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Mathematics
Volume 9
Issue 4
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Mathematics, Volume 9, Issue 4 (February-2 2021) – 160 articles

Cover Story (view full-size image): We characterize the complete monotonicity of the Kilbas–Saigo function on the negative half-line, provide the exact asymptotics at −∞, and derive uniform hyperbolic bounds. We address the same questions for the Le Roy function. We achieve this thanks to a probabilistic representation of these functions in terms of the stable subordinator. View this paper.
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30 pages, 459 KiB  
Article
Unified Polynomial Dynamic Programming Algorithms for P-Center Variants in a 2D Pareto Front
by Nicolas Dupin, Frank Nielsen and El-Ghazali Talbi
Mathematics 2021, 9(4), 453; https://doi.org/10.3390/math9040453 - 23 Feb 2021
Cited by 10 | Viewed by 2530
Abstract
With many efficient solutions for a multi-objective optimization problem, this paper aims to cluster the Pareto Front in a given number of clusters K and to detect isolated points. K-center problems and variants are investigated with a unified formulation considering the discrete [...] Read more.
With many efficient solutions for a multi-objective optimization problem, this paper aims to cluster the Pareto Front in a given number of clusters K and to detect isolated points. K-center problems and variants are investigated with a unified formulation considering the discrete and continuous versions, partial K-center problems, and their min-sum-K-radii variants. In dimension three (or upper), this induces NP-hard complexities. In the planar case, common optimality property is proven: non-nested optimal solutions exist. This induces a common dynamic programming algorithm running in polynomial time. Specific improvements hold for some variants, such as K-center problems and min-sum K-radii on a line. When applied to N points and allowing to uncover M<N points, K-center and min-sum-K-radii variants are, respectively, solvable in O(K(M+1)NlogN) and O(K(M+1)N2) time. Such complexity of results allows an efficient straightforward implementation. Parallel implementations can also be designed for a practical speed-up. Their application inside multi-objective heuristics is discussed to archive partial Pareto fronts, with a special interest in partial clustering variants. Full article
(This article belongs to the Special Issue Mathematical Methods for Operations Research Problems)
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33 pages, 1474 KiB  
Article
A Full Description of ω-Limit Sets of Cournot Maps Having Non-Empty Interior and Some Economic Applications
by Antonio Linero-Bas and María Muñoz-Guillermo
Mathematics 2021, 9(4), 452; https://doi.org/10.3390/math9040452 - 23 Feb 2021
Cited by 1 | Viewed by 1534
Abstract
Given a continuous Cournot map F(x,y)=(f2(y),f1(x)) defined from I2=[0,1]×[0,1] into itself, [...] Read more.
Given a continuous Cournot map F(x,y)=(f2(y),f1(x)) defined from I2=[0,1]×[0,1] into itself, we give a full description of its ω-limit sets with non-empty interior. Additionally, we present some partial results for the empty interior case. The distribution of the ω-limits with non-empty interior gives information about the dynamics and the possible outputs of each firm in a Cournot model. We present some economic models to illustrate, with examples, the type of ω-limits that appear. Full article
(This article belongs to the Special Issue Mathematical Methods on Economic Dynamics)
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27 pages, 2617 KiB  
Article
Rule-Based EEG Classifier Utilizing Local Entropy of Time–Frequency Distributions
by Jonatan Lerga, Nicoletta Saulig, Ljubiša Stanković and Damir Seršić
Mathematics 2021, 9(4), 451; https://doi.org/10.3390/math9040451 - 23 Feb 2021
Cited by 7 | Viewed by 2384
Abstract
Electroencephalogram (EEG) signals are known to contain signatures of stimuli that induce brain activities. However, detecting these signatures to classify captured EEG waveforms is one of the most challenging tasks of EEG analysis. This paper proposes a novel time–frequency-based method for EEG analysis [...] Read more.
Electroencephalogram (EEG) signals are known to contain signatures of stimuli that induce brain activities. However, detecting these signatures to classify captured EEG waveforms is one of the most challenging tasks of EEG analysis. This paper proposes a novel time–frequency-based method for EEG analysis and characterization implemented in a computer-aided decision-support system that can be used to assist medical experts in interpreting EEG patterns. The computerized method utilizes EEG spectral non-stationarity, which is clearly revealed in the time–frequency distributions (TFDs) of multicomponent signals. The proposed algorithm, which is based on the modification of the Rényi entropy, called local or short-term Rényi entropy (STRE), was upgraded with a blind component separation procedure and instantaneous frequency (IF) estimation. The method was applied to EEGs of both forward and backward movements of the left and right hands, as well as to EEGs of imagined hand movements, which were captured by a 19-channel EEG recording system. The obtained results show that in a given virtual instrument, the proposed methods efficiently distinguish between real and imagined limb movements by considering their signatures in terms of the dominant EEG component’s IFs at the specified subset of EEG channels (namely, F3, F4, F7, F8, T3, and T4). Furthermore, computing the number of EEG signal components, their extraction, and IF estimation provide important information that shows potential to enhance existing clinical diagnostic techniques for detecting the intensity, location, and type of brain function abnormalities in patients with neurological motor control disorders. Full article
(This article belongs to the Special Issue New Trends in Graph and Complexity Based Data Analysis and Processing)
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17 pages, 3994 KiB  
Article
Frequent Itemset Mining and Multi-Layer Network-Based Analysis of RDF Databases
by Gergely Honti and János Abonyi
Mathematics 2021, 9(4), 450; https://doi.org/10.3390/math9040450 - 23 Feb 2021
Cited by 4 | Viewed by 1911
Abstract
Triplestores or resource description framework (RDF) stores are purpose-built databases used to organise, store and share data with context. Knowledge extraction from a large amount of interconnected data requires effective tools and methods to address the complexity and the underlying structure of semantic [...] Read more.
Triplestores or resource description framework (RDF) stores are purpose-built databases used to organise, store and share data with context. Knowledge extraction from a large amount of interconnected data requires effective tools and methods to address the complexity and the underlying structure of semantic information. We propose a method that generates an interpretable multilayered network from an RDF database. The method utilises frequent itemset mining (FIM) of the subjects, predicates and the objects of the RDF data, and automatically extracts informative subsets of the database for the analysis. The results are used to form layers in an analysable multidimensional network. The methodology enables a consistent, transparent, multi-aspect-oriented knowledge extraction from the linked dataset. To demonstrate the usability and effectiveness of the methodology, we analyse how the science of sustainability and climate change are structured using the Microsoft Academic Knowledge Graph. In the case study, the FIM forms networks of disciplines to reveal the significant interdisciplinary science communities in sustainability and climate change. The constructed multilayer network then enables an analysis of the significant disciplines and interdisciplinary scientific areas. To demonstrate the proposed knowledge extraction process, we search for interdisciplinary science communities and then measure and rank their multidisciplinary effects. The analysis identifies discipline similarities, pinpointing the similarity between atmospheric science and meteorology as well as between geomorphology and oceanography. The results confirm that frequent itemset mining provides an informative sampled subsets of RDF databases which can be simultaneously analysed as layers of a multilayer network. Full article
(This article belongs to the Special Issue Information Systems Modeling Based on Graph Theory)
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24 pages, 336 KiB  
Article
Qi Type Diamond-Alpha Integral Inequalities
by Zhong-Xuan Mao, Ya-Ru Zhu, Bao-Hua Guo, Fu-Hai Wang, Yu-Hua Yang and Hai-Qing Zhao
Mathematics 2021, 9(4), 449; https://doi.org/10.3390/math9040449 - 23 Feb 2021
Cited by 3 | Viewed by 1528
Abstract
In this paper, we establish sufficient conditions for Qi type diamond-alpha integral inequalities and its generalized form on time scales. Full article
16 pages, 7058 KiB  
Article
Flow towards a Stagnation Region of a Vertical Plate in a Hybrid Nanofluid: Assisting and Opposing Flows
by Iskandar Waini, Anuar Ishak and Ioan Pop
Mathematics 2021, 9(4), 448; https://doi.org/10.3390/math9040448 - 23 Feb 2021
Cited by 10 | Viewed by 1628
Abstract
This study investigates a hybrid nanofluid flow towards a stagnation region of a vertical plate with radiation effects. The hybrid nanofluid consists of copper (Cu) and alumina (Al2O3) nanoparticles which are added into water to form Cu-Al2O [...] Read more.
This study investigates a hybrid nanofluid flow towards a stagnation region of a vertical plate with radiation effects. The hybrid nanofluid consists of copper (Cu) and alumina (Al2O3) nanoparticles which are added into water to form Cu-Al2O3/water nanofluid. The stagnation point flow describes the fluid motion in the stagnation region of a solid surface. In this study, both buoyancy assisting and opposing flows are considered. The similarity equations are obtained using a similarity transformation and numerical results are obtained via the boundary value problem solver (bvp4c) in MATLAB software. Findings discovered that dual solutions exist for both opposing and assisting flows. The heat transfer rate is intensified with the thermal radiation (49.63%) and the hybrid nanoparticles (32.37%). Full article
(This article belongs to the Special Issue Applications of Mathematical Models in Engineering)
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26 pages, 364 KiB  
Article
On Unification of Methods in Theories of Fuzzy Sets, Hesitant Fuzzy Set, Fuzzy Soft Sets and Intuitionistic Fuzzy Sets
by Jiří Močkoř and David Hýnar
Mathematics 2021, 9(4), 447; https://doi.org/10.3390/math9040447 - 23 Feb 2021
Cited by 12 | Viewed by 1788
Abstract
The main goal of this publication is to show that the basic constructions in the theories of fuzzy sets, fuzzy soft sets, fuzzy hesitant sets or intuitionistic fuzzy sets have a common background, based on the theory of monads in categories. It is [...] Read more.
The main goal of this publication is to show that the basic constructions in the theories of fuzzy sets, fuzzy soft sets, fuzzy hesitant sets or intuitionistic fuzzy sets have a common background, based on the theory of monads in categories. It is proven that ad hoc defined basic concepts in individual theories, such as concepts of power set structures in these theories, relations or approximation operators defined by these relations are only special examples of applications of the monad theory in categories. This makes it possible, on the one hand, to unify basic constructions in all these theories and, on the other hand, to verify the legitimacy of ad hoc definitions of these constructions in individual theories. This common background also makes it possible to transform these basic concepts from one theory to another. Full article
(This article belongs to the Special Issue Fuzzy Sets and Soft Computing)
12 pages, 798 KiB  
Article
Refinements of Hermite–Hadamard Inequalities for Continuous Convex Functions via (p,q)-Calculus
by Julalak Prabseang, Kamsing Nonlaopon, Jessada Tariboon and Sotiris K. Ntouyas
Mathematics 2021, 9(4), 446; https://doi.org/10.3390/math9040446 - 23 Feb 2021
Cited by 7 | Viewed by 1588
Abstract
In this paper, we present some new refinements of Hermite–Hadamard inequalities for continuous convex functions by using (p,q)-calculus. Moreover, we study some new (p,q)-Hermite–Hadamard inequalities for multiple integrals. Many results given in this [...] Read more.
In this paper, we present some new refinements of Hermite–Hadamard inequalities for continuous convex functions by using (p,q)-calculus. Moreover, we study some new (p,q)-Hermite–Hadamard inequalities for multiple integrals. Many results given in this paper provide extensions of others given in previous research. Full article
17 pages, 8208 KiB  
Article
Meshing Drive Mechanism of Double Traveling Waves for Rotary Piezoelectric Motors
by Dawei An, Weiqing Huang, Weiquan Liu, Jinrui Xiao, Xiaochu Liu and Zhongwei Liang
Mathematics 2021, 9(4), 445; https://doi.org/10.3390/math9040445 - 23 Feb 2021
Cited by 3 | Viewed by 1705
Abstract
Rotary piezoelectric motors based on converse piezoelectric effect are very competitive in the fields of precision driving and positioning. Miniaturization and larger output capability are the crucial design objectives, and the efforts on structural modification, new materials application and optimization of control systems [...] Read more.
Rotary piezoelectric motors based on converse piezoelectric effect are very competitive in the fields of precision driving and positioning. Miniaturization and larger output capability are the crucial design objectives, and the efforts on structural modification, new materials application and optimization of control systems are persistent but the effectiveness is limited. In this paper, the resonance rotor excited by stator is investigated and the meshing drive mechanism of double traveling waves is proposed. Based on the theoretical analysis of bending vibration, the finite element method (FEM) is used to compare the modal shape and modal response in the peripheric, axial, and radial directions for the stator and three rotors. By analyzing the phase offset and vibrational orientation of contact particles at the interface, the principle of meshing traveling waves is discussed graphically and the concise formula obtaining the output performance is summarized, which is analogous with the principles of gear connection. Verified by the prototype experimental results, the speed of the proposed motor is the sum of the velocity of the stator’s contact particle and the resonance rotor’s contact particle, while the torque is less than twice the motor using the reference rotor. Full article
(This article belongs to the Special Issue Finite Element Modeling in Computational Friction Contact Mechanics)
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24 pages, 1561 KiB  
Review
Mathematical Representation Competency in Relation to Use of Digital Technology and Task Design—A Literature Review
by Mathilde Kjær Pedersen, Cecilie Carlsen Bach, Rikke Maagaard Gregersen, Ingi Heinesen Højsted and Uffe Thomas Jankvist
Mathematics 2021, 9(4), 444; https://doi.org/10.3390/math9040444 - 23 Feb 2021
Cited by 5 | Viewed by 4382
Abstract
Representations are crucial to mathematical activity, both for learners and skilled mathematicians. Digital technologies (DT) to support mathematical activity offer a plethora of new possibilities, not least in the context of mathematics education. This paper presents a literature review on representations and activation [...] Read more.
Representations are crucial to mathematical activity, both for learners and skilled mathematicians. Digital technologies (DT) to support mathematical activity offer a plethora of new possibilities, not least in the context of mathematics education. This paper presents a literature review on representations and activation of students’ representation competency when using DT in mathematics teaching and learning situations. It does so with a starting point in task designs involving digital tools aiming to activate representation competency, drawing on the notion of Mathematical Digital Boundary Object (MDBO). The 30 studies included in the literature review are analyzed using Duval’s registers of semiotic representations and the representation competency from the Danish KOM framework. The results reveal a clear connection between the mathematical topics addressed and the types of representation utilized, and further indicate that certain aspects of the representation competency are outsourced when DT are used. To activate the representation competency in relation to the use of DT, we offer five suggestions for consideration when designing mathematical tasks. Finally, we raise the question of whether DT create new representations or merely new activities. Full article
(This article belongs to the Special Issue Designing Tasks within Dynamic and Interactive Mathematics Learning Environments)
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27 pages, 1778 KiB  
Article
Community Detection Problem Based on Polarization Measures: An Application to Twitter: The COVID-19 Case in Spain
by Inmaculada Gutiérrez, Juan Antonio Guevara, Daniel Gómez, Javier Castro and Rosa Espínola
Mathematics 2021, 9(4), 443; https://doi.org/10.3390/math9040443 - 23 Feb 2021
Cited by 5 | Viewed by 2644
Abstract
In this paper, we address one of the most important topics in the field of Social Networks Analysis: the community detection problem with additional information. That additional information is modeled by a fuzzy measure that represents the risk of polarization. Particularly, we are [...] Read more.
In this paper, we address one of the most important topics in the field of Social Networks Analysis: the community detection problem with additional information. That additional information is modeled by a fuzzy measure that represents the risk of polarization. Particularly, we are interested in dealing with the problem of taking into account the polarization of nodes in the community detection problem. Adding this type of information to the community detection problem makes it more realistic, as a community is more likely to be defined if the corresponding elements are willing to maintain a peaceful dialogue. The polarization capacity is modeled by a fuzzy measure based on the JDJpol measure of polarization related to two poles. We also present an efficient algorithm for finding groups whose elements are no polarized. Hereafter, we work in a real case. It is a network obtained from Twitter, concerning the political position against the Spanish government taken by several influential users. We analyze how the partitions obtained change when some additional information related to how polarized that society is, is added to the problem. Full article
(This article belongs to the Special Issue Artificial Intelligence with Applications of Soft Computing)
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18 pages, 2887 KiB  
Article
A Novel Geometric Modeling and Calculation Method for Forward Displacement Analysis of 6-3 Stewart Platforms
by Ganmin Zhu, Shimin Wei, Ying Zhang and Qizheng Liao
Mathematics 2021, 9(4), 442; https://doi.org/10.3390/math9040442 - 23 Feb 2021
Cited by 6 | Viewed by 1872
Abstract
A novel geometric modeling and calculation method for forward displacement analysis of the 6-3 Stewart platforms is proposed by using the conformal geometric algebra (CGA) framework. Firstly, two formulas between 2-blade and 1-blade are formulated. Secondly, the expressions for two spherical joints of [...] Read more.
A novel geometric modeling and calculation method for forward displacement analysis of the 6-3 Stewart platforms is proposed by using the conformal geometric algebra (CGA) framework. Firstly, two formulas between 2-blade and 1-blade are formulated. Secondly, the expressions for two spherical joints of the moving platform are given via CGA operation. Thirdly, a coordinate-invariant geometric constraint equation is deduced. Fourthly, a 16-degree univariate polynomial equation without algebraic elimination by using the Euler angle substitution is presented. Fifthly, the coordinates of three spherical joints on the moving platform are calculated without judging the radical symbols. Finally, two numerical examples are used to verify the method. The highlight of this paper is that a new geometric modeling and calculation method without algebraic elimination is obtained by using the determinant form of the CGA inner product algorithm, which provides a new idea to solve a more complex spatial parallel mechanism in the future. Full article
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26 pages, 1455 KiB  
Article
Spillover and Drivers of Uncertainty among Oil and Commodity Markets
by Muhammad Abubakr Naeem, Saqib Farid, Safwan Mohd Nor and Syed Jawad Hussain Shahzad
Mathematics 2021, 9(4), 441; https://doi.org/10.3390/math9040441 - 23 Feb 2021
Cited by 20 | Viewed by 2558
Abstract
The paper aims to examine the spillover of uncertainty among commodity markets using Diebold–Yilmaz approach based on forecast error variance decomposition. Next, causal impact of global factors as drivers of uncertainty transmission between oil and other commodity markets is analyzed. Our analysis suggests [...] Read more.
The paper aims to examine the spillover of uncertainty among commodity markets using Diebold–Yilmaz approach based on forecast error variance decomposition. Next, causal impact of global factors as drivers of uncertainty transmission between oil and other commodity markets is analyzed. Our analysis suggests that oil is a net transmitter to other commodity uncertainties, and this transmission significantly increased during the global financial crisis of 2008–2009. The use of linear and nonlinear causality tests indicates that the global factors have a causal effect on the overall connectedness, and especially on the spillovers from oil to other commodity uncertainties. Further segregation of transmissions between oil to individual commodity markets indicates that stock market implied volatility, risk spread, and economic policy uncertainty are the influential drivers of connectedness among commodity markets. Full article
(This article belongs to the Special Issue Mathematical and Statistical Methods Applications in Finance)
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18 pages, 5261 KiB  
Article
Improving the Gridshells’ Regularity by Using Evolutionary Techniques
by Marjan Goodarzi, Ali Mohades and Majid Forghani-elahabad
Mathematics 2021, 9(4), 440; https://doi.org/10.3390/math9040440 - 23 Feb 2021
Cited by 3 | Viewed by 1487
Abstract
Designing and optimizing gridshell structures have been very attractive problems in the last decades. In this work, two indexes are introduced as “length ratio” and “shape ratio” to measure the regularity of a gridshell and are compared to the existing indexes in the [...] Read more.
Designing and optimizing gridshell structures have been very attractive problems in the last decades. In this work, two indexes are introduced as “length ratio” and “shape ratio” to measure the regularity of a gridshell and are compared to the existing indexes in the literature. Two evolutionary techniques, genetic algorithm (GA) and particle swarm optimization (PSO) method, are utilized to improve the gridshells’ regularity by using the indexes. An approach is presented to generate the initial gridshells for a given surface in MATLAB. The two methods are implemented in MATLAB and compared on three benchmarks with different Gaussian curvatures. For each grid, both triangular and quadrangular meshes are generated. Experimental results show that the regularity of some gridshell is improved more than 50%, the regularity of quadrangular gridshells can be improved more than the regularity of triangular gridshells on the same surfaces, and there may be some relationship between Gaussian curvature of a surface and the improvement percentage of generated gridshells on it. Moreover, it is seen that PSO technique outperforms GA technique slightly in almost all the considered test problems. Finally, the Dolan–Moré performance profile is produced to compare the two methods according to running times. Full article
(This article belongs to the Special Issue Applications of Mathematical Models in Engineering)
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9 pages, 267 KiB  
Article
On the Paired-Domination Subdivision Number of a Graph
by Guoliang Hao, Seyed Mahmoud Sheikholeslami, Mustapha Chellali, Rana Khoeilar and Hossein Karami
Mathematics 2021, 9(4), 439; https://doi.org/10.3390/math9040439 - 23 Feb 2021
Cited by 4 | Viewed by 1500
Abstract
In order to increase the paired-domination number of a graph G, the minimum number of edges that must be subdivided (where each edge in G can be subdivided no more than once) is called the paired-domination subdivision number [...] Read more.
In order to increase the paired-domination number of a graph G, the minimum number of edges that must be subdivided (where each edge in G can be subdivided no more than once) is called the paired-domination subdivision number sdγpr(G) of G. It is well known that sdγpr(G+e) can be smaller or larger than sdγpr(G) for some edge e∉E(G). In this note, we show that, if G is an isolated-free graph different from mK2, then, for every edge e∉E(G), sdγpr(G+e)≤sdγpr(G)+2Δ(G). Full article
(This article belongs to the Special Issue Graphs, Metrics and Models)
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14 pages, 862 KiB  
Article
Several Limit Theorems on Fuzzy Quantum Space
by Viliam Ďuriš, Renáta Bartková and Anna Tirpáková
Mathematics 2021, 9(4), 438; https://doi.org/10.3390/math9040438 - 23 Feb 2021
Cited by 1 | Viewed by 1720
Abstract
The probability theory using fuzzy random variables has applications in several scientific disciplines. These are mainly technical in scope, such as in the automotive industry and in consumer electronics, for example, in washing machines, televisions, and microwaves. The theory is gradually entering the [...] Read more.
The probability theory using fuzzy random variables has applications in several scientific disciplines. These are mainly technical in scope, such as in the automotive industry and in consumer electronics, for example, in washing machines, televisions, and microwaves. The theory is gradually entering the domain of finance where people work with incomplete data. We often find that events in the financial markets cannot be described precisely, and this is where we can use fuzzy random variables. By proving the validity of the theorem on extreme values of fuzzy quantum space in our article, we see possible applications for estimating financial risks with incomplete data. Full article
(This article belongs to the Special Issue Fuzzy Sets and Soft Computing)
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12 pages, 297 KiB  
Article
Canonical Almost Geodesic Mappings of the First Type of Spaces with Affine Connections onto Generalized m-Ricci-Symmetric Spaces
by Volodymyr Berezovski, Yevhen Cherevko, Josef Mikeš and Lenka Rýparová
Mathematics 2021, 9(4), 437; https://doi.org/10.3390/math9040437 - 22 Feb 2021
Cited by 10 | Viewed by 1719
Abstract
In the paper we consider almost geodesic mappings of the first type of spaces with affine connections onto generalized 2-Ricci-symmetric spaces, generalized 3-Ricci-symmetric spaces, and generalized m-Ricci-symmetric spaces. In either case the main equations for the mappings are obtained as a closed [...] Read more.
In the paper we consider almost geodesic mappings of the first type of spaces with affine connections onto generalized 2-Ricci-symmetric spaces, generalized 3-Ricci-symmetric spaces, and generalized m-Ricci-symmetric spaces. In either case the main equations for the mappings are obtained as a closed system of linear differential equations of Cauchy type in the covariant derivatives. The obtained results extend an amount of research produced by N.S. Sinyukov, V.E. Berezovski, J. Mikeš. Full article
(This article belongs to the Special Issue Differential Geometry: Structures on Manifolds and Their Applications)
22 pages, 709 KiB  
Article
Dynamics of a Two Prey and One Predator System with Indirect Effect
by Renato Colucci, Érika Diz-Pita and M. Victoria Otero-Espinar
Mathematics 2021, 9(4), 436; https://doi.org/10.3390/math9040436 - 22 Feb 2021
Cited by 2 | Viewed by 2101
Abstract
We study a population model with two preys and one predator, considering a Holling type II functional response for the interaction between first prey and predator and taking into account indirect effect of predation. We perform the stability analysis of equilibria and study [...] Read more.
We study a population model with two preys and one predator, considering a Holling type II functional response for the interaction between first prey and predator and taking into account indirect effect of predation. We perform the stability analysis of equilibria and study the possibility of Hopf bifurcation. We also include a detailed discussion on the problem of persistence. Several numerical simulations are provided in order to illustrate the theoretical results of the paper. Full article
(This article belongs to the Special Issue Modelling and Analysis in Biomathematics)
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16 pages, 317 KiB  
Article
Stability Concepts of Riemann-Liouville Fractional-Order Delay Nonlinear Systems
by Ravi Agarwal, Snezhana Hristova and Donal O’Regan
Mathematics 2021, 9(4), 435; https://doi.org/10.3390/math9040435 - 22 Feb 2021
Cited by 10 | Viewed by 1598
Abstract
First, we set up in an appropriate way the initial value problem for nonlinear delay differential equations with a Riemann-Liouville (RL) fractional derivative. We define stability in time and generalize Mittag-Leffler stability for RL fractional differential equations and we study stability properties by [...] Read more.
First, we set up in an appropriate way the initial value problem for nonlinear delay differential equations with a Riemann-Liouville (RL) fractional derivative. We define stability in time and generalize Mittag-Leffler stability for RL fractional differential equations and we study stability properties by an appropriate modification of the Razumikhin method. Two different types of derivatives of Lyapunov functions are studied: the RL fractional derivative when the argument of the Lyapunov function is any solution of the studied problem and a special type of Dini fractional derivative among the studied problem. Full article
(This article belongs to the Special Issue Nonlinear Equations: Theory, Methods, and Applications)
20 pages, 2047 KiB  
Article
Reliable Learning with PDE-Based CNNs and DenseNets for Detecting COVID-19, Pneumonia, and Tuberculosis from Chest X-Ray Images
by Anca Nicoleta Marginean, Delia Doris Muntean, George Adrian Muntean, Adelina Priscu, Adrian Groza, Radu Razvan Slavescu, Calin Lucian Timbus, Gabriel Zeno Munteanu, Cezar Octavian Morosanu, Maria Margareta Cosnarovici and Camelia-M. Pintea
Mathematics 2021, 9(4), 434; https://doi.org/10.3390/math9040434 - 22 Feb 2021
Cited by 8 | Viewed by 2505
Abstract
It has recently been shown that the interpretation by partial differential equations (PDEs) of a class of convolutional neural networks (CNNs) supports definition of architectures such as parabolic and hyperbolic networks. These networks have provable properties regarding the stability against the perturbations of [...] Read more.
It has recently been shown that the interpretation by partial differential equations (PDEs) of a class of convolutional neural networks (CNNs) supports definition of architectures such as parabolic and hyperbolic networks. These networks have provable properties regarding the stability against the perturbations of the input features. Aiming for robustness, we tackle the problem of detecting changes in chest X-ray images that may be suggestive of COVID-19 with parabolic and hyperbolic CNNs and with domain-specific transfer learning. To this end, we compile public data on patients diagnosed with COVID-19, pneumonia, and tuberculosis, along with normal chest X-ray images. The negative impact of the small number of COVID-19 images is reduced by applying transfer learning in several ways. For the parabolic and hyperbolic networks, we pretrain the networks on normal and pneumonia images and further use the obtained weights as the initializers for the networks to discriminate between COVID-19, pneumonia, tuberculosis, and normal aspects. For DenseNets, we apply transfer learning twice. First, the ImageNet pretrained weights are used to train on the CheXpert dataset, which includes 14 common radiological observations (e.g., lung opacity, cardiomegaly, fracture, support devices). Then, the weights are used to initialize the network which detects COVID-19 and the three other classes. The resulting networks are compared in terms of how well they adapt to the small number of COVID-19 images. According to our quantitative and qualitative analysis, the resulting networks are more reliable compared to those obtained by direct training on the targeted dataset. Full article
(This article belongs to the Special Issue Advances in PDE-Based Methods for Image Processing)
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18 pages, 1511 KiB  
Article
Statistical Evaluation of BIS-11 and DAQ Tools in the Field of Traffic Psychology
by Kristián Čulík and Alica Kalašová
Mathematics 2021, 9(4), 433; https://doi.org/10.3390/math9040433 - 22 Feb 2021
Cited by 11 | Viewed by 2408
Abstract
This paper focuses on the statistical evaluation of two independent research tools in the field of traffic psychology. Our research focuses on young drivers in the Slovak Republic and conducts an international comparison. At present, these young drivers make up only about 7% [...] Read more.
This paper focuses on the statistical evaluation of two independent research tools in the field of traffic psychology. Our research focuses on young drivers in the Slovak Republic and conducts an international comparison. At present, these young drivers make up only about 7% of the total number of drivers, but they cause about 20% of accidents. The paper analyzes the traffic accident rate of young as well as inexperienced drivers. All drivers in the survey had a short period of driving experience. The traffic-psychological survey obtained detailed data via two independent tools. We aimed to find relations between the factors and subfactors of the tools used, namely the BIS-11 (Barratt Impulsiveness Scale) and DAQ (Driver Attitude Questionnaire). The researchers also used these tools in other countries, so it was possible to compare the results obtained. The results from these tools should reveal the psychological causes of as many traffic accidents as possible. Our paper shows the possibilities for the evaluation of the tools used with correlation analysis. The results of our research are shown in symmetrical matrixes of correlation coefficients. Our study also compares its values with the results of foreign authors. Such research has revealed some facts about young drivers’ violations connected with drunk driving, speeding, and other traffic offenses. Our aim was to find connections between the driver’s history (skills, traffic accidents, age, etc.) and psychological characteristics, and we have answered several research questions. In conclusion, we have highlighted the most significant relationships between the factors of driver psychology. Full article
(This article belongs to the Section Probability and Statistics)
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12 pages, 2889 KiB  
Article
On the Multistage Differential Transformation Method for Analyzing Damping Duffing Oscillator and Its Applications to Plasma Physics
by Noufe H. Aljahdaly and S. A. El-Tantawy
Mathematics 2021, 9(4), 432; https://doi.org/10.3390/math9040432 - 22 Feb 2021
Cited by 48 | Viewed by 2149
Abstract
The multistage differential transformation method (MSDTM) is used to find an approximate solution to the forced damping Duffing equation (FDDE). In this paper, we prove that the MSDTM can predict the solution in the long domain as compared to differential transformation method (DTM) [...] Read more.
The multistage differential transformation method (MSDTM) is used to find an approximate solution to the forced damping Duffing equation (FDDE). In this paper, we prove that the MSDTM can predict the solution in the long domain as compared to differential transformation method (DTM) and more accurately than the modified differential transformation method (MDTM). In addition, the maximum residual errors for DTM and its modification methods (MSDTM and MDTM) are estimated. As a real application to the obtained solution, we investigate the oscillations in a complex unmagnetized plasma. To do that, the fluid govern equations of plasma species is reduced to the modified Korteweg–de Vries–Burgers (mKdVB) equation. After that, by using a suitable transformation, the mKdVB equation is transformed into the forced damping Duffing equation. Full article
(This article belongs to the Special Issue Special Functions with Applications to Mathematical Physics)
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29 pages, 12058 KiB  
Article
The Influence of an Integration Time Step on Dynamic Calculation of a Vehicle-Track-Bridge under High-Speed Railway
by Junjie Ye and Hao Sun
Mathematics 2021, 9(4), 431; https://doi.org/10.3390/math9040431 - 22 Feb 2021
Cited by 1 | Viewed by 1650
Abstract
In order to study the influence of an integration time step on dynamic calculation of a vehicle-track-bridge under high-speed railway, a vehicle-track-bridge (VTB) coupled model is established. The influence of the integration time step on calculation accuracy and calculation stability under different speeds [...] Read more.
In order to study the influence of an integration time step on dynamic calculation of a vehicle-track-bridge under high-speed railway, a vehicle-track-bridge (VTB) coupled model is established. The influence of the integration time step on calculation accuracy and calculation stability under different speeds or different track regularity states is studied. The influence of the track irregularity on the integration time step is further analyzed by using the spectral characteristic of sensitive wavelength. According to the results, the disparity among the effect of the integration time step on the calculation accuracy of the VTB coupled model at different speeds is very small. Higher speed requires a smaller integration time step to keep the calculation results stable. The effect of the integration time step on the calculation stability of the maximum vertical acceleration of each component at different speeds is somewhat different, and the mechanism of the effect of the integration time step on the calculation stability of the vehicle-track-bridge coupled system is that corresponding displacement at the integration time step is different. The calculation deviation of the maximum vertical acceleration of the car body, wheel-sets and bridge under the track short wave irregularity state are greatly increased compared with that without track irregularity. The maximum vertical acceleration of wheel-sets, rails, track slabs and the bridge under the track short wave irregularity state all show a significant declining trend. The larger the vibration frequency is, the smaller the range of integration time step is for dynamic calculation. Full article
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26 pages, 2462 KiB  
Article
Multidimensional Fairness Equilibrium Evaluation of Urban Housing Expropriation Compensation Based on VIKOR
by Zhaoyu Cao, Yucheng Zou, Xu Zhao, Kairong Hong and Yanwei Zhang
Mathematics 2021, 9(4), 430; https://doi.org/10.3390/math9040430 - 22 Feb 2021
Cited by 6 | Viewed by 1957
Abstract
Against the backdrop of emerging markets and the transitional society, the large-scale start-up of real estate development projects has brought about rapid economic growth and accelerated urban expansion, followed by extreme disputes between social groups. This paper aims to effectively solve the real [...] Read more.
Against the backdrop of emerging markets and the transitional society, the large-scale start-up of real estate development projects has brought about rapid economic growth and accelerated urban expansion, followed by extreme disputes between social groups. This paper aims to effectively solve the real dilemma of urban housing expropriation by obtaining a consensus regarding the fairness of compensation standards among expropriation compensation-related subjects. Three behavioral preferences—profit-seeking fairness, loss aversion and interactive fairness—were added to a multidimensional fairness equilibrium evaluation indicator system of urban housing expropriation compensation. The entropy method was used to calculate their weights. A multidimensional fairness game model and a multidimensional fairness equilibrium evaluation method based on compromise multi-criteria decision-making VlseKriterijumska Optimizacija I Kompromisno Resenje (VIKOR) of urban housing expropriation compensation were constructed to combine different strategic schemes of related subjects for the purpose of obtaining the compromise optimal solution, that is, the multidimensional fairness game equilibrium solution. The stability of the multidimensional fairness game model and the objectivity of the multidimensional fairness equilibrium evaluation were tested and verified through case data analysis and sensitivity analysis. The conclusion is drawn that the multidimensional fairness game equilibrium solution can effectively resolve extreme disputes regarding urban housing expropriation. Full article
(This article belongs to the Section Fuzzy Sets, Systems and Decision Making)
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19 pages, 769 KiB  
Article
Robust Stabilization of Interval Plants with Uncertain Time-Delay Using the Value Set Concept
by Pedro Zamora, Alejandro Arceo, Noé Martínez, Gerardo Romero and Luis E. Garza
Mathematics 2021, 9(4), 429; https://doi.org/10.3390/math9040429 - 22 Feb 2021
Cited by 4 | Viewed by 1545
Abstract
This paper considers the robust stabilization problem for interval plants with parametric uncertainty and uncertain time-delay based on the value set characterization of closed-loop control systems and the zero exclusion principle. Using Kharitonov’s polynomials, it is possible to establish a sufficient condition to [...] Read more.
This paper considers the robust stabilization problem for interval plants with parametric uncertainty and uncertain time-delay based on the value set characterization of closed-loop control systems and the zero exclusion principle. Using Kharitonov’s polynomials, it is possible to establish a sufficient condition to guarantee the robust stability property. This condition allows us to solve the control synthesis problem using conditions similar to those established in the loopshaping technique and to parameterize the controllers using stable polynomials constructed from classical orthogonal polynomials. Full article
(This article belongs to the Special Issue Robust Stabilization of Linear and Nonlinear Systems)
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17 pages, 285 KiB  
Article
Method for Obtaining Coefficients of Powers of Bivariate Generating Functions
by Dmitry Kruchinin, Vladimir Kruchinin and Yuriy Shablya
Mathematics 2021, 9(4), 428; https://doi.org/10.3390/math9040428 - 22 Feb 2021
Cited by 6 | Viewed by 2090
Abstract
In this paper, we study methods for obtaining explicit formulas for the coefficients of generating functions. To solve this problem, we consider the methods that are based on using the powers of generating functions. We propose to generalize the concept of compositae to [...] Read more.
In this paper, we study methods for obtaining explicit formulas for the coefficients of generating functions. To solve this problem, we consider the methods that are based on using the powers of generating functions. We propose to generalize the concept of compositae to the case of generating functions in two variables and define basic operations on such compositae: composition, addition, multiplication, reciprocation and compositional inversion. These operations allow obtaining explicit formulas for compositae and coefficients of bivariate generating functions. In addition, we present several examples of applying the obtained results for getting explicit formulas for the coefficients of bivariate generating functions. The introduced mathematical apparatus can be used for solving different problems that are related to the theory of generating functions. Full article
(This article belongs to the Special Issue Polynomial Sequences and Their Applications)
20 pages, 1845 KiB  
Article
Differential Evolution Optimal Parameters Tuning with Artificial Neural Network
by Manu Centeno-Telleria, Ekaitz Zulueta, Unai Fernandez-Gamiz, Daniel Teso-Fz-Betoño and Adrián Teso-Fz-Betoño
Mathematics 2021, 9(4), 427; https://doi.org/10.3390/math9040427 - 21 Feb 2021
Cited by 17 | Viewed by 3959
Abstract
Differential evolution (DE) is a simple and efficient population-based stochastic algorithm for solving global numerical optimization problems. DE largely depends on algorithm parameter values and search strategy. Knowledge on how to tune the best values of these parameters is scarce. This paper aims [...] Read more.
Differential evolution (DE) is a simple and efficient population-based stochastic algorithm for solving global numerical optimization problems. DE largely depends on algorithm parameter values and search strategy. Knowledge on how to tune the best values of these parameters is scarce. This paper aims to present a consistent methodology for tuning optimal parameters. At the heart of the methodology is the use of an artificial neural network (ANN) that learns to draw links between the algorithm performance and parameter values. To do so, first, a data-set is generated and normalized, then the ANN approach is performed, and finally, the best parameter values are extracted. The proposed method is evaluated on a set of 24 test problems from the Black-Box Optimization Benchmarking (BBOB) benchmark. Experimental results show that three distinct cases may arise with the application of this method. For each case, specifications about the procedure to follow are given. Finally, a comparison with four tuning rules is performed in order to verify and validate the proposed method’s performance. This study provides a thorough insight into optimal parameter tuning, which may be of great use for users. Full article
(This article belongs to the Section Engineering Mathematics)
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5 pages, 259 KiB  
Article
Fibonacci, Golden Ratio, and Vector Bundles
by Noah Giansiracusa
Mathematics 2021, 9(4), 426; https://doi.org/10.3390/math9040426 - 21 Feb 2021
Viewed by 2311
Abstract
There is a family of vector bundles over the moduli space of stable curves that, while first appearing in theoretical physics, has been an active topic of study for algebraic geometers since the 1990s. By computing the rank of the exceptional Lie algebra [...] Read more.
There is a family of vector bundles over the moduli space of stable curves that, while first appearing in theoretical physics, has been an active topic of study for algebraic geometers since the 1990s. By computing the rank of the exceptional Lie algebra g2 case of these bundles in three different ways, a family of summation formulas for Fibonacci numbers in terms of the golden ratio is derived. Full article
(This article belongs to the Section Algebra, Geometry and Topology)
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15 pages, 729 KiB  
Article
An Enhanced Adaptive Bernstein Collocation Method for Solving Systems of ODEs
by Ahmad Sami Bataineh, Osman Rasit Isik, Moa’ath Oqielat and Ishak Hashim
Mathematics 2021, 9(4), 425; https://doi.org/10.3390/math9040425 - 21 Feb 2021
Cited by 7 | Viewed by 1790
Abstract
In this paper, we introduce two new methods to solve systems of ordinary differential equations. The first method is constituted of the generalized Bernstein functions, which are obtained by Bernstein polynomials, and operational matrix of differentiation with collocation method. The second method depends [...] Read more.
In this paper, we introduce two new methods to solve systems of ordinary differential equations. The first method is constituted of the generalized Bernstein functions, which are obtained by Bernstein polynomials, and operational matrix of differentiation with collocation method. The second method depends on tau method, the generalized Bernstein functions and operational matrix of differentiation. These methods produce a series which is obtained by non-polynomial functions set. We give the standard Bernstein polynomials to explain the generalizations for both methods. By applying the residual correction procedure to the methods, one can estimate the absolute errors for both methods and may obtain more accurate results. We apply the methods to some test examples including linear system, non-homogeneous linear system, nonlinear stiff systems, non-homogeneous nonlinear system and chaotic Genesio system. The numerical shows that the methods are efficient and work well. Increasing m yields a decrease on the errors for all methods. One can estimate the errors by using the residual correction procedure. Full article
(This article belongs to the Special Issue Computational Mathematics and Neural Systems)
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34 pages, 483 KiB  
Article
Long Dimodules and Quasitriangular Weak Hopf Monoids
by José Nicanor Alonso Álvarez, José Manuel Fernández Vilaboa and Ramón González Rodríguez
Mathematics 2021, 9(4), 424; https://doi.org/10.3390/math9040424 - 21 Feb 2021
Cited by 1 | Viewed by 1442
Abstract
In this paper, we prove that for any pair of weak Hopf monoids H and B in a symmetric monoidal category where every idempotent morphism splits, the category of H-B-Long dimodules HBLong is monoidal. Moreover, if H is [...] Read more.
In this paper, we prove that for any pair of weak Hopf monoids H and B in a symmetric monoidal category where every idempotent morphism splits, the category of H-B-Long dimodules HBLong is monoidal. Moreover, if H is quasitriangular and B coquasitriangular, we also prove that HBLong is braided. As a consequence of this result, we obtain that if H is triangular and B cotriangular, HBLong is an example of a symmetric monoidal category. Full article
(This article belongs to the Special Issue New Advances in Algebra, Ring Theory and Homological Algebra)
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