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Mathematics, Volume 9, Issue 19 (October-1 2021) – 181 articles

Cover Story (view full-size image): Degradation of services is very common, especially in production, manufacturing, and service industries. This is due to a variety of reasons, including the wear and tear of machinery and fatigue of operators/servers. In this paper, we study MAP/PH/1-type queueing models with degradation of services. Starting from normal service rates, degradation results in reduced service rates and then resets to normal. Two types of reset to normalcy are considered in this paper. Classical Neuts’ matrix-analytic methods are employed to analyze the model in steady state. Illustrative numerical examples are presented. View this paper
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Article
Vibration and Flutter of a Honeycomb Sandwich Plate with Zero Poisson’s Ratio
Mathematics 2021, 9(19), 2528; https://doi.org/10.3390/math9192528 - 08 Oct 2021
Viewed by 525
Abstract
A honeycomb is a kind of excellent lightweight structure and a honeycomb sandwich plate with zero Poisson’s ratio (ZPR) core is used widely in morphing structures. In this paper, a sandwich plate composed of a honeycomb core with zero Poisson’s ratio is analyzed [...] Read more.
A honeycomb is a kind of excellent lightweight structure and a honeycomb sandwich plate with zero Poisson’s ratio (ZPR) core is used widely in morphing structures. In this paper, a sandwich plate composed of a honeycomb core with zero Poisson’s ratio is analyzed for free vibrations and flutter under supersonic airflows. The equivalent elastic parametric formulas of the honeycomb core for zero Poisson’s ratio are proposed. The models are compared for their natural frequencies by theoretical and finite element methods respectively, which verifies the validity of the equivalent elastic parametric formulas and the model for the honeycomb sandwich plate with zero Poisson’s ratio. The influence of the geometric parameters of the honeycomb plate on the vibration frequencies is obtained. Three kinds of honeycomb cores, namely, regular hexagon, auxetic and hybrid with zero Poisson’s ratio, are compared through natural frequencies of the sandwich plate. It is found that the frequency of the zero Poisson’s ratio honeycomb sandwich plate is the second one when the other parameters are the same. The flutter of the honeycomb plate is analyzed by using the first order piston theory under supersonic flows. The critical flutter velocity of the plate is obtained, and the influence of geometric parameters of the honeycomb plate on the critical flutter velocities is obtained. Full article
(This article belongs to the Topic Dynamical Systems: Theory and Applications)
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Article
ABS-Based Direct Method for Solving Complex Systems of Linear Equations
Mathematics 2021, 9(19), 2527; https://doi.org/10.3390/math9192527 - 08 Oct 2021
Viewed by 373
Abstract
Efficient solution of linear systems of equations is one of the central topics of numerical computation. Linear systems with complex coefficients arise from various physics and quantum chemistry problems. In this paper, we propose a novel ABS-based algorithm, which is able to solve [...] Read more.
Efficient solution of linear systems of equations is one of the central topics of numerical computation. Linear systems with complex coefficients arise from various physics and quantum chemistry problems. In this paper, we propose a novel ABS-based algorithm, which is able to solve complex systems of linear equations. Theoretical analysis is given to highlight the basic features of our new algorithm. Four variants of our algorithm were also implemented and intensively tested on randomly generated full and sparse matrices and real-life problems. The results of numerical experiments reveal that our ABS-based algorithm is able to compute the solution with high accuracy. The performance of our algorithm was compared with a commercially available software, Matlab’s mldivide (\) algorithm. Our algorithm outperformed the Matlab algorithm in most cases in terms of computational accuracy. These results expand the practical usefulness of our algorithm. Full article
(This article belongs to the Special Issue Numerical Methods II)
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Article
Prospective Mathematics Teachers Understanding of Classical and Frequentist Probability
Mathematics 2021, 9(19), 2526; https://doi.org/10.3390/math9192526 - 08 Oct 2021
Cited by 1 | Viewed by 1012
Abstract
Strengthening the teaching of probability requires an adequate training of prospective teachers, which should be based on the prior assessment of their knowledge. Consequently, the aim of this study was to analyse how 139 prospective Spanish mathematics teachers relate the classical and frequentist [...] Read more.
Strengthening the teaching of probability requires an adequate training of prospective teachers, which should be based on the prior assessment of their knowledge. Consequently, the aim of this study was to analyse how 139 prospective Spanish mathematics teachers relate the classical and frequentist approaches to probability. To achieve this goal, content analysis was used to categorize the prospective teachers’ answers to a questionnaire with open-ended tasks in which they had to estimate and justify the composition of an urn, basing their answers on the results of 1000 extractions from the urn. Most of the sample proposed an urn model consistent with the data provided; however, the percentage that adequately justified the construction was lower. Although the majority of the sample correctly calculated the probability of an event in a new extraction and chose the urn giving the highest probability, a large proportion of the sample forgot the previously constructed urn model, using only the frequency data. Difficulties, such as equiprobability bias or not perceiving independence of trials in replacement sampling, were also observed for a small part of the sample. These results should be considered in the organisation of probabilistic training for prospective teachers. Full article
(This article belongs to the Special Issue Statistics Education: An Immediate Need in a Changing World)
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Article
Heat Transport Phenomena for the Darcy–Forchheimer Flow of Casson Fluid over Stretching Sheets with Electro-Osmosis Forces and Newtonian Heating
Mathematics 2021, 9(19), 2525; https://doi.org/10.3390/math9192525 - 08 Oct 2021
Cited by 1 | Viewed by 465
Abstract
In this study, an investigation has been carried out to analyze the impact of electro-osmotic effects on the Darcy–Forchheimer flow of Casson nanofluid past a stretching sheet. The energy equation was modelled with the inclusion of electro-osmotic effects with viscous and Joule dissipations. [...] Read more.
In this study, an investigation has been carried out to analyze the impact of electro-osmotic effects on the Darcy–Forchheimer flow of Casson nanofluid past a stretching sheet. The energy equation was modelled with the inclusion of electro-osmotic effects with viscous and Joule dissipations. The governing system of partial differential equations were transformed by using the suitable similarity transformations to a system of ordinary differential equations and then numerically solved by using the Runge–Kutta–Fehlberg method with a shooting scheme. The effects of various parameters of interest on dimensionless velocity and temperature distributions, as well as skin friction and heat transfer coefficient, have been adequately delineated via graphs and tables. A comparison with previous published results was performed, and good agreement was found. The results suggested that the electric and Forchheimer parameters have the tendency to enhance the fluid velocity as well as momentum boundary layer thickness. Enhancements in temperature distribution were observed for growing values of Eckert number. It was also observed that higher values of electric field parameter diminished the wall shear stress and local Nusselt number. Full article
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Article
A Dimension Splitting Generalized Interpolating Element-Free Galerkin Method for the Singularly Perturbed Steady Convection–Diffusion–Reaction Problems
Mathematics 2021, 9(19), 2524; https://doi.org/10.3390/math9192524 - 08 Oct 2021
Viewed by 416
Abstract
By introducing the dimension splitting method (DSM) into the generalized element-free Galerkin (GEFG) method, a dimension splitting generalized interpolating element-free Galerkin (DS-GIEFG) method is presented for analyzing the numerical solutions of the singularly perturbed steady convection–diffusion–reaction (CDR) problems. In the DS-GIEFG method, the [...] Read more.
By introducing the dimension splitting method (DSM) into the generalized element-free Galerkin (GEFG) method, a dimension splitting generalized interpolating element-free Galerkin (DS-GIEFG) method is presented for analyzing the numerical solutions of the singularly perturbed steady convection–diffusion–reaction (CDR) problems. In the DS-GIEFG method, the DSM is used to divide the two-dimensional CDR problem into a series of lower-dimensional problems. The GEFG and the improved interpolated moving least squares (IIMLS) methods are used to obtain the discrete equations on the subdivision plane. Finally, the IIMLS method is applied to assemble the discrete equations of the entire problem. Some examples are solved to verify the effectiveness of the DS-GIEFG method. The numerical results show that the numerical solution converges to the analytical solution with the decrease in node spacing, and the DS-GIEFG method has high computational efficiency and accuracy. Full article
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Article
Machine Learning Applied to the Oxygen-18 Isotopic Composition, Salinity and Temperature/Potential Temperature in the Mediterranean Sea
Mathematics 2021, 9(19), 2523; https://doi.org/10.3390/math9192523 - 08 Oct 2021
Cited by 2 | Viewed by 687
Abstract
This study proposed different techniques to estimate the isotope composition (δ18O), salinity and temperature/potential temperature in the Mediterranean Sea using five different variables: (i–ii) geographic coordinates (Longitude, Latitude), (iii) year, (iv) month and (v) depth. Three kinds of models based on [...] Read more.
This study proposed different techniques to estimate the isotope composition (δ18O), salinity and temperature/potential temperature in the Mediterranean Sea using five different variables: (i–ii) geographic coordinates (Longitude, Latitude), (iii) year, (iv) month and (v) depth. Three kinds of models based on artificial neural network (ANN), random forest (RF) and support vector machine (SVM) were developed. According to the results, the random forest models presents the best prediction accuracy for the querying phase and can be used to predict the isotope composition (mean absolute percentage error (MAPE) around 4.98%), salinity (MAPE below 0.20%) and temperature (MAPE around 2.44%). These models could be useful for research works that require the use of past data for these variables. Full article
(This article belongs to the Special Issue Numerical Analysis and Scientific Computing)
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Article
Optimized Task Group Aggregation-Based Overflow Handling on Fog Computing Environment Using Neural Computing
Mathematics 2021, 9(19), 2522; https://doi.org/10.3390/math9192522 - 07 Oct 2021
Cited by 1 | Viewed by 616
Abstract
It is a non-deterministic challenge on a fog computing network to schedule resources or jobs in a manner that increases device efficacy and throughput, diminishes reply period, and maintains the system well-adjusted. Using Machine Learning as a component of neural computing, we developed [...] Read more.
It is a non-deterministic challenge on a fog computing network to schedule resources or jobs in a manner that increases device efficacy and throughput, diminishes reply period, and maintains the system well-adjusted. Using Machine Learning as a component of neural computing, we developed an improved Task Group Aggregation (TGA) overflow handling system for fog computing environments. As a result of TGA usage in conjunction with an Artificial Neural Network (ANN), we may assess the model’s QoS characteristics to detect an overloaded server and then move the model’s data to virtual machines (VMs). Overloaded and underloaded virtual machines will be balanced according to parameters, such as CPU, memory, and bandwidth to control fog computing overflow concerns with the help of ANN and the machine learning concept. Additionally, the Artificial Bee Colony (ABC) algorithm, which is a neural computing system, is employed as an optimization technique to separate the services and users depending on their individual qualities. The response time and success rate were both enhanced using the newly proposed optimized ANN-based TGA algorithm. Compared to the present work’s minimal reaction time, the total improvement in average success rate is about 3.6189 percent, and Resource Scheduling Efficiency has improved by 3.9832 percent. In terms of virtual machine efficiency for resource scheduling, average success rate, average task completion success rate, and virtual machine response time are improved. The proposed TGA-based overflow handling on a fog computing domain enhances response time compared to the current approaches. Fog computing, for example, demonstrates how artificial intelligence-based systems can be made more efficient. Full article
(This article belongs to the Special Issue Distributed Computer and Communication Networks)
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Article
Automatically Tightening Tiny Screw Using Two Images and Positioning Control
Mathematics 2021, 9(19), 2521; https://doi.org/10.3390/math9192521 - 07 Oct 2021
Viewed by 577
Abstract
This paper describes how to tighten M1.4 screws by controlling a manipulator. The whole process is based on a human–machine interface designed using Visual Studio C++ to run image processing algorithms and control the position of a manipulator. Two charge-coupled device cameras are [...] Read more.
This paper describes how to tighten M1.4 screws by controlling a manipulator. The whole process is based on a human–machine interface designed using Visual Studio C++ to run image processing algorithms and control the position of a manipulator. Two charge-coupled device cameras are used. One is fixed on the stationary frame above screw holes and used to take pictures of the holes. The positions of the holes are determined using image processing algorithms and then transformed into the coordinate system of the manipulator by using coordinate transformation. The other camera, installed on the end effect of the manipulator, photographs the screw hole to fine-tune the position of the manipulator, improving positioning control. The image processing methods including grayscale, Gaussian filter, bilateral filter, binarization, edge detection, center of gravity, and minimum circumcircle are used to find the center coordinates of the target holes. Experimental study shows that M1.4 screws can be tightened into the target holes with the manipulator. Full article
(This article belongs to the Special Issue Mathematical Problems in Mechanical Engineering)
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Article
Environmental Management through Coopetitive Urban Waste Recycling in Eco-Industrial Parks
Mathematics 2021, 9(19), 2520; https://doi.org/10.3390/math9192520 - 07 Oct 2021
Cited by 1 | Viewed by 588
Abstract
In this article, we consider the coexistence of competing actors within a specific eco-industrial park. The competing firms dynamics evolves by means of an interplay agreement determined among the competitors themselves. In particular, we show a possible scenario in which the selected eco-industrial [...] Read more.
In this article, we consider the coexistence of competing actors within a specific eco-industrial park. The competing firms dynamics evolves by means of an interplay agreement determined among the competitors themselves. In particular, we show a possible scenario in which the selected eco-industrial competitors could greatly benefit from a coopetitive interaction, within their common eco-park, while improving the general conditions of a near residential area. The associated dynamical coopetitive agreement, aims at the growth and improvement of the firms themselves and of their industrial network (within a virtuous environmental path). As an example, we assume the existence of two competitors selling the same good on the same market, so that, from a competitive point of view, we construct a classic Cournot duopoly model upon which we build up a multidimensional coopetitive agreement. Our eco-friendly deal allows to “enlarge the pie” of possible gains by diminishing sunk costs and other forms of costs, especially the environmental costs associated to the management of urban waste recycling. Consequently, we suggest production methods and production quantitative profiles in order to “share the gains fairly”. We show a complete mathematical analysis of our new economic game and show some of its possible and relevant solutions. Full article
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Article
Computational Geometry of Period-3 Hyperbolic Components in the Mandelbrot Set
Mathematics 2021, 9(19), 2519; https://doi.org/10.3390/math9192519 - 07 Oct 2021
Viewed by 455
Abstract
A parametric theoretical boundary equation of a period-3 hyperbolic component in the Mandelbrot set is established from a perspective of Euclidean plane geometry. We not only calculate the interior area, perimeter and curvature of the boundary line but also derive some relevant geometrical [...] Read more.
A parametric theoretical boundary equation of a period-3 hyperbolic component in the Mandelbrot set is established from a perspective of Euclidean plane geometry. We not only calculate the interior area, perimeter and curvature of the boundary line but also derive some relevant geometrical properties. The budding point of the period-3k component, which is born on the boundary of the period-3 component, and its relevant period-3k points are theoretically obtained by means of Cardano’s formula for the cubic equation. In addition, computational results are presented in tables and figures to support the theoretical background of this paper. Full article
(This article belongs to the Special Issue New Trends and Developments in Numerical Analysis)
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Article
Hierarchical Bayesian Modeling and Randomized Response Method for Inferring the Sensitive-Nature Proportion
Mathematics 2021, 9(19), 2518; https://doi.org/10.3390/math9192518 - 07 Oct 2021
Viewed by 404
Abstract
In this study, a new three-statement randomized response estimation method is proposed to improve the drawback that the maximum likelihood estimation method could generate a negative value to estimate the sensitive-nature proportion (SNP) when its true value is small. The Bayes estimator of [...] Read more.
In this study, a new three-statement randomized response estimation method is proposed to improve the drawback that the maximum likelihood estimation method could generate a negative value to estimate the sensitive-nature proportion (SNP) when its true value is small. The Bayes estimator of the SNP is obtained via using a hierarchical Bayesian modeling procedure. Moreover, a hybrid algorithm using Gibbs sampling in Metropolis–Hastings algorithms is used to obtain the Bayes estimator of the SNP. The highest posterior density interval of the SNP is obtained based on the empirical distribution of Markov chains. We use the term 3RR-HB to denote the proposed method here. Monte Carlo simulations show that the quality of 3RR-HB procedure is good and that it can improve the drawback of the maximum likelihood estimation method. The proposed 3RR-HB procedure is simple for use. An example regarding the homosexual proportion of college freshmen is used for illustration. Full article
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Article
Experiments with Fuzzy Methods for Forecasting Time Series as Alternatives to Classical Methods
Mathematics 2021, 9(19), 2517; https://doi.org/10.3390/math9192517 - 07 Oct 2021
Viewed by 594
Abstract
Even though forecasting methods have advanced in the last few decades, economists still face a simple question: which prediction method gives the most accurate results? Econometric forecasting methods can deal with different types of time series and have good results, but in specific [...] Read more.
Even though forecasting methods have advanced in the last few decades, economists still face a simple question: which prediction method gives the most accurate results? Econometric forecasting methods can deal with different types of time series and have good results, but in specific cases, they may fail to provide accurate predictions. Recently, new techniques borrowed from the soft computing area were adopted for economic forecasting. Starting from the importance of economic forecasts, we present an experimental study where we compared the accuracy of some of the most used econometric forecasting methods, namely the simple exponential smoothing, Holt and ARIMA methods, with that of two new methods based on the concept of fuzzy time series. We used a set of time series extracted from the Eurostat database and the R software for all data processing. The results of the experiments show that despite not being fully superior to the econometric techniques, the fuzzy time series forecasting methods could be considered as an alternative for specific time series. Full article
(This article belongs to the Special Issue Analysis and Mathematical Modeling of Economic - Related Data)
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Article
Searching for a New Model of Governance in the High Seas: Game Theory Applied to International Commons Management
Mathematics 2021, 9(19), 2516; https://doi.org/10.3390/math9192516 - 07 Oct 2021
Viewed by 445
Abstract
In the last decade, the United Nations took important steps for the creation of a new instrument for biodiversity protection in areas beyond national jurisdiction. This put under discussion the central issues of international commons management and of the governance model for the [...] Read more.
In the last decade, the United Nations took important steps for the creation of a new instrument for biodiversity protection in areas beyond national jurisdiction. This put under discussion the central issues of international commons management and of the governance model for the High Seas. The aim of this paper is to discuss and evaluate critically the political negotiations already made and yet to come, as well as their rationale. For this purpose, the paper applies game theory to fisheries management to get insights. This research aims to contribute toward more qualified and grounded decisions. The key role of cooperation in the sustainable use of common resources is stressed. Full article
Article
Stochastic Analysis of the RT-PCR Process in Single-Cell RNA-Seq
Mathematics 2021, 9(19), 2515; https://doi.org/10.3390/math9192515 - 07 Oct 2021
Viewed by 541
Abstract
The single-cell RNA-seq allows exploring the transcriptome for one cell at a time. By doing so, cellular regulation is pictured. One limitation is the dropout events phenomenon, where a gene is observed at a low or moderate expression level in one cell but [...] Read more.
The single-cell RNA-seq allows exploring the transcriptome for one cell at a time. By doing so, cellular regulation is pictured. One limitation is the dropout events phenomenon, where a gene is observed at a low or moderate expression level in one cell but not detected in another. Dropouts obscure legitimate biological heterogeneity leading to the description of a small fraction of the meaningful relations. We used a stochastic approach to model the Reverse Transcription Polymerase Chain Reaction (RT-PCR) kinetic, in which we contemplated the temperature profile, RT-PCR duration, and reaction rates. By studying the underlying biochemical processes of RT-PCR, using a computational and analytical framework, we show a minimal amount of RNA to avoid dropout events. We further use this fact to characterize the limits in the dispersion reduction. Dispersion asymptotically decreases as the RNA initial value increases. Despite always being a basal dispersion, their decreasing speed is modulated mainly by the degradation rates, particularly for the RNA. We concluded that the critical step into the RT-PCR is the RT phase due to the fragile nature of the RNA. We propose that limiting RNA degradation might ensure that the portraited transcriptional landscape is unbiased by technical error. Full article
(This article belongs to the Section Mathematical Biology)
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Article
Darcy–Brinkman–Forchheimer Model for Nano-Bioconvection Stratified MHD Flow through an Elastic Surface: A Successive Relaxation Approach
Mathematics 2021, 9(19), 2514; https://doi.org/10.3390/math9192514 - 07 Oct 2021
Cited by 3 | Viewed by 499
Abstract
The present study deals with the Darcy–Brinkman–Forchheimer model for bioconvection-stratified nanofluid flow through a porous elastic surface. The mathematical modeling for MHD nanofluid flow with motile gyrotactic microorganisms is formulated under the influence of an inclined magnetic field, Brownian motion, thermophoresis, viscous dissipation, [...] Read more.
The present study deals with the Darcy–Brinkman–Forchheimer model for bioconvection-stratified nanofluid flow through a porous elastic surface. The mathematical modeling for MHD nanofluid flow with motile gyrotactic microorganisms is formulated under the influence of an inclined magnetic field, Brownian motion, thermophoresis, viscous dissipation, Joule heating, and stratifi-cation. In addition, the momentum equation is formulated using the Darcy–Brinkman–Forchheimer model. Using similarity transforms, governing partial differential equations are reconstructed into ordinary differential equations. The spectral relaxation method (SRM) is used to solve the nonlinear coupled differential equations. The SRM is a straightforward technique to develop, because it is based on decoupling the system of equations and then integrating the coupled system using the Chebyshev pseudo-spectral method to obtain the required results. The numerical interpretation of SRM is admirable because it establishes a system of equations that sequentially solve by providing the results of the first equation into the next equation. The numerical results of temperature, velocity, concentration, and motile microorganism density profiles are presented with graphical curves and tables for all the governing parametric quantities. A numerical comparison of the SRM with the previously investigated work is also shown in tables, which demonstrate excellent agreement. Full article
(This article belongs to the Special Issue Computational Fluid Dynamics II)
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Article
A Fuzzy Evaluation Model Aimed at Smaller-the-Better-Type Quality Characteristics
Mathematics 2021, 9(19), 2513; https://doi.org/10.3390/math9192513 - 07 Oct 2021
Cited by 3 | Viewed by 464
Abstract
Numerous key components of tool machines possess critical smaller-the-better-type quality characteristics. Under the assumption of normality, a one-to-one mathematical relationship exists between the process quality index and the process yield. Therefore, this paper utilized the index to produce a quality fuzzy evaluation model [...] Read more.
Numerous key components of tool machines possess critical smaller-the-better-type quality characteristics. Under the assumption of normality, a one-to-one mathematical relationship exists between the process quality index and the process yield. Therefore, this paper utilized the index to produce a quality fuzzy evaluation model aimed at the small-the-better-type quality characteristics and adopted the model as a decision-making basis for improvement. First, we derived the 100(1 α)% confidence region of the process mean and process standard deviation. Next, we obtained the 100(1 α)% confidence interval of the quality index using the mathematical programming method. Furthermore, a one-tailed fuzzy testing method based on this confidence interval was proposed, aiming to assess the process quality. In addition, enterprises’ pursuit of rapid response often results in small sample sizes. Since the evaluation model is built on the basis of the confidence interval, not only can it diminish the risk of wrong judgment due to sampling errors, but it also can enhance the accuracy of evaluations for small sample sizes. Full article
(This article belongs to the Special Issue Fuzzy Applications in Industrial Engineering)
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Article
The Fear of Covid-19 Scale (FCV-19S) in Spain: Adaptation and Confirmatory Evidence of Construct and Concurrent Validity
Mathematics 2021, 9(19), 2512; https://doi.org/10.3390/math9192512 - 07 Oct 2021
Viewed by 1018
Abstract
Fear of the coronavirus has important implications on mental health. In western countries, a significant degree of vaccination has been achieved, but in Spain, less than 75% of the population has received both doses. The current situation is still seen as a threat [...] Read more.
Fear of the coronavirus has important implications on mental health. In western countries, a significant degree of vaccination has been achieved, but in Spain, less than 75% of the population has received both doses. The current situation is still seen as a threat by many people. Therefore, it is important to have reliable and valid measurement instruments to assess the impact of COVID-19 on the population. In this study, the Fear of COVID-19 Scale has been adapted to Spain, and its psychometric properties have been studied in a Spanish sample using Structural Equation Modeling. This methodology allows obtaining more reliable estimates, regardless of the measurement scale of the variables. The unifactorial structure was confirmed. The correlations with Neuroticism were statistically significant, and the concurrent validity structural equation model yielded good fit indices. However, neither age nor belonging to a risk group directly predict fear of the coronavirus in this sample, but gender and neuroticism are direct predictors. Likewise, neuroticism mediates the relationship between age and fear of COVID-19, and between gender and fear of COVID-19. So being young and being a woman show high scores on neuroticism, leading to their most intense fear of COVID-19. With this reliable and valid measurement instrument, it will be possible to assess the degree of fear of the coronavirus in the Spanish population and improve psychological interventions. Full article
(This article belongs to the Special Issue Quantitative Methods for Social Sciences)
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Article
Construction and Analysis of Queuing and Reliability Models Using Random Graphs
Mathematics 2021, 9(19), 2511; https://doi.org/10.3390/math9192511 - 07 Oct 2021
Viewed by 501
Abstract
In this paper, the use of the construction of random processes on graphs allows us to expand the models of the theory of queuing and reliability by constructing. These problems are important because the emphasis on the legal component largely determines functioning of [...] Read more.
In this paper, the use of the construction of random processes on graphs allows us to expand the models of the theory of queuing and reliability by constructing. These problems are important because the emphasis on the legal component largely determines functioning of these models. The considered models are reliability and queuing. Reliability models arranged according to the modular principle and reliability networks in the form of planar graphs. The queuing models considered here are queuing networks with multi server nodes and failures, changing the parameters of the queuing system in a random environment with absorbing states, and the process of growth of a random network. This is determined by the possibility of using, as traditional probability methods, mathematical logic theorems, geometric images of a queuing network, dual graphs to planar graphs, and a solution to the Dirichlet problem. Full article
(This article belongs to the Special Issue Random Processes on Graphs)
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Article
Convergence Analysis and Dynamical Nature of an Efficient Iterative Method in Banach Spaces
Mathematics 2021, 9(19), 2510; https://doi.org/10.3390/math9192510 - 07 Oct 2021
Viewed by 458
Abstract
We study the local convergence analysis of a fifth order method and its multi-step version in Banach spaces. The hypotheses used are based on the first Fréchet-derivative only. The new approach provides a computable radius of convergence, error bounds on the distances involved, [...] Read more.
We study the local convergence analysis of a fifth order method and its multi-step version in Banach spaces. The hypotheses used are based on the first Fréchet-derivative only. The new approach provides a computable radius of convergence, error bounds on the distances involved, and estimates on the uniqueness of the solution. Such estimates are not provided in the approaches using Taylor expansions of higher order derivatives, which may not exist or may be very expensive or impossible to compute. Numerical examples are provided to validate the theoretical results. Convergence domains of the methods are also checked through complex geometry shown by drawing basins of attraction. The boundaries of the basins show fractal-like shapes through which the basins are symmetric. Full article
(This article belongs to the Special Issue Mathematical and Molecular Topology)
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Article
Investigation of Drift Phenomena at the Pore Scale during Flow and Transport in Porous Media
Mathematics 2021, 9(19), 2509; https://doi.org/10.3390/math9192509 - 07 Oct 2021
Viewed by 922
Abstract
This paper reports an analytical study conducted to investigate the behaviour of tracers undergoing creeping flow between two parallel plates in porous media. A new coupled model for the characterisation of fluid flow and transport of tracers at pore scale is formulated. Precisely, [...] Read more.
This paper reports an analytical study conducted to investigate the behaviour of tracers undergoing creeping flow between two parallel plates in porous media. A new coupled model for the characterisation of fluid flow and transport of tracers at pore scale is formulated. Precisely, a weak-form solution of radial transport of tracers under convection–diffusion-dominated flow is established using hypergeometric functions. The velocity field associated with the radial transport is informed by the solution of the Stokes equations. Channel thickness as a function of velocities, maximum Reynolds number of each thickness as a function of maximum velocities and concentration profile for different drift and dispersion coefficients are computed and analysed. Analysis of the simulation results reveals that the dispersion coefficient appears to be a significant factor controlling the concentration distribution of the tracer at pore scale. Further analysis shows that the drift coefficient appears to influence tracer concentration distribution but only after a prolonged period. This indicates that even at pore scale, tracer drift characteristics can provide useful information about the flow and transport properties of individual pores in porous media. Full article
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Article
Two-Dimensional Compact-Finite-Difference Schemes for Solving the bi-Laplacian Operator with Homogeneous Wall-Normal Derivatives
Mathematics 2021, 9(19), 2508; https://doi.org/10.3390/math9192508 - 07 Oct 2021
Viewed by 682
Abstract
In fluid mechanics, the bi-Laplacian operator with Neumann homogeneous boundary conditions emerges when transforming the Navier–Stokes equations to the vorticity–velocity formulation. In the case of problems with a periodic direction, the problem can be transformed into multiple, independent, two-dimensional fourth-order elliptic problems. An [...] Read more.
In fluid mechanics, the bi-Laplacian operator with Neumann homogeneous boundary conditions emerges when transforming the Navier–Stokes equations to the vorticity–velocity formulation. In the case of problems with a periodic direction, the problem can be transformed into multiple, independent, two-dimensional fourth-order elliptic problems. An efficient method to solve these two-dimensional bi-Laplacian operators with Neumann homogeneus boundary conditions was designed and validated using 2D compact finite difference schemes. The solution is formulated as a linear combination of auxiliary solutions, as many as the number of points on the boundary, a method that was prohibitive some years ago due to the large memory requirements to store all these auxiliary functions. The validation has been made for different field configurations, grid sizes, and stencils of the numerical scheme, showing its potential to tackle high gradient fields as those that can be found in turbulent flows. Full article
(This article belongs to the Special Issue Computational Mechanics in Engineering Mathematics)
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Article
Energy Based Calculation of the Second-Order Levitation in Magnetic Fluid
Mathematics 2021, 9(19), 2507; https://doi.org/10.3390/math9192507 - 07 Oct 2021
Viewed by 409
Abstract
A permanent magnet immersed in magnetic fluid experiences magnetic levitation force which is of the buoyant type. This phenomenon commonly refers to self-levitation or second-order buoyancy. The stable levitation height of the permanent magnet can be attained by numerical evaluation of the force. [...] Read more.
A permanent magnet immersed in magnetic fluid experiences magnetic levitation force which is of the buoyant type. This phenomenon commonly refers to self-levitation or second-order buoyancy. The stable levitation height of the permanent magnet can be attained by numerical evaluation of the force. Various authors have proposed different computational methods, but all of them rely on force formulation. This paper presents an alternative energy approach in the equilibrium height calculation, which was settled on the minimum energy principle. The problem, involving a cylindrical magnet suspended in a closed cylindrical container full of magnetic fluid, was considered in the study. The results accomplished by the proposed method were compared with those of the well-established surface integral method already verified by experiments. The difference in the results gained by both methods appears to be under 2.5%. Full article
(This article belongs to the Special Issue Numerical Model and Methods for Magnetic Fluids)
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Communication
Formulas, Algorithms and Examples for Binomial Distributed Data Confidence Interval Calculation: Excess Risk, Relative Risk and Odds Ratio
Mathematics 2021, 9(19), 2506; https://doi.org/10.3390/math9192506 - 07 Oct 2021
Cited by 2 | Viewed by 509
Abstract
Medical studies often involve a comparison between two outcomes, each collected from a sample. The probability associated with, and confidence in the result of the study is of most importance, since one may argue that having been wrong with a percent could be [...] Read more.
Medical studies often involve a comparison between two outcomes, each collected from a sample. The probability associated with, and confidence in the result of the study is of most importance, since one may argue that having been wrong with a percent could be what killed a patient. Sampling is usually done from a finite and discrete population and it follows a Bernoulli trial, leading to a contingency of two binomially distributed samples (better known as 2×2 contingency table). Current guidelines recommend reporting relative measures of association (such as the relative risk and odds ratio) in conjunction with absolute measures of association (which include risk difference or excess risk). Because the distribution is discrete, the evaluation of the exact confidence interval for either of those measures of association is a mathematical challenge. Some alternate scenarios were analyzed (continuous vs. discrete; hypergeometric vs. binomial), and in the main case—bivariate binomial experiment—a strategy for providing exact p-values and confidence intervals is proposed. Algorithms implementing the strategy are given. Full article
(This article belongs to the Special Issue Applied Medical Statistics: Theory, Computation, Applicability)
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Article
Pointwise k-Pseudo Metric Space
Mathematics 2021, 9(19), 2505; https://doi.org/10.3390/math9192505 - 06 Oct 2021
Cited by 1 | Viewed by 497
Abstract
In this paper, the concept of a k-(quasi) pseudo metric is generalized to the L-fuzzy case, called a pointwise k-(quasi) pseudo metric, which is considered to be a map [...] Read more.
In this paper, the concept of a k-(quasi) pseudo metric is generalized to the L-fuzzy case, called a pointwise k-(quasi) pseudo metric, which is considered to be a map d:J(LX)×J(LX)[0,) satisfying some conditions. What is more, it is proved that the category of pointwise k-pseudo metric spaces is isomorphic to the category of symmetric pointwise k-remote neighborhood ball spaces. Besides, some L-topological structures induced by a pointwise k-quasi-pseudo metric are obtained, including an L-quasi neighborhood system, an L-topology, an L-closure operator, an L-interior operator, and a pointwise quasi-uniformity. Full article
(This article belongs to the Special Issue Fuzzy Logic and Its Applications)
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Article
μ-Synthesis FO-PID for Twin Rotor Aerodynamic System
Mathematics 2021, 9(19), 2504; https://doi.org/10.3390/math9192504 - 06 Oct 2021
Cited by 1 | Viewed by 500
Abstract
μ-synthesis is a NP-hard optimization problem based on the generalized Robust Control framework which manages to find a controller which fulfills both robust stability and robust performance. In order to solve such problems, nonsmooth optimization techniques are employed to find nearly-optimal parameters [...] Read more.
μ-synthesis is a NP-hard optimization problem based on the generalized Robust Control framework which manages to find a controller which fulfills both robust stability and robust performance. In order to solve such problems, nonsmooth optimization techniques are employed to find nearly-optimal parameters values. However, the free parameters available for tuning must be involved only in classical arithmetic operations, which leads to a problem for the fractional-order operator or for its integer-order approximation, exponential operations being involved. The main goal of the current article consists of presenting a possibility to integrate a fixed-structure multiple-input-multiple-output (MIMO) fractional-order proportional-integral-derivative (FO-PID) controller in the μ-synthesis optimization problem. The solution consists in a possibility to find a set of tunable parameters isomorphic with the fractional-order such that the coefficients involved in the approximation of the fractional element, along with the formulation of a fixed-structure mixed-sensitivity loop shaping μ-synthesis control problem. The proposed design procedure is applied to a twin rotor aerodynamic system (TRAS) using both MATLAB numerical simulation and practical experiments on laboratory scale equipment. Moreover, a comparison with the unstructured μ-synthesis is performed, highlighting the advantages of the proposed solution: simpler form and guaranteed robust stability and performance. Full article
(This article belongs to the Special Issue Applications of Mathematical Models in Engineering)
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Article
Brownian Behavior in Coupled Chaotic Oscillators
Mathematics 2021, 9(19), 2503; https://doi.org/10.3390/math9192503 - 06 Oct 2021
Viewed by 493
Abstract
Since the dynamical behavior of chaotic and stochastic systems is very similar, it is sometimes difficult to determine the nature of the movement. One of the best-studied stochastic processes is Brownian motion, a random walk that accurately describes many phenomena that occur in [...] Read more.
Since the dynamical behavior of chaotic and stochastic systems is very similar, it is sometimes difficult to determine the nature of the movement. One of the best-studied stochastic processes is Brownian motion, a random walk that accurately describes many phenomena that occur in nature, including quantum mechanics. In this paper, we propose an approach that allows us to analyze chaotic dynamics using the Langevin equation describing dynamics of the phase difference between identical coupled chaotic oscillators. The time evolution of this phase difference can be explained by the biased Brownian motion, which is accepted in quantum mechanics for modeling thermal phenomena. Using a deterministic model based on chaotic Rössler oscillators, we are able to reproduce a similar time evolution for the phase difference. We show how the phenomenon of intermittent phase synchronization can be explained in terms of both stochastic and deterministic models. In addition, the existence of phase multistability in the phase synchronization regime is demonstrated. Full article
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Article
Definition Extraction from Generic and Mathematical Domains with Deep Ensemble Learning
Mathematics 2021, 9(19), 2502; https://doi.org/10.3390/math9192502 - 06 Oct 2021
Viewed by 532
Abstract
Definitions are extremely important for efficient learning of new materials. In particular, mathematical definitions are necessary for understanding mathematics-related areas. Automated extraction of definitions could be very useful for automated indexing educational materials, building taxonomies of relevant concepts, and more. For definitions that [...] Read more.
Definitions are extremely important for efficient learning of new materials. In particular, mathematical definitions are necessary for understanding mathematics-related areas. Automated extraction of definitions could be very useful for automated indexing educational materials, building taxonomies of relevant concepts, and more. For definitions that are contained within a single sentence, this problem can be viewed as a binary classification of sentences into definitions and non-definitions. In this paper, we focus on automatic detection of one-sentence definitions in mathematical and general texts. We experiment with different classification models arranged in an ensemble and applied to a sentence representation containing syntactic and semantic information, to classify sentences. Our ensemble model is applied to the data adjusted with oversampling. Our experiments demonstrate the superiority of our approach over state-of-the-art methods in both general and mathematical domains. Full article
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Article
On the Calculation of the Moore–Penrose and Drazin Inverses: Application to Fractional Calculus
Mathematics 2021, 9(19), 2501; https://doi.org/10.3390/math9192501 - 06 Oct 2021
Cited by 2 | Viewed by 468
Abstract
This paper presents a third order iterative method for obtaining the Moore–Penrose and Drazin inverses with a computational cost of O(n3), where nN. The performance of the new approach is compared with other methods discussed [...] Read more.
This paper presents a third order iterative method for obtaining the Moore–Penrose and Drazin inverses with a computational cost of O(n3), where nN. The performance of the new approach is compared with other methods discussed in the literature. The results show that the algorithm is remarkably efficient and accurate. Furthermore, sufficient criteria in the fractional sense are presented, both for smooth and non-smooth solutions. The fractional elliptic Poisson and fractional sub-diffusion equations in the Caputo sense are considered as prototype examples. The results can be extended to other scientific areas involving numerical linear algebra. Full article
(This article belongs to the Section Dynamical Systems)
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Article
Solving a University Course Timetabling Problem Based on AACSB Policies
Mathematics 2021, 9(19), 2500; https://doi.org/10.3390/math9192500 - 06 Oct 2021
Cited by 1 | Viewed by 516
Abstract
The purpose of this research is to solve the university course timetabling problem (UCTP) that consists of designing a schedule of the courses to be offered in one academic period based on students’ demand, faculty composition and institutional constraints considering the policies established [...] Read more.
The purpose of this research is to solve the university course timetabling problem (UCTP) that consists of designing a schedule of the courses to be offered in one academic period based on students’ demand, faculty composition and institutional constraints considering the policies established in the standards of the Association to Advance Collegiate Schools of Business (AACSB) accreditation. These standards involve faculty assignment with high level credentials that have to be fulfilled for business schools on the road to seek recognition and differentiation while providing exceptional learning. A new mathematical model for UCTP is proposed. The model allows the course-section-professor-time slot to be assigned for an academic department strategically using the faculty workload, course overload, and the fulfillment of the AACSB criteria. Further, the courses that will require new hires are classified according to the faculty qualifications stablished by AACSB. A real-world case is described and solved to show the efficiency of the proposed model. An analysis of different strategies derived from institutional policies that impacts the resulting timetabling is also presented. The results show the course overload could be a valuable strategy for helping mitigate the total of new hires needed. The proposed model allows to create the course at the same time the AACSB standards are met. Full article
(This article belongs to the Special Issue Mathematical Methods for Operations Research Problems)
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Article
Gender Classification Using Proposed CNN-Based Model and Ant Colony Optimization
Mathematics 2021, 9(19), 2499; https://doi.org/10.3390/math9192499 - 06 Oct 2021
Viewed by 728
Abstract
Pedestrian gender classification is one of the key assignments of pedestrian study, and it finds practical applications in content-based image retrieval, population statistics, human–computer interaction, health care, multimedia retrieval systems, demographic collection, and visual surveillance. In this research work, gender classification was carried [...] Read more.
Pedestrian gender classification is one of the key assignments of pedestrian study, and it finds practical applications in content-based image retrieval, population statistics, human–computer interaction, health care, multimedia retrieval systems, demographic collection, and visual surveillance. In this research work, gender classification was carried out using a deep learning approach. A new 64-layer architecture named 4-BSMAB derived from deep AlexNet is proposed. The proposed model was trained on CIFAR-100 dataset utilizing SoftMax classifier. Then, features were obtained from applied datasets with this pre-trained model. The obtained feature set was optimized with ant colony system (ACS) optimization technique. Various classifiers of SVM and KNN were used to perform gender classification utilizing the optimized feature set. Comprehensive experimentation was performed on gender classification datasets, and proposed model produced better results than the existing methods. The suggested model attained highest accuracy, i.e., 85.4%, and 92% AUC on MIT dataset, and best classification results, i.e., 93% accuracy and 96% AUC, on PKU-Reid dataset. The outcomes of extensive experiments carried out on existing standard pedestrian datasets demonstrate that the proposed framework outperformed existing pedestrian gender classification methods, and acceptable results prove the proposed model as a robust model. Full article
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