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Mathematics, Volume 9, Issue 22 (November-2 2021) – 153 articles

Cover Story (view full-size image): The problem of multicriteria optimization of a dynamic model is solved using the methods of similarity theory and criteria importance theory. The authors propose an original model of a positional system with two hydraulic actuators, synchronously moving a heavy object with a given accuracy. In order to reduce the number of optimizing parameters, the mathematical model of the system is presented in a dimensionless form. Three dimensionless optimization criteria that characterize the accuracy, size, and quality of the dynamic positioning process are considered. It is shown that the application of the criteria importance method significantly reduces the Pareto set (the set of the best solutions). This opens up the possibility of reducing many optimal solutions to one solution, which greatly facilitates the choice of parameters when designing a mechanical object. View this paper
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Article
Inverse Spectral Problems for Arbitrary-Order Differential Operators with Distribution Coefficients
Mathematics 2021, 9(22), 2989; https://0-doi-org.brum.beds.ac.uk/10.3390/math9222989 - 22 Nov 2021
Viewed by 393
Abstract
In this paper, we propose an approach to inverse spectral problems for the n-th order (n2) ordinary differential operators with distribution coefficients. The inverse problems which consist in the reconstruction of the differential expression coefficients by the Weyl [...] Read more.
In this paper, we propose an approach to inverse spectral problems for the n-th order (n2) ordinary differential operators with distribution coefficients. The inverse problems which consist in the reconstruction of the differential expression coefficients by the Weyl matrix and by several spectra are studied. We prove the uniqueness of solution for these inverse problems, by developing the method of spectral mappings. The results of this paper generalize the previously known results for the second-order differential operators with singular potentials and for the higher-order differential operators with regular coefficients. In the future, the approach of this paper can be used for constructive solution and for investigation of solvability of the considered inverse problems. Full article
(This article belongs to the Special Issue New Trends on Boundary Value Problems)
Article
Can Fake News Detection Models Maintain the Performance through Time? A Longitudinal Evaluation of Twitter Publications
Mathematics 2021, 9(22), 2988; https://0-doi-org.brum.beds.ac.uk/10.3390/math9222988 - 22 Nov 2021
Viewed by 504
Abstract
The negative impact of false information on social networks is rapidly growing. Current research on the topic focused on the detection of fake news in a particular context or event (such as elections) or using data from a short period of time. Therefore, [...] Read more.
The negative impact of false information on social networks is rapidly growing. Current research on the topic focused on the detection of fake news in a particular context or event (such as elections) or using data from a short period of time. Therefore, an evaluation of the current proposals in a long-term scenario where the topics discussed may change is lacking. In this work, we deviate from current approaches to the problem and instead focus on a longitudinal evaluation using social network publications spanning an 18-month period. We evaluate different combinations of features and supervised models in a long-term scenario where the training and testing data are ordered chronologically, and thus the robustness and stability of the models can be evaluated through time. We experimented with 3 different scenarios where the models are trained with 15-, 30-, and 60-day data periods. The results show that detection models trained with word-embedding features are the ones that perform better and are less likely to be affected by the change of topics (for example, the rise of COVID-19 conspiracy theories). Furthermore, the additional days of training data also increase the performance of the best feature/model combinations, although not very significantly (around 2%). The results presented in this paper build the foundations towards a more pragmatic approach to the evaluation of fake news detection models in social networks. Full article
(This article belongs to the Special Issue Analytics and Big Data)
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Article
Graph, Spectra, Control and Epidemics: An Example with a SEIR Model
Mathematics 2021, 9(22), 2987; https://0-doi-org.brum.beds.ac.uk/10.3390/math9222987 - 22 Nov 2021
Viewed by 463
Abstract
Networks and graphs offer a suitable and powerful framework for studying the spread of infection in human and animal populations. In the case of a heterogeneous population, the social contact network has a pivotal role in the analysis of directly transmitted infectious diseases. [...] Read more.
Networks and graphs offer a suitable and powerful framework for studying the spread of infection in human and animal populations. In the case of a heterogeneous population, the social contact network has a pivotal role in the analysis of directly transmitted infectious diseases. The literature presents several works where network-based models encompass realistic features (such as contacts networks or host–pathogen biological data), but analytical results are nonetheless scarce. As a significant example, in this paper, we develop a multi-group version of the epidemiological SEIR population-based model. Each group can represent a social subpopulation with the same habits or a group of geographically localized people. We consider also heterogeneity in the weighting of contacts between two groups. As a simple application, we propose a simple control algorithm in which we optimize the connection weights in order to minimize the combination between an economic cost and a social cost. Some numerical simulations are also provided. Full article
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Article
Supercyclic and Hypercyclic Generalized Weighted Backward Shifts over a Non-Archimedean c0(N) Space
Mathematics 2021, 9(22), 2986; https://0-doi-org.brum.beds.ac.uk/10.3390/math9222986 - 22 Nov 2021
Viewed by 347
Abstract
In the present paper, we propose to study generalized weighted backward shifts BB over non-Archimedean c0(N) spaces; here, B=(bij) is an upper triangular matrix with [...] Read more.
In the present paper, we propose to study generalized weighted backward shifts BB over non-Archimedean c0(N) spaces; here, B=(bij) is an upper triangular matrix with supi,j|bij|<. We investigate the sypercyclic and hypercyclic properties of BB. Furthermore, certain properties of the operator I+BB are studied as well. To establish the hypercyclic property of I+BB we have essentially used the non-Archimedeanity of the norm which leads to the difference between the real case. Full article
(This article belongs to the Topic Dynamical Systems: Theory and Applications)
Article
Strong Maximum Principle for Viscosity Solutions of Fully Nonlinear Cooperative Elliptic Systems
Mathematics 2021, 9(22), 2985; https://0-doi-org.brum.beds.ac.uk/10.3390/math9222985 - 22 Nov 2021
Viewed by 241
Abstract
In this paper, we consider the validity of the strong maximum principle for weakly coupled, degenerate and cooperative elliptic systems in a bounded domain. In particular, we are interested in the viscosity solutions of elliptic systems with fully nonlinear degenerated principal symbol. Applying [...] Read more.
In this paper, we consider the validity of the strong maximum principle for weakly coupled, degenerate and cooperative elliptic systems in a bounded domain. In particular, we are interested in the viscosity solutions of elliptic systems with fully nonlinear degenerated principal symbol. Applying the method of viscosity solutions, introduced by Crandall, Ishii and Lions in 1992, we prove the validity of strong interior and boundary maximum principle for semi-continuous viscosity sub- and super-solutions of such nonlinear systems. For the first time in the literature, the strong maximum principle is considered for viscosity solutions to nonlinear elliptic systems. As a consequence of the strong interior maximum principle, we derive comparison principle for viscosity sub- and super-solutions in case when on of them is a classical one. The main novelty of this work is the reduction of the smoothness of the solution. In the literature the strong maximum principle is proved for classical C2 or generalized C1 solutions, while we prove it for semi-continuous ones. Full article
Article
Ensemble of Deep Learning-Based Multimodal Remote Sensing Image Classification Model on Unmanned Aerial Vehicle Networks
Mathematics 2021, 9(22), 2984; https://0-doi-org.brum.beds.ac.uk/10.3390/math9222984 - 22 Nov 2021
Viewed by 436
Abstract
Recently, unmanned aerial vehicles (UAVs) have been used in several applications of environmental modeling and land use inventories. At the same time, the computer vision-based remote sensing image classification models are needed to monitor the modifications over time such as vegetation, inland water, [...] Read more.
Recently, unmanned aerial vehicles (UAVs) have been used in several applications of environmental modeling and land use inventories. At the same time, the computer vision-based remote sensing image classification models are needed to monitor the modifications over time such as vegetation, inland water, bare soil or human infrastructure regardless of spectral, spatial, temporal, and radiometric resolutions. In this aspect, this paper proposes an ensemble of DL-based multimodal land cover classification (EDL-MMLCC) models using remote sensing images. The EDL-MMLCC technique aims to classify remote sensing images into the different cloud, shades, and land cover classes. Primarily, median filtering-based preprocessing and data augmentation techniques take place. In addition, an ensemble of DL models, namely VGG-19, Capsule Network (CapsNet), and MobileNet, is used for feature extraction. In addition, the training process of the DL models can be enhanced by the use of hosted cuckoo optimization (HCO) algorithm. Finally, the salp swarm algorithm (SSA) with regularized extreme learning machine (RELM) classifier is applied for land cover classification. The design of the HCO algorithm for hyperparameter optimization and SSA for parameter tuning of the RELM model helps to increase the classification outcome to a maximum level considerably. The proposed EDL-MMLCC technique is tested using an Amazon dataset from the Kaggle repository. The experimental results pointed out the promising performance of the EDL-MMLCC technique over the recent state of art approaches. Full article
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Article
Efficient or Fractal Market Hypothesis? A Stock Indexes Modelling Using Geometric Brownian Motion and Geometric Fractional Brownian Motion
Mathematics 2021, 9(22), 2983; https://0-doi-org.brum.beds.ac.uk/10.3390/math9222983 - 22 Nov 2021
Viewed by 352
Abstract
In this article, we propose a test of the dynamics of stock market indexes typical of the US and EU capital markets in order to determine which of the two fundamental hypotheses, efficient market hypothesis (EMH) or fractal market hypothesis (FMH), best describes [...] Read more.
In this article, we propose a test of the dynamics of stock market indexes typical of the US and EU capital markets in order to determine which of the two fundamental hypotheses, efficient market hypothesis (EMH) or fractal market hypothesis (FMH), best describes market behavior. The article’s major goal is to show how to appropriately model return distributions for financial market indexes, specifically which geometric Brownian motion (GBM) and geometric fractional Brownian motion (GFBM) dynamic equations best define the evolution of the S&P 500 and Stoxx Europe 600 stock indexes. Daily stock index data were acquired from the Thomson Reuters Eikon database during a ten-year period, from January 2011 to December 2020. The main contribution of this work is determining whether these markets are efficient (as defined by the EMH), in which case the appropriate stock indexes dynamic equation is the GBM, or fractal (as described by the FMH), in which case the appropriate stock indexes dynamic equation is the GFBM. In this paper, we consider two methods for calculating the Hurst exponent: the rescaled range method (RS) and the periodogram method (PE). To determine which of the dynamics (GBM, GFBM) is more appropriate, we employed the mean absolute percentage error (MAPE) method. The simulation results demonstrate that the GFBM is better suited for forecasting stock market indexes than the GBM when the analyzed markets display fractality. However, while these findings cannot be generalized, they are verisimilar. Full article
(This article belongs to the Special Issue Advanced Methods in the Mathematical Modeling of Financial Markets)
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Article
A Novel Hybrid Approach: Instance Weighted Hidden Naive Bayes
Mathematics 2021, 9(22), 2982; https://0-doi-org.brum.beds.ac.uk/10.3390/math9222982 - 22 Nov 2021
Viewed by 329
Abstract
Naive Bayes (NB) is easy to construct but surprisingly effective, and it is one of the top ten classification algorithms in data mining. The conditional independence assumption of NB ignores the dependency between attributes, so its probability estimates are often suboptimal. Hidden naive [...] Read more.
Naive Bayes (NB) is easy to construct but surprisingly effective, and it is one of the top ten classification algorithms in data mining. The conditional independence assumption of NB ignores the dependency between attributes, so its probability estimates are often suboptimal. Hidden naive Bayes (HNB) adds a hidden parent to each attribute, which can reflect dependencies from all the other attributes. Compared with other Bayesian network algorithms, it offers significant improvements in classification performance and avoids structure learning. However, the assumption that HNB regards each instance equivalent in terms of probability estimation is not always true in real-world applications. In order to reflect different influences of different instances in HNB, the HNB model is modified into the improved HNB model. The novel hybrid approach called instance weighted hidden naive Bayes (IWHNB) is proposed in this paper. IWHNB combines instance weighting with the improved HNB model into one uniform framework. Instance weights are incorporated into the improved HNB model to calculate probability estimates in IWHNB. Extensive experimental results show that IWHNB obtains significant improvements in classification performance compared with NB, HNB and other state-of-the-art competitors. Meanwhile, IWHNB maintains the low time complexity that characterizes HNB. Full article
(This article belongs to the Special Issue Machine Learning and Data Mining: Techniques and Tasks)
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Article
A Global Optimization Algorithm for Solving Linearly Constrained Quadratic Fractional Problems
Mathematics 2021, 9(22), 2981; https://0-doi-org.brum.beds.ac.uk/10.3390/math9222981 - 22 Nov 2021
Viewed by 337
Abstract
This paper first proposes a new and enhanced second order cone programming relaxation using the simultaneous matrix diagonalization technique for the linearly constrained quadratic fractional programming problem. The problem has wide applications in statics, economics and signal processing. Thus, fast and effective algorithm [...] Read more.
This paper first proposes a new and enhanced second order cone programming relaxation using the simultaneous matrix diagonalization technique for the linearly constrained quadratic fractional programming problem. The problem has wide applications in statics, economics and signal processing. Thus, fast and effective algorithm is required. The enhanced second order cone programming relaxation improves the relaxation effect and computational efficiency compared to the classical second order cone programming relaxation. Moreover, although the bound quality of the enhanced second order cone programming relaxation is worse than that of the copositive relaxation, the computational efficiency is significantly enhanced. Then we present a global algorithm based on the branch and bound framework. Extensive numerical experiments show that the enhanced second order cone programming relaxation-based branch and bound algorithm globally solves the problem in less computing time than the copositive relaxation approach. Full article
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Article
Semi-Hyers–Ulam–Rassias Stability of the Convection Partial Differential Equation via Laplace Transform
Mathematics 2021, 9(22), 2980; https://0-doi-org.brum.beds.ac.uk/10.3390/math9222980 - 22 Nov 2021
Cited by 1 | Viewed by 235
Abstract
In this paper, we study the semi-Hyers–Ulam–Rassias stability and the generalized semi-Hyers–Ulam–Rassias stability of some partial differential equations using Laplace transform. One of them is the convection partial differential equation. Full article
(This article belongs to the Special Issue Recent Advances in Differential Equations and Applications)
Article
Optimality Conditions and Duality for a Class of Generalized Convex Interval-Valued Optimization Problems
Mathematics 2021, 9(22), 2979; https://0-doi-org.brum.beds.ac.uk/10.3390/math9222979 - 22 Nov 2021
Cited by 1 | Viewed by 305
Abstract
This paper is devoted to derive optimality conditions and duality theorems for interval-valued optimization problems based on gH-symmetrically derivative. Further, the concepts of symmetric pseudo-convexity and symmetric quasi-convexity for interval-valued functions are proposed to extend above optimization conditions. Examples are also presented to [...] Read more.
This paper is devoted to derive optimality conditions and duality theorems for interval-valued optimization problems based on gH-symmetrically derivative. Further, the concepts of symmetric pseudo-convexity and symmetric quasi-convexity for interval-valued functions are proposed to extend above optimization conditions. Examples are also presented to illustrate corresponding results. Full article
(This article belongs to the Special Issue Variational Problems and Applications)
Article
The Hankel Determinants from a Singularly Perturbed Jacobi Weight
Mathematics 2021, 9(22), 2978; https://0-doi-org.brum.beds.ac.uk/10.3390/math9222978 - 22 Nov 2021
Viewed by 262
Abstract
We study the Hankel determinant generated by a singularly perturbed Jacobi weight [...] Read more.
We study the Hankel determinant generated by a singularly perturbed Jacobi weight w(x,s):=(1x)α(1+x)βes1x,x[1,1],α>0,β>0s0. If s=0, it is reduced to the classical Jacobi weight. For s>0, the factor es1x induces an infinitely strong zero at x=1. For the finite n case, we obtain four auxiliary quantities Rn(s), rn(s), R˜n(s), and r˜n(s) by using the ladder operator approach. We show that the recurrence coefficients are expressed in terms of the four auxiliary quantities with the aid of the compatibility conditions. Furthermore, we derive a shifted Jimbo–Miwa–Okamoto σ-function of a particular Painlevé V for the logarithmic derivative of the Hankel determinant Dn(s). By variable substitution and some complicated calculations, we show that the quantity Rn(s) satisfies the four Painlevé equations. For the large n case, we show that, under a double scaling, where n tends to and s tends to 0+, such that τ:=n2s is finite, the scaled Hankel determinant can be expressed by a particular PIII. Full article
Article
Calderón Operator on Local Morrey Spaces with Variable Exponents
Mathematics 2021, 9(22), 2977; https://0-doi-org.brum.beds.ac.uk/10.3390/math9222977 - 22 Nov 2021
Viewed by 288
Abstract
In this paper, we establish the boundedness of the Calderón operator on local Morrey spaces with variable exponents. We obtain our result by extending the extrapolation theory of Rubio de Francia to the local Morrey spaces with variable exponents. The exponent functions of [...] Read more.
In this paper, we establish the boundedness of the Calderón operator on local Morrey spaces with variable exponents. We obtain our result by extending the extrapolation theory of Rubio de Francia to the local Morrey spaces with variable exponents. The exponent functions of the local Morrey spaces with the exponent functions are only required to satisfy the log-Hölder continuity assumption at the origin and infinity only. As special cases of the main result, we have Hardy’s inequalities, the Hilbert inequalities and the boundedness of the Riemann–Liouville and Weyl averaging operators on local Morrey spaces with variable exponents. Full article
(This article belongs to the Special Issue Recent Developments of Function Spaces and Their Applications I)
Article
Multimodal Identification Based on Fingerprint and Face Images via a Hetero-Associative Memory Method
Mathematics 2021, 9(22), 2976; https://0-doi-org.brum.beds.ac.uk/10.3390/math9222976 - 22 Nov 2021
Viewed by 239
Abstract
Multimodal identification, which exploits biometric information from more than one biometric modality, is more secure and reliable than unimodal identification. Face recognition and fingerprint recognition have received a lot of attention in recent years for their unique advantages. However, how to integrate these [...] Read more.
Multimodal identification, which exploits biometric information from more than one biometric modality, is more secure and reliable than unimodal identification. Face recognition and fingerprint recognition have received a lot of attention in recent years for their unique advantages. However, how to integrate these two modalities and develop an effective multimodal identification system are still challenging problems. Hetero-associative memory (HAM) models store some patterns that can be reliably retrieved from other patterns in a robust way. Therefore, in this paper, face and fingerprint biometric features are integrated by the use of a hetero-associative memory method for multimodal identification. The proposed multimodal identification system can integrate face and fingerprint biometric features at feature level when the system converges to the state of asymptotic stability. In experiment 1, the predicted fingerprint by inputting an authorized user’s face is compared with the real fingerprint, and the matching rate of each group is higher than the given threshold. In experiment 2 and experiment 3, the predicted fingerprint by inputting the face of an unauthorized user and the stealing authorized user’s face is compared with its real fingerprint input, respectively, and the matching rate of each group is lower than the given threshold. The experimental results prove the feasibility of the proposed multimodal identification system. Full article
(This article belongs to the Special Issue Modeling and Analysis of Complex Networks)
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Article
Professional Development in Mathematics Education—Evaluation of a MOOC on Outdoor Mathematics
Mathematics 2021, 9(22), 2975; https://0-doi-org.brum.beds.ac.uk/10.3390/math9222975 - 22 Nov 2021
Viewed by 335
Abstract
In this paper, we examine the impact of a massive open online course (MOOC) in the context of outdoor mathematics on the participating teachers’ professional development. We firstly introduce the theoretical background on outdoor mathematics, focusing on math trails with the digital tool [...] Read more.
In this paper, we examine the impact of a massive open online course (MOOC) in the context of outdoor mathematics on the participating teachers’ professional development. We firstly introduce the theoretical background on outdoor mathematics, focusing on math trails with the digital tool MathCityMap and professional development to be accomplished using MOOCs. By taking into account the MOOC “Task Design for Math Trails”, with 93 finalists, we analyze the learning progress of 19 selected case studies from different nations and learning levels by taking into account their answers in a pre- and post-questionnaire and their posts on a specific communication message board, with a special focus on the MOOC’s topics’ task design for outdoor mathematics and the digital tool MathCityMap. The analysis is performed using different quantitative and qualitative approaches. The results show that the teachers studied have benefited from professional development, which is evident in the expansion/evolution of their knowledge from a content, pedagogical, and technological perspective. Finally, we formulate consequences for professional development in STEM education, and conclude the paper with limitations to be drawn and a perspective for further research. Full article
(This article belongs to the Special Issue STEAM Teacher Education: Problems and Proposals)
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Article
Automatic Image Characterization of Psoriasis Lesions
Mathematics 2021, 9(22), 2974; https://0-doi-org.brum.beds.ac.uk/10.3390/math9222974 - 22 Nov 2021
Viewed by 369
Abstract
Psoriasis is a chronic skin disease that affects 125 million people worldwide and, particularly, 2% of the Spanish population, characterized by the appearance of skin lesions due to a growth of the epidermis that is seven times larger than usual. Its diagnosis and [...] Read more.
Psoriasis is a chronic skin disease that affects 125 million people worldwide and, particularly, 2% of the Spanish population, characterized by the appearance of skin lesions due to a growth of the epidermis that is seven times larger than usual. Its diagnosis and monitoring are based on the use of methodologies for measuring the severity and extent of these spots, and this includes a large subjective component. For this reason, this paper presents an automatic method for characterizing psoriasis images that is divided into four parts: image preparation or pre-processing, feature extraction, classification of the lesions, and the obtaining of parameters. The methodology proposed in this work covers different digital-image processing techniques, namely, marker-based image delimitation, hair removal, nipple detection, lesion contour detection, areal-measurement-based lesion classification, as well as lesion characterization by means of red and white intensity. The results obtained were also endorsed by a professional dermatologist. This methodology provides professionals with a common software tool for monitoring the different existing typologies, which proved satisfactory in the cases analyzed for a set of 20 images corresponding to different types of lesions. Full article
(This article belongs to the Special Issue Mathematical Approaches to Image Processing with Applications)
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Article
Using PLS-SEM to Analyze the Effect of CSR on Corporate Performance: The Mediating Role of Human Resources Management and Customer Satisfaction. An Empirical Study in the Spanish Food and Beverage Manufacturing Sector
Mathematics 2021, 9(22), 2973; https://0-doi-org.brum.beds.ac.uk/10.3390/math9222973 - 21 Nov 2021
Viewed by 583
Abstract
Although in recent decades corporate social responsibility (CSR) has been subjected to numerous studies in management and marketing literature about its impact on business results, the mechanism by which it affects performance has not been established. There is a lack of consensus when [...] Read more.
Although in recent decades corporate social responsibility (CSR) has been subjected to numerous studies in management and marketing literature about its impact on business results, the mechanism by which it affects performance has not been established. There is a lack of consensus when it comes to explaining how CSR actions are related to firm performance. Our research helps to understand this relationship through mediating effects such as CSR-oriented human resource management and customer satisfaction because employees and customers are critical stakeholders of companies and contribute directly to the determination of the corporate results. Through a study on a sample of small and medium-sized Spanish food and beverage manufacturing companies, and by using partial least squares structural equation modelling (PLS-SEM), we found that CSR does indeed impact business performance when CSR actions are mainly oriented towards more efficient management of human resources and customer satisfaction. In this way, the results lead us to conclude that depending on the stakeholder to which these actions are oriented, a specific orientation of the company’s CSR policy can be more efficient in corporate performance. Full article
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Article
Staggered Semi-Implicit Hybrid Finite Volume/Finite Element Schemes for Turbulent and Non-Newtonian Flows
Mathematics 2021, 9(22), 2972; https://doi.org/10.3390/math9222972 - 21 Nov 2021
Cited by 1 | Viewed by 371
Abstract
This paper presents a new family of semi-implicit hybrid finite volume/finite element schemes on edge-based staggered meshes for the numerical solution of the incompressible Reynolds-Averaged Navier–Stokes (RANS) equations in combination with the kε turbulence model. The rheology for calculating the laminar [...] Read more.
This paper presents a new family of semi-implicit hybrid finite volume/finite element schemes on edge-based staggered meshes for the numerical solution of the incompressible Reynolds-Averaged Navier–Stokes (RANS) equations in combination with the kε turbulence model. The rheology for calculating the laminar viscosity coefficient under consideration in this work is the one of a non-Newtonian Herschel–Bulkley (power-law) fluid with yield stress, which includes the Bingham fluid and classical Newtonian fluids as special cases. For the spatial discretization, we use edge-based staggered unstructured simplex meshes, as well as staggered non-uniform Cartesian grids. In order to get a simple and computationally efficient algorithm, we apply an operator splitting technique, where the hyperbolic convective terms of the RANS equations are discretized explicitly at the aid of a Godunov-type finite volume scheme, while the viscous parabolic terms, the elliptic pressure terms and the stiff algebraic source terms of the kε model are discretized implicitly. For the discretization of the elliptic pressure Poisson equation, we use classical conforming P1 and Q1 finite elements on triangles and rectangles, respectively. The implicit discretization of the viscous terms is mandatory for non-Newtonian fluids, since the apparent viscosity can tend to infinity for fluids with yield stress and certain power-law fluids. It is carried out with P1 finite elements on triangular simplex meshes and with finite volumes on rectangles. For Cartesian grids and more general orthogonal unstructured meshes, we can prove that our new scheme can preserve the positivity of k and ε. This is achieved via a special implicit discretization of the stiff algebraic relaxation source terms, using a suitable combination of the discrete evolution equations for the logarithms of k and ε. The method is applied to some classical academic benchmark problems for non-Newtonian and turbulent flows in two space dimensions, comparing the obtained numerical results with available exact or numerical reference solutions. In all cases, an excellent agreement is observed. Full article
(This article belongs to the Special Issue Computational Methods in Nonlinear Analysis and Their Applications)
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Article
Parameter Identification of Optimized Fractional Maximum Power Point Tracking for Thermoelectric Generation Systems Using Manta Ray Foraging Optimization
Mathematics 2021, 9(22), 2971; https://0-doi-org.brum.beds.ac.uk/10.3390/math9222971 - 21 Nov 2021
Viewed by 372
Abstract
Thermoelectric generation systems (TEGSs) are used to convert temperature difference and heat flow into DC power based on the Seebeck theorem. The basic unit of TEGS is the thermoelectric module (TEM). TEGSs have gained increasing interest in the research fields of sustainable energy. [...] Read more.
Thermoelectric generation systems (TEGSs) are used to convert temperature difference and heat flow into DC power based on the Seebeck theorem. The basic unit of TEGS is the thermoelectric module (TEM). TEGSs have gained increasing interest in the research fields of sustainable energy. The output power from TEM is mostly reliant on differential temperature between the hot and cold sides of the TEM added to the value of the load. As such, a robust MPPT strategy (MPPTS) is required to ensure that the TEGS is operating near to the MPP while varying the operating conditions. Two main drawbacks may occur in the conventional MPPTSs: low dynamic response, such as in the incremental resistance (INR) method, and oscillations around MPP at steady state, such as in the hill climbing (HC) method. In the current research work, an optimized fractional MPPTS is developed to improve the tracking performance of the TEGS, and remove the two drawbacks of the conventional MPPTSs. The proposed strategy is based on fractional order control (FOC). The main advantage of FOC is that it offers extra flexible time and frequency responses of the control system consent for better and robust performance. The optimal parameters of the optimized fractional MPPTS are identified by a manta ray foraging optimization (MRFO). To verify the robustness of the MRFO, the obtained results are compared with ten other algorithms: particle swarm optimization; whale optimization algorithm; Harris hawks optimization; heap-based optimizer; gradient-based optimizer; grey wolf optimizer; slime mould algorithm; genetic algorithm; seagull optimization algorithm (SOA); and tunicate swarm algorithm. The maximum average cost function of 4.92934 kWh has been achieved by MRFO, followed by SOA (4.5721 kWh). The lowest STD of 0.04867 was also accomplished by MRFO. The maximum efficiency of 99.46% has been obtained by MRFO, whereas the lowest efficiency of 74.01% was obtained by GA. Finally, the main findings proved the superiority of optimized fractional MPPTS compared with conventional methods for both steady-state and dynamic responses. Full article
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Review
Machine Learning (ML) in Medicine: Review, Applications, and Challenges
Mathematics 2021, 9(22), 2970; https://0-doi-org.brum.beds.ac.uk/10.3390/math9222970 - 21 Nov 2021
Viewed by 394
Abstract
Today, artificial intelligence (AI) and machine learning (ML) have dramatically advanced in various industries, especially medicine. AI describes computational programs that mimic and simulate human intelligence, for example, a person’s behavior in solving problems or his ability for learning. Furthermore, ML is a [...] Read more.
Today, artificial intelligence (AI) and machine learning (ML) have dramatically advanced in various industries, especially medicine. AI describes computational programs that mimic and simulate human intelligence, for example, a person’s behavior in solving problems or his ability for learning. Furthermore, ML is a subset of artificial intelligence. It extracts patterns from raw data automatically. The purpose of this paper is to help researchers gain a proper understanding of machine learning and its applications in healthcare. In this paper, we first present a classification of machine learning-based schemes in healthcare. According to our proposed taxonomy, machine learning-based schemes in healthcare are categorized based on data pre-processing methods (data cleaning methods, data reduction methods), learning methods (unsupervised learning, supervised learning, semi-supervised learning, and reinforcement learning), evaluation methods (simulation-based evaluation and practical implementation-based evaluation in real environment) and applications (diagnosis, treatment). According to our proposed classification, we review some studies presented in machine learning applications for healthcare. We believe that this review paper helps researchers to familiarize themselves with the newest research on ML applications in medicine, recognize their challenges and limitations in this area, and identify future research directions. Full article
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Article
Numerical Investigation of the Heat Transfer Characteristics of R290 Flow Boiling in Corrugated Tubes with Different Internal Corrugated Structures
Mathematics 2021, 9(22), 2969; https://0-doi-org.brum.beds.ac.uk/10.3390/math9222969 - 21 Nov 2021
Viewed by 376
Abstract
The heat transfer and pressure drop characteristics of R290 flow boiling in a corrugated tube were investigated through computational fluid dynamics (CFD) in this study. We established a model of flow boiling in a corrugated tube with different corrugated structures (rectangular and circular [...] Read more.
The heat transfer and pressure drop characteristics of R290 flow boiling in a corrugated tube were investigated through computational fluid dynamics (CFD) in this study. We established a model of flow boiling in a corrugated tube with different corrugated structures (rectangular and circular corrugations) and validated the model using the Liu–Winterton and Xu–Fang empirical equations. The heat transfer coefficient (HTC) and pressure drop were obtained at a mass flow rate of 0.04–0.2 kg/s and a water inlet temperature of 310–330 K. The results show that the HTC and the drop in the pressure of the corrugated tubes both obviously increased compared with a smooth tube as the mass flow rate increased. The HTC decreased for the three tubes as the water inlet temperature increased, while the drop in pressure slightly increased for the three tubes. Moreover, the corrugated structure was found to significantly enhance the heat transfer; the heat transfer enhancement factor (E1) of the corrugated tube with the rectangular corrugations and the corrugated tube with the circular corrugations was 2.01–2.36 and 1.67–1.98, respectively. The efficiency index (I) for both the rectangular corrugated pipe and the circular corrugated pipe was greater than 1 (1.05–1.24 and 1.13–1.29, respectively). The application of corrugated tubes with round and rectangular corrugations can reduce the heat transfer area required for the exchange of heat and, thus, reduce the cost. Full article
(This article belongs to the Special Issue Modeling and Numerical Analysis of Energy and Environment 2021)
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Article
Observer-Based Control for Nonlinear Time-Delayed Asynchronously Switching Systems: A New LMI Approach
Mathematics 2021, 9(22), 2968; https://0-doi-org.brum.beds.ac.uk/10.3390/math9222968 - 21 Nov 2021
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Abstract
This paper designs an observer-based controller for switched systems (SSs) with nonlinear dynamics, exogenous disturbances, parametric uncertainties, and time-delay. Based on the multiple Lyapunov–Krasovskii and average dwell time (DT) approaches, some conditions are presented to ensure the robustness and investigate the effect of [...] Read more.
This paper designs an observer-based controller for switched systems (SSs) with nonlinear dynamics, exogenous disturbances, parametric uncertainties, and time-delay. Based on the multiple Lyapunov–Krasovskii and average dwell time (DT) approaches, some conditions are presented to ensure the robustness and investigate the effect of time-delay, uncertainties, and lag issues between switching times. The control parameters are determined through solving the established linear matrix inequalities (LMIs) under asynchronous switching. A novel LMI-based conditions are suggested to guarantee the H performance. Finally, the accuracy of the designed observer-based controller is examined by simulations on practical case-study plants. Full article
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Article
Inviscid Modes within the Boundary-Layer Flow of a Rotating Disk with Wall Suction and in an External Free-Stream
Mathematics 2021, 9(22), 2967; https://0-doi-org.brum.beds.ac.uk/10.3390/math9222967 - 21 Nov 2021
Viewed by 361
Abstract
The purpose of this paper is to investigate the linear stability analysis for the laminar-turbulent transition region of the high-Reynolds-number instabilities for the boundary layer flow on a rotating disk. This investigation considers axial flow along the surface-normal direction, by studying analytical expressions [...] Read more.
The purpose of this paper is to investigate the linear stability analysis for the laminar-turbulent transition region of the high-Reynolds-number instabilities for the boundary layer flow on a rotating disk. This investigation considers axial flow along the surface-normal direction, by studying analytical expressions for the steady solution, laminar, incompressible and inviscid fluid of the boundary layer flow due to a rotating disk in the presence of a uniform injection and suction. Essentially, the physical problem represents flow entrainment into the boundary layer from the axial flow, which is transferred by the spinning disk surface into flow in the azimuthal and radial directions. In addition, through the formation of spiral vortices, the boundary layer instability is visualised which develops along the surface in spiral nature. To this end, this study illustrates that combining axial flow and suction together may act to stabilize the boundary layer flow for inviscid modes. Full article
(This article belongs to the Special Issue Asymptotics for Differential Equations)
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Article
Parallel Algorithms for Solving Inverse Gravimetry Problems: Application for Earth’s Crust Density Models Creation
Mathematics 2021, 9(22), 2966; https://0-doi-org.brum.beds.ac.uk/10.3390/math9222966 - 20 Nov 2021
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Abstract
The paper describes a method of gravity data inversion, which is based on parallel algorithms. The choice of the density model of the initial approximation and the set on which the solution is sought guarantees the stability of the algorithms. We offer a [...] Read more.
The paper describes a method of gravity data inversion, which is based on parallel algorithms. The choice of the density model of the initial approximation and the set on which the solution is sought guarantees the stability of the algorithms. We offer a new upward and downward continuation algorithm for separating the effects of shallow and deep sources. Using separated field of layers, the density distribution is restored in a form of 3D grid. We use the iterative parallel algorithms for the downward continuation and restoration of the density values (by solving the inverse linear gravity problem). The algorithms are based on the ideas of local minimization; they do not require a nonlinear minimization; they are easier to implement and have better stability. We also suggest an optimization of the gravity field calculation, which speeds up the inversion. A practical example of interpretation is presented for the gravity data of the Urals region, Russia. Full article
(This article belongs to the Special Issue Numerical Analysis and Scientific Computing)
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Article
Rockburst Interpretation by a Data-Driven Approach: A Comparative Study
Mathematics 2021, 9(22), 2965; https://0-doi-org.brum.beds.ac.uk/10.3390/math9222965 - 20 Nov 2021
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Abstract
Accurately evaluating rockburst intensity has attracted much attention in these recent years, as it can guide the design of engineering in deep underground conditions and avoid injury to people. In this study, a new ensemble classifier combining a random forest classifier (RF) and [...] Read more.
Accurately evaluating rockburst intensity has attracted much attention in these recent years, as it can guide the design of engineering in deep underground conditions and avoid injury to people. In this study, a new ensemble classifier combining a random forest classifier (RF) and beetle antennae search algorithm (BAS) has been designed and applied to improve the accuracy of rockburst classification. A large dataset was collected from across the world to achieve a comprehensive representation, in which five key influencing factors were selected as the input variables, and the rockburst intensity was selected as the output. The proposed model BAS-RF was then validated by the dataset. The results show that BAS could tune the hyperparameters of RF efficiently, and the optimum model exhibited a high performance on an independent test set of rockburst data and new engineering projects. According to the ensemble RF-BAS model, the feature importance was calculated. Furthermore, the accuracy of the proposed model on rockburst prediction was higher than the conventional machine learning models and empirical models, which means that the proposed model is efficient and accurate. Full article
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Article
Novel Fractional Dynamic Hardy–Hilbert-Type Inequalities on Time Scales with Applications
Mathematics 2021, 9(22), 2964; https://0-doi-org.brum.beds.ac.uk/10.3390/math9222964 - 20 Nov 2021
Viewed by 308
Abstract
The main objective of the present article is to prove some new ∇ dynamic inequalities of Hardy–Hilbert type on time scales. We present and prove very important generalized results with the help of Fenchel–Legendre transform, submultiplicative functions. We prove the [...] Read more.
The main objective of the present article is to prove some new ∇ dynamic inequalities of Hardy–Hilbert type on time scales. We present and prove very important generalized results with the help of Fenchel–Legendre transform, submultiplicative functions. We prove the (γ,a)-nabla conformable Hölder’s and Jensen’s inequality on time scales. We prove several inequalities due to Hardy–Hilbert inequalities on time scales. Furthermore, we introduce the continuous inequalities and discrete inequalities as special case. Full article
(This article belongs to the Topic Dynamical Systems: Theory and Applications)
Article
Overview in Summabilities: Summation Methods for Divergent Series, Ramanujan Summation and Fractional Finite Sums
Mathematics 2021, 9(22), 2963; https://0-doi-org.brum.beds.ac.uk/10.3390/math9222963 - 20 Nov 2021
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Abstract
This work presents an overview of the summability of divergent series and fractional finite sums, including their connections. Several summation methods listed, including the smoothed sum, permit obtaining an algebraic constant related to a divergent series. The first goal is to revisit the [...] Read more.
This work presents an overview of the summability of divergent series and fractional finite sums, including their connections. Several summation methods listed, including the smoothed sum, permit obtaining an algebraic constant related to a divergent series. The first goal is to revisit the discussion about the existence of an algebraic constant related to a divergent series, which does not contradict the divergence of the series in the classical sense. The well-known Euler–Maclaurin summation formula is presented as an important tool. Throughout a systematic discussion, we seek to promote the Ramanujan summation method for divergent series and the methods recently developed for fractional finite sums. Full article
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Article
On the State Approach Representations of Convolutional Codes over Rings of Modular Integers
Mathematics 2021, 9(22), 2962; https://0-doi-org.brum.beds.ac.uk/10.3390/math9222962 - 20 Nov 2021
Viewed by 430
Abstract
In this study, we prove the existence of minimal first-order representations for convolutional codes with the predictable degree property over principal ideal artinian rings. Further, we prove that any such first-order representation leads to an input/state/output representation of the code provided the base [...] Read more.
In this study, we prove the existence of minimal first-order representations for convolutional codes with the predictable degree property over principal ideal artinian rings. Further, we prove that any such first-order representation leads to an input/state/output representation of the code provided the base ring is local. When the base ring is a finite field, we recover the classical construction, studied in depth by J. Rosenthal and E. V. York. This allows us to construct observable convolutional codes over such rings in the same way as is carried out in classical convolutional coding theory. Furthermore, we prove the minimality of the obtained representations. This completes the study of the existence of input/state/output representations of convolutional codes over rings of modular integers. Full article
(This article belongs to the Special Issue Advances in Contemporary Coding Theory)
Article
The Distributed and Centralized Fusion Filtering Problems of Tessarine Signals from Multi-Sensor Randomly Delayed and Missing Observations under Tk-Properness Conditions
Mathematics 2021, 9(22), 2961; https://0-doi-org.brum.beds.ac.uk/10.3390/math9222961 - 19 Nov 2021
Viewed by 300
Abstract
This paper addresses the fusion estimation problem in tessarine systems with multi-sensor observations affected by mixed uncertainties when under Tk-properness conditions. Observations from each sensor can be updated, delayed, or contain only noise, and a correlation is assumed between the state [...] Read more.
This paper addresses the fusion estimation problem in tessarine systems with multi-sensor observations affected by mixed uncertainties when under Tk-properness conditions. Observations from each sensor can be updated, delayed, or contain only noise, and a correlation is assumed between the state and the observation noises. Recursive algorithms for the optimal local linear filter at each sensor as well as both centralized and distributed linear fusion estimators are derived using an innovation approach. The Tk-properness assumption implies a reduction in the dimension of the augmented system, which yields computational savings in the previously mentioned algorithms compared to their counterparts, which are derived from real or widely linear processing. A numerical simulation example illustrates the obtained theoretical results and allows us to visualize, among other aspects, the insignificant difference in the accuracy of both fusion filters, which means that the distributed filter, although suboptimal, is preferable in practice as it implies a lower computational cost. Full article
(This article belongs to the Section Probability and Statistics Theory)
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Article
Fast Hyperparameter Calibration of Sparsity Enforcing Penalties in Total Generalised Variation Penalised Reconstruction Methods for XCT Using a Planted Virtual Reference Image
Mathematics 2021, 9(22), 2960; https://0-doi-org.brum.beds.ac.uk/10.3390/math9222960 - 19 Nov 2021
Viewed by 264
Abstract
The reconstruction problem in X-ray computed tomography (XCT) is notoriously difficult in the case where only a small number of measurements are made. Based on the recently discovered Compressed Sensing paradigm, many methods have been proposed in order to address the reconstruction problem [...] Read more.
The reconstruction problem in X-ray computed tomography (XCT) is notoriously difficult in the case where only a small number of measurements are made. Based on the recently discovered Compressed Sensing paradigm, many methods have been proposed in order to address the reconstruction problem by leveraging inherent sparsity of the object’s decompositions in various appropriate bases or dictionaries. In practice, reconstruction is usually achieved by incorporating weighted sparsity enforcing penalisation functionals into the least-squares objective of the associated optimisation problem. One such penalisation functional is the Total Variation (TV) norm, which has been successfully employed since the early days of Compressed Sensing. Total Generalised Variation (TGV) is a recent improvement of this approach. One of the main advantages of such penalisation based approaches is that the resulting optimisation problem is convex and as such, cannot be affected by the possible existence of spurious solutions. Using the TGV penalisation nevertheless comes with the drawback of having to tune the two hyperparameters governing the TGV semi-norms. In this short note, we provide a simple and efficient recipe for fast hyperparameters tuning, based on the simple idea of virtually planting a mock image into the model. The proposed trick potentially applies to all linear inverse problems under the assumption that relevant prior information is available about the sought for solution, whilst being very different from the Bayesian method. Full article
(This article belongs to the Topic Machine and Deep Learning)
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