Axioms doi: 10.3390/axioms13100688

Authors: Asra Hadadfard Mohammad Bagher Ghaemi António M. Lopes

This paper introduces a new measure of non-compactness within a bounded domain of RN in the generalized Morrey space. This measure is used to establish the existence of solutions for a coupled Hadamard fractional system of integral equations in generalized Morrey spaces. To illustrate the application of the main result, an example is presented.

]]>Axioms doi: 10.3390/axioms13100687

Authors: Viktor Abramov

We propose a new approach to extend the notion of commutator and Lie algebra to algebras with ternary multiplication laws. Our approach is based on the ternary associativity of the first and second kinds. We propose a ternary commutator, which is a linear combination of six triple products (all permutations of three elements). The coefficients of this linear combination are the cube roots of unity. We find an identity for the ternary commutator that holds due to the ternary associativity of either the first or second kind. The form of this identity is determined by the permutations of the general affine group GA(1,5)&sub;S5. We consider this identity as a ternary analog of the Jacobi identity. Based on the results obtained, we introduce the concept of a ternary Lie algebra at cube roots of unity and provide examples of such algebras constructed using ternary multiplications of rectangular and three-dimensional matrices. We also highlight the connection between the structure constants of a ternary Lie algebra with three generators and an irreducible representation of the rotation group. The classification of two-dimensional ternary Lie algebras at cube roots of unity is proposed.

]]>Axioms doi: 10.3390/axioms13100686

Authors: Safyan Mukhtar Weaam Alhejaili Mohammad Alqudah Ali M. Mahnashi Rasool Shah Samir A. El-Tantawy

This paper provides several new traveling wave solutions for a nonlinear partial differential equation (PDE) by applying symbolic computation and a new approach, the Riccati&ndash;Bernoulli sub-ODE method, in a computer algebra system. Herein, employing the B&auml;cklund transformation, we solve a nonlinear PDE associated with nanobiosciences and biophysics based on the transmission line model of microtubules for nanoionic currents. The equation introduced here in this form is suitable for critical nanoscience concerns like cell signaling and might continue to explain some of the basic cognitive functions in neurons. We employ advanced procedures to replicate the previously detected solitary waves. We offer our solutions in graphical forms, such as 3D and contour plots, using Mathematica. We can generalize the elementary method to other nonlinear equations in physics, requiring only a few steps.

]]>Axioms doi: 10.3390/axioms13100685

Authors: Hui Wu Shuangjian Guo Xiaohui Zhang

In this paper, we introduce two-term differential Leib&infin;-conformal algebras and give characterizations of some particular classes of such two-term differential Leib&infin;-conformal algebras. Furthermore, we discuss the classification of the non-Abelian extensions in terms of non-Abelian cohomology groups. Finally, we explore the inducibility of pairs of automorphisms and derive the analog Wells exact sequences under the circumstance of differential Leibniz conformal algebras.

]]>Axioms doi: 10.3390/axioms13100684

Authors: Hanan Alohali Valer-Daniel Breaz Omar Mutab Alsalami Luminita-Ioana Cotirla Ahmed Alamer

Integral inequalities with generalized convexity play a vital role in both theoretical and applied mathematics. The theory of integral inequalities is one of the branches of mathematics that is now developing at the quickest rate due to its wide range of applications. We define a new Hermite&ndash;Hadamard inequality for the novel class of coordinated &#411;-pre-invex fuzzy number-valued mappings (C-&#411;-pre-invex &#120333; &#120341; &#120349; &#120340;s) and examine the idea of C-&#411;-pre-invex &#120333; &#120341; &#120349; &#120340;s in this paper. Furthermore, using C-&#411;-pre-invex &#120333; &#120341; &#120349; &#120340;s, we construct several new integral inequalities for fuzzy double Riemann integrals. Several well-known results, as well as recently discovered results, are included in these findings as special circumstances. We think that the findings in this work are new and will help to stimulate more research in this area in the future. Additionally, unique choices lead to new outcomes.

]]>Axioms doi: 10.3390/axioms13100683

Authors: Mohanad Kadhim Ahmed Alkarafi Ali Ebadian Saeid Shams

In this paper, we employ the theory of differential subordination to establish a theorem that delineates certain sufficient conditions for starlikeness, convexity, close-to-convexity, and quasi-convexity in relation to functions with fixed initial coefficients. Furthermore, we introduce some results derived from these conditions. Building upon this framework, we derive an extension of Nunokawa&rsquo;s lemma for analytic functions with fixed initial coefficients.

]]>Axioms doi: 10.3390/axioms13100682

Authors: Xiaojun Lv Kaihong Zhao Haiping Xie

In this article, we delve into delayed fractional differential equations with Riemann&ndash;Stieltjes integral boundary conditions and fractional impulses. By using differential inequality techniques and some fixed-point theorems, some novel sufficient assessments for convenient verification have been devised to ensure the existence and uniqueness of solutions. We further employ the nonlinear analysis to reveal that this problem is Ulam&ndash;Hyers (UH) stable. Finally, some examples and numerical simulations are presented to illustrate the reliability and validity of our main results.

]]>Axioms doi: 10.3390/axioms13100681

Authors: Ahmed Alemam Asma Al-Jaser Osama Moaaz Fahd Masood Hamdy El-Metwally

This article highlights the oscillatory properties of second-order Emden&ndash;Fowler delay differential equations featuring sublinear neutral terms and multiple delays, encompassing both canonical and noncanonical cases. Through the proofs of several theorems, we investigate criteria for the oscillation of all solutions to the equations under study. By employing the Riccati technique in various ways, we derive results that expand the scope of previous research and enhance the cognitive understanding of this mathematical domain. Additionally, we provide three illustrative examples to demonstrate the validity and applicability of our findings.

]]>Axioms doi: 10.3390/axioms13100680

Authors: Michal Pospíšil Lucia Pospíšilová Škripková Pospíšilová

The method of the equivalent system of fractional integral equations is used to prove the existence results of a unique solution for initial value problems corresponding to various classes of nonlinear fractional differential equations involving the tempered &Psi;&ndash;Caputo fractional derivative. These include equations with their right side depending on ordinary as well as fractional-order derivatives, or fractional integrals of the solution.

]]>Axioms doi: 10.3390/axioms13100679

Authors: Kamil Aida-zade Alexander Handzel Efthimios Providas

The numerical solution of optimal control problems through second-order methods is examined in this paper. Controlled processes are described by a system of nonlinear ordinary differential equations. There are two specific characteristics of the class of control actions used. The first one is that controls are searched for in a given class of functions, which depend on unknown parameters to be found by minimizing an objective functional. The parameter values, in general, may be different at different time intervals. The second feature of the considered problem is that the boundaries of time intervals are also optimized with fixed values of the parameters of the control actions in each of the intervals. The special cases of the problem under study are relay control problems with optimized switching moments. In this work, formulas for the gradient and the Hessian matrix of the objective functional with respect to the optimized parameters are obtained. For this, the technique of fast differentiation is used. A comparison of numerical experiment results obtained with the use of first- and second-order optimization methods is presented.

]]>Axioms doi: 10.3390/axioms13100678

Authors: Mohammed B. Alamari Fatimah A. Almulhim Zoulikha Kaid Ali Laksaci

The main aim of this paper is to consider a new risk metric that permits taking into account the spatial interactions of data. The considered risk metric explores the spatial tail-expectation of the data. Indeed, it is obtained by combining the ideas of expected shortfall regression with an expectile risk model. A spatio-functional Nadaraya&ndash;Watson estimator of the studied metric risk is constructed. The main asymptotic results of this work are the establishment of almost complete convergence under a mixed spatial structure. The claimed asymptotic result is obtained under standard assumptions covering the double functionality of the model as well as the data. The impact of the spatial interaction of the data in the proposed risk metric is evaluated using simulated data. A real experiment was conducted to measure the feasibility of the Spatio-Functional Expectile Shortfall Regression (SFESR) in practice.

]]>Axioms doi: 10.3390/axioms13100677

Authors: Can Kızılateş Wei-Shih Du Nazlıhan Terzioğlu Ren-Chuen Chen

In this paper, by using q-integers and higher-order generalized Fibonacci numbers, we define the higher-order generalized Fibonacci quaternions with q-integer components. We give some special cases of these newly established quaternions. This article examines q-calculus and quaternions together. We obtain a Binet-like formula, some new identities, a generating function, a recurrence relation, an exponential generating function, and sum properties of quaternions with quantum integer coefficients. In addition, we obtain some new identities for these types of quaternions by using three new special matrices.

]]>Axioms doi: 10.3390/axioms13100676

Authors: Edson Donizete de Carvalho Waldir Silva Soares Douglas Fernando Copatti Carlos Alexandre Ribeiro Martins Eduardo Brandani da Silva

Current work provides an algebraic and geometric technique for building topological quantum codes. From the lattice partition derived of quotient lattices &Lambda;&prime;/&Lambda; of index m combined with geometric technique of the projections of vector basis &Lambda;&prime; over vector basis &Lambda;, we reproduce surface codes found in the literature with parameter [[2m2,2,|a|+|b|]] for the case &Lambda;=Z2 and m=a2+b2, where a and b are integers that are not null, simultaneously. We also obtain a new class of surface code with parameters [[2m,2,|a|+|b|]] from the &Lambda;=A2-lattice when m can be expressed as m=a2+ab+b2, where a and b are integer values. Finally, we will show how this technique can be extended to the construction of color codes with parameters [[18m,4,6(|a|+|b|)]] by considering honeycomb lattices partition A2/&Lambda;&prime; of index m=9(a2+ab+b2) where a and b are not null integers.

]]>Axioms doi: 10.3390/axioms13100675

Authors: Shahid Abdullah Neha Choubey Suresh Dara Moin-ud-Din Junjua Tawseef Abdullah

This study introduces a novel, iterative algorithm that achieves fourth-order convergence for solving nonlinear equations. Satisfying the Kung&ndash;Traub conjecture, the proposed technique achieves an optimal order of four with an efficiency index (I) of 1.587, requiring three function evaluations. An analysis of convergence is presented to show the optimal fourth-order convergence. To verify the theoretical results, in-depth numerical comparisons are presented for both real and complex domains. The proposed algorithm is specifically examined on a variety of polynomial functions, and it is shown by the efficient and accurate results that it outperforms many existing algorithms in terms of speed and accuracy. The study not only explores the proposed method&rsquo;s convergence properties, computational efficiency, and stability but also introduces a novel perspective by considering the count of black points as an indicator of a method&rsquo;s divergence. By analyzing the mean number of iterations necessary for methods to converge within a cycle and measuring CPU time in seconds, this research provides a holistic assessment of both the efficiency and speed of iterative methods. Notably, the analysis of basins of attraction illustrates that our proposed method has larger sets of initial points that yield convergence.

]]>Axioms doi: 10.3390/axioms13100674

Authors: Wenxiu Gong Zuoliang Xu Yesen Sun

This paper explores a numerical method for European and American option pricing under time fractional jump-diffusion model in Caputo scene. The pricing problem for European options is formulated using a time fractional partial integro-differential equation, whereas the pricing of American options is described by a linear complementarity problem. For European option, we present nonuniform discretization along time and the radial basis function (RBF) method for spatial discretization. The stability and convergence analysis of the discrete scheme are carried out in the case of European options. For American option, the operator splitting method is adopted which split linear complementary problem into two simple equations. The numerical results confirm the accuracy of the proposed method.

]]>Axioms doi: 10.3390/axioms13100673

Authors: Po-Chun Huang Bo-Yu Pan

This article investigates the local well-posedness of a coupled system of wave equations on a half-line, with a particular emphasis on Robin boundary conditions within Sobolev spaces. We provide estimates for the solutions to linear initial-boundary-value problems related to the coupled system of wave equations, utilizing the Unified Transform Method in conjunction with the Hadamard norm while considering the influence of external forces. Furthermore, we demonstrate that replacing the external force with a nonlinear term alters the iteration map defined by the unified transform solutions, making it a contraction map in a suitable solution space. By employing the contraction mapping theorem, we establish the existence of a unique solution. Finally, we show that the data-to-solution map is locally Lipschitz continuous, thus confirming the local well-posedness of the coupled system of wave equations under consideration.

]]>Axioms doi: 10.3390/axioms13100672

Authors: Claudia I. Gonzalez

Dementia is the most critical neurodegenerative disease that gradually destroys memory and other cognitive functions. Therefore, early detection is essential, and to build an effective detection model, it is required to understand its type, symptoms, stages and causes, and diagnosis methodologies. This paper presents a novel approach to classify dementia based on a data set with some relevant patient features. The classification methodology employs non-singleton general type-2 fuzzy sets, non-singleton interval type-2 fuzzy sets, and non-singleton type 1 fuzzy sets. These advanced fuzzy sets are compared with traditional singleton fuzzy sets to evaluate their performance. The Takagi&ndash;Sugeno&ndash;Kang TSK inference method is used to handle fuzzy reasoning. In the process, the parameters of the membership functions (MFs) and rules are obtained using ANFIS, and non-singleton MFs are optimized with PSO. The results demonstrate that non-singleton general type-2 fuzzy sets improve classification accuracy compared to singleton fuzzy sets, demonstrating their ability to model the uncertainties inherent in the diagnosis of dementia. This improvement suggests that non-singleton fuzzy systems offer a more robust framework for developing effective diagnostic tools in the medical domain. Accurate classification of dementia is of utmost importance to improve patient care and advance medical research.

]]>Axioms doi: 10.3390/axioms13100671

Authors: Mudassir Shams Bruno Carpentieri

Nonlinear problems, which often arise in various scientific and engineering disciplines, typically involve nonlinear equations or functions with multiple solutions. Analytical solutions to these problems are often impossible to obtain, necessitating the use of numerical techniques. This research proposes an efficient and stable Caputo-type inverse numerical fractional scheme for simultaneously approximating all roots of nonlinear equations, with a convergence order of 2&psi;+2. The scheme is applied to various nonlinear problems, utilizing dynamical analysis to determine efficient initial values for a single root-finding Caputo-type fractional scheme, which is further employed in inverse fractional parallel schemes to accelerate convergence rates. Several sets of random initial vectors demonstrate the global convergence behavior of the proposed method. The newly developed scheme outperforms existing methods in terms of accuracy, consistency, validation, computational CPU time, residual error, and stability.

]]>Axioms doi: 10.3390/axioms13100670

Authors: Valeriu Popa Alina-Mihaela Patriciu

Over the years, the concept of metric space has been extended in several directions, and numerous common fixed point theorems for multivalued mappings in complete metric space have been demonstrated. In this paper, we prove a general fixed point theorem for a pair of multivalued mappings satisfying implicit relations, extending some results from the literature to S-metric spaces. As an application, we obtain new results for a sequence of multivalued mappings in S-metric spaces, generalizing some known results.

]]>Axioms doi: 10.3390/axioms13100669

Authors: Ali Yahya Hummdi Emine Koç Sögütcü Öznur Gölbaşı Nadeem ur Rehman

This paper investigates the relationship between the commutativity of rings and the properties of their multiplicative generalized derivations. Let F be a ring with a semiprime ideal &Pi;. A map &#981;:F&rarr;F is classified as a multiplicative generalized derivation if there exists a map &sigma;:F&rarr;F such that &#981;(xy)=&#981;(x)y+x&sigma;(y) for all x,y&isin;F. This study focuses on semiprime ideals &Pi; that admit multiplicative generalized derivations &#981; and G that satisfy certain differential identities within F. By examining these conditions, the paper aims to provide new insights into the structural aspects of rings, particularly their commutativity in relation to the behavior of such derivations.

]]>Axioms doi: 10.3390/axioms13100668

Authors: Alexey Bosov

The paper presents an approach to solving the problem of unknown motion parameters Bayesian identification for the stochastic dynamic system model with randomly delayed observations. The system identification and the object tracking tasks obtain solutions in the form of recurrent Bayesian relations for a posteriori probability density. These relations are not practically applicable due to the computational challenges they present. For practical implementation, we propose a conditionally minimax nonlinear filter that implements the concept of conditionally optimal estimation. The random delays model source is the area of autonomous underwater vehicle control. The paper discusses in detail a computational experiment based on a model that is closely aligned with this practical need. The discussion includes both a description of the filter synthesis features based on the geometric interpretation of the simulated measurements and an impact analysis of the effectiveness of model special factors, such as time delays and model unknown parameters. Furthermore, the paper puts forth a novel approach to the identification problem statement, positing a random jumping change in the motion parameters values.

]]>Axioms doi: 10.3390/axioms13100667

Authors: Joan Grandes Umbert Tom Mestdag

We construct the smooth vector bundle of tensor densities of arbitrary weight in a coordinate-independent way. We prove the general existence of a globally smooth tensor density field, as well as the existence of a globally smooth metric density for a pseudo-Riemannian manifold, specifically. We study the coordinate description of a covariant derivative over densities, and define a natural extension of affine connections to densities. We provide an equivalent characterization, in the case of a pseudo-Riemannian manifold.

]]>Axioms doi: 10.3390/axioms13100666

Authors: Zizhao Zhou Ahmad Aziz Al Ahmadi Alina Alb Lupas Khalil Hadi Hakami

The correct derivation of integral inequalities on fuzzy-number-valued mappings depends on applying fractional calculus to fuzzy number analysis. The purpose of this article is to introduce a new class of convex mappings and generalize various previously published results on the fuzzy number and interval-valued mappings via fuzzy-order relations using fuzzy coordinated &#7933;-convexity mappings so that the new version of the well-known Hermite&ndash;Hadamard (H-H) inequality can be presented in various variants via the fractional integral operators (Riemann&ndash;Liouville). Some new product forms of these inequalities for coordinated &#7933;-convex fuzzy-number-valued mappings (coordinated &#7933;-convex FNVMs) are also discussed. Additionally, we provide several fascinating non-trivial examples and exceptional cases to show that these results are accurate.

]]>Axioms doi: 10.3390/axioms13100665

Authors: Yazen M. Alawaideh Alina Alb Lupas Bashar M. Al-khamiseh Majeed A. Yousif Pshtiwan Othman Mohammed Y. S. Hamed

This paper presents an analysis of the Hamiltonian formulation for continuous systems with second-order derivatives derived from Dirac&rsquo;s theory. This approach offers a unique perspective on the equations of motion compared to the traditional Euler&ndash;Lagrange formulation. Focusing on Podolsky&rsquo;s generalized electrodynamics, the Hamiltonian and corresponding equations of motion are derived. The findings demonstrate that both Hamiltonian and Euler&ndash;Lagrange formulations yield equivalent results. This study highlights the Hamiltonian approach as a valuable alternative for understanding the dynamics of second-order systems, validated through a specific application within generalized electrodynamics. The novelty of the research lies in developing advanced theoretical models through Hamiltonian formalism for continuous systems with second-order derivatives. The research employs an alternative method to the Euler&ndash;Lagrange formulas by applying Dirac&rsquo;s theory to study the generalized Podolsky electrodynamics, contributing to a better understanding of complex continuous systems.

]]>Axioms doi: 10.3390/axioms13100664

Authors: Aisha Fayomi Ehab M. Almetwally Maha E. Qura

In this paper, we address the analysis of bivariate lifetime data from a length-biased exponential distribution observed under Type II progressive censoring with random removals, where the number of units removed at each failure time follows a binomial distribution. We derive the likelihood function for the progressive Type II censoring scheme with random removals and apply it to the bivariate length-biased exponential distribution. The parameters of the proposed model are estimated using both likelihood and Bayesian methods for point and interval estimators, including asymptotic confidence intervals and bootstrap confidence intervals. We also employ different loss functions to construct Bayesian estimators. Additionally, a simulation study is conducted to compare the performance of censoring schemes. The effectiveness of the proposed methodology is demonstrated through the analysis of two real datasets from the industrial and computer science domains, providing valuable insights for illustrative purposes.

]]>Axioms doi: 10.3390/axioms13100663

Authors: Guangyuan Tian Xianji Meng

In this paper, we consider the fractional Schr&ouml;dinger&ndash;Hirota (FSH) equation in the sense of a conformable fractional derivative. Through a traveling wave transformation, we change the FSH equation to an ordinary differential equation. We obtain several exact solutions through the auxiliary equation method, including soliton, exponential and periodic solutions, which are useful to analyze the behaviors of the FSH equation. We show that the auxiliary equation method improves the speed of the discovery of exact solutions.

]]>Axioms doi: 10.3390/axioms13100662

Authors: Jimmy Reyes Josu Najera-Zuloaga Dae-Jin Lee Jaime Arrué Yuri A. Iriarte

In this paper, we propose an alternative distribution to model count data exhibiting uni/bimodality. It arises as a weighted version of the beta-binomial distribution, which is defined by a parametric weight function that admits up to two modes for the resulting probability mass function. Like the baseline beta-binomial distribution, the proposed distribution performs well in modeling overdispersed binomial data. Structural properties of the new distribution are studied. Raw moments are derived, which are used to describe the dispersion behavior relative to the mean and the skewness behavior. Parameter estimation is carried out using the maximum likelihood method. A simulation study is conducted in order to illustrate the behavior of the estimators. Finally, two applications illustrating the usefulness of the proposal are presented.

]]>Axioms doi: 10.3390/axioms13100661

Authors: Svetozar R. Rančić Ljubica S. Velimirović Marija S. Najdanović

This paper deals with the study of torsional energy (total squared torsion) at infinitesimal bending of curves and knots in three dimensional Euclidean space. During bending, the curve is subject to change, and its properties are changed. The effect that deformation has on the curve is measured by variations. Here, we observe the infinitesimal bending of the second order and variations of the first and the second order that occur in this occasion. The subjects of study are curves and knots, in particular torus knots. We analyze various examples both analytically and graphically, using our own calculation and visualization software tool.

]]>Axioms doi: 10.3390/axioms13100660

Authors: Cristhian R. Uzeta-Obregon Tanya S. Garcia-Gastelum Pavel A. Alvarez Cristhian Mellado-Cid Fabio Blanco-Mesa Ernesto Leon-Castro

The main objective of this article is to present the formulation of a Capital Asset Pricing Model ordered weighted average CAPMOWAand its extensions, called CAPM-induced OWA (CAPMIOWA), CAPM Bonferroni OWA (CAPMBon-OWA), and CAPM Bonferroni-induced OWA CAPMBon-IOWA. A step-by-step process for applying this new proposal in a real case of formulating investment portfolios is generated. These methods show several scenarios, considering the attitude, preferences, and relationship of each argument, when underestimation or overestimation of the information by the decision maker may influence the decision-making process regarding portfolio investments. Finally, the complexity of the method and the incorporation of soft information into the modeling process lead to generating a greater number of scenarios and reflect the attitudes and preferences of decision makers.

]]>Axioms doi: 10.3390/axioms13100659

Authors: Welagedara Arachchilage Dhanushka M. Welagedara David J. Olive

When the bootstrap sample size is moderate, bootstrap confidence regions tend to have undercoverage. Improving the coverage is known as calibrating the confidence region. Consider testing H0:&theta;=&theta;0 versus H1:&theta;&ne;&theta;0. We reject H0 only if &theta;0 is not contained in a large-sample 95% confidence region. If the confidence region has 3% undercoverage for the data set sample size, then the type I error is 8% instead of the nominal 5%. Hence, calibrating confidence regions is also useful for testing hypotheses. Several bootstrap confidence regions are also prediction regions for a future value of a bootstrap statistic. A new bootstrap confidence region uses a simple prediction region calibration technique to improve the coverage. The DD plot for visualizing prediction regions can also be used to visualize some bootstrap confidence regions.

]]>Axioms doi: 10.3390/axioms13100658

Authors: Roberto Cruz Mateo Lopez Juan Rada

A vertex-degree-based topological index &phi; associates a real number to a graph G which is invariant under graph isomorphism. It is defined in terms of the degrees of the vertices of G and plays an important role in chemical graph theory, especially in QSPR/QSAR investigations. A subset of k edges in G with no common vertices is called a k-matching of G, and the number of such subsets is denoted by mG,k. Recently, this number was naturally extended to weighted graphs, where the weight function is induced by the topological index &phi;. This number was denoted by mkG,&phi; and called the k-matchings of G with respect to the topological index &phi;. It turns out that m1G,&phi;=&phi;G, and so for k&ge;2, the k-matching numbers mkG,&phi; can be viewed as kth order topological indices which involve both the topological index &phi; and the k-matching numbers. In this work, we solve the extremal value problem for the number of 2-matchings with respect to general sum-connectivity indices SC&alpha;, over the set Tn of trees with n vertices, when &alpha; is a real number in the interval &minus;1,0.

]]>Axioms doi: 10.3390/axioms13100657

Authors: Yongge Tian

Algebraic expressions and equalities can be constructed arbitrarily in a given algebraic framework according to the operational rules provided, and thus it is a prominent and necessary task in mathematics and applications to construct, classify, and characterize various simple general algebraic expressions and equalities. As an update to this prominent topic in matrix algebra, this article reviews and improves upon the well-known block matrix methodology and matrix rank methodology in the construction and characterization of matrix equalities. We present a collection of fundamental and useful formulas for calculating the ranks of a wide range of block matrices and then derive from these rank formulas various valuable consequences. In particular, we present several groups of equivalent conditions in the characterizations of the Hermitian matrix, the skew-Hermitian matrix, the normal matrix, etc.

]]>Axioms doi: 10.3390/axioms13100655

Authors: Hai Q. Dinh Hiep L. Thi Roengchai Tansuchat

In this article, the notion of &gamma;-dual codes over finite chain rings is introduced as an extension of dual codes over finite chain rings. Various characteristics and properties of &gamma;-dual codes over finite chain rings are explored. We provide both necessary and sufficient conditions for the existence of &gamma;-self-dual codes over finite chain rings. Additionally, we investigate the &gamma;-dual of skew &#981;-&alpha;-constacyclic codes over finite chain rings.

]]>Axioms doi: 10.3390/axioms13100656

Authors: Hidayet Hüda Kösal Emre Kişi Mahmut Akyiğit Beyza Çelik

In this study, we obtained results for the computation of eigen-pairs, singular value decomposition, pseudoinverse, and the least squares problem for elliptic quaternion matrices. Moreover, we established algorithms based on these results and provided illustrative numerical experiments to substantiate the accuracy of our conclusions. In the experiments, it was observed that the p-value in the algebra of elliptic quaternions directly affects the performance of the problem under consideration. Selecting the optimal p-value for problem-solving and the elliptic behavior of many physical systems make this number system advantageous in applied sciences.

]]>Axioms doi: 10.3390/axioms13090654

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

This study contains a mathematical model for river pollution and its remediation for an unsteady state and investigates the effect of aeration on the degradation of pollutants. The governing equation is a pair of nonlinear time-fractional two-dimensional advection-diffusion equations for pollutant and dissolved oxygen (DO) concentration. The coupling of these equations arises due to the chemical interactions between oxygen and pollutants, forming harmless chemicals. The Fractional Reduced Differential Transform Method (FRDTM) is applied to provide approximate solutions for the given model. Also, the convergence of solutions is checked for efficacy and accuracy. The effect of longitudinal and transverse diffusion coefficients of pollutant and DO on the concentration of pollutant and DO is analyzed numerically and graphically. Also, we checked the effect of change in the river&rsquo;s longitudinal and transverse seepage velocity on pollutant and DO concentration numerically and graphically. We analyzed the comparison of change in the value of half-saturated oxygen demand concentration for pollutant decay on pollutant and DO concentration numerically and graphically. Also, numerical and graphical analysis examined the effect of fractional parameters on pollution levels.

]]>Axioms doi: 10.3390/axioms13090653

Authors: Bandar Bin-Mohsin Abdelghani Lakhdari Nour El Islem Karabadji Muhammad Uzair Awan Abdellatif Ben Makhlouf Badreddine Meftah Silvestru Sever Dragomir

In this study, we introduce a novel local fractional integral identity related to the Gaussian two-point left Radau rule. Based on this identity, we establish some new fractal inequalities for functions whose first-order local fractional derivatives are generalized convex and concave. The obtained results not only represent an extension of certain previously established findings to fractal sets but also a refinement of these when the fractal dimension &mu; is equal to one. Finally, to support our findings, we present a practical application to demonstrate the effectiveness of our results.

]]>Axioms doi: 10.3390/axioms13090652

Authors: Osama Moaaz Shaimaa Elsaeed Asma Al-Jaser Samia Ibrahim Amira Essam

This paper investigates the oscillatory behavior of solutions to fourth-order functional differential equations (FDEs) with multiple delays and a middle term. By employing a different comparison method approach with lower-order equations, the study introduces enhanced oscillation criteria. A key strength of the proposed method is its ability to reduce the complexity of the fourth-order equation by converting it into first- and second-order forms, allowing for the application of well-established oscillation theories. This approach not only extends existing criteria to higher-order FDEs but also offers more efficient and broadly applicable results. Detailed comparisons with previous research confirm the method&rsquo;s effectiveness and broader relevance while demonstrating the feasibility and significance of our results as an expansion and improvement of previous results.

]]>Axioms doi: 10.3390/axioms13090651

Authors: Azhar Ali Zafar

This editorial concerns the Special Issue of Axioms entitled &ldquo;Advances in Difference Equations&rdquo; [...]

]]>Axioms doi: 10.3390/axioms13090650

Authors: Maryam Iqbal Afshan Batool Aftab Hussain Hamed Alsulami

This manuscript examines fuzzy fixed point results using the concepts of S-metric space. We introduce two contractive maps, &gamma;- and &gamma;-weak contractions, within the context of S-metric spaces. These contractive maps form the cornerstone of our research, offering a novel approach to solving mathematical problems. We explore fixed point results derived from the application of these maps, showcasing their utility in finding solutions in diverse mathematical scenarios. Furthermore, we provide concrete examples that illustrate the practical relevance and versatility of our theorems, emphasizing their potential applications across a wide range of scientific and engineering domains. This manuscript presents the novel concepts of &gamma;- and &gamma;-weak contractions and establishes their importance in mathematical research. By demonstrating their effectiveness in solving real-world problems and offering illustrative examples, our work contributes valuable tools and insights to the broader scientific community, enhancing our understanding of contractive maps and their applications.

]]>Axioms doi: 10.3390/axioms13090649

Authors: Theodore E. Simos

A theory for the calculation of the phase&ndash;lag and amplification&ndash;factor for explicit and implicit multistep techniques for first&ndash;order differential equations was recently established by the author. His presentation also covered how the approaches&rsquo; efficacy is affected by the elimination of the phase&ndash;lag and amplification&ndash;factor derivatives. This paper will apply the theory for computing the phase&ndash;lag and amplification&ndash;factor, originally developed for implicit multistep methods, to a subset of implicit methods, called backward differentiation formulae (BDF), and will examine the impact of the phase&ndash;lag and amplification&ndash;factor derivatives on the efficiency of these strategies. Next, we will show you the stability zones of these brand-new approaches. Lastly, we will discuss the results of numerical experiments and draw some conclusions about the established approaches.

]]>Axioms doi: 10.3390/axioms13090648

Authors: Peter M. Mphekgwana Yehenew G. Kifle Chioneso S. Marange

The estimation of unknown quantities from multiple independent yet non-homogeneous samples has garnered increasing attention in various fields over the past decade. This interest is evidenced by the wide range of applications discussed in recent literature. In this study, we propose a preliminary test estimator for the common mean (&mu;) with unknown and unequal variances. When there exists prior information regarding the population mean with consideration that &mu; might be equal to the reference value for the population mean, a hypothesis test can be conducted: H0:&mu;=&mu;0 versus H1:&mu;&ne;&mu;0. The initial sample is used to test H0, and if H0 is not rejected, we become more confident in using our prior information (after the test) to estimate &mu;. However, if H0 is rejected, the prior information is discarded. Our simulations indicate that the proposed preliminary test estimator significantly decreases the mean squared error (MSE) values compared to unbiased estimators such as the Garybill-Deal (GD) estimator, particularly when &mu; closely aligns with the hypothesized mean (&mu;0). Furthermore, our analysis indicates that the proposed test estimator outperforms the existing method, particularly in cases with minimal sample sizes. We advocate for its adoption to improve the accuracy of common mean estimation. Our findings suggest that through careful application to real meta-analyses, the proposed test estimator shows promising potential.

]]>Axioms doi: 10.3390/axioms13090647

Authors: Juan Luis González-Santander Alexander Apelblat

In the framework of linear viscoelasticity, the authors have previously calculated a novel inverse Laplace transform involving the Mittag&ndash;Leffler function in order to calculate the relaxation modulus in the Andrade model. Here, we generalize this result, calculating the inverse Laplace transform of a given function F&alpha;,&beta;s by using two different approaches: the Bromwich integral and the decomposition of F&alpha;,&beta;s in simple fractions. From both calculations, we obtain a set of novel Laplace and Stieltjes transforms.

]]>Axioms doi: 10.3390/axioms13090646

Authors: Said Mesloub Eman Alhazzani Hassan Eltayeb Gadain

In this paper, we investigate a two-dimensional singular fractional-order parabolic partial differential equation in the Caputo sense. The partial differential equation is supplemented with Dirichlet and weighted integral boundary conditions. By employing a functional analysis method based on operator theory techniques, we prove the existence and uniqueness of the solution to the posed nonlocal initial boundary value problem. More precisely, we establish an a priori bound for the solution from which we deduce the uniqueness of the solution. For proof of its existence, we use various density arguments.

]]>Axioms doi: 10.3390/axioms13090645

Authors: Noor Jamal Muhammad Sarwar Kamaleldin Abodayeh Manel Hleili Saowaluck Chasreechai Thanin Sitthiwirattham

In this manuscript, we will discuss the solutions of Goursat problems with fuzzy boundary conditions involving gH-differentiability. The solutions to these problems face two main challenges. The first challenge is to deal with the two types of fuzzy gH-differentiability: (i)-differentiability and (ii)-differentiability. The sign of coefficients in Goursat problems and gH-differentiability produces sixteen possible cases. The existing literature does not afford a solution method that addresses all the possible cases of this problem. The second challenge is the mixed derivative term in Goursat problems with fuzzy boundary conditions. Therefore, we propose to discuss the solutions of fuzzy Goursat problems with gH-differentiability. We will discuss the solutions of fuzzy Goursat problems in series form with natural transform and Adomian decompositions. To demonstrate the usability of the established solution methods, we will provide some numerical examples.

]]>Axioms doi: 10.3390/axioms13090644

Authors: Guangjian Li Mingfa Zheng Guangjun He Yu Mei Gaoji Sun Haitao Zhong

Multi-objective optimization problems (MOPs) constitute a vital component in the field of mathematical optimization and operations research. The multi-objective evolutionary algorithm based on decomposition (MOEA/D) decomposes a MOP into a set of single-objective subproblems and approximates the true Pareto front (PF) by optimizing these subproblems in a collaborative manner. However, most existing MOEA/Ds maintain population diversity by limiting the replacement region or scale, which come at the cost of decreasing convergence. To better balance convergence and diversity, we introduce auction theory into algorithm design and propose an auction-based matching (ABM) mechanism to coordinate the replacement procedure in MOEA/D. In the ABM mechanism, each subproblem can be associated with its preferred individual in a competitive manner by simulating the auction process in economic activities. The integration of ABM into MOEA/D forms the proposed MOEA/D-ABM. Furthermore, to make the appropriate distribution of weight vectors, a modified adjustment strategy is utilized to adaptively adjust the weight vectors during the evolution process, where the trigger timing is determined by the convergence activity of the population. Finally, MOEA/D-ABM is compared with six state-of-the-art multi-objective evolutionary algorithms (MOEAs) on some benchmark problems with two to ten objectives. The experimental results show the competitiveness of MOEA/D-ABM in the performance of diversity and convergence. They also demonstrate that the use of the ABM mechanism can greatly improve the convergence rate of the algorithm.

]]>Axioms doi: 10.3390/axioms13090643

Authors: Fenglin Tian Yong Wang Qi Qin Boping Tian

In periods of dramatic stock price volatility, the identification of change points in stock price time series is important for analyzing the structural changes in financial market data, as well as for risk prevention and control in the financial market. As their residuals follow a generalized error distribution, the problem of estimating the change point parameters of the &beta;-ARCH model is solved by combining the Kalman filtering method and the Bayes method innovatively, and we give a method for parameter estimation of the Bayes factors for the occurrences of change points, the expected values of the change point positions, and the variance of the change points. By detecting the change points of the price of eight stocks with a high number of limit up and limit down changes occurring in the observation period, the following conclusions are obtained: (1) Change point detection using the &beta;-ARCH model based on the Bayes method is effective. (2) For different values of &beta;, this research study finds that based on the classical ARCH model (i.e., &beta;=1) of the change point parameter, the results are relatively optimal. (3) The accuracy of change point detection can be improved by correcting stock short-term effects by using the Kalman filtering method.

]]>Axioms doi: 10.3390/axioms13090642

Authors: Wenjun Gao Xiu Jia Ruiqing Shi

In this paper, a mathematical analysis of fractional order fishery model with stage structure for predator is carried out under the background of prey refuge and protected area. First, it is demonstrated that the solution exists and is unique. The paper aims to analyze predator-prey dynamics in a fishery model through the application of fractional derivatives. It is worth emphasizing that we explicitly examine how fractional derivatives affect the dynamics of the model. The existence of each equilibrium point and the stability of the system at the equilibrium point are proved. The theoretical results are proved by numerical simulation. Alternatively, allocate harvesting efforts within an improved model aimed at maximizing economic benefits and ecologically sustainable development. The ideal solution is obtained by applying Pontryagin&rsquo;s optimal control principle. A large number of numerical simulations show that the optimal control scheme can realize the sustainable development of the ecosystem.

]]>Axioms doi: 10.3390/axioms13090641

Authors: Sasanka Adikari Norou Diawara Haim Bar

There has been increasing interest in best&ndash;worst discrete choice experiments (BWDCEs) in health economics, transportation research, and other fields over the last few years. BWDCEs have distinct advantages compared to other measurement approaches in discrete choice experiments (DCEs). A systematic study of best&ndash;worst (BW) choice pairs can be traced back to the 1990s. Recently, new ideas have been introduced to the subject. Calculating utility helps measure the attractiveness of BW choices. The goal of this paper is twofold. First, we extend the idea of the BW choice pair to include dynamic, time-dependent transition probability and capture utility at each time and for each choice pair. Second, we used the geometry of BW choice pairs to capture the correlations among them and to characterize and clarify the BW choice pairs in the network, where properties can be derived within each class. This paper discusses BWDCEs, the probability transition matrix of choices over time, and the utility function. The proposed network classification for BW choice pairs is laid out. A detailed simulated example is presented, and the results are compared with the classical K-means classification.

]]>Axioms doi: 10.3390/axioms13090640

Authors: Şahap Çetin Yalçın Yılmaz Coşkun Yakar

In this paper, a nonlinear dynamic equation with an initial value problem (IVP) on a time scale is considered. First, applying comparison results with a coupled lower solution (LS) and an upper solution (US), we improved the quasilinearization method (QLM) for the IVP. Unlike other studies, we consider the LS and US pair of the seventh type instead of the natural type. It was determined that the solutions of the dynamic equation converge uniformly and monotonically to the unique solution of the IVP, and the convergence is quadratic. Moreover, we will use the delta derivative (&Delta;&gamma;) instead of the classical derivative (d&gamma;) in the proof because it studies a time scale. In the second part of the paper, we applied the monotone iterative technique (MIT) coupled with the LS and US, which is an effective method, proving a clear analytical representation for the solution of the equation when the relevant functions are monotonically non-decreasing and non-increasing. Then an example is given to illustrate the results obtained.

]]>Axioms doi: 10.3390/axioms13090639

Authors: Tanushri Ayaz Ahmad Ayhan Esi

In this study, we investigate the concept of I*-statistical convergence for sequences of fuzzy numbers. We establish several theorems that provide a comprehensive understanding of this notion, including the uniqueness of limits, the relationship between I*-statistical convergence and classical convergence, and the algebraic properties of I*-statistically convergent sequences. We also introduce the concept of I*-statistical pre-Cauchy and I*-statistical Cauchy sequences and explore its connection to I*-statistical convergence. Our results show that every I*-statistically convergent sequence is I*-statistically pre-Cauchy, but the converse is not necessarily true. Furthermore, we provide a sufficient condition for an I*-statistically pre-Cauchy sequence to be I*-statistically convergent, which involves the concept of I*&minus;liminf.

]]>Axioms doi: 10.3390/axioms13090638

Authors: Dimple Singh Priya Goel Ramandeep Behl Iñigo Sarría

In numerous scientific and engineering domains, fractional-order derivatives and integral operators are frequently used to represent many complex phenomena. They also have numerous practical applications in the area of fixed point iteration. In this article, we introduce the notion of generalized Meir-Keeler-Khan-Rational type (&psi;&minus;&alpha;)-contraction mapping and propose fixed point results in partial metric spaces. Our proposed results extend, unify, and generalize existing findings in the literature. In regards to applicability, we provide evidence for the existence of a solution for the fractional-order differential operator. In addition, the solution of the integral equation and its uniqueness are also discussed. Finally, we conclude that our results are superior and generalized as compared to the existing ones.

]]>Axioms doi: 10.3390/axioms13090637

Authors: Zuhur Alqahtani Areej Almuneef Moustafa El-Shahed

The red palm weevil (Rhynchophorus ferrugineus) is a highly destructive pest, causing severe damage to palm trees and significantly reducing their productivity. This paper aims to develop and analyze a mathematical model that captures the interactions between palm trees, Rhynchophorus ferrugineus, and entomopathogenic nematodes as a means of integrated control. We identify the equilibrium points of the system and perform a stability analysis to assess the system&rsquo;s behavior. Additionally, we design a linear quadratic regulator (LQR) to limit the spread of the red palm weevil within a locally linearized framework. The feedback control law, which is both straightforward and immediately implementable, is employed to avoid the need for complex cost calculations, thus simplifying the solution to the optimal control problem. Numerical simulations demonstrate that the proposed control strategy is effective in reducing the number of infected palm trees. The results indicate that increasing the population of entomopathogenic nematodes can significantly decrease the red palm weevil population, offering a promising approach to mitigating this pest&rsquo;s impact.

]]>Axioms doi: 10.3390/axioms13090636

Authors: Norah Alessa Mohammed Guediri

This paper investigates generalized Robertson&ndash;Walker (GRW) spacetimes by analyzing Riemannian hypersurfaces within pseudo-Riemannian warped product manifolds of the form (M&macr;,g&macr;), where M&macr;=R&times;fM and g&macr;=&#1013;dt2+f2(t)gM. We focus on the scalar curvature of these hypersurfaces, establishing upper and lower bounds, particularly in the case where (M&macr;,g&macr;) is an Einstein manifold. These bounds facilitate the characterization of slices in GRW spacetimes. In addition, we use the vector field &part;t and the so-called support function &theta; to derive generalized Minkowski-type integral formulas for compact Riemannian and spacelike hypersurfaces. These formulas are applied to establish, under certain conditions, results concerning the existence or non-existence of such compact hypersurfaces with scalar curvature, either bounded from above or below.

]]>Axioms doi: 10.3390/axioms13090635

Authors: Erxin Zhang

Let &Phi;i(i=1,2) be two N-functions, f be a &mu;-measurable function, and &omega;i(i=1,2,3,4) be four weight functions. This study presents necessary and sufficient conditions for weight functions (&omega;1,&omega;2,&omega;3,&omega;4) such that the inequality &int;{x:Mf(x)&gt;&lambda;}&Phi;1(&lambda;&omega;1(x))&omega;2(x)d&mu;(x)&le;c1&int;X&Phi;2(c1|f(x)|&omega;3(x))&omega;4(x)d&mu;(x) holds, which extends several established results.

]]>Axioms doi: 10.3390/axioms13090634

Authors: Chih-Peng Huang

This study addresses the state feedback control associated with D-admissible assurance for discrete singular systems subjected to parameter uncertainties in both the difference term and system matrices. Firstly, a refined analysis criterion of D-admissible assurance is presented, where the distinct form embraces multiple slack matrices and has lessened linear matrix inequalities (LMIs) constraints, which may be beneficial for reducing the conservatism of admissibility analysis. In consequence, by hiring the state feedback control, controller design issues with pole locations, which directly dominate the system performance, are mainly treated. For all the presented criteria can be formulated by the strict LMIs, they are thus suitably solved via current LMI solvers to conduct a state feedback controller with specific poles&rsquo; locations of system&rsquo;s performance requirements. Finally, two numerical examples illustrate that the presented results are efficient and practicable.

]]>Axioms doi: 10.3390/axioms13090633

Authors: Yulia Kempner Vadim E. Levit

This research explores the interplay between violator spaces and greedoids&mdash;two distinct theoretical frameworks developed independently. Violator spaces were introduced as a generalization of linear programming, while greedoids were designed to characterize combinatorial structures where greedy algorithms yield optimal solutions. These frameworks have, until now, existed in isolation. This paper bridges the gap by showing that greedoids can be defined using a modified violator operator. The established connections not only deepen our understanding of these theories but also provide a new characterization of antimatroids.

]]>Axioms doi: 10.3390/axioms13090632

Authors: Zhenhua Su Hanyuan Deng

Vertex-degree-based (VDB) topological indices have been applied in the study of molecular structures and chemical properties. At present, the exponential VDB index has been studied extensively. Naturally, we began to consider the logarithmic VDB index lnTf. In this paper, we first discuss the necessity of a logarithmic VDB index, and then present sufficient conditions so that Pn and Sn are the only trees with the smallest and greatest values of lnTf(T). As applications, the minimal and maximal trees of some logarithmic VDB indices are determined. Through our work, we found that the logarithmic VDB index lnTf has excellent discriminability, but the relevant results are not completely opposite to the exponential VDB index. The study of logarithmic VDB indices is an interesting but difficult task that requires further resolution.

]]>Axioms doi: 10.3390/axioms13090630

Authors: Emilio Ramón Negrín Benito Juan González Jeetendrasingh Maan

This paper investigates Parseval&ndash;Goldstein-type relationships in the framework of Lebedev&ndash;Skalskaya transforms. The research also examines the continuity properties of these transforms, along with their adjoint counterparts over weighted Lebesgue spaces. Furthermore, the behavior of Lebedev&ndash;Skalskaya transforms and their adjoint transforms in the context of weighted Lebesgue spaces is analyzed. This study aims to provide deeper insights into the functional properties and applications of these transforms in mathematical analysis.

]]>Axioms doi: 10.3390/axioms13090631

Authors: Slobodan B. Tričković Miomir S. Stanković

We have derived alternative closed-form formulas for the trigonometric series over sine or cosine functions when the immediate replacement of the parameter appearing in the denominator with a positive integer gives rise to a singularity. By applying the Choi&ndash;Srivastava theorem, we reduce these trigonometric series to expressions over Hurwitz&rsquo;s zeta function derivative.

]]>Axioms doi: 10.3390/axioms13090629

Authors: Rafik Aguech

The ERW model was introduced twenty years ago to study memory effects in a one-dimensional discrete-time random walk with a complete memory of its past throughout a parameter p between zero and one. Several variations of the ERW model have recently been introduced. In this work, we investigate the asymptotic normality of the ERW model with a random step size and gradually increasing memory and delays. In particular, we extend some recent results in this subject.

]]>Axioms doi: 10.3390/axioms13090628

Authors: Samuel L. Krushkal

Biunivalent holomorphic functions form an interesting class in geometric function theory and are connected with special functions and solutions of complex differential equations. This class has been investigated by many authors, mainly to find the coefficient estimates. The assumption of biunivalence is rigid; this rigidity means that, for example, only the initial Taylor coefficients have been estimated. The aim of this paper is to develop a variational technique for biunivalent functions, which provides a power tool for solving the general extremal problems on the classes of such functions. It involves quasiconformal analysis.

]]>Axioms doi: 10.3390/axioms13090627

Authors: Nazim I. Mahmudov Suzan Cival Buranay Mtema James Chin

In this research paper, we consider a model of the fractional Cauchy&ndash;Euler-type equation, where the fractional derivative operator is the Caputo with order 0&lt;&alpha;&lt;2. The problem also constitutes a class of examples of the Cauchy problem of the Bagley&ndash;Torvik equation with variable coefficients. For proving the existence and uniqueness of the solution of the given problem, the contraction mapping principle is utilized. Furthermore, a numerical method and an algorithm are developed for obtaining the approximate solution. Also, convergence analyses are studied, and simulations on some test problems are given. It is shown that the proposed method and the algorithm are easy to implement on a computer and efficient in computational time and storage.

]]>Axioms doi: 10.3390/axioms13090625

Authors: Guiyao Ke Jun Pan Feiyu Hu Haijun Wang

Aiming to explore the subtle connection between the number of nonlinear terms in Lorenz-like systems and hidden attractors, this paper introduces a new simple sub-quadratic four-thirds-degree Lorenz-like system, where x&#729;=a(y&minus;x), y&#729;=cx&minus;x3z, z&#729;=&minus;bz+x3y, and uncovers the following property of these systems: decreasing the powers of the nonlinear terms in a quadratic Lorenz-like system where x&#729;=a(y&minus;x), y&#729;=cx&minus;xz, z&#729;=&minus;bz+xy, may narrow, or even eliminate the range of the parameter c for hidden attractors, but enlarge it for self-excited attractors. By combining numerical simulation, stability and bifurcation theory, most of the important dynamics of the Lorenz system family are revealed, including self-excited Lorenz-like attractors, Hopf bifurcation and generic pitchfork bifurcation at the origin, singularly degenerate heteroclinic cycles, degenerate pitchfork bifurcation at non-isolated equilibria, invariant algebraic surface, heteroclinic orbits and so on. The obtained results may verify the generalization of the second part of the celebrated Hilbert&rsquo;s sixteenth problem to some degree, showing that the number and mutual disposition of attractors and repellers may depend on the degree of chaotic multidimensional dynamical systems.

]]>Axioms doi: 10.3390/axioms13090626

Authors: Lian-Ta Su Ravi Kumar Sunil K. Sharma Ajay K. Sharma Qing-Bo Cai

In this paper, we introduce and rigorously define a novel class of difference sequence spaces, denoted by wI(M,&#8710;vu,r)&alpha;&beta;, w0I(M,&#8710;vu,r)&alpha;&beta;,&nbsp;w&infin;I(M,&#8710;vu,r)&alpha;&beta;, and w&infin;(M,&#8710;vu,r)&alpha;&beta;. These spaces are constructed through the application of the concept of I-convergence of sequences, combined with a Musielak&ndash;Orlicz function of order (&alpha;,&nbsp;&beta;). The primary focus of our work is to thoroughly investigate the algebraic and topological properties of these defined sequence spaces. We explore their linearity, examine their structure within the framework of paranormed spaces, and analyze various other algebraic characteristics pertinent to these spaces. In addition, we examine the topological nature of these sequence spaces, identifying the conditions under which they exhibit specific topological properties. A significant part of our study is dedicated to examining the inclusion relationships between these sequence spaces, thereby providing a comprehensive understanding of how these spaces are interrelated. Our analysis contributes to the broader field of functional analysis and sequence space theory, offering new insights and potential applications of these advanced mathematical constructs.

]]>Axioms doi: 10.3390/axioms13090624

Authors: Kristijan Kuk Aleksandar Stanojević Petar Čisar Brankica Popović Mihailo Jovanović Zoran Stanković Olivera Pronić-Rančić

The key point in the process of agent-based management in e-service for malware detection (according to accuracy criteria) is a decision-making process. To determine the optimal e-service for malware detection, two concepts were investigated: Fuzzy Logic (FL) and Probabilistic Neural Networks (PNN). In this study, three evolutionary variants of fuzzy partitioning, including regular, hierarchical fuzzy partitioning, and k-means, were used to automatically process the design of the fuzzy partition. Also, this study demonstrates the application of a feature selection method to reduce the dimensionality of the data by removing irrelevant features to create fuzzy logic in a dataset. The behaviors of malware are analyzed by fuzzifying relevant features for pattern recognition. The Apriori algorithm was applied to the fuzzified features to find the fuzzy-based rules, and these rules were used for predicting the output of malware detection e-services. Probabilistic neural networks were also used to find the ideal agent-based model for numerous classification problems. The numerical results show that the agent-based management performances trained with the clustering method achieve an accuracy of 100% with the PNN-MCD model. This is followed by the FL model, which classifies on the basis of linguistic variables and achieves an average accuracy of 82%.

]]>Axioms doi: 10.3390/axioms13090623

Authors: Marko Kostić

In this paper, we introduce several new types of partial fractional derivatives in the continuous setting and the discrete setting. We analyze some classes of the abstract fractional differential equations and the abstract fractional difference equations depending on several variables, providing a great number of structural results, useful remarks and illustrative examples. Concerning some specific applications, we would like to mention here our investigation of the fractional partial differential inclusions with Riemann&ndash;Liouville and Caputo derivatives. We also establish the complex characterization theorem for the multidimensional vector-valued Laplace transform and provide certain applications.

]]>Axioms doi: 10.3390/axioms13090622

Authors: Ray-Ming Chen

In this article, we study the properties of 4-by-4 metric matrices and characterize their dependence and independence by M4&times;4=(M4&times;4&minus;DM4&times;4)&cup;DM4&times;4, where DM4&times;4 is the set of all dependent metric matrices. DM4&times;4 is further characterized by DM4&times;4=DM14&times;4&cup;DM24&times;4, where DM24&times;4 is characterized by DM24&times;4=DM214&times;4&cup;DM224&times;4. These characterizations provide some insightful findings that go beyond the Euclidean distance or Euclidean distance matrix and link the distance functions to vector spaces, which offers some theoretical and application-related advantages. In the application parts, we show that the metric matrices associated with all Minkowski distance functions over four different points are linearly independent, and that the metric matrices associated with any four concyclic points are also linearly independent.

]]>Axioms doi: 10.3390/axioms13090621

Authors: Jihan Alahmadi Mohamed A. Abdou Mohamed A. Abdel-Aty

A quadratic integral Equation (QIE) of the second kind with continuous kernels is solved in the space C([0,T]&times;[0,T]). The existence of at least one solution to the QIE is discussed in this article. Our evidence depends on a suitable combination of the measures of the noncompactness approach and the fixed-point principle of Darbo. The quadratic integral equation can be used to derive a system of integral equations of the second kind using the quadrature method. With the aid of two different polynomials, Laguerre and Hermite, the system of integral equations is solved using the collocation method. In each numerical approach, the estimation of the error is discussed. Finally, using some examples, the accuracy and scalability of the proposed method are demonstrated along with comparisons. Mathematica 11 was used to obtain all of the results from the techniques that were shown.

]]>Axioms doi: 10.3390/axioms13090620

Authors: Basem Aref Frasin Luminiţa-Ioana Cotîrlă

S&#259;l&#259;gean differential operator D&kappa; plays an important role in the geometric function theory, where many studies are using this operator to introduce new subclasses of analytic functions defined in the open unit disk. Studies of S&#259;l&#259;gean differential operator D&kappa; in connection with Stirling numbers are relatively new. In this paper, the differential operator D&kappa; involving Stirling numbers is considered. A new sufficient condition involving Stirling numbers for the series &Upsilon;&theta;s(&#1008;) written with the Pascal distribution are discussed for the subclass T&kappa;(&#1013;,&#9837;). Also, we provide a sufficient condition for the inclusion relation I&theta;sR&piv;(E,D)&sub;T&kappa;(&#1013;,&#9837;). Further, we consider the properties of an integral operator related to Pascal distribution series. New special cases as a consequences of the main results are also obtained.

]]>Axioms doi: 10.3390/axioms13090619

Authors: Andronikos Paliathanasis

Within the framework of symmetric teleparallel fQ-gravity, using a connection defined in the non-coincidence gauge, we derive the Wheeler&ndash;DeWitt equation of quantum cosmology. The gravitational field equation in fQ-gravity permits a minisuperspace description, rendering the Wheeler&ndash;DeWitt equation a single inhomogeneous partial differential equation. We use the power-law fQ=f0Q&mu; model, and with the application of linear quantum observables, we calculate the wave function of the universe. Finally, we investigate the effects of the quantum correction terms in the semi-classical limit.

]]>Axioms doi: 10.3390/axioms13090618

Authors: Juan Wang Baoyu Cui Zhiliang Ren

To solve complex multi-attribute decision-making (MADM) problems within a triangular dual hesitant fuzzy (TDHF) environment where the attribute weights (Aws) are either fully or partially known, a novel bidirectional projection method is proposed, named multi-attribute decision-making and based on the consistent bidirectional projection measures of triangular dual hesitant fuzzy sets (TDHFSs). First, some notions are developed, such as the operation laws, score and accuracy functions, negative ideal points (NIPs), and positive ideal points (PIPs) of TDHFSs. The correlation coefficients and the cosine of the angle between the vectors of each alternative and the triangular dual hesitant fuzzy (TDHF) points are introduced. Then, the consistent bidirectional projection decision-making method based on the TDHFSs&rsquo; correlation coefficients is proposed. Additionally, an optimization model is established via maximizing the consistent coefficient to determine the Aws. Furthermore, some approaches are investigated based on the proposed approaches concerning the MADM issues with attribute values represented by triangular dual hesitant fuzzy elements (TDHFEs). Finally, a supply chain management (SCM) problem is illustrated, and comparative analyses are implemented to demonstrate the presented approach&rsquo;s feasibility and efficiency.

]]>Axioms doi: 10.3390/axioms13090617

Authors: Ioannis Diamantis

In this paper, we present two different ways for computing the Kauffman bracket skein module of S1&times;S2, KBSMS1&times;S2, via braids. We first extend the universal Kauffman bracket type invariant V for knots and links in the Solid Torus ST, which is obtained via a unique Markov trace constructed on the generalized Temperley&ndash;Lieb algebra of type B, to an invariant for knots and links in S1&times;S2. We do that by imposing on V relations coming from the braid band moves. These moves reflect isotopy in S1&times;S2 and they are similar to the second Kirby move. We obtain an infinite system of equations, a solution of which is equivalent to computing KBSMS1&times;S2. We show that KBSMS1&times;S2 is not torsion free and that its free part is generated by the unknot (or the empty knot). We then present a diagrammatic method for computing KBSMS1&times;S2 via braids. Using this diagrammatic method, we also obtain a closed formula for the torsion part of KBSMS1&times;S2.

]]>Axioms doi: 10.3390/axioms13090616

Authors: Abdulrahman F. Aljohani Ali Althobaiti Saad Althobaiti

This paper aims to introduce a new fractional extension of the interval Hermite&ndash;Hadamard (HH), HH&ndash;Fej&eacute;r, and Pachpatte-type inequalities for left- and right-interval-valued harmonically convex mappings (LRIVH convex mappings) with an exponential function in the kernel. We use fractional operators to develop several generalizations, capturing unique outcomes that are currently under investigation, while also introducing a new operator. Generally, we propose two methods that, in conjunction with more generalized fractional integral operators with an exponential function in the kernel, can address certain novel generalizations of increasing mappings under the assumption of LRIV convexity, yielding some noteworthy results. The results produced by applying the suggested scheme show that the computational effects are extremely accurate, flexible, efficient, and simple to implement in order to explore the path of upcoming intricate waveform and circuit theory research.

]]>Axioms doi: 10.3390/axioms13090615

Authors: Andrej Liptaj

Regarding round-off errors as random is often a necessary simplification to describe their behavior. Assuming, in addition, the symmetry of their distributions, we show that one can, in unstable (ill-conditioned) computer calculations, suppress their effect by statistical averaging. For this, one slightly perturbs the argument of fx0 many times and averages the resulting function values. In this text, we forward arguments to support the assumed properties of round-off errors and critically evaluate the validity of the averaging approach in several numerical experiments.

]]>Axioms doi: 10.3390/axioms13090614

Authors: Wei Xu Savin Treanţă

In this paper, we investigate and characterize a family of optimization problems introduced by interval-valued functionals that are determined by curvilinear integrals. To this end, we first state the path independence and (strictly) LU convexity properties of the considered functionals. Thereafter, we formulate the corresponding controlled variational inequalities. The main results of this paper provide some connections for the above-mentioned variational models. Since the objective functionals have a physical importance, an illustrative application is considered and studied by using the theoretical elements obtained in this study.

]]>Axioms doi: 10.3390/axioms13090613

Authors: Zijun Zheng Jiaru Shao Ziying Zhang Chu Li

By anchoring the lower rollers and dynamically adjusting the upper roller&rsquo;s downfeed of a pyramid roll bender, one can achieve the precise bending of a workpiece into a desired planar form characterized by variable curvature. To ensure the seamless processing of individual cross sections without impinging upon adjacent areas, critical roller spacings are identified through theoretical mechanics analyses. The reaction force exerted on the top roller is calculated by integrating the desired curvature into the elastoplastic constitutive equation and subsequently deriving a dynamic adjustment of the downfeed from quasi-static finite element simulations. This preliminary downfeed protocol undergoes refinement to mitigate discrepancies between the targeted and the actual curvatures. Numerical instances demonstrate that the application of roller configurations, as outlined herein, yields a product profile that closely mirrors the intended curve. This congruence can be further improved with an additional iteration; however, subsequent iterations are seen to yield negligible improvements, indicating a rapid convergence of this algorithm.

]]>Axioms doi: 10.3390/axioms13090612

Authors: Soley Ersoy Kemal Eren Abdussamet Çalışkan

In this paper, we investigate the spatial quaternionic expressions of partner-ruled surfaces. Moreover, we formulate the striction curves and dralls of these surfaces by use of the quaternionic product. Furthermore, the pitches and angles of pitches are interpreted for the spatial quaternionic ruled surfaces that are closed. Additionally, we calculate the integral invariants of these surfaces using quaternionic formulas. Finally, the partner-ruled surfaces of a given spatial quaternionic ruled surface are demonstrated as an example, and their graphics are drawn.

]]>Axioms doi: 10.3390/axioms13090611

Authors: Clara Carlota Mário Lopes António Ornelas

This paper concerns control BVPs, driven by ODEs x&prime;t=ut, using controls u0&middot;&nbsp;&amp;u1&middot; in L1a,b,R2. We ask these two controls to satisfy a very simple restriction: at points where their first coordinates coincide, also their second coordinates must coincide; which allows one to write (u1&minus;u0)&middot;=v&middot;1,f&middot; for some f&middot;. Given a relaxed non bang-bang solution x&macr;&middot;&isin;W1,1a,b,R2, a question relevant to applications was first posed three decades ago by A. Cellina: does there exist a bang-bang solution x^&middot; having lower first-coordinate x^1&middot;&le;x&macr;1&middot;? Being the answer always yes in dimension d=1, hence without f&middot;, as proved by Amar and Cellina, for d=2 the problem is to find out which functions f&middot; &ldquo;are good&rdquo;, namely &ldquo;allow such 1-lower bang-bang solution x^&middot; to exist&rdquo;. The aim of this paper is to characterize &ldquo;goodness of f&middot;&rdquo; geometrically, under &ldquo;good data&rdquo;. We do it so well that a simple computational app in a smartphone allows one to easily determine whether an explicitly given f&middot; is good. For example: non-monotonic functions tend to be good; while, on the contrary, strictly monotonic functions are never good.

]]>Axioms doi: 10.3390/axioms13090610

Authors: Attaullah Sultan Alyobi Mohammed Alharthi Yasser Alrashedi

In this research, we introduce the intuitionistic hesitant fuzzy rough set by integrating the notions of an intuitionistic hesitant fuzzy set and rough set and present some intuitionistic hesitant fuzzy rough set theoretical operations. We compile a list of aggregation operators based on the intuitionistic hesitant fuzzy rough set, including the intuitionistic hesitant fuzzy rough Dombi weighted arithmetic averaging aggregation operator, the intuitionistic hesitant fuzzy rough Dombi ordered weighted arithmetic averaging aggregation operator, and the intuitionistic hesitant fuzzy rough Dombi hybrid weighted arithmetic averaging aggregation operator, and demonstrate several essential characteristics of the aforementioned aggregation operators. Furthermore, we provide a multi attribute decision-making approach and the technique of the suggested approach in the context of the intuitionistic hesitant fuzzy rough set. A real-world problem for selecting a suitable worldwide partner for companies is employed to demonstrate the effectiveness of the suggested approach. The sensitivity analysis of the decision-making results of the suggested aggregation operators are evaluated. The demonstrative analysis reveals that the outlined strategy has applicability and flexibility in aggregating intuitionistic hesitant fuzzy rough information and is feasible and insightful for dealing with multi attribute decision making issues based on the intuitionistic hesitant fuzzy rough set. In addition, we present a comparison study with the TOPSIS approach to illustrate the advantages and authenticity of the novel procedure. Furthermore, the characteristics and analytic comparison of the current technique to those outlined in the literature are addressed.

]]>Axioms doi: 10.3390/axioms13090609

Authors: Badriah Alamri

The aim of this research article is to broaden the scope of fixed point theory in F-bipolar metric spaces by introducing the concept of rational (&#8911;,&#8910;,&psi;)-contractions. These new contractions allow for the formulation of fixed point theorems specifically designed for contravariant mappings. The validity of our approach is substantiated by a meticulously crafted example. Moreover, we explore the practical implications of these theorems beyond the realm of fixed point theory. Notably, we demonstrate their effectiveness in establishing the existence and uniqueness of solutions to integral equations. Additionally, we investigate homotopy problems, focusing on the conditions for the existence of a unique solution within this framework.

]]>Axioms doi: 10.3390/axioms13090608

Authors: Jiaxin Mu Takao Komatsu

Many people, including Horadam, have studied the numbers Wn, satisfying the recurrence relation Wn=uWn&minus;1+vWn&minus;2 (n&ge;2) with W0=0 and W1=1. In this paper, we study the p-numerical semigroups of the triple (Wi,Wi+2,Wi+k) for integers i,k(&ge;3). For a nonnegative integer p, the p-numerical semigroup Sp is defined as the set of integers whose nonnegative integral linear combinations of given positive integers a1,a2,&hellip;,a&kappa; with gcd(a1,a2,&hellip;,a&kappa;)=1 are expressed in more than p ways. When p=0, S=S0 is the original numerical semigroup. The largest element and the cardinality of N0&#8726;Sp are called the p-Frobenius number and the p-genus, respectively.

]]>Axioms doi: 10.3390/axioms13090607

Authors: Fang Liu Xiangeng Zhou Li Liu Shou Lin

Symmetric spaces and sn-symmetric spaces, as a generalization of metric spaces, have many important properties and have been widely discussed. We consider characterizations and mapping properties of sn-symmetric spaces under ideal convergence. I-symmetric spaces and I-sn-symmetric spaces are defined and studied. These not only generalize some classical results on symmetric spaces but also provide new directions to study generalized metric spaces using the notion of ideal convergence. As an application of I-sn-symmetric spaces, some relevant properties of statistical convergence are obtained. Some unanswered questions in this field are raised.

]]>Axioms doi: 10.3390/axioms13090606

Authors: Pierre-Henri Chavanis

In this paper, we review and compare the stochastic quantum mechanics of Nelson and the scale relativity theory of Nottale. We consider both nonrelativistic and relativistic frameworks and include the electromagnetic field. These theories propose a derivation of the Schr&ouml;dinger and Klein&ndash;Gordon equations from microscopic processes. We show their formal equivalence. Specifically, we show that the real and imaginary parts of the complex Lorentz equation in Nottale&rsquo;s theory are equivalent to the Nelson equations, which are themselves equivalent to the Madelung and de Broglie hydrodynamical representations of the Schr&ouml;dinger and Klein&ndash;Gordon equations, respectively. We discuss the different physical interpretations of the Nelson and Nottale theories and stress their strengths and weaknesses. We mention potential applications of these theories to dark matter.

]]>Axioms doi: 10.3390/axioms13090605

Authors: Ravi Agarwal Snezhana Hristova Donal O’Regan

The Cohen&ndash;Grossberg neural network is studied in the case when the dynamics of the neurons is modeled by a Riemann&ndash;Liouville fractional derivative with respect to another function and an appropriate initial condition is set up. Some inequalities about both the quadratic function and the absolute values functions and their fractional derivatives with respect to another function are proved and they are based on an appropriate modification of the Razumikhin method. These inequalities are applied to obtain the bounds of the norms of any solution of the model. In particular, we apply the squared norm and the absolute values norms. These bounds depend significantly on the function applied in the fractional derivative. We study the asymptotic behavior of the solutions of the model. In the case when the function applied in the fractional derivative is increasing without any bound, the norms of the solution of the model approach zero. In the case when the applied function in the fractional derivative is equal to the current time, the studied problem reduces to the model with the classical Riemann&ndash;Liouville fractional derivative and the obtained results gives us sufficient conditions for asymptotic behavior of the solutions for the corresponding model. In the case when the function applied in the fractional derivative is bounded, we obtain a finite bound for the solutions of the model. This bound depends on the initial function and the solution does not approach zero. An example is given illustrating the theoretical results.

]]>Axioms doi: 10.3390/axioms13090604

Authors: Yuri Luchko

In this paper, a generic fractional derivative is defined as a set of the linear operators left-inverse to the Riemann&ndash;Liouville fractional integral. Then, the theory of the left-invertible operators developed by Przeworska-Rolewicz is applied to deduce its properties. In particular, we characterize its domain, null-space, and projector operator; establish the interrelations between its different realizations; and present a generalized fractional Taylor formula involving the generic fractional derivative. Then, we consider the fractional relaxation equation containing the generic fractional derivative, derive a closed-form formula for its unique solution, and study its complete monotonicity.

]]>Axioms doi: 10.3390/axioms13090603

Authors: Ran Yang Qin Xing

In this paper, we demonstrate that when saddle point reduction is applicable, there is a clear relationship between the Morse index and the critical groups before and after the reduction. As an application of this result, we use saddle point reduction along with the critical point theorem to show the existence of periodic solutions in second-order Hamiltonian systems.

]]>Axioms doi: 10.3390/axioms13090602

Authors: Chuanyang Ruan Lin Yan

In the realm of management decision-making, the selection of green suppliers has long been a complex issue. Companies must take a holistic approach, evaluating potential suppliers based on their capabilities, economic viability, and environmental impact. The decision-making process, fraught with intricacies and uncertainties, urgently demands the development of a scientifically sound and efficient method for guidance. Since the concept of Fermatean fuzzy sets (FFSs) was proposed, it has been proved to be an effective tool for solving multi-attribute decision-making (MADM) problems in complicated realistic situations. And the Power Bonferroni mean (PBM) operator, combining the strengths of the power average (PA) and Bonferroni mean (BM), excels in considering attribute interactions for a thorough evaluation. To ensure a comprehensive and sufficient evaluation framework for supplier selection, this paper introduces innovative aggregation operators that extend the PBM and integrate probabilistic information into Fermatean hesitant fuzzy sets (FHFSs) and Fermatean probabilistic hesitant fuzzy sets (FPHFSs). It successively proposes the Fermatean hesitant fuzzy power Bonferroni mean (FHFPBM), Fermatean hesitant fuzzy weighted power Bonferroni mean (FHFWPBM), and Fermatean hesitant fuzzy probabilistic weighted power Bonferroni mean (FHFPWPBM) operators, examining their key properties like idempotency, boundedness, and permutation invariance. By further integrating PBM with probabilistic information into FPHFSs, three new Fermatean probabilistic hesitant fuzzy power Bonferroni aggregation operators are developed: the Fermatean probabilistic hesitant fuzzy power Bonferroni mean (FPHFPBM), Fermatean probabilistic hesitant fuzzy weighted power Bonferroni mean (FPHFWPBM), and Fermatean probabilistic hesitant fuzzy probabilistic weighted power Bonferroni mean (FPHFPWPBM). Subsequently, a MADM method based on these operators is constructed. Finally, a numerical example concerning the selection of green suppliers is presented to demonstrate the applicability and effectiveness of this method using the FPHFPWPBM operator.

]]>Axioms doi: 10.3390/axioms13090601

Authors: Indra Bate Muniyasamy Murugan Santhosh George Kedarnath Senapati Ioannis K. Argyros Samundra Regmi

In this paper, we present a technique that improves the applicability of the result obtained by Cordero et al. in 2024 for solving nonlinear equations. Cordero et al. assumed the involved operator to be differentiable at least five times to extend a two-step p-order method to order p+3. We obtained the convergence order of Cordero et al.&rsquo;s method by assuming only up to the third-order derivative of the operator. Our analysis is in a more general commutative Banach algebra setting and provides a radius of the convergence ball. Finally, we validate our theoretical findings with several numerical examples. Also, the concept of basin of attraction is discussed with examples.

]]>Axioms doi: 10.3390/axioms13090600

Authors: Ali Hamzah Alibrahim Saptarshi Das

In this paper, we introduce the concept of generalized Fourier series, generated by the p-trigonometric functions, namely cosp and sinp, recently introduced related to the generalized complex numbers systems. The aim of this study is to represent a periodic signal as a sum of p-sine and p-cosine functions. In order to achieve this, we first present the integrals of the product of the same or different family of p-trigonometric functions over the full period of these functions to understand the orthogonality properties. Next, we use these integrals to derive the coefficients of the generalized p-Fourier series along with a few examples. The generalized Fourier series can be used to expand an arbitrary forcing function in the solution of a non-homogeneous linear ordinary differential equation (ODE) with constant coefficients.

]]>Axioms doi: 10.3390/axioms13090599

Authors: Karol I. Santoro Yolanda M. Gómez Darlin Soto Inmaculada Barranco-Chamorro

In this paper, we present the unit-power half-normal distribution, derived from the power half-normal distribution, for data analysis in the open unit interval. The statistical properties of the unit-power half-normal model are described in detail. Simulation studies are carried out to evaluate the performance of the parameter estimators. Additionally, we implement the quantile regression for this model, which is applied to two real healthcare data sets. Our findings suggest that the unit power half-normal distribution provides a robust and flexible alternative for existing models for proportion data.

]]>Axioms doi: 10.3390/axioms13090598

Authors: Roshdi Khalil Abdelrahman Yousef Waseem Ghazi Alshanti Ma’mon Abu Hammad

In this paper, we prove that every bounded linear operator on a separable Hilbert space has a non-trivial invariant subspace. This answers the well-known invariant subspace problem.

]]>Axioms doi: 10.3390/axioms13090597

Authors: Petko H. Petkov

In this paper, we derive new probabilistic bounds on the sensitivity of invariant subspaces, deflation subspaces and singular subspaces of matrices. The analysis exploits a unified method for deriving asymptotic perturbation bounds of the subspaces under interest and utilizes probabilistic approximations of the entries of random perturbation matrices implementing the Markoff inequality. As a result of the analysis, we determine with a prescribed probability asymptotic perturbation bounds on the angles between the corresponding perturbed and unperturbed subspaces. It is shown that the probabilistic asymptotic bounds proposed are significantly less conservative than the corresponding deterministic perturbation bounds. The results obtained are illustrated by examples comparing the known deterministic perturbation bounds with the new probabilistic bounds.

]]>Axioms doi: 10.3390/axioms13090596

Authors: Muneerah AL Nuwairan T. S. Amer W. S. Amer

This paper examines the stability behavior of the nonlinear dynamical motion of a vibrating cart with two degrees of freedom (DOFs). Lagrange&rsquo;s equations are employed to establish the mechanical regulating system of the examined motion. The proposed approximate solutions (ASs) of this system are estimated through the use of the multiple-scales method (MSM). These solutions are considered novel as the MSM is being applied to a new dynamical model. Secular terms have been eliminated to meet the solvability criteria, and every instance of resonance that arises is categorized, where two of them are examined concurrently. Therefore, the modulation equations are developed based on the representations of the unknown complex function in polar form. The solutions for the steady state are calculated using the corresponding fixed points. The achieved solutions are displayed graphically to illustrate the impact of manipulating the system&rsquo;s parameters and are compared to the numerical solutions (NSs) of the system&rsquo;s original equations. This comparison shows a great deal of consistency with the numerical solution, which indicates the accuracy of the applied method. The nonlinear stability criteria of Routh&ndash;Hurwitz are employed to assess the stability and instability zones. The value of the proposed model is exhibited by its wide range of applications involving ship motion, swaying architecture, transportation infrastructure, and rotor dynamics.

]]>Axioms doi: 10.3390/axioms13090595

Authors: Mu Sun Yinmei Zhang

This paper is devoted to the study of a multi-parameter subsequential version of the &ldquo;Wiener&ndash;Wintner&rdquo; ergodic theorem for the noncommutative Dunford&ndash;Schwartz system. We establish a structure to prove &ldquo;Wiener&ndash;Wintner&rdquo;-type convergence over a multi-parameter subsequence class &Delta; instead of the weight class case. In our subsequence class, every term of k&#818;&isin;&Delta; is one of the three kinds of nonzero density subsequences we consider. As key ingredients, we give the maximal ergodic inequalities of multi-parameter subsequential averages and obtain a noncommutative subsequential analogue of the Banach principle. Then, by combining the critical result of the uniform convergence for a dense subset of the noncommutative Lp(M) space and the noncommutative Orlicz space, we immediately obtain the main theorem.

]]>Axioms doi: 10.3390/axioms13090594

Authors: Mario Lefebvre Roozbeh Yaghoubi

Suppose that in an M/G/1 waiting queue, the server can choose between two service time distributions. We look for the choice that enables us to minimize the expected value of a cost criterion that takes into account the cost incurred by working faster and the time needed to empty the waiting line. The random final time is the first time there is no customer waiting for service. When the service times are exponential random variables, we can appeal to dynamic programming to obtain the optimal solution. In the general case, conditional probability is used. Particular problems in which the capacity of the system is finite are solved explicitly.

]]>Axioms doi: 10.3390/axioms13090593

Authors: Huimei Liu Meilan Cai Feng Li

In this paper, two classes of near-Hamiltonian systems with a nilpotent center are considered: the coexistence of algebraic limit cycles and small limit cycles. For the first class of systems, there exist 2n+1 limit cycles, which include an algebraic limit cycle and 2n small limit cycles. For the second class of systems, there exist n2+3n+22 limit cycles, including an algebraic limit cycle and n2+3n2 small limit cycles.

]]>Axioms doi: 10.3390/axioms13090592

Authors: Joaquín Pérez-Ortega Carlos Fernando Moreno-Calderón Sandra Silvia Roblero-Aguilar Nelva Nely Almanza-Ortega Juan Frausto-Solís Rodolfo Pazos-Rangel Alicia Martínez-Rebollar

Fuzzy C-Means is a clustering algorithm widely used in many applications. However, its computational complexity is very large, which prevents its use for large problem instances. Therefore, a hybrid improvement is proposed for the algorithm, which considerably reduces the number of iterations and, in many cases, improves the solution quality, expressed as the value of the objective function. This improvement integrates two heuristics, one in the initialization phase and the other in the convergence phase or the convergence criterion. This improvement was called HPFCM. A set of experiments was designed to validate this proposal; to this end, four sets of real data were solved from a prestigious repository. The solutions obtained by HPFCM were compared against those of the Fuzzy C-Means algorithm. In the best case, reductions of an average of 97.65% in the number of required iterations and an improvement in quality solution of 82.42% were observed when solving the SPAM dataset. Finally, we consider that the proposed heuristics may inspire improvements in other specific purpose variants of Fuzzy C-Means.

]]>Axioms doi: 10.3390/axioms13090591

Authors: Yizhuo Zhao Yu Li Jiaxin Zhu Yang Cao

In this paper, we present a novel explicit structure-preserving numerical method for solving nonlinear space-fractional Schr&ouml;dinger equations based on the concept of the scalar auxiliary variable approach. Firstly, we convert the equations into an equivalent system through the introduction of a scalar variable. Subsequently, a semi-discrete energy-preserving scheme is developed by employing a fourth-order fractional difference operator to discretize the equivalent system in spatial direction, and obtain the fully discrete version by using an explicit relaxed Runge&ndash;Kutta method for temporal integration. The proposed method preserves the energy conservation property of the space-fractional nonlinear Schr&ouml;dinger equation and achieves high accuracy. Numerical experiments are carried out to verify the structure-preserving qualities of the proposed method.

]]>Axioms doi: 10.3390/axioms13090590

Authors: Mustapha Rachidi Elen V. P. Spreafico Paula Catarino

In this study, we investigate some new properties of the sequence of bi-periodic Fibonacci numbers with arbitrary initial conditions, through an approach that combines the matrix aspect and the fundamental Fibonacci system. Indeed, by considering the properties of the eigenvalues of their related 2&times;2 matrix, we provide a new approach to studying the analytic representations of these numbers. Moreover, the similarity of the associated 2&times;2 matrix with a companion matrix, allows us to formulate the bi-periodic Fibonacci numbers in terms of a homogeneous linear recursive sequence of the Fibonacci type. Therefore, the combinatorial aspect and other analytic representations formulas of the Binet type for the bi-periodic Fibonacci numbers are achieved. The case of bi-periodic Lucas numbers is outlined, and special cases are exposed. Finally, some illustrative examples are given.

]]>Axioms doi: 10.3390/axioms13090589

Authors: Pablo Díaz Esmeralda Mainar Beatriz Rubio

The elements of the bidiagonal decomposition (BD) of a totally positive (TP) collocation matrix can be expressed in terms of symmetric functions of the nodes. Making use of this result, and studying the relation between Wronskian and collocation matrices of a given TP basis of functions, we can express the entries of the BD of Wronskian matrices as the values of certain symmetric functions evaluated at a single node. Moreover, in the case of polynomial bases, we obtain compact formulae for the entries of the BD of their Wronskian matrices. Interesting examples illustrate the applications of the obtained formulae.

]]>