Axioms, Volume 13, Issue 10

This paper is dedicated to the memory of Professor Gary Gruenhage (1947–2023). This survey introduces the formation and early development of the topic of point-countable covers and sequence-covering mappings, and lists the recent progress of 38...

The lifetime performance index (LPI) is an important metric for evaluating product quality, and research on the statistical inference of the LPI is of great significance. This paper discusses both the classical and Bayesian estimations of the LPI und...

In this study, we introduce a new space called the modular b-metric-like space. We investigate some properties of this new concept and define notions of $\xi$-convergence, $\xi$-Cauchy sequence, $\xi$-completeness and $\xi$-contraction. The existence and...

The generalized theory of the double reduction of systems of partial differential equations (PDEs) based on the association of conservation laws with Lie–Bäcklund symmetries is one of the most effective algorithms for performing symmetry r...

In differential geometry, the concept of golden structure represents a compelling area with wide-ranging applications. The exploration of golden Riemannian manifolds was initiated by C. E. Hretcanu and M. Crasmareanu in 2008, following the principles...

This research investigates innovative extensions of Hardy-type inequalities through the use of nabla Hölder’s and nabla Jensen’s inequalities, combined with the nabla chain rule and the characteristics of convex and submultiplicative...

The problem of testing the equi-correlation coefficient of a standard symmetric multivariate normal distribution is considered. Constrained Bayesian and classical Bayes methods, using the maximum likelihood estimation and Stein’s approach, are...

We consider an elliptic variational–hemivariational inequality $\mathcal{P}$ in a real reflexive Banach space, governed by a set of constraints K. Under appropriate assumptions of the data, this inequality has a unique solution $u\in K$. We associate inequ...

In this paper, we propose a new modified planar Kelvin–Stuart model. We demonstrate some modules for investigating the dynamics of the proposed model. This will be included as an integral part of a planned, much more general Web-based applicati...

The existence or nonexistence of a complex structure on a differential manifold is a central problem in differential geometry. In particular, this problem on ${\mathrm{S}}^6$ was a long-standing unsolved problem, and differential geometry is an important tool. Rec...

Given the risk and impact of infectious-contagious X diseases, which are expected to increase in frequency and unpredictability due to climate change and anthropogenic penetration of the wilderness, it is crucial to advance descriptions and explanati...

This paper focuses on examining a new type of n-additive map called the symmetric reverse n-derivation. As implied by its name, it combines the ideas of n-additive maps and reverse derivations, with a 1-reverse derivation being the ordinary reverse d...

In the paper, we consider the $P{H}_2$-distribution, which is a particular case of the $PH$-distribution. In other words, The first service phase is exponentially distributed, and the service rate is $\mu$. After the first service phase, the customer can to...

The aim of this paper is to extend the concept of the orthogonal derivative to provide a new integral representation of the fractional Riesz derivative. Specifically, we investigate the orthogonal derivative associated with Gegenbauer polynomials&nbs...

The purpose of this paper is to consider a transmission problem of a viscoelastic wave with nonlocal boundary control. It should be noted that the present paper is based on the previous C. G. Gal and M. Warma works, together with H. Atoui and A. Bena...

In this paper, we introduce the homogeneous grand mixed Herz–Morrey spaces $M{\dot{K}}_{\tilde{q},\lambda }^{\alpha ,p),\theta }\left({\mathbb{R}}^n\right)$ and investigate their fundamental properties. We further explore the boundedness of sublinear operators and fractional-ty...

From the finite gap solutions of the KdV equation expressed in terms of abelian functions we construct solutions to the Schrödinger equation with a KdV potential in terms of fourfold Fredholm determinants. For this we establish a connection betw...

The current work proposes the incorporation of an artificial neural network to solve the Gross–Pitaevskii equation (GPE) efficiently, using a few realistic external potentials. With the assistance of neural networks, a model is formed that is c...

A reduced-dimension (RD) method based on the proper orthogonal decomposition (POD) technology and the linearized Crank–Nicolson mixed finite element (CNMFE) scheme for solving the 2D nonlinear extended Fisher–Kolmogorov (EFK) equation is...

In this paper, we study the initial boundary value problem for wave equations with combined logarithmic and power-type nonlinearities. For arbitrary initial energy, we prove a necessary and sufficient condition for blow up at infinity of the global w...

In the present research note, we discuss the energy–momentum squared gravity model $\mathcal{F}(\mathcal{R},{\mathcal{T}}^2)$ coupled with perfect fluid. We obtain the equation of state for the perfect fluid in the $\mathcal{F}(\mathcal{R},{\mathcal{T}}^2)$-gravity model. Furthermore, we deal with the energy&ndas...

In recent decades, the study of discrete distributions has received increasing attention in the field of statistics, mainly because discrete distributions can model a wide range of count data. One common distribution used for modeling count data, for...

Cavitation is a disadvantageous phenomenon that occurs when fluid pressure drops below its vapor pressure. Under these conditions, bubbles form in the fluid. When these bubbles flow into a high-pressure area or tube, they erupt, causing harm to mecha...

Hypergroups represent a generalization of groups, introduced by Marty, that are rich in applications in several sectors of mathematics and in other fields. An important class of hypergroups called join spaces is presented in this paper, along with so...

A Leslie–Gower predator–prey model with nonlinear harvesting and a generalist predator is considered in this paper. It is shown that the degenerate positive equilibrium of the system is a cusp of codimension up to 4, and the system admits...

In this paper, we address the study of the oscillatory properties of the solutions of a class of third-order delay differential equations. The primary objective of this study is to provide new relationships that can be employed to obtain criteria for...

A control design for a linear large-scale interconnected system composed of identical subsystems is presented in this paper. The control signal of all subsystems is sampled. For different subsystems, the sampling times are not identical. Nonetheless,...

The Pareto–Feller distribution has been widely used across various disciplines to model “heavy-tailed” phenomena, where extreme events such as high incomes or large losses are of interest. In this paper, we present a new bivariate d...

The Mach number effect on the Richtmyer–Meshkov instability (RMI) evolution of the shocked V-shaped ${\mathrm{N}}_2$/${\mathrm{SF}}_6$ interface is numerically studied in this research. Four distinct Mach numbers are taken into consideration for this purpose: ${\mathrm{M}}_s=1.12,1.22$...

Distributionally robust optimization (DRO) is an advanced framework within the realm of optimization theory that addresses scenarios where the underlying probability distribution governing the data is uncertain or ambiguous. In this paper, we introdu...

In this paper, one-to-one correspondences and equivalences between ideals, primals, filters and grills are introduced. It is shown that the local functions and the topological spaces induced by them are the same. From this point of view, the topologi...

The main focus of this paper is to analyze the algebraic structure of constacyclic codes over the ring $\mathcal{R}={\mathbb{F}}_p+w_1{\mathbb{F}}_p+w_2{\mathbb{F}}_p+w_2^2{\mathbb{F}}_p+w_1{w}_2{\mathbb{F}}_p+w_1{w}_2^2{\mathbb{F}}_p$, where $w_1^2-{\alpha }^2=0$, $w_1{w}_2=w_2{w}_1$, $w_2^3-{\beta }^2{w}_2=0$, and $\alpha ,\beta \in {\mathbb{F}}_p\setminus \left\{0\right\}$, for a prim...

In this paper, we introduce a new Orlicz function, namely a b-Orlicz function, which is not necessarily convex. The Orlicz spaces $L^{\Phi }$ generated by the b-Orlicz function $\Phi$ equipped with a Luxemburg quasi-norm contain both classical spaces $L^p(p\&$...

This paper aims to develop a meshless radial point interpolation (RPI) method for obtaining the numerical solution of fractional Navier–Stokes equations. The proposed RPI method discretizes differential equations into highly nonlinear algebraic...

The consensus problem in stochastic multi-agent systems (MASs) with Markovian switching is addressed by proposing a novel distributed dynamic event-triggered (DDET) technique based on periodic sampling to reduce information transmission. Unlike tradi...

We study Lorentzian contact and Lorentzian–Sasakian structures in Hom-Lie algebras. We find that the three-dimensional $\mathfrak{sl}(2,\mathbb{R})$ and Heisenberg Lie algebras provide examples of such structures, respectively. Curvature tensor properties in Lorentz...

Based on Type-I generalized progressive hybrid censored samples (GPHCSs), the parameter estimate for the unit-half logistic-geometry (UHLG) distribution is investigated in this work. Using maximum likelihood estimation (MLE) and Bayesian estimation,...

The main objective of this research is to examine a specific sufficiency criteria for the starlikeness and convexity of order $\delta$, k-uniform starlikeness, k-uniform convexity, lemniscate starlikeness and convexity, exponential starlikeness and co...

The aim of this paper is to introduce to a pair of fuzzy graphic rational F-contraction multivalued mappings and to study the necessary condition for the existence of common fixed points of fuzzy multivalued mappings in the setup of generalized param...

Fractional calculus extends the conventional concepts of derivatives and integrals to non-integer orders, providing a robust mathematical framework for modeling complex systems characterized by memory and hereditary properties. This study enhances th...

This paper introduces a new measure of non-compactness within a bounded domain of ${\mathbb{R}}^{\mathbb{N}}$ in the generalized Morrey space. This measure is used to establish the existence of solutions for a coupled Hadamard fractional system of integral equations in gener...

We propose a new approach to extend the notion of commutator and Lie algebra to algebras with ternary multiplication laws. Our approach is based on the ternary associativity of the first and second kinds. We propose a ternary commutator, which is a l...

In this paper, we introduce two-term differential $Lei{b}_{\infty }$-conformal algebras and give characterizations of some particular classes of such two-term differential $Lei{b}_{\infty }$-conformal algebras. Furthermore, we discuss the classification of the non...

This paper provides several new traveling wave solutions for a nonlinear partial differential equation (PDE) by applying symbolic computation and a new approach, the Riccati–Bernoulli sub-ODE method, in a computer algebra system. Herein, employ...

Integral inequalities with generalized convexity play a vital role in both theoretical and applied mathematics. The theory of integral inequalities is one of the branches of mathematics that is now developing at the quickest rate due to its wide rang...

In this paper, we employ the theory of differential subordination to establish a theorem that delineates certain sufficient conditions for starlikeness, convexity, close-to-convexity, and quasi-convexity in relation to functions with fixed initial co...

In this article, we delve into delayed fractional differential equations with Riemann–Stieltjes integral boundary conditions and fractional impulses. By using differential inequality techniques and some fixed-point theorems, some novel sufficie...

This article highlights the oscillatory properties of second-order Emden–Fowler delay differential equations featuring sublinear neutral terms and multiple delays, encompassing both canonical and noncanonical cases. Through the proofs of severa...

The method of the equivalent system of fractional integral equations is used to prove the existence results of a unique solution for initial value problems corresponding to various classes of nonlinear fractional differential equations involving the...

The numerical solution of optimal control problems through second-order methods is examined in this paper. Controlled processes are described by a system of nonlinear ordinary differential equations. There are two specific characteristics of the clas...