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Mathematics
Volume 10
Issue 17
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Mathematics, Volume 10, Issue 17 (September-1 2022) – 190 articles

Cover Story (view full-size image): We establish several new functional bounds and uniform bounds (with respect to the variable) for the lower incomplete generalized Fox–Wright functions by means of the representation formulae for the McKay Iv Bessel probability distribution’s cumulative distribution function. New cumulative distribution functions are generated and expressed in terms of lower incomplete Fox–Wright functions and/or generalized hypergeometric functions, whilst in the closing part of the article, related bounding inequalities are obtained for them. View this paper
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13 pages, 791 KiB  
Article
NFTs and Cryptocurrencies—The Metamorphosis of the Economy under the Sign of Blockchain: A Time Series Approach
by Simona Andreea Apostu, Mirela Panait, Làszló Vasa, Constanta Mihaescu and Zbyslaw Dobrowolski
Mathematics 2022, 10(17), 3218; https://doi.org/10.3390/math10173218 - 5 Sep 2022
Cited by 18 | Viewed by 6159
Abstract
Although NFTs (non-fungible tokens) and cryptocurrencies are active on the same market, their prices are not so closely related over time. The objective of this paper is to identify the relationship between the two types of assets (NFTs and the cryptocurrencies Ethereum, Crypto [...] Read more.
Although NFTs (non-fungible tokens) and cryptocurrencies are active on the same market, their prices are not so closely related over time. The objective of this paper is to identify the relationship between the two types of assets (NFTs and the cryptocurrencies Ethereum, Crypto Coin, and Bitcoin), using data for the period between September 2020 until February 2022. The conclusions of the study are useful for cryptocurrency and NFT issuers, but also for investors on the financial market who are reconfiguring their portfolios with increasing frequency, and use these new assets for speculative or hedging purposes based on blockchain technology. The results highlighted relationships between NFTs and Ethereum, between Ethereum and Crypto Coin, and between Bitcoin and Ethereum, Ethereum being a bridge between all four. Therefore, NFTs present a relationship with Ethereum, the NFTs price had a causal effect on the price of Ethereum. Full article
(This article belongs to the Special Issue Uncertainty Quantification Techniques in Statistics, Machine Learning and FinTech)
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25 pages, 841 KiB  
Article
An Efficient Zero-Knowledge Dual Membership Proof Supporting Pos-and-Neg Membership Decision
by Hongjian Yin, E Chen, Yan Zhu, Rongquan Feng and Stephen S. Yau
Mathematics 2022, 10(17), 3217; https://doi.org/10.3390/math10173217 - 5 Sep 2022
Cited by 3 | Viewed by 1795
Abstract
In this paper, we address the problem of secure decision of membership. We present a Zero-Knowledge Dual Membership Proof (ZKDMP) protocol, which can support positive and negative (Pos-and-Neg) membership decisions simultaneously. To do it, two secure aggregation functions are used to compact an [...] Read more.
In this paper, we address the problem of secure decision of membership. We present a Zero-Knowledge Dual Membership Proof (ZKDMP) protocol, which can support positive and negative (Pos-and-Neg) membership decisions simultaneously. To do it, two secure aggregation functions are used to compact an arbitrarily-sized subset into an element in a cryptographic space. By using these aggregation functions, a subset can achieve a secure representation, and the representation size of the subsets is reduced to the theoretical lower limit. Moreover, the zeros-based and poles-based secure representation of the subset are used to decide Pos-and-Neg membership, respectively. We further verify the feasibility of combining these two secure representations of the subset, so this result is used to construct our dual membership decision cryptosystem. Specifically, our ZKDMP protocol is proposed for dual membership decisions, which can realize a cryptographic proof of strict Pos-and-Neg membership simultaneously. Furthermore, the zero-knowledge property of our construction ensures that the information of the tested element will not be leaked during the implementation of the protocol. In addition, we provide detailed security proof of our ZKDMP protocol, including positive completeness, negative completeness, soundness and zero-knowledge. Full article
(This article belongs to the Section Mathematics and Computer Science)
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3 pages, 156 KiB  
Editorial
Fuzzy Logic and Soft Computing—Dedicated to the Centenary of the Birth of Lotfi A. Zadeh (1921–2017)
by Sorin Nădăban
Mathematics 2022, 10(17), 3216; https://doi.org/10.3390/math10173216 - 5 Sep 2022
Cited by 5 | Viewed by 1297
Abstract
In 1965, Lotfi A. Zadeh published “Fuzzy Sets”, his pioneering and controversialpaper, which has now reached over 115,000 citations [...] Full article
(This article belongs to the Special Issue Fuzzy Logic and Soft Computing – Dedicated to the Centenary of the Birth of Lotfi A. Zadeh (1921-2017))
21 pages, 1466 KiB  
Article
Deployment of the Microeconomic Consumer Theory in the Artificial Neural Networks Modelling: Case of Organic Food Consumption
by Ivan Jajić, Tomislav Herceg and Mirjana Pejić Bach
Mathematics 2022, 10(17), 3215; https://doi.org/10.3390/math10173215 - 5 Sep 2022
Cited by 1 | Viewed by 2138
Abstract
Organic food consumption has become a significant trend in consumer behaviour, determined by various motives, among which the price does not play a major role, thus reflecting the Lancaster approach to the microeconomic consumer theory. Additionally, artificial neural networks (ANNs) have proven to [...] Read more.
Organic food consumption has become a significant trend in consumer behaviour, determined by various motives, among which the price does not play a major role, thus reflecting the Lancaster approach to the microeconomic consumer theory. Additionally, artificial neural networks (ANNs) have proven to have significant potential in providing accurate and efficient models for predicting consumer behaviour. Considering these two trends, this study aims to deploy the Lancaster approach in the emerging area of artificial intelligence. The paper aims to develop the ANN-based predictive model to investigate the relationship between organic food consumption, demographic characteristics, and health awareness attitudes. Survey research has been conducted on a sample of Croatian inhabitants, and ANN models have been used to assess the importance of various determinants for organic food consumption. A Three-layer Multilayer Perceptron Neural Networks (MLPNN) structure has been constructed and validated to select the optimal number of neurons and transfer functions. One layer is used as the first input, while the other two are hidden layers (the first covers the radially symmetrical input, sigmoid function; the second covers the output, softmax function). Three versions of the testing, training, and holdout data structures were used to develop ANNs. The highest accuracy was achieved with a 7-2-1 partition. The best ANN model was determined as the model that was showing the smallest percent of incorrect predictions in the holdout stage, the second-lowest cross-entropy error, the correct classification rate, and the area under the ROC curve. The research results show that the availability of healthy food shops and consumer awareness of these shops strongly impacts organic food consumption. Using the ANN methodology, this analysis confirmed the validity of the Lancaster approach, stating that the characteristics or attributes of goods are defined by the consumer and not by the product itself. Full article
(This article belongs to the Special Issue Analysis and Mathematical Modeling of Economic - Related Data)
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15 pages, 2990 KiB  
Article
Prediction of Surface Roughness in Turning Applying the Model of Nonlinear Oscillator with Complex Deflection
by Richárd Horváth, Livija Cveticanin and Ivona Ninkov
Mathematics 2022, 10(17), 3214; https://doi.org/10.3390/math10173214 - 5 Sep 2022
Cited by 1 | Viewed by 1602
Abstract
This paper deals with prediction of the roughness of a cutting surface in the turning process, applying the vibration data of the system. A new type of dynamic model for a workpiece-cutting tool system, appropriate for vibration simulation, is developed. The workpiece is [...] Read more.
This paper deals with prediction of the roughness of a cutting surface in the turning process, applying the vibration data of the system. A new type of dynamic model for a workpiece-cutting tool system, appropriate for vibration simulation, is developed. The workpiece is modelled as a mass-spring system with nonlinear elastic property. The cutting tool acts on the workpiece with the cutting force which causes strong in-plane vibration. Based on the experimentally measured values, the cutting force is analytically described as the function of feed ratio and cutting speed. The mathematical model of the vibrating system is a non-homogenous strong nonlinear differential equation with complex function. A new approximate solution for the nonlinear equation is derived and analytic description of vibration is obtained. The solution depends on parameters of the excitation force, velocity of rotation and nonlinear properties of the system. Increasing the feed ratio at a constant velocity of the working piece, the frequency of vibration decreases and the amplitude of vibration increases; increasing the velocity of working piece for constant feed ratio causes an increase of the frequency and a decrease of the amplitude of vibration. Experiments demonstrate that the analytical solution of the nonlinear vibration model in turning process is in direct correlation with the cutting surface roughness. The predicted surface roughness is approximately (1–2) × 10−3 times smaller than the amplitude of vibration of the nonlinear model considered in this paper. Full article
(This article belongs to the Special Issue Analytical Approaches to Nonlinear Dynamical Systems and Applications II)
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13 pages, 283 KiB  
Article
Recovering a Space-Dependent Source Term in the Fractional Diffusion Equation with the Riemann–Liouville Derivative
by Songshu Liu
Mathematics 2022, 10(17), 3213; https://doi.org/10.3390/math10173213 - 5 Sep 2022
Viewed by 1539
Abstract
This research determines an unknown source term in the fractional diffusion equation with the Riemann–Liouville derivative. This problem is ill-posed. Conditional stability for the inverse source problem can be given. Further, a fractional Tikhonov regularization method was applied to regularize the inverse source [...] Read more.
This research determines an unknown source term in the fractional diffusion equation with the Riemann–Liouville derivative. This problem is ill-posed. Conditional stability for the inverse source problem can be given. Further, a fractional Tikhonov regularization method was applied to regularize the inverse source problem. In the theoretical results, we propose a priori and a posteriori regularization parameter choice rules and obtain the convergence estimates. Full article
(This article belongs to the Special Issue Fractional-Order Systems: Control, Modeling and Applications)
20 pages, 643 KiB  
Article
Efficient Ontology Meta-Matching Based on Interpolation Model Assisted Evolutionary Algorithm
by Xingsi Xue, Qi Wu, Miao Ye and Jianhui Lv
Mathematics 2022, 10(17), 3212; https://doi.org/10.3390/math10173212 - 5 Sep 2022
Cited by 3 | Viewed by 1574
Abstract
Ontology is the kernel technique of the Semantic Web (SW), which models the domain knowledge in a formal and machine-understandable way. To ensure different ontologies’ communications, the cutting-edge technology is to determine the heterogeneous entity mappings through the ontology matching process. During this [...] Read more.
Ontology is the kernel technique of the Semantic Web (SW), which models the domain knowledge in a formal and machine-understandable way. To ensure different ontologies’ communications, the cutting-edge technology is to determine the heterogeneous entity mappings through the ontology matching process. During this procedure, it is of utmost importance to integrate different similarity measures to distinguish heterogeneous entity correspondence. The way to find the most appropriate aggregating weights to enhance the ontology alignment’s quality is called ontology meta-matching problem, and recently, Evolutionary Algorithm (EA) has become a great methodology of addressing it. Classic EA-based meta-matching technique evaluates each individual through traversing the reference alignment, which increases the computational complexity and the algorithm’s running time. For overcoming this drawback, an Interpolation Model assisted EA (EA-IM) is proposed, which introduces the IM to predict the fitness value of each newly generated individual. In particular, we first divide the feasible region into several uniform sub-regions using lattice design method, and then precisely evaluate the Interpolating Individuals (INIDs). On this basis, an IM is constructed for each new individual to forecast its fitness value, with the help of its neighborhood. For testing EA-IM’s performance, we use the Ontology Alignment Evaluation Initiative (OAEI) Benchmark in the experiment and the final results show that EA-IM is capable of improving EA’s searching efficiency without sacrificing the solution’s quality, and the alignment’s f-measure values of EA-IM are better than OAEI’s participants. Full article
(This article belongs to the Special Issue Evolutionary Computation for Deep Learning and Machine Learning)
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16 pages, 2036 KiB  
Article
Analysis of Electromagnetic Scattering from Large Arrays of Cylinders via a Hybrid of the Method of Auxiliary Sources (MAS) with the Fast Multipole Method (FMM)
by Eleftherios Mastorakis, Panagiotis J. Papakanellos, Hristos T. Anastassiu and Nikolaos L. Tsitsas
Mathematics 2022, 10(17), 3211; https://doi.org/10.3390/math10173211 - 5 Sep 2022
Cited by 8 | Viewed by 1676
Abstract
The Method of Auxiliary Sources (MAS) is an established technique for the numerical solution of electromagnetic (EM) scattering and radiation problems. This paper presents a hybrid of MAS with the Fast Multipole Method (FMM), which provides a strategy for reducing the computational cost [...] Read more.
The Method of Auxiliary Sources (MAS) is an established technique for the numerical solution of electromagnetic (EM) scattering and radiation problems. This paper presents a hybrid of MAS with the Fast Multipole Method (FMM), which provides a strategy for reducing the computational cost and for solving large-scale problems without notable accuracy loss (and in a reasonable time). The hybrid MAS-FMM scheme is applied to the problem of EM scattering from an arbitrarily large array of lossless/lossy dielectric cylinders. Numerical results are presented to verify the MAS and MAS-FMM schemes, as well as to illuminate the improvements stemming from the proposed hybridization (especially the ones regarding the associated complexity and computational cost). A few concluding remarks offer a summary of this work, along with a list of possible future extensions. Full article
(This article belongs to the Special Issue Analytical Methods in Wave Scattering and Diffraction)
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18 pages, 5569 KiB  
Article
Rain Rendering and Construction of Rain Vehicle Color-24 Dataset
by Mingdi Hu, Chenrui Wang, Jingbing Yang, Yi Wu, Jiulun Fan and Bingyi Jing
Mathematics 2022, 10(17), 3210; https://doi.org/10.3390/math10173210 - 5 Sep 2022
Cited by 9 | Viewed by 2420
Abstract
The fine identification of vehicle color can assist in criminal investigation or intelligent traffic management law enforcement. Since almost all vehicle-color datasets that are used to train models are collected in good weather, the existing vehicle-color recognition algorithms typically show poor performance for [...] Read more.
The fine identification of vehicle color can assist in criminal investigation or intelligent traffic management law enforcement. Since almost all vehicle-color datasets that are used to train models are collected in good weather, the existing vehicle-color recognition algorithms typically show poor performance for outdoor visual tasks. In this paper we construct a new RainVehicleColor-24 dataset by rain-image rendering using PS technology and a SyRaGAN algorithm based on the VehicleColor-24 dataset. The dataset contains a total of 40,300 rain images with 125 different rain patterns, which can be used to train deep neural networks for specific vehicle-color recognition tasks. Experiments show that the vehicle-color recognition algorithms trained on the new dataset RainVehicleColor-24 improve accuracy to around 72% and 90% on rainy and sunny days, respectively. The code is available at [email protected]. Full article
(This article belongs to the Special Issue Advances in Pattern Recognition and Image Analysis)
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26 pages, 377 KiB  
Article
Preimage Problem Inspired by the F-Transform
by Jiří Janeček and Irina Perfilieva
Mathematics 2022, 10(17), 3209; https://doi.org/10.3390/math10173209 - 5 Sep 2022
Cited by 4 | Viewed by 1966
Abstract
In this article, we focus on discrete data processing. We propose to use the concept of closeness, which is less restrictive than a metric, to describe a certain relationship between objects. We establish a fuzzy partition of a given set of objects in [...] Read more.
In this article, we focus on discrete data processing. We propose to use the concept of closeness, which is less restrictive than a metric, to describe a certain relationship between objects. We establish a fuzzy partition of a given set of objects in a way that admits a closeness space to emerge. The fuzzy (F-) transform is a tool that maps objects with common characteristics to the same discrete image—the direct F-transform. We are interested in the inverse (preimage) problem: How can we describe the class of all functions mapped onto the same direct F-transform? In this manuscript, we focus on this preimage problem, formulated accordingly. Its solution is presented from three different points of view and shows which functions belong to the same class determined by a given image (by the direct F-transform). Conditions under which a solution to the preimage problem is given by the inverse F-transform over the same fuzzy partition, or by transforming a given image using a new system of basic functions, are formulated. The developed theory contributes to a better understanding of ill-posed problems that are typical for machine learning. The appendix contains illustrative numerical examples. Full article
(This article belongs to the Special Issue Fuzzy Natural Logic in IFSA-EUSFLAT 2021)
18 pages, 307 KiB  
Article
New Generalized Contractions by Employing Two Control Functions and Coupled Fixed-Point Theorems with Applications
by Hasanen A. Hammad and Mohra Zayed
Mathematics 2022, 10(17), 3208; https://doi.org/10.3390/math10173208 - 5 Sep 2022
Viewed by 1042
Abstract
In this study, we obtain certain coupled fixed-point results for generalized contractions involving two control functions in a controlled metric space. Additionally, we establish some coupled fixed-point results in graph-enabled controlled metric spaces. Many well-known results from the literature will be expanded upon [...] Read more.
In this study, we obtain certain coupled fixed-point results for generalized contractions involving two control functions in a controlled metric space. Additionally, we establish some coupled fixed-point results in graph-enabled controlled metric spaces. Many well-known results from the literature will be expanded upon and modified by our results. In order to demonstrate the validity of the stated results, we also offer some examples. Finally, we apply the theoretical results to obtain the solution to a system of integral equations. Full article
(This article belongs to the Special Issue Mathematical Analysis and Functional Analysis and Their Applications)
22 pages, 834 KiB  
Article
Wave Dispersion Analysis of Functionally Graded GPLs-Reinforced Sandwich Piezoelectromagnetic Plates with a Honeycomb Core
by Mohammed Sobhy and Fatemah H. H. Al Mukahal
Mathematics 2022, 10(17), 3207; https://doi.org/10.3390/math10173207 - 5 Sep 2022
Cited by 13 | Viewed by 1911
Abstract
This paper studies wave propagation in a new structure composed of three layers. The upper and lower layers are made of a piezoelectromagnetic material reinforced with graphene platelets (GPLs) that may be uniformly disseminated or continuously varied throughout the thickness of the layers. [...] Read more.
This paper studies wave propagation in a new structure composed of three layers. The upper and lower layers are made of a piezoelectromagnetic material reinforced with graphene platelets (GPLs) that may be uniformly disseminated or continuously varied throughout the thickness of the layers. To produce a lighter plate, the core layer is assumed to comprise honeycomb structures. The smart nanocomposite plate is exposed to external electric and magnetic potentials. The effective elastic modulus of the face layers of the sandwich plate is evaluated based on Halpin-Tsai model. Whereas, the mixture rule is utilized to calculate mass density, Poisson’s ratio and electric and magnetic properties of both upper and lower layers of the sandwich plate. The governing motion equations of the lightweight sandwich plate are obtained by refined higher-order shear deformation plate theory and Hamilton’s principle. These equations are solved analytically to obtain wave dispersion relations. Impacts of the geometry of plates, GPLs weight fraction, GPLs distribution patterns, piezoelectric properties, external electric voltage and external magnetic potential on the wave frequency and phase velocity of the GPLs lightweight plates are discussed in detail. Full article
(This article belongs to the Section Engineering Mathematics)
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25 pages, 13123 KiB  
Article
A Study of Learning Issues in Feedforward Neural Networks
by Adrian Teso-Fz-Betoño, Ekaitz Zulueta, Mireya Cabezas-Olivenza, Daniel Teso-Fz-Betoño and Unai Fernandez-Gamiz
Mathematics 2022, 10(17), 3206; https://doi.org/10.3390/math10173206 - 5 Sep 2022
Cited by 2 | Viewed by 2420
Abstract
When training a feedforward stochastic gradient descendent trained neural network, there is a possibility of not learning a batch of patterns correctly that causes the network to fail in the predictions in the areas adjacent to those patterns. This problem has usually been [...] Read more.
When training a feedforward stochastic gradient descendent trained neural network, there is a possibility of not learning a batch of patterns correctly that causes the network to fail in the predictions in the areas adjacent to those patterns. This problem has usually been resolved by directly adding more complexity to the network, normally by increasing the number of learning layers, which means it will be heavier to run on the workstation. In this paper, the properties and the effect of the patterns on the network are analysed and two main reasons why the patterns are not learned correctly are distinguished: the disappearance of the Jacobian gradient on the processing layers of the network and the opposite direction of the gradient of those patterns. A simplified experiment has been carried out on a simple neural network and the errors appearing during and after training have been monitored. Taking into account the data obtained, the initial hypothesis of causes seems to be correct. Finally, some corrections to the network are proposed with the aim of solving those training issues and to be able to offer a sufficiently correct prediction, in order to increase the complexity of the network as little as possible. Full article
(This article belongs to the Section Network Science)
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18 pages, 8091 KiB  
Article
Pollutant Migration Pattern during Open-Pit Rock Blasting Based on Digital Image Analysis Technology
by Jiangjiang Yin, Jianyou Lu, Fuchao Tian and Shaofeng Wang
Mathematics 2022, 10(17), 3205; https://doi.org/10.3390/math10173205 - 5 Sep 2022
Cited by 7 | Viewed by 2422
Abstract
Previous studies have revealed that toxic gases and dust (smoke dust) are the most common pollutants generated by the blasting operations in open-pit mines, which might lead to a threat to the environment’s condition, health and safety, and properties protection around the blasting [...] Read more.
Previous studies have revealed that toxic gases and dust (smoke dust) are the most common pollutants generated by the blasting operations in open-pit mines, which might lead to a threat to the environment’s condition, health and safety, and properties protection around the blasting site. In order to deal with the problems, a pollution evaluation system was established based on the fractal dimension theory (Dbox(P)) and grayscale average algorithm (Ga) in digital image-processing technology to recognize and analyze the distributions of the smoke-dust cloud, and subsequently determine the pollution degrees. The computation processes of Dbox(P) and Ga indicate three fitted correlations between the parameters and diffusion time of smoke dust. Then, a pollution index (Pi) is put forward to integrate the global and local features of Dbox(P) and Ga, and develop a hazard classification mechanism for the blasting pollutants. Results obviously denote three diffusion stages of the pollutants, mainly including generation stage, cloud-formation stage, and diffusion stage. In addition, it has been validated that the proposed system can also be utilized in single-point areas within a whole digital image. Besides, there are variation trends of the thresholds T1 and T2 in binarization with the diffusion of pollutants. With this identification and evaluation system, the pollution condition of smoke dust can be obviously determined and analyzed. Full article
(This article belongs to the Special Issue Mathematical Problems in Rock Mechanics and Rock Engineering)
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15 pages, 466 KiB  
Article
Lie Symmetry Classification and Qualitative Analysis for the Fourth-Order Schrödinger Equation
by Andronikos Paliathanasis, Genly Leon and Peter G. L. Leach
Mathematics 2022, 10(17), 3204; https://doi.org/10.3390/math10173204 - 5 Sep 2022
Cited by 1 | Viewed by 1442
Abstract
The Lie symmetry analysis for the study of a 1+n fourth-order Schrödinger equation inspired by the modification of the deformation algebra in the presence of a minimum length is applied. Specifically, we perform a detailed classification for the scalar field potential [...] Read more.
The Lie symmetry analysis for the study of a 1+n fourth-order Schrödinger equation inspired by the modification of the deformation algebra in the presence of a minimum length is applied. Specifically, we perform a detailed classification for the scalar field potential function where non-trivial Lie symmetries exist and simplify the Schrödinger equation. Then, a qualitative analysis allows for the reduced ordinary differential equation to be analysed to understand the asymptotic dynamics. Full article
(This article belongs to the Special Issue Mathematical Modeling and Simulation in Mechanics and Dynamic Systems, 2nd Edition)
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30 pages, 611 KiB  
Review
Semantic Protocol and Resource Description Framework Query Language: A Comprehensive Review
by Essam H. Houssein, Nahed Ibrahem, Alaa M. Zaki and Awny Sayed
Mathematics 2022, 10(17), 3203; https://doi.org/10.3390/math10173203 - 5 Sep 2022
Cited by 5 | Viewed by 2492
Abstract
This review presents various perspectives on converting user keywords into a formal query. Without understanding the dataset’s underlying structure, how can a user input a text-based query and then convert this text into semantic protocol and resource description framework query language (SPARQL) that [...] Read more.
This review presents various perspectives on converting user keywords into a formal query. Without understanding the dataset’s underlying structure, how can a user input a text-based query and then convert this text into semantic protocol and resource description framework query language (SPARQL) that deals with the resource description framework (RDF) knowledge base? The user may not know the structure and syntax of SPARQL, a formal query language and a sophisticated tool for the semantic web (SEW) and its vast and growing collection of interconnected open data repositories. As a result, this study examines various strategies for turning natural language into formal queries, their workings, and their results. In an Internet search engine from a single query, such as on Google, numerous matching documents are returned, with several related to the inquiry while others are not. Since a considerable percentage of the information retrieved is likely unrelated, sophisticated information retrieval systems based on SEW technologies, such as RDF and web ontology language (OWL), can help end users organize vast amounts of data to address this issue. This study reviews this research field and discusses two different approaches to show how users with no knowledge of the syntax of semantic web technologies deal with queries. Full article
(This article belongs to the Section Mathematics and Computer Science)
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17 pages, 6412 KiB  
Article
Research on b Value Estimation Based on Apparent Amplitude-Frequency Distribution in Rock Acoustic Emission Tests
by Daolong Chen, Changgen Xia, Huini Liu, Xiling Liu and Kun Du
Mathematics 2022, 10(17), 3202; https://doi.org/10.3390/math10173202 - 5 Sep 2022
Cited by 11 | Viewed by 2270
Abstract
The rock acoustic emission (AE) technique has often been used to study rock destruction properties and has also been considered an important measure for simulating earthquake foreshock sequences. Among them, the AE b value is an essential parameter for the size distribution characteristics [...] Read more.
The rock acoustic emission (AE) technique has often been used to study rock destruction properties and has also been considered an important measure for simulating earthquake foreshock sequences. Among them, the AE b value is an essential parameter for the size distribution characteristics and probabilistic hazard analysis of rock fractures. Variations in b values obtained in rock AE tests and earthquakes are often compared to establish analogies in the damage process and precursory analysis. Nevertheless, because the amplitudes measured on the sample boundary by an acoustic sensor (apparent amplitude) are often used to estimate the b value, which cannot descript the source size distribution, it is necessary to develop a method to obtain the size distribution characteristics of the real source from the apparent amplitude in doubly truncated distribution. In this study, we obtain AE apparent amplitudes by applying an attenuation operator to source amplitudes generated by a computer with an underlying exponential distribution and then use these simulated apparent amplitudes to perform a comparative analysis of various b value estimation methods that are used in earthquakes and propose an optimal b value estimation procedure for rock AE tests through apparent amplitudes. To further verify the reliability of the newly proposed procedure, a b value characteristics analysis was carried out on a non-explosive expansion agent rock AE test and transparent refractive index experiment with red sandstone, marble, granite, and limestone. The results indicate that mineral grains of different sizes and compositions and different types of discontinuities of rock specimens determine the rock fracture characteristics, as well as the b value. The dynamic b values decreased linearly during the loading process, which confirms that variations in the b value also depend on the stress. These results indicate that the newly proposed procedure for estimating the b value in rock AE tests based on apparent amplitudes has high reliability. Full article
(This article belongs to the Special Issue Mathematical Problems in Rock Mechanics and Rock Engineering)
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14 pages, 3898 KiB  
Article
Analysis of Jet Wall Flow and Heat Transfer Conveying ZnO-SAE50 Nano Lubricants Saturated in Darcy-Brinkman Porous Medium
by Umair Khan, Aurang Zaib, Anuar Ishak, Iskandar Waini, El-Sayed M. Sherif and Ioan Pop
Mathematics 2022, 10(17), 3201; https://doi.org/10.3390/math10173201 - 5 Sep 2022
Cited by 6 | Viewed by 1553
Abstract
The problem of 2D (two-dimensional) wall jet flow, along with heat transfer incorporated by nanofluid in a Darcy-Brinkman medium, while recognizing the requirement for efficient heating and cooling systems. Following the use of similarity variables, the resultant system of ODEs (ordinary differential equations) [...] Read more.
The problem of 2D (two-dimensional) wall jet flow, along with heat transfer incorporated by nanofluid in a Darcy-Brinkman medium, while recognizing the requirement for efficient heating and cooling systems. Following the use of similarity variables, the resultant system of ODEs (ordinary differential equations) is solved using the well-known and efficient bvp4c (boundary-value problem of the 4th order) technique. The significance of physical quantities for the under-consideration parameters is illustrated and explained. The findings show that the nanoparticle volume fraction and porosity parameters decrease the velocity, but increase the temperature. In addition, the temperature uplifts in the presence of radiation effect. The suction parameter initially decreases and then increases the velocity near the surface, while the temperature declines. Full article
(This article belongs to the Special Issue Recent Advances in Numerical Methods for Scientific and Engineering Applications)
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12 pages, 977 KiB  
Article
Generalized Johnson Distributions and Risk Functionals
by Christos Floros, Konstantinos Gkillas and Christos Kountzakis
Mathematics 2022, 10(17), 3200; https://doi.org/10.3390/math10173200 - 5 Sep 2022
Cited by 1 | Viewed by 1567
Abstract
In this paper, we study the generalized Johnson distributions’ class and its applications in finance and risk theory. The recent literature on Johnson distributions displays a better gooodness of fitting for data coming from financial markets, such as portfolio returns. However, a gereral [...] Read more.
In this paper, we study the generalized Johnson distributions’ class and its applications in finance and risk theory. The recent literature on Johnson distributions displays a better gooodness of fitting for data coming from financial markets, such as portfolio returns. However, a gereral question in risk theory and finance is the following: Which class of distributions is more appropriate in order to determine the behaviour of data coming from financial markets and insurance claims? Another question is the following one: Is ther any class of distributions that is appropriate for calculations related to any kind of risk faced by financial isntitutions and insurance companies? The answer proposed to these questions is the use of generalized Johnson’s distributions. The parameters of such distributions are estimated by the order statistics of a single or more samples. Risk functionals represent a unified approach comprising every kind of risk metric. Risk functionals include value-at-risk and expected shortfall, coherent risk measures, and endpoints and thresholds. We deduce that the risk functionals sastisfy convexity—like properties with respect to finitely-mixed distributions. We also prove in detail that the empirical distribution is a reasonable way for the estimation of the above risk functionals. In the Appendix, we provide two numerical examples for fitting samples of portfolio returns under the Johnson’s transformation. Full article
(This article belongs to the Special Issue Advances in Financial Modeling)
33 pages, 906 KiB  
Review
Role of Artificial Intelligence for Analysis of COVID-19 Vaccination-Related Tweets: Opportunities, Challenges, and Future Trends
by Wajdi Aljedaani, Eysha Saad, Furqan Rustam, Isabel de la Torre Díez and Imran Ashraf
Mathematics 2022, 10(17), 3199; https://doi.org/10.3390/math10173199 - 5 Sep 2022
Cited by 9 | Viewed by 3861
Abstract
Pandemics and infectious diseases are overcome by vaccination, which serves as a preventative measure. Nevertheless, vaccines also raise public concerns; public apprehension and doubts challenge the acceptance of new vaccines. COVID-19 vaccines received a similarly hostile reaction from the public. In addition, misinformation [...] Read more.
Pandemics and infectious diseases are overcome by vaccination, which serves as a preventative measure. Nevertheless, vaccines also raise public concerns; public apprehension and doubts challenge the acceptance of new vaccines. COVID-19 vaccines received a similarly hostile reaction from the public. In addition, misinformation from social media, contradictory comments from medical experts, and reports of worse reactions led to negative COVID-19 vaccine perceptions. Many researchers analyzed people’s varying sentiments regarding the COVID-19 vaccine using artificial intelligence (AI) approaches. This study is the first attempt to review the role of AI approaches in COVID-19 vaccination-related sentiment analysis. For this purpose, insights from publications are gathered that analyze the (a) approaches used to develop sentiment analysis tools, (b) major sources of data, (c) available data sources, and (d) the public perception of COVID-19 vaccine. Analysis suggests that public perception-related COVID-19 tweets are predominantly analyzed using TextBlob. Moreover, to a large extent, researchers have employed the Latent Dirichlet Allocation model for topic modeling of Twitter data. Another pertinent discovery made in our study is the variation in people’s sentiments regarding the COVID-19 vaccine across different regions. We anticipate that our systematic review will serve as an all-in-one source for the research community in determining the right technique and data source for their requirements. Our findings also provide insight into the research community to assist them in their future work in the current domain. Full article
(This article belongs to the Special Issue Computational Intelligence and Machine Learning in Bioinformatics)
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17 pages, 578 KiB  
Article
A New Regression Model on the Unit Interval: Properties, Estimation, and Application
by Yury R. Benites, Vicente G. Cancho, Edwin M. M. Ortega, Roberto Vila and Gauss M. Cordeiro
Mathematics 2022, 10(17), 3198; https://doi.org/10.3390/math10173198 - 4 Sep 2022
Cited by 1 | Viewed by 1762
Abstract
A new and flexible distribution is introduced for modeling proportional data based on the quantile of the generalized extreme value distribution. We obtain explicit expressions for the moments, quantiles, and other structural properties. An extended regression model is constructed as an alternative to [...] Read more.
A new and flexible distribution is introduced for modeling proportional data based on the quantile of the generalized extreme value distribution. We obtain explicit expressions for the moments, quantiles, and other structural properties. An extended regression model is constructed as an alternative to compete with the beta regression. Some simulations from the Bayesian perspectives are developed, and an illustrative application to real data involving the comparison of models and influence diagnostics is also addressed. Full article
(This article belongs to the Section Probability and Statistics)
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18 pages, 537 KiB  
Article
Dispersive Optical Solitons to Stochastic Resonant NLSE with Both Spatio-Temporal and Inter-Modal Dispersions Having Multiplicative White Noise
by Elsayed M. E. Zayed, Mohamed E. M. Alngar and Reham M. A. Shohib
Mathematics 2022, 10(17), 3197; https://doi.org/10.3390/math10173197 - 4 Sep 2022
Cited by 31 | Viewed by 1661
Abstract
The current article studies optical solitons solutions for the dimensionless form of the stochastic resonant nonlinear Schrödinger equation (NLSE) with both spatio-temporal dispersion (STD) and inter-modal dispersion (IMD) having multiplicative noise in the itô sense. We will discuss seven laws of nonlinearities, namely, [...] Read more.
The current article studies optical solitons solutions for the dimensionless form of the stochastic resonant nonlinear Schrödinger equation (NLSE) with both spatio-temporal dispersion (STD) and inter-modal dispersion (IMD) having multiplicative noise in the itô sense. We will discuss seven laws of nonlinearities, namely, the Kerr law, power law, parabolic law, dual-power law, quadratic–cubic law, polynomial law, and triple-power law. The new auxiliary equation method is investigated. We secure the bright, dark, and singular soliton solutions for the model. Full article
(This article belongs to the Section Engineering Mathematics)
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16 pages, 306 KiB  
Article
A Unified Local-Semilocal Convergence Analysis of Efficient Higher Order Iterative Methods in Banach Spaces
by Janak Raj Sharma, Harmandeep Singh and Ioannis K. Argyros
Mathematics 2022, 10(17), 3196; https://doi.org/10.3390/math10173196 - 4 Sep 2022
Cited by 1 | Viewed by 1192
Abstract
To deal with the estimation of the locally unique solutions of nonlinear systems in Banach spaces, the local as well as semilocal convergence analysis is established for two higher order iterative methods. The given methods do not involve the computation of derivatives of [...] Read more.
To deal with the estimation of the locally unique solutions of nonlinear systems in Banach spaces, the local as well as semilocal convergence analysis is established for two higher order iterative methods. The given methods do not involve the computation of derivatives of an order higher than one. However, the convergence analysis was carried out in earlier studies by using the assumptions on the higher order derivatives as well. Such types of assumptions limit the applicability of techniques. In this regard, the convergence analysis is developed in the present study by imposing the conditions on first order derivatives only. The central idea for the local analysis is to estimate the bounds on convergence domain as well as the error approximations of the iterates along with the formulation of sufficient conditions for the uniqueness of the solution. Based on the choice of initial estimate in the given domain, the semilocal analysis is established, which ensures the convergence of iterates to a unique solution in that domain. Further, some applied problems are tested to certify the theoretical deductions. Full article
21 pages, 826 KiB  
Article
BlockCrime: Blockchain and Deep Learning-Based Collaborative Intelligence Framework to Detect Malicious Activities for Public Safety
by Dev Patel, Harshil Sanghvi, Nilesh Kumar Jadav, Rajesh Gupta, Sudeep Tanwar, Bogdan Cristian Florea, Dragos Daniel Taralunga, Ahmed Altameem, Torki Altameem and Ravi Sharma
Mathematics 2022, 10(17), 3195; https://doi.org/10.3390/math10173195 - 4 Sep 2022
Cited by 7 | Viewed by 2805
Abstract
Detecting malicious activity in advance has become increasingly important for public safety, economic stability, and national security. However, the disparity in living standards incites the minds of certain undesirable members of society to commit crimes, which may disrupt society’s stability and mental calm. [...] Read more.
Detecting malicious activity in advance has become increasingly important for public safety, economic stability, and national security. However, the disparity in living standards incites the minds of certain undesirable members of society to commit crimes, which may disrupt society’s stability and mental calm. Breakthroughs in deep learning (DL) make it feasible to address such challenges and construct a complete intelligent framework that automatically detects such malicious behaviors. Motivated by this, we propose a convolutional neural network (CNN)-based Xception model, i.e., BlockCrime, to detect crimes and improve public safety. Furthermore, we integrate blockchain technology to securely store the detected crime scene locations and alert the nearest law enforcement authorities. Due to the scarcity of the dataset, transfer learning has been preferred, in which a CNN-based Xception model is used. The redesigned Xception architecture is evaluated against various assessment measures, including accuracy, F1 score, precision, and recall, where it outperforms existing CNN architectures in terms of train accuracy, i.e., 96.57%. Full article
(This article belongs to the Special Issue Blockchain Technology Applied in Accounting)
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30 pages, 3178 KiB  
Article
Short Tasks for Scaffolding Computational Thinking by the Global Bebras Challenge
by Valentina Dagiene and Vladimiras Dolgopolovas
Mathematics 2022, 10(17), 3194; https://doi.org/10.3390/math10173194 - 4 Sep 2022
Cited by 10 | Viewed by 4739
Abstract
The short task methodology enhances the Bebras constructive environment, and provides an emotional context that triggers the convolution of initially biased mental models and corresponding emotional reactions into an unbiased set of conceptual models for informatics education. This provides the motivation of our [...] Read more.
The short task methodology enhances the Bebras constructive environment, and provides an emotional context that triggers the convolution of initially biased mental models and corresponding emotional reactions into an unbiased set of conceptual models for informatics education. This provides the motivation of our research–to explore the process of pedagogical design of short informatics concept-based tasks from the standpoint of mindset formation, which allows one to build conceptual models for CT education. The aim of the research is to gain a conceptual understanding of what a short task is in the context of the global Bebras Challenge initiative. We explore the principles which should underlie the pedagogical design of short tasks for informatics education that scaffold CT. Exploration of a number of practical examples of the Bebras short tasks is the background of our research methodology. The results include an analysis of the structure of short tasks, focusing on the interaction of mental models, conceptual models, and heuristics inherent in the task design. The discussion provides a comprehensive insight into the issues of the short tasks in relation to CT and the Bebras environment. We conclude with recommendations for organizing an effective pedagogical design of a short task. Full article
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16 pages, 1980 KiB  
Article
Numerical Simulation of Single Droplet Impingement upon Dynamic Liquid Film Obliquely
by Shanshan Yang, Quanyuan Zeng, Xiaohua Zhang, Chunzhu Dong and Ling Guan
Mathematics 2022, 10(17), 3193; https://doi.org/10.3390/math10173193 - 4 Sep 2022
Cited by 4 | Viewed by 1701
Abstract
To better understand the application of droplet impingement in industry and agriculture, in this paper, the coupled level set and volume of fluid (CLSVOF) method is applied to study droplet oblique impact on a dynamic liquid [...] Read more.
To better understand the application of droplet impingement in industry and agriculture, in this paper, the coupled level set and volume of fluid (CLSVOF) method is applied to study droplet oblique impact on a dynamic liquid film. The conclusions are the following: the downstream crown height increases and then decreases as the impact angle increases, whereas upstream crown height and spreading length decrease significantly; moreover, the spreading length and upstream crown height increase with the increase of film velocity, while the downstream crown height decreases instead. The increase of gas density inhibits both upstream and downstream crowns. When the fluid viscosity decreases or the impact velocity increases, the crown height increases significantly, which easily leads to crown rupture or droplet splash. The increase in impact velocity leads to an increase in spreading length; however, viscosity has almost no effect on the spreading length. Full article
(This article belongs to the Special Issue Numerical Methods for Computational Fluid Dynamics)
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22 pages, 1068 KiB  
Article
Analysis of a Non-Discriminating Criterion in Simple Additive Weighting Deep Hierarchy
by Ozan Çakır, İbrahim Gürler and Bora Gündüzyeli
Mathematics 2022, 10(17), 3192; https://doi.org/10.3390/math10173192 - 4 Sep 2022
Cited by 1 | Viewed by 1667
Abstract
In the current account, we present an analysis of a non-discriminating criterion under simple additive weighting synthesis, considering a deep decision hierarchy. A non-discriminating criterion describes a criterion where all decision alternatives under consideration perform equally. We question eliminating such a criterion from [...] Read more.
In the current account, we present an analysis of a non-discriminating criterion under simple additive weighting synthesis, considering a deep decision hierarchy. A non-discriminating criterion describes a criterion where all decision alternatives under consideration perform equally. We question eliminating such a criterion from the decision hierarchy in search of simpler problem representation and computational efficiency. Yet, we prove such an approach may result in order misrepresentations between decision alternatives. This analysis is performed in the form of four research questions that relate to the detection of certain conditions under which such distortions in the order integrity of decision alternatives will occur, calculating the change in their final performances, distinguishing the alternatives whose performances are consistent, and examining the role of the normalization procedure adopted in averting such distortions when the non-discriminating criterion is ignored. Along these lines, this study provides clear inferences which are of interest to researchers and decision makers, using simple additive weighting and similar methods that rely on additive synthesis. Full article
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19 pages, 10943 KiB  
Article
Combined Convective Energy Transmission Performance of Williamson Hybrid Nanofluid over a Cylindrical Shape with Magnetic and Radiation Impressions
by Firas A. Alwawi, Feras M. Al Faqih, Mohammed Z. Swalmeh and Mohd Asrul Hery Ibrahim
Mathematics 2022, 10(17), 3191; https://doi.org/10.3390/math10173191 - 4 Sep 2022
Cited by 10 | Viewed by 1666
Abstract
This analysis focuses on extending and developing some previous studies of energy transport through nanofluids to include the states of combined convection flow of a Williamson hybrid nanofluid that flows around a cylinder. Mathematical models that simulate the behavior of these upgraded nanofluids [...] Read more.
This analysis focuses on extending and developing some previous studies of energy transport through nanofluids to include the states of combined convection flow of a Williamson hybrid nanofluid that flows around a cylinder. Mathematical models that simulate the behavior of these upgraded nanofluids are constructed by expanding the Tiwari and Das model, which are then solved numerically via Keller box approaches. The accuracy of the results is emphasized by comparing them with the previous published outcomes. Nanosolid volume fraction 0≤χ≤0.1, combined convection −1≤λ≤5, radiation factor 0.1≤R≤6, Weissenberg number 0.2≤We≤ 0.9, and magnetic factor  0.1≤M≤1 are the factors that have been taken into consideration to examine the energy transfer performance of Williamson hybrid nanofluid. Numerical and graphical outcomes are obtained using MATLAB, analyzed, and discussed in depth. According to the outcomes, the Weissenberg number reduces energy transfer and friction forces. Both the combined convective coefficient and the radiation factor improved the rate of energy transfer and increased the velocity of the host fluid. The fluid velocity and rate of energy transfer can be reduced by increasing the magnetic factor. The nanoparticle combination of silver and aluminum oxide (Ag-Al2O3) has demonstrated superiority in enhancing the energy transfer rate and velocity of the host fluid. Full article
(This article belongs to the Special Issue Computational Fluid Dynamics II)
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15 pages, 4056 KiB  
Article
Forecasting the Volatility of Cryptocurrencies in the Presence of COVID-19 with the State Space Model and Kalman Filter
by Shafiqah Azman, Dharini Pathmanathan and Aerambamoorthy Thavaneswaran
Mathematics 2022, 10(17), 3190; https://doi.org/10.3390/math10173190 - 4 Sep 2022
Cited by 1 | Viewed by 2467
Abstract
During the COVID-19 pandemic, cryptocurrency prices showed abnormal volatility that attracted the participation of many investors. Studying the behaviour of volatility for the prices of cryptocurrency is an interesting problem to be investigated. This research implements the state space model framework for volatility [...] Read more.
During the COVID-19 pandemic, cryptocurrency prices showed abnormal volatility that attracted the participation of many investors. Studying the behaviour of volatility for the prices of cryptocurrency is an interesting problem to be investigated. This research implements the state space model framework for volatility incorporating the Kalman filter. This method directly forecasts the conditional volatility of five cryptocurrency prices (Bitcoin (BTC), Ethereum (ETH), Ripple (XRP), Litecoin (LTC) and Bitcoin Cash (BCH)) for 10,000 consecutive hours, i.e., approximately 417 days during the COVID-19 pandemic from 26 February 2020, 00:00 h until 18 April 2021, 00:00 h. The performance of this model is compared to the GARCH (1,1) model and the neural network autoregressive (NNAR) based on root mean square error (RMSE), mean absolute error (MAE) and the volatility plot. The autocorrelation function plot, histogram and the residuals plot are used to examine the model adequacy. Among the three models, the state space model gives the best fit. The state space model gives the narrowest confidence interval of volatility and value-at-risk forecasts among the three models. Full article
(This article belongs to the Special Issue Volatility Models Applied to Geophysics, Financial Market Data and Other Disciplines II)
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14 pages, 310 KiB  
Article
Maximum-Profit Inventory Model with Generalized Deterioration Rate
by Yu-Lan Wang, Ming-Li Chen and Peterson Julian
Mathematics 2022, 10(17), 3189; https://doi.org/10.3390/math10173189 - 3 Sep 2022
Cited by 1 | Viewed by 1359
Abstract
We developed a maximum profit inventory model with a generalized deterioration rate where the selling rate is dependent on the inventory level that is an extension of two published papers. A complete solution structure is provided to decide the optimal solution with reasonable [...] Read more.
We developed a maximum profit inventory model with a generalized deterioration rate where the selling rate is dependent on the inventory level that is an extension of two published papers. A complete solution structure is provided to decide the optimal solution with reasonable conditions supported by numerical examples, and then we prove that the optimal solution is independent of the demand pattern. Numerical examples are provided to illustrate our findings. In a previously published paper, three examples had symmetric conditions to decide the local maximum solution. Our approach provides a reasonable explanation for this symmetric phenomenon. Our findings will help researchers develop new inventory models in the future. Full article
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