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Mathematics, Volume 9, Issue 12 (June-2 2021) – 142 articles

Cover Story (view full-size image): This paper presents a proposal of a modular robot with origami structure. The proposal is based on a self-scalable and modular link made of soft parts. The kinematics of a single link and several links interconnected is studied and validated. The link has been prototyped, identified, and controlled in position. The experimental data show that the system meets the scalability requirements and that its response is totally reliable and robust. View this paper
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10 pages, 415 KiB  
Article
The Asymptotic Expansion of a Function Introduced by L.L. Karasheva
by Richard Paris
Mathematics 2021, 9(12), 1454; https://doi.org/10.3390/math9121454 - 21 Jun 2021
Viewed by 1319
Abstract
The asymptotic expansion for x± of the entire function [...] Read more.
The asymptotic expansion for x± of the entire function Fn,σ(x;μ)=k=0sin(nγk)sinγkxkk!Γ(μσk),γk=(k+1)π2n for μ>0, 0<σ<1 and n=1,2, is considered. In the special case σ=α/(2n), with 0<α<1, this function was recently introduced by L.L. Karasheva (J. Math. Sciences, 250 (2020) 753–759) as a solution of a fractional-order partial differential equation. By expressing Fn,σ(x;μ) as a finite sum of Wright functions, we employ the standard asymptotics of integral functions of hypergeometric type to determine its asymptotic expansion. This was found to depend critically on the parameter σ (and to a lesser extent on the integer n). Numerical results are presented to illustrate the accuracy of the different expansions obtained. Full article
(This article belongs to the Special Issue Special Functions with Applications to Mathematical Physics)
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12 pages, 294 KiB  
Article
Simultaneous Contour Method of a Trigonometric Integral by Prudnikov et al.
by Robert Reynolds and Allan Stauffer
Mathematics 2021, 9(12), 1453; https://doi.org/10.3390/math9121453 - 21 Jun 2021
Cited by 1 | Viewed by 1165
Abstract
In this present work we derive, evaluate and produce a table of definite integrals involving logarithmic and exponential functions. Some of the closed form solutions derived are expressed in terms of elementary or transcendental functions. A substantial part of this work is new. [...] Read more.
In this present work we derive, evaluate and produce a table of definite integrals involving logarithmic and exponential functions. Some of the closed form solutions derived are expressed in terms of elementary or transcendental functions. A substantial part of this work is new. Full article
20 pages, 597 KiB  
Article
Stochastic Analysis of the Time Continuum
by Miloš Milovanović, Srđan Vukmirović and Nicoletta Saulig
Mathematics 2021, 9(12), 1452; https://doi.org/10.3390/math9121452 - 21 Jun 2021
Cited by 3 | Viewed by 1848
Abstract
This paper considers the time continuum of Brouwer in terms of the complex system physics. It is based upon a processual definition of real numbers which concern the measurement problem. The multiresolution hierarchy of the measurement process is represented by the time operator [...] Read more.
This paper considers the time continuum of Brouwer in terms of the complex system physics. It is based upon a processual definition of real numbers which concern the measurement problem. The multiresolution hierarchy of the measurement process is represented by the time operator acting on continuous signals. The wavelet domain hidden Markov model, which recapitulates statistical properties of the hierarchy, is verified experimentally on a wide range of signal ensembles. It indicates a novel method that has already been proved to be tremendously useful in applied mathematics. Full article
(This article belongs to the Section Mathematics and Computer Science)
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12 pages, 265 KiB  
Article
Representations of Rectifying Isotropic Curves and Their Centrodes in Complex 3-Space
by Jinhua Qian, Pei Yin, Xueshan Fu and Hongzeng Wang
Mathematics 2021, 9(12), 1451; https://doi.org/10.3390/math9121451 - 21 Jun 2021
Cited by 2 | Viewed by 1315
Abstract
In this work, the rectifying isotropic curves are investigated in three-dimensional complex space C3. The conclusion that an isotropic curve is a rectifying curve if and only if its pseudo curvature is a linear function of its pseudo arc-length is achieved. [...] Read more.
In this work, the rectifying isotropic curves are investigated in three-dimensional complex space C3. The conclusion that an isotropic curve is a rectifying curve if and only if its pseudo curvature is a linear function of its pseudo arc-length is achieved. Meanwhile, the rectifying isotropic curves are expressed by the Bessel functions explicitly. Last but not least, the centrodes of rectifying isotropic curves are explored in detail. Full article
(This article belongs to the Special Issue Differential Geometry: Structures on Manifolds and Their Applications)
15 pages, 6820 KiB  
Article
Application of Hyperelastic Nodal Force Method to Evaluation of Aortic Valve Cusps Coaptation: Thin Shell vs. Membrane Formulations
by Yuri Vassilevski, Alexey Liogky and Victoria Salamatova
Mathematics 2021, 9(12), 1450; https://doi.org/10.3390/math9121450 - 21 Jun 2021
Cited by 6 | Viewed by 1709
Abstract
Coaptation characteristics are crucial in an assessment of the competence of reconstructed aortic valves. Shell or membrane formulations can be used to model the valve cusps coaptation. In this paper we compare both formulations in terms of their coaptation characteristics for the first [...] Read more.
Coaptation characteristics are crucial in an assessment of the competence of reconstructed aortic valves. Shell or membrane formulations can be used to model the valve cusps coaptation. In this paper we compare both formulations in terms of their coaptation characteristics for the first time. Our numerical thin shell model is based on a combination of the hyperelastic nodal forces method and the rotation-free finite elements. The shell model is verified on several popular benchmarks for thin-shell analysis. The relative error with respect to reference solutions does not exceed 1–2%. We apply our numerical shell and membrane formulations to model the closure of an idealized aortic valve varying hyperelasticity models and their shear moduli. The coaptation characteristics become almost insensitive to elastic potentials and sensitive to bending stiffness, which reduces the coaptation zone. Full article
(This article belongs to the Special Issue Mathematics in Biomedicine)
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22 pages, 794 KiB  
Article
Lexical Sense Labeling and Sentiment Potential Analysis Using Corpus-Based Dependency Graph
by Tajana Ban Kirigin, Sanda Bujačić Babić and Benedikt Perak
Mathematics 2021, 9(12), 1449; https://doi.org/10.3390/math9121449 - 21 Jun 2021
Cited by 5 | Viewed by 3576
Abstract
This paper describes a graph method for labeling word senses and identifying lexical sentiment potential by integrating the corpus-based syntactic-semantic dependency graph layer, lexical semantic and sentiment dictionaries. The method, implemented as ConGraCNet application on different languages and corpora, projects a semantic function [...] Read more.
This paper describes a graph method for labeling word senses and identifying lexical sentiment potential by integrating the corpus-based syntactic-semantic dependency graph layer, lexical semantic and sentiment dictionaries. The method, implemented as ConGraCNet application on different languages and corpora, projects a semantic function onto a particular syntactical dependency layer and constructs a seed lexeme graph with collocates of high conceptual similarity. The seed lexeme graph is clustered into subgraphs that reveal the polysemous semantic nature of a lexeme in a corpus. The construction of the WordNet hypernym graph provides a set of synset labels that generalize the senses for each lexical cluster. By integrating sentiment dictionaries, we introduce graph propagation methods for sentiment analysis. Original dictionary sentiment values are integrated into ConGraCNet lexical graph to compute sentiment values of node lexemes and lexical clusters, and identify the sentiment potential of lexemes with respect to a corpus. The method can be used to resolve sparseness of sentiment dictionaries and enrich the sentiment evaluation of lexical structures in sentiment dictionaries by revealing the relative sentiment potential of polysemous lexemes with respect to a specific corpus. The proposed approach has the potential to be used as a complementary method to other NLP resources and tasks, including word disambiguation, domain relatedness, sense structure, metaphoricity, as well as a cross- and intra-cultural discourse variations of prototypical conceptualization patterns and knowledge representations. Full article
(This article belongs to the Special Issue New Trends in Graph and Complexity Based Data Analysis and Processing)
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20 pages, 368 KiB  
Article
Variable Selection for the Spatial Autoregressive Model with Autoregressive Disturbances
by Xuan Liu and Jianbao Chen
Mathematics 2021, 9(12), 1448; https://doi.org/10.3390/math9121448 - 21 Jun 2021
Cited by 2 | Viewed by 1884
Abstract
Along with the rapid development of the geographic information system, high-dimensional spatial heterogeneous data has emerged bringing theoretical and computational challenges to statistical modeling and analysis. As a result, effective dimensionality reduction and spatial effect recognition has become very important. This paper focuses [...] Read more.
Along with the rapid development of the geographic information system, high-dimensional spatial heterogeneous data has emerged bringing theoretical and computational challenges to statistical modeling and analysis. As a result, effective dimensionality reduction and spatial effect recognition has become very important. This paper focuses on variable selection in the spatial autoregressive model with autoregressive disturbances (SARAR) which contains a more comprehensive spatial effect. The variable selection procedure is presented by using the so-called penalized quasi-likelihood approach. Under suitable regular conditions, we obtain the rate of convergence and the asymptotic normality of the estimators. The theoretical results ensure that the proposed method can effectively identify spatial effects of dependent variables, find spatial heterogeneity in error terms, reduce the dimension, and estimate unknown parameters simultaneously. Based on step-by-step transformation, a feasible iterative algorithm is developed to realize spatial effect identification, variable selection, and parameter estimation. In the setting of finite samples, Monte Carlo studies and real data analysis demonstrate that the proposed penalized method performs well and is consistent with the theoretical results. Full article
(This article belongs to the Special Issue Multivariate Statistics: Theory and Its Applications)
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13 pages, 1414 KiB  
Article
Computing the Exact Number of Similarity Classes in the Longest Edge Bisection of Tetrahedra
by Jose P. Suárez, Agustín Trujillo and Tania Moreno
Mathematics 2021, 9(12), 1447; https://doi.org/10.3390/math9121447 - 21 Jun 2021
Cited by 2 | Viewed by 1388
Abstract
Showing whether the longest-edge (LE) bisection of tetrahedra meshes degenerates the stability condition or not is still an open problem. Some reasons, in part, are due to the cost for achieving the computation of similarity classes of millions of tetrahedra. We prove the [...] Read more.
Showing whether the longest-edge (LE) bisection of tetrahedra meshes degenerates the stability condition or not is still an open problem. Some reasons, in part, are due to the cost for achieving the computation of similarity classes of millions of tetrahedra. We prove the existence of tetrahedra where the LE bisection introduces, at most, 37 similarity classes. This family of new tetrahedra was roughly pointed out by Adler in 1983. However, as far as we know, there has been no evidence confirming its existence. We also introduce a new data structure and algorithm for computing the number of similarity tetrahedral classes based on integer arithmetic, storing only the square of edges. The algorithm lets us perform compact and efficient high-level similarity class computations with a cost that is only dependent on the number of similarity classes. Full article
(This article belongs to the Section Mathematics and Computer Science)
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20 pages, 403 KiB  
Article
On Some Reversible Cubic Systems
by Barbara Arcet and Valery G. Romanovski
Mathematics 2021, 9(12), 1446; https://doi.org/10.3390/math9121446 - 21 Jun 2021
Cited by 3 | Viewed by 1399
Abstract
We study three systems from the classification of cubic reversible systems given by Żoła̧dek in 1994. Using affine transformations and elimination algorithms from these three families the six components of the center variety are derived and limit-cycle bifurcations in neighborhoods of the components [...] Read more.
We study three systems from the classification of cubic reversible systems given by Żoła̧dek in 1994. Using affine transformations and elimination algorithms from these three families the six components of the center variety are derived and limit-cycle bifurcations in neighborhoods of the components are investigated. The invariance of the systems with respect to the generalized involutions introduced by Bastos, Buzzi and Torregrosa in 2021 is discussed. Computations are performed using the computer algebra systems Mathematica and Singular. Full article
(This article belongs to the Topic Dynamical Systems: Theory and Applications)
16 pages, 1686 KiB  
Article
Particle Filtering: A Priori Estimation of Observational Errors of a State-Space Model with Linear Observation Equation
by Rodi Lykou and George Tsaklidis
Mathematics 2021, 9(12), 1445; https://doi.org/10.3390/math9121445 - 21 Jun 2021
Cited by 4 | Viewed by 1774
Abstract
Observational errors of Particle Filtering are studied over the case of a state-space model with a linear observation equation. In this study, the observational errors are estimated prior to the upcoming observations. This action is added to the basic algorithm of the filter [...] Read more.
Observational errors of Particle Filtering are studied over the case of a state-space model with a linear observation equation. In this study, the observational errors are estimated prior to the upcoming observations. This action is added to the basic algorithm of the filter as a new step for the acquisition of the state estimations. This intervention is useful in the presence of missing data problems mainly, as well as sample tracking for impoverishment issues. It applies theory of Homogeneous and Non-Homogeneous closed Markov Systems to the study of particle distribution over the state domain and, thus, lays the foundations for the employment of stochastic control against impoverishment. A simulating example is quoted to demonstrate the effectiveness of the proposed method in comparison with existing ones, showing that the proposed method is able to combine satisfactory precision of results with a low computational cost and provide an example to achieve impoverishment prediction and tracking. Full article
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34 pages, 714 KiB  
Article
Single-Threshold Model Resource Network and Its Double-Threshold Modifications
by Liudmila Zhilyakova
Mathematics 2021, 9(12), 1444; https://doi.org/10.3390/math9121444 - 21 Jun 2021
Cited by 2 | Viewed by 1753
Abstract
A resource network is a non-classical flow model where the infinitely divisible resource is iteratively distributed among the vertices of a weighted digraph. The model operates in discrete time. The weights of the edges denote their throughputs. The basic model, a standard resource [...] Read more.
A resource network is a non-classical flow model where the infinitely divisible resource is iteratively distributed among the vertices of a weighted digraph. The model operates in discrete time. The weights of the edges denote their throughputs. The basic model, a standard resource network, has one general characteristic of resource amount—the network threshold value. This value depends on graph topology and weights of edges. This paper briefly outlines the main characteristics of standard resource networks and describes two its modifications. In both non-standard models, the changes concern the rules of receiving the resource by the vertices. The first modification imposes restrictions on the selected vertices’ capacity, preventing them from accumulating resource surpluses. In the second modification, a network with so-called greedy vertices, on the contrary, vertices first accumulate resource themselves and only then begin to give it away. It is noteworthy that completely different changes lead, in general, to the same consequences: the appearance of a second threshold value. At some intervals of resource values in networks, their functioning is described by a homogeneous Markov chain, at others by more complex rules. Transient processes and limit states in networks with different topologies and different operation rules are investigated and described. Full article
(This article belongs to the Special Issue Distributed Computer and Communication Networks)
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10 pages, 910 KiB  
Article
The Superiority of Quantum Strategy in 3-Player Prisoner’s Dilemma
by Zhiyuan Dong and Ai-Guo Wu
Mathematics 2021, 9(12), 1443; https://doi.org/10.3390/math9121443 - 21 Jun 2021
Viewed by 1876
Abstract
In this paper, we extend the quantum game theory of Prisoner’s Dilemma to the N-player case. The final state of quantum game theory of N-player Prisoner’s Dilemma is derived, which can be used to investigate the payoff of each player. As [...] Read more.
In this paper, we extend the quantum game theory of Prisoner’s Dilemma to the N-player case. The final state of quantum game theory of N-player Prisoner’s Dilemma is derived, which can be used to investigate the payoff of each player. As demonstration, two cases (2-player and 3-player) are studied to illustrate the superiority of quantum strategy in the game theory. Specifically, the non-unique entanglement parameter is found to maximize the total payoff, which oscillates periodically. Finally, the optimal strategic set is proved to depend on the selection of initial states. Full article
(This article belongs to the Special Issue Advances in Quantum Field Theory and Applications)
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12 pages, 7392 KiB  
Article
Applications of the Network Simulation Method to Differential Equations with Singularities and Chaotic Behaviour
by Joaquín Solano, Francisco Balibrea and José Andrés Moreno
Mathematics 2021, 9(12), 1442; https://doi.org/10.3390/math9121442 - 21 Jun 2021
Cited by 8 | Viewed by 1561
Abstract
In this paper, we deal with some applications of the network simulation method (NMS) to the non-linear differential equations derived of a parametric family associated to stated problems by Newton in and others like the parabolic mirror and van der Pol non-linear equation. [...] Read more.
In this paper, we deal with some applications of the network simulation method (NMS) to the non-linear differential equations derived of a parametric family associated to stated problems by Newton in and others like the parabolic mirror and van der Pol non-linear equation. We underly the efficientcy of the (NMS) method, compare it with Matlab procedures and present figures of solutions of the equations obtained by it on the mentioned problems. Additionally, we introduce also the electric-electronic circuits we have designed to be able of obtaining the solutions of the referred equations. Full article
(This article belongs to the Special Issue Dynamical Systems and Their Applications Methods)
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12 pages, 273 KiB  
Article
Aggregation of Indistinguishability Fuzzy Relations Revisited
by Juan-De-Dios González-Hedström, Juan-José Miñana and Oscar Valero
Mathematics 2021, 9(12), 1441; https://doi.org/10.3390/math9121441 - 21 Jun 2021
Cited by 3 | Viewed by 1510
Abstract
Indistinguishability fuzzy relations were introduced with the aim of providing a fuzzy notion of equivalence relation. Many works have explored their relation to metrics, since they can be interpreted as a kind of measure of similarity and this is, in fact, a dual [...] Read more.
Indistinguishability fuzzy relations were introduced with the aim of providing a fuzzy notion of equivalence relation. Many works have explored their relation to metrics, since they can be interpreted as a kind of measure of similarity and this is, in fact, a dual notion to dissimilarity. Moreover, the problem of how to construct new indistinguishability fuzzy relations by means of aggregation has been explored in the literature. In this paper, we provide new characterizations of those functions that allow us to merge a collection of indistinguishability fuzzy relations into a new one in terms of triangular triplets and, in addition, we explore the relationship between such functions and those that aggregate extended pseudo-metrics, which are the natural distances associated to indistinguishability fuzzy relations. Our new results extend some already known characterizations which involve only bounded pseudo-metrics. In addition, we provide a completely new description of those indistinguishability fuzzy relations that separate points, and we show that both differ a lot. Full article
13 pages, 9270 KiB  
Article
Multiple Novels and Accurate Traveling Wave and Numerical Solutions of the (2+1) Dimensional Fisher-Kolmogorov- Petrovskii-Piskunov Equation
by Mostafa M. A. Khater and Aliaa Mahfooz Alabdali
Mathematics 2021, 9(12), 1440; https://doi.org/10.3390/math9121440 - 21 Jun 2021
Cited by 27 | Viewed by 2093
Abstract
The analytical and numerical solutions of the (2+1) dimensional, Fisher-Kolmogorov-Petrovskii-Piskunov ((2+1) D-Fisher-KPP) model are investigated by employing the modified direct algebraic (MDA), modified Kudryashov (MKud.), and trigonometric-quantic B-spline (TQBS) schemes. This model, which arises in population genetics and nematic liquid crystals, describes the [...] Read more.
The analytical and numerical solutions of the (2+1) dimensional, Fisher-Kolmogorov-Petrovskii-Piskunov ((2+1) D-Fisher-KPP) model are investigated by employing the modified direct algebraic (MDA), modified Kudryashov (MKud.), and trigonometric-quantic B-spline (TQBS) schemes. This model, which arises in population genetics and nematic liquid crystals, describes the reaction–diffusion system by traveling waves in population genetics and the propagation of domain walls, pattern formation in bi-stable systems, and nematic liquid crystals. Many novel analytical solutions are constructed. These solutions are used to evaluate the requested numerical technique’s conditions. The numerical solutions of the considered model are studied, and the absolute value of error between analytical and numerical is calculated to demonstrate the matching between both solutions. Some figures are represented to explain the obtained analytical solutions and the match between analytical and numerical results. The used schemes’ performance shows their effectiveness and power and their ability to handle many nonlinear evolution equations. Full article
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17 pages, 3136 KiB  
Article
Exact Solutions and Conserved Vectors of the Two-Dimensional Generalized Shallow Water Wave Equation
by Chaudry Masood Khalique and Karabo Plaatjie
Mathematics 2021, 9(12), 1439; https://doi.org/10.3390/math9121439 - 21 Jun 2021
Cited by 9 | Viewed by 2248
Abstract
In this article, we investigate a two-dimensional generalized shallow water wave equation. Lie symmetries of the equation are computed first and then used to perform symmetry reductions. By utilizing the three translation symmetries of the equation, a fourth-order ordinary differential equation is obtained [...] Read more.
In this article, we investigate a two-dimensional generalized shallow water wave equation. Lie symmetries of the equation are computed first and then used to perform symmetry reductions. By utilizing the three translation symmetries of the equation, a fourth-order ordinary differential equation is obtained and solved in terms of an incomplete elliptic integral. Moreover, with the aid of Kudryashov’s approach, more closed-form solutions are constructed. In addition, energy and linear momentum conservation laws for the underlying equation are computed by engaging the multiplier approach as well as Noether’s theorem. Full article
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12 pages, 1935 KiB  
Article
Research on Vibration Suppression Method Based on Coaxial Stacking Measurement
by Chuanzhi Sun, Ruirui Li, Ze Chen, Yingjie Mei, Xiaoming Wang, Chengtian Li and Yongmeng Liu
Mathematics 2021, 9(12), 1438; https://doi.org/10.3390/math9121438 - 21 Jun 2021
Cited by 1 | Viewed by 1636
Abstract
A dynamic analysis model of the unbalanced vibration response of a single-rotor system is established to study the corresponding mechanism of the unbalanced excitation force and vibration response caused by the deviation of the rotor mass centroid in this paper, and finally to [...] Read more.
A dynamic analysis model of the unbalanced vibration response of a single-rotor system is established to study the corresponding mechanism of the unbalanced excitation force and vibration response caused by the deviation of the rotor mass centroid in this paper, and finally to achieve the combined rotor vibration suppression. First, the installation of multi-stage rotors during vibration was studied, and the rotor mass centroid transfer model in the rotating coordinate system was established to obtain the unbalanced excitation force vectors of the rotors at all levels based on the traditional stacking assembly method and axiality measurement. Second, the rotor unbalance excitation force vectors were substituted at all levels to establish the finite element analysis model of the single-rotor system. Finally, a simulation analysis was carried out for the stacking assembly of the three-stage rotor, and the rotor test piece was used for the vibration experiment. The results show that the optimal assembly phase of the multi-stage rotor obtained by the dynamic analysis model of the unbalanced vibration response of the single-rotor system can effectively suppress the vibration of the combined rotor. Full article
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17 pages, 1932 KiB  
Article
Multi-Output Learning Based on Multimodal GCN and Co-Attention for Image Aesthetics and Emotion Analysis
by Haotian Miao, Yifei Zhang, Daling Wang and Shi Feng
Mathematics 2021, 9(12), 1437; https://doi.org/10.3390/math9121437 - 20 Jun 2021
Cited by 14 | Viewed by 2386
Abstract
With the development of social networks and intelligent terminals, it is becoming more convenient to share and acquire images. The massive growth of the number of social images makes people have higher demands for automatic image processing, especially in the aesthetic and emotional [...] Read more.
With the development of social networks and intelligent terminals, it is becoming more convenient to share and acquire images. The massive growth of the number of social images makes people have higher demands for automatic image processing, especially in the aesthetic and emotional perspective. Both aesthetics assessment and emotion recognition require a higher ability for the computer to simulate high-level visual perception understanding, which belongs to the field of image processing and pattern recognition. However, existing methods often ignore the prior knowledge of images and intrinsic relationships between aesthetic and emotional perspectives. Recently, machine learning and deep learning have become powerful methods for researchers to solve mathematical problems in computing, such as image processing and pattern recognition. Both images and abstract concepts can be converted into numerical matrices and then establish the mapping relations using mathematics on computers. In this work, we propose an end-to-end multi-output deep learning model based on multimodal Graph Convolutional Network (GCN) and co-attention for aesthetic and emotion conjoint analysis. In our model, a stacked multimodal GCN network is proposed to encode the features under the guidance of the correlation matrix, and a co-attention module is designed to help the aesthetics and emotion feature representation learn from each other interactively. Experimental results indicate that our proposed model achieves competitive performance on the IAE dataset. Progressive results on the AVA and ArtPhoto datasets also prove the generalization ability of our model. Full article
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13 pages, 509 KiB  
Article
Quasistatic Porous-Thermoelastic Problems: An a Priori Error Analysis
by Jacobo Baldonedo, José R. Fernández and José A. López-Campos
Mathematics 2021, 9(12), 1436; https://doi.org/10.3390/math9121436 - 20 Jun 2021
Viewed by 1179
Abstract
In this paper, we deal with the numerical approximation of some porous-thermoelastic problems. Since the inertial effects are assumed to be negligible, the resulting motion equations are quasistatic. Then, by using the finite element method and the implicit Euler scheme, a fully discrete [...] Read more.
In this paper, we deal with the numerical approximation of some porous-thermoelastic problems. Since the inertial effects are assumed to be negligible, the resulting motion equations are quasistatic. Then, by using the finite element method and the implicit Euler scheme, a fully discrete approximation is introduced. We prove a discrete stability property and a main error estimates result, from which we conclude the linear convergence under appropriate regularity conditions on the continuous solution. Finally, several numerical simulations are shown to demonstrate the accuracy of the approximation, the behavior of the solution and the decay of the discrete energy. Full article
(This article belongs to the Special Issue Applied Mathematics and Solid Mechanics)
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17 pages, 606 KiB  
Article
A Comparative Study between Discrete Stochastic Arithmetic and Floating-Point Arithmetic to Validate the Results of Fractional Order Model of Malaria Infection
by Samad Noeiaghdam, Aliona Dreglea, Hüseyin Işık and Muhammad Suleman
Mathematics 2021, 9(12), 1435; https://doi.org/10.3390/math9121435 - 20 Jun 2021
Cited by 16 | Viewed by 1535
Abstract
The researchers aimed to study the nonlinear fractional order model of malaria infection based on the Caputo-Fabrizio fractional derivative. The homotopy analysis transform method (HATM) is applied based on the floating-point arithmetic (FPA) and the discrete stochastic arithmetic (DSA). In the FPA, to [...] Read more.
The researchers aimed to study the nonlinear fractional order model of malaria infection based on the Caputo-Fabrizio fractional derivative. The homotopy analysis transform method (HATM) is applied based on the floating-point arithmetic (FPA) and the discrete stochastic arithmetic (DSA). In the FPA, to show the accuracy of the method we use the absolute error which depends on the exact solution and a positive value ε. Because in real life problems we do not have the exact solution and the optimal value of ε, we need to introduce a new condition and arithmetic to show the efficiency of the method. Thus the CESTAC (Controle et Estimation Stochastique des Arrondis de Calculs) method and the CADNA (Control of Accuracy and Debugging for Numerical Applications) library are applied. The CESTAC method is based on the DSA. Also, a new termination criterion is used which is based on two successive approximations. Using the CESTAC method we can find the optimal approximation, the optimal error and the optimal iteration of the method. The main theorem of the CESTAC method is proved to show that the number of common significant digits (NCSDs) between two successive approximations are almost equal to the NCSDs of the exact and approximate solutions. Plotting several graphs, the regions of convergence are demonstrated for different number of iterations k = 5, 10. The numerical results based on the simulated data show the advantages of the DSA in comparison with the FPA. Full article
(This article belongs to the Special Issue Mathematical Modeling and Its Application in Medicine)
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32 pages, 4630 KiB  
Article
On Self-Interference Cancellation and Non-Idealities Suppression in Full-Duplex Radio Transceivers
by Areeba Ayesha, MuhibUr Rahman, Amir Haider and Shabbir Majeed Chaudhry
Mathematics 2021, 9(12), 1434; https://doi.org/10.3390/math9121434 - 20 Jun 2021
Cited by 10 | Viewed by 2853
Abstract
One of the major impediments in the design and operation of a full-duplex radio transceiver is the presence of self-interference (SI), that is, the transceiver’s transmitted signal, 60–100 dB stronger than the desired signal of interest. To reduce the SI signal below the [...] Read more.
One of the major impediments in the design and operation of a full-duplex radio transceiver is the presence of self-interference (SI), that is, the transceiver’s transmitted signal, 60–100 dB stronger than the desired signal of interest. To reduce the SI signal below the receiver’s sensitivity before coupling it to the receiver, radio frequency (RF)/analog domain cancellation is carried out. Even after SI cancellation to the required level in the analog domain, the residual SI signal still exits and lowers the transceiver’s performance. For residual SI cancellation, a digital domain cancellation is carried out. RF impairments are the major obstacle in the residual SI cancellation path in the digital domain. Linearization of RF impairments such as IQ mixer imbalance in the transmitter and receiver chain, non-linear PA with memory, and non-linear LNA are also carried out. Performance evaluation of the proposed techniques is carried out based on SINR, the power of different SI signal components, PSD, output to input relationship, SNR vs. BER, spectrum analyzer, constellation diagram, and link budget analysis. The proposed techniques provide attractive RF/analog SI cancellation of up to 80–90 dB, digital residual SI cancellation of up to 35 to 40 dB, total SI cancellation of up to 110 to 130 dB, and an SINR improvement of up to 50 dB. Full article
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12 pages, 281 KiB  
Article
A New Approach of Some Contractive Mappings on Metric Spaces
by Ion Marian Olaru and Nicolae Adrian Secelean
Mathematics 2021, 9(12), 1433; https://doi.org/10.3390/math9121433 - 19 Jun 2021
Cited by 6 | Viewed by 1653
Abstract
In this paper, we introduce a new contraction-type mapping and provide a fixed-point theorem which generalizes and improves some existing results in the literature. Thus, we prove that the Boyd and Wong theorem (1969) and, more recently, the fixed-point results due to Wardowski [...] Read more.
In this paper, we introduce a new contraction-type mapping and provide a fixed-point theorem which generalizes and improves some existing results in the literature. Thus, we prove that the Boyd and Wong theorem (1969) and, more recently, the fixed-point results due to Wardowski (2012), Turinici (2012), Piri and Kumam (2016), Secelean (2016), Proinov (2020), and others are consequences of our main result. An application in integral equations and some illustrative examples are indicated. Full article
(This article belongs to the Special Issue Fixed Point, Optimization, and Applications)
13 pages, 360 KiB  
Article
Estimating the Quadratic Form xTA−mx for Symmetric Matrices: Further Progress and Numerical Computations
by Marilena Mitrouli, Athanasios Polychronou, Paraskevi Roupa and Ondřej Turek
Mathematics 2021, 9(12), 1432; https://doi.org/10.3390/math9121432 - 19 Jun 2021
Cited by 3 | Viewed by 1692
Abstract
In this paper, we study estimates for quadratic forms of the type xTAmx, mN, for symmetric matrices. We derive a general approach for estimating this type of quadratic form and we present some upper [...] Read more.
In this paper, we study estimates for quadratic forms of the type xTAmx, mN, for symmetric matrices. We derive a general approach for estimating this type of quadratic form and we present some upper bounds for the corresponding absolute error. Specifically, we consider three different approaches for estimating the quadratic form xTAmx. The first approach is based on a projection method, the second is a minimization procedure, and the last approach is heuristic. Numerical examples showing the effectiveness of the estimates are presented. Furthermore, we compare the behavior of the proposed estimates with other methods that are derived in the literature. Full article
(This article belongs to the Special Issue Numerical Linear Algebra and the Applications)
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9 pages, 303 KiB  
Article
An Efficient Approach to Point-Counting on Elliptic Curves from a Prominent Family over the Prime Field Fp
by Yuri Borissov and Miroslav Markov
Mathematics 2021, 9(12), 1431; https://doi.org/10.3390/math9121431 - 19 Jun 2021
Viewed by 4015
Abstract
Here, we elaborate an approach for determining the number of points on elliptic curves from the family Ep={Ea:y2=x3+a(modp),a0}, where p [...] Read more.
Here, we elaborate an approach for determining the number of points on elliptic curves from the family Ep={Ea:y2=x3+a(modp),a0}, where p is a prime number >3. The essence of this approach consists in combining the well-known Hasse bound with an explicit formula for the quantities of interest-reduced modulo p. It allows to advance an efficient technique to compute the six cardinalities associated with the family Ep, for p1(mod3), whose complexity is O˜(log2p), thus improving the best-known algorithmic solution with almost an order of magnitude. Full article
18 pages, 2201 KiB  
Article
A Selectively Fuzzified Back Propagation Network Approach for Precisely Estimating the Cycle Time Range in Wafer Fabrication
by Yu-Cheng Wang, Horng-Ren Tsai and Toly Chen
Mathematics 2021, 9(12), 1430; https://doi.org/10.3390/math9121430 - 19 Jun 2021
Cited by 13 | Viewed by 1589
Abstract
Forecasting the cycle time of each job is a critical task for a factory. However, recent studies have shown that it is a challenging task, even with state-of-the-art deep learning techniques. To address this challenge, a selectively fuzzified back propagation network (SFBPN) approach [...] Read more.
Forecasting the cycle time of each job is a critical task for a factory. However, recent studies have shown that it is a challenging task, even with state-of-the-art deep learning techniques. To address this challenge, a selectively fuzzified back propagation network (SFBPN) approach is proposed to estimate the range of a cycle time, the results of which provide valuable information for many managerial purposes. The SFBPN approach is distinct from existing methods, because the thresholds on both the hidden and output layers of a back propagation network are fuzzified to tighten the range of a cycle time, while most of the existing methods only fuzzify the threshold on the output node. In addition, a random search and local optimization algorithm is also proposed to derive the optimal values of the fuzzy thresholds. The proposed methodology is applied to a real case from the literature. The experimental results show that the proposed methodology improved the forecasting precision by up to 65%. Full article
(This article belongs to the Special Issue Fuzzy Group Decision Making)
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15 pages, 4507 KiB  
Article
Electromagnetic Scattering from a Graphene Disk: Helmholtz-Galerkin Technique and Surface Plasmon Resonances
by Mario Lucido
Mathematics 2021, 9(12), 1429; https://doi.org/10.3390/math9121429 - 19 Jun 2021
Cited by 10 | Viewed by 1797
Abstract
The surface plasmon resonances of a monolayer graphene disk, excited by an impinging plane wave, are studied by means of an analytical-numerical technique based on the Helmholtz decomposition and the Galerkin method. An integral equation is obtained by imposing the impedance boundary condition [...] Read more.
The surface plasmon resonances of a monolayer graphene disk, excited by an impinging plane wave, are studied by means of an analytical-numerical technique based on the Helmholtz decomposition and the Galerkin method. An integral equation is obtained by imposing the impedance boundary condition on the disk surface, assuming the graphene surface conductivity provided by the Kubo formalism. The problem is equivalently formulated as a set of one-dimensional integral equations for the harmonics of the surface current density. The Helmholtz decomposition of each harmonic allows for scalar unknowns in the vector Hankel transform domain. A fast-converging Fredholm second-kind matrix operator equation is achieved by selecting the eigenfunctions of the most singular part of the integral operator, reconstructing the physical behavior of the unknowns, as expansion functions in a Galerkin scheme. The surface plasmon resonance frequencies are simply individuated by the peaks of the total scattering cross-section and the absorption cross-section, which are expressed in closed form. It is shown that the surface plasmon resonance frequencies can be tuned by operating on the chemical potential of the graphene and that, for orthogonal incidence, the corresponding near field behavior resembles a cylindrical standing wave with one variation along the disk azimuth. Full article
(This article belongs to the Special Issue Analytical Methods in Wave Scattering and Diffraction)
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39 pages, 3635 KiB  
Article
A Multispecies Cross-Diffusion Model for Territorial Development
by Abdulaziz Alsenafi and Alethea B. T. Barbaro
Mathematics 2021, 9(12), 1428; https://doi.org/10.3390/math9121428 - 19 Jun 2021
Cited by 2 | Viewed by 1725
Abstract
We develop an agent-based model on a lattice to investigate territorial development motivated by markings such as graffiti, generalizing a previously-published model to account for K groups instead of two groups. We then analyze this model and present two novel variations. Our model [...] Read more.
We develop an agent-based model on a lattice to investigate territorial development motivated by markings such as graffiti, generalizing a previously-published model to account for K groups instead of two groups. We then analyze this model and present two novel variations. Our model assumes that agents’ movement is a biased random walk away from rival groups’ markings. All interactions between agents are indirect, mediated through the markings. We numerically demonstrate that in a system of three groups, the groups segregate in certain parameter regimes. Starting from the discrete model, we formally derive the continuum system of 2K convection–diffusion equations for our model. These equations exhibit cross-diffusion due to the avoidance of the rival groups’ markings. Both through numerical simulations and through a linear stability analysis of the continuum system, we find that many of the same properties hold for the K-group model as for the two-group model. We then introduce two novel variations of the agent-based model, one corresponding to some groups being more timid than others, and the other corresponding to some groups being more threatening than others. These variations present different territorial patterns than those found in the original model. We derive corresponding systems of convection–diffusion equations for each of these variations, finding both numerically and through linear stability analysis that each variation exhibits a phase transition. Full article
(This article belongs to the Special Issue Nonlinear Equations: Theory, Methods, and Applications II)
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24 pages, 3686 KiB  
Article
A Fuzzy Recommendation System for the Automatic Personalization of Physical Rehabilitation Exercises in Stroke Patients
by Cristian Gmez-Portes, José Jesús Castro-Schez, Javier Albusac, Dorothy N. Monekosso and David Vallejo
Mathematics 2021, 9(12), 1427; https://doi.org/10.3390/math9121427 - 19 Jun 2021
Cited by 3 | Viewed by 2058
Abstract
Stroke is among the top 10 leading causes of death and disability around the world. Patients who suffer from this disease usually perform physical exercises at home to improve their condition. These exercises are recommended by therapists based on the patient’s progress level, [...] Read more.
Stroke is among the top 10 leading causes of death and disability around the world. Patients who suffer from this disease usually perform physical exercises at home to improve their condition. These exercises are recommended by therapists based on the patient’s progress level, and may be remotely supervised by them if technology is an option for both. At this point, two major challenges must be faced. The first one is the lack of specialized medical staff to remotely handle the growing number of stroke patients. The second one is the difficulty of dynamically adapt the patient’s therapy plan in real time whilst they rehabilitate at home, since their evolution varies as the rehabilitation process progresses. In this context, we present a fuzzy system that is able to automatically adapt the rehabilitation plan of stroke patients. The use of fuzzy logic greatly facilitates the monitoring and guidance of stroke patients. Moreover, the system is capable of automatically generating modifications of existent exercises whilst considering their particularities at any given time. A preliminary experiment was conducted to show the advantages of the proposal, and the results suggest that the application of fuzzy logic may help make correct decisions based on the patient’s progress level. Full article
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30 pages, 3148 KiB  
Article
Coupling the Cell Method with the Boundary Element Method in Static and Quasi–Static Electromagnetic Problems
by Federico Moro and Lorenzo Codecasa
Mathematics 2021, 9(12), 1426; https://doi.org/10.3390/math9121426 - 19 Jun 2021
Cited by 6 | Viewed by 1607
Abstract
A unified discretization framework, based on the concept of augmented dual grids, is proposed for devising hybrid formulations which combine the Cell Method and the Boundary Element Method for static and quasi-static electromagnetic field problems. It is shown that hybrid approaches, already proposed [...] Read more.
A unified discretization framework, based on the concept of augmented dual grids, is proposed for devising hybrid formulations which combine the Cell Method and the Boundary Element Method for static and quasi-static electromagnetic field problems. It is shown that hybrid approaches, already proposed in literature, can be rigorously formulated within this framework. As a main outcome, a novel direct hybrid approach amenable to iterative solution is derived. Both direct and indirect hybrid approaches, applied to an axisymmetric model, are compared with a reference third-order 2D FEM solution. The effectiveness of the indirect approach, equivalent to the direct approach, is finally tested on a fully 3D benchmark with more complex topology. Full article
(This article belongs to the Special Issue The BEM and FEM/BEM Methods in Computational Electromagnetics)
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24 pages, 6119 KiB  
Article
Interrelationship among CE Adoption Obstacles of Supply Chain in the Textile Sector: Based on the DEMATEL-ISM Approach
by Wen-Kuo Chen and Ching-Torng Lin
Mathematics 2021, 9(12), 1425; https://doi.org/10.3390/math9121425 - 19 Jun 2021
Cited by 9 | Viewed by 2733
Abstract
Globally, in the innovative and distributional circular textiles, the textile sector of Taiwan has a prominent place. Within the textile industry, the circular economy (CE) obstacles adopted have been studied by several scholars. However, the interrelationships among these obstacles are easily ignored. The [...] Read more.
Globally, in the innovative and distributional circular textiles, the textile sector of Taiwan has a prominent place. Within the textile industry, the circular economy (CE) obstacles adopted have been studied by several scholars. However, the interrelationships among these obstacles are easily ignored. The present study aimed to identify CE adoption obstacles from the supply chain (SC) perspective in Taiwan’s textile sector by analyzing the interrelationships among the CE adoption obstacles and establishing a hierarchical network and the causal inter relationships of the identified obstacles. Furthermore, the CE adoption obstacles and interrelationships were analyzed using interpretative structural modeling and the decision-making trial and evaluation laboratory (ISM-DEMATEL). The common results of the two methods demonstrated that two obstacles, consumers not having sufficient knowledge and awareness of reuse/recycling (B1) and a lack of successful business models and frameworks for CE implementation (B3), were the significant obstacles influencing adopting CE in the textile supply chain, while the obstacle making the most efficient way (B12) of the right decision to implement CE was minor. Thus, the government should formulate friendly laws and regulations that encourage CE adoption, while textile firms should monitor and control recycling and efficiency approaches handling the CE adoption problems. Our results could offer first-hand knowledge to textile firms or managers to effetely achieve CE implementation objectives. Full article
(This article belongs to the Special Issue Advances in Multiple Criteria Decision Analysis)
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