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Mathematics
Volume 10
Issue 6
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Mathematics, Volume 10, Issue 6 (March-2 2022) – 159 articles

Cover Story (view full-size image): General fractional integrals and derivatives are a far-reaching generalization of the Riemann–Liouville fractional integral and derivative. They are obtained by replacing the power law kernels of the Riemann–Liouville fractional integral and derivative with more general kernels. For applications, the fractional differential equations of these derivatives are especially important. Yuri Luchko has developed an Mikusinski-type operational calculus for general fractional derivatives and has applied it to derive an explicit form of solutions to Cauchy problems in linear fractional differential equations that can be determined these derivatives. Solutions are provided in form of convolution series that are generated by the kernels of the corresponding general fractional integrals. View this paper
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16 pages, 490 KiB  
Article
A Modified Grey Wolf Optimization Algorithm for an Intrusion Detection System
by Abdullah Alzaqebah, Ibrahim Aljarah, Omar Al-Kadi and Robertas Damaševičius
Mathematics 2022, 10(6), 999; https://doi.org/10.3390/math10060999 - 21 Mar 2022
Cited by 54 | Viewed by 4828
Abstract
Cyber-attacks and unauthorized application usage have increased due to the extensive use of Internet services and applications over computer networks, posing a threat to the service’s availability and consumers’ privacy. A network Intrusion Detection System (IDS) aims to detect aberrant traffic behavior that [...] Read more.
Cyber-attacks and unauthorized application usage have increased due to the extensive use of Internet services and applications over computer networks, posing a threat to the service’s availability and consumers’ privacy. A network Intrusion Detection System (IDS) aims to detect aberrant traffic behavior that firewalls cannot detect. In IDSs, dimension reduction using the feature selection strategy has been shown to be more efficient. By reducing the data dimension and eliminating irrelevant and noisy data, several bio-inspired algorithms have been employed to improve the performance of an IDS. This paper discusses a modified bio-inspired algorithm, which is the Grey Wolf Optimization algorithm (GWO), that enhances the efficacy of the IDS in detecting both normal and anomalous traffic in the network. The main improvements cover the smart initialization phase that combines the filter and wrapper approaches to ensure that the informative features will be included in early iterations. In addition, we adopted a high-speed classification method, the Extreme Learning Machine (ELM), and used the modified GWO to tune the ELM’s parameters. The proposed technique was tested against various meta-heuristic algorithms using the UNSWNB-15 dataset. Because the generic attack is the most common attack type in the dataset, the primary goal of this paper was to detect generic attacks in network traffic. The proposed model outperformed other methods in minimizing the crossover error rate and false positive rate to less than 30%. Furthermore, it obtained the best results with 81%, 78%, and 84% for the accuracy, F1-score, and G-mean measures, respectively. Full article
(This article belongs to the Section Mathematics and Computer Science)
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12 pages, 330 KiB  
Article
Domination Coloring of Graphs
by Yangyang Zhou, Dongyang Zhao, Mingyuan Ma and Jin Xu
Mathematics 2022, 10(6), 998; https://doi.org/10.3390/math10060998 - 21 Mar 2022
Cited by 3 | Viewed by 3465
Abstract
A domination coloring of a graph G is a proper vertex coloring of G, such that each vertex of G dominates at least one color class (possibly its own class), and each color class is dominated by at least one vertex. The [...] Read more.
A domination coloring of a graph G is a proper vertex coloring of G, such that each vertex of G dominates at least one color class (possibly its own class), and each color class is dominated by at least one vertex. The minimum number of colors among all domination colorings is called the domination chromatic number, denoted by χdd(G). In this paper, we study the complexity of the k-domination coloring problem by proving its NP-completeness for arbitrary graphs. We give basic results and properties of χdd(G), including the bounds and characterization results, and further research χdd(G) of some special classes of graphs, such as the split graphs, the generalized Petersen graphs, corona products, and edge corona products. Several results on graphs with χdd(G)=χ(G) are presented. Moreover, an application of domination colorings in social networks is proposed. Full article
(This article belongs to the Special Issue Advances in Discrete Applied Mathematics and Graph Theory)
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22 pages, 1881 KiB  
Article
Meshless Generalized Finite Difference Method for the Propagation of Nonlinear Water Waves under Complex Wave Conditions
by Ji Huang, Chia-Ming Fan, Jiahn-Horng Chen and Jin Yan
Mathematics 2022, 10(6), 1007; https://doi.org/10.3390/math10061007 - 21 Mar 2022
Cited by 7 | Viewed by 2695
Abstract
The propagation of nonlinear water waves under complex wave conditions is the key issue of hydrodynamics both in coastal and ocean engineering, which is significant in the prediction of strongly nonlinear phenomena regarding wave–structure interactions. In the present study, the meshless generalized finite [...] Read more.
The propagation of nonlinear water waves under complex wave conditions is the key issue of hydrodynamics both in coastal and ocean engineering, which is significant in the prediction of strongly nonlinear phenomena regarding wave–structure interactions. In the present study, the meshless generalized finite difference method (GFDM) together with the second-order Runge–Kutta method (RKM2) is employed to construct a fully three-dimensional (3D) meshless numerical wave flume (NWF). Three numerical examples, i.e., the propagation of freak waves, irregular waves and focused waves, are implemented to verify the accuracy and stability of the developed 3D GFDM model. The results show that the present numerical model possesses good performance in the simulation of nonlinear water waves and suggest that the 3D “RKM2-GFDM” meshless scheme can be adopted to further simulate more complex nonlinear problems regarding wave–structure interactions in ocean engineering. Full article
(This article belongs to the Special Issue Numerical Methods for Computational Fluid Dynamics)
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15 pages, 660 KiB  
Article
The Game Model of Blue Carbon Collaboration along MSR—From the Regret Theory Perspective
by Changping Zhao, Maliyamu Sadula, Xiangmeng Huang, Yali Yang, Yu Gong and Shuai Yang
Mathematics 2022, 10(6), 1006; https://doi.org/10.3390/math10061006 - 21 Mar 2022
Cited by 4 | Viewed by 1972
Abstract
Ocean pollution and global warming are two pressing environmental problems exacerbated by human economic behavior. Building a blue carbon cooperation platform along the Maritime Silk Road (MSR) to promote sustainable development of countries along the route is of practical value to solving these [...] Read more.
Ocean pollution and global warming are two pressing environmental problems exacerbated by human economic behavior. Building a blue carbon cooperation platform along the Maritime Silk Road (MSR) to promote sustainable development of countries along the route is of practical value to solving these two problems. Based on the analysis and review of the latest research on blue carbon, cooperative game and MSR, Weber’s law and regret theory are introduced to establish an economic model of blue carbon international cooperation, which proves the economic feasibility of blue carbon cooperation along MSR. The influence of psychological factors on the decision making of blue carbon international cooperation is also discussed. In addition, the measures to promote international cooperation are also discussed according to the current situation of marine blue carbon resources. Full article
(This article belongs to the Special Issue Feature Papers in Complex Networks and Their Applications)
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17 pages, 2063 KiB  
Article
A Blockchain-Empowered Arbitrable Multimedia Data Auditing Scheme in IoT Cloud Computing
by Shenling Wang, Yifang Zhang and Yu Guo
Mathematics 2022, 10(6), 1005; https://doi.org/10.3390/math10061005 - 21 Mar 2022
Cited by 12 | Viewed by 2094
Abstract
As increasing clients tend to outsource massive multimedia data generated by Internet of Things (IoT) devices to the cloud, data auditing is becoming crucial, as it enables clients to verify the integrity of their outsourcing data. However, most existing data auditing schemes cannot [...] Read more.
As increasing clients tend to outsource massive multimedia data generated by Internet of Things (IoT) devices to the cloud, data auditing is becoming crucial, as it enables clients to verify the integrity of their outsourcing data. However, most existing data auditing schemes cannot guarantee 100% data integrity and cannot meet the security requirement of practical multimedia services. Moreover, the lack of fair arbitration leads to clients not receiving compensation in a timely manner when the outsourced data is corrupted by the cloud service provider (CSP). In this work, we propose an arbitrable data auditing scheme based on the blockchain. In our scheme, clients usually only need to conduct private audits, and public auditing by a smart contract is triggered only when verification fails in private auditing. This hybrid auditing design enables clients to save audit fees and receive compensation automatically and in a timely manner when the outsourced data are corrupted by the CSP. In addition, by applying the deterministic checking technique based on a bilinear map accumulator, our scheme can guarantee 100% data integrity. Furthermore, our scheme can prevent fraudulent claims when clients apply for compensation from the CSP. We analyze the security strengths and complete the prototype’s implementation. The experimental results show that our blockchain-based data auditing scheme is secure, efficient, and practical. Full article
(This article belongs to the Special Issue Advanced Mathematical Methods in Intelligent Multimedia: Security and Applications)
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21 pages, 41854 KiB  
Article
Multifractality via Stochasticity in Atmospheric Dynamics Description Validated through Remote Sensing Data
by Dragos-Constantin Nica, Mirela Voiculescu, Daniel-Eduard Constantin, Manuela Gîrțu, Liliana Topliceanu, Decebal Vasincu, Iulian-Alin Roșu and Maricel Agop
Mathematics 2022, 10(6), 1004; https://doi.org/10.3390/math10061004 - 21 Mar 2022
Viewed by 1336
Abstract
In the present paper, correlations between multifractality and stochasticity in atmospheric dynamics are investigated. Starting with two descriptions of atmospheric scenarios, one based on scale relativity theory and another based on stochastic theory, correspondences between parameters and variables belonging to both scenarios are [...] Read more.
In the present paper, correlations between multifractality and stochasticity in atmospheric dynamics are investigated. Starting with two descriptions of atmospheric scenarios, one based on scale relativity theory and another based on stochastic theory, correspondences between parameters and variables belonging to both scenarios are found. In such a context, by replacing an atmospheric conservative passive additive with a non-differentiable component of the atmospheric multifractal velocity, stochastic evolution equations are found for this component, which reveal the multifractal variational transport coefficient and the multifractal molecular diffusion coefficient, along with the multifractal inhomogeneity variation. Furthermore, equations which describe a multifractal Reynolds number and singularity spectrum are also found. Finally, these theoretical results are validated through remote sensing data obtained with the aid of a ceilometer platform. Full article
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17 pages, 1359 KiB  
Article
A Neural Controller for Induction Motors: Fractional-Order Stability Analysis and Online Learning Algorithm
by Mohammad Hosein Sabzalian, Khalid A. Alattas, Fayez F. M. El-Sousy, Ardashir Mohammadzadeh, Saleh Mobayen, Mai The Vu and Mauricio Aredes
Mathematics 2022, 10(6), 1003; https://doi.org/10.3390/math10061003 - 21 Mar 2022
Cited by 5 | Viewed by 1889
Abstract
In this study, an intelligent control scheme is developed for induction motors (IMs). The dynamics of IMs are unknown and are perturbed by the variation of rotor resistance and load changes. The control system has two stages. In the identification stage, the group [...] Read more.
In this study, an intelligent control scheme is developed for induction motors (IMs). The dynamics of IMs are unknown and are perturbed by the variation of rotor resistance and load changes. The control system has two stages. In the identification stage, the group method of data-handling (GMDH) neural network (NN) was designed for online modeling of the IM. In the control stage, the GMDH-NN was applied to compensate for the impacts of disturbances and uncertainties. The stability is shown by the Lyapunov approach. Simulations demonstrated the good accuracy of the suggested new control approach under disturbances and unknown dynamics. Full article
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15 pages, 735 KiB  
Article
Mathematical Modeling of Pricing and Service in the Dual Channel Supply Chain Considering Underservice
by Qingren He, Taiwei Shi and Ping Wang
Mathematics 2022, 10(6), 1002; https://doi.org/10.3390/math10061002 - 21 Mar 2022
Cited by 2 | Viewed by 1583
Abstract
The retailer cannot often identify consumers’ preference for personalized and refined services. This poses a lower service than the consumer expects, which will lead to a decline in consumers’ satisfaction and loyalty. To cope with this problem, we consider a dual-channel supply chain [...] Read more.
The retailer cannot often identify consumers’ preference for personalized and refined services. This poses a lower service than the consumer expects, which will lead to a decline in consumers’ satisfaction and loyalty. To cope with this problem, we consider a dual-channel supply chain composed of a manufacturer who has the online channel and an offline retailer and introduce the concept of underservice into the framework of pricing and service decision. The influence of consumers’ service expectations and the sensitive coefficient of consumers’ perceptive service on optimal decision-making were explored by optimization theory. First, the mathematical model of profit functions of the offline retailer and the manufacturer was developed by taking into account the service expectation respectively. Based on this, the Stackelberg game was adopted to prove that there is a linkage mechanism between the optimal retail price and the optimal service level under certain conditions. Second, we examined the conditions under which underservice occurs and the factors that influence them. Finally, we explored the stability condition under which the offline retailer’s optimal service level is against pricing. Results show that for newly launched products, the offline retailer will take the risk of increased service costs to adopt a strategy of high profit and good sales as a result of underservice. With regard to expiring products, it is impossible for the offline retailer to provide a lower-than-expected service level. Therefore, the offline retailer will adopt a strategy of small profits but quick turnover. In addition, the optimal service level of the offline retailer is stable against the optimal retail price, which greatly simplifies the service decision of the offline retailer, that is, the offline retailer does not need to consider the pricing strategy of the manufacturer and only needs to offer a level of service equal to the consumers’ service expectation. Full article
(This article belongs to the Special Issue Operational Research in Service-oriented Manufacturing)
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20 pages, 4308 KiB  
Article
Adaptive Evolutionary Computation for Nonlinear Hammerstein Control Autoregressive Systems with Key Term Separation Principle
by Faisal Altaf, Ching-Lung Chang, Naveed Ishtiaq Chaudhary, Muhammad Asif Zahoor Raja, Khalid Mehmood Cheema, Chi-Min Shu and Ahmad H. Milyani
Mathematics 2022, 10(6), 1001; https://doi.org/10.3390/math10061001 - 21 Mar 2022
Cited by 16 | Viewed by 1548
Abstract
The knacks of evolutionary and swarm computing paradigms have been exploited to solve complex engineering and applied science problems, including parameter estimation for nonlinear systems. The population-based computational heuristics applied for parameter identification of nonlinear systems estimate the redundant parameters due to an [...] Read more.
The knacks of evolutionary and swarm computing paradigms have been exploited to solve complex engineering and applied science problems, including parameter estimation for nonlinear systems. The population-based computational heuristics applied for parameter identification of nonlinear systems estimate the redundant parameters due to an overparameterization problem. The aim of this study was to exploit the key term separation (KTS) principle-based identification model with adaptive evolutionary computing to overcome the overparameterization issue. The parameter estimation of Hammerstein control autoregressive (HC-AR) systems was conducted through integration of the KTS idea with the global optimization efficacy of genetic algorithms (GAs). The proposed approach effectively estimated the actual parameters of the HC-AR system for noiseless as well as noisy scenarios. The simulation results verified the accuracy, convergence, and robustness of the proposed scheme. While consistent accuracy and reliability of the designed approach was validated through statistical assessments on multiple independent trials. Full article
(This article belongs to the Special Issue Nonlinear Systems: Dynamics, Control, Optimization and Applications to the Science and Engineering)
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24 pages, 825 KiB  
Article
FedGCN: Federated Learning-Based Graph Convolutional Networks for Non-Euclidean Spatial Data
by Kai Hu, Jiasheng Wu, Yaogen Li, Meixia Lu, Liguo Weng and Min Xia
Mathematics 2022, 10(6), 1000; https://doi.org/10.3390/math10061000 - 21 Mar 2022
Cited by 18 | Viewed by 5041
Abstract
Federated Learning (FL) can combine multiple clients for training and keep client data local, which is a good way to protect data privacy. There are many excellent FL algorithms. However, most of these can only process data with regular structures, such as images [...] Read more.
Federated Learning (FL) can combine multiple clients for training and keep client data local, which is a good way to protect data privacy. There are many excellent FL algorithms. However, most of these can only process data with regular structures, such as images and videos. They cannot process non-Euclidean spatial data, that is, irregular data. To address this problem, we propose a Federated Learning-Based Graph Convolutional Network (FedGCN). First, we propose a Graph Convolutional Network (GCN) as a local model of FL. Based on the classical graph convolutional neural network, TopK pooling layers and full connection layers are added to this model to improve the feature extraction ability. Furthermore, to prevent pooling layers from losing information, cross-layer fusion is used in the GCN, giving FL an excellent ability to process non-Euclidean spatial data. Second, in this paper, a federated aggregation algorithm based on an online adjustable attention mechanism is proposed. The trainable parameter ρ is introduced into the attention mechanism. The aggregation method assigns the corresponding attention coefficient to each local model, which reduces the damage caused by the inefficient local model parameters to the global model and improves the fault tolerance and accuracy of the FL algorithm. Finally, we conduct experiments on six non-Euclidean spatial datasets to verify that the proposed algorithm not only has good accuracy but also has a certain degree of generality. The proposed algorithm can also perform well in different graph neural networks. Full article
(This article belongs to the Section Mathematics and Computer Science)
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16 pages, 303 KiB  
Article
Computation and Hypercomputation
by Andrew Powell
Mathematics 2022, 10(6), 997; https://doi.org/10.3390/math10060997 - 20 Mar 2022
Cited by 1 | Viewed by 2177
Abstract
This paper shows some of the differences and similarities between computation and hypercomputation, the similarities relating to the complexity of propositional computation and the differences being the propositions that can be decided computationally or hypercomputationally. The methods used are ordinal Turing machines with [...] Read more.
This paper shows some of the differences and similarities between computation and hypercomputation, the similarities relating to the complexity of propositional computation and the differences being the propositions that can be decided computationally or hypercomputationally. The methods used are ordinal Turing machines with infinitely long programs and diagonalization out of computing complexity classes. The main results are the characterization of inequalities of run time complexities of serial, indeterministic serial and parallel computers and hypercomputers and the specification of a hierarchy of hypercomputers that can hypercompute the truths of all propositions in the standard class model of set theory, the von Neumann hierarchy of pure sets. Full article
(This article belongs to the Special Issue Theory of Algorithms and Recursion Theory)
11 pages, 475 KiB  
Article
Security and Efficiency of Linear Feedback Shift Registers in GF(2n) Using n-Bit Grouped Operations
by Javier Espinosa García, Guillermo Cotrina, Alberto Peinado and Andrés Ortiz
Mathematics 2022, 10(6), 996; https://doi.org/10.3390/math10060996 - 19 Mar 2022
Cited by 4 | Viewed by 2693
Abstract
Many stream ciphers employ linear feedback shift registers (LFSRs) to generate pseudorandom sequences. Many recent LFSRs are defined in GF(2n) to take advantage of the n-bit processors, instead of using the classic binary field. In this way, [...] Read more.
Many stream ciphers employ linear feedback shift registers (LFSRs) to generate pseudorandom sequences. Many recent LFSRs are defined in GF(2n) to take advantage of the n-bit processors, instead of using the classic binary field. In this way, the bit generation rate increases at the expense of a higher complexity in computations. For this reason, only certain primitive polynomials in GF(2n) are used as feedback polynomials in real ciphers. In this article, we present an efficient implementation of the LFSRs defined in GF(2n). The efficiency is achieved by using equivalent binary LFSRs in combination with binary n-bit grouped operations, n being the processor word’s length. This improvement affects the general considerations about the security of cryptographic systems that uses LFSR. The model also allows the development of a faster method to test the primitiveness of polynomials in GF(2n). Full article
(This article belongs to the Special Issue Mathematics Cryptography and Information Security 2021)
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10 pages, 760 KiB  
Article
Nonlinear Differential Equations with Distributed Delay: Some New Oscillatory Solutions
by Barakah Almarri, Ali Hasan Ali, António M. Lopes and Omar Bazighifan
Mathematics 2022, 10(6), 995; https://doi.org/10.3390/math10060995 - 19 Mar 2022
Cited by 29 | Viewed by 1940
Abstract
The oscillation of a class of fourth-order nonlinear damped delay differential equations with distributed deviating arguments is the subject of this research. We propose a new explanation of the fourth-order equation oscillation in terms of the oscillation of a similar well-studied second-order linear [...] Read more.
The oscillation of a class of fourth-order nonlinear damped delay differential equations with distributed deviating arguments is the subject of this research. We propose a new explanation of the fourth-order equation oscillation in terms of the oscillation of a similar well-studied second-order linear differential equation without damping. The extended Riccati transformation, integral averaging approach, and comparison principles are used to provide some additional oscillatory criteria. An example demonstrates the efficacy of the acquired criteria. Full article
(This article belongs to the Special Issue Dynamical Systems and Their Applications (DSTA) — In Memory of Prof. Dr. José A. Tenreiro Machado)
12 pages, 837 KiB  
Article
Mathematical Modeling of Changes in the Dispersed Composition of Solid Phase Particles in Technological Apparatuses of Periodic and Continuous Action
by Oleg M. Flisyuk, Nicolay A. Martsulevich, Valery P. Meshalkin and Alexandr V. Garabadzhiu
Mathematics 2022, 10(6), 994; https://doi.org/10.3390/math10060994 - 19 Mar 2022
Viewed by 1823
Abstract
This article presents a methodological approach to modeling the processes of changing the dispersed composition of solid phase particles, such as granulation, crystallization, pyrolysis, and others. Granulation is considered as a complex process consisting of simpler (elementary) processes such as continuous particle growth, [...] Read more.
This article presents a methodological approach to modeling the processes of changing the dispersed composition of solid phase particles, such as granulation, crystallization, pyrolysis, and others. Granulation is considered as a complex process consisting of simpler (elementary) processes such as continuous particle growth, agglomeration, crushing and abrasion. All these elementary processes, which are also complex in themselves, usually participate in the formation of the dispersed composition of particles and proceed simultaneously with the predominance of one process or another, depending on the method of its organization and the physicochemical properties of substances. A quantitative description of the evolution of the dispersed composition of the solid phase in technological processes in which the particle size does not remain constant is proposed. Considering the stochastic nature of elementary mass transfer events in individual particles, the methods of the theory of probability are applied. The analysis of the change in the dispersed composition is based on the balanced equation of the particle mass distribution function. The equation accounts for all possible physical mechanisms that effect changes in particle size during chemical and technological processes. Examples of solutions to this equation for specific processes of practical importance are provided. The obtained analytical solutions are of independent interest and are in good agreement with the experimental data, which indicates the adequacy of the proposed approach. These solutions can also be used to analyze similar processes. The effectiveness has been confirmed during the analysis and calculation of the processes of granulation of various solutions and disposal of oil-containing waste to obtain a granular mineral additive. Full article
(This article belongs to the Special Issue Application of Mathematics for Modeling Industrial Innovative Systems and Processes)
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22 pages, 3548 KiB  
Review
Statistical Methods with Applications in Data Mining: A Review of the Most Recent Works
by Joaquim Fernando Pinto da Costa and Manuel Cabral
Mathematics 2022, 10(6), 993; https://doi.org/10.3390/math10060993 - 19 Mar 2022
Cited by 9 | Viewed by 4306
Abstract
The importance of statistical methods in finding patterns and trends in otherwise unstructured and complex large sets of data has grown over the past decade, as the amount of data produced keeps growing exponentially and knowledge obtained from understanding data allows to make [...] Read more.
The importance of statistical methods in finding patterns and trends in otherwise unstructured and complex large sets of data has grown over the past decade, as the amount of data produced keeps growing exponentially and knowledge obtained from understanding data allows to make quick and informed decisions that save time and provide a competitive advantage. For this reason, we have seen considerable advances over the past few years in statistical methods in data mining. This paper is a comprehensive and systematic review of these recent developments in the area of data mining. Full article
(This article belongs to the Special Issue Statistical Methods in Data Mining)
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12 pages, 287 KiB  
Article
Random Perturbation of Invariant Manifolds for Non-Autonomous Dynamical Systems
by Tao Jiang, Zhongkai Guo and Xingjie Yan
Mathematics 2022, 10(6), 992; https://doi.org/10.3390/math10060992 - 19 Mar 2022
Viewed by 1413
Abstract
Random invariant manifolds are geometric objects useful for understanding dynamics near the random fixed point under stochastic influences. Under the framework of a dynamical system, we compared perturbed random non-autonomous partial differential equations with original stochastic non-autonomous partial differential equations. Mainly, we derived [...] Read more.
Random invariant manifolds are geometric objects useful for understanding dynamics near the random fixed point under stochastic influences. Under the framework of a dynamical system, we compared perturbed random non-autonomous partial differential equations with original stochastic non-autonomous partial differential equations. Mainly, we derived some pathwise approximation results of random invariant manifolds when the Gaussian white noise was replaced by colored noise, which is a type of Wong–Zakai approximation. Full article
14 pages, 289 KiB  
Article
Continuous Dependence for the Boussinesq Equations under Reaction Boundary Conditions in R2
by Jincheng Shi and Yan Liu
Mathematics 2022, 10(6), 991; https://doi.org/10.3390/math10060991 - 19 Mar 2022
Viewed by 1071
Abstract
In this paper, we studied the continuous dependence result for the Boussinesq equations. We considered the case where Ω was a bounded domain in R2. Temperatures T and C satisfied reaction boundary conditions. A first-order inequality for the differences of energy [...] Read more.
In this paper, we studied the continuous dependence result for the Boussinesq equations. We considered the case where Ω was a bounded domain in R2. Temperatures T and C satisfied reaction boundary conditions. A first-order inequality for the differences of energy could be derived. An integration of this inequality produced a continuous dependence result. The result told us that the continuous dependence type stability was also valid for the Boussinesq coefficient λ of the Boussinesq equations with reaction boundary conditions. Full article
(This article belongs to the Special Issue Applications of Partial Differential Equations in Mathematical Physics, 1st Edition)
12 pages, 255 KiB  
Article
On Statistical and Semi-Weyl Manifolds Admitting Torsion
by Adara M. Blaga and Antonella Nannicini
Mathematics 2022, 10(6), 990; https://doi.org/10.3390/math10060990 - 19 Mar 2022
Cited by 3 | Viewed by 1609
Abstract
We introduce the concept of quasi-semi-Weyl structure, we provide a couple of ways for constructing quasi-statistical and quasi-semi-Weyl structures by means of a pseudo-Riemannian metric, an affine connection and a tensor field on a smooth manifold, and we place these structures in relation [...] Read more.
We introduce the concept of quasi-semi-Weyl structure, we provide a couple of ways for constructing quasi-statistical and quasi-semi-Weyl structures by means of a pseudo-Riemannian metric, an affine connection and a tensor field on a smooth manifold, and we place these structures in relation with one another. Full article
(This article belongs to the Special Issue Geometry of Manifolds and Applications)
24 pages, 4710 KiB  
Article
Description of the Distribution Law and Non-Linear Dynamics of Growth of Comments Number in News and Blogs Based on the Fokker-Planck Equation
by Dmitry Zhukov, Julia Perova and Vladimir Kalinin
Mathematics 2022, 10(6), 989; https://doi.org/10.3390/math10060989 - 19 Mar 2022
Cited by 2 | Viewed by 1824
Abstract
The article considers stationary and dynamic distributions of news by the number of comments. The processing of the observed data showed that static distribution of news by the number of comments relating to that news obeys a power law, and the dynamic distribution [...] Read more.
The article considers stationary and dynamic distributions of news by the number of comments. The processing of the observed data showed that static distribution of news by the number of comments relating to that news obeys a power law, and the dynamic distribution (the change in number of comments over time) in some cases has an S-shaped character, and in some cases a more complex two-stage character. This depends on the time interval between the appearance of a comment at the first level and a comment attached to that comment. The power law for the stationary probability density of news distribution by the number of comments can be obtained from the solution of the stationary Fokker-Planck equation, if a number of assumptions are made in its derivation. In particular, we assume that the drift coefficient μ(x) responsible in the Fokker-Planck equation for a purposeful change in the state of system x (x is the current number of comments on that piece of news) linearly depends on the state x, and the diffusion coefficient D(x) responsible for a random change depends quadratically on x. The solution of the unsteady Fokker-Planck differential equation with these assumptions made it possible to obtain an analytical equation for the probability density of transitions between the states of the system per unit of time, which is in good agreement with the observed data, considering the effect of the delay time between the appearance of the first-level comment and the comment on that comment. Full article
(This article belongs to the Special Issue Applied and Computational Mathematics for Digital Environments)
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33 pages, 650 KiB  
Article
T-Spherical Fuzzy Bonferroni Mean Operators and Their Application in Multiple Attribute Decision Making
by Wei Yang and Yongfeng Pang
Mathematics 2022, 10(6), 988; https://doi.org/10.3390/math10060988 - 19 Mar 2022
Cited by 25 | Viewed by 1995
Abstract
To deal with complicated decision problems with T-Spherical fuzzy values in the aggregation process, T-Spherical fuzzy Bonferroni mean operators are developed by extending the Bonferroni mean and Dombi mean to a T-Spherical fuzzy environment. The T-spherical fuzzy interaction Bonferroni mean operator and the [...] Read more.
To deal with complicated decision problems with T-Spherical fuzzy values in the aggregation process, T-Spherical fuzzy Bonferroni mean operators are developed by extending the Bonferroni mean and Dombi mean to a T-Spherical fuzzy environment. The T-spherical fuzzy interaction Bonferroni mean operator and the T-spherical fuzzy interaction geometric Bonferroni mean operator are first defined. Then, the T-spherical fuzzy interaction weighted Bonferroni mean operator and the T-spherical fuzzy weighted interaction geometric Bonferroni mean operator are defined. Based on the Dombi mean and the Bonferroni mean operator, some T-Spherical fuzzy Dombi Bonferroni mean operators are proposed, including the T-spherical fuzzy Dombi Bonferroni mean operator, T-spherical fuzzy geometric Dombi Bonferroni mean operator, T-spherical fuzzy weighted Dombi Bonferroni mean operator and the T-spherical fuzzy weighted geometric Dombi Bonferroni mean operator. The properties of these proposed operators are studied. An attribute weight determining method based on the T-spherical fuzzy entropy and symmetric T-spherical fuzzy cross-entropy is developed. A new decision making method based on the proposed T-Spherical fuzzy Bonferroni mean operators is proposed for partly known or completely unknown attribute weight situations. The furniture procurement problem is presented to illustrate the new algorithm, and some comparisons are made. Full article
(This article belongs to the Special Issue New Trends in Fuzzy Sets Theory and Their Extensions)
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11 pages, 1242 KiB  
Article
Highly Dispersive Optical Soliton Perturbation, with Maximum Intensity, for the Complex Ginzburg–Landau Equation by Semi-Inverse Variation
by Anjan Biswas, Trevor Berkemeyer, Salam Khan, Luminita Moraru, Yakup Yıldırım and Hashim M. Alshehri
Mathematics 2022, 10(6), 987; https://doi.org/10.3390/math10060987 - 18 Mar 2022
Cited by 9 | Viewed by 2347
Abstract
This work analytically recovers the highly dispersive bright 1–soliton solution using for the perturbed complex Ginzburg–Landau equation, which is studied with three forms of nonlinear refractive index structures. They are Kerr law, parabolic law, and polynomial law. The perturbation terms appear with maximum [...] Read more.
This work analytically recovers the highly dispersive bright 1–soliton solution using for the perturbed complex Ginzburg–Landau equation, which is studied with three forms of nonlinear refractive index structures. They are Kerr law, parabolic law, and polynomial law. The perturbation terms appear with maximum allowable intensity, also known as full nonlinearity. The semi-inverse variational principle makes this retrieval possible. The amplitude–width relation is obtained by solving a cubic polynomial equation using Cardano’s approach. The parameter constraints for the existence of such solitons are also enumerated. Full article
(This article belongs to the Special Issue Nonlinear Partial Differential Equations: Exact Solutions, Symmetries, Methods, and Applications)
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16 pages, 2839 KiB  
Article
Optimal Harvest Problem for Fish Population—Structural Stabilization
by Aleksandr Abakumov and Yuri Izrailsky
Mathematics 2022, 10(6), 986; https://doi.org/10.3390/math10060986 - 18 Mar 2022
Cited by 3 | Viewed by 2766
Abstract
The influence of environmental conditions and fishery on a typical pelagic or semi-pelagic fish population is studied. A mathematical model of population dynamics with a size structure is constructed. The problem of the optimal harvest of a population in unstable environment conditions is [...] Read more.
The influence of environmental conditions and fishery on a typical pelagic or semi-pelagic fish population is studied. A mathematical model of population dynamics with a size structure is constructed. The problem of the optimal harvest of a population in unstable environment conditions is investigated and an optimality system to the problem research is constructed. The solutions properties in various cases have also been investigated. Environmental conditions influence the fish population through recruitment. Modelling of recruitment rate is made by using a stochastic imitation of environmental conditions. In the case of stationary environment, a population model admits nontrivial equilibrium state. The parameters of fish population are obtained from this equilibrium condition. The variability of environment leads to large oscillations of generation size. The fluctuations of the fish population density follow the dynamics of recruitment rate fluctuations but have smaller gradients than recruitment. The dynamics of the optimal fishing effort is characterized by high variability. The population and the average size of individuals decrease under the influence of fishery. In general, the results of computer calculations indicate the stabilization of the population dynamics under influence of size structure. Optimal harvesting also contributes to stabilization. Full article
(This article belongs to the Collection Theoretical and Mathematical Ecology)
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8 pages, 288 KiB  
Article
The Basic Locally Primitive Graphs of Order Twice a Prime Square
by Yulong Ma and Bengong Lou
Mathematics 2022, 10(6), 985; https://doi.org/10.3390/math10060985 - 18 Mar 2022
Viewed by 1298
Abstract
A graph Γ is called G-basic if G is quasiprimitive or bi-quasiprimitive on the vertex set of Γ, where G⩽Aut(Γ). It is known that locally primitive vertex-transitive graphs are normal covers of basic ones. In [...] Read more.
A graph Γ is called G-basic if G is quasiprimitive or bi-quasiprimitive on the vertex set of Γ, where G⩽Aut(Γ). It is known that locally primitive vertex-transitive graphs are normal covers of basic ones. In this paper, a complete classification of the basic locally primitive vertex-transitive graph of order 2p2 is given, where p is an odd prime. Full article
(This article belongs to the Special Issue Algebra and Discrete Mathematics 2021)
14 pages, 4527 KiB  
Communication
Modified Elliptic Integral Approach for the Forced Vibration and Sound Transmission Analysis of a Nonlinear Panel Backed by a Partitioned Cavity
by Yiu-Yin Lee
Mathematics 2022, 10(6), 984; https://doi.org/10.3390/math10060984 - 18 Mar 2022
Cited by 2 | Viewed by 1362
Abstract
This article is the further work of previous papers and also the first study to adopt the elliptic integral approach to solve the forced nonlinear structural acoustic problem. A previous elliptic integral approach, which was only used for the free vibration analyses of [...] Read more.
This article is the further work of previous papers and also the first study to adopt the elliptic integral approach to solve the forced nonlinear structural acoustic problem. A previous elliptic integral approach, which was only used for the free vibration analyses of various nonlinear structural acoustic problems, is modified and custom designed for conducting this forced vibration analysis. The main advantage of the proposed approach is that one elliptic cosine contains various harmonic components, while one simple cosine term only carries one particular harmonic component. That is why the proposed solution form can be more concise than those in the harmonic balance procedures. This is the first study to employ the proposed elliptic cosine solution form for the forced vibration and sound transmission of a nonlinear panel backed by a partitioned cavity. This study has two focuses: (1) the development of elliptic integral approach for solving the nonlinear structural acoustic governing equations, and (2) the effect of partitioned cavities on the forced vibration response and sound transmission loss. Moreover, a set of elliptic cosine solutions is verified by that from the modified residue harmonic balance method. A mode convergence study and a harmonic contribution analysis are also conducted. Full article
(This article belongs to the Topic Engineering Mathematics)
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23 pages, 2348 KiB  
Article
Automatic Classification of National Health Service Feedback
by Christopher Haynes, Marco A. Palomino, Liz Stuart, David Viira, Frances Hannon, Gemma Crossingham and Kate Tantam
Mathematics 2022, 10(6), 983; https://doi.org/10.3390/math10060983 - 18 Mar 2022
Cited by 9 | Viewed by 2223
Abstract
Text datasets come in an abundance of shapes, sizes and styles. However, determining what factors limit classification accuracy remains a difficult task which is still the subject of intensive research. Using a challenging UK National Health Service (NHS) dataset, which contains many characteristics [...] Read more.
Text datasets come in an abundance of shapes, sizes and styles. However, determining what factors limit classification accuracy remains a difficult task which is still the subject of intensive research. Using a challenging UK National Health Service (NHS) dataset, which contains many characteristics known to increase the complexity of classification, we propose an innovative classification pipeline. This pipeline switches between different text pre-processing, scoring and classification techniques during execution. Using this flexible pipeline, a high level of accuracy has been achieved in the classification of a range of datasets, attaining a micro-averaged F1 score of 93.30% on the Reuters-21578 “ApteMod” corpus. An evaluation of this flexible pipeline was carried out using a variety of complex datasets compared against an unsupervised clustering approach. The paper describes how classification accuracy is impacted by an unbalanced category distribution, the rare use of generic terms and the subjective nature of manual human classification. Full article
(This article belongs to the Special Issue Natural Language Processing (NLP) and Machine Learning (ML)—Theory and Applications)
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21 pages, 1368 KiB  
Article
IoT Analytics and Agile Optimization for Solving Dynamic Team Orienteering Problems with Mandatory Visits
by Yuda Li, Mohammad Peyman, Javier Panadero, Angel A. Juan and Fatos Xhafa
Mathematics 2022, 10(6), 982; https://doi.org/10.3390/math10060982 - 18 Mar 2022
Cited by 3 | Viewed by 2121
Abstract
Transport activities and citizen mobility have a deep impact on enlarged smart cities. By analyzing Big Data streams generated through Internet of Things (IoT) devices, this paper aims to show the efficiency of using IoT analytics, as an agile optimization input for solving [...] Read more.
Transport activities and citizen mobility have a deep impact on enlarged smart cities. By analyzing Big Data streams generated through Internet of Things (IoT) devices, this paper aims to show the efficiency of using IoT analytics, as an agile optimization input for solving real-time problems in smart cities. IoT analytics has become the main core of large-scale Internet applications, however, its utilization in optimization approaches for real-time configuration and dynamic conditions of a smart city has been less discussed. The challenging research topic is how to reach real-time IoT analytics for use in optimization approaches. In this paper, we consider integrating IoT analytics into agile optimization problems. A realistic waste collection problem is modeled as a dynamic team orienteering problem with mandatory visits. Open data repositories from smart cities are used for extracting the IoT analytics to achieve maximum advantage under the city environment condition. Our developed methodology allows us to process real-time information gathered from IoT systems in order to optimize the vehicle routing decision under dynamic changes of the traffic environments. A series of computational experiments is provided in order to illustrate our approach and discuss its effectiveness. In these experiments, a traditional static approach is compared against a dynamic one. In the former, the solution is calculated only once at the beginning, while in the latter, the solution is re-calculated periodically as new data are obtained. The results of the experiments clearly show that our proposed dynamic approach outperforms the static one in terms of rewards. Full article
(This article belongs to the Special Issue Analytics and Big Data)
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17 pages, 353 KiB  
Article
Commutativity and Completeness Degrees of Weakly Complete Hypergroups
by Mario De Salvo, Dario Fasino, Domenico Freni and Giovanni Lo Faro
Mathematics 2022, 10(6), 981; https://doi.org/10.3390/math10060981 - 18 Mar 2022
Cited by 4 | Viewed by 1206
Abstract
We introduce a family of hypergroups, called weakly complete, generalizing the construction of complete hypergroups. Starting from a given group G, our construction prescribes the β-classes of the hypergroups and allows some hyperproducts not to be complete parts, based on a [...] Read more.
We introduce a family of hypergroups, called weakly complete, generalizing the construction of complete hypergroups. Starting from a given group G, our construction prescribes the β-classes of the hypergroups and allows some hyperproducts not to be complete parts, based on a suitably defined relation over G. The commutativity degree of weakly complete hypergroups can be related to that of the underlying group. Furthermore, in analogy to the degree of commutativity, we introduce the degree of completeness of finite hypergroups and analyze this degree for weakly complete hypergroups in terms of their β-classes. Full article
(This article belongs to the Special Issue Hypergroup Theory and Algebrization of Incidence Structures)
13 pages, 6613 KiB  
Article
Quasi-Unimodal Distributions for Ordinal Classification
by Tomé Albuquerque, Ricardo Cruz and Jaime S. Cardoso
Mathematics 2022, 10(6), 980; https://doi.org/10.3390/math10060980 - 18 Mar 2022
Cited by 2 | Viewed by 2265
Abstract
Ordinal classification tasks are present in a large number of different domains. However, common losses for deep neural networks, such as cross-entropy, do not properly weight the relative ordering between classes. For that reason, many losses have been proposed in the literature, which [...] Read more.
Ordinal classification tasks are present in a large number of different domains. However, common losses for deep neural networks, such as cross-entropy, do not properly weight the relative ordering between classes. For that reason, many losses have been proposed in the literature, which model the output probabilities as following a unimodal distribution. This manuscript reviews many of these losses on three different datasets and suggests a potential improvement that focuses the unimodal constraint on the neighborhood around the true class, allowing for a more flexible distribution, aptly called quasi-unimodal loss. For this purpose, two constraints are proposed: A first constraint concerns the relative order of the top-three probabilities, and a second constraint ensures that the remaining output probabilities are not higher than the top three. Therefore, gradient descent focuses on improving the decision boundary around the true class in detriment to the more distant classes. The proposed loss is found to be competitive in several cases. Full article
(This article belongs to the Special Issue Statistical Methods in Data Mining)
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16 pages, 418 KiB  
Article
Mean-Square Strong Stability and Stabilization of Discrete-Time Markov Jump Systems with Multiplicative Noises
by Zhiguo Yan and Fangxu Su
Mathematics 2022, 10(6), 979; https://doi.org/10.3390/math10060979 - 18 Mar 2022
Viewed by 1320
Abstract
In this paper, the mean-square strong stability and stabilization of discrete-time Markov jump systems are studied. Firstly, the definition of mean-square strong stability is given, and the necessary and sufficient conditions for mean-square strong stability are derived. Secondly, several necessary and sufficient conditions [...] Read more.
In this paper, the mean-square strong stability and stabilization of discrete-time Markov jump systems are studied. Firstly, the definition of mean-square strong stability is given, and the necessary and sufficient conditions for mean-square strong stability are derived. Secondly, several necessary and sufficient conditions for mean-square strong stabilization via a state feedback controller and an output feedback controller are obtained. Furthermore, explicit expressions for the state feedback controller and static output feedback controller are obtained. Finally, two examples are given to illustrate the validity of the above results. Full article
(This article belongs to the Special Issue Impulsive Control Systems and Complexity II)
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22 pages, 476 KiB  
Article
General Odd and Even Central Factorial Polynomial Sequences
by Francesco Aldo Costabile, Maria Italia Gualtieri and Anna Napoli
Mathematics 2022, 10(6), 978; https://doi.org/10.3390/math10060978 - 18 Mar 2022
Cited by 4 | Viewed by 1354
Abstract
The δ2(·) operator, where δ(·) is the known central difference operator, is considered. The associated odd and even polynomial sequences are determined and their generalizations studied. Particularly, matrix and determinant forms, recurrence formulas, generating functions and [...] Read more.
The δ2(·) operator, where δ(·) is the known central difference operator, is considered. The associated odd and even polynomial sequences are determined and their generalizations studied. Particularly, matrix and determinant forms, recurrence formulas, generating functions and an algorithm for effective calculation are provided. An interesting property of biorthogonality is also demonstrated. New examples of odd and even central polynomial sequences are given. Full article
(This article belongs to the Special Issue Polynomial Sequences and Their Applications)
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