Axioms doi: 10.3390/axioms13040264

Authors: Xinguang Zhang Jingsong Chen Li Yonghong Wu

In this paper, we establish some new results on the existence of positive solutions for a singular tempered sub-diffusion fractional equation involving a changing-sign perturbation and a lower-order sub-diffusion term of the unknown function. By employing multiple transformations, we transform the changing-sign singular perturbation problem to a positive problem, then establish some sufficient conditions for the existence of positive solutions of the problem. The asymptotic properties of solutions are also derived. In deriving the results, we only require that the singular perturbation term satisfies the Carath&eacute;odory condition, which means that the disturbance influence is significant and may even achieve negative infinity near some time singular points.

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Authors: Ru Li Guolin Yu

This paper considers a multi-product, multi-criteria supply&ndash;demand network equilibrium model with capacity constraints and uncertain demands. Strict network equilibrium principles are proposed both in the case of a single criterion and multi-criteria, respectively. Based on a single criterion, it proves that strict network equilibrium flows are equivalent to vector variational inequalities, and the existence of strict network equilibrium flows is derived by virtue of the Fan&ndash;Browder fixed point theorem. Based on multi-criteria, the scalarization of strict network equilibrium flows is given by using Gerstewitz&rsquo;s function without any convexity assumptions. Meanwhile, the necessary and sufficient conditions of strict network equilibrium flows are derived in terms of vector variational inequalities. Finally, an example is given to illustrate the application of the derived theoretical results.

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Authors: Miloš Mićović Branko Malešević

In this paper, two double Jordan-type inequalities are introduced that generalize some previously established inequalities. As a result, some new upper and lower bounds and approximations of the sinc function are obtained. This extension of Jordan&rsquo;s inequality is enabled by considering the corresponding inequalities through the concept of stratified families of functions. Based on this approach, some optimal approximations of the sinc function are derived by determining the corresponding minimax approximants.

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Authors: José-Javier Martínez

The approach to solving linear systems with structured matrices by means of the bidiagonal factorization of the inverse of the coefficient matrix is first considered in this review article, the starting point being the classical Bj&ouml;rck&ndash;Pereyra algorithms for Vandermonde systems, published in 1970 and carefully analyzed by Higham in 1987. The work of Higham briefly considered the role of total positivity in obtaining accurate results, which led to the generalization of this approach to totally positive Cauchy, Cauchy&ndash;Vandermonde and generalized Vandermonde matrices. Then, the solution of other linear algebra problems (eigenvalue and singular value computation, least squares problems) is addressed, a fundamental tool being the bidiagonal decomposition of the corresponding matrices. This bidiagonal decomposition is related to the theory of Neville elimination, although for achieving high relative accuracy the algorithm of Neville elimination is not used. Numerical experiments showing the good behavior of these algorithms when compared with algorithms that ignore the matrix structure are also included.

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Authors: Faruk Özger Merve Temizer Ersoy Zeynep Ödemiş Özger

Integral equations, which are defined as &ldquo;the equation containing an unknown function under the integral sign&rdquo;, have many applications of real-world problems. The second type of Fredholm integral equations is generally used in radiation transfer theory, kinetic theory of gases, and neutron transfer theory. A special case of these equations, known as the quadratic Chandrasekhar integral equation, given by x(s)=1+&lambda;x(s)&int;01st+sx(t)dt, can be very often encountered in many applications, where x is the function to be determined, &lambda; is a parameter, and t,s&isin;[0,1]. In this paper, using a fixed-point theorem, the existence conditions for the solution of Fredholm integral equations of the form &chi;(l)=&#1009;(l)+&chi;(l)&int;pqk(l,z)(V&chi;)(z)dz are investigated in the space C&omega;p,q, where &chi; is the unknown function to be determined, V is a given operator, and &#1009;,k are two given functions. Moreover, certain important applications demonstrating the applicability of the existence theorem presented in this paper are provided.

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Authors: Shuanghong Zhang

Non-negative integer-valued time series are usually encountered in practice, and a variety of integer-valued autoregressive processes based on various thinning operators are commonly used to model these count data with temporal dependence. In this paper, we consider a first-order integer-valued autoregressive process constructed by the negative binomial thinning operator with random coefficients, to address the problem of constant thinning parameters which might not always accurately represent real-world settings because of numerous external and internal causes. We estimate the model parameters of interest by the two-step conditional least squares method, obtain the asymptotic behaviors of the estimators, and furthermore devise a technique to test the constancy of the thinning parameters, which is essential for determining whether or not the proposed model should consider the parameters&rsquo; randomness. The effectiveness and dependability of the suggested approach are illustrated by a series of thorough simulation studies. Finally, two real-world data analysis examples reveal that the suggested approach is very useful and flexible for applications.

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Authors: Jialong Tang Huaqing Li Menggang Chen Yawei Shi Lifeng Zheng Huiwei Wang

In this article, a distributed charging strategy problem for plug-in electric vehicles (PEVs) with feeder constraints based on generalized Nash equilibria (GNE) in a novel smart charging station (SCS) is investigated. The purpose is to coordinate the charging strategies of all PEVs in SCS to minimize the energy cost of SCS. Therefore, we build a non-cooperative game framework and propose a new price-driven charging control game by considering the overload constraint of the assigned feeder, where each PEV minimizes the fees it pays to satisfy its optimal charging strategy. On this basis, the existence of GNE is given. Furthermore, we employ a distributed algorithm based on forward&ndash;backward operator splitting methods to find the GNE. The effectiveness of the employed algorithm is verified by the final simulation results.

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Authors: Wenyue Tao Chaoran Wu Ting Wu Fuyuan Chen

Vegetables have a short period of freshness, and therefore, the purchase of vegetables has to be carefully matched with sales, especially in the &ldquo;small production and big market&rdquo; setting prevalent in China. Therefore, it is worthwhile to develop a systematic and comprehensive mathematical model of replenishment plans and pricing strategies for each category of vegetables and individual products. In this paper, we analyze the following three questions: Question One: What is the distribution law and relationship between the sales volume of vegetable categories and single products? Question Two: What is the relationship between total sales volume and cost-plus pricing of vegetable categories? And is it possible to provide the daily total replenishment and pricing strategy of each vegetable category for the following week to maximize supermarket profit? Question Three: How can we incorporate the market demand for single vegetable products into a profit-maximizing program for supermarkets? Is it possible to further formulate the replenishment plan requirements for single products? To answer the first question, we created pivot tables to analyze occupancy. We found that mosaic leaves, peppers, and edible mushrooms accounted for a larger proportion of occupacy, while cauliflowers, aquatic rhizomes, and eggplants accounted for a smaller proportion. For the single items, lettuce, cabbage, green pepper, screw pepper, enoki mushroom, and shiitake mushroom accounted for a large proportion of their respective categories. We used the Pearson correlation coefficient and the Mfuzz package based on fuzzy c-means (FCM) algorithm to analyze the correlation between vegetable categories and single products. We found that there was a strong correlation between vegetable categories. Moreover, the sale of vegetable items belonging to the same category exhibited the same patterns of change over time. In order to address the second question, we established the LightGBM sales forecasting model. Combined with previous sales data, we forecasted and planned an efficient daily replenishment volume for each vegetable category in the coming week. In addition, we developed a pricing strategy for vegetable categories to maximize supermarket profits. For the third question, we built a dynamic programming model combining an optimal replenishment volume with a product pricing strategy for single items, which let the supermarket maximize its expected profits.

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Authors: Juan Antonio Rojas-Quintero François Dubois José Guadalupe Cabrera-Díaz

This contribution proposes a variational symplectic integrator aimed at linear systems issued from the least action principle. An internal quadratic finite-element interpolation of the state is performed at each time step. Then, the action is approximated by Simpson&rsquo;s quadrature formula. The implemented scheme is implicit, symplectic, and conditionally stable. It is applied to the time integration of systems with quadratic Lagrangians. The example of the linearized double pendulum is treated. Our method is compared with Newmark&rsquo;s variational integrator. The exact solution of the linearized double pendulum example is used for benchmarking. Simulation results illustrate the precision and convergence of the proposed integrator.

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Authors: Krassimir Atanassov

In a series of papers, we have discussed the concept of a modal topological structure modified, extended and illustrated by examples from intuitionistic fuzzy sets. Here, the concept of a temporal modal topological structure is introduced and illustrated with four different intuitionistic fuzzy temporal modal topological structures. These structures are based on intuitionistic fuzzy topological, temporal and modal operators. They are extensions of the temporal topological structures as well as of the modal topological structures.

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Authors: Xun Yang Shuwen Xiang Changgen Peng Weijie Tan Yue Wang Hai Liu Hongfa Ding

The distributed training of federated machine learning, referred to as federated learning (FL), is discussed in models by multiple participants using local data without compromising data privacy and violating laws. In this paper, we consider the training of federated machine models with uncertain participation attitudes and uncertain benefits of each federated participant, and to encourage all participants to train the desired FL models, we design a fuzzy Shapley value incentive mechanism with supervision. In this incentive mechanism, if the supervision of the supervised mechanism detects that the payoffs of a federated participant reach a value that satisfies the Pareto optimality condition, the federated participant receives a distribution of federated payoffs. The results of numerical experiments demonstrate that the mechanism successfully achieves a fair and Pareto optimal distribution of payoffs. The contradiction between fairness and Pareto-efficient optimization is solved by introducing a supervised mechanism.

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Authors: Yolanda M. Gómez Inmaculada Barranco-Chamorro Jaime S. Castillo Héctor W. Gómez

This paper presents the Slash-Exponential-Fr&eacute;chet distribution, which is an expanded version of the Fr&eacute;chet distribution. Through its stochastic representation, probability distribution function, moments and other relevant features are obtained. Evidence supports that the updated model displays a lighter right tail than the Fr&eacute;chet model and is more flexible as for skewness and kurtosis. Results on maximum likelihood estimators are given. Our proposition&rsquo;s applicability is demonstrated through a simulation study and the evaluation of two real-world datasets.

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Authors: Satish Shukla Nikita Dubey Juan-José Miñana

The purpose of this paper is to generalize the concept of classical fuzzy set to vector-valued fuzzy set which can attend values not only in the real interval [0,&nbsp;1], but in an ordered interval of a Banach algebra as well. This notion allows us to introduce the concept of vector-valued fuzzy metric space which generalizes, extends and unifies the notion of classical fuzzy metric space and complex-valued fuzzy metric space and permits us to consider the fuzzy sets and metrics in a larger domain. Some topological properties of such spaces are discussed and some fixed point results in this new setting are proved. Multifarious examples are presented which clarify and justify our claims and results.

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Authors: Antanas Laurinčikas Darius Šiaučiūnas

In the paper, we prove a limit theorem in the sense of the weak convergence of probability measures for the modified Mellin transform Z(s), s=&sigma;+it, with fixed 1/2&lt;&sigma;&lt;1, of the square |&zeta;(1/2+it)|2 of the Riemann zeta-function. We consider probability measures defined by means of Z(&sigma;+i&phi;(t)), where &phi;(t), t&#10878;t0&gt;0, is an increasing to +&infin; differentiable function with monotonically decreasing derivative &phi;&prime;(t) satisfying a certain normalizing estimate related to the mean square of the function Z(&sigma;+i&phi;(t)). This allows us to extend the distribution laws for Z(s).

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Authors: Xueting Zhao Kai Duo Aiping Gan Yichuan Yang

In this paper,&nbsp;(&#8857;,&or;)-multiderivations on an MV-algebra A are introduced, the relations between&nbsp;(&#8857;,&or;)-multiderivations and&nbsp;(&#8857;,&or;)-derivations are discussed. The set&nbsp;MD(A)&nbsp;of&nbsp;(&#8857;,&or;)-multiderivations on A can be equipped with a preorder, and&nbsp;(MD(A)/&sim;,&#8828;)&nbsp;can be made into a partially ordered set with respect to some equivalence relation &sim;. In particular, for any finite MV-chain&nbsp;Ln,&nbsp;(MD(Ln)/&sim;,&#8828;)&nbsp;becomes a complete lattice. Finally, a counting principle is built to obtain the enumeration of&nbsp;MD(Ln).

]]>Axioms doi: 10.3390/axioms13040249

Authors: Bo Yu Ning Dong Baiquan Hu

Consider a class of coupled Stein equations arising from jump control systems. An operator Smith algorithm is proposed for calculating the solution of the system. Convergence of the algorithm is established under certain conditions. For large-scale systems, the operator Smith algorithm is extended to a low-rank structured format, and the error of the algorithm is analyzed. Numerical experiments demonstrate that the operator Smith iteration outperforms existing linearly convergent iterative methods in terms of computation time and accuracy. The low-rank structured iterative format is highly effective in approximating the solutions of large-scale structured problems.

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Authors: Ndivhuwo Ndou Phumlani Dlamini Byron Alexander Jacobs

This study introduces the higher-order unconditionally positive finite difference (HUPFD) methods to solve the linear, nonlinear, and system of advection&ndash;diffusion&ndash;reaction (ADR) equations. The stability and consistency of the developed methods are analyzed, which are necessary and sufficient for the numerical approach to converge to the exact solution. The problem under consideration is of the Cauchy type, and hence, Von Neumann stability analysis is used to analyze the stability of the proposed schemes. The HUPFD&rsquo;s efficacy and efficiency are investigated by calculating the error, convergence rate, and computing time. For validation purposes, the higher-order unconditionally positive finite difference solutions are compared to analytical calculations. The numerical results demonstrate that the proposed methods produce accurate solutions to solve the advection diffusion reaction equations. The results also show that increasing the order of the unconditionally positive finite difference leads an implicit scheme that is conditionally stable and has a higher order of accuracy with respect to time and space.

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Authors: K. A. Alzahrani N. A. Alzaid H. O. Bakodah M. H. Almazmumy

The present manuscript proposes a computational approach to efficiently tackle a class of two-point boundary value problems that features third-order nonlinear ordinary differential equations. Specifically, this approach is based upon a combination of the shooting method with a modification of the renowned Adomian decomposition method. The approach starts by transforming the governing BVP into two appropriate initial-value problems, and thereafter, solves the resulting IVPs recurrently. In addition, the application of this method to varied test models remains feasible&mdash;of course, this is supported by the competing Runge&ndash;Kutta method, among others, and reported through comparison plots and tables.

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Authors: Rafael Luís

In this paper, we present a survey about the latest results in global stability concerning the discrete-time evolutionary Ricker competition model with n species, in both, autonomous and periodic models. The main purpose is to convey some arguments and new ideas concerning the techniques for showing global asymptotic stability of fixed points or periodic cycles in these kind of discrete-time models. In order to achieve this, some open problems and conjectures related to the evolutionary Ricker competition model are presented, which may be a starting point to study global stability, not only in other competition models, but in predator&ndash;prey models and Leslie&ndash;Gower-type models as well.

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Authors: Marco Frego Cristian Consonni

One nappe of a right circular cone, cut by a transverse plane, splits the cone into an infinite frustum and a cone with an elliptical section of finite volume. There is a standard way of computing this finite volume, which involves finding the parameters of the so-called shadow ellipse, the characteristics of the oblique ellipse (the cut) and, finally, the projection of the vertex of the cone onto the oblique ellipse. This paper shows that it is possible to compute that volume just by using the information of the shadow ellipse and the height of the cone. Indeed, the finite slant cone has the same volume of an elliptic right cone, with the base being the shadow ellipse of the cut portion and with the height being the distance between the vertex of the cone and the intersection of the height of the original cone with the cutting plane. This is proved by introducing a volume-preserving shear transformation of the elliptical slant cone to a right cone, so that the standard volume formula for a cone can be straightforwardly applied. This implies a simplification in the procedure for computing the volume, since the oblique ellipse&mdash;i.e., the difficult part&mdash;can be neglected because only the shadow ellipse needs to be determined.

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Authors: Raimondas Čiegis Olga Suboč Remigijus Čiegis

The aim of this article is to analyze the efficiency and accuracy of finite-difference and finite-element Galerkin schemes for non-stationary hyperbolic and parabolic problems. The main problem solved in this article deals with the construction of accurate and efficient discrete schemes on nonuniform and dynamic grids in time and space. The presented stability and convergence analysis enables improving the existing accuracy estimates. The obtained stability results show explicitly the rate of accumulation of interpolation and projection errors that arise due to the movement of grid points. It is shown that the cases when the time grid steps are doubled or halved have different stability properties. As an additional technique to improve the accuracy of discretizations on non-stationary space grids, it is recommended to use projection operators instead of interpolation operators. This technique is used to solve a test parabolic problem. The results of specially selected computational experiments are also presented, and they confirm the accuracy of all theoretical error estimates obtained in this article.

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Authors: Yanli Liu Yangyang Xue Yunan Cui

Lower strict monotonicity points and lower local uniform monotonicity points are considered in the case of Musielak&ndash;Orlicz function spaces L&Phi; endowed with the Mazur&ndash;Orlicz F-norm. The findings outlined in this study extend the scope of geometric characteristics observed in F-normed Orlicz spaces, as well as monotonicity properties within specific F-normed lattices. They are suitable for the Orlicz spaces of ordered continuous elements, specifically in relation to the Mazur&ndash;Orlicz F-norm. In addition, in this paper presents results that can be used to derive certain monotonicity properties in F-normed Musielak&ndash;Orlicz spaces.

]]>Axioms doi: 10.3390/axioms13040242

Authors: Leon Cohen

We develop the concept of covariance for waves and show that it plays a fundamental role in understanding the evolution of a propagating pulse. The concept clarifies several issues regarding the spread of a pulse and the motion of the mean. Exact results are obtained for the time dependence of the covariance between position and wavenumber and the covariance between position and group velocity. We also derive relevant uncertainty principles for waves.

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Authors: Zaihang Su Yisong Wang Renyan Feng Chan Zhou

Modal logic S5, which isan important knowledge representation and reasoning paradigm, has been successfully applied in various artificial-intelligence-related domains. Similar to the random propositional theories in conjunctive clause form, the phase transition plays an important role in designing efficient algorithms for computing models of propositional S5 theories. In this paper, a new form of S5 formula is proposed, which fixes the number of modal operators and literals in the clauses of the formula. This form consists of reduced 3-3-S5 clauses of the form l1&or;l2&or;&xi;, where &xi; takes the form &#9633;(l3&or;l4&or;l5), &loz;(l3&and;l4&and;l5), or a propositional literal, and li(1&le;i&le;5) is a classical literal. Moreover, it is demonstrated that any S5 formula can be translated into a set of reduced 3-3-S5 clauses while preserving its satisfiability. This work further investigates the probability of a random 3-c-S5 formula with c=1,2,3 being satisfied by random assignment. In particular, we show that the satisfiability threshold of random 3-1-S5 clauses is &minus;ln2(1&minus;Pd&minus;Ps)ln78+Ps&middot;ln34, where Ps and Pd denote the probabilities of different modal operators appearing in a clause. Preliminary experimental results on random 3-1-S5 formulas confirm this theoretical threshold.

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Authors: Vladimir Krutikov Elena Tovbis Predrag Stanimirović Lev Kazakovtsev Darjan Karabašević

In this article, we consider the correction of metric matrices in quasi-Newton methods (QNM) from the perspective of machine learning theory. Based on training information for estimating the matrix of the second derivatives of a function, we formulate a quality functional and minimize it by using gradient machine learning algorithms. We demonstrate that this approach leads us to the well-known ways of updating metric matrices used in QNM. The learning algorithm for finding metric matrices performs minimization along a system of directions, the orthogonality of which determines the convergence rate of the learning process. The degree of learning vectors&rsquo; orthogonality can be increased both by choosing a QNM and by using additional orthogonalization methods. It has been shown theoretically that the orthogonality degree of learning vectors in the Broyden&ndash;Fletcher&ndash;Goldfarb&ndash;Shanno (BFGS) method is higher than in the Davidon&ndash;Fletcher&ndash;Powell (DFP) method, which determines the advantage of the BFGS method. In our paper, we discuss some orthogonalization techniques. One of them is to include iterations with orthogonalization or an exact one-dimensional descent. As a result, it is theoretically possible to detect the cumulative effect of reducing the optimization space on quadratic functions. Another way to increase the orthogonality degree of learning vectors at the initial stages of the QNM is a special choice of initial metric matrices. Our computational experiments on problems with a high degree of conditionality have confirmed the stated theoretical assumptions.

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Authors: Juan Luis González-Santander Fernando Sánchez Lasheras

We propose a heuristic method to solve polynomial matrix equations of the type &sum;k=1makXk=B, where ak are scalar coefficients and X and B are square matrices of order n. The method is based on the decomposition of the B matrix as a linear combination of the identity matrix and an idempotent, involutive, or nilpotent matrix. We prove that this decomposition is always possible when n=2. Moreover, in some cases we can compute solutions when we have an infinite number of them (singular solutions). This method has been coded in MATLAB and has been compared to other methods found in the existing literature, such as the diagonalization and the interpolation methods. It turns out that the proposed method is considerably faster than the latter methods. Furthermore, the proposed method can calculate solutions when diagonalization and interpolation methods fail or calculate singular solutions when these methods are not capable of doing so.

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Authors: Hongfen Yuan Guohong Shi Xiushen Hu

The perturbed Dirac operators yield a factorization for the well-known Helmholtz equation. In this paper, using the fundamental solution for the perturbed Dirac operator, we define Cauchy-type integral operators (singular integral operators with a Cauchy kernel). With the help of these operators, we investigate generalized Riemann and Dirichlet problems for the perturbed Dirac equation which is a higher-dimensional generalization of a Vekua-type equation. Furthermore, applying the generalized Cauchy-type integral operator F&tilde;&lambda;, we construct the Mann iterative sequence and prove that the iterative sequence strongly converges to the fixed point of operator F&tilde;&lambda;.

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Authors: Hyun Soo Chung

In this paper, we first establish an evaluation formula to calculate Wiener integrals of functionals on Wiener space. We then apply our evaluation formula to carry out easy an calculation for the analytic Fourier&ndash;Feynman transform of the functionals. Some examples are furnished to illustrate the usefulness of the evaluation formula. Finally, using the evaluation formula, we establish the series approximation for the analytic Fourier&ndash;Feynman transform.

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Authors: Aljoša Šubašić Tanja Vojković

In this paper, we observe a special class of graphs known as multilayered graphs and their subclasses, namely multilayered cycles and multilayered paths. These graphs model layouts of shopping malls, city street grids, and even resemble the topology of certain famous board games. We analyze the values of all vertex spans (strong, direct, and Cartesian span) for these subclasses of graphs. Surprisingly, our results for multilayered cycles reveal that, regardless of the chosen movement rules, the span values depend solely on the length of the individual cycles, rather than the number of layers. This finding carries significant implications for the application of graph spans in maintaining safety distances.

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Authors: Haytham M. Rezk Ahmed I. Saied Maha Ali Ghada AlNemer Mohammed Zakarya

In this article, we discuss several novel generalized Ostrowski-type inequalities for functions whose derivative module is relatively convex in time scales calculus. Our core findings are proved by using the integration by parts technique, H&ouml;lder&rsquo;s inequality, and the chain rule on time scales. These derived inequalities expand the existing literature, enriching specific integral inequalities within this domain.

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Authors: Asma Al-Jaser Clemente Cesarano Belgees Qaraad Loredana Florentina Iambor

This paper focuses on establishing new criteria to guarantee the oscillation of solutions for second-order differential equations with a superlinear and a damping term. New sufficient conditions are presented, aimed at analysing the oscillatory properties of the solutions to the equation under study. To prove these results, we employed various analysis methods, establishing new relationships to address certain problems that have hindered previous research. Consequently, by applying the principles of comparison and the Riccati transformation, we obtained findings that develop and complement those reported in earlier literature. The significance of our results is illustrated with several examples.

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Authors: Satyvir Singh Bidesh Sengupta Seetu Rana

The present study presents a computational investigation into the thermal mixing along with entropy generation throughout the natural convection flow within an arbitrarily eccentric annulus. Salt water is filled inside the eccentric annulus, in which the outer and inner cylinders have Tc and Th constant temperatures. The Boussinesq approximation is used to develop the governing equations for the natural convection flow, which are then solved on a structured quadrilateral mesh using the OpenFOAM software package (FOAM-Extend 4.0). The computational simulations are performed for Rayleigh numbers (Ra=103&ndash;105), eccentricity (&#1013;=0,0.4,0.8), angular positions (&phi;=0&#8728;,45&#8728;,90&#8728;), and Prandtl number (Pr=10, salt water). The computational results are visualized in terms of streamlines, isotherms, and entropy generation caused by fluid friction and heat transfer. Additionally, a thorough examination of the variations in the average and local Nusselt numbers, circulation intensity with eccentricities, and angular positions is provided. The optimal state of heat transfer is shown to be influenced by the eccentricity, angular positions, uniform temperature sources, and Boussinesq state. Moreover, the rate of thermal mixing and the production of total entropy increase as Ra increases. It is found that, compared to a concentric annulus, an eccentric annulus has a higher rate of thermal mixing and entropy generation. The findings show which configurations and types of eccentric annulus are ideal and could be used in any thermal processing activity where a salt fluid (Pr=10) is involved.

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Authors: Zhenwei Li Yuting Ding

The protection of forests and the mitigation of pest damage to trees play a crucial role in mitigating the greenhouse effect. In this paper, we first establish a delayed differential equation model for Ips subelongatus Motschulsky-Larix spp., where the delay parameter represents the time required for trees to undergo curing. Second, we analyze the stability of the equilibrium of the model and derive the normal form of Hopf bifurcation using a multiple-time-scales method. Then, we analyze the stability and direction of Hopf bifurcating periodic solutions. Finally, we conduct simulations to analyze the changing trends in pest and tree populations. Additionally, we investigate the impact of altering the rate of artificial planting on the system and provide corresponding biological explanations.

]]>Axioms doi: 10.3390/axioms13040231

Authors: Hazhe Ye Yingzhi Tian

The restricted edge-connectivity of a connected graph G, denoted by &lambda;&prime;(G), if it exists, is the minimum cardinality of a set of edges whose deletion makes G disconnected, and each component has at least two vertices. It was proved that &lambda;&prime;(G) exists if and only if G has at least four vertices and G is not a star. In this case, a graph G is called maximally restricted edge-connected if &lambda;&prime;(G)=&xi;(G), and a graph G is called super restricted edge-connected if each minimum restricted edge-cut isolates an edge of G. The strong product of graphs G and H, denoted by G&#8864;H, is the graph with the vertex set V(G)&times;V(H) and the edge set {(x1,y1)(x2,y2)|x1=x2 and y1y2&isin;E(H); or y1=y2 and x1x2&isin;E(G); or x1x2&isin;E(G) and y1y2&isin;E(H)}. In this paper, we determine, for any nontrivial connected graph G, the restricted edge-connectivity of G&#8864;Pn, G&#8864;Cn and G&#8864;Kn, where Pn, Cn and Kn are the path, cycle and complete graph of order n, respectively. As corollaries, we give sufficient conditions for these strong product graphs G&#8864;Pn, G&#8864;Cn and G&#8864;Kn to be maximally restricted edge-connected and super restricted edge-connected.

]]>Axioms doi: 10.3390/axioms13040230

Authors: Yulei Chen Dongwei Guo

Making use of integration by parts and variable replacement methods, we derive some interesting explicit definite integral formulae involving trigonometric or hyperbolic functions, whose results are expressed in terms of Catalan&rsquo;s constant, Dirichlet&rsquo;s beta function, and Riemann&rsquo;s zeta function, as well as &pi; in the denominator.

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Authors: Laura Augusta Vasconcelos de Albuquerque Mariana Fernandes dos Santos Villela Felipe Pamplona Mariano

The present work proposes the application of a computational methodology based on the coupling of the Fourier Pseudospectral Method (FPSM) and the Immersed Boundary Method (IBM) for conducting flow simulations over slender airfoils. This methodology, termed IMERSPEC, leverages the benefits of both high accuracy and low computational cost inherent in pseudospectral methods, thanks to the utilization of the Fast Fourier Transform algorithm. IBM is employed to impose non-periodic boundary conditions in the Navier&ndash;Stokes equations, addressing the requirement of periodicity at boundaries for FPSM convergence and to accurately represent the immersed slender airfoil in the flow. The aerodynamic behavior of the analyzed profiles was assessed by calculating lift and drag coefficients, which were then compared with existing literature results. Consistently favorable outcomes were observed, particularly in flows at lower Reynolds numbers, demonstrating the effectiveness of the IMERSPEC methodology for simulating complex flows computationally. Additionally, weight functions, fundamental to IBM, are employed flexibly for aerodynamic force calculations. Specifically, within the same simulation, a Cubic function is utilized for drag calculation while a Hat function is employed for lift calculation, yielding results more closely aligned with the literature&rsquo;s findings. This approach offers an alternative to previously proposed methods for IBM implementation.

]]>Axioms doi: 10.3390/axioms13040229

Authors: Reem Alrebdi Hind K. Al-Jeaid

The pantograph equation is a basic model in the field of delay differential equations. This paper deals with an extended version of the pantograph delay equation by incorporating a variable coefficient of exponential order. At specific values of the involved parameters, the exact solution is obtained by applying the regular Maclaurin series expansion (MSE). A second approach is also applied on the current model based on a hybrid method combining the Laplace transform (LT) and the Adomian decomposition method (ADM) denoted as (LTADM). Although the MSE derives the exact solution in a straightforward manner, the LTADM determines the solution in a closed series form which is theoretically proved for convergence. Further, the accuracy of such a closed-form solution is examined through various comparisons with the exact solution. For validation, the residual errors are calculated and displayed in graphs. The results show that the solution obtained utilizing the LTADM is in full agreement with the exact solution using only a few terms of the closed-form series solution. Moreover, it is found that the residual errors tend to zero, which reflects the effectiveness of the LTADM. The present approach may merit further extension by including other types of linear delay differential equations with variable coefficients.

]]>Axioms doi: 10.3390/axioms13040227

Authors: Yarema A. Prykarpatskyy Petro Ya. Pukach Myroslava I. Vovk Michal Greguš

We analyze smooth nonlinear mappings for Hilbert and Banach spaces that carry small balls to convex sets, provided that the radii of the balls are small enough. We focus on the study of new and mildly sufficient conditions for the nonlinear mapping of Hilbert and Banach spaces to be locally convex, and address a suitably reformulated local convexity problem analyzed within the Leray&ndash;Schauder homotopy method approach for Hilbert spaces, and within the Lipschitz smoothness condition for both Hilbert and Banach spaces. Some of the results presented in this work prove to be interesting and novel, even for finite-dimensional problems. Open problems related to the local convexity property for nonlinear mappings of Banach spaces are also formulated.

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Authors: Cenker Biçer Hassan S. Bakouch Hayrinisa Demirci Biçer Gadir Alomair Tassaddaq Hussain Amal Almohisen

In the vast statistical literature, there are numerous probability distribution models that can model data from real-world phenomena. New probability models, nevertheless, are still required in order to represent data with various spread behaviors. It is a known fact that there is a great need for new models with limited support. In this study, a flexible probability model called the unit Maxwell-Boltzmann distribution, which can model data values in the unit interval, is derived by selecting the Maxwell-Boltzmann distribution as a base-line model. The important characteristics of the derived distribution in terms of statistics and mathematics are investigated in detail in this study. Furthermore, the inference problem for the mentioned distribution is addressed from the perspectives of maximum likelihood, method of moments, least squares, and maximum product space, and different estimators are obtained for the unknown parameter of the distribution. The derived distribution outperforms competitive models according to different fit tests and information criteria in the applications performed on four actual air pollutant concentration data sets, indicating that it is an effective model for modeling air pollutant concentration data.

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Authors: Savin Treanţă Tareq Saeed

Weak sharp type solutions are analyzed for a variational integral inequality defined by a convex functional of the multiple integral type. A connection with the sufficiency property associated with the minimum principle is formulated, as well. Also, an illustrative numerical application is provided.

]]>Axioms doi: 10.3390/axioms13040224

Authors: Georgia Irina Oros

This Special Issue is a sequel to the successful first volume entitled &ldquo;New Developments in Geometric Function Theory&rdquo; [...]

]]>Axioms doi: 10.3390/axioms13040223

Authors: Juan Manuel Peña

A space with a normalized totally positive basis has a unique normalized B-basis. In computer-aided geometric design, normalized B-bases present optimal shape-preserving properties. More optimal properties of normalized B-bases were proved previously. This paper provides a new optimal property concerning the modified Richardson iterative method when applied to collocation matrices of normalized B-bases. Moreover, a similar optimal property is proved for the tensor product of normalized B-bases.

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Authors: Richard Avery Douglas R. Anderson Jeffrey Lyons

Due to the restrictive growth and/or monotonicity requirements inherent in their employment, classical iterative fixed-point theorems are rarely used to approximate solutions to an integral operator with Green&rsquo;s function kernel whose fixed points are solutions of a boundary value problem. In this paper, we show how one can decompose a fixed-point problem into multiple fixed-point problems that one can easily iterate to approximate a solution of a differential equation satisfying one boundary condition, then apply a bisection method in an intermediate value theorem argument to meet a second boundary condition. Error estimates on the iterates are also established. The technique will be illustrated on a second-order right focal boundary value problem, with an example provided showing how to apply the results.

]]>Axioms doi: 10.3390/axioms13040221

Authors: Areen Al-Khateeb

In this study, we explore fractional partial differential equations as a more generalized version of classical partial differential equations. These fractional equations have shown promise in providing improved descriptions of certain phenomena under specific circumstances. The main focus of this paper comprises the development, analysis, and application of two explicit finite difference schemes to solve an initial boundary value problem involving a fuzzy time fractional convection&ndash;diffusion equation with a fractional order in the range of 0&le;&nbsp;&xi;&nbsp;&le;&nbsp;1. The uniqueness of this problem lies in its consideration of fuzziness within both the initial and boundary conditions. To handle the uncertainty, we propose a computational mechanism based on the double parametric form of fuzzy numbers, effectively converting the problem from an uncertain format to a crisp one. To assess the stability of our proposed schemes, we employ the von Neumann method and find that they demonstrate unconditional stability. To illustrate the feasibility and practicality of our approach, we apply the developed scheme to a specific example.

]]>Axioms doi: 10.3390/axioms13040220

Authors: Jie Ge Yan Sun

This study models a container routing problem using multimodal transportation to improve its economy, timeliness, and reliability. Pickup and delivery time windows are simultaneously formulated in optimization to provide the shipper and the receiver with time-efficient services, in which early pickup and delayed delivery can be avoided, and nonlinear storage periods at the origin and the destination can be minimized. Furthermore, the capacity uncertainty of the multimodal network is incorporated into the advanced routing to enhance its reliability in practical transportation. The LR triangular fuzzy number is adopted to model the capacity uncertainty, in which its spread ratio is defined to measure the uncertainty level of the fuzzy capacity. Due to the nonlinearity introduced by the time windows and the fuzziness from the network capacity, this study establishes a fuzzy nonlinear optimization model for optimization problem. A chance-constrained linear reformulation equivalent to the proposed model is then generated based on the credibility measure, which makes the global optimum solution attainable by using Lingo software. A numerical case verification demonstrates that the proposed model can effectively solve the problem. The case analysis points out that the formulation of pickup and delivery time windows can improve the timeliness of the entire transportation process and help to achieve on-time transportation. Furthermore, improving the confidence level and the uncertainty level increases the total costs of the optimal route. Therefore, the shipper and the receiver must prepare more transportation budget to improve reliability and address the increasing uncertainty level. Further analysis draws some insights to help the shipper, receiver, and multimodal transport operator to organize a reliable and cost-efficient multimodal transportation under capacity uncertainty through confidence level balance and transportation service and transfer service selection.

]]>Axioms doi: 10.3390/axioms13040219

Authors: Yasmina Khiar Esmeralda Mainar Juan Manuel Peña Eduardo Royo-Amondarain Beatriz Rubio

Extensions of Filbert and Lilbert matrices are addressed in this work. They are reciprocal Hankel matrices based on Fibonacci and Lucas numbers, respectively, and both are related to Hilbert matrices. The Neville elimination is applied to provide explicit expressions for their bidiagonal factorization. As a byproduct, formulae for the determinants of these matrices are obtained. Finally, numerical experiments show that several algebraic problems involving these matrices can be solved with outstanding accuracy, in contrast with traditional approaches.

]]>Axioms doi: 10.3390/axioms13040218

Authors: Jiangshan Zhu Conghua Wen Rong Li

In this paper, we explore a novel model for pricing Chinese convertible bonds that seamlessly integrates machine learning techniques with traditional models. The least squares Monte Carlo (LSM) method is effective in handling multiple state variables and complex path dependencies through simple regression analysis. In our approach, we incorporate machine learning techniques, specifically support vector regression (SVR) and random forest (RF). By employing Bayesian optimization to fine-tune the random forest, we achieve improved predictive performance. This integration is designed to enhance the precision and predictive capabilities of convertible bond pricing. Through the use of simulated data and real data from the Chinese convertible bond market, the results demonstrate the superiority of our proposed model over the classic LSM, confirming its effectiveness. The development of a pricing model incorporating machine learning techniques proves particularly effective in addressing the complex pricing system of Chinese convertible bonds. Our study contributes to the body of knowledge on convertible bond pricing and further deepens the application of machine learning in the field in an integrated and supportive manner.

]]>Axioms doi: 10.3390/axioms13040217

Authors: Chunyan Zhang Yuanyang Qiao

In this paper, we propose an efficient numerical method to solve the problems of diffusive logistic models with free boundaries, which are often used to simulate the spreading of new or invasive species. The boundary movement is tracked by the level-set method, where the Hamilton&ndash;Jacobi weighted essentially nonoscillatory (HJ-WENO) scheme is utilized to capture the boundary curve embedded by the Cartesian grids via the embedded boundary method. Then the radial basis function&ndash;finite difference (RBF-FD) method is adopted for spatial discretization and the implicit&ndash;explicit (IMEX) scheme is considered for time integration. A variety of numerical examples are utilized to demonstrate the evolution of the diffusive logistic model with different initial boundaries.

]]>Axioms doi: 10.3390/axioms13040216

Authors: Naveed Hussain Ahmad N. Al-Kenani Muhammad Asif

Lie algebra plays an important role in the study of singularity theory and other fields of sciences. Finding numerous invariants linked with isolated singularities has always been a primary interest in the field of classification theory of isolated singularities. Any Lie algebra that characterizes simple singularity produces a natural question. The study of properties such as to find the dimensions of newly defined algebra is a remarkable work. Hussain, Yau and Zuo have found a new class of Lie algebra Lk(V), k&ge;1, i.e., Der (Mk(V),Mk(V)) and proposed a conjecture over its dimension &delta;k(V) for k&ge;0. Later, they proved it true for k up to k=1,2,3,4,5. In this work, the main concern is whether it is true for a higher value of k. According to this, we first calculate the dimension of Lie algebra Lk(V) for k=6 and then compute the upper estimate conjecture of fewnomial isolated singularities. Additionally, we also justify the inequality conjecture &delta;k+1(V)&lt;&delta;k(V) for k=6. Our calculated results are innovative and serve as a new addition to the study of singularity theory.

]]>Axioms doi: 10.3390/axioms13040215

Authors: Hanan A. Hosni Mahmoud

The Axioms Editorial Office retracts the article Diabetic Retinopathy Progression Prediction Using a Deep Learning Model [...]

]]>Axioms doi: 10.3390/axioms13040214

Authors: Sergei A. Dudin Olga S. Dudina Alexander N. Dudin

In this paper, we consider a tandem dual queuing system consisting of multi-server stages. Stage 1 is characterized by an infinite buffer, one-by-one service of customers, and an exponential distribution of service times. Stage 2 is characterized by a finite buffer and a phase-type distribution of service times. Service at Stage 2 is provided to groups of customers. The service time of a group depends on the size of the group. The size is restricted by two thresholds. The waiting time of a customer at each stage is limited by a random variable with an exponential distribution, with the parameter depending on the stage. After service at Stage 1, a customer can depart from the system or try to enter Stage 2. If the buffer at this stage is full, the customer is either lost or returns for service at Stage 1. Customer arrivals are described by the versatile Markov arrival process. The system is studied via consideration of a multi-dimensional continuous-time Markov chain. Numerical examples, which highlight the influence of the thresholds on the system performance measures, are presented. The possibility of solving optimization problems is illustrated.

]]>Axioms doi: 10.3390/axioms13040213

Authors: Aakash Mohandoss Gunasundari Chandrasekar Mutum Zico Meetei Ahmed H. Msmali

This paper studies a nonlinear fractional mathematical model for hand, foot, and mouth Disease (HFMD), incorporating a vaccinated compartment. Our initial focus involves establishing the non-negativity and boundedness of the fractional order dynamical model. The existence and uniqueness of the system are discussed using the Caputo derivative operator formulation. Applying a fixed-point approach, we obtain results that confirm the presence of at least one solution. We analyze the stability behavior at the two equilibrium points (disease-free and endemic states) of the model and derive the basic reproduction number. Numerical simulations are conducted using the fractional Euler approach, and the simulation results confirm our analytical conclusions. This comprehensive approach enhances the understanding of HFMD dynamics and facilitates the policy making of health care centers to control the further spread of this disease.

]]>Axioms doi: 10.3390/axioms13040212

Authors: Jeongjin Lee Jong-Min Kim

This research paper presents the Buckley-James Q-learning (BJ-Q) algorithm, a cutting-edge method designed to optimize personalized treatment strategies, especially in the presence of right censoring. We critically assess the algorithm&rsquo;s effectiveness in improving patient outcomes and its resilience across various scenarios. Central to our approach is the innovative use of the survival time to impute the reward in Q-learning, employing the Buckley-James method for enhanced accuracy and reliability. Our findings highlight the significant potential of personalized treatment regimens and introduce the BJ-Q learning algorithm as a viable and promising approach. This work marks a substantial advancement in our comprehension of treatment dynamics and offers valuable insights for augmenting patient care in the ever-evolving clinical landscape.

]]>Axioms doi: 10.3390/axioms13040211

Authors: Shahroud Azami Mehdi Jafari Abdul Haseeb Abdullah Ali H. Ahmadini

In this paper, we study left-invariant cross curvature solitons on Lorentzian three-dimensional Lie groups and classify these solitons.

]]>Axioms doi: 10.3390/axioms13040210

Authors: Jianqiang Zhao

In this paper, we will study finite multiple T-values (MTVs) and their alternating versions, which are level two and level four variations of finite multiple zeta values, respectively. We will first provide some structural results for level two finite multiple zeta values (i.e., finite Euler sums) for small weights, guided by the author&rsquo;s previous conjecture that the finite Euler sum space of weight, w, is isomorphic to a quotient Euler sum space of weight, w. Then, by utilizing some well-known properties of the classical alternating MTVs, we will derive a few important Q-linear relations among the finite alternating MTVs, including the reversal, linear shuffle, and sum relations. We then compute the upper bound for the dimension of the Q-span of finite (alternating) MTVs for some small weights by rigorously using the newly discovered relations, numerically aided by computers.

]]>Axioms doi: 10.3390/axioms13030209

Authors: Luyao Wang Guolin Liu

In this study, the ill-conditioning of the iterative method for nonlinear models is discussed. Due to the effectiveness of ridge estimation for ill-conditioned problems and the lack of a combination of the H-K formula with the iterative method, the improvement of the LM algorithm is studied in this paper. Considering the LM algorithm for ill-conditioned nonlinear least squares, an improved LM algorithm based on the H-K formula is proposed for image distortion correction using self-calibration. Three finite difference methods are used to approximate the Jacobian matrix, and the H-K formula is used to calculate the damping factor in each iteration. The Brown model, quadratic polynomial model and Fourier model are applied to the self-calibration, and the improved LM algorithm is used to solve the model parameters. In the simulation experiment of space resection of a single image, we evaluate the performance of the LM algorithm based on the gain ratio (LMh) and the improved LM algorithm based on the H-K formula (LMHK), and the accuracy of different models and algorithms is compared. A ridge trace analysis is carried out on the damping factor to illustrate the effects of the improved algorithm in handling ill-conditioning. In the second experiment, the improved algorithm is applied to measure the diameter of a coin using a single camera. The experimental results show that the improved LM algorithm can reach the same or higher accuracy as the LMh algorithm, and it can weaken the ill-conditioning to a certain extent and enhance the stability of the solution. Meanwhile, the applicability of the improved LM algorithm in self-calibration is verified.

]]>Axioms doi: 10.3390/axioms13030208

Authors: Zhaoting Ju Guangfeng Jiang Weili Guo

Freeness occupies an important position in the study of hyperplane arrangements. In this paper, we conclude the freeness of three special classes of signed graphic arrangements based on the addition&ndash;deletion theorem and Abe&rsquo;s free path theory.

]]>Axioms doi: 10.3390/axioms13030207

Authors: Zhulu Chu Xihan Wang Meilin Jin Ning Zhang Quanli Gao Lianhe Shao

Sentiment analysis aims to study, analyse and identify the sentiment polarity contained in subjective documents. In the realm of natural language processing (NLP), the study of sentiment analysis and its subtask research is a hot topic, which has very important significance. The existing sentiment analysis methods based on sentiment lexicon and machine learning take into account contextual semantic information, but these methods still lack the ability to utilize context information, so they cannot effectively encode context information. Inspired by the concept of density matrix in quantum mechanics, we propose a sentiment analysis method, named Complex-valued Quantum-enhanced Long Short-term Memory Neural Network (CQLSTM). It leverages complex-valued embedding to incorporate more semantic information and utilizes the Complex-valued Quantum-enhanced Long Short-term Memory Neural Network for feature extraction. Specifically, a complex-valued neural network based on density matrix is used to capture interactions between words (i.e., the correlation between words). Additionally, the Complex-valued Quantum-enhanced Long Short-term Memory Neural Network, which is inspired by the quantum measurement theory and quantum long short-term memory neural network, is developed to learn interactions between sentences (i.e., contextual semantic information). This approach effectively encodes semantic dependencies, which reflects the dispersion of words in the embedded space of sentences and comprehensively captures interactive information and long-term dependencies among the emotional features between words. Comparative experiments were performed on four sentiment analysis datasets using five traditional models, showcasing the effectiveness of the CQLSTM model.

]]>Axioms doi: 10.3390/axioms13030206

Authors: Benito Chen-Charpentier

The current values of many populations depend on the past values of the population. In many cases, this dependence is caused by the time certain processes take. This dependence on the past can be introduced into mathematical models by adding delays. For example, the growth rate of a population depends on the population &tau; time units ago, where &tau; is the maturation time. For an epidemic, there is a time &tau; between the contact of an infected individual and a susceptible one, and the time the susceptible individual actually becomes infected. This time &tau; is also a delay. So, the number of infected individuals depends on the population at the time &tau; units ago. A second way of introducing this dependence on past values is to use non-local operators in the description of the model. Fractional derivatives have commonly been used to provide non-local effects. In population growth models, it can also be done by introducing a new compartment, the immature population, and in epidemic models, by introducing an additional exposed population. In this paper, we study and compare these methods of adding dependence on past values. For models of processes that involve delays, all three methods include dependence on past values, but fractional-order models do not justify the form of the dependence. Simulations show that for the models studied, the fractional differential equation method produces similar results to those obtained by explicitly incorporating the delay, but only for specific values of the fractional derivative order, which is an extra parameter. But in all three methods, the results are improved compared to using ordinary differential equations.

]]>Axioms doi: 10.3390/axioms13030205

Authors: Fatmah B. Jamjoom Fadwa M. Algamdei

The objective of our study is to generalize the results on product states of the tensor product of two JC-algebras to infinite tensor product JC-algebras. Also, we characterize the tracial product state of the tensor product of two JC-algebras, and the tracial product state of infinite tensor products of JC-algebras.

]]>Axioms doi: 10.3390/axioms13030204

Authors: Asifa Tassaddiq Amna Kalsoom Maliha Rashid Kainat Sehr Dalal Khalid Almutairi

Iterative procedures have been proved as a milestone in the generation of fractals. This paper presents a novel approach for generating and visualizing fractals, specifically Mandelbrot and Julia sets, by utilizing complex polynomials of the form QC(p)=apn+mp+c, where n&ge;2. It establishes escape criteria that play a vital role in generating these sets and provides escape time results using different iterative schemes. In addition, the study includes the visualization of graphical images of Julia and Mandelbrot sets, revealing distinct patterns. Furthermore, the study also explores the impact of parameters on the deviation of dynamics, color, and appearance of fractals.

]]>Axioms doi: 10.3390/axioms13030203

Authors: Jack C. Straton

This paper shows that certain&nbsp;3F4 hypergeometric functions can be expanded in sums of pair products of&nbsp;2F3 functions, which reduce in special cases to&nbsp;2F3 functions expanded in sums of pair products of&nbsp;1F2 functions. This expands the class of hypergeometric functions having summation theorems beyond those expressible as pair-products of generalized Whittaker functions,&nbsp;2F1 functions, and&nbsp;3F2 functions into the realm of&nbsp;pFq functions where p&lt;q for both the summand and terms in the series. In addition to its intrinsic value, this result has a specific application in calculating the response of the atoms to laser stimulation in the Strong Field Approximation.

]]>Axioms doi: 10.3390/axioms13030202

Authors: Ahmed Bakhet Shahid Hussain Mohamed Niyaz Mohammed Zakarya Ghada AlNemer

In this paper, we explore a study focused on a two-variable extension of matrix Bessel polynomials. We initiate the discussion by introducing the matrix Bessel polynomials involving two variables and derive specific differential formulas and recurrence relations associated with them. Additionally, we present a segment detailing integral formulas for the extended matrix Bessel polynomials. Lastly, we introduce the Laplace&ndash;Carson transform for the two-variable matrix Bessel polynomial analogue.

]]>Axioms doi: 10.3390/axioms13030201

Authors: Lazhar Bougoffa Smail Bougouffa Ammar Khanfer

This article provides a detailed exploration of the SIR epidemic model, starting with its meticulous formulation. The study employs a novel approach called the upper and lower bounds technique to approximate the solution to the SIR model, providing insights into the dynamic interplay between susceptible S, infected I, and recovered R populations. A new parametric solution to this model has been presented. Applying the Adomian decomposition method (ADM) allows for the attaining of highly accurate approximate solutions in the context of the SIR epidemic model. To validate the accuracy and robustness of the proposed approach, a numerical exploration is conducted, considering a diverse range of experimental parameters. This numerical analysis provides valuable insights into the sensitivity and responsiveness of the SIR epidemic model under varying conditions, contributing to the broader understanding of infectious disease dynamics. The interplay between theoretical formulation and numerical exploration establishes a comprehensive framework for studying the SIR model, with implications for refining our ability to predict and manage the spread of infectious diseases.

]]>Axioms doi: 10.3390/axioms13030200

Authors: Xinya Li Yan Sun Jinfeng Qi Danzhu Wang

This study investigates a green multimodal routing problem with soft time window. The objective of routing is to minimize the total costs of accomplishing the multimodal transportation of a batch of goods. To improve the feasibility of optimization, this study formulates the routing problem in an uncertain environment where the capacities and carbon emission factors of the travel process and the transfer process in the multimodal network are considered fuzzy. Taking triangular fuzzy numbers to describe the uncertainty, this study proposes a fuzzy nonlinear programming model to deal with the specific routing problem. To make the problem solvable, this study adopts the fuzzy chance-constrained programming approach based on the possibility measure to remove the fuzziness of the proposed model. Furthermore, we use linear inequality constraints to reformulate the nonlinear equality constraints represented by the continuous piecewise linear functions and realize the linearization of the nonlinear programming model to improve the computational efficiency of problem solving. After model processing, we can utilize mathematical programming software to run exact solution algorithms to solve the specific routing problem. A numerical experiment is given to show the feasibility of the proposed model. The sensitivity analysis of the numerical experiment further clarifies how improving the confidence level of the chance constraints to enhance the possibility that the multimodal route planned in advance satisfies the real-time capacity constraint in the actual transportation, i.e., the reliability of the routing, increases both the total costs and carbon emissions of the route. The numerical experiment also finds that charging carbon emissions is not absolutely effective in emission reduction. In this condition, bi-objective analysis indicates the conflicting relationship between lowering transportation activity costs and reducing carbon emissions in routing optimization. The sensitivity of the Pareto solutions concerning the confidence level reveals that reliability, economy, and environmental sustainability are in conflict with each other. Based on the findings of this study, the customer and the multimodal transport operator can organize efficient multimodal transportation, balancing the above objectives using the proposed model.

]]>Axioms doi: 10.3390/axioms13030199

Authors: Jong Il Baek S. E. Abbas Kul Hur Ismail Ibedou

Based on equivalence relation R on X, equivalence class [x] of a point and equivalence class [A] of a subset represent the neighborhoods of x and A, respectively. These neighborhoods play the main role in defining separation axioms, metric spaces, proximity relations and uniformity structures on an approximation space (X,R) depending on the lower approximation and the upper approximation of rough sets. The properties and the possible implications of these definitions are studied. The generated approximation topology &tau;R on X is equivalent to the generated topologies associated with metric d, proximity &delta; and uniformity U on X. Separated metric spaces, separated proximity spaces and separated uniform spaces are defined and it is proven that both are associating exactly discrete topology &tau;R on X.

]]>Axioms doi: 10.3390/axioms13030198

Authors: Kuen-Suan Chen Tsung-Hua Hsieh Chia-Pao Chang Kai-Chao Yao Tsun-Hung Huang

The Performance Evaluation Matrix (PEM) is an excellent decision-making tool for assessment and resource management. Satisfaction Index and Importance Index are two important evaluation indicators of construction and PEM. Managers can decide whether the service item needs to be improved based on the Satisfaction Index of the service item. When resources are limited, managers can determine the priority of improving the service item based on the Importance Index. In order to avoid the risk of misjudgment caused by sample errors and meet the needs of enterprises&rsquo; rapid decision-making, this study proposed a fuzzy test built on the confidence intervals of the above two key indicators to decide whether essential service items should be improved and determine the priority of improvement. Since the fuzzy test was relatively complex, this study further came up with fuzzy evaluation values and fuzzy evaluation critical values of service items following fuzzy testing rules. Besides, evaluation rules were established to facilitate industrial applications. This approach can be completed with any common word processing software, so it is relatively convenient in application and easy to manage. Finally, an application example was presented in this paper to explain the applicability of the proposed approach.

]]>Axioms doi: 10.3390/axioms13030197

Authors: Raquel Pinto Marcos Spreafico Carlos Vela

In general, the problem of building optimal convolutional codes under a certain criteria is hard, especially when size field restrictions are applied. In this paper, we confront the challenge of constructing an optimal 2D convolutional code when communicating over an erasure channel. We propose a general construction method for these codes. Specifically, we provide an optimal construction where the decoding method presented in the bibliography is considered.

]]>Axioms doi: 10.3390/axioms13030196

Authors: Nusrat Raza Mohammed Fadel Wei-Shih Du

In this paper, we introduce and study new features for 2-variable (p,q)-Hermite polynomials, such as the (p,q)-diffusion equation, (p,q)-differential formula and integral representations. In addition, we establish some summation models and their (p,q)-derivatives. Certain parting remarks and nontrivial examples are also provided.

]]>Axioms doi: 10.3390/axioms13030195

Authors: Mohammed Mohammed Fortuné Massamba Ion Mihai Abd Elmotaleb A. M. A. Elamin M. Saif Aldien

In the present article, we study submanifolds tangent to the Reeb vector field in trans-Sasakian manifolds. We prove Chen&rsquo;s first inequality and the Chen&ndash;Ricci inequality, respectively, for such submanifolds in trans-Sasakian manifolds which admit a semi-symmetric non-metric connection. Moreover, a generalized Euler inequality for special contact slant submanifolds in trans-Sasakian manifolds endowed with a semi-symmetric non-metric connection is obtained.

]]>Axioms doi: 10.3390/axioms13030194

Authors: Wantao Ning Hao Li

For S&sube;V(G),&kappa;G(S) denotes the maximum number k of edge disjoint trees T1,T2,&hellip;,Tk in G, such that V(Ti)&cap;V(Tj)=S for any i,j&isin;{1,2,&hellip;,k} and i&ne;j. For an integer 2&le;r&le;|V(G)|, the generalized r-connectivity of G is defined as &kappa;r(G)=min{&kappa;G(S)|S&sube;V(G)and|S|=r}. In fact, &kappa;2(G) is the traditional connectivity of G. Hence, the generalized r-connectivity is an extension of traditional connectivity. The exchanged folded hypercube EFH(s,t), in which s&ge;1 and t&ge;1 are positive integers, is a variant of the hypercube. In this paper, we find that &kappa;3(EFH(s,t))=s+1 with 3&le;s&le;t.

]]>Axioms doi: 10.3390/axioms13030193

Authors: María Ángeles Moreno-Frías José Carlos Rosales

In this work, we will introduce the concept of ratio-covariety, as a family R of numerical semigroups that has a minimum, denoted by min(R), is closed under intersection, and if S&isin;R and S&ne;min(R), then S\{r(S)}&isin;R, where r(S) denotes the ratio of S. The notion of ratio-covariety will allow us to: (1) describe an algorithmic procedure to compute R; (2) prove the existence of the smallest element of R that contains a set of positive integers; and (3) talk about the smallest ratio-covariety that contains a finite set of numerical semigroups. In addition, in this paper we will apply the previous results to the study of the ratio-covariety R(F,m)={S&#8739;S&nbsp;is&nbsp;a&nbsp;numerical&nbsp;semigroup&nbsp;with&nbsp;Frobenius&nbsp;number&nbsp;F&nbsp;and&nbsp;multiplicitym}.

]]>Axioms doi: 10.3390/axioms13030192

Authors: Roger Arnau Jose M. Calabuig Álvaro González Enrique A. Sánchez Pérez

Index spaces serve as valuable metric models for studying properties relevant to various applications, such as social science or economics. These properties are represented by real Lipschitz functions that describe the degree of association with each element within the underlying metric space. After determining the index value within a given sample subset, the classic McShane and Whitney formulas allow a Lipschitz regression procedure to be performed to extend the index values over the entire metric space. To improve the adaptability of the metric model to specific scenarios, this paper introduces the concept of a composition metric, which involves composing a metric with an increasing, positive and subadditive function &#981;. The results presented here extend well-established results for Lipschitz indices on metric spaces to composition metrics. In addition, we establish the corresponding approximation properties that facilitate the use of this functional structure. To illustrate the power and simplicity of this mathematical framework, we provide a concrete application involving the modeling of livability indices in North American cities.

]]>Axioms doi: 10.3390/axioms13030191

Authors: Huiling Niu Abdoulaye Ali Youssouf Binhua Feng

In this paper, we consider blow-up solutions for the fourth-order nonlinear Schr&ouml;dinger equation with mixed dispersions. We study the dynamical properties of blow-up solutions for this equation, including the H&#729;&gamma;c-concentration and limiting profiles, which extend and improve the existing results in the literature.

]]>Axioms doi: 10.3390/axioms13030190

Authors: Yang Li Yingmei Xu Qianhai Xu Yu Zhang

New high-order weak schemes are proposed and simplified to solve stochastic differential equations with Markovian switching driven by pure jumps (PJ-SDEwMs). Using Malliavin calculus theory, it is rigorously proven that the new numerical schemes can achieve a high-order convergence rate. Some numerical experiments are provided to show the efficiency and accuracy.

]]>Axioms doi: 10.3390/axioms13030189

Authors: Danica Fatić Dragan Djurčić Ljubiša D. R. Kočinac

This paper deals with translational regular and rapid variations. By using a new method of proving the Galambos&ndash;Bojani&#263;-Seneta type theorems, we prove two theorems of this type for translationally regularly varying and translationally rapidly varying functions and sequences, important objects in the asymptotic analysis of divergent processes. Also, we introduce and study the index functions for translationally regularly varying functions and sequences. For example, we prove that the index function of a translationally regularly varying function is also in the same class of functions.

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Authors: Zhongtian Dong Marçal Comajoan Cara Gopal Ramesh Dahale Roy T. Forestano Sergei Gleyzer Daniel Justice Kyoungchul Kong Tom Magorsch Konstantin T. Matchev Katia Matcheva Eyup B. Unlu

This paper presents a comparative analysis of the performance of Equivariant Quantum Neural Networks (EQNNs) and Quantum Neural Networks (QNNs), juxtaposed against their classical counterparts: Equivariant Neural Networks (ENNs) and Deep Neural Networks (DNNs). We evaluate the performance of each network with three two-dimensional toy examples for a binary classification task, focusing on model complexity (measured by the number of parameters) and the size of the training dataset. Our results show that the Z2&times;Z2 EQNN and the QNN provide superior performance for smaller parameter sets and modest training data samples.

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Authors: Eyup B. Unlu Marçal Comajoan Cara Gopal Ramesh Dahale Zhongtian Dong Roy T. Forestano Sergei Gleyzer Daniel Justice Kyoungchul Kong Tom Magorsch Konstantin T. Matchev Katia Matcheva

Models based on vision transformer architectures are considered state-of-the-art when it comes to image classification tasks. However, they require extensive computational resources both for training and deployment. The problem is exacerbated as the amount and complexity of the data increases. Quantum-based vision transformer models could potentially alleviate this issue by reducing the training and operating time while maintaining the same predictive power. Although current quantum computers are not yet able to perform high-dimensional tasks, they do offer one of the most efficient solutions for the future. In this work, we construct several variations of a quantum hybrid vision transformer for a classification problem in high-energy physics (distinguishing photons and electrons in the electromagnetic calorimeter). We test them against classical vision transformer architectures. Our findings indicate that the hybrid models can achieve comparable performance to their classical analogs with a similar number of parameters.

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Authors: Nanbin Cao Yue Zhang Xia Liu

This paper studies a particular type of planar Filippov system that consists of two discontinuity boundaries separating the phase plane into three disjoint regions with different dynamics. This type of system has wide applications in various subjects. As an illustration, a plant disease model and an avian-only model are presented, and their bifurcation scenarios are investigated. By means of the regularization approach, the blowing up method, and the singular perturbation theory, we provide a different way to analyze the dynamics of this type of Filippov system. In particular, the boundary equilibrium bifurcations of such systems are studied. As a consequence, the nonsmooth fold bifurcation becomes a saddle-node bifurcation, while the persistence bifurcation disappears after regularization.

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Authors: Sydney Day Zhidong Xiao Ehtzaz Chaudhry Matthew Hooker Xiaoqiang Zhu Jian Chang Andrés Iglesias Lihua You Jianjun Zhang

How to create realistic shapes by interpolating two known shapes for facial blendshapes has not been investigated in the existing literature. In this paper, we propose a physics-based mathematical model and its analytical solutions to obtain more realistic facial shape changes. To this end, we first introduce the internal force of elastic beam bending into the equation of motion and integrate it with the constraints of two known shapes to develop the physics-based mathematical model represented with dynamic partial differential equations (PDEs). Second, we propose a unified mathematical expression of the external force represented with linear and various nonlinear time-dependent Fourier series, introduce it into the mathematical model to create linear and various nonlinear dynamic deformations of the curves defining a human face model, and derive analytical solutions of the mathematical model. Third, we evaluate the realism of the obtained analytical solutions in interpolating two known shapes to create new shape changes by comparing the shape changes calculated with the obtained analytical solutions and geometric linear interpolation to the ground-truth shape changes and conclude that among linear and various nonlinear PDE-based analytical solutions named as linear, quadratic, and cubic PDE-based interpolation, quadratic PDE-based interpolation creates the most realistic shape changes, which are more realistic than those obtained with the geometric linear interpolation. Finally, we use the quadratic PDE-based interpolation to develop a facial blendshape method and demonstrate that the proposed approach is more efficient than numerical physics-based facial blendshapes.

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Authors: Jorge De Andrés-Sánchez

A highly relevant topic in the actuarial literature is so-called &ldquo;claim reserving&rdquo; or &ldquo;loss reserving&rdquo;, which involves estimating reserves to be provisioned for pending claims, as they can be deferred over various periods. This explains the proliferation of methods that aim to estimate these reserves and their variability. Regression methods are widely used in this setting. If we model error terms as random variables, the variability of provisions can consequently be modelled stochastically. The use of fuzzy regression methods also allows modelling uncertainty for reserve values using tools from the theory of fuzzy subsets. This study follows this second approach and proposes projecting claim reserves using a generalization of fuzzy numbers (FNs), so-called intuitionistic fuzzy numbers (IFNs), through the use of intuitionistic fuzzy regression. While FNs allow epistemic uncertainty to be considered in variable estimation, IFNs add bipolarity to the analysis by incorporating both positive and negative information regarding actuarial variables. Our analysis is grounded in the ANOVA two-way framework, which is adapted to the use of intuitionistic regression. Similarly, we compare our results with those obtained using deterministic and stochastic chain-ladder methods and those obtained using two-way statistical ANOVA.

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Authors: Yanlin Li Meraj Ali Khan MD Aquib Ibrahim Al-Dayel Maged Zakaria Youssef

In this article, we study isotropic submanifolds in locally metallic product space forms. Firstly, we establish the Chen&ndash;Ricci inequality for such submanifolds and determine the conditions under which the inequality becomes equality. Additionally, we explore the minimality of Lagrangian submanifolds in locally metallic product space forms, and we apply the result to create a classification theorem for isotropic submanifolds whose mean curvature is constant. More specifically, we have demonstrated that the submanifolds are either a product of two Einstein manifolds with Einstein constants, or they are isometric to a totally geodesic submanifold. To support our findings, we provide several examples.

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Authors: Xue Zhang Jing Zhang

In this thesis, we research quasilinear Schr&ouml;dinger system as follows in which 3&lt;N&isin;R, 2&lt;p&lt;N, 2&lt;q&lt;N, V1(x),V2(x) are continuous functions, k,&iota; are parameters with k,&iota;&gt;0, and nonlinear terms f,h&isin;C(RN&times;R2,R). We find a nontrivial solution (u,v) for all &iota;&gt;&iota;1(k) by means of the mountain-pass theorem and change of variable theorem. Our main novelty of the thesis is that we extend &Delta; to &Delta;p and &Delta;q to find the existence of a nontrivial solution.

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Authors: Oktay Duman Biancamaria Della Vecchia Esra Erkus-Duman

In the present work, in order to approximate integrable vector-valued functions, we study the Kantorovich version of vector-valued Shepard operators. We also display some applications supporting our results by using parametric plots of a surface and a space curve. Finally, we also investigate how nonnegative regular (matrix) summability methods affect the approximation.

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Authors: Talip Can Termen Ozgur Ege

In this work, the notion of digital fiber homotopy is defined and its properties are given. We present some new results on digital fibrations. Moreover, we introduce digital h-fibrations. We prove some of the properties of these digital h-fibrations. We show that a digital fibration and a digital map p are fiber homotopic equivalent if and only if p is a digital h-fibration. Finally, we explore a relation between digital fibrations and digital h-fibrations.

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Authors: Xiaoqing Hong Weiping Zhou Xiao Wang Min Li

Supersaturated designs (SSDs) refer to those designs in which the run size is much smaller than the main effects to be estimated. They are commonly used to identify a few, but critical, active factors from a large set of potentially active ones, keeping the cost as low as possible. In this regard, the development of new construction and analysis methods has recently seen a rapid increase. In this paper, we provide some methods to construct equi- and mixed-level E(f&nbsp;NOD) optimal SSDs with a large number of inert factors using the substitution method. The proposed methods are easy to implement, and many new SSDs can then be constructed from them. We also study a variable selection method based on the screening-selection network (SSnet) method for regression problems. A real example is analyzed to illustrate that it is able to effectively identify active factors. Eight different analysis methods are used to analyze the data generated from the proposed designs. Three scenarios with different setups of parameters are designed, and the performances of each method are illustrated by extensive simulation studies. Among all these methods, SSnet produced the most satisfactory results according to power.

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Authors: Ilaria Cacciari Anedio Ranfagni

Experimental results of delay-time measurements in the transfer of modulation between microwave beams, as reported in previous articles, were interpreted on a competition (interference) between two waves, one of which is modulated and the other is a continuous wave (c.w.). The creation of one of these waves was attributed to a saddle-point contribution, while the other was attributed to pole singularities. In this paper, such an assumption is justified by a quantitative field-amplitude analysis in order to make the modeling plausible. In particular, two ways of calculating field amplitudes are considered. These lead to results that are quantitatively markedly different, although qualitatively similar.

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Authors: Abel Cabrera-Martínez Juan Manuel Rueda-Vázquez Jaime Segarra

Let G be a nontrivial connected graph. For a set D&sube;V(G), we define D&macr;=V(G)&#8726;D. The set D is a total outer-independent dominating set of G if |N(v)&cap;D|&ge;1 for every vertex v&isin;V(G) and D&macr; is an independent set of G. Moreover, D is a double outer-independent dominating set of G if |N[v]&cap;D|&ge;2 for every vertex v&isin;V(G) and D&macr; is an independent set of G. In addition, D is a 2-outer-independent dominating set of G if |N(v)&cap;D|&ge;2 for every vertex v&isin;D&macr; and D&macr; is an independent set of G. The total, double or 2-outer-independent domination number of G, denoted by &gamma;toi(G), &gamma;&times;2oi(G) or &gamma;2oi(G), is the minimum cardinality among all total, double or 2-outer-independent dominating sets of G, respectively. In this paper, we first show that for any cactus graph G of order n(G)&ge;4 with k(G) cycles, &gamma;2oi(G)&le;n(G)+l(G)2+k(G), &gamma;toi(G)&le;2n(G)&minus;l(G)+s(G)3+k(G) and &gamma;&times;2oi(G)&le;2n(G)+l(G)+s(G)3+k(G), where l(G) and s(G) represent the number of leaves and the number of support vertices of G, respectively. These previous bounds extend three known results given for trees. In addition, we characterize the trees T with &gamma;&times;2oi(T)=&gamma;toi(T). Moreover, we show that &gamma;2oi(T)&ge;n(T)+l(T)&minus;s(T)+12 for any tree T with n(T)&ge;3. Finally, we give a constructive characterization of the trees T that satisfy the equality above.

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Authors: Assma Leulmi

In this work, we integrate some new approximate functions using the logarithmic penalty method to solve nonlinear optimization problems. Firstly, we determine the direction by Newton&rsquo;s method. Then, we establish an efficient algorithm to compute the displacement step according to the direction. Finally, we illustrate the superior performance of our new approximate function with respect to the line search one through a numerical experiment on numerous collections of test problems.

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Authors: Liangyu Wang Hongyu Li

Monge&ndash;Amp&egrave;re equations have important research significance in many fields such as geometry, convex geometry and mathematical physics. In this paper, under some superlinear and sublinear conditions, the existence of nontrivial solutions for a system arising from Monge&ndash;Amp&egrave;re equations with two parameters is investigated based on the Guo&ndash;Krasnosel&rsquo;skii fixed point theorem. In the end, two examples are given to illustrate our theoretical results.

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Authors: Najla Altwaijry Silvestru Sever Dragomir Kais Feki

The main focus of this paper is on establishing inequalities for the norm and numerical radius of various operators applied to a power series with the complex coefficients h(&lambda;)=&sum;k=0&infin;ak&lambda;k and its modified version ha(&lambda;)=&sum;k=0&infin;|ak|&lambda;k. The convergence of h(&lambda;) is assumed on the open disk D(0,R), where R is the radius of convergence. Additionally, we explore some operator inequalities related to these concepts. The findings contribute to our understanding of operator behavior in bounded operator spaces and offer insights into norm and numerical radius inequalities.

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Authors: Ayed. R. A. Alanzi Raouf Fakhfakh Fatimah Alshahrani

In this article, we provide some new limiting laws related to the free multiplicative law of large numbers and involving free and Boolean additive convolutions. Some examples of these limiting laws are presented within the framework of non-commutative probability theory.

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Authors: Najla Altwaijry Silvestru Sever Dragomir Kais Feki

Consider the power series with complex coefficients h(z)=&sum;k=0&infin;akzk and its modified version ha(z)=&sum;k=0&infin;|ak|zk. In this article, we explore the application of certain H&ouml;lder-type inequalities for deriving various inequalities for operators acting on the aforementioned power series. We establish these inequalities under the assumption of the convergence of h(z) on the open disk D(0,&rho;), where &rho; denotes the radius of convergence. Additionally, we investigate the norm and numerical radius inequalities associated with these concepts.

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Authors: Yuting Xu Qianfan Liu Yao Chen Yang Lei Minghua Yang

In this article, we study the Cauchy problem of the chemotaxis-Navier&ndash;Stokes system with the consumption and production of chemosignals with a logistic source. The parameters &chi;&ne;0,&nbsp;&xi;&ne;0,&nbsp;&lambda;&gt;0 and &mu;&gt;0. The system is a model that involves double chemosignals; one is an attractant consumed by the cells themselves, and the other is an attractant or a repellent produced by the cells themselves. We prove the global-in-time existence and uniqueness of the weak solution to the system for a large class of initial data on the whole space R2.

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Authors: Taiyong Song Zexian Liu

The subspace minimization conjugate gradient (SMCG) methods proposed by Yuan and Store are efficient iterative methods for unconstrained optimization, where the search directions are generated by minimizing the quadratic approximate models of the objective function at the current iterative point. Although the SMCG methods have illustrated excellent numerical performance, they are only used to solve unconstrained optimization problems at present. In this paper, we extend the SMCG methods and present an efficient SMCG method for solving nonlinear monotone equations with convex constraints by combining it with the projection technique, where the search direction is sufficiently descent.Under mild conditions, we establish the global convergence and R-linear convergence rate of the proposed method. The numerical experiment indicates that the proposed method is very promising.

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Authors: Li Zhang Yang Liu

A class of fractional viscoelastic Kirchhoff equations involving two nonlinear source terms of different signs are studied. Under suitable assumptions on the exponents of nonlinear source terms and the memory kernel, the existence of global solutions in an appropriate functional space is established by a combination of the theory of potential wells and the Galerkin approximations. Furthermore, the asymptotic behavior of global solutions is obtained by a combination of the theory of potential wells and the perturbed energy method.

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Authors: Inna Kal’chuk

In this editorial, we present &ldquo;Theory of Functions and Applications&rdquo;, a Special Issue of Axioms [...]

]]>Axioms doi: 10.3390/axioms13030167

Authors: Mona Aljoufi

The homotopy perturbation method (HPM) is one of the recent fundamental methods for solving differential equations. However, checking the accuracy of this method has been ignored by some authors in the literature. This paper reanalyzes the nonlinear system of ordinary differential equations (ODEs) describing the SIR epidemic model, which has been solved in the literature utilizing the HPM. The main objective of this work is to obtain a highly accurate analytical solution for this model via a direct technique. The proposed technique is mainly based on reducing the given system to a single nonlinear ODE that can be easily solved. Numerical results are conducted to compare our approach with the previous HPM, where the Runge&ndash;Kutta numerical method is chosen as a reference solution. The obtained results reveal that the current technique exhibits better accuracy over HPM in the literature. Moreover, some physical properties are introduced and discussed in detail regarding the influence of the transmission rate on the behavior of the SIR model.

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Authors: Tingzeng Wu Xueji Jiu

Let G be a graph with n vertices and m edges. A(G) and I denote, respectively, the adjacency matrix of G and an n by n identity matrix. For a graph G, the permanent of matrix (I+A(G)) is called the permanental sum of G. In this paper, we give a relation between the Hosoya index and the permanental sum of G. This implies that the computational complexity of the permanental sum is NP-complete. Furthermore, we characterize the graphs with the minimum permanental sum among all graphs of n vertices and m edges, where n+3&le;m&le;2n&minus;3.

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Authors: Richard Olatokunbo Akinola Ali Shokri Joshua Sunday Daniela Marian Oyindamola D. Akinlabi

In this paper, we compare the performances of two Butcher-based block hybrid methods for the numerical integration of initial value problems. We compare the condition numbers of the linear system of equations arising from both methods and the absolute errors of the solution obtained. The results of the numerical experiments illustrate that the better conditioned method outperformed its less conditioned counterpart based on the absolute errors. In addition, after applying our method on some examples, it was discovered that the absolute errors in this work were better than those of a recent study in the literature. Hence, we recommend this method for the numerical solution of stiff and non-stiff initial value problems.

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