral method for their research needs without difficulties. Several standard computational tests are done to demonstrate the performance of the method. Furthermore, we provide the MATLAB codes implementation in the Appendix A. Full article
(This article belongs to the Special Issue Open Source Codes for Numerical Analysis)
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29 pages, 2895 KiB  
Article
Waste Segregation FMEA Model Integrating Intuitionistic Fuzzy Set and the PAPRIKA Method
by María Carmen Carnero
Mathematics 2020, 8(8), 1375; https://doi.org/10.3390/math8081375 - 17 Aug 2020
Cited by 30 | Viewed by 7158
Abstract
Segregation is an important step in health care waste management. If done incorrectly, the risk of preventable infections, toxic effects, and injuries to care and non-care staff, waste handlers, patients, visitors, and the community at large, is increased. It also increases the risk [...] Read more.
Segregation is an important step in health care waste management. If done incorrectly, the risk of preventable infections, toxic effects, and injuries to care and non-care staff, waste handlers, patients, visitors, and the community at large, is increased. It also increases the risk of environmental pollution and prevents recyclable waste from being recovered. Despite its importance, it is acknowledged that poor waste segregation occurs in most health care organizations. This study therefore intends to produce, for the first time, a classification of failure modes related to segregation in the Nuclear Medicine Department of a health care organization. This will be done using Failure Mode and Effects Analysis (FMEA), by combining an intuitionistic fuzzy hybrid weighted Euclidean distance operator, and the multicriteria method Potentially All Pairwise RanKings of all possible Alternatives (PAPRIKA). Subjective and objective weights of risk factors were considered simultaneously. The failure modes identified in the top three positions are: improper storage of waste (placing items in the wrong bins), improper labeling of containers, and bad waste management (inappropriate collection periods and bin set-up). Full article
(This article belongs to the Special Issue Applications of Fuzzy Optimization and Fuzzy Decision Making)
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18 pages, 1553 KiB  
Article
Analyzing the Impact of the Renewable Energy Sources on Economic Growth at the EU Level Using an ARDL Model
by Mihail Busu
Mathematics 2020, 8(8), 1367; https://doi.org/10.3390/math8081367 - 14 Aug 2020
Cited by 37 | Viewed by 6465
Abstract
Energy is one of the most important drivers of economic growth, but as the population is increasing, in normal circumstances, in all countries of the world, there is a demand for energy produced from conventional resources. Increasing prices of conventional energy and the [...] Read more.
Energy is one of the most important drivers of economic growth, but as the population is increasing, in normal circumstances, in all countries of the world, there is a demand for energy produced from conventional resources. Increasing prices of conventional energy and the negative impact on the environment are two of the main reasons for switching to renewable energy sources (RESs). The aim of the paper is to quantify the impact of the RESs, by type, on the sustainable economic growth at the European Union (EU) level. The research was performed for all 28 EU member states, for a time frame from 2004 to 2017, through a panel autoregressive distributed lag (ARDL) approach and causality analysis. Furthermore, Hausman test was performed on the regression model. By estimating the panel data regression model with random effects, we reveal through our results that RESs, namely wind, solar, biomass, geothermal, and hydropower energy, have a positive influence on economic growth at EU level. Moreover, biomass has the highest impact on economic growth among all RES. In fact, a 1% increase in biomass primary production would impact the economic growth by 0.15%. Based on econometric analysis, our findings suggest that public policies at the EU level should be focused on investment in RESs. Full article
(This article belongs to the Special Issue Modeling and Numerical Analysis of Energy and Environment)
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15 pages, 637 KiB  
Article
A Novel Methodology to Calculate the Probability of Volatility Clusters in Financial Series: An Application to Cryptocurrency Markets
by Venelina Nikolova, Juan E. Trinidad Segovia, Manuel Fernández-Martínez and Miguel Angel Sánchez-Granero
Mathematics 2020, 8(8), 1216; https://doi.org/10.3390/math8081216 - 24 Jul 2020
Cited by 20 | Viewed by 4561
Abstract
One of the main characteristics of cryptocurrencies is the high volatility of their exchange rates. In a previous work, the authors found that a process with volatility clusters displays a volatility series with a high Hurst exponent. In this paper, we provide a [...] Read more.
One of the main characteristics of cryptocurrencies is the high volatility of their exchange rates. In a previous work, the authors found that a process with volatility clusters displays a volatility series with a high Hurst exponent. In this paper, we provide a novel methodology to calculate the probability of volatility clusters with a special emphasis on cryptocurrencies. With this aim, we calculate the Hurst exponent of a volatility series by means of the FD4 approach. An explicit criterion to computationally determine whether there exist volatility clusters of a fixed size is described. We found that the probabilities of volatility clusters of an index (S&P500) and a stock (Apple) showed a similar profile, whereas the probability of volatility clusters of a forex pair (Euro/USD) became quite lower. On the other hand, a similar profile appeared for Bitcoin/USD, Ethereum/USD, and Ripple/USD cryptocurrencies, with the probabilities of volatility clusters of all such cryptocurrencies being much greater than the ones of the three traditional assets. Our results suggest that the volatility in cryptocurrencies changes faster than in traditional assets, and much faster than in forex pairs. Full article
(This article belongs to the Special Issue Quantitative Methods for Economics and Finance)
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26 pages, 3025 KiB  
Article
Supportiveness of Low-Carbon Energy Technology Policy Using Fuzzy Multicriteria Decision-Making Methodologies
by Konstantinos Kokkinos and Vayos Karayannis
Mathematics 2020, 8(7), 1178; https://doi.org/10.3390/math8071178 - 17 Jul 2020
Cited by 23 | Viewed by 5538
Abstract
The deployment of low-carbon energy (LCE) technologies and management of installations represents an imperative to face climate change. LCE planning is an interminable process affected by a multitude of social, economic, environmental, and health factors. A major challenge for policy makers is to [...] Read more.
The deployment of low-carbon energy (LCE) technologies and management of installations represents an imperative to face climate change. LCE planning is an interminable process affected by a multitude of social, economic, environmental, and health factors. A major challenge for policy makers is to select a future clean energy strategy that maximizes sustainability. Thus, policy formulation and evaluation need to be addressed in an analytical manner including multidisciplinary knowledge emanating from diverse social stakeholders. In the current work, a comparative analysis of LCE planning is provided, evaluating different multicriteria decision-making (MCDM) methodologies. Initially, by applying strengths, weaknesses, opportunities, and threats (SWOT) analysis, the available energy alternative technologies are prioritized. A variety of stakeholders is surveyed for that reason. To deal with the ambiguity that occurred in their judgements, fuzzy goal programming (FGP) is used for the translation into fuzzy numbers. Then, the stochastic fuzzy analytic hierarchical process (SF-AHP) and fuzzy technique for order performance by similarity to ideal solution (F-TOPSIS) are applied to evaluate a repertoire of energy alternative forms including biofuel, solar, hydro, and wind power. The methodologies are estimated based on the same set of tangible and intangible criteria for the case study of Thessaly Region, Greece. The application of FGP ranked the four energy types in terms of feasibility and positioned solar-generated energy as first, with a membership function of 0.99. Among the criteria repertoire used by the stakeholders, the SF-AHP evaluated all the criteria categories separately and selected the most significant category representative. Finally, F-TOPSIS assessed these criteria ordering the energy forms, in terms of descending order of ideal solution, as follows: solar, biofuel, hydro, and wind. Full article
(This article belongs to the Special Issue Applications of Fuzzy Optimization and Fuzzy Decision Making)
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18 pages, 4078 KiB  
Article
Improving the Accuracy of Convolutional Neural Networks by Identifying and Removing Outlier Images in Datasets Using t-SNE
by Husein Perez and Joseph H. M. Tah
Mathematics 2020, 8(5), 662; https://doi.org/10.3390/math8050662 - 27 Apr 2020
Cited by 58 | Viewed by 8138
Abstract
In the field of supervised machine learning, the quality of a classifier model is directly correlated with the quality of the data that is used to train the model. The presence of unwanted outliers in the data could significantly reduce the accuracy of [...] Read more.
In the field of supervised machine learning, the quality of a classifier model is directly correlated with the quality of the data that is used to train the model. The presence of unwanted outliers in the data could significantly reduce the accuracy of a model or, even worse, result in a biased model leading to an inaccurate classification. Identifying the presence of outliers and eliminating them is, therefore, crucial for building good quality training datasets. Pre-processing procedures for dealing with missing and outlier data, commonly known as feature engineering, are standard practice in machine learning problems. They help to make better assumptions about the data and also prepare datasets in a way that best expose the underlying problem to the machine learning algorithms. In this work, we propose a multistage method for detecting and removing outliers in high-dimensional data. Our proposed method is based on utilising a technique called t-distributed stochastic neighbour embedding (t-SNE) to reduce high-dimensional map of features into a lower, two-dimensional, probability density distribution and then use a simple descriptive statistical method called interquartile range (IQR) to identifying any outlier values from the density distribution of the features. t-SNE is a machine learning algorithm and a nonlinear dimensionality reduction technique well-suited for embedding high-dimensional data for visualisation in a low-dimensional space of two or three dimensions. We applied this method on a dataset containing images for training a convolutional neural network model (ConvNet) for an image classification problem. The dataset contains four different classes of images: three classes contain defects in construction (mould, stain, and paint deterioration) and a no-defect class (normal). We used the transfer learning technique to modify a pre-trained VGG-16 model. We used this model as a feature extractor and as a benchmark to evaluate our method. We have shown that, when using this method, we can identify and remove the outlier images in the dataset. After removing the outlier images from the dataset and re-training the VGG-16 model, the results have also shown that the accuracy of the classification has significantly improved and the number of misclassified cases has also dropped. While many feature engineering techniques for handling missing and outlier data are common in predictive machine learning problems involving numerical or categorical data, there is little work on developing techniques for handling outliers in high-dimensional data which can be used to improve the quality of machine learning problems involving images such as ConvNet models for image classification and object detection problems. Full article
(This article belongs to the Special Issue Advances in Machine Learning Prediction Models)
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9 pages, 1916 KiB  
Article
On Estimating the Number of Deaths Related to Covid-19
by Hoang Pham
Mathematics 2020, 8(5), 655; https://doi.org/10.3390/math8050655 - 26 Apr 2020
Cited by 36 | Viewed by 11673
Abstract
In this paper, we discuss an explicit model function that can estimate the total number of deaths in the population, and particularly, estimate the cumulative number of deaths in the United States due to the current Covid-19 virus. We compare the modeling results [...] Read more.
In this paper, we discuss an explicit model function that can estimate the total number of deaths in the population, and particularly, estimate the cumulative number of deaths in the United States due to the current Covid-19 virus. We compare the modeling results to two related existing models based on a new criteria and several existing criteria for model selection. The results show the proposed model fits significantly better than the other two related models based on the U.S. Covid-19 death data. We observe that the errors of the fitted data and the predicted data points on the total number of deaths in the U.S. on the last available data point and the next coming day are less than 0.5% and 2.0%, respectively. The results show very encouraging predictability for the model. The new model predicts that the maximum total number of deaths will be approximately 62,100 across the United States due to the Covid-19 virus, and with a 95% confidence that the expected total death toll will be between 60,951 and 63,249 deaths based on the data until 22 April, 2020. If there is a significant change in the coming days due to various testing strategies, social-distancing policies, the reopening of community strategies, or a stay-home policy, the predicted death tolls will definitely change. Future work can be explored further to apply the proposed model to global Covid-19 death data and to other applications, including human population mortality, the spread of disease, and different topics such as movie reviews in recommender systems. Full article
(This article belongs to the Special Issue Reliability and Statistical Learning and Its Applications)
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7 pages, 249 KiB  
Article
Fibonacci Numbers with a Prescribed Block of Digits
by Pavel Trojovský
Mathematics 2020, 8(4), 639; https://doi.org/10.3390/math8040639 - 21 Apr 2020
Cited by 20 | Viewed by 3673
Abstract
In this paper, we prove that F 22 = 17711 is the largest Fibonacci number whose decimal expansion is of the form a b … b c … c . The proof uses lower bounds for linear forms in three logarithms of algebraic [...] Read more.
In this paper, we prove that F 22 = 17711 is the largest Fibonacci number whose decimal expansion is of the form a b … b c … c . The proof uses lower bounds for linear forms in three logarithms of algebraic numbers and some tools from Diophantine approximation. Full article
(This article belongs to the Section E1: Mathematics and Computer Science)
32 pages, 3229 KiB  
Article
Global Research Trends in Financial Transactions
by Emilio Abad-Segura and Mariana-Daniela González-Zamar
Mathematics 2020, 8(4), 614; https://doi.org/10.3390/math8040614 - 16 Apr 2020
Cited by 33 | Viewed by 9312
Abstract
Traditionally, financial mathematics has been used to solve financial problems. With globalization, financial transactions require new analysis based on tools of probability, statistics, and economic theory. Global research trends in this topic during the period 1935–2019 have been analyzed. With this objective, a [...] Read more.
Traditionally, financial mathematics has been used to solve financial problems. With globalization, financial transactions require new analysis based on tools of probability, statistics, and economic theory. Global research trends in this topic during the period 1935–2019 have been analyzed. With this objective, a bibliometric methodology of 1486 articles from the Scopus database was applied. The obtained results offer data on the scientific activity of countries, institutions, authors, and institutions that promote this research topic. The results reveal an increasing trend, mainly in the last decade. The main subjects of knowledge are social sciences and economics, econometrics, and finance. The author with the most articles is Khare from the Indian Institute of Management Rohtak. The most prolific affiliation is the British University of Oxford. The country with the most academic publications and international collaborations is the United States. In addition, the most used keywords in articles are “financial management”, “financial transaction tax”, “banking”, “financial service”, “blockchain”, “decision making”, and “financial market”. The increase in publications in recent years at the international level confirms the growing trend in research on financial transactions. Full article
(This article belongs to the Special Issue Financial Mathematics)
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12 pages, 262 KiB  
Article
Some Results in Green–Lindsay Thermoelasticity of Bodies with Dipolar Structure
by Marin Marin, Eduard M. Craciun and Nicolae Pop
Mathematics 2020, 8(4), 497; https://doi.org/10.3390/math8040497 - 2 Apr 2020
Cited by 30 | Viewed by 2877
Abstract
The main concern of this study is an extension of some results, proposed by Green and Lindsay in the classical theory of elasticity, in order to cover the theory of thermoelasticity for dipolar bodies. For dynamical mixed problem we prove a reciprocal theorem, [...] Read more.
The main concern of this study is an extension of some results, proposed by Green and Lindsay in the classical theory of elasticity, in order to cover the theory of thermoelasticity for dipolar bodies. For dynamical mixed problem we prove a reciprocal theorem, in the general case of an anisotropic thermoelastic body. Furthermore, in this general context we have proven a result regarding the uniqueness of the solution of the mixed problem in the dynamical case. We must emphasize that these fundamental results are obtained under conditions that are not very restrictive. Full article
(This article belongs to the Special Issue Applied Mathematics and Solid Mechanics)
14 pages, 2085 KiB  
Article
Robust Design Optimization for Low-Cost Concrete Box-Girder Bridge
by Vicent Penadés-Plà, Tatiana García-Segura and Víctor Yepes
Mathematics 2020, 8(3), 398; https://doi.org/10.3390/math8030398 - 11 Mar 2020
Cited by 25 | Viewed by 6205
Abstract
The design of a structure is generally carried out according to a deterministic approach. However, all structural problems have associated initial uncertain parameters that can differ from the design value. This becomes important when the goal is to reach optimized structures, as a [...] Read more.
The design of a structure is generally carried out according to a deterministic approach. However, all structural problems have associated initial uncertain parameters that can differ from the design value. This becomes important when the goal is to reach optimized structures, as a small variation of these initial uncertain parameters can have a big influence on the structural behavior. The objective of robust design optimization is to obtain an optimum design with the lowest possible variation of the objective functions. For this purpose, a probabilistic optimization is necessary to obtain the statistical parameters that represent the mean value and variation of the objective function considered. However, one of the disadvantages of the optimal robust design is its high computational cost. In this paper, robust design optimization is applied to design a continuous prestressed concrete box-girder pedestrian bridge that is optimum in terms of its cost and robust in terms of structural stability. Furthermore, Latin hypercube sampling and the kriging metamodel are used to deal with the high computational cost. Results show that the main variables that control the structural behavior are the depth of the cross-section and compressive strength of the concrete and that a compromise solution between the optimal cost and the robustness of the design can be reached. Full article
(This article belongs to the Special Issue Optimization for Decision Making II)
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21 pages, 403 KiB  
Article
Good (and Not So Good) Practices in Computational Methods for Fractional Calculus
by Kai Diethelm, Roberto Garrappa and Martin Stynes
Mathematics 2020, 8(3), 324; https://doi.org/10.3390/math8030324 - 2 Mar 2020
Cited by 50 | Viewed by 5909
Abstract
The solution of fractional-order differential problems requires in the majority of cases the use of some computational approach. In general, the numerical treatment of fractional differential equations is much more difficult than in the integer-order case, and very often non-specialist researchers are unaware [...] Read more.
The solution of fractional-order differential problems requires in the majority of cases the use of some computational approach. In general, the numerical treatment of fractional differential equations is much more difficult than in the integer-order case, and very often non-specialist researchers are unaware of the specific difficulties. As a consequence, numerical methods are often applied in an incorrect way or unreliable methods are devised and proposed in the literature. In this paper we try to identify some common pitfalls in the use of numerical methods in fractional calculus, to explain their nature and to list some good practices that should be followed in order to obtain correct results. Full article
(This article belongs to the Special Issue Fractional Integrals and Derivatives: “True” versus “False”)
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13 pages, 945 KiB  
Article
Improved Decentralized Fractional PD Control of Structure Vibrations
by Kang Xu, Liping Chen, Minwu Wang, António M. Lopes, J. A. Tenreiro Machado and Houzhen Zhai
Mathematics 2020, 8(3), 326; https://doi.org/10.3390/math8030326 - 2 Mar 2020
Cited by 25 | Viewed by 2630
Abstract
This paper presents a new strategy for the control of large displacements in structures under earthquake excitation. Firstly, an improved fractional order proportional-derivative (FOPD) controller is proposed. Secondly, a decentralized strategy is designed by adding a regulator and fault self-regulation to a standard [...] Read more.
This paper presents a new strategy for the control of large displacements in structures under earthquake excitation. Firstly, an improved fractional order proportional-derivative (FOPD) controller is proposed. Secondly, a decentralized strategy is designed by adding a regulator and fault self-regulation to a standard decentralized controller. A new control architecture is obtained by combining the improved FOPD and the decentralized strategy. The parameters of the control system are tuned using an intelligent optimization algorithm. Simulation results demonstrate the performance and reliability of the proposed method. Full article
(This article belongs to the Special Issue Advances in Fractional Order Control and Applications)
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24 pages, 810 KiB  
Article
An Alternative Approach to Measure Co-Movement between Two Time Series
by José Pedro Ramos-Requena, Juan Evangelista Trinidad-Segovia and Miguel Ángel Sánchez-Granero
Mathematics 2020, 8(2), 261; https://doi.org/10.3390/math8020261 - 17 Feb 2020
Cited by 12 | Viewed by 5135
Abstract
The study of the dependences between different assets is a classic topic in financial literature. To understand how the movements of one asset affect to others is critical for derivatives pricing, portfolio management, risk control, or trading strategies. Over time, different methodologies were [...] Read more.
The study of the dependences between different assets is a classic topic in financial literature. To understand how the movements of one asset affect to others is critical for derivatives pricing, portfolio management, risk control, or trading strategies. Over time, different methodologies were proposed by researchers. ARCH, GARCH or EGARCH models, among others, are very popular to model volatility autocorrelation. In this paper, a new simple method called HP is introduced to measure the co-movement between two time series. This method, based on the Hurst exponent of the product series, is designed to detect correlation, even if the relationship is weak, but it also works fine with cointegration as well as non linear correlations or more complex relationships given by a copula. This method and different variations thereaof are tested in statistical arbitrage. Results show that HP is able to detect the relationship between assets better than the traditional correlation method. Full article
(This article belongs to the Section E5: Financial Mathematics)
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22 pages, 354 KiB  
Article
Fractional Derivatives and Integrals: What Are They Needed For?
by Vasily E. Tarasov and Svetlana S. Tarasova
Mathematics 2020, 8(2), 164; https://doi.org/10.3390/math8020164 - 25 Jan 2020
Cited by 39 | Viewed by 5502
Abstract
The question raised in the title of the article is not philosophical. We do not expect general answers of the form “to describe the reality surrounding us”. The question should actually be formulated as a mathematical problem of applied mathematics, a task for [...] Read more.
The question raised in the title of the article is not philosophical. We do not expect general answers of the form “to describe the reality surrounding us”. The question should actually be formulated as a mathematical problem of applied mathematics, a task for new research. This question should be answered in mathematically rigorous statements about the interrelations between the properties of the operator’s kernels and the types of phenomena. This article is devoted to a discussion of the question of what is fractional operator from the point of view of not pure mathematics, but applied mathematics. The imposed restrictions on the kernel of the fractional operator should actually be divided by types of phenomena, in addition to the principles of self-consistency of mathematical theory. In applications of fractional calculus, we have a fundamental question about conditions of kernels of fractional operator of non-integer orders that allow us to describe a particular type of phenomenon. It is necessary to obtain exact correspondences between sets of properties of kernel and type of phenomena. In this paper, we discuss the properties of kernels of fractional operators to distinguish the following types of phenomena: fading memory (forgetting) and power-law frequency dispersion, spatial non-locality and power-law spatial dispersion, distributed lag (time delay), distributed scaling (dilation), depreciation, and aging. Full article
(This article belongs to the Special Issue Fractional Integrals and Derivatives: “True” versus “False”)
21 pages, 1057 KiB  
Article
Fractional Derivatives for Economic Growth Modelling of the Group of Twenty: Application to Prediction
by Inés Tejado, Emiliano Pérez and Duarte Valério
Mathematics 2020, 8(1), 50; https://doi.org/10.3390/math8010050 - 1 Jan 2020
Cited by 23 | Viewed by 4621
Abstract
This paper studies the economic growth of the countries in the Group of Twenty (G20) in the period 1970–2018. It presents dynamic models for the world’s most important national economies, including for the first time several economies which are not highly developed. Additional [...] Read more.
This paper studies the economic growth of the countries in the Group of Twenty (G20) in the period 1970–2018. It presents dynamic models for the world’s most important national economies, including for the first time several economies which are not highly developed. Additional care has been devoted to the number of years needed for an accurate short-term prediction of future outputs. Integer order and fractional order differential equation models were obtained from the data. Their output is the gross domestic product (GDP) of a G20 country. Models are multi-input; GDP is found from all or some of the following variables: country’s land area, arable land, population, school attendance, gross capital formation (GCF), exports of goods and services, general government final consumption expenditure (GGFCE), and broad money (M3). Results confirm the better performance of fractional models. This has been established employing several summary statistics. Fractional models do not require increasing the number of parameters, neither do they sacrifice the ability to predict GDP evolution in the short-term. It was found that data over 15 years allows building a model with a satisfactory prediction of the evolution of the GDP. Full article
(This article belongs to the Special Issue Mathematical Economics: Application of Fractional Calculus)
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14 pages, 813 KiB  
Article
Formative Transcendence of Flipped Learning in Mathematics Students of Secondary Education
by Jesús López Belmonte, Arturo Fuentes Cabrera, Juan Antonio López Núñez and Santiago Pozo Sánchez
Mathematics 2019, 7(12), 1226; https://doi.org/10.3390/math7121226 - 12 Dec 2019
Cited by 43 | Viewed by 8010
Abstract
Educational technology is achieving great potential in the formative processes of today’s society. Flipped learning is considered as a pedagogical innovation derived from the technological influence in learning spaces. The general objective of the research is to analyze the effectiveness of flipped learning [...] Read more.
Educational technology is achieving great potential in the formative processes of today’s society. Flipped learning is considered as a pedagogical innovation derived from the technological influence in learning spaces. The general objective of the research is to analyze the effectiveness of flipped learning on a traditional teaching and learning approach in the subject of Mathematics. To achieve this objective, an experimental design of a descriptive and correlational type has been followed through a quantitative research method. Two study groups have been set up. In the control group, the contents have been imparted from a traditional perspective, and in the experimental group, innovation has been applied through the use of flipped learning. The sample of participants has been chosen by means of intentional sampling and reached the figure of 60 students in the 4th year of Secondary Education at an educational center in Ceuta (Spain). A questionnaire has been used for data collection. The results reflect that the application of flipped learning has obtained better assessment in established attitudinal and mathematical indicators. It is concluded that with the use of flipped learning, motivation and skills are increased in the analysis and representation of graphs. Full article
(This article belongs to the Special Issue Futuring Mathematics Education—Core Teaching Practices to Prepare Students for the 21st Century: An International Perspective)
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12 pages, 677 KiB  
Article
A New Criterion for Model Selection
by Hoang Pham
Mathematics 2019, 7(12), 1215; https://doi.org/10.3390/math7121215 - 10 Dec 2019
Cited by 146 | Viewed by 8343
Abstract
Selecting the best model from a set of candidates for a given set of data is obviously not an easy task. In this paper, we propose a new criterion that takes into account a larger penalty when adding too many coefficients (or estimated [...] Read more.
Selecting the best model from a set of candidates for a given set of data is obviously not an easy task. In this paper, we propose a new criterion that takes into account a larger penalty when adding too many coefficients (or estimated parameters) in the model from too small a sample in the presence of too much noise, in addition to minimizing the sum of squares error. We discuss several real applications that illustrate the proposed criterion and compare its results to some existing criteria based on a simulated data set and some real datasets including advertising budget data, newly collected heart blood pressure health data sets and software failure data. Full article
(This article belongs to the Special Issue Statistics and Modeling in Reliability Engineering)
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18 pages, 472 KiB  
Article
A 2D Non-Linear Second-Order Differential Model for Electrostatic Circular Membrane MEMS Devices: A Result of Existence and Uniqueness
by Paolo Di Barba, Luisa Fattorusso and Mario Versaci
Mathematics 2019, 7(12), 1193; https://doi.org/10.3390/math7121193 - 5 Dec 2019
Cited by 21 | Viewed by 3098
Abstract
In the framework of 2D circular membrane Micro-Electric-Mechanical-Systems (MEMS), a new non-linear second-order differential model with singularity in the steady-state case is presented in this paper. In particular, starting from the fact that the electric field magnitude is locally proportional to the curvature [...] Read more.
In the framework of 2D circular membrane Micro-Electric-Mechanical-Systems (MEMS), a new non-linear second-order differential model with singularity in the steady-state case is presented in this paper. In particular, starting from the fact that the electric field magnitude is locally proportional to the curvature of the membrane, the problem is formalized in terms of the mean curvature. Then, a result of the existence of at least one solution is achieved. Finally, two different approaches prove that the uniqueness of the solutions is not ensured. Full article
(This article belongs to the Special Issue Mathematical Modeling in Industrial Engineering and Electrical Engineering)
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10 pages, 794 KiB  
Article
Some Results on (s − q)-Graphic Contraction Mappings in b-Metric-Like Spaces
by Manuel De la Sen, Nebojša Nikolić, Tatjana Došenović, Mirjana Pavlović and Stojan Radenović
Mathematics 2019, 7(12), 1190; https://doi.org/10.3390/math7121190 - 4 Dec 2019
Cited by 20 | Viewed by 2693
Abstract
In this paper we consider ( s − q ) -graphic contraction mapping in b-metric like spaces. By using our new approach for the proof that a Picard sequence is Cauchy in the context of b-metric-like space, our results generalize, improve [...] Read more.
In this paper we consider ( s − q ) -graphic contraction mapping in b-metric like spaces. By using our new approach for the proof that a Picard sequence is Cauchy in the context of b-metric-like space, our results generalize, improve and complement several approaches in the existing literature. Moreover, some examples are presented here to illustrate the usability of the obtained theoretical results. Full article
(This article belongs to the Special Issue Graph-Theoretic Problems and Their New Applications)
17 pages, 493 KiB  
Article
Significance of Double Stratification in Stagnation Point Flow of Third-Grade Fluid towards a Radiative Stretching Cylinder
by Anum Shafiq, Ilyas Khan, Ghulam Rasool, Asiful H. Seikh and El-Sayed M. Sherif
Mathematics 2019, 7(11), 1103; https://doi.org/10.3390/math7111103 - 14 Nov 2019
Cited by 38 | Viewed by 3927
Abstract
The present article is devoted to examine the significance of double stratification in third grade stagnation point flow towards a radiative stretching cylinder. The stagnation point is discussed categorically. Analysis is scrutinized in the presence of Thermophoresis, Brownian diffusion, double stratification and heat [...] Read more.
The present article is devoted to examine the significance of double stratification in third grade stagnation point flow towards a radiative stretching cylinder. The stagnation point is discussed categorically. Analysis is scrutinized in the presence of Thermophoresis, Brownian diffusion, double stratification and heat source/sink. Suitable typical transformations are used to drive the system of ordinary differential equation. The governing system is subjected to optimal homotopy analysis method (OHAM) for convergent series solutions. The impact of pertinent fluid parameters on the velocity field, temperature distribution and concentration of the nanoparticles is shown graphically. Numerical data is compiled in tabulare form for skin friction, Nusselt and Sherwood numbers to analyze the variation caused by the present model and to see the impact for industrial and engineering point of view. Full article
(This article belongs to the Special Issue Computational Fluid Dynamics 2020)
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12 pages, 326 KiB  
Article
Topologies on Z n that Are Not Homeomorphic to the n-Dimensional Khalimsky Topological Space
by Sang-Eon Han, Saeid Jafari and Jeong Min Kang
Mathematics 2019, 7(11), 1072; https://doi.org/10.3390/math7111072 - 7 Nov 2019
Cited by 17 | Viewed by 3428
Abstract
The present paper deals with two types of topologies on the set of integers, Z : a quasi-discrete topology and a topology satisfying the T 1 2 -separation axiom. Furthermore, for each n ∈ N , we develop countably many topologies on [...] Read more.
The present paper deals with two types of topologies on the set of integers, Z : a quasi-discrete topology and a topology satisfying the T 1 2 -separation axiom. Furthermore, for each n ∈ N , we develop countably many topologies on Z n which are not homeomorphic to the typical n-dimensional Khalimsky topological space. Based on these different types of new topological structures on Z n , many new mathematical approaches can be done in the fields of pure and applied sciences, such as fixed point theory, rough set theory, and so on. Full article
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20 pages, 341 KiB  
Article
An Optimisation-Driven Prediction Method for Automated Diagnosis and Prognosis
by Valentino Santucci, Alfredo Milani and Fabio Caraffini
Mathematics 2019, 7(11), 1051; https://doi.org/10.3390/math7111051 - 4 Nov 2019
Cited by 20 | Viewed by 3263
Abstract
This article presents a novel hybrid classification paradigm for medical diagnoses and prognoses prediction. The core mechanism of the proposed method relies on a centroid classification algorithm whose logic is exploited to formulate the classification task as a real-valued optimisation problem. A novel [...] Read more.
This article presents a novel hybrid classification paradigm for medical diagnoses and prognoses prediction. The core mechanism of the proposed method relies on a centroid classification algorithm whose logic is exploited to formulate the classification task as a real-valued optimisation problem. A novel metaheuristic combining the algorithmic structure of Swarm Intelligence optimisers with the probabilistic search models of Estimation of Distribution Algorithms is designed to optimise such a problem, thus leading to high-accuracy predictions. This method is tested over 11 medical datasets and compared against 14 cherry-picked classification algorithms. Results show that the proposed approach is competitive and superior to the state-of-the-art on several occasions. Full article
(This article belongs to the Special Issue Numerical Optimization and Applications)
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9 pages, 253 KiB  
Article
Universal Function Approximation by Deep Neural Nets with Bounded Width and ReLU Activations
by Boris Hanin
Mathematics 2019, 7(10), 992; https://doi.org/10.3390/math7100992 - 18 Oct 2019
Cited by 181 | Viewed by 12914
Abstract
This article concerns the expressive power of depth in neural nets with ReLU activations and a bounded width. We are particularly interested in the following questions: What is the minimal width w min ( d ) so that ReLU nets of width [...] Read more.
This article concerns the expressive power of depth in neural nets with ReLU activations and a bounded width. We are particularly interested in the following questions: What is the minimal width w min ( d ) so that ReLU nets of width w min ( d ) (and arbitrary depth) can approximate any continuous function on the unit cube [ 0 , 1 ] d arbitrarily well? For ReLU nets near this minimal width, what can one say about the depth necessary to approximate a given function? We obtain an essentially complete answer to these questions for convex functions. Our approach is based on the observation that, due to the convexity of the ReLU activation, ReLU nets are particularly well suited to represent convex functions. In particular, we prove that ReLU nets with width d + 1 can approximate any continuous convex function of d variables arbitrarily well. These results then give quantitative depth estimates for the rate of approximation of any continuous scalar function on the d-dimensional cube [ 0 , 1 ] d by ReLU nets with width d + 3 . Full article
(This article belongs to the Special Issue Computational Mathematics, Algorithms, and Data Processing)
16 pages, 2867 KiB  
Article
Developing an ANFIS-PSO Model to Predict Mercury Emissions in Combustion Flue Gases
by Shahaboddin Shamshirband, Masoud Hadipoor, Alireza Baghban, Amir Mosavi, Jozsef Bukor and Annamária R. Várkonyi-Kóczy
Mathematics 2019, 7(10), 965; https://doi.org/10.3390/math7100965 - 14 Oct 2019
Cited by 46 | Viewed by 5401
Abstract
Accurate prediction of mercury content emitted from fossil-fueled power stations is of the utmost importance for environmental pollution assessment and hazard mitigation. In this paper, mercury content in the output gas of power stations’ boilers was predicted using an adaptive neuro-fuzzy inference system [...] Read more.
Accurate prediction of mercury content emitted from fossil-fueled power stations is of the utmost importance for environmental pollution assessment and hazard mitigation. In this paper, mercury content in the output gas of power stations’ boilers was predicted using an adaptive neuro-fuzzy inference system (ANFIS) method integrated with particle swarm optimization (PSO). The input parameters of the model included coal characteristics and the operational parameters of the boilers. The dataset was collected from 82 sample points in power plants and employed to educate and examine the proposed model. To evaluate the performance of the proposed hybrid model of the ANFIS-PSO, the statistical meter of MARE% was implemented, which resulted in 0.003266 and 0.013272 for training and testing, respectively. Furthermore, relative errors between the acquired data and predicted values were between −0.25% and 0.1%, which confirm the accuracy of the model to deal non-linearity and represent the dependency of flue gas mercury content into the specifications of coal and the boiler type. Full article
(This article belongs to the Special Issue Hybrid Machine Learning Techniques Applied in Real Engineering Applications)
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25 pages, 906 KiB  
Article
Real-Time Optimization and Control of Nonlinear Processes Using Machine Learning
by Zhihao Zhang, Zhe Wu, David Rincon and Panagiotis D. Christofides
Mathematics 2019, 7(10), 890; https://doi.org/10.3390/math7100890 - 24 Sep 2019
Cited by 60 | Viewed by 8979
Abstract
Machine learning has attracted extensive interest in the process engineering field, due to the capability of modeling complex nonlinear process behavior. This work presents a method for combining neural network models with first-principles models in real-time optimization (RTO) and model predictive control (MPC) [...] Read more.
Machine learning has attracted extensive interest in the process engineering field, due to the capability of modeling complex nonlinear process behavior. This work presents a method for combining neural network models with first-principles models in real-time optimization (RTO) and model predictive control (MPC) and demonstrates the application to two chemical process examples. First, the proposed methodology that integrates a neural network model and a first-principles model in the optimization problems of RTO and MPC is discussed. Then, two chemical process examples are presented. In the first example, a continuous stirred tank reactor (CSTR) with a reversible exothermic reaction is studied. A feed-forward neural network model is used to approximate the nonlinear reaction rate and is combined with a first-principles model in RTO and MPC. An RTO is designed to find the optimal reactor operating condition balancing energy cost and reactant conversion, and an MPC is designed to drive the process to the optimal operating condition. A variation in energy price is introduced to demonstrate that the developed RTO scheme is able to minimize operation cost and yields a closed-loop performance that is very close to the one attained by RTO/MPC using the first-principles model. In the second example, a distillation column is used to demonstrate an industrial application of the use of machine learning to model nonlinearities in RTO. A feed-forward neural network is first built to obtain the phase equilibrium properties and then combined with a first-principles model in RTO, which is designed to maximize the operation profit and calculate optimal set-points for the controllers. A variation in feed concentration is introduced to demonstrate that the developed RTO scheme can increase operation profit for all considered conditions. Full article
(This article belongs to the Special Issue Mathematics and Engineering)
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12 pages, 311 KiB  
Article
The Fixed Point Property of Non-Retractable Topological Spaces
by Jeong Min Kang, Sang-Eon Han and Sik Lee
Mathematics 2019, 7(10), 879; https://doi.org/10.3390/math7100879 - 21 Sep 2019
Cited by 8 | Viewed by 3103
Abstract
Unlike the study of the fixed point property (FPP, for brevity) of retractable topological spaces, the research of the FPP of non-retractable topological spaces remains. The present paper deals with the issue. Based on order-theoretic foundations and fixed point theory for [...] Read more.
Unlike the study of the fixed point property (FPP, for brevity) of retractable topological spaces, the research of the FPP of non-retractable topological spaces remains. The present paper deals with the issue. Based on order-theoretic foundations and fixed point theory for Khalimsky (K-, for short) topological spaces, the present paper studies the product property of the FPP for K-topological spaces. Furthermore, the paper investigates the FPP of various types of connected K-topological spaces such as non-K-retractable spaces and some points deleted K-topological (finite) planes, and so on. To be specific, after proving that not every one point deleted subspace of a finite K-topological plane X is a K-retract of X, we study the FPP of a non-retractable topological space Y, such as one point deleted space Y ∖ { p } . Full article
(This article belongs to the Special Issue Fixed Point Theory and Related Nonlinear Problems with Applications)
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20 pages, 611 KiB  
Article
A Novel FMEA Model Based on Rough BWM and Rough TOPSIS-AL for Risk Assessment
by Tai-Wu Chang, Huai-Wei Lo, Kai-Ying Chen and James J. H. Liou
Mathematics 2019, 7(10), 874; https://doi.org/10.3390/math7100874 - 20 Sep 2019
Cited by 63 | Viewed by 4962
Abstract
Failure mode and effects analysis (FMEA) is a risk assessment method that effectively diagnoses a product’s potential failure modes. It is based on expert experience and investigation to determine the potential failure modes of the system or product to develop improvement strategies to [...] Read more.
Failure mode and effects analysis (FMEA) is a risk assessment method that effectively diagnoses a product’s potential failure modes. It is based on expert experience and investigation to determine the potential failure modes of the system or product to develop improvement strategies to reduce the risk of failures. However, the traditional FMEA has many shortcomings that were proposed by many studies. This study proposes a hybrid FMEA and multi-attribute decision-making (MADM) model to establish an evaluation framework, combining the rough best worst method (R-BWM) and rough technique for order preference by similarity to an ideal solution technique (R-TOPSIS) to determine the improvement order of failure modes. In addition, this study adds the concept of aspiration level to R-TOPSIS technology (called R-TOPSIS-AL), which not only optimizes the reliability of the TOPSIS calculation program, but also obtains more potential information. This study then demonstrates the effectiveness and robustness of the proposed model through a multinational audio equipment manufacturing company. The results show that the proposed model can overcome many shortcomings of traditional FMEA, and effectively assist decision-makers and research and development (R&D) departments in improving the reliability of products. Full article
(This article belongs to the Special Issue Recent Advances in Modeling for Reliability Analysis)
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23 pages, 479 KiB  
Article
Applications of the Fractional Diffusion Equation to Option Pricing and Risk Calculations
by Jean-Philippe Aguilar, Jan Korbel and Yuri Luchko
Mathematics 2019, 7(9), 796; https://doi.org/10.3390/math7090796 - 1 Sep 2019
Cited by 23 | Viewed by 6146
Abstract
In this article, we first provide a survey of the exponential option pricing models and show that in the framework of the risk-neutral approach, they are governed by the space-fractional diffusion equation. Then, we introduce a more general class of models based on [...] Read more.
In this article, we first provide a survey of the exponential option pricing models and show that in the framework of the risk-neutral approach, they are governed by the space-fractional diffusion equation. Then, we introduce a more general class of models based on the space-time-fractional diffusion equation and recall some recent results in this field concerning the European option pricing and the risk-neutral parameter. We proceed with an extension of these results to the class of exotic options. In particular, we show that the call and put prices can be expressed in the form of simple power series in terms of the log-forward moneyness and the risk-neutral parameter. Finally, we provide the closed-form formulas for the first and second order risk sensitivities and study the dependencies of the portfolio hedging and profit-and-loss calculations upon the model parameters. Full article
(This article belongs to the Special Issue Mathematical Economics: Application of Fractional Calculus)
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23 pages, 372 KiB  
Article
Hybrid Control Scheme for Projective Lag Synchronization of Riemann–Liouville Sense Fractional Order Memristive BAM NeuralNetworks with Mixed Delays
by Grienggrai Rajchakit, Anbalagan Pratap, Ramachandran Raja, Jinde Cao, Jehad Alzabut and Chuangxia Huang
Mathematics 2019, 7(8), 759; https://doi.org/10.3390/math7080759 - 19 Aug 2019
Cited by 155 | Viewed by 5533
Abstract
This sequel is concerned with the analysis of projective lag synchronization of Riemann–Liouville sense fractional order memristive BAM neural networks (FOMBNNs) with mixed time delays via hybrid controller. Firstly, a new type of hybrid control scheme, which is the combination of open loop [...] Read more.
This sequel is concerned with the analysis of projective lag synchronization of Riemann–Liouville sense fractional order memristive BAM neural networks (FOMBNNs) with mixed time delays via hybrid controller. Firstly, a new type of hybrid control scheme, which is the combination of open loop control and adaptive state feedback control is designed to guarantee the global projective lag synchronization of the addressed FOMBNNs model. Secondly, by using a Lyapunov–Krasovskii functional and Barbalet’s lemma, a new brand of sufficient criterion is proposed to ensure the projective lag synchronization of the FOMBNNs model considered. Moreover, as special cases by using a hybrid control scheme, some sufficient conditions are derived to ensure the global projective synchronization, global complete synchronization and global anti-synchronization for the FOMBNNs model considered. Finally, numerical simulations are provided to check the accuracy and validity of our obtained synchronization results. Full article
(This article belongs to the Special Issue Impulsive Control Systems and Complexity)
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19 pages, 8152 KiB  
Article
Development of Public Key Cryptographic Algorithm Using Matrix Pattern for Tele-Ultrasound Applications
by Seung-Hyeok Shin, Won-Sok Yoo and Hojong Choi
Mathematics 2019, 7(8), 752; https://doi.org/10.3390/math7080752 - 17 Aug 2019
Cited by 20 | Viewed by 4797
Abstract
A novel public key cryptographic algorithm using a matrix pattern is developed to improve encrypting strength. Compared to the Rivest–Sharmir–Adleman (RSA) and Elliptic Curve Cryptography (ECC) algorithms, our proposed algorithm has superior encrypting strength due to several unknown quantities and one additional sub-equation [...] Read more.
A novel public key cryptographic algorithm using a matrix pattern is developed to improve encrypting strength. Compared to the Rivest–Sharmir–Adleman (RSA) and Elliptic Curve Cryptography (ECC) algorithms, our proposed algorithm has superior encrypting strength due to several unknown quantities and one additional sub-equation during the encrypting process. Our proposed algorithm also provides a faster encoding/decoding speed when the patient’s images for tele-ultrasound applications are transmitted/received, compared to the RSA and ECC encrypting algorithms, because it encodes/decodes the plain memory block by simple addition and multiplication operations of n terms. However, the RSA and ECC algorithms encode/decode each memory block using complex mathematical exponentiation and congruence. To implement encrypting algorithms for tele-ultrasound applications, a streaming server was constructed to transmit the images to the systems using ultrasound machines. Using the obtained ultrasound images from a breast phantom, we compared our developed algorithm, utilizing a matrix pattern, with the RSA and ECC algorithms. The elapsed average time for our proposed algorithm is much faster than that for the RSA and ECC algorithms. Full article
(This article belongs to the Special Issue Information Theory, Cryptography, Randomness and Statistical Modeling)
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6 pages, 255 KiB  
Article
The Application of Fractional Calculus in Chinese Economic Growth Models
by Hao Ming, JinRong Wang and Michal Fečkan
Mathematics 2019, 7(8), 665; https://doi.org/10.3390/math7080665 - 25 Jul 2019
Cited by 36 | Viewed by 4887
Abstract
In this paper, we apply Caputo-type fractional order calculus to simulate China’s gross domestic product (GDP) growth based on R software, which is a free software environment for statistical computing and graphics. Moreover, we compare the results for the fractional model with the [...] Read more.
In this paper, we apply Caputo-type fractional order calculus to simulate China’s gross domestic product (GDP) growth based on R software, which is a free software environment for statistical computing and graphics. Moreover, we compare the results for the fractional model with the integer order model. In addition, we show the importance of variables according to the BIC criterion. The study shows that Caputo fractional order calculus can produce a better model and perform more accurately in predicting the GDP values from 2012–2016. Full article
(This article belongs to the Special Issue Mathematical Economics: Application of Fractional Calculus)
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8 pages, 224 KiB  
Article
Growth Equation of the General Fractional Calculus
by Anatoly N. Kochubei and Yuri Kondratiev
Mathematics 2019, 7(7), 615; https://doi.org/10.3390/math7070615 - 11 Jul 2019
Cited by 49 | Viewed by 3428
Abstract
We consider the Cauchy problem ( D ( k ) u ) ( t ) = λ u ( t ) , u ( 0 ) = 1 , where D ( k ) is the general convolutional derivative introduced in the paper [...] Read more.
We consider the Cauchy problem ( D ( k ) u ) ( t ) = λ u ( t ) , u ( 0 ) = 1 , where D ( k ) is the general convolutional derivative introduced in the paper (A. N. Kochubei, Integral Equations Oper. Theory 71 (2011), 583–600), λ > 0 . The solution is a generalization of the function t ↦ E α ( λ t α ) , where 0 < α < 1 , E α is the Mittag–Leffler function. The asymptotics of this solution, as t → ∞ , are studied. Full article
(This article belongs to the Special Issue Mathematical Economics: Application of Fractional Calculus)
9 pages, 254 KiB  
Article
Some New Oscillation Criteria for Second Order Neutral Differential Equations with Delayed Arguments
by Omar Bazighifan and Clemente Cesarano
Mathematics 2019, 7(7), 619; https://doi.org/10.3390/math7070619 - 11 Jul 2019
Cited by 43 | Viewed by 2806
Abstract
In this paper, we study the oscillation of second-order neutral differential equations with delayed arguments. Some new oscillatory criteria are obtained by a Riccati transformation. To illustrate the importance of the results, one example is also given. Full article
(This article belongs to the Special Issue Multivariate Approximation for solving ODE and PDE)
10 pages, 254 KiB  
Article
Robust Synchronization of Fractional-Order Uncertain Chaotic Systems Based on Output Feedback Sliding Mode Control
by Chao Song, Shumin Fei, Jinde Cao and Chuangxia Huang
Mathematics 2019, 7(7), 599; https://doi.org/10.3390/math7070599 - 5 Jul 2019
Cited by 74 | Viewed by 3768
Abstract
This paper mainly focuses on the robust synchronization issue for drive-response fractional-order chaotic systems (FOCS) when they have unknown parameters and external disturbances. In order to achieve the goal, the sliding mode control scheme only using output information is designed, and at the [...] Read more.
This paper mainly focuses on the robust synchronization issue for drive-response fractional-order chaotic systems (FOCS) when they have unknown parameters and external disturbances. In order to achieve the goal, the sliding mode control scheme only using output information is designed, and at the same time, the structures of a sliding mode surface and a sliding mode controller are also constructed. A sufficient criterion is presented to ensure the robust synchronization of FOCS according to the stability theory of the fractional calculus and sliding mode control technique. In addition, the result can be applied to identical or non-identical chaotic systems with fractional-order. In the end, we build two practical examples to illustrate the feasibility of our theoretical results. Full article
(This article belongs to the Special Issue Impulsive Control Systems and Complexity)
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