Axioms doi: 10.3390/axioms12121101

Authors: Jiri Petrzela

This paper contributes to the problem of chaos and hyperchaos localization in the fundamental structure of analog building blocks dedicated to single-tone harmonic signal generation. This time, the known Reinartz sinusoidal oscillator is addressed, considering its conventional topology, both via numerical analysis and experiments using a flow-equivalent lumped electronic circuit. It is shown that physically reasonable values of circuit parameters can result in robust dynamical behavior characterized by a pair of positive Lyapunov exponents. Mandatory numerical results prove that discovered strange attractors exhibit all necessary fingerprints of structurally stable chaos. The new &ldquo;chaotic&rdquo; parameters are closely related to the standard operation of the investigated analog functional block. A few interestingly shaped, strange attractors have been captured as oscilloscope screenshots.

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Authors: Guillem A. Devin Alejandro Couce

The accurate quantification of mutation rates holds significance across diverse fields, including evolution, cancer research, and antimicrobial resistance. Eighty years ago, Luria and Delbr&uuml;ck demonstrated that the proper quantification of mutation rates requires one to account for the non-linear relationship between the number of mutations and the final number of mutants in a cell population. An extensive body of literature has since emerged, offering increasingly efficient methods to account for this phenomenon, with different alternatives balancing accuracy and user-friendliness for experimentalists. Nevertheless, statistically inappropriate approaches, such as using arithmetic averages of mutant frequencies as a proxy for the mutation rate, continue to be commonplace. Here, we conducted a comprehensive re-analysis of 140 publications from the last two decades, revealing general trends in the adoption of proper mutation rate estimation methods. Our findings demonstrate an upward trajectory in the utilization of best statistical practices, likely due to the wider availability of off-the-shelf computational tools. However, the usage of inappropriate statistical approaches varies substantially across specific research areas, and it is still present even in journals with the highest impact factors. These findings aim to inspire both experimentalists and theoreticians to find ways to further promote the adoption of best statistical practices for the reliable estimation of mutation rates in all fields.

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Authors: Yu-Ru Syau En-Bing Lin Churn-Jung Liau

This paper employs an order-theoretic framework to explore the intricacies of formal concepts. Initially, we establish a natural correspondence among formal contexts, preorders, and the resulting partially ordered sets (posets). Leveraging this foundation, we provide insightful characterizations of atoms and coatoms within finite concept lattices, drawing upon object intents. Expanding from the induced poset originating from a formal context, we extend these characterizations to discern join-irreducible and meet-irreducible elements within finite concept lattices. Contrary to a longstanding misunderstanding, our analysis reveals that not all object and attribute concepts are irreducible. This revelation challenges the conventional belief that rough approximations, grounded in irreducible concepts, offer sufficient coverage. Motivated by this realization, the paper introduces a novel concept: rough conceptual approximations. Unlike the conventional definition of object equivalence classes in Pawlakian approximation spaces, we redefine them by tapping into the extent of an object concept. Demonstrating their equivalence, we establish that rough conceptual approximations align seamlessly with approximation operators in the generalized approximation space associated with the preorder corresponding to a formal context. To illustrate the practical implications of these theoretical findings, we present concrete examples. Furthermore, we delve into the significance and potential applications of our proposed rough conceptual approximations, shedding light on their utility in real-world scenarios.

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Authors: Constantin Fetecau Costică Moroşanu Dorin-Cătălin Stoicescu

Here, we consider the phase field transition system (a nonlinear system of parabolic type) introduced by Caginalp to distinguish between the phases of the material that are involved in the solidification process. We start by investigating the solvability of such boundary value problems in the class Wp1,2(Q)&times;W&nu;1,2(Q). One proves the existence, the regularity, and the uniqueness of solutions, in the presence of the cubic nonlinearity type. On the basis of the convergence of an iterative scheme of the fractional steps type, a conceptual numerical algorithm, alg-frac_sec-ord-varphi_PHT, is elaborated in order to approximate the solution of the nonlinear parabolic problem. The advantage of such an approach is that the new method simplifies the numerical computations due to its decoupling feature. An example of the numerical implementation of the principal step in the conceptual algorithm is also reported. Some conclusions are given are also given as new directions to extend the results and methods presented in the present paper.

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Authors: Salem A. Alyami I. Elbatal Amal S. Hassan Ehab M. Almetwally

In this paper, we suggest a brand new extension of the inverse Lomax distribution for fitting engineering time data. The newly developed distribution, termed the transmuted Topp&ndash;Leone inverse Lomax (TTLILo) distribution, is characterized by an additional shape and transmuted parameters. It is critical to notice that the skewness, kurtosis, and tail weights of the distribution are strongly influenced by these additional characteristics of the extra parameters. The TTLILo model is capable of producing right-skewed, J-shaped, uni-modal, and reversed-J-shaped densities. The proposed model&rsquo;s statistical characteristics, including the moments, entropy values, stochastic ordering, stress-strength model, incomplete moments, and quantile function, are examined. Moreover, characterization based on two truncated moments is offered. Using Bayesian and non-Bayesian estimating techniques, we estimate the distribution parameters of the suggested distribution. The bootstrap procedure, approximation, and Bayesian credibility are the three forms of confidence intervals that have been created. A simulation study is used to assess the efficiency of the estimated parameters. The TTLILo model is then put to the test by being applied to actual engineering datasets, demonstrating that it offers a good match when compared to alternative models. Two applications based on real engineering datasets are taken into consideration: one on the failure times of airplane air conditioning systems and the other on the active repair times of airborne communication transceivers. Also, we consider the problem of estimating the stress-strength parameter R=P(Z2&lt;Z1) with engineering application.

]]>Axioms doi: 10.3390/axioms12121096

Authors: Rani Kumari Yogesh Mani Tripathi Rajesh Kumar Sinha Liang Wang

In this paper, different estimation is discussed for a general family of inverse exponentiated distributions. Under the classical perspective, maximum likelihood and uniformly minimum variance unbiased are proposed for the model parameters. Based on informative and non-informative priors, various Bayes estimators of the shape parameter and reliability function are derived under different losses, including general entropy, squared-log error, and weighted squared-error loss functions as well as another new loss function. The behavior of the proposed estimators is evaluated through extensive simulation studies. Finally, two real-life datasets are analyzed from an illustration perspective.

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Authors: Xiaoyu Zhang Yichao Wang Xiting Peng Chaofeng Zhang

Partial differential equations (PDEs) usually apply for modeling complex physical phenomena in the real world, and the corresponding solution is the key to interpreting these problems. Generally, traditional solving methods suffer from inefficiency and time consumption. At the same time, the current rise in machine learning algorithms, represented by the Deep Operator Network (DeepONet), could compensate for these shortcomings and effectively predict the solutions of PDEs by learning the operators from the data. The current deep learning-based methods focus on solving one-dimensional PDEs, but the research on higher-dimensional problems is still in development. Therefore, this paper proposes an efficient scheme to predict the solution of two-dimensional PDEs with improved DeepONet. In order to construct the data needed for training, the functions are sampled from a classical function space and produce the corresponding two-dimensional data. The difference method is used to obtain the numerical solutions of the PDEs and form a point-value data set. For training the network, the matrix representing two-dimensional functions is processed to form vectors and adapt the DeepONet model perfectly. In addition, we theoretically prove that the discrete point division of the data ensures that the model loss is guaranteed to be in a small range. This method is verified for predicting the two-dimensional Poisson equation and heat conduction equation solutions through experiments. Compared with other methods, the proposed scheme is simple and effective.

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Authors: Mohamed Jaber Farag Hamad Robert D. Breininger Nezamoddin N. Kachouie

Spatial capture models are broadly used for population analysis in ecological statistics. Spatial capture models for unidentified individuals rely on data augmentation to create a zero-inflated population. The unknown true population size can be considered as the number of successes of a binomial distribution with an unknown number of independent trials and an unknown probability of success. Augmented population size is a realization of the unknown number of trials and is recommended to be much larger than the unknown population size. As a result, the probability of success of binomial distribution, i.e., the unknown probability that a hypothetical individual in the augmented population belongs to the true population, can be obtained by dividing the unknown true population size by the augmented population size. This is an inverse problem as neither the true population size nor the probability of success is known, and the accuracy of their estimates strongly relies on the augmented population size. Therefore, the estimated population size in spatial capture models is very sensitive to the size of a zero-inflated population and in turn to the estimated probability of success. This is an important issue in spatial capture models as a typical count model with censored data (unidentified and/or undetected). Hence, in this research, we investigated the sensitivity and accuracy of the spatial capture model to address this problem with the objective of improving the robustness of the model. We demonstrated that the estimated population size using the proposed enhanced capture model was more accurate in comparison with the previous spatial capture model.

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Authors: Dimitris M. Christodoulou Demosthenes Kazanas

The commonly quoted bistable Higgs potential is not a proper description of the Higgs field because, among other technical reasons, one of its stable states acquires a negative expectation value in vacuum. We rely on formal catastrophe theory to derive the form of the Higgs potential that admits only one positive mean value in vacuum. No symmetry is broken during the ensuing phase transition that assigns mass to the Higgs field; only gauge redundancy is &ldquo;broken&rdquo; by the appearance of phase in the massive state, but this redundancy is not a true symmetry of the massless field. Furthermore, a secondary, certainly amusing conclusion, is that, in its high-energy state, the field oscillates about its potential minimum between positive and negative masses, but it is doubtful that such evanescent states can survive below the critical temperature of 159.5 GeV, where the known particles were actually created.

]]>Axioms doi: 10.3390/axioms12121092

Authors: Yoon-Tae Kim Hyun-Suk Park

In the case where the square of an eigenfunction F with respect to an eigenvalue of Markov generator L can be expressed as a sum of eigenfunctions, we find the largest number excluding zero among the eigenvalues in the terms of the sum. Using this number, we obtain an improved bound of the fourth moment theorem for Markov diffusion generators. To see how this number depends on an improved bound, we give some examples of eigenfunctions of the diffusion generators L such as Ornstein&ndash;Uhlenbeck, Jacobi, and Romanovski&ndash;Routh.

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Authors: Eleni Vrochidou Vladan Papić Theofanis Kalampokas George A. Papakostas

Automated solutions for medical diagnosis based on computer vision form an emerging field of science aiming to enhance diagnosis and early disease detection. The detection and quantification of facial asymmetries enable facial palsy evaluation. In this work, a detailed review of the quantification of facial palsy takes place, covering all methods ranging from traditional manual mathematical modeling to automated computer vision-based methods. Moreover, facial palsy quantification is defined in terms of facial asymmetry indices calculation for different image modalities. The aim is to introduce readers to the concept of mathematical modeling approaches for facial palsy detection and evaluation and present the process of the development of this separate application field over time. Facial landmark extraction, facial datasets, and palsy grading systems are included in this research. As a general conclusion, machine learning methods for the evaluation of facial palsy lead to limited performance due to the use of handcrafted features, combined with the scarcity of the available datasets. Deep learning methods allow the automatic learning of discriminative deep facial features, leading to comparatively higher performance accuracies. Datasets limitations, proposed solutions, and future research directions in the field are also presented.

]]>Axioms doi: 10.3390/axioms12121090

Authors: Ferhat Taş Rushan Ziatdinov

Ruled surfaces play an important role in various types of design, architecture, manufacturing, art, and sculpture. They can be created in a variety of ways, which is a topic that has been the subject of a lot of discussion in mathematics and engineering journals. In geometric modelling, ideas are successful if they are not too complex for engineers and practitioners to understand and not too difficult to implement, because these specialists put mathematical theories into practice by implementing them in CAD/CAM systems. Some of these popular systems such as AutoCAD, Solidworks, CATIA, Rhinoceros 3D, and others are based on simple polynomial or rational splines and many other beautiful mathematical theories that have not yet been implemented due to their complexity. Based on this philosophy, in the present work, we investigate a simple method of generating ruled surfaces whose generators are the curvature axes of curves. We show that this type of ruled surface is a developable surface and that there is at least one curve whose curvature axis is a line on the given developable surface. In addition, we discuss the classifications of developable surfaces corresponding to space curves with singularities, as these curves and surfaces are most often avoided in practical design. Our research also contributes to the understanding of the singularities of developable surfaces and, in their visualisation, proposes the use of environmental maps with a circular pattern that creates flower-like structures around the singularities.

]]>Axioms doi: 10.3390/axioms12121089

Authors: Weiwei Xiao Songxuan Li Haiyan Liu

In existing models with an unknown link function, the issue of predictors containing both multiple functional data and multiple scalar data has not been studied. To fill this gap, we propose a generalized partially functional linear model, which not only models the relationship between multiple scalar and functional predictors and responses, but also automatically estimates the link function. Specifically, we use the functional principal component analysis method to reduce the dimensionality of functional predictors, estimate the regression coefficients using the maximum likelihood estimation method, estimate the link function using the method of local linear regression, iteratively obtain the final estimator, and establish the asymptotic normality of the estimator. The asymptotic normality is illustrated through simulation experiments. Finally, the proposed model is applied to study the influence of environmental, economic, and medical levels on life expectancy in China. In the study, functional predictors are the daily air quality index, temperature, and humidity of 58 cities in 2020, and scalar predictors are GDP and the number of beds in hospitals. The experimental results indicate that the unknown link function model has a smaller prediction error and better performance than both the model with the known link function and the model without a link function.

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Authors: Alma Y. Alanis Jesus Hernandez-Barragan Daniel Ríos-Rivera Oscar D. Sanchez Gabriel Martinez-Soltero

In complex dynamical networks, pinning control techniques are often applied to control a small fraction of the nodes in order to stabilize the network with reduced control effort and energy, facilitating adequate development of the complex network. Selecting the controlled nodes is a key challenge to achieving optimal performance. Theoretical analysis of the network provides the minimum quantity of nodes to control but does not specify which ones should be controlled. Analytically, controllability analysis of the entire network would be ideal, but this becomes difficult for complex networks with a large number of nodes and non-linear dynamics. Another option is to evaluate all possible combinations with the minimum number of necessary nodes or the nodes that can be controlled, but this presents a computational challenge due to the large number of possible combinations. Therefore, the remaining option is the use of metaheuristic algorithms for the rapid and practical evaluation of these combinations. In this work, we propose to optimize the selection of nodes for pinning control based on binary optimization algorithms, subject to control and development constraints. The proposed approach involves finding a binary combination with a fixed number of controlled nodes that best stabilizes the network state to zero. This paper includes a comparative study among state-of-the-art binary optimization algorithms and modified classic optimization algorithms. The applicability of the proposed approach is validated through simulations considering a dynamical discrete-time complex network.

]]>Axioms doi: 10.3390/axioms12121087

Authors: Atif Avdović Vesna Jevremović

In recent research endeavors, discrete models have gained considerable attention, even in cases where the observed variables are continuous. These variables can often be effectively approximated by a normal distribution. Given the prevalence of processes requiring robust quality control, models associated with the normal distribution have found widespread applicability; nevertheless, there remains a persistent need for enhanced accuracy in normality analysis, prompting the exploration of novel and improved solutions. This paper introduces a discrete parameter-free distribution linked to the normal distribution, derived from a quality control methodology rooted in the renowned &lsquo;3-sigma&rsquo; rule. The development of a novel normality test, based on this distribution, is presented. A comprehensive examination encompasses mathematical derivation, distribution tables generated through Monte Carlo simulation studies, properties, power analysis, and comparative analysis, all with key features illustrated graphically. Notably, the proposed normality test surpasses conventional methods in performance. Termed the &lsquo;Zone distribution&rsquo;, this newly introduced distribution, along with its accompanying &lsquo;Zone test&rsquo;, demonstrates superior efficacy through illustrative examples. This research contributes a valuable tool to the field of normality analysis, offering a robust alternative for applications requiring precise and reliable assessments.

]]>Axioms doi: 10.3390/axioms12121086

Authors: Amira Essam Osama Moaaz Moutaz Ramadan Ghada AlNemer Ibrahim M. Hanafy

The monotonic properties of positive solutions to functional differential equations of the third order are examined in this paper. It is generally known that by optimizing the relationships between a solution and its corresponding function, as well as its derivatives, one can improve the oscillation criterion for neutral differential equations. Based on this, we obtain new relationships and inequalities and test their effect on the oscillation parameters of the studied equation. To obtain the oscillation parameters, we used Riccati techniques and comparison with lower-order equations. Finally, the progress achieved in oscillation theory for third-order equations was measured by comparing our results with previous relevant results.

]]>Axioms doi: 10.3390/axioms12121085

Authors: Yuan Xue Jinli Xu Yuting Ding

In this paper, we introduce the Crowley&ndash;Martin functional response and nonlocal competition into a reaction&ndash;diffusion immunosuppressive infection model. First, we analyze the existence and stability of the positive constant steady states of the systems with nonlocal competition and local competition, respectively. Second, we deduce the conditions for the occurrence of Turing, Hopf, and Turing&ndash;Hopf bifurcations of the system with nonlocal competition, as well as the conditions for the occurrence of Hopf bifurcations of the system with local competition. Furthermore, we employ the multiple time scales method to derive the normal forms of the Hopf bifurcations reduced on the center manifold for both systems. Finally, we conduct numerical simulations for both systems under the same parameter settings, compare the impact of nonlocal competition, and find that the nonlocal term can induce spatially inhomogeneous stable periodic solutions. We also provide corresponding biological explanations for the simulation results.

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Authors: Yury V. Monich Yury D. Nechipurenko

This article proposes a method for determining the p-value of correlations in compositional data, i.e., those data that arise as a result of dividing original values by their sum. Data organized in this way are typical for many fields of knowledge, but there is still no consensus on methods for interpreting correlations in such data. In the second decade of the new millennium, almost all newly emerging methods for solving this problem have become based on the log transformation of data. In the method proposed here, there are no log transformations. We return to the early stages of attempting to solve the problem and rely on negative shifts in correlations in the multinomial distribution. In modeling the data, we use a hybrid method that combines the hypergeometric distribution with the distribution of any other law. During our work on the calculation method, we found that the number of degrees of freedom in compositional data measures discretely only when all normalizing sums are equal and that it decreases when the sums are not equal, becoming a continuously varying quantity. Estimation of the number of degrees of freedom and the strength of its influence on the magnitude of the shift in the distribution of correlation coefficients is the basis of the proposed method.

]]>Axioms doi: 10.3390/axioms12121083

Authors: Camelia Delcea Adrian Domenteanu Corina Ioanăș Vanesa Mădălina Vargas Alexandra Nicoleta Ciucu-Durnoi

In recent years, neutrosophic theory has garnered increasing attention within scholarly circles due to its applicability in various domains. Within these domains, the field of decision-making has derived significant advantages from the progressions in neutrosophic theory. Notably, neutrosophic theory has made substantial contributions by advancing and offering a range of aggregation operators and information measures specifically designed for enhancing decision-making processes. In this context, this study aims to conduct a comprehensive bibliometric analysis of the current research landscape in the field of neutrosophic theory, with a specific focus on understanding its applications and development trends. Our analysis reveals that the scientific literature addresses neutrosophic theory in a diverse range of applications. This examination encompasses a scrutiny of key contributors, affiliated academic institutions, influential publications, and noteworthy journals within the neutrosophic domain. To achieve this, we have curated a dataset comprising scholarly papers retrieved from Clarivate Analytics&rsquo; Web of Science Core Collection database, employing keywords closely aligned with neutrosophic theory and its applications, spanning a specified timeframe starting from the year in which the first paper on neutrosophic theory was published, namely, from 2005 until 2022. Our findings underscore sustained and robust scholarly interest in neutrosophic theory, characterized by a considerable high annual growth rate of 43.74% during the specified period. Additionally, our investigation delves into the identification and analysis of pivotal keywords and emerging trends, shedding light on prominent research trajectories within this domain. Furthermore, we elucidate collaborative networks among authors, their academic affiliations, and the global distribution across diverse countries and territories, providing valuable insights into the worldwide proliferation of neutrosophic research and applications. Employing n-gram analysis techniques across titles, keywords, abstracts, and keyword-plus fields unveils a multitude of applications where neutrosophic theory plays a central role. The analysis culminates in a review of globally cited documents and a comprehensive discussion highlighting the significance of neutrosophic theory in contemporary research and problem-solving contexts.

]]>Axioms doi: 10.3390/axioms12121082

Authors: Mohd Danish Siddiqi Ali H. Hakami

In the current research, we develop optimal inequalities for submanifolds in trans-Sasakian manifolds or (&alpha;,&beta;)-type almost contact manifolds endowed with the Schouten&ndash;Van Kampen connection (SVK-connection), including generalized normalized &delta;-Casorati Curvatures (&delta;-CC). We also discuss submanifolds on which the equality situations occur. Lastly, we provided an example derived from this research.

]]>Axioms doi: 10.3390/axioms12121081

Authors: Alexander Khludnev

This paper concerns an equilibrium problem for an an elastic body with a thin rigid inclusion crossing an external boundary of the body at zero angle. The inclusion is assumed to be exfoliated from the surrounding elastic material that provides an interfacial crack. To avoid nonphysical interpenetration of the opposite crack faces, we impose inequality type constraints. Moreover, boundary conditions at the crack faces depend on a positive parameter describing a cohesion. A solution existence of the problem with different conditions on the external boundary is proved. Passages to the limit are analyzed as the damage parameter tends to infinity and to zero. Finally, an optimal control problem with a suitable cost functional is investigated. In this case, a part of the rigid inclusion is located outside of the elastic body, and a control function is a shape of the inclusion.

]]>Axioms doi: 10.3390/axioms12121080

Authors: Carlos González-Flores Luis Alfredo Dupont-García Raquiel Rufino López-Martínez Francisco Gabriel Hérnandez-Zamora

The first goal of this paper is to find a representation of the Fock space on Cn in terms of the weighted Bergman spaces of the projective spaces CPn&minus;1; i.e., every function in the Fock space can be written as a direct sum of elements in weighted Bergman space on CPn&minus;1. Also, we study the C* algebras generated by Toeplitz operators where the symbols are taken from the following two families of functions: Firstly, the symbols depend on the moment map associated with the unit circle, and secondly, the symbols are invariant under the same action. Moreover, we analyze the commutative relations between these algebras, and we apply these results to find new commutative Banach algebras generated by Toeplitz operators on Fock space of Cn.

]]>Axioms doi: 10.3390/axioms12121079

Authors: Hanh-Thao Le Ta-Chung Chu

The process of evaluating and ranking alternatives, including the aggregation of various qualitative and quantitative criteria and weights of criteria, can be recognized as a fuzzy multiple criteria decision-making (MCDM) problem. In fuzzy MCDM problems, qualitative criteria and criteria weights are usually indicated in linguistic values expressed in terms of fuzzy numbers, and values under quantitative criteria are usually crisp numbers. How to properly aggregate them for evaluating and selecting alternatives has been an important research issue. To help decision-makers make the most suitable selection, this paper proposes a fuzzy preference relation-based fuzzy VIKOR method. VIKOR is a compromise ranking method to solve discrete MCDM problems in complex systems. In this study, the F-preference relation is applied to compare fuzzy numbers with their means to produce a single index of a dominance level while still maintaining fuzzy meaning of the original linguistic values. The inverse function is applied to obtain the defuzzification values of Beta 1&ndash;4 to assist in the completion of the proposed method, and formulas can be clearly derived to facilitate the ranking procedure. Introducing fuzzy preference relation into fuzzy VIKOR can simplify the calculation procedure for more efficient decision-making. The proposed method is new and has never been seen before. A numerical example and a comparison of the proposed method are conducted to show and verify its expedience and advantage.

]]>Axioms doi: 10.3390/axioms12121078

Authors: Samesh Shenawy Alaa Rabie Uday Chand De Carlo Mantica Nasser Bin Turki

This paper investigates singly warped product manifolds admitting semi-conformal curvature tensors. The form of the Riemann tensor and Ricci tensor of the base and fiber manifolds of a semi-conformally flat singly warped product manifold are provided. It is demonstrated that the fiber manifold of a semi-conformally flat warped product manifold has a constant curvature. Sufficient requirements on the warping function to ensure that the base manifold is a quasi-Einstein or an Einstein manifold are provided.

]]>Axioms doi: 10.3390/axioms12121077

Authors: María Jesús Campión Esteban Induráin Armajac Raventós-Pujol

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.

]]>Axioms doi: 10.3390/axioms12121076

Authors: Rachel M. Morin Nicholas A. Mecholsky

The drift velocity of a particle under a driving force has its roots in the theory of electrical conduction. Although it has been studied for over 100 years, it still yields surprises. At the heart of a particle&rsquo;s drift velocity is an interplay of classical, quantum, and statistical mechanics. Irreversibility and energy loss have been assumed as essential features of drift velocities and very little effort has been made to isolate the aspects of particle transport that are due to elastic mechanisms alone. In this paper, we remove energy loss and quantum mechanics to investigate the classical and statistical factors that can produce a drift velocity using only elastic scattering. A Monte Carlo simulation is used to model a particle in a uniform force field, subject to randomly placed scatterers. Time-, space-, and energy-dependent scattering models, with varied ranges of scattering angles, are investigated. A constant drift velocity is achieved with the time scattering model, which has a constant average time between scattering events. A decreasing drift velocity is observed for space and energy-dependent models. The arrival of a constant drift velocity has to do with a balance of momentum gained between collisions and momentum lost after a collision.

]]>Axioms doi: 10.3390/axioms12121075

Authors: Mohammed Al-Refai Yuri Luchko

In this paper, two types of general fractional derivatives of distributed order and a corresponding fractional integral of distributed type are defined, and their basic properties are investigated. The general fractional derivatives of distributed order are constructed for a special class of one-parametric Sonin kernels with power law singularities at the origin. The conventional fractional derivatives of distributed order based on the Riemann&ndash;Liouville and Caputo fractional derivatives are particular cases of the general fractional derivatives of distributed order introduced in this paper.

]]>Axioms doi: 10.3390/axioms12121074

Authors: Oleksandr Boryseiko Oleksandr Laptiev Oleh Perehuda Anton Ryzhov

Piezoceramic products are actively used in modern technical devices and appliances. Disk piezoelectric devices are widely used in elements of information systems: in wireless communication, elements of satellite communication, global positioning systems. Among such devices, microwave piezo motors on traveling waves of various types are distinguished, including a motor built on an electromechanical disk converter, which performs non-axisymmetric oscillations under the action of a harmonic electric load. In this study, we perform separation of the electrode coating of the plate with thin diametrical dielectric sections and introduce a time-varying electric potential difference of different amplitude or phase to individual parts of the plate. We study the problem of non-axisymmetric planar oscillations of a piezoceramic disk with thickness polarization and the problem of optimization of the electromechanical coupling coefficient (EMCO) value as a function of an infinite number of parameters in space l2 of square summable sequences.

]]>Axioms doi: 10.3390/axioms12121073

Authors: Peter Kogut Yaroslav Kohut

We discuss the optimal control formulation for enhancement and denoising of satellite multiband images and propose to take it in the form of an L1 control problem for a quasi-linear parabolic equation with a nonlocal p[u] Laplacian and with a cost functional of a tracking type. The main characteristic features of the considered parabolic problem is that the variable exponent p(t,x) and the diffusion anisotropic tensor D(t,x) are not predefined well a priori; instead, these characteristics nonlocally depend on the form of the solution of this problem (i.e., pu=p(t,x,u) and Du=D(t,x,u)). We prove the existence of optimal pairs with sparse L1 controls used for the indirect approach and a special family of approximation problems.

]]>Axioms doi: 10.3390/axioms12121072

Authors: Mohamed Abdelkader

In this paper, we provide the decay of correlations for random dynamical systems. Precisely, we consider the uniformly C2 piecewise expanding maps defined on the unit interval satisfying &lambda;(T&omega;&prime;)=inf|T&omega;&prime;|&gt;2. As a principal tool of these studies, we use a coupling method for analyzing the coupling time of observables with bounded variation.

]]>Axioms doi: 10.3390/axioms12121071

Authors: Ebrahim Analouei Adegani Mostafa Jafari Teodor Bulboacă Paweł Zaprawa

A branch of complex analysis with a rich history is geometric function theory, which first appeared in the early 20th century. The function theory deals with a variety of analytical tools to study the geometric features of complex-valued functions. The main purpose of this paper is to estimate more accurate bounds for the coefficient |an| of the functions that belong to a class of bi-univalent functions with missing coefficients that are defined by using the subordination. The significance of our present results consists of improvements to some previous results concerning different recent subclasses of bi-univalent functions, and the aim of this paper is to improve the results of previous outcomes. In addition, important examples of some classes of such functions are provided, which can help to understand the issues related to these functions.

]]>Axioms doi: 10.3390/axioms12121070

Authors: Alptekin Ulutaş Senevi Kiridena Nagesh Shukla Ayse Topal

In light of the rapid rate of change and unforeseen occurrences seen in the realms of technology, market dynamics, and the wider business landscape, there is a growing need for the inclusion of uncertainty and risk factors in the realm of supply chain planning. Supplier evaluation and selection (SES) is a major strategic decision area where the impact of uncertainty and risk can be more proactively dealt with. A review of extant literature reveals that there is a strong need for developing practitioner-oriented and more comprehensive frameworks and models to mitigate both the capability- and performance-related risks, in the context of SES decisions. This paper presents an integrated model to support SES decisions involving quantity discounts and multiple planning periods under stochastic conditions. The proposed model employs the Fuzzy Analytical Hierarchy Process (FAHP), Fuzzy Evaluation Based on Distance from Average Solution EDAS (EDAS-F), and fuzzy stochastic goal programming (FSGP) to effectively address the above requirements. A case study from a garment manufacturing industry is used to demonstrate the efficacy of the proposed model. The findings of the study provide confirmation that the suggested FSIM has the ability to provide substantial advantages in the context of making choices related to quantity discounts in SES. The proposed FSIM model incorporates the use of FAHP and EDAS-F techniques to effectively reduce the number of suppliers to a manageable level, taking into consideration capability-based risks. Additionally, fuzzy stochastic goal programming (FSGP) is employed to mitigate performance-based risks, enabling the selection of suppliers and the allocation of orders among them. The paper contributes to the literature by proposing a comprehensive framework to solve the SES problem, considering certain practical situations faced by organizations.

]]>Axioms doi: 10.3390/axioms12121069

Authors: Xianghe Zhu Jun Guo Haibing Wang

Consider three electromagnetic scattering models, namely, electromagnetic scattering by an elastic body, by a chiral medium, and by a cylinder at oblique incidence. We are concerned with the corresponding inverse problems of determining the locations and shapes of the scatterers from phaseless far-field patterns. There are certain essential differences from the usual inverse electromagnetic scattering problems, and some fundamental conclusions need to be proved. First, we show that the phaseless far-field data are invariant under the translation of the scatterers and prove the reciprocity relations of the scattering data. Then, we justify the unique determination of the scatterers by utilizing the reference ball approach and the superpositions of a fixed point source and plane waves as the incident fields. The proofs are based on the reciprocity relations, Green&rsquo;s formulas, and the analyses of the wave fields in the reference ball.

]]>Axioms doi: 10.3390/axioms12121068

Authors: Mhamed Eddahbi Omar Kebiri Abou Sene

In an infinite time horizon, we focused on examining the well-posedness of problems for a particular category of Backward Stochastic Differential Equations having quadratic growth (QBSDEs) with terminal conditions that are merely square integrable and generators that are measurable. Our approach employs a Zvonkin-type transformation in conjunction with the It&ocirc;&ndash;Krylov&rsquo;s formula. We applied our findings to derive probabilistic representation of a particular set of Partial Differential Equations par have quadratic growth in the gradient (QPDEs) characterized by coefficients that are measurable and almost surely continuous. Additionally, we explored a stochastic control optimization problem related to an epidemic model, interpreting it as an infinite time horizon QBSDE with a measurable and integrable drifts.

]]>Axioms doi: 10.3390/axioms12121067

Authors: Serhii O. Mashchenko Olena A. Kapustian Bruno Rubino

The present paper investigated the aggregation of individual preferences into a group fuzzy preference relation for a fuzzy set of decision-makers (DMs). This aggregation is based on the Kemeny optimization scheme. It was proven that this group relation is a Type-2 fuzzy relation (T2FR). The decomposition approach was used to analyze the group T2FR. It is shown that the group T2FR can be decomposed according to secondary membership grades into a finite collection of Type-1 fuzzy relations. Each of them is a group fuzzy relation for a crisp set of DMs, which is the corresponding &alpha;-cut of the original fuzzy set of DMs. Illustrative examples are given.

]]>Axioms doi: 10.3390/axioms12121066

Authors: Satyanad Kichenassamy

We show that relativistic rotation transformations represent transfer maps between the laboratory system and a local observer on an observer manifold, rather than an event manifold, in the spirit of C-equivalence. Rotation is, therefore, not a parameterised motion on a background space or spacetime, but is determined by a particular sequence of tetrads related by specific special Lorentz transformations or boosts. Because such Lorentz boosts do not form a group, these tetrads represent distinct observers that cannot put together their local descriptions into a manifold in the usual sense. The choice of observer manifold depends on the dynamical situation under consideration, and is not solely determined by the kinematics. Three examples are given: Franklin&rsquo;s rotation transformation for uniform plane rotation, the Thomas precession of a vector attached to an electron, and the motion of a charged particle in an electromagnetic field. In each case, at each point of its trajectory, there is a distinguished tetrad and a special Lorentz transformation that maps Minkowski space to the spacetime of the local observer on the curve.

]]>Axioms doi: 10.3390/axioms12121065

Authors: Radko Mesiar Anna Kolesárová Adam Šeliga Radomír Halaš

We introduce and discuss the concept of n-ary K-increasing fusion functions and n-ary K-increasing aggregation functions, K being a subset of the index set {1,&hellip;,n} indicating in which variables a considered function is increasing. It is also assumed that this function is decreasing in all other variables. We show that each n-ary K-increasing aggregation function is generated by some aggregation function which enables us to introduce and study the properties of n-ary K-increasing aggregation functions related to the properties of their generating aggregation functions. In particular, we also discuss binary K-increasing aggregation functions, including fuzzy implication and complication functions, among others.

]]>Axioms doi: 10.3390/axioms12121064

Authors: Queralt Viladevall Salvador Linares-Mustarós Maria Antonia Huertas Joan-Carles Ferrer-Comalat

This article presents different artistic raster images as a resource for correcting misconceptions about different laws and assumptions that underlie the propositional systems of binary logic, &#321;ukasiewicz&rsquo;s trivalent logic, Peirce&rsquo;s trivalent logic, Post&rsquo;s n-valent logic, and Black and Zadeh&rsquo;s infinite-valent logic. Recognizing similarities and differences in how images are constructed allows us to deepen, through comparison, the laws of bivalence, non-contradiction, and excluded middle, as well as understanding other multivalent logic assumptions from another perspective, such as their number of truth values. Consequently, the first goal of this article is to illustrate how the use of visualization can be a powerful tool for better understanding some logic systems. To demonstrate the utility of this objective, we illustrate how a deeper understanding of logic systems helps us appreciate the necessity of employing Likert scales based on the logic of Post or Zadeh, which is the second goal of the article.

]]>Axioms doi: 10.3390/axioms12111063

Authors: Safia Meftah Elhabib Hadjadj Mohamad Biomy Fares Yazid

In this work, by using the iterative method, we discuss the existence and uniqueness of solutions for multiterm fractional boundary value problems. Next, we examine some existence and uniqueness returns for semilinear fractional differential inclusions and equations for multiterm problems by using some notions and properties on set-valued maps and give some examples to explain our main results. We explore and use in this paper the fundamental properties of set-valued maps, which are needed for the study of differential inclusions. It began only in the mid-1900s, when mathematicians realized that their uses go far beyond a mere generalization of single-valued maps.

]]>Axioms doi: 10.3390/axioms12111062

Authors: Xiaowen Wu Zhengge Huang Jingjing Cui Yanping Long

By applying the weighted relaxation technique to the gradient-based iterative (GI) algorithm and taking proper weighted combinations of the solutions, this paper proposes the weighted, relaxed gradient-based iterative (WRGI) algorithm to solve the generalized coupled conjugate and transpose Sylvester matrix equations. With the real representation of a complex matrix as a tool, the necessary and sufficient conditions for the convergence of the WRGI algorithm are determined. Also, some sufficient convergence conditions of the WRGI algorithm are presented. Moreover, the optimal step size and the corresponding optimal convergence factor of the WRGI algorithm are given. Lastly, some numerical examples are provided to demonstrate the effectiveness, feasibility and superiority of the proposed algorithm.

]]>Axioms doi: 10.3390/axioms12111061

Authors: Vladimir V. Kassandrov Joseph A. Rizcallah Ivan A. Matveev

We briefly present our version of noncommutative analysis over matrix algebras, the algebra of biquaternions (B) in particular. We demonstrate that any B-differentiable function gives rise to a null shear-free congruence (NSFC) on the B-vector space CM and on its Minkowski subspace M. Making use of the Kerr&ndash;Penrose correspondence between NSFC and twistor functions, we obtain the general solution to the equations of B-differentiability and demonstrate that the source of an NSFC is, generically, a world sheet of a string in CM. Any singular point, caustic of an NSFC, is located on the complex null cone of a point on the generating string. Further we describe symmetries and associated gauge and spinor fields, with two electromagnetic types among them. A number of familiar and novel examples of NSFC and their singular loci are described. Finally, we describe a conservative algebraic dynamics of a set of identical particles on the &ldquo;Unique Worldline&rdquo; and discuss the connections of the theory with the Feynman&ndash;Wheeler concept of &ldquo;One-Electron Universe&rdquo;.

]]>Axioms doi: 10.3390/axioms12111060

Authors: Simon Gluzman Vyacheslav I. Yukalov

The method of Fractional Borel Summation is suggested in conjunction with self-similar factor approximants. The method used for extrapolating asymptotic expansions at small variables to large variables, including the variables tending to infinity, is described. The method is based on the combination of optimized perturbation theory, self-similar approximation theory, and Borel-type transformations. General Borel Fractional transformation of the original series is employed. The transformed series is resummed in order to adhere to the asymptotic power laws. The starting point is the formulation of dynamics in the approximations space by employing the notion of self-similarity. The flow in the approximation space is controlled, and &ldquo;deep&rdquo; control is incorporated into the definitions of the self-similar approximants. The class of self-similar approximations, satisfying, by design, the power law behavior, such as the use of self-similar factor approximants, is chosen for the reasons of transparency, explicitness, and convenience. A detailed comparison of different methods is performed on a rather large set of examples, employing self-similar factor approximants, self-similar iterated root approximants, as well as the approximation technique of self-similarly modified Pad&eacute;&ndash;Borel approximations.

]]>Axioms doi: 10.3390/axioms12111059

Authors: Tucker Hartland Ravi Shankar

We consider a class of nonlinear integro-differential equations that model degenerate nonlocal diffusion. We investigate whether the strong maximum principle is valid for this nonlocal equation. For degenerate parabolic PDEs, the strong maximum principle is not valid. In contrast, for nonlocal diffusion, we can formulate a strong maximum principle for nonlinearities satisfying a geometric condition related to the flux operator of the equation. In our formulation of the strong maximum principle, we find a physical re-interpretation and generalization of the standard PDE conclusion of the principle: we replace constant solutions with solutions of zero flux. We also consider nonlinearities outside the scope of our principle. For highly degenerate conductivities, we demonstrate the invalidity of the strong maximum principle. We also consider intermediate, inconclusive examples, and provide numerical evidence that the strong maximum principle is valid. This suggests that our geometric condition is sharp.

]]>Axioms doi: 10.3390/axioms12111058

Authors: Nikolay Popov Ivan Matveev

The paper shows that it is possible to construct quantum chromodynamics as a rigorous theory on the basis of employment of hyperbolic unitary group SUh(3), which is a symmetry group for the three-dimensional complex space of the hyperbolic type. Such an approach allows researchers to discover a profound connection between conserved color charges of the quarks and the symmetries of the hyperbolic three-dimensional complex space. Further, it allows a correct introduction of the Hermitian operators to describe the eight gluons, which are carriers of strong interactions.

]]>Axioms doi: 10.3390/axioms12111057

Authors: Jingying Gao Qingmei Bai Siriguleng He Eerdun Buhe

The paper introduces a new two-level time-mesh difference scheme for solving the symmetric regularized long wave equation. The scheme consists of three steps. A coarse time-mesh and a fine time-mesh are defined, and the equation is solved using an existing nonlinear scheme on the coarse time-mesh. Lagrange&rsquo;s linear interpolation formula is employed to obtain all preliminary solutions on the fine time-mesh. Based on the preliminary solutions, Taylor&rsquo;s formula is utilized to construct a linear system for the equation on the fine time-mesh. The convergence and stability of the scheme is analyzed, providing the convergence rates of O(&tau;F2+&tau;C4+h4) in the discrete L&infin;-norm for u(x,t) and in the discrete L2-norm for &rho;(x,t). Numerical simulation results show that the proposed scheme achieves equivalent error levels and convergence rates to the nonlinear scheme, while also reducing CPU time by over half, which indicates that the new method is more efficient. Furthermore, compared to the earlier time two-mesh method developed by the authors, the proposed scheme significantly reduces the error between the numerical and exact solutions, which means that the proposed scheme is more accurate. Additionally, the effectiveness of the new scheme is discussed in terms of the corresponding conservation laws and long-time simulations.

]]>Axioms doi: 10.3390/axioms12111056

Authors: Fang Tian Mingjing Wang Yongbin Ge

In this paper, some rational high-accuracy compact finite difference schemes on nonuniform grids (NRHOC) are introduced for solving convection&ndash;diffusion equations. The derived NRHOC schemes not only can suppress the oscillatory property of numerical solutions but can also obtain a high-accuracy approximate solution, and they can effectively solve the convection&ndash;diffusion problem with boundary layers by flexibly adjusting the discrete grid, which can be obtained with the singularity in the computational region. Three numerical experiments with boundary layers are conducted to verify the accuracy of the proposed NRHOC schemes. We compare the computed results with the analytical solutions, the results of the rational high-accuracy compact finite difference schemes on uniform grids (RHOC), and the other schemes in the literature. For all test problems, good computed results are obtained with the presented NRHOC schemes. It is shown that the presented NRHOC schemes have a better resolution for the solution of convection-dominated problems.

]]>Axioms doi: 10.3390/axioms12111055

Authors: Aiman Albarakati Asifa Tassaddiq Rekha Srivastava

Graph theory is a branch of mathematics that is crucial to modelling applicable systems and networks using matrix representations. In this article, a novel graph-theoretic model was used to assess an urban water distribution system (WDS) in Saudi Arabia. This graph model is based on representing its elements through nodes and links using a weighted adjacency matrix. The nodes represent the points where there can be a water input or output (sources, treatment plants, tanks, reservoirs, consumers, connections), and links represent the edges of the graph that carry water from one node to another (pipes, pumps, valves). Four WDS benchmarks, pumps, tanks, reservoirs, and external sources were used to validate the framework at first. This validation showed that the worst-case scenarios for vulnerability were provided by the fault sequence iterating the calculation of the centrality measurements. The vulnerability framework&rsquo;s application to the Saudi Arabian WDS enabled the identification of the system&rsquo;s most vulnerable junctions and zones. As anticipated, the regions with the fewest reservoirs were most at risk from unmet demand, indicating that this system is vulnerable to the removal of junctions and pipes that are intricately associated with their neighbours. Different centrality metrics were computed, from which the betweenness centrality offered the worst vulnerability prediction measures. The aspects and zones of the WDS that can more significantly impact the water supply in the event of a failure were identified by the vulnerability framework utilising attack tactics.

]]>Axioms doi: 10.3390/axioms12111054

Authors: Ibrahim Elbatal Amal S. Hassan L. S. Diab Anis Ben Ghorbal Mohammed Elgarhy Ahmed R. El-Saeed

In the statistical literature, one of the most important subjects that is commonly used is stress&ndash;strength reliability, which is defined as &delta;=PW&lt;V, where V and W are the strength and stress random variables, respectively, and &delta; is reliability parameter. Type-II progressive censoring with binomial removal is used in this study to examine the inference of &delta;=PW&lt;V for a component with strength V and being subjected to stress W. We suppose that V and W are independent random variables taken from the Burr XII distribution and the Burr III distribution, respectively, with a common shape parameter. The maximum likelihood estimator of &delta; is derived. The Bayes estimator of &delta; under the assumption of independent gamma priors is derived. To determine the Bayes estimates for squared error and linear exponential loss functions in the lack of explicit forms, the Metropolis&ndash;Hastings method was provided. Utilizing comprehensive simulations and two metrics (average of estimates and root mean squared errors), we compare these estimators. Further, an analysis is performed on two actual data sets based on breakdown times for insulating fluid between electrodes recorded under varying voltages.

]]>Axioms doi: 10.3390/axioms12111053

Authors: Niko Tratnik

The Zhang&ndash;Zhang polynomial of a benzenoid system is a well-known counting polynomial that was introduced in 1996. It was designed to enumerate Clar covers, which are spanning subgraphs with only hexagons and edges as connected components. In 2018, the generalized Zhang&ndash;Zhang polynomial of two variables was defined such that it also takes into account 10-cycles of a benzenoid system. The aim of this paper is to introduce and study a new variation of the Zhang&ndash;Zhang polynomial for phenylenes, which are important molecular graphs composed of 6-membered and 4-membered rings. In our case, Clar covers can contain 4-cycles, 6-cycles, 8-cycles, and edges. Since this new polynomial has three variables, we call it the multivariable Zhang&ndash;Zhang (MZZ) polynomial. In the main part of the paper, some recursive formulas for calculating the MZZ polynomial from subgraphs of a given phenylene are developed and an algorithm for phenylene chains is deduced. Interestingly, computing the MZZ polynomial of a phenylene chain requires some techniques that are different to those used to calculate the (generalized) Zhang&ndash;Zhang polynomial of benzenoid chains. Finally, we prove a result that enables us to find the MZZ polynomial of a phenylene with branched hexagons.

]]>Axioms doi: 10.3390/axioms12111052

Authors: Timothy Ganesan

In this work, an analogue to the Pauli spin matrices is presented and investigated. The proposed Hermitian spin matrices exhibit four symmetries for spin-1/n particles. The spin projection operators are derived, and the electrodynamics for hypothetical spin-1/2 fermions are explored using the proposed spin matrices. The fermionic quantum Heisenberg model is constructed using the proposed spin matrices, and comparative studies against simulation results using the Pauli spin matrices are conducted. Further analysis of the key findings as well as discussions on extending the proposed spin matrix framework to describe hypothetical bosonic systems (spin-1 particles) are provided.

]]>Axioms doi: 10.3390/axioms12111051

Authors: Haichuan Yang Yuxin Zhang Chaofeng Zhang Wei Xia Yifei Yang Zhenwei Zhang

In recent years, artificial neural networks (ANNs), which are based on the foundational model established by McCulloch and Pitts in 1943, have been at the forefront of computational research. Despite their prominence, ANNs have encountered a number of challenges, including hyperparameter tuning and the need for vast datasets. It is because many strategies have predominantly focused on enhancing the depth and intricacy of these networks that the essence of the processing capabilities of individual neurons is occasionally overlooked. Consequently, a model emphasizing a biologically accurate dendritic neuron model (DNM) that mirrors the spatio-temporal features of real neurons was introduced. However, while the DNM shows outstanding performance in classification tasks, it struggles with complexities in parameter adjustments. In this study, we introduced the hyperparameters of the DNM into an evolutionary algorithm, thereby transforming the method of setting DNM&rsquo;s hyperparameters from the previous manual adjustments to adaptive adjustments as the algorithm iterates. The newly proposed framework, represents a neuron that evolves alongside the iterations, thus simplifying the parameter-tuning process. Comparative evaluation on benchmark classification datasets from the UCI Machine Learning Repository indicates that our minor enhancements lead to significant improvements in the performance of DNM, surpassing other leading-edge algorithms in terms of both accuracy and efficiency. In addition, we also analyzed the iterative process using complex networks, and the results indicated that the information interaction during the iteration and evolution of the DNM follows a power-law distribution. With this finding, some insights could be provided for the study of neuron model training.

]]>Axioms doi: 10.3390/axioms12111050

Authors: Andrei Horvat-Marc Mariana Cufoian Adriana Mitre Ioana Taşcu

The purpose of this paper is to present some fixed-point results for self-generalized contractions in ordered rectangular b-metric spaces. We also provide some examples that illustrate the non-triviality and richness of this area of research.

]]>Axioms doi: 10.3390/axioms12111049

Authors: Thi Hong Phuong Le Ta-Chung Chu

This paper proposes a method for ranking generalized fuzzy numbers, which guarantees that both horizontal and vertical values are important parameters affecting the final ranking score. In this method, the normalized height coefficient is introduced to evaluate the influence of the height of fuzzy numbers on the final ranking score. The higher the normalized height coefficient of a generalized fuzzy number is, the higher its ranking. The left and right areas are presented to calculate the impact of the vertical value on the final ranking score. The left area is considered the benefit area. The right area is considered the cost area. A generalized fuzzy number is preferred if the benefit area is larger and the cost area is smaller. The proposed method can be employed to rank both normal and non-normal fuzzy numbers without normalization or height minimization. Numerical examples and comparisons with other methods highlight the feasibility and robustness of the proposed method, which can overcome the shortcomings of some existing methods and can support decision-makers in selecting the best alternative.

]]>Axioms doi: 10.3390/axioms12111048

Authors: Salma Iqbal Naveed Yaqoob Muhammad Gulistan

Due to various unpredictable factors, a decision maker frequently experiences uncertainty and hesitation when dealing with real-world practical optimization problems. At times, it&rsquo;s necessary to simultaneously optimize a number of non-linear and competing objectives. Linear Diophantine fuzzy numbers are used to address the uncertain parameters that arise in these circumstances. The objective of this manuscript is to present a method for solving a linear Diophantine fuzzy multi-objective nonlinear programming problem (LDFMONLPP). All the coefficients of the nonlinear multi-objective functions and the constraints are linear Diophantine fuzzy numbers (LDFNs). Here we find the solution of the nonlinear programming problem by using Karush-Kuhn-Tucker condition. A numerical example is presented.

]]>Axioms doi: 10.3390/axioms12111047

Authors: Elen Viviani Pereira Spreafico Paula Catarino Paulo Vasco

Many different number systems have been the topic of research. One of the recently studied number systems is that of hybrid numbers, which are generalizations of other number systems. In this work, we introduce and study the hybrid hyper k-Pell, hybrid hyper k-Pell&ndash;Lucas, and hybrid hyper Modified k-Pell numbers. In order to study these new sequences, we established new properties, generating functions, and the Binet formula of the hyper k-Pell, hyper k-Pell&ndash;Lucas, and hyper Modified k-Pell sequences. Thus, we present some algebraic properties, recurrence relations, generating functions, the Binet formulas, and some identities for the hybrid hyper k-Pell, hybrid hyper k-Pell&ndash;Lucas, and hybrid hyper Modified k-Pell numbers.

]]>Axioms doi: 10.3390/axioms12111046

Authors: Asifa Tassaddiq Rekha Srivastava Ruhaila Md Kasmani Rabab Alharbi

Firstly, a basic question to find the Laplace transform using the classical representation of gamma function makes no sense because the singularity at the origin nurtures so rapidly that &Gamma;ze&minus;sz cannot be integrated over positive real numbers. Secondly, Dirac delta function is a linear functional under which every function f is mapped to f(0). This article combines both functions to solve the problems that have remained unsolved for many years. For instance, it has been demonstrated that the power law feature is ubiquitous in theory but challenging to observe in practice. Since the fractional derivatives of the delta function are proportional to the power law, we express the gamma function as a complex series of fractional derivatives of the delta function. Therefore, a unified approach is used to obtain a large class of ordinary, fractional derivatives and integral transforms. All kinds of q-derivatives of these transforms are also computed. The most general form of the fractional kinetic integrodifferential equation available in the literature is solved using this particular representation. We extend the models that were valid only for a class of locally integrable functions to a class of singular (generalized) functions. Furthermore, we solve a singular fractional integral equation whose coefficients have infinite number of singularities, being the poles of gamma function. It is interesting to note that new solutions were obtained using generalized functions with complex coefficients.

]]>Axioms doi: 10.3390/axioms12111045

Authors: Reem K. Alhefthi Akhlaq A. Siddiqui Fatmah B. Jamjoom

The notion of quasi-Jordan algebras was originally proposed by R. Velasquez and R. Fellipe. Later, M. R. Bremner provided a modification called K-B quasi-Jordan algebras; these include all Jordan algebras and all dialgebras, and hence all associative algebras. Any quasi-Jordan algebra is special if it is isomorphic to a quasi-Jordan subalgebra of some dialgebras. Keeping in view the pivotal role of homotopes in the theory of Jordan algebras, we begin a study of the homotopes of quasi-Jordan algebras; among other related results, we show that the homotopes of any special quasi-Jordan algebra are special quasi-Jordan algebras and that the homotopes of a K-B quasi-Jordan algebra is a quasi-Jordan algebra. In the sequel, we also give some open problems.

]]>Axioms doi: 10.3390/axioms12111044

Authors: Simo Sun Yadong Shu Jinxiu Pi Die Zhou

We developed a repeated quantum game of public goods by using quantum entanglement and strong reciprocity mechanisms. Utilizing the framework of quantum game analysis, a comparative investigation incorporating both entangled and non-entangled states reveals that the player will choose a fully cooperative strategy when the expected cooperation strategy of the competitor exceeds a certain threshold. When the entanglement of states is not considered, the prisoner&rsquo;s dilemma still exists, and the cooperating party must bear the cost of defactoring the quantum strategy themselves; when considering the entanglement of states, the benefits of both parties in the game are closely related, forming a community of benefits. By signing a strong reciprocity contract, the degree of cooperation between the game parties can be considered using the strong reciprocity entanglement contract mechanism. The party striving to cooperate does not have to bear the risk of the other party&rsquo;s defector, and to some extent, it can solve the prisoner&rsquo;s dilemma problem. Finally, taking the public goods green planting industry project as an example, by jointly entrusting a third party to determine and sign a strong reciprocity entanglement contract, both parties can ensure a complete quantum strategy to maximize cooperation and achieve Pareto optimality, ultimately enabling the long-term and stable development of the public goods industry project.

]]>Axioms doi: 10.3390/axioms12111043

Authors: Xiaolong Shi Saira Hameed Sadia Akhter Aysha Khan Maryam Akhoundi

Spectral graph theory is like a special tool for understanding graphs. It helps us find patterns and connections in complex networks, using the magic of eigenvalues. Let G be the graph and A(G) be its adjacency matrix, then G is singular if the determinant of the adjacency matrix A(G) is 0, otherwise it is nonsingular. Within the realm of nonsingular graphs, there is the concept of property R, where each eigenvalue&rsquo;s reciprocal is also an eigenvalue of G. By introducing multiplicity constraints on both eigenvalues and their reciprocals, it becomes property SR. Similarly, the world of nonsingular graphs reveals property &minus;R, where the negative reciprocal of each eigenvalue also finds a place within the spectrum of G. Moreover, when the multiplicity of each eigenvalue and its negative reciprocal is equal, this results in a graph with a property of &minus;SR. Some classes of unweighted nonbipartite graphs are already constructed in the literature with the help of the complete graph Kn and a copy of the path graph P4 satisfying property R but not SR. This article takes this a step further. The main aim is to construct several weighted classes of graphs which satisfy property R but not SR. For this purpose, the weight functions are determined that enable these nonbipartite graph classes to satisfy the &minus;SR and R properties, even if the unweighted graph does not satisfy these properties. Some examples are presented to support the investigated results. These examples explain how certain weight functions make these special types of graphs meet the properties R or &minus;SR, even when the original graphs without weights do not meet these properties.

]]>Axioms doi: 10.3390/axioms12111042

Authors: Roy M. Howard

Schr&ouml;der approximations of the first kind, modified for the inverse function approximation case, are utilized to establish general analytical approximation forms for an inverse function. Such general forms are used to establish arbitrarily accurate analytical approximations, with a set relative error bound, for an inverse function when an initial approximation, typically with low accuracy, is known. Approximations for arcsine, the inverse of x &minus; sin(x), the inverse Langevin function and the Lambert W function are used to illustrate this approach. Several applications are detailed. For the root approximation of a function, Schr&ouml;der approximations of the first kind, based on the inverse of a function, have an advantage over the corresponding generalization of the standard Newton&ndash;Raphson method, as explicit analytical expressions for all orders of approximation can be obtained.

]]>Axioms doi: 10.3390/axioms12111041

Authors: Felix D. Ajibade Francis Monday Nkwuda Hussaini Joshua Taiwo P. Fajusigbe Kayode Oshinubi

In the context of uniformly convex Banach space, this paper focuses on examining the strong convergence of the F* iterative algorithm to the fixed point of a strongly pseudocontractive mapping. Furthermore, we demonstrate through numerical methods that the F* iterative algorithm converges strongly and faster than other current iterative schemes in the literature and extends to the fixed point of a strong pseudocontractive mapping. Finally, under a nonlinear quadratic Volterra integral equation, the application of our findings is shown.

]]>Axioms doi: 10.3390/axioms12111040

Authors: Nikolaos P. Theodorakatos Rohit Babu Angelos P. Moschoudis

Phasor Measurement Units (PMUs) are the backbone of smart grids that are able to measure power system observability in real-time. The deployment of synchronized sensors in power networks opens up the advantage of real-time monitoring of the network state. An optimal number of PMUs must be installed to ensure system observability. For that reason, an objective function is minimized, reflecting the cost of PMU installation around the power grid. As a result, a minimization model is declared where the objective function is defined over an adequate number of constraints on a binary decision variable domain. To achieve maximum network observability, there is a need to find the best number of PMUs and put them in appropriate locations around the power grid. Hence, maximization models are declared in a decision-making way to obtain optimality satisfying a guaranteed stopping and optimality criteria. The best performance metrics are achieved using binary integer, semi-definite, and binary polynomial models to encounter the optimal number of PMUs with suitable PMU positioning sites. All optimization models are implemented with powerful optimization solvers in MATLAB to obtain the global solution point.

]]>Axioms doi: 10.3390/axioms12111039

Authors: Manan A. Maisuria Priti V. Tandel Trushitkumar Patel

This study contains a two-dimensional mathematical model of solute transport in a river with temporally and spatially dependent flow, explicitly focusing on pulse-type input point sources with a fractional approach. This model is analyzed by assuming an initial concentration function as a declining exponential function in both the longitudinal and transverse directions. The governing equation is a time-fractional two-dimensional advection&ndash;dispersion equation with a variable form of dispersion coefficients, velocities, decay constant of the first order, production rate coefficient for the solute at the zero-order level, and retardation factor. The solution of the present problem is obtained by the fractional reduced differential transform method (FRDTM). The analysis of the initial retardation factor has been carried out via plots. Also, the influence of initial longitudinal and transverse dispersion coefficients and velocities has been examined by graphical analysis. The impact of fractional parameters on pollution levels is also analyzed numerically and graphically. The study of convergence for the FRDTM technique has been conducted to assess its efficacy and accuracy.

]]>Axioms doi: 10.3390/axioms12111038

Authors: Luciano Barcellos-Paula Aline Castro-Rezende Daniela Fantoni Alvares

Innovation plays a crucial role in the economy of nations worldwide. In Latin America, countries foster competitiveness through public and private incentives to support innovation. Moreover, entrepreneurship incentives seek to improve countries&rsquo; performance, although factors such as low business growth rates and informality can compromise it. Despite the efforts, there are several difficulties in achieving competitiveness, and few studies in developing countries. Therefore, the article explores the relationship between the factors that influence competitiveness, especially the role of innovation and entrepreneurship in Brazil and Peru. The research uses quantitative-qualitative methodology through modeling and simulation and a case study. The authors use the Affinities Theory to verify the relationship between the indicators that make up the competitiveness landscape and its most significant and attractive factors, adapting the methodology established by the International Institute for Management Development (IMD) World Competitiveness ranking. As a result, this algorithm allows us to know the relationships between five factors of economic attractiveness and four competitiveness indicators. As its main contributions, the study advances the frontier of knowledge about innovation and entrepreneurship, as few studies explore competitiveness in developing countries. Also, it offers a detailed explanation of the application of this algorithm, allowing researchers to reproduce this methodology in other scenarios. Practically, it might support policymakers in formulating development strategies and stimuli for business competitiveness. In addition, academic and business leaders can strengthen university-business collaboration with applied research in innovation and entrepreneurship. One limitation would be the number of countries participating in the research. The authors suggest future lines of research.

]]>Axioms doi: 10.3390/axioms12111037

Authors: Adeolu Taiwo Simeon Reich

We study three classes of variational inclusion problems in the framework of a real Hilbert space and propose a simple modification of Tseng&rsquo;s forward-backward-forward splitting method for solving such problems. Our algorithm is obtained via a certain regularization procedure and uses self-adaptive step sizes. We show that the approximating sequences generated by our algorithm converge strongly to a solution of the problems under suitable assumptions on the regularization parameters. Furthermore, we apply our results to an elastic net penalty problem in statistical learning theory and to split feasibility problems. Moreover, we illustrate the usefulness and effectiveness of our algorithm by using numerical examples in comparison with some existing relevant algorithms that can be found in the literature.

]]>Axioms doi: 10.3390/axioms12111036

Authors: Richard D. Carmichael

Vector-valued analytic functions in Cn, which are known to have vector-valued tempered distributional boundary values, are shown to be in the Hardy space Hp,1&le;p&lt;2, if the boundary value is in the vector-valued Lp,1&le;p&lt;2, functions. The analysis of this paper extends the analysis of a previous paper that considered the cases for 2&le;p&le;&infin;. Thus, with the addition of the results of this paper, the considered problems are proved for all p,1&le;p&le;&infin;.

]]>Axioms doi: 10.3390/axioms12111035

Authors: Luca Rondi

In this paper, we develop in detail the geometric constructions that lead to many uniqueness results for the determination of polyhedral sets, typically scatterers, by a finite minimal number of measurements. We highlight how unique continuation and a suitable reflection principle are enough to proceed with the constructions without any other assumption on the underlying partial differential equation or the boundary condition. We also aim to keep the geometric constructions and their proofs as simple as possible. To illustrate the applicability of this theory, we show how several uniqueness results present in the literature immediately follow from our arguments. Indeed, we believe that this theory may serve as a roadmap for establishing similar uniqueness results for other partial differential equations or boundary conditions.

]]>Axioms doi: 10.3390/axioms12111034

Authors: Gao Zhang Shao-Qun Zhang

For a quantale I, the unit interval endowed with a continuous triangular norm, we introduce the canonical, op-canonical and Kleisli extensions of the conical I-semifilter monad to I-Rel. It is proved that the op-canonical extension coincides with the Kleisli extension.

]]>Axioms doi: 10.3390/axioms12111033

Authors: Ge You Hao Guo Abd Alwahed Dagestani Ibrahim Alnafrah

To reduce the economic losses caused by debt evasion amongst lost-link borrowers (LBs) and improve the efficiency of finding information on LBs, this paper focuses on the cross-platform information collaborative search optimization problem for LBs. Given the limitations of platform/system heterogeneity, data type diversity, and the complexity of collaborative control in cross-platform information search for LBs, a collaborative search model for LBs&rsquo; information based on multi-agent technology is proposed. Additionally, a multi-agent Q-learning algorithm for the collaborative scheduling of multi-search subtasks is designed. We use the Q-learning algorithm based on function approximation to update the description model of the LBs. The multi-agent collaborative search problem is transformed into a reinforcement learning problem by defining search states, search actions, and reward functions. The results indicate that: (i) this model greatly improves the comprehensiveness and accuracy of the search for key information of LBs compared with traditional search engines; (ii) during searching for the information of LBs, the agent is more inclined to search on platforms and data types with larger environmental rewards, and the multi-agent Q-learning algorithm has a stronger ability to acquire information value than the transition probability matrix algorithm and the probability statistical algorithm for the same number of searches; (iii) the optimal search times of the multi-agent Q-learning algorithm are between 14 and 100. Users can flexibly set the number of searches within this range. It is significant for improving the efficiency of finding key information related to LBs.

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Authors: Xinhui Wu Jiawei Hu Ning Zhang

The 4&times;4 trace-free complex matrix set is introduced in this study. By using it, we are able to create a novel soliton hierarchy that is reduced to demonstrate its bi-Hamiltonian structure. Additionally, we give the Darboux matrix T, whose elements are connected to the spectral parameter in accordance with the various positions and numbers of the spectral parameter &lambda;. The Darboux transformation approach has also been successfully applicated to superintegrable systems.

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Authors: Yanbo Chong Ankur Jyoti Kashyap Shangming Chen Fengde Chen

We propose and study a class of discrete-time commensalism systems with additive Allee effects on the host species. First, the single species with additive Allee effects is analyzed for existence and stability, then the existence of fixed points of discrete systems is given, and the local stability of fixed points is given by characteristic root analysis. Second, we used the center manifold theorem and bifurcation theory to study the bifurcation of a codimension of one of the system at non-hyperbolic fixed points, including flip, transcritical, pitchfork, and fold bifurcations. Furthermore, this paper used the hybrid chaos method to control the chaos that occurs in the flip bifurcation of the system. Finally, the analysis conclusions were verified by numerical simulations. Compared with the continuous system, the similarities are that both species&rsquo; densities decrease with increasing Allee values under the weak Allee effect and that the host species hastens extinction under the strong Allee effect. Further, when the birth rate of the benefited species is low and the time is large enough, the benefited species will be locally asymptotically stabilized. Thus, our new finding is that both strong and weak Allee effects contribute to the stability of the benefited species under certain conditions.

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Authors: Lyudmila Frishter

A relevant problem in the development and improvement of numeric analytical methods for the research of structures, buildings and construction is studying the stress&ndash;strain state of structures and construction with boundaries that have complex shapes. Deformations and stresses arise in a domain with a geometrically non-linear shape of the boundary (cut-outs and cuts). These stresses and deformations have great values and gradients. Experiments carried out using the photoelasticity method show a change in the deformation order ratios for different subareas of the boundary cut-out area depending on proximity to the apex of the angular cut-out. Areas with minor deformations are observed, and areas where linear deformations and shears are more significant than rotations are also observed. In addition, areas where section rotations are more significant than linear and shear deformations are observed. According to the experimental data, the mathematical model of the SSS in the area of the apex of the cut-out of the domain boundary should take into account non-linear deformations. Hence, it is necessary to formulate the boundary value problem of the theory of elasticity, taking into account the geometrical non-linearity. The research aim of this paper is to formulate the problem of the elasticity theory taking into account the geometrical non-linearity in furtherance of the proposed mathematical model justified by the experimental data obtained using the photoelasticity method. The obtained formulation of the elasticity theory problem allows analyzing the form of the system of equations of the boundary value problem depending on the proximity of the considered area to the irregular point of the boundary, i.e., taking into account the difference in the effect of linear and shear deformations, rotations and forced deformations on the solution to the geometrically non-linear elastic problem dealing with forced deformations in the area of an angular cut-out of the boundary of the plane domain.

]]>Axioms doi: 10.3390/axioms12111029

Authors: Xiaole Guo

This article is focused on the investigation of Mond&ndash;Weir-type robust duality for a class of semi-infinite multi-objective fractional optimization with uncertainty in the constraint functions. We first establish a Mond&ndash;Weir-type robust dual problem for this fractional optimization problem. Then, by combining a new robust-type subdifferential constraint qualification condition and a generalized convex-inclusion assumption, we present robust &epsilon;-quasi-weak and strong duality properties between this uncertain fractional optimization and its uncertain Mond&ndash;Weir-type robust dual problem. Moreover, we also investigate robust &epsilon;-quasi converse-like duality properties between them.

]]>Axioms doi: 10.3390/axioms12111028

Authors: Kadda Maazouz Moussa Daif Allah Zaak Rosana Rodríguez-López

This paper discusses the problem of the existence and uniqueness of solutions to the boundary value problem for the nonlinear fractional-order pantograph equation, using the fractional derivative of variable order of Hadamard type. The main results are proved through the application of fractional calculus and Krasnoselskii&rsquo;s fixed-point theorem. Moreover, the Ulam&ndash;Hyers&ndash;Rassias stability of the nonlinear fractional pantograph equation is analyzed. To conclude this paper, we provide an example illustrating our findings and approach.

]]>Axioms doi: 10.3390/axioms12111027

Authors: Gabriela M. Rodrigues Edwin M. M. Ortega Gauss M. Cordeiro

Regression analysis can be appropriate to describe a nonlinear relationship between the response variable and the explanatory variables. This article describes the construction of a partially linear regression model with two systematic components based on the exponentiated odd log-logistic normal distribution. The parameters are estimated by the penalized maximum likelihood method. Simulations for some parameter settings and sample sizes empirically prove the accuracy of the estimators. The superiority of the proposed regression model over other regression models is shown by means of agronomic experimentation data. The predictive performance of the new model is compared with two machine learning techniques: decision trees and random forests. These methods achieved similar prediction performance, i.e., none stands out as a better predictor. In this sense, the objective of the research is to choose the best method. If the objective is only predictive, the decision tree can be used due to its simplicity. For inference purposes, the regression model is recommended, which can provide much more information regarding the relationship of the variables under study.

]]>Axioms doi: 10.3390/axioms12111026

Authors: Anatoliy Malyarenko Yuliya Mishura Kostiantyn Ralchenko Yevheniia Anastasiia Rudyk

We consider five types of entropies for Gaussian distribution: Shannon, R&eacute;nyi, generalized R&eacute;nyi, Tsallis and Sharma&ndash;Mittal entropy, establishing their interrelations and their properties as the functions of parameters. Then, we consider fractional Gaussian processes, namely fractional, subfractional, bifractional, multifractional and tempered fractional Brownian motions, and compare the entropies of one-dimensional distributions of these processes.

]]>Axioms doi: 10.3390/axioms12111025

Authors: Sajad Iqbal Francisco Martínez

In this study, we utilize the properties of the Sumudu transform (SuT) and combine it with the homotopy perturbation method to address the time fractional Navier-Stokes equation. We introduce a new technique called the homotopy perturbation Sumudu transform Strategy (HPSuTS), which combines the SuT with the homotopy perturbation method using He&rsquo;s polynomials. This approach proves to be powerful and practical for solving various linear and nonlinear fractional partial differential equations (FPDEs) in scientific and engineering fields. We demonstrate the efficiency and simplicity of this method through examples, showcasing its ability to approximate solutions for FPDEs. Additionally, we compare the numerical results obtained using this technique for different values of alpha, showing that as the value moves from a fractional order to an integer order, the solution becomes increasingly similar to the exact solution. Furthermore, we provide the tabular representations of the solution for each example.

]]>Axioms doi: 10.3390/axioms12111024

Authors: Mansour Shrahili Mohamed Kayid

This paper explores the concept of residual extropy as an uncertainty measure for order statistics. We specifically derive the residual extropy for the ith-order statistic and establish its relationship with the residual extropy of the ith-order statistic from a random sample generated from a uniform distribution. By employing this approach, we obtain a formula for the residual extropy of order statistics applicable to general continuous distributions. In addition, we offer two lower bounds that can be applied in situations where obtaining closed-form expressions for the residual extropy of order statistics in diverse distributions proves to be challenging. Additionally, we investigate the monotonicity properties of the residual extropy of order statistics. Furthermore, we present other aspects of the residual extropy of order statistics, including its dependence on the position of order statistics and various features of the underlying distribution.

]]>Axioms doi: 10.3390/axioms12111023

Authors: Rogério M. Saldanha da Gama José Julio Pedrosa Filho Rogério Pazetto S. da Gama Daniel Cunha da Silva Carlos Henrique Alexandrino Maria Laura Martins-Costa

This work uses a mixture theory approach to describe kinematically constrained flows through porous media using an adequate constitutive relation for pressure that preserves the problem hyperbolicity even when the flow becomes saturated. This feature allows using the same mathematical tool for handling unsaturated and saturated flows. The mechanical model can represent the saturated&ndash;unsaturated transition and vice-versa. The constitutive relation for pressure is a continuous and differentiable function of saturation: an increasing function with a strictly convex, increasing, and positive first derivative. This significant characteristic permits the fluid to establish a tiny controlled supersaturation of the porous matrix. The associated Riemann problem&rsquo;s complete solution is addressed in detail, with explicit expressions for the Riemann invariants. Glimm&rsquo;s semi-analytical scheme advances from a given instant to a subsequent one, employing the associated Riemann problem solution for each two consecutive time steps. The simulations employ a variation in Glimm&rsquo;s scheme, which uses the mean of four independent sequences for each considered time, ensuring computational solutions with reliable positions of rarefaction and shock waves. The results permit verifying this significant characteristic.

]]>Axioms doi: 10.3390/axioms12111022

Authors: Nadia Alluhaibi Rashad A. Abdel-Baky

A principal curve on a surface plays a paramount role in reasonable implementations. A curve on a surface is a principal curve if its tangents are principal directions. Using the Serret&ndash;Frenet frame, the surface pencil couple can be expressed as linear combinations of the components of the local frames in Galilean 3-space G3. With these parametric representations, a family of surfaces using principal curves (curvature lines) are constructed, and the necessary and sufficient condition for the given Bertrand couple to be the principal curves on these surfaces are derived in our approach. Moreover, the necessary and sufficient condition for the given Bertrand couple to satisfy the principal curves and the geodesic requirements are also analyzed. As implementations of our main consequences, we expound upon some models to confirm the method.

]]>Axioms doi: 10.3390/axioms12111021

Authors: Mikhail Kolev Nikolay Netov Iveta Nikolova Irina Naskinova Velika Kuneva Marian Milev

The proposed paper is devoted to presenting and analyzing a kinetic model describing the development of autoimmune disorders. The proposed model is a nonlinear system of differential equations that considers the biological activity of the interacting populations. The main characteristics of autoimmune diseases are taken into account. Preliminaries to the research area are provided. The modeling problem is discretized and solved approximately. The numerical results illustrate typical outcomes of autoimmune diseases.

]]>Axioms doi: 10.3390/axioms12111020

Authors: Akbar Azam Maliha Rashid Amna Kalsoom Faryad Ali

This paper is dedicated to the advancement of fixed-point results for multi-valued asymptotically non-expansive maps regarding convergence criteria in complete uniformly convex hyperbolic metric spaces that are endowed with a graph. The famous fixed-point theorems of Goebel and Kirk, Khamsi and Khan, along with other recent results in the literature can be obtained as corollaries of these main results. A nice graph and an interesting example are also provided in support of the hypothesis of the main results.

]]>Axioms doi: 10.3390/axioms12111019

Authors: Gary Chartrand Ritabrato Chatterjee Ping Zhang

Every red&ndash;blue coloring of the edges of a graph G results in a sequence G1, G2, &hellip;, G&#8467; of pairwise edge-disjoint monochromatic subgraphs Gi (1&le;i&le;&#8467;) of size i, such that Gi is isomorphic to a subgraph of Gi+1 for 1&le;i&le;&#8467;&minus;1. Such a sequence is called a Ramsey chain in G, and ARc(G) is the maximum length of a Ramsey chain in G, with respect to a red&ndash;blue coloring c. The Ramsey index AR(G) of G is the minimum value of ARc(G) among all the red&ndash;blue colorings c of G. If G has size m, then k+12&le;m&lt;k+22 for some positive integer k. It has been shown that there are infinite classes S of graphs, such that for every graph G of size m in S, AR(G)=k if and only if k+12&le;m&lt;k+22. Two of these classes are the matchings mK2 and paths Pm+1 of size m. These are both subclasses of linear forests (a forest of which each of the components is a path). It is shown that if F is any linear forest of size m with k+12&lt;m&lt;k+22, then AR(F)=k. Furthermore, if F is a linear forest of size k+12, where k&ge;4, that has at most k&minus;12 components, then AR(F)=k, while for each integer t with k&minus;12&lt;t&lt;k+12 there is a linear forest F of size k+12 with t components, such that AR(F)=k&minus;1.

]]>Axioms doi: 10.3390/axioms12111018

Authors: Yahya Almalki Abbas Kareem Wanas Timilehin Gideon Shaba Alina Alb Lupaş Mohamed Abdalla

The purpose of this article is to introduce and study certain families of normalized certain functions with symmetric points connected to Gegenbauer polynomials. Moreover, we determine the upper bounds for the initial Taylor&ndash;Maclaurin coefficients |a2| and |a3| and resolve the Fekete&ndash;Szeg&ouml;problem for these functions. In addition, we establish links to a few of the earlier discovered outcomes.

]]>Axioms doi: 10.3390/axioms12111017

Authors: Jing Li Weizhong Wang

With the intensification of global competition and the increasing awareness of reducing energy consumption, sustainable supplier selection is crucial for establishing a solid cooperative relationship in sustainable supply chain management. This paper proposes a new framework that considers both the effective expression of uncertain information and the objective weights of decision makers to select sustainable suppliers. We first apply an interval-valued intuitionistic fuzzy set to express the information of decision makers. Moreover, this paper applies a plant growth simulation algorithm to aggregate decision makers&rsquo; information. Next, we adopt the similarity measure method to derive the target weight of each decision maker. Then, we apply the score function to rank the candidate sustainable suppliers. Finally, two practical cases are presented to verify the effectiveness of the proposed framework. The outcomes and comparative discussion show that the developed framework is efficient for sustainable supplier selection. Therefore, the proposed framework can be used to establish a solid cooperative relationship in the process of sustainable supply chain management.

]]>Axioms doi: 10.3390/axioms12111016

Authors: Ekaterina A. Titova Peter K. Galenko Margarita A. Nikishina Liubov V. Toropova Dmitri V. Alexandrov

The boundary integral equation defining the interface function for a curved solid/liquid phase transition boundary is analytically solved in steady-state growth conditions. This solution describes dendrite tips evolving in undercooled melts with a constant crystallization velocity, which is the sum of the steady-state and translational velocities. The dendrite tips in the form of a parabola, paraboloid, and elliptic paraboloid are considered. Taking this solution into account, we obtain the modified boundary integral equation describing the evolution of the patterns and dendrites in undercooled binary melts. Our analysis shows that dendritic tips always evolve in a steady-state manner when considering a kinetically controlled crystallization scenario. The steady-state growth velocity as a factor that is dependent on the melt undercooling, solute concentration, atomic kinetics, and other system parameters is derived. This expression can be used for determining the selection constant of the stable dendrite growth mode in the case of kinetically controlled crystallization.

]]>Axioms doi: 10.3390/axioms12111015

Authors: Zanyar A. Ameen Mesfer H. Alqahtani

This article starts with a study of the congruence of soft sets modulo soft ideals. Different types of soft ideals in soft topological spaces are used to introduce new weak classes of soft open sets. Namely, soft open sets modulo soft nowhere dense sets and soft open sets modulo soft sets of the first category. The basic properties and representations of these classes are established. The class of soft open sets modulo the soft nowhere dense sets forms a soft algebra. Elements in this soft algebra are primarily the soft sets whose soft boundaries are soft nowhere dense sets. The class of soft open sets modulo soft sets of the first category, known as soft sets of the Baire property, is a soft &sigma;-algebra. In this work, we mainly focus on the soft &sigma;-algebra of soft sets with the Baire property. We show that soft sets with the Baire property can be represented in terms of various natural classes of soft sets in soft topological spaces. In addition, we see that the soft &sigma;-algebra of soft sets with the Baire property includes the soft Borel &sigma;-algebra. We further show that soft sets with the Baire property in a certain soft topology are equal to soft Borel sets in the cluster soft topology formed by the original one.

]]>Axioms doi: 10.3390/axioms12111014

Authors: Andrei Panteleev Vladislav Rakitianskii

The problem of finding the optimal open-loop control for discrete-time stochastic dynamical systems is considered. It is assumed that the initial conditions and external influences are random. The average value of the Bolza functional defined on individual trajectories is minimized. It is proposed to solve the problem by means of classical and modified migrating optimization algorithms. The modification of the migrating algorithm consists of cloning the members of the initial population and choosing different strategies of migratory behavior for the main population and for populations formed by clones. At the final stage of the search for an extremum, an intensively clarifying migration cycle is implemented with the participation of three leaders of the populations participating in the search process. Problems of optimal control of bundles of trajectories of deterministic discrete dynamical systems, as well as individual trajectories, are considered as special cases. Seven model examples illustrating the performance of the proposed approach are solved.

]]>Axioms doi: 10.3390/axioms12111013

Authors: Vladimir E. Fedorov Marina V. Plekhanova Daria V. Melekhina

Nonlinear identification problems for evolution differential equations, solved with respect to the highest-order Dzhrbashyan&ndash;Nersesyan fractional derivative, are studied. An equation of the considered class contains a linear unbounded operator, which generates analytic resolving families for the corresponding linear homogeneous equation, and a continuous nonlinear operator, which depends on lower-order Dzhrbashyan&ndash;Nersesyan derivatives and a depending on time unknown element. The identification problem consists of the equation, Dzhrbashyan&ndash;Nersesyan initial value conditions and an abstract overdetermination condition, which is defined by a linear continuous operator. Using the contraction mappings theorem, we prove the unique local solvability of the identification problem. The cases of mild and classical solutions are studied. The obtained abstract results are applied to an investigation of a nonlinear identification problem to a linearized phase field system with time dependent unknown coefficients at Dzhrbashyan&ndash;Nersesyan time-derivatives of lower orders.

]]>Axioms doi: 10.3390/axioms12111012

Authors: Yiting Huang Qiong Tang Bo Yu

The partial singular value assignment problem stems from the development of observers for discrete-time descriptor systems and the resolution of ordinary differential equations. Conventional techniques mostly utilize singular value decomposition, which is unfeasible for large-scale systems owing to their relatively high complexity. By calculating the sparse basis of the null space associated with some orthogonal projections, the existence of the matrix in partial singular value assignment is proven and an algorithm is subsequently proposed for implementation, effectively avoiding the full singular value decomposition of the existing methods. Numerical examples exhibit the efficiency of the presented method.

]]>Axioms doi: 10.3390/axioms12111011

Authors: Suresh Alapati Wooseong Che Sunkara Srinivasa Rao Giang T. T. Phan

Mathematical modeling and analysis of biologically inspired systems has been a fascinating research topic in recent years. In this work, we present the results obtained from the simulation of an elastic rod (that mimics a flagellum axoneme) rotational motion in a viscous fluid by using the lattice Boltzmann method (LBM) combined with an immersed boundary method (IBM). A finite element model consists of a set of beam and truss elements used to discretize the flagellum axoneme while the fluid flow is solved by the well-known LBM. The hydrodynamic coupling to maintain the no-slip boundary condition between the fluid and the elastic rod is conducted with the IBM. The rod is actuated with a torque applied at its base cross-section that acts as a driving motor of the axoneme. We simulated the rotational dynamics of the rod for three different rotational frequencies (low, medium, and high) of the motor. To compare with previous publication results, we chose the sperm number Sp=L(4&pi;&mu;&omega;)/(EI)1/4 as the validation parameter. We found that at the low rotational frequency, f = 1.5 Hz, the rod performs stable twirling motion after attaining an equilibrium state (the rod undergoes rigid rotation about its axis). At the medium frequency, f = 2.65 Hz, the rod undergoes whirling motion, where the tip of the rod rotates about the central rotational axis of the driving motor. When the frequency increases further, i.e., when it reaches the critical value, fc&nbsp;&asymp;&nbsp;2.7 Hz, the whirling motion becomes over-whirling, where the tip of the filament falls back to the base and performs a steady crank-shafting motion. All three rotational dynamics, twirling, whirling, and over-whirling, and the critical value of rotational frequency are in good agreement with the previously published results. We also observed that our present simulation technique is computationally more efficient than previous works.

]]>Axioms doi: 10.3390/axioms12111010

Authors: Yurii Kharkevych Inna Kal’chuk

In this paper, we considered arbitrary linear summation methods of Fourier series specified by a set of continuous functions dependent on the real parameter and established their approximation properties. We obtained asymptotic formulas for the exact upper bounds of the deviations of operators generated by &lambda;-methods of Fourier series summation from the functions of the classes C&beta;&psi;H&alpha; under certain restrictions on the functions &psi;.

]]>Axioms doi: 10.3390/axioms12111009

Authors: Hsiu-Chen Huang Chun-Nen Huang Huai-Wei Lo Tyan-Muh Thai

International airports are responding to the threat of climate change and various man-made hazards by proposing impact protection measures. Airport managers and risk controllers should develop a comprehensive risk assessment model to measure the mutual influence relationships of resilience factors. In this paper, the problem of treating resilience factors as independent ones in previous studies is overcome. In this study, we not only develop a framework for assessing resilience factors in international airports based on an aviation safety perspective, but also develop the Fermatean fuzzy decision-making trial and evaluation laboratory (FF-DEMATEL) to identify the mutual influence relationships of resilience factors. Fermatean fuzzy sets are incorporated in DEMATEL to reflect information incompleteness and uncertainty. The critical resilience factors of international airports were identified through real-case analysis. In terms of importance, the results show that rescue capability is a core capability that is important for airport resilience. In addition, &ldquo;security management system (SeMS) integrity&rdquo;, &ldquo;education and training of ground staff on airport safety awareness&rdquo;, &ldquo;first aid mechanism for the injured&rdquo;, and &ldquo;adequate maintenance equipment for rapid restoration tasks&rdquo; are identified as key factors that are given more weights. On the other hand, in terms of influence strength, the detection capability has the highest total influence and significantly influenced the other resilience capabilities. Finally, the influential network relation map (INRM) is utilized to assist decisionmakers in swiftly comprehending the impact of factors and formulating viable strategies to enhance airport resilience. This enables airport managers and risk controllers to make informed decisions and allocate resources efficiently.

]]>Axioms doi: 10.3390/axioms12111008

Authors: Binghua Jiang Huaping Huang Stojan Radenović

The purpose of this paper is to attain the existence of coincidences and common fixed points in four mappings satisfying (&psi;,&beta;,L)-generalized contractive conditions in the framework of partially ordered b-metric spaces. The main results presented in this paper generalize some recent results in the existing literature. Furthermore, a nontrivial example is presented to support the obtained results.

]]>Axioms doi: 10.3390/axioms12111007

Authors: Chuanyang Ruan Shicheng Gong Xiangjing Chen

Probabilistic interval ordering, as a helpful tool for expressing positive and negative information, can effectively address multi-attribute decision-making (MADM) problems in reality. However, when dealing with a significant number of decision-makers and decision attributes, the priority relationships between different attributes and their relative importance are often neglected, resulting in deviations in decision outcomes. Therefore, this paper combines probability interval ordering, the prioritized aggregation (PA) operator, and the Gauss&ndash;Legendre algorithm to address the MADM problem with prioritized attributes. First, considering the significance of interval priority ordering and the distribution characteristics of attribute priority, the paper introduces probability interval ordering elements that incorporate attribute priority, and it proposes the probabilistic interval ordering prioritized averaging (PIOPA) operator. Then, the probabilistic interval ordering Gauss&ndash;Legendre prioritized averaging operator (PIOGPA) is defined based on the Gauss&ndash;Legendre algorithm, and various excellent properties of this operator are explored. This operator considers the priority relationships between attributes and their importance level, making it more capable of handling uncertainty. Finally, a new MADM method is constructed based on the PIOGPA operator using probability intervals and employs the arithmetic&ndash;geometric mean (AGM) algorithm to compute the weight of each attribute. The feasibility and soundness of the proposed method are confirmed through a numerical example and comparative analysis. The MADM method introduced in this paper assigns higher weights to higher-priority attributes to establish fixed attribute weights, and it reduces the impact of other attributes on decision-making results. It also utilizes the Gauss AGM algorithm to streamline the computational complexity and enhance the decision-making effectiveness.

]]>Axioms doi: 10.3390/axioms12111006

Authors: Baodong Li Jiafu Su Boqiao Yuan Lvcheng Li Yihuan Zhao Zhidan Qin Li Qian

During the development process of complex products, selecting the best desirable alternative supplier is a challenge since an improperly selected alternative may cause losing capacity and increasing the cycle time and cost of development for a company. For this multiple-attribute decision-making problem of supplier selection, in this paper, a supplier selection problem in which the decision data are hesitant fuzzy information and the attribute weight is unknown in complex product development is investigated, and a supplier selection decision-making approach based on hesitant fuzzy information is proposed. Firstly, a bidirectional projection based on hesitant fuzzy information is established, and then the measurement equation for the degree of closeness is improved. Further, an attribute weight determination model which minimizes the projection total deviation for the hesitant fuzzy elements is constructed. By solving this model, scientific and reasonable attribute weights are provided. Subsequently, an illustrative example is employed to not only give the ranking result of alternative suppliers but also demonstrate the validity and feasibility of the developed approach. Meanwhile, sensitivity analysis and comparative analysis are put forward to illustrate the stability of the given final ranking result and the advantages and reliability of the constructed method. For alternative or strategy selection, this proposed approach can be used as a decision-making means when uncertainties are inherent.

]]>Axioms doi: 10.3390/axioms12111005

Authors: Hail S. Alrashdi Osama Moaaz Sameh S. Askar Ahmad M. Alshamrani Elmetwally M. Elabbasy

This paper presents an investigation into the qualitative behavior of solutions for a specific class of fourth-order half-linear neutral differential equations. The main objective of this study is to improve the relationship between the solution and its corresponding function. By developing improved relationships, a novel criterion is proposed to determine the oscillatory behavior of the studied equation. The exclusion of positive solutions is achieved through a comparative approach in which the examined equation is compared to second-order equations. Additionally, the significance of the obtained results is demonstrated by applying them to various illustrative examples.

]]>Axioms doi: 10.3390/axioms12111004

Authors: Satyvir Singh Ahmed Hussein Msmali

Nonlinear coupled reaction&ndash;diffusion (NCRD) systems have played a crucial role in the emergence of spatiotemporal patterns across various scientific and engineering domains. The NCRD systems considered in this study encompass various models, such as linear, Gray&ndash;Scott, Brusselator, isothermal chemical, and Schnakenberg, with the aim of capturing the spatiotemporal patterns they generate. These models cover a diverse range of intricate spatiotemporal patterns found in nature, including spots, spot replication, stripes, hexagons, and more. A mixed-type modal discontinuous Galerkin approach is employed for solving one- and two-dimensional NCRD systems. This approach introduces a mathematical formulation to handle the occurrence of second-order derivatives in diffusion terms. For spatial discretization, hierarchical modal basis functions premised on orthogonal scaled Legendre polynomials are used. Moreover, a novel reaction term treatment is proposed for the NCRD systems, demonstrating an intrinsic feature of the new DG scheme and preventing erroneous solutions due to extremely nonlinear reaction terms. The proposed approach reduces the NCRD systems into a framework of ordinary differential equations in time, which are addressed by an explicit third-order TVD Runge&ndash;Kutta algorithm. The spatiotemporal patterns generated with the present approach are comparable to those found in the literature. This approach can readily be expanded to handle large multi-dimensional problems that appear as model equations in developed biological and chemical applications.

]]>Axioms doi: 10.3390/axioms12111003

Authors: Wajid Ali Tanzeela Shaheen Hamza Ghazanfar Toor Tmader Alballa Alhanouf Alburaikan Hamiden Abd El-Wahed Khalifa

The Decision-Theoretic Rough Set model stands as a compelling advancement in the realm of rough sets, offering a broader scope of applicability. This approach, deeply rooted in Bayesian theory, contributes significantly to delineating regions of minimal risk. Within the Decision-Theoretic Rough Set paradigm, the universal set undergoes a tripartite division, where distinct regions emerge and losses are intelligently distributed through the utilization of membership functions. This research endeavors to present an enhanced and more encompassing iteration of the Decision-Theoretic Rough Set framework. Our work culminates in the creation of the Generalized Intuitionistic Decision-Theoretic Rough Set (GI-DTRS), a fusion that melds the principles of Decision-Theoretic Rough Sets and intuitionistic fuzzy sets. Notably, this synthesis bridges the gaps that exist within the conventional approach. The innovation lies in the incorporation of an error function tailored to the hesitancy grade inherent in intuitionistic fuzzy sets. This integration harmonizes seamlessly with the contours of the membership function. Furthermore, our methodology deviates from established norms by constructing similarity classes based on similarity measures, as opposed to relying on equivalence classes. This shift holds particular relevance in the context of aggregating information systems, effectively circumventing the challenges associated with the process. To demonstrate the practical efficacy of our proposed approach, we delve into a concrete experiment within the information technology domain. Through this empirical exploration, the real-world utility of our approach becomes vividly apparent. Additionally, a comprehensive comparative analysis is undertaken, juxtaposing our approach against existing techniques for aggregation and decision modeling. The culmination of our efforts is a well-rounded article, punctuated by the insights, recommendations, and future directions delineated by the authors.

]]>Axioms doi: 10.3390/axioms12101002

Authors: Francesc Aràndiga Sara Remogna

The aim of this paper is to present and study nonlinear bivariate C1 quadratic spline quasi-interpolants on uniform criss-cross triangulations for the approximation of piecewise smooth functions. Indeed, by using classical spline quasi-interpolants, the Gibbs phenomenon appears when approximating near discontinuities. Here, we use weighted essentially non-oscillatory techniques to modify classical quasi-interpolants in order to avoid oscillations near discontinuities and maintain high-order accuracy in smooth regions. We study the convergence properties of the proposed quasi-interpolants and we provide some numerical and graphical tests confirming the theoretical results.

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