Axioms, Volume 12, Issue 10

The aim of this paper is to present and study nonlinear bivariate $C^1$ quadratic spline quasi-interpolants on uniform criss-cross triangulations for the approximation of piecewise smooth functions. Indeed, by using classical spline quasi-interpolants,...

In this paper, we study the optimality conditions for set optimization problems with set criterion. Firstly, we establish a few important properties of the Minkowski difference for sets. Then, we introduce the generalized second-order lower radial ep...

In the literature, it is usually assumed that Leibniz described proof for the Fundamental Theorem of Calculus (FTC) in 1693. However, did he really prove it? If the answer is no from today’s perspective, are there works in which Leibniz introdu...

In this work we show that if iterates of a nonexpansive self-mapping of a complete metric with a graph converge uniformly on a subset of the space, then this convergence is stable under the presence of small computational errors.

In this paper we investigate the solutions of the so-called $\overline{\alpha }$-Poisson equation in the complex plane. In particular, we will give sufficient conditions for Lipschitz continuity of such solutions. We also review some recently obtained resul...

In the explainable artificial intelligence (XAI) field, an algorithm or a tool can help people understand how a model makes a decision. And this can help to select important features to reduce computational costs to realize high-performance computing...

The space, ${Ƒ}_{cc}\left(\mathbb{R}\right)$, of all fuzzy intervals in $\mathbb{R}$ cannot form a vector space. However, the space ${Ƒ}_{cc}\left(\mathbb{R}\right)$ maintains a vector structure by treating the addition of fuzzy intervals as a vector addition and treating the scalar multiplication of fuz...

To quantitatively identify internal wire breakage damage in mining wire ropes, a wire rope internal wire breakage signal identification method is proposed. First, the whale optimization algorithm is used to find the optimal value of the variational m...

In this paper, we investigate a delayed matrix exponential and utilize it to derive a representation of solutions to a linear nonsingular delay problem with permutable matrices. To begin with, we present a novel definition of $\alpha$-exponential stab...

Several phenomena from natural sciences can be described by partial differential equations of Sobolev-type. On the other hand, it was shown that in many cases, the use of fractional derivatives provides a more realistic model than the use of standard...

This paper considers nonparametric regression estimation with errors in the variables. It is a standard assumption that the characteristic function of the covariate error does not vanish on the real line. This assumption is rather strong. In this pap...

The existence of at least three weak solutions to a discrete fractional boundary value problem containing a p-Laplacian operator and subject to perturbations is proved using variational methods. Some applications of the main results are presented. Th...

This paper calculates numerical solutions of an extended three-coupled Korteweg–de Vries system by the q-homotopy analysis transformation method (q-HATM), which is a hybrid of the Laplace transform and the q-homotopy analysis method. Multiple i...

In this paper, we have parameterized a timelike ($\mathcal{T}like$) circular surface ($\mathcal{CI}\mathit{surface}$) and have obtained its geometric properties, including striction curves, singularities, Gaussian and mean curvatures. Afterward, the situation for a $\mathcal{T}like$ roller coas...

In this paper, the idea of two transformations is first proposed and applied. Some new different sufficient conditions for the asymptotical stability of the exact solutions of nonlinear impulsive neutral delay differential equations (INDDEs) are obta...

The purpose of the present study is to propose an interval-valued type 2 fuzzy set (IT2FS)-based analytic hierarchy process (AHP) framework to unfold the critical challenging factors influencing the sustenance and growth of the Indian tea industry. T...

Let R be a commutative ring with identity, and $Z\left(R\right)$ be the set of zero-divisors of R. The weakly zero-divisor graph of R denoted by $W\Gamma \left(R\right)$ is an undirected (simple) graph with vertex set $Z{\left(R\right)}^{*}$, and two distinct vertices...

Agricultural product prices are subject to various uncertainties, including unpredictable weather conditions, pest infestations, and market fluctuations, which can significantly impact agricultural yields and productivity. Accurately assessing and un...

In the pursuance of engineering excellence and sustainable practices, the optimization of material selection processes plays a crucial role. Using Fermatean fuzzy aggregation Operators (AOs), this study introduces an innovative method for improving m...

Currently, two-component integrable nonlinear equations from the hierarchies of the vector nonlinear Schrodinger equation and the vector derivative nonlinear Schrödinger equation are being actively investigated. In this paper, we propose a new h...

The Burgers’ equation is solved using the explicit finite difference method (EFDM) and physics-informed neural networks (PINN). We compare our numerical results, obtained using the EFDM and PINN for three test problems with various initial cond...

To significantly reduce the amplitude of longitudinal vibrations of the beam in the vicinity of its natural frequencies, a fundamentally new method of damping vibrations is used. For this purpose, the beam surfaces are covered with layers of polarize...

The need to find the global minimum in multivariable functions is a critical problem in many fields of science and technology. Effectively solving this problem requires the creation of initial solution estimates, which are subsequently used by the op...

It is difficult to describe the hesitation and uncertainty of experts by single-valued information, and the differences in the importance of attributes are often ignored during the decision-making process. This paper introduces the probability and in...

The quantum-inspired genetic algorithm (QGA), which combines quantum mechanics concepts and GA to enhance search capability, has been popular and provides an efficient search mechanism. This paper proposes a modified QGA, called dynamic QGA (DQGA). T...

We shall present some more generalized and further refinements of reversed AM-GM operator inequalities for positive linear maps due to Xue’s and Ali’s publications.

Many phenomena can be described by random variables that follow asymmetrical distributions. In the context of regression, when the response variable Y follows such a distribution, it is preferable to estimate the response variable for predictor value...

Efficient truck flow is essential for the efficient operation of a factory and the distribution of its products. This study demonstrated methods to improve truck loading times and overall efficiency at a major sugar manufacturing facility in the Midd...

In this paper, we investigate the existence of positive solutions to a system of fractional differential equations that include the $(r_1,r_2,r_3)$-Laplacian operator, three-point boundary conditions, and various fractional derivatives. We use a combinati...

With the burgeoning growth of the internet, online evaluation systems have become increasingly pivotal in shaping consumer decision making. In this context, this study introduces an intuitionistic fuzzy TODIM (an acronym in Portuguese for interactive...

Recently, there has been a lot of interest in comparative life testing for items under jointly censored schemes for products from multiple production lines. The inverse Weibull distribution (IWD) is commonly used in life testing and reliability theor...

The multi-criteria group decision-making approach, rooted in fuzzy mathematics theory, is employed to address the globally significant issue of green construction in this paper. The construction industry is one of the most prominent contributors to c...

This manuscript is related to undertaking a mathematical model (susceptible, vaccinated, infected, and recovered) of rotavirus. Some qualitative results are established for the mentioned challenging childhood disease epidemic model of rotavirus as it...

In this study, the propagation of internal solitary waves in oceans at great depths was analyzed. Using multi-scale analysis and perturbation expansion, the basic equation is simplified to the classical Benjamin–Ono equation with variable coeff...

The clustering coefficient of a vertex v, of degree at least 2, in a graph $\Gamma$ is obtained using the formula $C\left(v\right)=\frac{2t\left(v\right)}{\mathrm{deg}\left(v\right)\left(\mathrm{deg}\right(v)-1)},$ where $t\left(v\right)$ denotes the number of triangles of the graph containing v as a vertex, and the clustering co...

To address the complexity of daily problems, soft set theory has emerged as a valuable tool, providing innovative mathematical techniques to manage vast amounts of data and ambiguity. The study of soft topology involves the investigation of various p...

Residuated basic logic ($\mathsf{RBL}$) is the logic of residuated basic algebras, which constitutes a conservative extension of basic propositional logic ($\mathsf{BPL}$). The basic implication is a residual of a non-associative binary operator in $\mathsf{RBL}$. The conservativity...

Fractional calculus has been a concept used to acquire new variants of some well-known integral inequalities. In this study, our primary goal is to develop majorized fractional Simpson’s type estimates by employing a differentiable function. Pr...

In this paper, we expose the ideas of point-wise statistical convergence, equi-statistical convergence and uniform statistical convergence in the sense of the deferred power-series method. We then propose a relation connecting them, which is followed...

The precise remaining useful life (RUL) prediction of turbofan engines benefits maintenance decisions. The training data quantity and quality are crucial for effective prediction modeling and accuracy improvement. However, the performance degradation...

This paper describes a problem of finding the contributions of multiple variables to a change in their function. Such a problem is well known in economics, for example, in the decomposition of a change in the mean price via the varying in time prices...

The inverse Weibull model is a simple and flexible model used for survival analysis, reliability theory, and other scientific fields. The main problem in this context is the estimation of the model parameters. In this study, a modified version of the...

In this paper, we introduce a new iterative method that combines the inertial subgradient extragradient method and the modified Mann method for solving the pseudomonotone variational inequality problem and the fixed point of quasi-Bregman nonexpansiv...

This paper is concerned with the lattice Boltzmann (LB) method for a class of time fractional partial differential equations (FPDEs) in the Caputo sense. By utilizing the properties of the Caputo derivative and discretization in time, FPDEs can be ap...

The current study employs the natural transform decomposition method (NTDM) to test fractional-order partial differential equations (FPDEs). The present technique is a mixture of the natural transform method and the Adomian decomposition method. For...

Let R be a commutative ring with identity $1\ne 0$ and let $Z{\left(R\right)}^{\prime }$ be the set of all non-unit and non-zero elements of ring R. ${\Gamma }^{\prime }\left(R\right)$ denotes the cozero-divisor graph of R and is an undirected graph with vertex set $Z{\left(R\right)}^{\prime }$, $w\notin z$...

By means of the weight functions, the idea of introduced parameters and the transfer formulas, two multidimensional Hilbert-type integral inequalities with the general nonhomogeneous kernel as $H(||x|{|}_{\alpha }^{{\lambda }_1}||y|{|}_{\beta }^{{\lambda }_2})$$({\lambda }_1,{\mathrm{\&l}}_{}$...

We consider a finite horizon multi-model linear-quadratic optimal control problem. For this problem, we treat the case where the problem’s functional does not contain a control function. The latter means that the problem under consideration is...

To improve the accuracy of color image completion with missing entries, we present a recovery method based on generalized higher-order scalars. We extend the traditional second-order matrix model to a more comprehensive higher-order matrix equivalent...

We introduce and study a new pseudo-type $\kappa$-fold symmetric bi-univalent function class that meets certain subordination conditions in this article. For functions in the newly formed class, the initial coefficient bounds are obtained. For members...