Axioms, Volume 13, Issue 5

The propagation of light beams in photovoltaic pyroelectric photorefractive crystals is modelled by a specific generalization of the nonlinear Schrödinger equation (GNLSE). We use a variational approximation (VA) to predict the propagation of so...

This paper concerns a fractional Kirchhoff equation with critical nonlinearities and a negative nonlocal term. In the case of high perturbations (large values of $\alpha$, i.e., the parameter of a subcritical nonlinearity), existence results are obtained by...

This paper is devoted to studying a type of elliptic equation that contains a varying nonlocal term. We provide a detailed analysis of the existence, non-existence, and blow-up behavior of $L^2$-norm solutions for the related equation when the potential...

Respiratory conditions have been a focal point in recent medical studies. Early detection and timely treatment are crucial factors in improving patient outcomes for any medical condition. Traditionally, doctors diagnose respiratory conditions through...

In this paper, we investigate the problem of the exponential stability of a stationary solution for a hyperbolic system with nonlocal characteristic velocities and measurement error. The formulation of the initial boundary value problem of boundary c...

In this paper, we investigate static spherically symmetric teleparallel $F\left(T\right)$ gravity containing a perfect isotropic fluid. We first write the field equations and proceed to find new teleparallel $F\left(T\right)$ solutions for perfect isotropic and linear fluids....

In this paper, we determine the variation formula for the first eigenvalue of $(p,q)$-biharmonic system on a closed Riemannian manifold. Several monotonic quantities are also derived.

The linearization of nonlinear differential equations represents a robust approach to solution derivation, typically achieved through Lie symmetry analysis. This study adopts a geometric methodology grounded in the Eisenhart lift, revealing transform...

Graph polynomials is one of the important research directions in mathematical chemistry. The coefficients of some graph polynomials, such as matching polynomial and permanental polynomial, are related to structural properties of graphs. The Hosoya in...

In this paper, the sampling and reconstruction problems in function subspaces of $L^p\left({\mathbb{R}}^n\right)$ associated with the multi-dimensional special affine Fourier transform (SAFT) are discussed. First, we give the definition of the multi-dimensional SAFT and study...

Impressed with the very recent developments of noncoercive complementarity problems and the use of recession sets in complementarity problems, here, we discuss mixed generalized complementarity problems in Hausdorff topological vector spaces. We used...

In this editorial, we introduce “Mathematical Methods in Applied Sciences”, a Special Issue of Axioms comprising 17 articles [...]

This paper examines the tractability of multivariate approximation problems under the normalized error criterion for a zero-mean Gaussian measure in an average-case setting. The Gaussian measure is associated with a covariance kernel, which is repres...

Considering the solutions of a class of noncooperative Kirchhoff-type $p\left(x\right)$-Laplacian elliptic systems with nonlinear boundary conditions, we derive a sequence of solutions utilizing both the variational method and limit index theory under certain und...

Hypercomplex numbers, which are multi-dimensional extensions of complex numbers, have been proven beneficial in the development of advanced signal processing algorithms, including multi-dimensional filter design, linear regression and classification....

We introduce a hybrid quantum-classical vision transformer architecture, notable for its integration of variational quantum circuits within both the attention mechanism and the multi-layer perceptrons. The research addresses the critical challenge of...

This paper investigates a novel $C^0$ nonconforming virtual element method (VEM) for solving the Kirchhoff plate obstacle problem, which is described by a fourth-order variational inequality (VI) of the first kind. In our study, we distinguish our appro...

A quasi-configuration is a point–line incidence structure in which each point is incident with at least three lines and each line is incident with at least three points. We investigate derived quasi-configurations that arise both by duality and...

In this paper, we prove the stability of the Brunn–Minkowski inequality for multiple convex bodies in terms of the concept of relative asymmetry. Using these stability results and the relationship of the compact support of functions, we establi...

In this article, we consider a make-to-stock queueing system with retrial customers. Upon their arrival, customers make a decision to either join the system or not based on a reward–cost function. If customers join the retrial queue, they becom...

Throughout this study, we discuss the subordinate Pompeiu–Hausdorff metric (SPHM) in subordinate semimetric spaces. Moreover, we present a well-behaved quasi-contraction (WBQC) to solve quasi-contraction (QC) problems in subordinate semimetric...

In this paper, the authors briefly review some closed-form formulas of the Gauss hypergeometric function at specific arguments, alternatively prove four of these formulas, newly extend a closed-form formula of the Gauss hypergeometric function at som...

We consider a history-dependent variational inequality in a real Hilbert space, for which we recall an existence and uniqueness result. We associate this inequality with a gap function, together with two additional problems: a nonlinear equation and...

This study addresses the problem of parameter estimation in spatial autoregressive models with missing data and measurement errors in covariates. Specifically, a corrected likelihood estimation approach is employed to rectify the bias in the log-maxi...

Rota–Baxter operators (RBOs) play a substantial role in many subfields of mathematics, especially in mathematical physics. In the article, RBOs on Zinbiel algebras (ZAs) and their sub-adjacent algebras are first investigated. Moreover, all the...

This manuscript describes the computational process to calculate an airplane path and display it in a 2D and 3D coordinate system on a computer screen. The airplane movement is calculated as a function of its dynamic’s conditions according to p...

The aim of this paper is to prove a theorem for holomorphic twisted quiver bundles over a special non-compact Gauduchon manifold, connecting the existence of $(\sigma ,\tau )$-Hermite–Yang–Mills metric in differential geometry and the analy...

The current study aims to utilize the homotopy perturbation method (HPM) to solve nonlinear dynamical models, with a particular focus on models related to predicting and controlling pandemics, such as the SIR model. Specifically, we apply this method...

This Special Issue of the scientific journal Axioms, entitled “Recent Advances in Fractional Calculus”, is dedicated to one of the most dynamic areas of mathematical sciences today [...]

In this paper, an SEAI epidemic model with asymptomatic infection is studied under the background of mass transmission of COVID-19. First, we use the next-generation matrix method to obtain the basic reproductive number $R_0$ and calculate the equilibri...

In this paper, we expand the theory of semi-vector spaces and semi-algebras, both over the semi-field of nonnegative real numbers ${\mathbb{R}}_0^{+}$. More precisely, we prove several new results concerning these theories. We introduce to the literature the concept...

Computational statistics is a critical skill for professionals in fields such as data science, statistics, and related disciplines. One essential aspect of computational statistics is the ability to simulate random variables from specified probabilit...

In the present paper, we address the following general question in the framework of classical first-order logic. Assume that a certain mathematical principle can be formalized in a first-order language by a set E of conditional formulas of the form $\&$...

Differentiation matrices are an important tool in the implementation of the spectral collocation method to solve various types of problems involving differential operators. Fractional differentiation of Jacobi orthogonal polynomials can be expressed...

The transformation formula under the action of a general linear fractional transformation for a generalized Dedekind eta function has been the subject of intensive study since the works of Rademacher, Dieter, Meyer, and Schoenberg et al. However, the...

Measurement error is common in many statistical problems and has received considerable attention in various regression contexts. In this study, we consider the random coefficient autoregressive model with measurement error possibly present in covaria...

In this paper, we focus on the asymptotic stability of the trajectories governed by the differential inequalities with mixed delays using the fixed-point theorem. It is interesting that the Halanay inequality is a special case of the differential ine...

In this paper, the tempered $\mathsf{\Psi }$–Riemann–Liouville fractional derivative and the tempered $\mathsf{\Psi }$–Caputo fractional derivative of order $n-1<\alpha <n\in \mathbb{N}$ are introduced for $C^{n-1}$–functions. A nonlinear versi...

We present a two-country model (North and South) that describes the phenomenon of offshoring and reshoring. The model is a continuous time-controlled Markov chain with binary states. The main trade-off involves production costs and transaction costs...

Let F be a field of characteristic, not 2 or 3. The first Tits construction is a well-known tripling process to construct separable cubic Jordan algebras, especially Albert algebras. We generalize the first Tits construction by choosing the scalar em...

A new methodology for solving the fuzzy multiobjective optimization problems is proposed in this paper by considering the fusion of cooperative game theory and genetic algorithm. The original fuzzy multiobjective optimization problem needs to be tran...

With the rapid development of the economy, data have become a new production factor and strategic asset, enhancing efficiency and energy for technological innovation and industrial upgrading in enterprises. The evaluation of enterprise digital asset...

The main aim of this article is to derive certain continuity and boundedness properties of the coupled fractional Fourier transform on Schwartz-like spaces. We extend the domain of the coupled fractional Fourier transform to the space of tempered dis...

A novel regression method is introduced and studied. The procedure weights squared residuals based on their magnitude. Unlike the classic least squares which treats every squared residual as equally important, the new procedure exponentially down-wei...

In this paper, we study the following non-local problem in fractional Orlicz–Sobolev spaces: ${(-{\Delta }_{\Phi })}^{s}u+V\left(x\right)a(|u|)u=f(x,u), x\in {\mathbb{R}}^N$, where ${(-{\Delta }_{\Phi })}^s(s\in (0,1))$ denotes the non-local and maybe non-homogeneous...

We study the properties of the constructive linear programming problems. The parameters of linear functions in such problems are constructive real numbers. Solving such a problem involves finding the optimal plan with the constructive real number com...

Recently, Milles and Hammami presented and studied the concept of a neutrosophic topology generated by a neutrosophic relation. As a continuation in the same direction, this paper studies the concepts of neutrosophic ideals and neutrosophic filters o...

In algebra, the sedenions, an extension of the octonion system, form a 16-dimensional noncommutative and nonassociative algebra over the real numbers. It can be expressed as two octonions, and a function and differential operator can be defined to tr...

The main objective of this article is to classify all finite singleton local rings, which are associative rings characterized by a unique maximal ideal and a distinguished basis consisting of a single element. These rings are associated with four pos...

In the present article, we build the excitedcoherent states associated with deformed $su(1,1)$ algebra (DSUA), called photon-added deformed Perelomov coherent states (PA-DPCSs). The constructed coherent states are obtained by using an alterationof the...