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Axioms, Volume 12, Issue 12 (December 2023) – 71 articles

Cover Story (view full-size image): In this article, we go deeper into the study of some types of decompositions defined by triangular norms and conorms. We work in the spirit of the classical Arrovian models in the fuzzy setting and their possible extensions. This allows us to achieve characterizations of existence and uniqueness for such decompositions. We provide rules to obtain them under some specific conditions. We conclude by applying the results achieved to the study of fuzzy preferences. View this paper
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12 pages, 1033 KiB  
Article
Equitable and Paired Equitable Domination in Inflated Graphs and Their Complements
Axioms 2023, 12(12), 1134; https://doi.org/10.3390/axioms12121134 - 18 Dec 2023
Viewed by 756
Abstract
Domination plays an indispensable role in graph theory. Various types of domination explore various types of applications. Equal-status people work together and interlace with each other easily. In this paper, the paired equitable domination of a graph, its inflated graph, and its complement [...] Read more.
Domination plays an indispensable role in graph theory. Various types of domination explore various types of applications. Equal-status people work together and interlace with each other easily. In this paper, the paired equitable domination of a graph, its inflated graph, and its complement of an inflated graph were studied. The relationship between the domination number of the graph, the equitable domination number, and the paired equitable domination number of complements of the inflated graph were established. Furthermore, we proved the Nordhaus–Gaddum-type inequality, that is, γpre(H)+γpre(H)6 if H is a graph with m nodes where m0, 2(mod 8) and d(ai) = (m/2) for all ai. The challenges and limitations of this parameter of paired equitable and equitable domination depends on the degree of the vertex of the graph. Practical applications are discussed in various fields and illustrated using the studied parameter. Full article
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16 pages, 571 KiB  
Article
KCC Theory of the Oregonator Model for Belousov-Zhabotinsky Reaction
Axioms 2023, 12(12), 1133; https://doi.org/10.3390/axioms12121133 - 18 Dec 2023
Viewed by 739
Abstract
The behavior of the simplest realistic Oregonator model of the BZ-reaction from the perspective of KCC theory has been investigated. In order to reduce the complexity of the model, we initially transformed the first-order differential equation of the Oregonator model into a system [...] Read more.
The behavior of the simplest realistic Oregonator model of the BZ-reaction from the perspective of KCC theory has been investigated. In order to reduce the complexity of the model, we initially transformed the first-order differential equation of the Oregonator model into a system of second-order differential equations. In this approach, we describe the evolution of the Oregonator model in geometric terms, by considering it as a geodesic in a Finsler space. We have found five KCC invariants using the general expression of the nonlinear and Berwald connections. To understand the chaotic behavior of the Oregonator model, the deviation vector and its curvature around equilibrium points are studied. We have obtained the necessary and sufficient conditions for the parameters of the system in order to have the Jacobi stability near the equilibrium points. Further, a comprehensive examination was conducted to compare the linear stability and Jacobi stability of the Oregonator model at its equilibrium points, and We highlight these instances with a few illustrative examples. Full article
(This article belongs to the Special Issue Differential Geometry and Its Application II)
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19 pages, 347 KiB  
Article
Neighbor Distinguishing Colorings of Graphs with the Restriction for Maximum Average Degree
Axioms 2023, 12(12), 1132; https://doi.org/10.3390/axioms12121132 - 18 Dec 2023
Viewed by 728
Abstract
Neighbor distinguishing colorings of graphs represent powerful tools for solving the channel assignment problem in wireless communication networks. They consist of two forms of coloring: neighbor distinguishing edge coloring, and neighbor distinguishing total coloring. The neighbor distinguishing edge (total) coloring of a graph [...] Read more.
Neighbor distinguishing colorings of graphs represent powerful tools for solving the channel assignment problem in wireless communication networks. They consist of two forms of coloring: neighbor distinguishing edge coloring, and neighbor distinguishing total coloring. The neighbor distinguishing edge (total) coloring of a graph G is an edge (total) coloring with the requirement that each pair of adjacent vertices contains different color sets. The neighbor distinguishing edge (total) chromatic number of G is the smallest integer k in cases where a neighbor distinguishing edge (total) coloring exists through the use of k colors in G. The maximum average degree of G is the maximum of the average degree of its non-empty subgraphs. In this paper, we characterize the neighbor distinguishing edge (total) chromatic numbers of graphs with a maximum average degree less than four by means of the discharging method. Full article
(This article belongs to the Special Issue Recent Advances in Graph Theory with Applications)
21 pages, 316 KiB  
Article
Multiplication Operators on Weighted Zygmund Spaces of the First Cartan Domain
Axioms 2023, 12(12), 1131; https://doi.org/10.3390/axioms12121131 - 17 Dec 2023
Viewed by 662
Abstract
Inspired by some recent studies of the multiplication operators on holomorphic function spaces of the classical domains such as the open unit disk, the unit ball and the unit polydisk, the purpose of the present paper is to study just the operators that [...] Read more.
Inspired by some recent studies of the multiplication operators on holomorphic function spaces of the classical domains such as the open unit disk, the unit ball and the unit polydisk, the purpose of the present paper is to study just the operators that are defined on weighted Zygmund spaces of the first Cartan domain. We obtain some necessary conditions and sufficient conditions for the operators to be bounded and compact. Full article
(This article belongs to the Special Issue Recent Advances in Functional Analysis and Operator Theory)
14 pages, 444 KiB  
Article
Coefficient Inequalities for q-Convex Functions with Respect to q-Analogue of the Exponential Function
Axioms 2023, 12(12), 1130; https://doi.org/10.3390/axioms12121130 - 15 Dec 2023
Viewed by 781
Abstract
In mathematical analysis, the q-analogue of a function refers to a modified version of the function that is derived from q-series expansions. This paper is focused on the q-analogue of the exponential function and investigates a class of convex functions [...] Read more.
In mathematical analysis, the q-analogue of a function refers to a modified version of the function that is derived from q-series expansions. This paper is focused on the q-analogue of the exponential function and investigates a class of convex functions associated with it. The main objective is to derive precise inequalities that bound the coefficients of these convex functions. In this research, the initial coefficient bounds, Fekete–Szegő problem, second and third Hankel determinant have been determined. These coefficient bounds provide valuable information about the behavior and properties of the functions within the considered class. Full article
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18 pages, 1090 KiB  
Article
Finite-Time Stability of Impulsive Fractional Differential Equations with Pure Delays
Axioms 2023, 12(12), 1129; https://doi.org/10.3390/axioms12121129 - 15 Dec 2023
Viewed by 755
Abstract
This paper introduces a novel concept of the impulsive delayed Mittag–Leffler-type vector function, an extension of the Mittag–Leffler matrix function. It is essential to seek explicit formulas for the solutions to linear impulsive fractional differential delay equations. Based on explicit formulas of the [...] Read more.
This paper introduces a novel concept of the impulsive delayed Mittag–Leffler-type vector function, an extension of the Mittag–Leffler matrix function. It is essential to seek explicit formulas for the solutions to linear impulsive fractional differential delay equations. Based on explicit formulas of the solutions, the finite-time stability results of impulsive fractional differential delay equations are presented. Finally, we present four examples to illustrate the validity of our theoretical results. Full article
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13 pages, 358 KiB  
Article
Spectral Analysis of the Adjacency Matrices for Alternating Quotients of Hyperbolic Triangle Group *(3,q,r) for q < r Primes
Axioms 2023, 12(12), 1128; https://doi.org/10.3390/axioms12121128 - 15 Dec 2023
Viewed by 699
Abstract
Hyperbolic triangle groups are found within the category of finitely generated groups. These are topological groups formed by the reflections along the sides of a hyperbolic triangle and acting properly discontinuously on the hyperbolic plane. Higman raised a question about the simplicity of [...] Read more.
Hyperbolic triangle groups are found within the category of finitely generated groups. These are topological groups formed by the reflections along the sides of a hyperbolic triangle and acting properly discontinuously on the hyperbolic plane. Higman raised a question about the simplicity of finitely generated groups. The best known example of a simple group is the alternating group An, where n5. This article establishes a relation between the hyperbolic triangle group denoted as *(3,7,r) and the alternating group. The approach involves employing coset diagrams to establish this connection. The construction of adjacency matrices for these coset diagrams is performed, followed by a detailed examination of their spectral characteristics. Full article
(This article belongs to the Special Issue Recent Advances in Representation Theory with Applications)
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15 pages, 328 KiB  
Article
On Boundary Controllability for the Higher-Order Nonlinear Schrödinger Equation
Axioms 2023, 12(12), 1127; https://doi.org/10.3390/axioms12121127 - 15 Dec 2023
Viewed by 725
Abstract
A control problem with final overdetermination is considered for the higher-order nonlinear Schrödinger equation on a bounded interval. The boundary condition on the space derivative is chosen as the control. Results on the global existence of solutions under small input data are established. [...] Read more.
A control problem with final overdetermination is considered for the higher-order nonlinear Schrödinger equation on a bounded interval. The boundary condition on the space derivative is chosen as the control. Results on the global existence of solutions under small input data are established. Full article
(This article belongs to the Special Issue Advances in Nonlinear Analysis and Boundary Value Problems)
16 pages, 321 KiB  
Article
Entropy and Multi-Fractal Analysis in Complex Fractal Systems Using Graph Theory
Axioms 2023, 12(12), 1126; https://doi.org/10.3390/axioms12121126 - 15 Dec 2023
Viewed by 714
Abstract
In 1997, Sierpinski graphs, S(n,k), were obtained by Klavzar and Milutinovic. The graph S(1,k) represents the complete graph Kk and S(n,3) is known as the graph [...] Read more.
In 1997, Sierpinski graphs, S(n,k), were obtained by Klavzar and Milutinovic. The graph S(1,k) represents the complete graph Kk and S(n,3) is known as the graph of the Tower of Hanoi. Through generalizing the notion of a Sierpinski graph, a graph named a generalized Sierpinski graph, denoted by Sie(Λ,t), already exists in the literature. For every graph, numerous polynomials are being studied, such as chromatic polynomials, matching polynomials, independence polynomials, and the M-polynomial. For every polynomial there is an underlying geometrical object which extracts everything that is hidden in a polynomial of a common framework. Now, we describe the steps by which we complete our task. In the first step, we generate an M-polynomial for a generalized Sierpinski graph Sie(Λ,t). In the second step, we extract some degree-based indices of a generalized Sierpinski graph Sie(Λ,t) using the M-polynomial generated in step 1. In step 3, we generate the entropy of a generalized Sierpinski graph Sie(Λ,t) by using the Randić index. Full article
(This article belongs to the Special Issue Advances in Graph Theory and Combinatorial Optimization)
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18 pages, 4656 KiB  
Article
Dynamical Analysis and Misalignment Projection Synchronization of a Novel RLCM Fractional-Order Memristor Circuit System
Axioms 2023, 12(12), 1125; https://doi.org/10.3390/axioms12121125 - 15 Dec 2023
Viewed by 742
Abstract
In this paper, a simple and novel fractional-order memristor circuit is established, which contains only resistance, inductance, capacitance and memristor. By using fractional calculus theory and the Adomian numerical algorithm, special bifurcations, chaotic degradation, C0 and Spectral Entropy (SE) complexity under one-dimensional [...] Read more.
In this paper, a simple and novel fractional-order memristor circuit is established, which contains only resistance, inductance, capacitance and memristor. By using fractional calculus theory and the Adomian numerical algorithm, special bifurcations, chaotic degradation, C0 and Spectral Entropy (SE) complexity under one-dimensional and two-dimensional parameter variations with different orders, parameters and initial memristor values of the system were studied. Meanwhile, in order to better utilize the applications of fractional-order memristor systems in communication and security, a misalignment projection synchronization scheme for fractional-order systems is proposed, which overcomes the shortcomings of constructing Lyapunov functions for fractional-order systems to prove stability and designing controllers for the Laplace transform matrix. Full article
(This article belongs to the Special Issue Advances in Theory and Applications of Chaotic and Nonlinear Dynamics)
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16 pages, 896 KiB  
Article
Vector-Valued Shepard Processes: Approximation with Summability
Axioms 2023, 12(12), 1124; https://doi.org/10.3390/axioms12121124 - 15 Dec 2023
Viewed by 711
Abstract
In this work, vector-valued continuous functions are approximated uniformly on the unit hypercube by Shepard operators. If λ denotes the usual parameter of the Shepard operators and m is the dimension of the hypercube, then our results show that it is possible to [...] Read more.
In this work, vector-valued continuous functions are approximated uniformly on the unit hypercube by Shepard operators. If λ denotes the usual parameter of the Shepard operators and m is the dimension of the hypercube, then our results show that it is possible to obtain a uniform approximation of a continuous vector-valued function by these operators when λm+1. By using three-dimensional parametric plots, we illustrate this uniform approximation for some vector-valued functions. Finally, the influence in approximation by regular summability processes is studied, and their motivation is shown. Full article
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15 pages, 353 KiB  
Article
The Algebra of Signatures for Extreme Two-Uniform Hypergraphs
Axioms 2023, 12(12), 1123; https://doi.org/10.3390/axioms12121123 - 15 Dec 2023
Viewed by 721
Abstract
In the last decade, several characterizations have been constructed for constructions such as extreme hypergraphs. One of the most recently described features is the signature. A signature is a number that uniquely describes an extremal and allows one to efficiently store the extremal [...] Read more.
In the last decade, several characterizations have been constructed for constructions such as extreme hypergraphs. One of the most recently described features is the signature. A signature is a number that uniquely describes an extremal and allows one to efficiently store the extremal two-uniform hypergraph itself. However, for the signature, although various algorithms have been derived for transforming it into other object-characteristics such as the base, the adjacency matrix, and the vector of vertex degrees, no isolated signature union and intersection apparatus has been constructed. This allows us to build efficient algorithms based on signatures, the most compact representation of extremal two-uniform hypergraphs. The nature of the algebraic construction that can be built on a set of signatures using union and intersection operations has also been defined. It is proved that an algebra on a set of signatures with either the union or intersection operation forms a monoid; if the algebra is defined on a set of signatures with both union and intersection operations, it forms a distributive lattice. Full article
(This article belongs to the Special Issue Advances in Graph Theory and Combinatorial Optimization)
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20 pages, 622 KiB  
Article
Multiplicative Consistent q-Rung Orthopair Fuzzy Preference Relations with Application to Critical Factor Analysis in Crowdsourcing Task Recommendation
Axioms 2023, 12(12), 1122; https://doi.org/10.3390/axioms12121122 - 14 Dec 2023
Viewed by 755
Abstract
This paper presents a group decision-making (GDM) method based on q-rung orthopair fuzzy preference relations (q-ROFPRs). Firstly, the multiplicative consistent q-ROFPRs (MCq-ROFPRs) and the normalized q-rung orthopair fuzzy priority weight vectors (q-ROFPWVs) are introduced. Then, to obtain q-ROFPWVs, a goal programming model under [...] Read more.
This paper presents a group decision-making (GDM) method based on q-rung orthopair fuzzy preference relations (q-ROFPRs). Firstly, the multiplicative consistent q-ROFPRs (MCq-ROFPRs) and the normalized q-rung orthopair fuzzy priority weight vectors (q-ROFPWVs) are introduced. Then, to obtain q-ROFPWVs, a goal programming model under q-ROFPRs is established to minimize their deviation from the MCq-ROFPRs and minimize the weight uncertainty. Further, a group goal programming model of ideal MCq-ROFPRs is constructed to obtain the expert weights using the compatibility measure between the ideal MCq-ROFPRs and the individual q-ROFPRs. Finally, a GDM method with unknown expert weights is solved by combining the group goal programming model and the simple q-rung orthopair fuzzy weighted geometric (Sq-ROFWG) operator. The effectiveness and practicality of the proposed GDM method are verified by solving the crucial factors in crowdsourcing task recommendation. The results show that the developed GDM method effectively considers the important measures of experts and identifies the crucial factors that are more reliable than two other methods. Full article
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24 pages, 11423 KiB  
Article
Application of the Euler–Lagrange Approach and Immersed Boundary Method to Investigate the Behavior of Rigid Particles in a Confined Flow
Axioms 2023, 12(12), 1121; https://doi.org/10.3390/axioms12121121 - 14 Dec 2023
Viewed by 876
Abstract
The presence of particles with a small but finite size, suspended in viscous fluids with low volumetric concentrations, is observed in many applications. The present study focuses on the tridimensional and incompressible lid-driven flow of Newtonian fluids through the application of the immersed [...] Read more.
The presence of particles with a small but finite size, suspended in viscous fluids with low volumetric concentrations, is observed in many applications. The present study focuses on the tridimensional and incompressible lid-driven flow of Newtonian fluids through the application of the immersed boundary method and the Euler–Lagrange approach. These methods are used to numerically predict three-dimensional particle motion by considering nearly neutrally buoyant conditions as well as all relevant elementary processes (drag and lift forces, particle rotation, particle–wall interactions, and coupling between phases). Considering the current stage of the numerical platform, two coupling approaches between phases are considered: one-way and two-way coupling. A single particle is inserted in the cavity after steady-state conditions are achieved. Its three-dimensional motion is obtained from numerical simulations and compared with research data, considering the same conditions, evidently showing that the particle trajectory follows the experimental data until the first collision with a solid surface. After this first contact, there is a deviation between the results, with the two-way coupling results better representing the experimental data than the one-way coupling results. The dimensionless forces’ peaks acting on the particles are associated with the relative velocity of the particle near the wall–particle collision position. In terms of magnitude, in general, the drag force has shown greater influence on the particle’s motion, followed by the rotation-induced and shear-induced lift forces. Finally, a special application is presented, in which 4225 particles are released into the domain and their dynamic is evaluated throughout dimensionless time, showing similar behavior for both couplings between phases, with variations in local concentrations observed in certain regions. The mean square displacement used to quantify the dispersion evolution of the particles showed that the particulate flow reaches an approximately homogeneous distribution from the moment of dimensionless time tU/S = 130. Full article
(This article belongs to the Special Issue Advances of Mathematical Modeling in Fluid Mechanics)
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24 pages, 1716 KiB  
Article
Some Connectivity Parameters of Interval-Valued Intuitionistic Fuzzy Graphs with Applications
Axioms 2023, 12(12), 1120; https://doi.org/10.3390/axioms12121120 - 13 Dec 2023
Viewed by 814
Abstract
Connectivity in graphs is useful in describing different types of communication systems like neural networks, computer networks, etc. In the design of any network, it is essential to evaluate the connections based on their strengths. In this manuscript, we comprehensively describe various connectivity [...] Read more.
Connectivity in graphs is useful in describing different types of communication systems like neural networks, computer networks, etc. In the design of any network, it is essential to evaluate the connections based on their strengths. In this manuscript, we comprehensively describe various connectivity parameters related to interval-valued intuitionistic fuzzy graphs (IVIFGs). These are the generalizations of the parameters defined for fuzzy graphs, interval-valued fuzzy graphs, and intuitionistic fuzzy graphs. First, we introduce interval-valued intuitionistic fuzzy bridges (IVIF bridges) and interval-valued intuitionistic fuzzy cut-nodes (IVIF cut-nodes). We discuss the many characteristics of these terms as well as establish the necessary and sufficient conditions for an arc to become an IVIF-bridge and a vertex to be an IVIF-cutnode. Furthermore, we initiate the concepts of interval-valued intuitionistic fuzzy cycles (IVIFCs) and interval-valued intuitionistic fuzzy trees (IVIFTs) and explore few relationships among them. In addition, we introduce the notions of fuzzy blocks and fuzzy block graphs and extend these terms as interval-valued fuzzy blocks (IVF-blocks) and interval-valued intuitionistic fuzzy block graphs (IVIF-block graphs). Finally, we provide the application of interval-valued intuitionistic fuzzy trees (IVIFTs) in a road transport network. Full article
(This article belongs to the Special Issue Fuzzy Graphs: Theory and Applications)
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26 pages, 396 KiB  
Article
Efficiency and Vulnerability in Networks: A Game Theoretical Approach
Axioms 2023, 12(12), 1119; https://doi.org/10.3390/axioms12121119 - 13 Dec 2023
Viewed by 741
Abstract
Defining measures of network efficiency and vulnerability is a pivotal aspect of modern networking paradigms. We approach this issue from a game theoretical perspective, considering networks where actors have social or economic interests modeled through a cooperative game. This allows us to define, [...] Read more.
Defining measures of network efficiency and vulnerability is a pivotal aspect of modern networking paradigms. We approach this issue from a game theoretical perspective, considering networks where actors have social or economic interests modeled through a cooperative game. This allows us to define, for each network, a family of efficiency measures and another of vulnerability measures, parameterized by the game. The proposed measures use the within groups’ and the between groups’ Myerson values. These values, respectively, measure the portion of the classical Myerson allocation corresponding to the productivity of players and the part related to intermediation costs. Additionally, they indicate the portion of total centrality in social networks attributed to communication or betweenness. In our proposal, the efficiency of a network is the proportion of total productivity (or centrality) that players can retain using the network topology. Intermediation costs (and betweenness centrality) can be seen as a weakness with a negative impact. Therefore, we suggest calculating vulnerability as the proportion of expenses players incur in intermediation payments. We explore the properties of these measures and tailor them to various structures and specific games, also analyzing their asymptotic behavior. Full article
(This article belongs to the Special Issue Decision-Making Modeling and Optimization)
18 pages, 1587 KiB  
Article
A Novel PM2.5 Concentration Forecasting Method Based on LFIG_DTW_HC Algorithm and Generalized Additive Model
Axioms 2023, 12(12), 1118; https://doi.org/10.3390/axioms12121118 - 13 Dec 2023
Viewed by 732
Abstract
As air pollution becomes more and more serious, PM2.5 is the primary pollutant, inevitably attracts wide public attention. Therefore, a novel PM2.5 concentration forecasting method based on linear fuzzy information granule_dynamic time warping_hierarchical clustering algorithm (LFIG_DTW_HC algorithm) and generalized additive model is proposed [...] Read more.
As air pollution becomes more and more serious, PM2.5 is the primary pollutant, inevitably attracts wide public attention. Therefore, a novel PM2.5 concentration forecasting method based on linear fuzzy information granule_dynamic time warping_hierarchical clustering algorithm (LFIG_DTW_HC algorithm) and generalized additive model is proposed in this paper. First, take 30 provincial capitals in China for example, the cities are divided into seven regions by LFIG_DTW_HC algorithm, and descriptive statistics of PM2.5 concentration in each region are carried out. Secondly, it is found that the influencing factors of PM2.5 concentration are different in different regions. The input variables of the PM2.5 concentration forecasting model in each region are determined by combining the variable correlation with the generalized additive model, and the main influencing factors of PM2.5 concentration in each region are analyzed. Finally, the empirical analysis is conducted based on the input variables selected above, the generalized additive model is established to forecast PM2.5 concentration in each region, the comparison of the evaluation indexes of the training set and the test set proves that the novel PM2.5 concentration forecasting method achieves better prediction effect. Then, the generalized additive model is established by selecting cities from each region, and compared with the auto-regressive integrated moving average (ARIMA) model. The results show that the novel PM2.5 concentration forecasting method can achieve better prediction effect on the premise of ensuring high accuracy. Full article
(This article belongs to the Special Issue Computational Statistics and Its Applications)
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30 pages, 2235 KiB  
Article
Regression of the Rician Noise Level in 3D Magnetic Resonance Images from the Distribution of the First Significant Digit
Axioms 2023, 12(12), 1117; https://doi.org/10.3390/axioms12121117 - 13 Dec 2023
Viewed by 902
Abstract
This paper investigates the distribution characteristics of Fourier, discrete cosine, and discrete sine transform coefficients in T1 MRI images. This paper reveals their adherence to Benford’s law, characterized by a logarithmic distribution of first digits. The impact of Rician noise on the first [...] Read more.
This paper investigates the distribution characteristics of Fourier, discrete cosine, and discrete sine transform coefficients in T1 MRI images. This paper reveals their adherence to Benford’s law, characterized by a logarithmic distribution of first digits. The impact of Rician noise on the first digit distribution is examined, which causes deviations from the ideal distribution. A novel methodology is proposed for noise level estimation, employing metrics such as the Bhattacharyya distance, Kullback–Leibler divergence, total variation distance, Hellinger distance, and Jensen–Shannon divergence. Supervised learning techniques utilize these metrics as regressors. Evaluations on MRI scans from several datasets coming from a wide range of different acquisition devices of 1.5 T and 3 T, comprising hundreds of patients, validate the adherence of noiseless T1 MRI frequency domain coefficients to Benford’s law. Through rigorous experimentation, our methodology has demonstrated competitiveness with established noise estimation techniques, even surpassing them in numerous conducted experiments. This research empirically supports the application of Benford’s law in transforms, offering a reliable approach for noise estimation in denoising algorithms and advancing image quality assessment. Full article
(This article belongs to the Special Issue Developments of Mathematical Methods in Image Processing)
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23 pages, 10265 KiB  
Article
A Hybrid DEMATEL and Bayesian Best–Worst Method Approach for Inland Port Development Evaluation
Axioms 2023, 12(12), 1116; https://doi.org/10.3390/axioms12121116 - 13 Dec 2023
Viewed by 754
Abstract
Inland ports are gaining more and more attention as important hubs for inland cities to promote foreign trade. However, studies on the evaluation of inland ports are lacking. In this work, we aim to construct an index system and propose a multi-criteria group [...] Read more.
Inland ports are gaining more and more attention as important hubs for inland cities to promote foreign trade. However, studies on the evaluation of inland ports are lacking. In this work, we aim to construct an index system and propose a multi-criteria group decision-making method to comprehensively evaluate the development of inland ports. Unlike previous studies, using pressure–state–response model as a reference, we built up a demand–risk–power–potential framework for the index system proposed in this study. To determine the different weights for each indicator, which is a typical multi-criteria decision-making problem, we innovatively combined the decision-making trial and evaluation laboratory (DEMATEL) and the Bayesian best–worst method (BBWM) based on their distinct advantages in dealing with data coupling and group decision-making. In addition, this work introduces a case study of inland ports in the Huaihai Economy Zone to validate the efficacy of the proposed evaluation model and method. After calculating and obtaining the comprehensive scores and rankings of each inland port in this case, we compared the evaluation results with those under the BBWM, TOPSIS, and CRITIC methodologies, and found that the results under the DEMATEL–BBWM methodology can provide better differentiation for inland port evaluation results. Moreover, based on the evaluation results, a performance–importance matrix is formulated to identify the areas requiring attention in the development process of each inland port. Subsequently, rational managerial insights are put forward to achieve the sustainable development of inland ports in the Huaihai Economy Zone. Full article
(This article belongs to the Special Issue Multi-Criteria Decision Making (MCDM) with Preference Modeling)
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22 pages, 370 KiB  
Article
Developing Constrained Interval Operators for Fuzzy Logic with Interval Values
Axioms 2023, 12(12), 1115; https://doi.org/10.3390/axioms12121115 - 13 Dec 2023
Viewed by 671
Abstract
A well-known problem in the interval analysis literature is the overestimation and loss of information. In this article, we define new interval operators, called constrained interval operators, that preserve information and mitigate overestimation. These operators are investigated in terms of correction, algebraic [...] Read more.
A well-known problem in the interval analysis literature is the overestimation and loss of information. In this article, we define new interval operators, called constrained interval operators, that preserve information and mitigate overestimation. These operators are investigated in terms of correction, algebraic properties, and orders. It is shown that a large part of the properties studied is preserved by this operator, while others remain preserved with the condition of continuity, as is the case of the exchange principle. In addition, a comparative study is carried out between this operator g¨ and the best interval representation: g^. Although g¨g^ and g¨ do not preserve the Moore correction, we do not have a loss of relevant information since everything that is lost is irrelevant, mitigating the overestimation. Full article
16 pages, 3260 KiB  
Article
Two Dynamic Remarks on the Chebyshev–Halley Family of Iterative Methods for Solving Nonlinear Equations
Axioms 2023, 12(12), 1114; https://doi.org/10.3390/axioms12121114 - 12 Dec 2023
Viewed by 805
Abstract
The aim of this paper is to delve into the dynamic study of the well-known Chebyshev–Halley family of iterative methods for solving nonlinear equations. Our objectives are twofold: On the one hand, we are interested in characterizing the existence of extraneous attracting fixed [...] Read more.
The aim of this paper is to delve into the dynamic study of the well-known Chebyshev–Halley family of iterative methods for solving nonlinear equations. Our objectives are twofold: On the one hand, we are interested in characterizing the existence of extraneous attracting fixed points when the methods in the family are applied to polynomial equations. On the other hand, we are also interested in studying the free critical points of the methods in the family, as a previous step to determine the existence of attracting cycles. In both cases, we want to identify situations where the methods in the family have bad behavior from the root-finding point of view. Finally, and joining these two studies, we look for polynomials for which there are methods in the family where these two situations happen simultaneously. The rational map obtained by applying a method in the Chebyshev–Halley family to a polynomial has both super-attracting extraneous fixed points and super-attracting cycles different from the roots of the polynomial. Full article
(This article belongs to the Special Issue Numerical Analysis and Applied Mathematics)
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13 pages, 4072 KiB  
Article
Analysis of the Burgers–Huxley Equation Using the Nondimensionalisation Technique: Universal Solution for Dirichlet and Symmetry Boundary Conditions
Axioms 2023, 12(12), 1113; https://doi.org/10.3390/axioms12121113 - 11 Dec 2023
Viewed by 808
Abstract
The Burgers–Huxley equation is important because it involves the phenomena of accumulation, drag, diffusion, and the generation or decay of species, which are common in various problems in science and engineering, such as heat transmission, the diffusion of atmospheric contaminants, etc. On the [...] Read more.
The Burgers–Huxley equation is important because it involves the phenomena of accumulation, drag, diffusion, and the generation or decay of species, which are common in various problems in science and engineering, such as heat transmission, the diffusion of atmospheric contaminants, etc. On the other hand, the mathematical technique of nondimensionalisation has proven to be very useful in the appropriate grouping of the variables involved in a physical–chemical phenomenon and in obtaining universal solutions to different complex engineering problems. Therefore, a deep analysis using this technique of the Burgers–Huxley equation and its possible boundary conditions can facilitate a common understanding of these problems through the appropriate grouping of variables and propose common universal solutions. Thus, in this case, the technique is applied to obtain a universal solution for Dirichlet and symmetric boundary conditions. The validation of the methodology is carried out by comparing different cases, where the coefficients or the value of the boundary condition are varied, with the results obtained through a numerical simulation. Furthermore, one of the cases presented presents a boundary condition that changes at a certain time. Finally, after applying the technique, it is studied which phenomenon is predominant, concluding that from a certain value diffusion predominates, with the rest being practically negligible. Full article
(This article belongs to the Special Issue Mathematical Models and Simulations)
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22 pages, 353 KiB  
Article
More Effective Criteria for Testing the Asymptotic and Oscillatory Behavior of Solutions of a Class of Third-Order Functional Differential Equations
Axioms 2023, 12(12), 1112; https://doi.org/10.3390/axioms12121112 - 11 Dec 2023
Viewed by 717
Abstract
This paper delves into the investigation of quasi-linear neutral differential equations in the third-order canonical case. In this study, we refine the relationship between the solution and its corresponding function, leading to improved preliminary results. These enhanced results play a crucial role in [...] Read more.
This paper delves into the investigation of quasi-linear neutral differential equations in the third-order canonical case. In this study, we refine the relationship between the solution and its corresponding function, leading to improved preliminary results. These enhanced results play a crucial role in excluding the existence of positive solutions to the investigated equation. By building upon the improved preliminary results, we introduce novel criteria that shed light on the nature of these solutions. These criteria help to distinguish whether the solutions exhibit oscillatory behavior or tend toward zero. Moreover, we present oscillation criteria for all solutions. To demonstrate the relevance of our results, we present an illustrative example. This example validates the theoretical framework we have developed and offers practical insights into the behavior of solutions for quasi-linear third-order neutral differential equations. Full article
(This article belongs to the Special Issue Special Topics in Differential Equations with Applications)
22 pages, 410 KiB  
Article
Certain Bounds of Formulas in Free Temporal Algebras
Axioms 2023, 12(12), 1111; https://doi.org/10.3390/axioms12121111 - 11 Dec 2023
Viewed by 771
Abstract
In this paper, we give a basic structure theorem based on the study of extreme cases for the value of ≺ (the classical precedence relation between ultrafilters), i.e., = and no isolated element in ≺. This gives rise, respectively, to the [...] Read more.
In this paper, we give a basic structure theorem based on the study of extreme cases for the value of ≺ (the classical precedence relation between ultrafilters), i.e., = and no isolated element in ≺. This gives rise, respectively, to the temporal varieties O and W, with the result that O generates a variety of temporal algebras. We also characterize the simple temporal algebras by means of arithmetical properties related to basical temporal operators; we conclude that the simplicity of the temporal algebra lies in being able to make 0 any element less than 1 by repeated application to it of the L operator. We then present an algebraic construction similar to a product but in which the temporal operations are not defined componentwise. This new “product” is shown to be useful in the study of algebra order and finding of bounds by means of something similar to a lifting process. Finally, we give an alternative proof of an already known result on atoms counting in free temporal algebras. Full article
(This article belongs to the Special Issue Non-classical Logics and Related Algebra Systems)
24 pages, 2748 KiB  
Article
Using SNAP to Analyze Policy Measures in e-Learning Roadmaps
Axioms 2023, 12(12), 1110; https://doi.org/10.3390/axioms12121110 - 11 Dec 2023
Viewed by 904
Abstract
Creating policy measures is the final step in the process of e-learning roadmap development. Policy measures can be seen as long-term activities that need to be implemented and constantly upgraded to achieve strategic goals. For resource allocation, it is useful to prioritize policy [...] Read more.
Creating policy measures is the final step in the process of e-learning roadmap development. Policy measures can be seen as long-term activities that need to be implemented and constantly upgraded to achieve strategic goals. For resource allocation, it is useful to prioritize policy measures. Prioritization can be implemented using multi-criteria decision-making methods. This paper analyzes policy measures in the Maldives National University’s e-learning roadmap using the social network analysis process (SNAP), which includes the analytic hierarchy process (AHP), the decision-making trial and evaluation laboratory (DEMATEL), and the PageRank centrality. In policy measure evaluation, there were more than 20 participants: persons with managerial functions at the Maldives National University (MNU) (deans, heads of departments) and persons in lecturer and researcher positions. By using the AHP, participants prioritized policy measures with respect to their importance to them. By using the DEMATEL, participants identified and prioritized policy measures with respect to their effect on other measures. Finally, by using the SNAP, it was possible to determine the prioritization list for resource allocation since it aggregates the aspects of the policy measures, their importance, and their effect on other measures. Full article
(This article belongs to the Special Issue Applied Optimization and Decision Analysis on Interdisciplinary Areas)
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20 pages, 370 KiB  
Article
Describing Conditional Independence Statements Using Undirected Graphs
Axioms 2023, 12(12), 1109; https://doi.org/10.3390/axioms12121109 - 08 Dec 2023
Viewed by 727
Abstract
This paper investigates the capability of undirected graphs (UGs) to represent a set of Conditional Independence (CI) statements derived from a given probability distribution of a random vector. While it is established that certain axioms can govern this set, providing sufficient conditions for [...] Read more.
This paper investigates the capability of undirected graphs (UGs) to represent a set of Conditional Independence (CI) statements derived from a given probability distribution of a random vector. While it is established that certain axioms can govern this set, providing sufficient conditions for UGs to capture specific CI statements, our focus is on covariance and concentration graphs. These remain the only known families of UGs capable of describing CI statements. We explore the issue of complete representation of CI statements through their corresponding covariance and concentration graphs. Two parameters are defined, one each from the covariance and concentration graphs, to determine the limitations concerning the cardinality of the conditioning subset that the graph can represent. We establish a relationship between these parameters and the cardinality of the separators in each graph, providing a straightforward computational method to evaluate them. In conclusion, we enhance the aforementioned procedure and introduce criteria to ascertain, without additional computations, whether the graphs can fully represent a given set of CI statements. We demonstrate that either the concentration or the covariance graph forms a cycle, and when considered in conjunction, they can represent the entire relation. These criteria also enable us, in specific cases, to deduce the covariance graph from the concentration graph and vice versa. Full article
(This article belongs to the Special Issue Graphical Models)
14 pages, 295 KiB  
Article
A Note on Finite Dimensional Odd Contact Lie Superalgebra in Prime Characteristic
Axioms 2023, 12(12), 1108; https://doi.org/10.3390/axioms12121108 - 08 Dec 2023
Viewed by 740
Abstract
Over a field of characteristic p>3, let KO(n,n+1;t̲) denote the odd contact Lie superalgebra. In this paper, the super-biderivations of odd Contact Lie superalgebra [...] Read more.
Over a field of characteristic p>3, let KO(n,n+1;t̲) denote the odd contact Lie superalgebra. In this paper, the super-biderivations of odd Contact Lie superalgebra KO(n,n+1;t̲) are studied. Let TKO be a torus of KO(n,n+1;t̲), which is an abelian subalgebra of KO(n,n+1;t̲). By applying the weight space decomposition approach of KO(n,n+1;t̲) with respect to TKO, we show that all skew-symmetric super-biderivations of KO(n,n+1;t̲) are inner super-biderivations. Full article
(This article belongs to the Section Algebra and Number Theory)
19 pages, 3847 KiB  
Article
A Novel Fractional Multi-Order High-Gain Observer Design to Estimate Temperature in a Heat Exchange Process
Axioms 2023, 12(12), 1107; https://doi.org/10.3390/axioms12121107 - 08 Dec 2023
Viewed by 731
Abstract
In the present manuscript, we design a fractional multi-order high-gain observer to estimate temperature in a double pipe heat exchange process. For comparison purposes and since we want to prove that when using our novel technique, the estimation is more robust than the [...] Read more.
In the present manuscript, we design a fractional multi-order high-gain observer to estimate temperature in a double pipe heat exchange process. For comparison purposes and since we want to prove that when using our novel technique, the estimation is more robust than the classical approach, we design a non-fractional high-gain observer, and then we compare the performance of both observers. We consider three scenarios: The first one considers the estimation of the system states by measuring only one output with no noise added on it and under ideal conditions. Second, we add noise to the measured output and then reconstruct the system states, and, third, in addition to the noise, we increase the gain parameter in both observers (non-fractional and fractional) due to the fact that we want to prove that the robustness changes in this parameter. The results showed that, using our approach, the estimated states can be recovered under noise circumstances in the measured output and under parameter change in the observer, contrary to using classical (non-fractional) observers where the states cannot be recovered. In all our tests, we used the normalized root-mean-square, integral square error, and integral absolute error indices, resulting in a better performance for our approach than that obtained using the classical approach. We concluded that our fractional multi-order high-gain observer is more robust to input noise than the classical high-gain observer. Full article
(This article belongs to the Special Issue Fractional Calculus: From Fundamentals to Modern Applications)
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28 pages, 1776 KiB  
Article
On the Method of Transformations: Obtaining Solutions of Nonlinear Differential Equations by Means of the Solutions of Simpler Linear or Nonlinear Differential Equations
Axioms 2023, 12(12), 1106; https://doi.org/10.3390/axioms12121106 - 08 Dec 2023
Viewed by 3666
Abstract
Transformations are much used to connect complicated nonlinear differential equations to simple equations with known exact solutions. Two examples of this are the Hopf–Cole transformation and the simple equations method. In this article, we follow an idea that is opposite to the idea [...] Read more.
Transformations are much used to connect complicated nonlinear differential equations to simple equations with known exact solutions. Two examples of this are the Hopf–Cole transformation and the simple equations method. In this article, we follow an idea that is opposite to the idea of Hopf and Cole: we use transformations in order to transform simpler linear or nonlinear differential equations (with known solutions) to more complicated nonlinear differential equations. In such a way, we can obtain numerous exact solutions of nonlinear differential equations. We apply this methodology to the classical parabolic differential equation (the wave equation), to the classical hyperbolic differential equation (the heat equation), and to the classical elliptic differential equation (Laplace equation). In addition, we use the methodology to obtain exact solutions of nonlinear ordinary differential equations by means of the solutions of linear differential equations and by means of the solutions of the nonlinear differential equations of Bernoulli and Riccati. Finally, we demonstrate the capacity of the methodology to lead to exact solutions of nonlinear partial differential equations on the basis of known solutions of other nonlinear partial differential equations. As an example of this, we use the Korteweg–de Vries equation and its solutions. Traveling wave solutions of nonlinear differential equations are of special interest in this article. We demonstrate the existence of the following phenomena described by some of the obtained solutions: (i) occurrence of the solitary wave–solitary antiwave from the solution, which is zero at the initial moment (analogy of an occurrence of particle and antiparticle from the vacuum); (ii) splitting of a nonlinear solitary wave into two solitary waves (analogy of splitting of a particle into two particles); (iii) soliton behavior of some of the obtained waves; (iv) existence of solitons which move with the same velocity despite the different shape and amplitude of the solitons. Full article
(This article belongs to the Topic Mathematical Modeling)
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15 pages, 375 KiB  
Article
A Simplified Approach to the Pricing of Vulnerable Options with Two Underlying Assets in an Intensity-Based Model
Axioms 2023, 12(12), 1105; https://doi.org/10.3390/axioms12121105 - 07 Dec 2023
Viewed by 657
Abstract
In this paper, we study a simplified approach to determine the pricing formula for vulnerable options involving two correlated underlying assets. We utilize an intensity-based model to describe the credit risk associated with these vulnerable options. Without the change of measure technique, we [...] Read more.
In this paper, we study a simplified approach to determine the pricing formula for vulnerable options involving two correlated underlying assets. We utilize an intensity-based model to describe the credit risk associated with these vulnerable options. Without the change of measure technique, we derive pricing formulas for vulnerable options involving two underlying assets based on the probabilistic approach. We provide closed-form pricing formulas for two specific types of options: the vulnerable exchange option and the vulnerable foreign equity option. Finally, we present numerical results to demonstrate the accuracy of our formulas using the Monte-Carlo method and the effect of various parameters on the price of options. Full article
(This article belongs to the Special Issue Applied Mathematical Models of Option Pricing)
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