Axioms, Volume 14, Issue 5

A secured communications system is a structure or infrastructure that is intended to ensure the confidentiality, integrity, and authenticity of data being exchanged between entities. Such systems use various security technologies to guarantee that co...

We present a new framework to study the stability of semantic projections based on word embeddings. Roughly speaking, semantic projections are indices taking values in the interval $[0,1]$ that measure how terms share contextual meaning with the words...

In this study, the Gumbel distribution is utilized to construct exact analytical representations for two pivotal measures in financial risk evaluation: Value at Risk (VaR) and Conditional Value at Risk (CVaR). These refined formulations are developed...

We consider spaces of smooth functions obtained by relaxing Gevrey-type regularity and decay conditions. It is shown that these classes can be introduced by using the general framework of the weighted matrices approach to ultradifferentiable function...

In this research, a groundbreaking framework for the octic B-spline collocation method in n-dimensional spaces is presented. This work is an extension of previous works that involved the creation of B-spline functions in n-dimensional space for the p...

This article introduces a novel iterative solver with memory, derived from Newton’s scheme, for nonlinear scalar equations. The key innovation lies in integrating memory into the iterative process, enhancing the convergence rate without increas...

This paper extends the concept of the total graph $T_{\mathsf{\Gamma }}\left(R\right)$ associated with a commutative ring to the three-fold Cartesian product $R={\mathbb{Z}}_n\times {\mathbb{Z}}_m\times {\mathbb{Z}}_p$, where $n,m,p>1$. We present complete and self-contained proofs for a wide range of graph-the...

This paper presents a physics-informed training framework for projection-based Reduced-Order Models (ROMs). We extend the original PROM-ANN architecture by complementing snapshot-based training with a FEM-based, discrete physics-informed residual los...

The study examines the onset of magnetoconvection in a Casson fluid-saturated inclined porous layer. Oberbeck–Boussinesq approximation and Darcy law employed to characterize the fluid motion. The stability of the system is examined using both l...

This paper investigates the controllability and synchronization of a newly designed three-dimensional chaotic system using active and adaptive control strategies. Although both controllers were designed with the help of a positive definite function u...

In this article, we will introduce a new generalized proximal $\theta$-contraction for multivalued and single-valued mappings named ${(\mathcal{f}-{\theta }_{\kappa })}_{C_P}$-proximal contraction and ${(\mathcal{f}-{\theta }_{\kappa })}_{B_P}$-proximal contraction. Using these newly...

This study addresses the challenge of effectively modeling uncertainty and hesitation in complex decision-making environments, where traditional fuzzy and vague set models often fall short. To overcome these limitations, we propose the Fermatean neut...

In this paper, we study asymptotic bounds on the m-th derivatives of general algebraic polynomials in weighted Bergman spaces. We consider regions in the complex plane defined by bounded, piecewise, asymptotically conformal curves with strictly posit...

In this paper, we introduce null Cartan normal helices in Minkowski space ${\mathbb{E}}_1^3$. We obtain explicit expressions for their torsions by considering the cases when the C-constant vector field is orthogonal to their axis or not orthogonal to it. We find th...

This work’s theorems and corollaries present new third-order fuzzy differential subordination and superordination results developed by using a novel convolution linear operator involving the Gaussian hypergeometric function and a previously stu...

In this paper, we obtain unique solution and stability results for coupled fractional differential equations with p-Laplacian operator and Riemann–Stieltjes integral conditions that expand and improve the works of some of the literature. In ord...

The well-known nonlinear Schrödinger equation (NLSE) plays a crucial role in describing the temporal evolution of disturbances in marginally stable or unstable media. However, when the media is a fractal form, it becomes ineffective. Thus, the f...

In this work, combined matrices of tridiagonal Toeplitz matrices are studied. The combined matrix is known as the Relative Gain Array in control theory. In particular, given a real tridiagonal Toeplitz matrix of order n, the characterization of its c...

We focus on solving stochastic differential equations driven by jump processes (SDEJs) with measurable drifts that may exhibit quadratic growth. Our approach leverages a space transformation and Itô-Krylov’s formula to effectively elimina...

Herein, we present two hybrid inertial self-adaptive iterative methods for determining the combined solution of the split variational inclusions and fixed-point problems. Our methods include viscosity approximation, fixed-point iteration, and inertia...

This paper looks into the dynamics of nonlinear systems of difference equations, with particular emphasis on fourth-order cases. Analytical solutions are derived for some cases of systems, a tedious task due to the lack of explicit mathematical techn...

This paper concerns the old problem of the connection between the dilatations of a given quasisymmetric homeomorphism h of a circle and the associated polygonal quasiconformal maps with a fixed finite number of boundary points, namely whether $k\left(h\right)=su$...

In logical geometry, Aristotelian diagrams are studied in a systematic fashion. Recent developments in this field have shown that the square of opposition generalizes in two ways, which correspond precisely to the theory of opposition (leading to $\mathrm{\&al}$...

This manuscript addresses an application study by employing a mathematical model of a thermoelastic plate weakened by multi-curved holes under the effect of stress forces in the presence of heat conduction. When the initial heat flow is directed to t...

In the present manuscript, we demonstrate the potential to control and enhance the accuracy of parameter estimation (P-E) in a two-level atom (TLA) immersed in a cavity field that interacts with another cavity. We investigate the dynamics of quantum...

This paper proposes a class of randomized Kaczmarz and Gauss–Seidel-type methods for solving the matrix equation $AXB=C$, where the matrices A and B may be either full-rank or rank deficient and the system may be consistent or inconsistent. These...

In this paper, the stability and Hopf bifurcation of fractional-order quaternion-valued neural networks (FOQVNNs) with various types of time delays are studied. The fractional-order quaternion neural networks with time delays are decomposed into an e...

In this article, we define and study graded 1-absorbing prime ideals and graded weakly 1-absorbing prime ideals in non-commutative graded rings as a new class of graded ideals that lies between graded prime ideals (graded weakly prime ideals) and gra...

In our previous works, we developed the superconvergence of a nonconforming finite element method based on unfitted meshes for an elliptic interface problem and elliptic problem, respectively. In this paper, a nonconforming interface penalty finite e...

In this study, we suggest a straightforward analytical/semi-analytical method based on the Elzaki transform (ET) method to find the solution to a number of differential fractional boundary value problems with initial conditions (ICs). The suggested a...

This article describes an effective computing method for singularly perturbed parabolic problems with small negative shifts in convection and reaction terms. To handle the small negative shifts, the Taylor series expansion is used. The asymptotically...

This paper is devoted to the analysis of a system of generalized variational inclusion problems involving $\alpha$-averaged and Cayley operators within the framework of a q-uniformly smooth Banach space. We demonstrate that the problem can be reformul...

In this paper, we study the convergence and complex dynamics of a novel higher-order multipoint iteration scheme to solve nonlinear equations. The approach is based upon utilizing cubic interpolation in the second step of the King–Werner method...

Various numerical techniques have been developed to address multiple problems in computational fluid dynamics (CFD). The finite volume method (FVM) is a numerical technique used for solving partial differential equations that represent conservation l...

In this study, we introduce a new hybrid identity that effectively combines Newton–Cotes and Gauss quadrature, allowing us to recover well-known formulas such as Simpson’s second rule and the left- and right-Radau two-point rules, among o...

In this paper, a structure-preserving local discontinuous Galerkin (LDG) method is proposed for parabolic stochastic partial differential equations with periodic boundary conditions and multiplicative noise. It is proven that under certain conditions...

This paper investigates totally real submanifolds in a locally conformal Kaehler space form. Using the moving-frame method and constant mean curvature, we obtain the upper and lower bounds of the first eigenvalue for totally real submanifolds in a lo...

Hilbert-type inequalities derive from the classical Hilbert inequality, and their theoretical work has key applications not only in operator theory but also in various analytic disciplines. In this paper, we have achieved the parametric conditions re...

In this work, we study a class of variational inequality problems defined over the intersection of sub-level sets of a countable family of convex functions. We propose a new iterative method for approximating the solution within the framework of Hilb...

In this paper, we study slant helices (or ${\stackrel{\_}{\xi }}_2$-helices) and Darboux helices in the Myller configuration M. We demonstrate that a curve in M is a slant helix if and only if it is a Darboux helix. We present the alternative frame for a curve in M. Fu...

Let $H\left(\mathbb{D}\right)$ be the set of analytic functions on the open unit disk $\mathbb{D}$. For $n\in {\mathbb{N}}_0:=\mathbb{N}\cup \left\{0\right\}$, define the iterated weighted-type Banach space ${\mathcal{V}}_n:=\left\{f\in H\left(\mathbb{D}\right):{sup}_{z\in \mathbb{D}}{(1-|z|}^2\left)\right|f^{\left(n\right)}\left(z\right)|<\infty \right\}.$ In this work, we study the boundedness and the...

Clustering plays a vital role in process mining as it organizes complex event logs into meaningful groups, helping to identify common patterns, outliers, and inefficiencies. This simplification enables organizations to detect bottlenecks and optimize...

We develop a unified analytical framework that systematically connects kinetic theory, optimal transport, and entropy dissipation through the novel integration of hypocoercivity methods with geometric structures. Building upon but distinctly extendin...

It is experimentally established that there is no ground triplet state of the natural $He$ atom. There is also no exact analytical solution to the Schrödinger equation corresponding to this state. For a two-dimensional two-electron ‘artifici...

In this paper, we propose a new variable selection method using a partitioning-based estimating equation for multivariate survival data to simultaneously perform variable selection and parameter estimation. The main idea of the partitioning-based est...

This study introduces the concept of an intuitionistic fuzzy SBCK-subalgebra (SBCK-ideal) and explores the level set of an intuitionistic fuzzy set within the context of Sheffer stroke BCK-algebras. These newly defined concepts are crucial for unders...

In this paper, we consider the nonlinear Neumann problem $\left(Q_{\epsilon }\right):-\Delta u+V\left(x\right)u=u^{{\displaystyle \frac{n+2}{n-2}}-\epsilon }$, with $u>0$ in $\Omega$ and $\partial u/\partial \nu =0$ on $\partial \Omega$, where $\Omega$ is a bounded regular domain in ${\mathbb{R}}^n$, with $n\ge 4$,...

This work establishes the multiplicity of solutions for the fractional Kazdan–Warner equation on finite graphs for the negative case. Our main focus lies in analyzing the nonlinear equation defined on a finite graph $(V,E,\mu ,w)$: ${(-\&Delta}^{}$...

By using the maximal and minimal ranks of some generalized Schur complement, the equivalent conditions for the reverse order law $\left(AB\right)\{1,3M,4K\}=B\{1,3N,4K\}A\{1,3M,4N\}$ are presented.

This paper presents a method for constructing polynomial Lyapunov functions to analyze the stability of nonlinear dynamical systems. The approach is based on genetic programming, a variant of genetic algorithms where the search space consists of hier...