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Mathematics
Volume 10
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Mathematics, Volume 10, Issue 2 (January-2 2022) – 123 articles

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In the last few decades the study of classical inequalities, such as Jensen’s, Hölder’s, Minkowski’s and similar inequalities, has experienced a great expansion. Many extensions, generalizations, improvements, refinements and applications of these inequalities have been proven to support different research ideas. The connection point between numerous generalizations is the theory of isotonic linear functionals.

A refinement of the converse Hölder’s inequality for functionals using an interpolation result for Jensen’s inequality is given. Additionally, similar improvements in the converse of Beckenbach’s inequality are obtained. We consider the converse Minkowski’s inequality for functionals and its continuous form, and give refinements of it.  An application on integral mixed means is given. View this paper.

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30 pages, 8408 KiB  
Article
Estimation of the Instantaneous Reproduction Number and Its Confidence Interval for Modeling the COVID-19 Pandemic
by Publio Darío Cortés-Carvajal, Mitzi Cubilla-Montilla and David Ricardo González-Cortés
Mathematics 2022, 10(2), 287; https://doi.org/10.3390/math10020287 - 17 Jan 2022
Cited by 5 | Viewed by 2407
Abstract
In this paper, we derive an optimal model for calculating the instantaneous reproduction number, which is an important metric to help in controlling the evolution of epidemics. Our approach, within a frequentist framework, gave us the opportunity to calculate a more realistic [...] Read more.
In this paper, we derive an optimal model for calculating the instantaneous reproduction number, which is an important metric to help in controlling the evolution of epidemics. Our approach, within a frequentist framework, gave us the opportunity to calculate a more realistic confidence interval, a fundamental tool for a safe interpretation of the instantaneous reproduction number value, so that health and governmental people pay more attention to it. Our reasoning begins by decoupling the incidence data in mean and Gaussian noise by using practical series analysis techniques; then, we continue with a likely relationship between the present and past incidence data. Monte Carlo simulations and numerical integrations were conducted to complement the analytical proofs, and illustrations are provided for each stage of analysis to validate the analytical results. Finally, a real case study is discussed with the incidence data of the Republic of Panama regarding the COVID-19 pandemic. We have shown that, for the calculation of the confidence interval of the instantaneous reproduction number, it is essential to include all sources of variability, not only the Poissonian processes of the incidences. This proposal is delivered with analysis tools developed with Microsoft Excel. Full article
(This article belongs to the Special Issue Machine Learning and Statistical Modeling with Applications in Real-World Data and Artificial Intelligence)
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17 pages, 1023 KiB  
Article
A Direct Method for Solving Singular Integrals in Three-Dimensional Time-Domain Boundary Element Method for Elastodynamics
by Xiaofei Qin, Youhua Fan, Hongjun Li and Weidong Lei
Mathematics 2022, 10(2), 286; https://doi.org/10.3390/math10020286 - 17 Jan 2022
Cited by 4 | Viewed by 1694
Abstract
The analytically time integrable time-space domain (ATI-TSD) is discovered based on which the minimum time-space domain is identified for treatment on singularities in the three-dimensional time-domain boundary element method (3D TD-BEM) formulation. A direct method to solve singular integrals in the 3D TD-BEM [...] Read more.
The analytically time integrable time-space domain (ATI-TSD) is discovered based on which the minimum time-space domain is identified for treatment on singularities in the three-dimensional time-domain boundary element method (3D TD-BEM) formulation. A direct method to solve singular integrals in the 3D TD-BEM formulation for elastodynamic problems is proposed. The wavefront singularity can be analytically eliminated in ATI-TSD, while the dual singularity can be treated by the direct method using Kutt’s quadrature in the identified minimum time-space domain. Three benchmark examples are presented to verify the correctness and the applicability of the direct method for solving the singular integrals in 3D TD-BEM. Full article
(This article belongs to the Special Issue Analytical Methods in Wave Scattering and Diffraction)
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18 pages, 3951 KiB  
Article
Voting-Based Ensemble Learning Algorithm for Fault Detection in Photovoltaic Systems under Different Weather Conditions
by Nien-Che Yang and Harun Ismail
Mathematics 2022, 10(2), 285; https://doi.org/10.3390/math10020285 - 17 Jan 2022
Cited by 12 | Viewed by 2558
Abstract
A photovoltaic (PV) system is one of the renewable energy resources that can help in meeting the ever-increasing energy demand. However, installation of PV systems is prone to faults that can occur unpredictably and remain challenging to detect. Major PV faults that can [...] Read more.
A photovoltaic (PV) system is one of the renewable energy resources that can help in meeting the ever-increasing energy demand. However, installation of PV systems is prone to faults that can occur unpredictably and remain challenging to detect. Major PV faults that can occur are line-line and open circuits faults, and if they are not addressed appropriately and timely, they may lead to serious problems in the PV system. To solve this problem, this study proposes a voting-based ensemble learning algorithm with linear regression, decision tree, and support vector machine (EL-VLR-DT-SVM) for PV fault detection and diagnosis. The data acquisition is performed for different weather conditions to trigger the nonlinear nature of the PV system characteristics. The voltage-current characteristics are used as input data. The dataset is studied for a deeper understanding, and pre-processing before feeding it to the EL-VLR-DT-SVM. In the pre-processing step, data are normalized to obtain more feature space, making it easy for the proposed algorithm to discriminate between healthy and faulty conditions. To verify the proposed method, it is compared with other algorithms in terms of accuracy, precision, recall, and F-1 score. The results show that the proposed EL-VLR-DT-SVM algorithm outperforms the other algorithms. Full article
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10 pages, 1454 KiB  
Article
Effects of the Nonlocal Thermoelastic Model in a Thermoelastic Nanoscale Material
by Tareq Saeed and Ibrahim Abbas
Mathematics 2022, 10(2), 284; https://doi.org/10.3390/math10020284 - 17 Jan 2022
Cited by 11 | Viewed by 1743
Abstract
In this work, a novel nonlocal model without energy dissipations is presented to investigate the impacts of the nonlocal thermoelastic parameters in a nanoscale material by the eigenvalue approach. The basic equations are applied under the Green and Naghdi model without energy dissipations. [...] Read more.
In this work, a novel nonlocal model without energy dissipations is presented to investigate the impacts of the nonlocal thermoelastic parameters in a nanoscale material by the eigenvalue approach. The basic equations are applied under the Green and Naghdi model without energy dissipations. To obtain this model, the theory of the non-local continuum suggested by Eringen is applied. The Laplace transformation technique is used for the basic formulations to obtain the analytical solutions of the thermal stress, the displacement, and the temperature during the nanoscale thermo-electric medium. The inverse of the Laplace transformation is used with the numerical technique to obtain the complete solutions of the studying fields in the time–space domains. The main physical fields are displayed graphically and theoretically discussed under the influence of nonlocal parameters. Full article
(This article belongs to the Special Issue Applied Mathematics and Continuum Mechanics)
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26 pages, 1245 KiB  
Review
Transformation and Linearization Techniques in Optimization: A State-of-the-Art Survey
by Mohammad Asghari, Amir M. Fathollahi-Fard, S. M. J. Mirzapour Al-e-hashem and Maxim A. Dulebenets
Mathematics 2022, 10(2), 283; https://doi.org/10.3390/math10020283 - 17 Jan 2022
Cited by 65 | Viewed by 12394
Abstract
To formulate a real-world optimization problem, it is sometimes necessary to adopt a set of non-linear terms in the mathematical formulation to capture specific operational characteristics of that decision problem. However, the use of non-linear terms generally increases computational complexity of the optimization [...] Read more.
To formulate a real-world optimization problem, it is sometimes necessary to adopt a set of non-linear terms in the mathematical formulation to capture specific operational characteristics of that decision problem. However, the use of non-linear terms generally increases computational complexity of the optimization model and the computational time required to solve it. This motivates the scientific community to develop efficient transformation and linearization approaches for the optimization models that have non-linear terms. Such transformations and linearizations are expected to decrease the computational complexity of the original non-linear optimization models and, ultimately, facilitate decision making. This study provides a detailed state-of-the-art review focusing on the existing transformation and linearization techniques that have been used for solving optimization models with non-linear terms within the objective functions and/or constraint sets. The existing transformation approaches are analyzed for a wide range of scenarios (multiplication of binary variables, multiplication of binary and continuous variables, multiplication of continuous variables, maximum/minimum operators, absolute value function, floor and ceiling functions, square root function, and multiple breakpoint function). Furthermore, a detailed review of piecewise approximating functions and log-linearization via Taylor series approximation is presented. Along with a review of the existing methods, this study proposes a new technique for linearizing the square root terms by means of transformation. The outcomes of this research are anticipated to reveal some important insights to researchers and practitioners, who are closely working with non-linear optimization models, and assist with effective decision making. Full article
(This article belongs to the Special Issue Operations Research and Optimization)
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22 pages, 7592 KiB  
Article
Forecasting the Passage Time of the Queue of Highly Automated Vehicles Based on Neural Networks in the Services of Cooperative Intelligent Transport Systems
by Vladimir Shepelev, Sultan Zhankaziev, Sergey Aliukov, Vitalii Varkentin, Aleksandr Marusin, Alexey Marusin and Aleksandr Gritsenko
Mathematics 2022, 10(2), 282; https://doi.org/10.3390/math10020282 - 17 Jan 2022
Cited by 23 | Viewed by 2596
Abstract
This study addresses the problem of non-stop passage by vehicles at intersections based on special processing of data from a road camera or video detector. The basic task in this article is formulated as a forecast for the release time of a controlled [...] Read more.
This study addresses the problem of non-stop passage by vehicles at intersections based on special processing of data from a road camera or video detector. The basic task in this article is formulated as a forecast for the release time of a controlled intersection by non-group vehicles, taking into account their classification and determining their number in the queue. To solve the problem posed, the YOLOv3 neural network and the modified SORT object tracker were used. The work uses a heuristic region-based algorithm in classifying and measuring the parameters of the queue of vehicles. On the basis of fuzzy logic methods, a model for predicting the passage time of a queue of vehicles at controlled intersections was developed and refined. The elaborated technique allows one to reduce the forced number of stops at controlled intersections of connected vehicles by choosing the optimal speed mode. The transmission of information on the predicted delay time at a controlled intersection is locally possible due to the V2X communication of the road controller equipment, and in the horizontally scaled mode due to the interaction of HAV—the Digital Road Model. Full article
(This article belongs to the Special Issue Intelligent Computing in Industry Applications)
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8 pages, 260 KiB  
Article
Dominating Broadcasts in Fuzzy Graphs
by Passawan Noppakaew, Kaewkan Hengthonglert and Sawanya Sakuntasathien
Mathematics 2022, 10(2), 281; https://doi.org/10.3390/math10020281 - 17 Jan 2022
Cited by 2 | Viewed by 1260
Abstract
Broadcasting problems in graph theory play a significant role in solving many complicated physical problems. However, in real life there are many vague situations that sometimes cannot be modeled using usual graphs. Consequently, the concept of a fuzzy graph [...] Read more.
Broadcasting problems in graph theory play a significant role in solving many complicated physical problems. However, in real life there are many vague situations that sometimes cannot be modeled using usual graphs. Consequently, the concept of a fuzzy graph GF:(V,σ,μ) has been introduced to deal with such problems. In this study, we are interested in defining the notion of dominating broadcasts in fuzzy graphs. We also show that, in a connected fuzzy graph containing more than one element in σ*, a dominating broadcast always exists, where σ* is {v∈V|σ(v)>0}. In addition, we investigate the relationship between broadcast domination numbers, radii, and domination numbers in a fuzzy graph as follows; γb(GF)≤min{r(GF),γ(GF)}, where γb(GF) is the broadcast domination number, r(GF) is the radius, and γ(GF) is domination numbers in fuzzy graph GF, with |σ*|>1. Full article
(This article belongs to the Section Fuzzy Sets, Systems and Decision Making)
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23 pages, 1528 KiB  
Article
Equal Access to University Education in Chile? An Application Using Spatial Heckman Probit Models
by Juan Luis Quiroz, Ludo Peeters, Coro Chasco and Patricio Aroca
Mathematics 2022, 10(2), 280; https://doi.org/10.3390/math10020280 - 17 Jan 2022
Cited by 5 | Viewed by 2818
Abstract
This study contributes to the debate on accessibility of higher education in Chile, with a special focus on the geospatial dimension of access to university studies. This paper addresses the central question of whether geography (physical distance and neighborhood effects) plays a significant [...] Read more.
This study contributes to the debate on accessibility of higher education in Chile, with a special focus on the geospatial dimension of access to university studies. This paper addresses the central question of whether geography (physical distance and neighborhood effects) plays a significant role in determining the accessibility of higher education to students in Chile. We use Heckman probit-type (Heckit) models to adjust for selection during application for higher education—that is, pre-selection among applications to study at university and, ultimately, admission (or denial) to a higher educational institution. Of all high school graduates who took the university selection test (PSU), only 37.9% were able to attend higher education. The results show that the geospatial elements—neighborhood characteristics and distance from the city of Santiago—have a significant local effect on the student’s application and access to Chilean universities. Specifically, the most significant local range for each candidate is 300 neighbors. We also find that, when distance to the capital city increases, the probability of applying to university increases to a threshold of 1400 km, at which point probability begins to decrease. Full article
(This article belongs to the Special Issue Economics of Education: Quantitative Methods for Educational Policies)
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16 pages, 360 KiB  
Article
Event-Triggered Impulsive Optimal Control for Continuous-Time Dynamic Systems with Input Time-Delay
by Quanyu Bai and Wei Zhu
Mathematics 2022, 10(2), 279; https://doi.org/10.3390/math10020279 - 17 Jan 2022
Cited by 7 | Viewed by 1636
Abstract
Time-delay is an inevitable factor in practice, which may affect the performance of optimal control. In this paper, the event-triggered impulsive optimal control for linear continuous-time dynamic systems is studied. The event-triggered impulsive optimal feedback controller with input time-delay is presented, where the [...] Read more.
Time-delay is an inevitable factor in practice, which may affect the performance of optimal control. In this paper, the event-triggered impulsive optimal control for linear continuous-time dynamic systems is studied. The event-triggered impulsive optimal feedback controller with input time-delay is presented, where the impulsive instants are determined by some designed event-triggering function and condition depending on the state of the system. Some sufficient conditions are given for guaranteeing the exponential stability with the optimal controller. Moreover, the Zeno-behavior for the impulsive instants is excluded. Finally, an example with numerical simulation is given to verify the validity of the theoretical results. Full article
(This article belongs to the Section Dynamical Systems)
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20 pages, 607 KiB  
Article
Geometric Compatibility Indexes in a Local AHP-Group Decision Making Context: A Framework for Reducing Incompatibility
by Juan Aguarón, María Teresa Escobar, José María Moreno-Jiménez and Alberto Turón
Mathematics 2022, 10(2), 278; https://doi.org/10.3390/math10020278 - 17 Jan 2022
Cited by 3 | Viewed by 1241
Abstract
This paper deals with the measurement of the compatibility in a local AHP-Group Decision Making context. Compatibility between two individuals or decision makers is understood as the property that reflects the proximity between their positions or preferences, usually measured by a distance function. [...] Read more.
This paper deals with the measurement of the compatibility in a local AHP-Group Decision Making context. Compatibility between two individuals or decision makers is understood as the property that reflects the proximity between their positions or preferences, usually measured by a distance function. An acceptable level of incompatibility between the individual and the group positions will favour the acceptance of the collective position by the individuals. To facilitate the compatibility measurement, the paper utilises four indicators based on log quadratic distances between matrices or vectors which can be employed in accordance with the information that is available from the individual decision makers and from the group. The indicators make it possible to measure compatibility in decision problems, regardless of how the collective position and the priorities are obtained. The paper also presents a theoretical framework and a general, semi-automatic procedure for reducing the incompatibility measured by the four indicators. Using relative variations, the procedure identifies and slightly modifies the judgement of the collective matrix that further improves the indicator. This process is undertaken without modifying the initial information provided by the individuals. A numerical example illustrates the application of the theoretical framework and the procedure. Full article
(This article belongs to the Special Issue Multicriteria Decision Making and the Analytic Hierarchy Process)
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24 pages, 1117 KiB  
Article
Graph-Based Siamese Network for Authorship Verification
by Daniel Embarcadero-Ruiz, Helena Gómez-Adorno, Alberto Embarcadero-Ruiz and Gerardo Sierra
Mathematics 2022, 10(2), 277; https://doi.org/10.3390/math10020277 - 17 Jan 2022
Cited by 6 | Viewed by 2148
Abstract
In this work, we propose a novel approach to solve the authorship identification task on a cross-topic and open-set scenario. Authorship verification is the task of determining whether or not two texts were written by the same author. We model the documents in [...] Read more.
In this work, we propose a novel approach to solve the authorship identification task on a cross-topic and open-set scenario. Authorship verification is the task of determining whether or not two texts were written by the same author. We model the documents in a graph representation and then a graph neural network extracts relevant features from these graph representations. We present three strategies to represent the texts as graphs based on the co-occurrence of the POS labels of words. We propose a Siamese Network architecture composed of graph convolutional networks along with pooling and classification layers. We present different variants of the architecture and discuss the performance of each one. To evaluate our approach we used a collection of fanfiction texts provided by the PAN@CLEF 2021 shared task in two settings: a “small” corpus and a “large” corpus. Our graph-based approach achieved average scores (AUC ROC, F1, Brier score, F0.5u, and C@1) between 90% and 92.83% when training on the “small” and “large” corpus, respectively. Our model obtain results comparable to those of the state of the art in this task and greater than traditional baselines. Full article
(This article belongs to the Special Issue Graphs, Metrics and Models)
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35 pages, 2591 KiB  
Article
Individual Disturbance and Attraction Repulsion Strategy Enhanced Seagull Optimization for Engineering Design
by Helong Yu, Shimeng Qiao, Ali Asghar Heidari, Chunguang Bi and Huiling Chen
Mathematics 2022, 10(2), 276; https://doi.org/10.3390/math10020276 - 16 Jan 2022
Cited by 27 | Viewed by 2255
Abstract
The seagull optimization algorithm (SOA) is a novel swarm intelligence algorithm proposed in recent years. The algorithm has some defects in the search process. To overcome the problem of poor convergence accuracy and easy to fall into local optimality of seagull optimization algorithm, [...] Read more.
The seagull optimization algorithm (SOA) is a novel swarm intelligence algorithm proposed in recent years. The algorithm has some defects in the search process. To overcome the problem of poor convergence accuracy and easy to fall into local optimality of seagull optimization algorithm, this paper proposed a new variant SOA based on individual disturbance (ID) and attraction-repulsion (AR) strategy, called IDARSOA, which employed ID to enhance the ability to jump out of local optimum and adopted AR to increase the diversity of population and make the exploration of solution space more efficient. The effectiveness of the IDARSOA has been verified using representative comprehensive benchmark functions and six practical engineering optimization problems. The experimental results show that the proposed IDARSOA has the advantages of better convergence accuracy and a strong optimization ability than the original SOA. Full article
(This article belongs to the Special Issue Evolutionary Computation 2022)
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19 pages, 19985 KiB  
Article
Single Image Super-Resolution with Arbitrary Magnification Based on High-Frequency Attention Network
by Jun-Seok Yun and Seok-Bong Yoo
Mathematics 2022, 10(2), 275; https://doi.org/10.3390/math10020275 - 16 Jan 2022
Cited by 10 | Viewed by 2922
Abstract
Among various developments in the field of computer vision, single image super-resolution of images is one of the most essential tasks. However, compared to the integer magnification model for super-resolution, research on arbitrary magnification has been overlooked. In addition, the importance of single [...] Read more.
Among various developments in the field of computer vision, single image super-resolution of images is one of the most essential tasks. However, compared to the integer magnification model for super-resolution, research on arbitrary magnification has been overlooked. In addition, the importance of single image super-resolution at arbitrary magnification is emphasized for tasks such as object recognition and satellite image magnification. In this study, we propose a model that performs arbitrary magnification while retaining the advantages of integer magnification. The proposed model extends the integer magnification image to the target magnification in the discrete cosine transform (DCT) spectral domain. The broadening of the DCT spectral domain results in a lack of high-frequency components. To solve this problem, we propose a high-frequency attention network for arbitrary magnification so that high-frequency information can be restored. In addition, only high-frequency components are extracted from the image with a mask generated by a hyperparameter in the DCT domain. Therefore, the high-frequency components that have a substantial impact on image quality are recovered by this procedure. The proposed framework achieves the performance of an integer magnification and correctly retrieves the high-frequency components lost between the arbitrary magnifications. We experimentally validated our model’s superiority over state-of-the-art models. Full article
(This article belongs to the Special Issue Mathematical Methods and Applications for Artificial Intelligence and Computer Vision)
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24 pages, 681 KiB  
Article
Applying Parallel and Distributed Models on Bio-Inspired Algorithms via a Clustering Method
by Álvaro Gómez-Rubio, Ricardo Soto, Broderick Crawford, Adrián Jaramillo, David Mancilla, Carlos Castro and Rodrigo Olivares
Mathematics 2022, 10(2), 274; https://doi.org/10.3390/math10020274 - 16 Jan 2022
Cited by 1 | Viewed by 1274
Abstract
In the world of optimization, especially concerning metaheuristics, solving complex problems represented by applying big data and constraint instances can be difficult. This is mainly due to the difficulty of implementing efficient solutions that can solve complex optimization problems in adequate time, which [...] Read more.
In the world of optimization, especially concerning metaheuristics, solving complex problems represented by applying big data and constraint instances can be difficult. This is mainly due to the difficulty of implementing efficient solutions that can solve complex optimization problems in adequate time, which do exist in different industries. Big data has demonstrated its efficiency in solving different concerns in information management. In this paper, an approach based on multiprocessing is proposed wherein clusterization and parallelism are used together to improve the search process of metaheuristics when solving large instances of complex optimization problems, incorporating collaborative elements that enhance the quality of the solution. The proposal deals with machine learning algorithms to improve the segmentation of the search space. Particularly, two different clustering methods belonging to automatic learning techniques, are implemented on bio-inspired algorithms to smartly initialize their solution population, and then organize the resolution from the beginning of the search. The results show that this approach is competitive with other techniques in solving a large set of cases of a well-known NP-hard problem without incorporating too much additional complexity into the metaheuristic algorithms. Full article
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20 pages, 324 KiB  
Article
Approximation of the Solution of Delay Fractional Differential Equation Using AA-Iterative Scheme
by Mujahid Abbas, Muhammad Waseem Asghar and Manuel De la Sen
Mathematics 2022, 10(2), 273; https://doi.org/10.3390/math10020273 - 16 Jan 2022
Cited by 7 | Viewed by 1563
Abstract
The aim of this paper is to propose a new faster iterative scheme (called AA-iteration) to approximate the fixed point of (b,η)-enriched contraction mapping in the framework of Banach spaces. It is also proved that our [...] Read more.
The aim of this paper is to propose a new faster iterative scheme (called AA-iteration) to approximate the fixed point of (b,η)-enriched contraction mapping in the framework of Banach spaces. It is also proved that our iteration is stable and converges faster than many iterations existing in the literature. For validity of our proposed scheme, we presented some numerical examples. Further, we proved some strong and weak convergence results for b-enriched nonexpansive mapping in the uniformly convex Banach space. Finally, we approximate the solution of delay fractional differential equations using AA-iterative scheme. Full article
(This article belongs to the Special Issue New Progress in General Topology and Its Applications)
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24 pages, 12786 KiB  
Article
Prediction of Airfoil Stall Based on a Modified k−v2¯−ω Turbulence Model
by Chenyu Wu, Haoran Li, Yufei Zhang and Haixin Chen
Mathematics 2022, 10(2), 272; https://doi.org/10.3390/math10020272 - 16 Jan 2022
Viewed by 2062
Abstract
The accuracy of an airfoil stall prediction heavily depends on the computation of the separated shear layer. Capturing the strong non-equilibrium turbulence in the shear layer is crucial for the accuracy of a stall prediction. In this paper, different Reynolds-averaged Navier–Stokes turbulence models [...] Read more.
The accuracy of an airfoil stall prediction heavily depends on the computation of the separated shear layer. Capturing the strong non-equilibrium turbulence in the shear layer is crucial for the accuracy of a stall prediction. In this paper, different Reynolds-averaged Navier–Stokes turbulence models are adopted and compared for airfoil stall prediction. The results show that the separated shear layer fixed k−v2¯−ω (abbreviated as SPF k−v2¯−ω) turbulence model captures the non-equilibrium turbulence in the separated shear layer well and gives satisfactory predictions of both thin-airfoil stall and trailing-edge stall. At small Reynolds numbers (Re~105), the relative error between the predicted CL,max of NACA64A010 by the SPF k−v2¯−ω model and the experimental data is less than 3.5%. At high Reynolds numbers (Re~106), the CL,max of NACA64A010 and NACA64A006 predicted by the SPF k−v2¯−ω model also has an error of less than 5.5% relative to the experimental data. The stall of the NACA0012 airfoil, which features trailing-edge stall, is also computed by the SPF k−v2¯−ω model. The SPF k−v2¯−ω model is also applied to a NACA0012 airfoil, which features trailing-edge stall and an error of CL relative to the experiment at CL>1.0 is smaller than 3.5%. The SPF k−v2¯−ω model shows higher accuracy than other turbulence models. Full article
(This article belongs to the Special Issue Advances in Computational Fluid Dynamics)
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3 pages, 173 KiB  
Editorial
Lattice Computing: A Mathematical Modelling Paradigm for Cyber-Physical System Applications
by Vassilis G. Kaburlasos
Mathematics 2022, 10(2), 271; https://doi.org/10.3390/math10020271 - 16 Jan 2022
Cited by 6 | Viewed by 1623
Abstract
By “model”, we mean a mathematical description of a world aspect [...] Full article
(This article belongs to the Special Issue Lattice Computing: A Mathematical Modelling Paradigm for Cyber–Physical System Applications)
18 pages, 346 KiB  
Article
A Relaxed and Bound Algorithm Based on Auxiliary Variables for Quadratically Constrained Quadratic Programming Problem
by Chenyang Hu, Yuelin Gao, Fuping Tian and Suxia Ma
Mathematics 2022, 10(2), 270; https://doi.org/10.3390/math10020270 - 16 Jan 2022
Viewed by 1272
Abstract
Quadratically constrained quadratic programs (QCQP), which often appear in engineering practice and management science, and other fields, are investigated in this paper. By introducing appropriate auxiliary variables, QCQP can be transformed into its equivalent problem (EP) with non-linear equality constraints. After these equality [...] Read more.
Quadratically constrained quadratic programs (QCQP), which often appear in engineering practice and management science, and other fields, are investigated in this paper. By introducing appropriate auxiliary variables, QCQP can be transformed into its equivalent problem (EP) with non-linear equality constraints. After these equality constraints are relaxed, a series of linear relaxation subproblems with auxiliary variables and bound constraints are generated, which can determine the effective lower bound of the global optimal value of QCQP. To enhance the compactness of sub-rectangles and improve the ability to remove sub-rectangles, two rectangle-reduction strategies are employed. Besides, two ϵ-subproblem deletion rules are introduced to improve the convergence speed of the algorithm. Therefore, a relaxation and bound algorithm based on auxiliary variables are proposed to solve QCQP. Numerical experiments show that this algorithm is effective and feasible. Full article
(This article belongs to the Special Issue Fixed Point, Optimization, and Applications II)
21 pages, 455 KiB  
Article
Retrial BMAP/PH/N Queueing System with a Threshold-Dependent Inter-Retrial Time Distribution
by Valentina I. Klimenok, Alexander N. Dudin, Vladimir M. Vishnevsky and Olga V. Semenova
Mathematics 2022, 10(2), 269; https://doi.org/10.3390/math10020269 - 16 Jan 2022
Cited by 5 | Viewed by 1317
Abstract
In this paper, we study a multi-server queueing system with retrials and an infinite orbit. The arrival of primary customers is described by a batch Markovian arrival process (BMAP), and the service times have a phase-type ( [...] Read more.
In this paper, we study a multi-server queueing system with retrials and an infinite orbit. The arrival of primary customers is described by a batch Markovian arrival process (BMAP), and the service times have a phase-type (PH) distribution. Previously, in the literature, such a system was mainly considered under the strict assumption that the intervals between the repeated attempts from the orbit have an exponential distribution. Only a few publications dealt with retrial queueing systems with non-exponential inter-retrial times. These publications assumed either the rate of retrials is constant regardless of the number of customers in the orbit or this rate is constant when the number of orbital customers exceeds a certain threshold. Such assumptions essentially simplify the mathematical analysis of the system, but do not reflect the nature of the majority of real-life retrial processes. The main feature of the model under study is that we considered the classical retrial strategy under which the retrial rate is proportional to the number of orbital customers. However, in this case, the assumption of the non-exponential distribution of inter-retrial times leads to insurmountable computational difficulties. To overcome these difficulties, we supposed that inter-retrial times have a phase-type distribution if the number of customers in the orbit is less than or equal to some non-negative integer (threshold) and have an exponential distribution in the contrary case. By appropriately choosing the threshold, one can obtain a sufficiently accurate approximation of the system with a PH distribution of the inter-retrial times. Thus, the model under study takes into account the realistic nature of the retrial process and, at the same time, does not resort to restrictions such as a constant retrial rate or to rough truncation methods often applied to the analysis of retrial queueing systems with an infinite orbit. We describe the behavior of the system by a multi-dimensional Markov chain, derive the stability condition, and calculate the steady-state distribution and the main performance indicators of the system. We made sure numerically that there was a reasonable value of the threshold under which our model can be served as a good approximation of the BMAP/PH/N queueing system with the PH distribution of inter-retrial times. We also numerically compared the system under consideration with the corresponding queueing system having exponentially distributed inter-retrial times and saw that the latter is a poor approximation of the system with the PH distribution of inter-retrial times. We present a number of illustrative numerical examples to analyze the behavior of the system performance indicators depending on the system parameters, the variance of inter-retrial times, and the correlation in the input flow. Full article
(This article belongs to the Section Dynamical Systems)
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15 pages, 4180 KiB  
Article
Series Solution-Based Approach for the Interlaminar Stress Analysis of Smart Composites under Thermo-Electro-Mechanical Loading
by Salman Khalid, Jaehun Lee and Heung Soo Kim
Mathematics 2022, 10(2), 268; https://doi.org/10.3390/math10020268 - 16 Jan 2022
Cited by 8 | Viewed by 1866
Abstract
This paper introduces a new loading condition considering the combined thermo-electro-mechanical coupling effect in a series solution-based approach to analyze the free-edge interlaminar stresses in smart composite laminates. The governing equations are developed using the principle of complementary virtual work. The assumed stress [...] Read more.
This paper introduces a new loading condition considering the combined thermo-electro-mechanical coupling effect in a series solution-based approach to analyze the free-edge interlaminar stresses in smart composite laminates. The governing equations are developed using the principle of complementary virtual work. The assumed stress fields satisfy the traction-free and free-edge boundary conditions. The accurate stress states of the composite structures are acquired through the procedure of generalized eigenvalue problems. The uniform temperature is employed throughout the laminate, and the electric field loading is applied to the symmetric piezo-bonded actuators to examine the combined effect of thermal and electrical stresses on the overall deformation of smart composite laminates. It was observed that the magnitude of the peeling stresses generated by mechanical loading was reduced by the combined thermal and electric excitation loading (up to 25.3%), which in turn resulted in expanding the service life of the smart composite structures. The proposed approach is implemented on three different layup configurations. The efficiency of the current methodology is confirmed by comparing the results with the 3D finite element (FEM) solution computed by ABAQUS. Full article
(This article belongs to the Special Issue Analytical and Computational Mechanics of Advanced Materials and Functional Structures)
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20 pages, 1352 KiB  
Article
Tree Inference: Response Time and Other Measures in a Binary Multinomial Processing Tree, Representation and Uniqueness of Parameters
by Richard Schweickert and Xiaofang Zheng
Mathematics 2022, 10(2), 267; https://doi.org/10.3390/math10020267 - 16 Jan 2022
Viewed by 1124
Abstract
A Multinomial Processing Tree (MPT) is a directed tree with a probability associated with each arc and partitioned terminal vertices. We consider an additional parameter for each arc, a measure such as time. Each vertex represents a process. An arc descending from a [...] Read more.
A Multinomial Processing Tree (MPT) is a directed tree with a probability associated with each arc and partitioned terminal vertices. We consider an additional parameter for each arc, a measure such as time. Each vertex represents a process. An arc descending from a vertex represents selection of a process outcome. A source vertex represents processing beginning with stimulus presentation and a terminal vertex represents a response. An experimental factor selectively influences a vertex if changing the factor level changes parameter values on arcs descending from that vertex and no others. Earlier work shows that if each of two factors selectively influences a different vertex in an arbitrary MPT it is equivalent to one of two simple MPTs. Which applies depends on whether the two selectively influenced vertices are ordered by the factors or not. A special case, the Standard Binary Tree for Ordered Processes, arises if the vertices are ordered and the factor selectively influencing the first vertex changes parameter values on only two arcs. We derive necessary and sufficient conditions, testable by bootstrapping, for this case. Parameter values are not unique. We give admissible transformations for them. We calculate degrees of freedom needed for goodness of fit tests. Full article
(This article belongs to the Special Issue Mathematical and Computational Models of Cognition)
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17 pages, 317 KiB  
Article
Water Carrying Capacity Evaluation Method Based on Cloud Model Theory and an Evidential Reasoning Approach
by Wenzhi Cao, Jilin Deng, Yi Yang, Yangyan Zeng and Limei Liu
Mathematics 2022, 10(2), 266; https://doi.org/10.3390/math10020266 - 16 Jan 2022
Cited by 11 | Viewed by 2528
Abstract
The scientific and reasonable evaluation of the carrying capacity of water resources is of guiding significance for solving the issues of water resource shortages and pollution control. It is also an important method for realizing the sustainable development of water resources. Aiming at [...] Read more.
The scientific and reasonable evaluation of the carrying capacity of water resources is of guiding significance for solving the issues of water resource shortages and pollution control. It is also an important method for realizing the sustainable development of water resources. Aiming at an evaluation of the carrying capacity of water resources, an evaluation model based on the cloud model theory and evidential reasoning approach is studied. First, based on the existing indicators, a water resources evaluation index system based on the pressure-state-response (PSR) model is constructed, and a classification method of carrying capacity grade is designed. The cloud model theory is used to realize the transformation between the measured value of indicators and the degree of correlation. Second, to obtain the weight of the evaluation index, the weight method of the index weights model based on the entropy weight method and evidential reasoning approach is proposed. Then, the reliability distribution function of the evaluation index and the graded probability distribution of the carrying capacity of water resources are obtained by an evidential reasoning approach. Finally, the evaluation method of the carrying capacity of water resources is constructed, and specific steps are provided. The proposed method is applied to the evaluation of water resources carrying capacity for Hunan Province, which verifies the feasibility and effectiveness of the method proposed in the present study. This paper applies this method of the evaluation of the water resources carrying capacity of Hunan Province from 2010 to 2019. It is concluded that the water resources carrying capacity of Hunan Province belongs to III~V, which is between the critical state and the strong carrying capacity state. The carrying capacity of the province’s water resources is basically on the rise. This shows that the carrying capacity of water resources in Hunan Province is in good condition, and corresponding protective measures should be taken to continue the current state. Full article
(This article belongs to the Special Issue New Trends in Fuzzy Sets Theory and Their Extensions)
6 pages, 229 KiB  
Article
Can Producers’ Price War End Up in an Optimal Allocation?
by Marta Kornafel
Mathematics 2022, 10(2), 265; https://doi.org/10.3390/math10020265 - 16 Jan 2022
Viewed by 1122
Abstract
The paper presents a theoretical framework for the phenomenon of the price war in the context of general equilibrium, with special attention to the production system. The natural question that arises is whether Nash-optimal production plans being the reactions to the changing prices [...] Read more.
The paper presents a theoretical framework for the phenomenon of the price war in the context of general equilibrium, with special attention to the production system. The natural question that arises is whether Nash-optimal production plans being the reactions to the changing prices can finally approximate a Nash-optimal production plan at the end of this war. To provide an answer, the production system is described as a parametric-multicriteria game. Referring to some results on the lower semicontinuty of the parametric weak-multicriteria Nash equilibria, we provide a positive answer for the stated problem. Full article
(This article belongs to the Special Issue Statistical and Probabilistic Methods in the Game Theory)
16 pages, 304 KiB  
Article
Hermite-Hadamard-Type Fractional Inclusions for Interval-Valued Preinvex Functions
by Kin Keung Lai, Jaya Bisht, Nidhi Sharma and Shashi Kant Mishra
Mathematics 2022, 10(2), 264; https://doi.org/10.3390/math10020264 - 16 Jan 2022
Cited by 14 | Viewed by 1351
Abstract
We introduce a new class of interval-valued preinvex functions termed as harmonically h-preinvex interval-valued functions. We establish new inclusion of Hermite–Hadamard for harmonically h-preinvex interval-valued function via interval-valued Riemann–Liouville fractional integrals. Further, we prove fractional Hermite–Hadamard-type inclusions for the product of [...] Read more.
We introduce a new class of interval-valued preinvex functions termed as harmonically h-preinvex interval-valued functions. We establish new inclusion of Hermite–Hadamard for harmonically h-preinvex interval-valued function via interval-valued Riemann–Liouville fractional integrals. Further, we prove fractional Hermite–Hadamard-type inclusions for the product of two harmonically h-preinvex interval-valued functions. In this way, these findings include several well-known results and newly obtained results of the existing literature as special cases. Moreover, applications of the main results are demonstrated by presenting some examples. Full article
(This article belongs to the Special Issue Variational Problems and Applications)
14 pages, 4339 KiB  
Article
Numerical Simulation of Solid and Porous Fins’ Impact on Heat Transfer Performance in a Differentially Heated Chamber
by Le Xuan Hoang Khoa, Ioan Pop and Mikhail A. Sheremet
Mathematics 2022, 10(2), 263; https://doi.org/10.3390/math10020263 - 16 Jan 2022
Cited by 9 | Viewed by 1559
Abstract
The development of different industrial fields, including mechanical and power engineering and electronics, demands the augmentation of heat transfer in engineering devices. Such enhancement can be achieved by adding extended heat transfer surfaces to the heated walls or heat-generating elements. This investigation is [...] Read more.
The development of different industrial fields, including mechanical and power engineering and electronics, demands the augmentation of heat transfer in engineering devices. Such enhancement can be achieved by adding extended heat transfer surfaces to the heated walls or heat-generating elements. This investigation is devoted to the numerical analysis of natural convective energy transport in a differentially heated chamber with isothermal vertical walls and a fin system mounted on the heated wall. The developed in-house computational code has been comprehensively validated. The Forchheimer–Brinkman extended Darcy model has been employed for the numerical simulation of transport phenomena in a porous material. The partial differential equations written, employing non-primitive variables, have been worked out by the finite difference technique. Analysis has been performed for solid and porous fins with various fin materials, amounts and heights. It has been revealed that porous fins provide a very good technique for the intensification of energy removal from heated surfaces. Full article
(This article belongs to the Special Issue State-of-the-Art Mathematical Applications in Europe)
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7 pages, 241 KiB  
Article
On Groups in Which Many Automorphisms Are Cyclic
by Mattia Brescia and Alessio Russo
Mathematics 2022, 10(2), 262; https://doi.org/10.3390/math10020262 - 15 Jan 2022
Viewed by 1291
Abstract
Let G be a group. An automorphism α of G is said to be a cyclic automorphism if the subgroup ⟨x,xα⟩ is cyclic for every element x of G. In [F. de Giovanni, M.L. Newell, A. Russo: [...] Read more.
Let G be a group. An automorphism α of G is said to be a cyclic automorphism if the subgroup ⟨x,xα⟩ is cyclic for every element x of G. In [F. de Giovanni, M.L. Newell, A. Russo: On a class of normal endomorphisms of groups, J. Algebra and its Applications 13, (2014), 6pp] the authors proved that every cyclic automorphism is central, namely, that every cyclic automorphism acts trivially on the factor group G/Z(G). In this paper, the class FW of groups in which every element induces by conjugation a cyclic automorphism on a (normal) subgroup of finite index will be investigated. Full article
(This article belongs to the Special Issue Group Theory and Related Topics)
13 pages, 269 KiB  
Article
An Optimal Estimate for the Anisotropic Logarithmic Potential
by Shaoxiong Hou
Mathematics 2022, 10(2), 261; https://doi.org/10.3390/math10020261 - 15 Jan 2022
Viewed by 921
Abstract
This paper introduces the new annulus body to establish the optimal lower bound for the anisotropic logarithmic potential as the complement to the theory of its upper bound estimate which has already been investigated. The connections with convex geometry analysis and some metric [...] Read more.
This paper introduces the new annulus body to establish the optimal lower bound for the anisotropic logarithmic potential as the complement to the theory of its upper bound estimate which has already been investigated. The connections with convex geometry analysis and some metric properties are also established. For the application, a polynomial dual log-mixed volume difference law is deduced from the optimal estimate. Full article
(This article belongs to the Special Issue Recent Developments of Function Spaces and Their Applications I)
15 pages, 4167 KiB  
Article
A Novel Deep Learning-Based State-of-Charge Estimation for Renewable Energy Management System in Hybrid Electric Vehicles
by Mahendiran T. Vellingiri, Ibrahim M. Mehedi and Thangam Palaniswamy
Mathematics 2022, 10(2), 260; https://doi.org/10.3390/math10020260 - 15 Jan 2022
Cited by 14 | Viewed by 1873
Abstract
In recent years, alternative engine technologies are necessary to resolve the problems related to conventional vehicles. Electric vehicles (EVs) and hybrid electric vehicles (HEVs) are effective solutions to decarbonize the transportation sector. It also becomes important to shift from traditional houses to smart [...] Read more.
In recent years, alternative engine technologies are necessary to resolve the problems related to conventional vehicles. Electric vehicles (EVs) and hybrid electric vehicles (HEVs) are effective solutions to decarbonize the transportation sector. It also becomes important to shift from traditional houses to smart houses and from classical vehicles to EVs or HEVs. It is needed to combine renewable energy sources (RESs) such as solar photovoltaics, wind energy systems, and various forms of bio-energies. Among various HEV technologies, an effective battery management system (BMS) still remains a crucial issue that is majorly used for indicating the battery state of charge (SOC). Since over-charging and over-discharging result in inevitable impairment to the batteries, accurate SOC estimation desires to be presented by the BMS. Although several SOC estimation techniques exist to regulate the SOC of the battery cell, it is needed to improvise the SOC estimation performance on HEVs. In this view, this paper focuses on the design of a novel deep learning (DL) with SOC estimation model for secure renewable energy management (DLSOC-REM) technique for HEVs. The presented model employs a hybrid convolution neural network and long short-term memory (HCNN-LSTM) model for the accurate estimation of SOC. In order to improve the SOC estimation outcomes of the HCNN-LSTM model, the barnacles mating optimizer (BMO) is applied for the hyperpower tuning process. The utilization of the HCNN-LSTM model makes the modeling process easier and offers a precise depiction of the input–output relationship of the battery model. The design of BMO based HCNN-LSTM model for SOC estimation shows the novelty of the work. An extensive experimental analysis highlighted the supremacy of the proposed model over other existing methods in terms of different aspects. Full article
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18 pages, 294 KiB  
Article
An Improved Modification of Accelerated Double Direction and Double Step-Size Optimization Schemes
by Milena J. Petrović, Dragana Valjarević, Dejan Ilić, Aleksandar Valjarević and Julija Mladenović
Mathematics 2022, 10(2), 259; https://doi.org/10.3390/math10020259 - 15 Jan 2022
Cited by 4 | Viewed by 1051
Abstract
We propose an improved variant of the accelerated gradient optimization models for solving unconstrained minimization problems. Merging the positive features of either double direction, as well as double step size accelerated gradient models, we define an iterative method of a simpler form which [...] Read more.
We propose an improved variant of the accelerated gradient optimization models for solving unconstrained minimization problems. Merging the positive features of either double direction, as well as double step size accelerated gradient models, we define an iterative method of a simpler form which is generally more effective. Performed convergence analysis shows that the defined iterative method is at least linearly convergent for uniformly convex and strictly convex functions. Numerical test results confirm the efficiency of the developed model regarding the CPU time, the number of iterations and the number of function evaluations metrics. Full article
25 pages, 383 KiB  
Article
Calculating Complete Lists of Belyi Pairs
by Nikolai M. Adrianov and George B. Shabat
Mathematics 2022, 10(2), 258; https://doi.org/10.3390/math10020258 - 15 Jan 2022
Cited by 1 | Viewed by 1456
Abstract
Belyi pairs constitute an important element of the program developed by Alexander Grothendieck in 1972–1984. This program related seemingly distant domains of mathematics; in the case of Belyi pairs, such domains are two-dimensional combinatorial topology and one-dimensional arithmetic geometry. The paper contains an [...] Read more.
Belyi pairs constitute an important element of the program developed by Alexander Grothendieck in 1972–1984. This program related seemingly distant domains of mathematics; in the case of Belyi pairs, such domains are two-dimensional combinatorial topology and one-dimensional arithmetic geometry. The paper contains an account of some computer-assisted calculations of Belyi pairs with fixed discrete invariants. We present three complete lists of polynomial-like Belyi pairs: (1) of genus 2 and (minimal possible) degree 5; (2) clean ones of genus 1 and degree 8; and (3) clean ones of genus 2 and degree 8. The explanation of some phenomena we encounter in these calculations will hopefully stimulate further development of the dessins d’enfants theory. Full article
(This article belongs to the Special Issue Combinatorial Algebra, Computation, and Logic)
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