Axioms, Volume 13, Issue 3

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 i...

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–deletion theorem and Abe’s free path th...

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 ver...

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....

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 t...

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 $Q_{\mathbb{C}}($...

This paper shows that certain${ }_3{F}_4$ hypergeometric functions can be expanded in sums of pair products of${ }_2{F}_3$ functions, which reduce in special cases to${ }_2{F}_3$ functions expanded in sums of pair products of${ }_1{F}_2$ functions. This expands...

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 recurren...

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 i...

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,...

Based on equivalence relation R on X, equivalence class $\left[x\right]$ of a point and equivalence class $\left[A\right]$ of a subset represent the neighborhoods of x and A, respectively. These neighborhoods play the main role in defining separation axioms, metric spaces, pr...

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...

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 comm...

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 $(p,q$...

In the present article, we study submanifolds tangent to the Reeb vector field in trans-Sasakian manifolds. We prove Chen’s first inequality and the Chen–Ricci inequality, respectively, for such submanifolds in trans-Sasakian manifolds wh...

For $S\subseteq V\left(G\right),{\kappa }_G\left(S\right)$ denotes the maximum number k of edge disjoint trees $T_1,T_2,\dots ,T_k$ in G, such that $V\left(T_i\right)\cap V\left(T_j\right)=S$ for any $i,j\in \{1,2,\dots ,k\}$ and $i\ne j$. For an integer $2\le r\le \left|V\right(G\left)\right|$, the generalized r-connectivity of G is...

In this work, we will introduce the concept of ratio-covariety, as a family $\mathcal{R}$ of numerical semigroups that has a minimum, denoted by $\min \left(\mathcal{R}\right),$ is closed under intersection, and if $S\in \mathcal{R}$ and $S\ne \min \left(\mathcal{R}\right)$, then $S\backslash \left\{\mathrm{r}\right(S\left)\right\}\in \mathcal{R},$ where $\mathrm{r}\left(S\right)$ denotes the r...

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...

In this paper, we consider blow-up solutions for the fourth-order nonlinear Schrödinger equation with mixed dispersions. We study the dynamical properties of blow-up solutions for this equation, including the ${\dot{H}}^{{\gamma }_c}$-concentration and li...

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...

This paper deals with translational regular and rapid variations. By using a new method of proving the Galambos–Bojanić-Seneta type theorems, we prove two theorems of this type for translationally regularly varying and translationally rapi...

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 Netwo...

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...

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...

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 rea...

A highly relevant topic in the actuarial literature is so-called “claim reserving” or “loss reserving”, which involves estimating reserves to be provisioned for pending claims, as they can be deferred over various periods. Thi...

In this article, we study isotropic submanifolds in locally metallic product space forms. Firstly, we establish the Chen–Ricci inequality for such submanifolds and determine the conditions under which the inequality becomes equality. Additional...

In this thesis, we research quasilinear Schrödinger system as follows in which $3<N\in \mathbb{R}$, $2<p<N$, $2<q<N$, $V_1(x),V_2(x)$ are continuous functions, $k,\iota$ are parameters with $k,\iota >0$, and nonlinear terms $f,h\in C({\mathbb{R}}^N\times {\mathbb{R}}^2,$...

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...

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....

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, keep...

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...

Let G be a nontrivial connected graph. For a set $D\subseteq V\left(G\right)$, we define $\overline{D}=V\left(G\right)\setminus D$. The set D is a total outer-independent dominating set of G if $\left|N\right(v)\cap D|\ge 1$ for every vertex $v\in V\left(G\right)$ and $\overline{D}$ is an independent set of G. Moreove...

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’s method. Then, we establish an efficient algorithm to comput...

Monge–Ampère 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...

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 $h\left(\lambda \right)={\sum }_{k=0}^{\infty }{a}_k{\lambda }^k$ and its modified version $h_a\left(\lambda \right)={\&}_{}^{}$...

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-commutativ...

Consider the power series with complex coefficients $h\left(z\right)={\sum }_{k=0}^{\infty }{a}_k{z}^k$ and its modified version $h_a\left(z\right)={\sum }_{k=0}^{\infty }\left|a_k\right|z^k$. In this article, we explore the application of certain Hölder-type inequalities for deriving various inequalities...

In this article, we study the Cauchy problem of the chemotaxis-Navier–Stokes system with the consumption and production of chemosignals with a logistic source. The parameters $\chi \ne 0, \xi \ne 0, \lambda >0$ and $\mu >0$. The sys...

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 obj...

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 this editorial, we present “Theory of Functions and Applications”, a Special Issue of Axioms [...]

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...

Let G be a graph with n vertices and m edges. $A\left(G\right)$ and I denote, respectively, the adjacency matrix of G and an n by n identity matrix. For a graph G, the permanent of matrix $(I+A(G\left)\right)$ is called the permanental sum of G. In this paper, we give a relat...

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 absolut...

A collection of functions organized according to their indexing based on non-negative integers is grouped by the common factor of fixed integer N. This grouping results in a summation of N series, each consisting of functions partitioned according to...

The purpose of this paper is to investigate the existence and multiplicity of nontrivial solutions with the ${\phi }_p$-Laplacian for the discrete $2n$-th order periodic boundary value issue. To support these conclusions, we have employed variational techni...

By computing definite integrals, we shall examine binomial series of convergence rate $\pm 1/2$ and weighted by harmonic-like numbers. Several closed formulae in terms of the Riemann and Hurwitz zeta functions as well as logarithm and polylogarithm...

In this article, we study the maximum number of limit cycles of discontinuous piecewise differential systems, formed by two Hamiltonians systems separated by a straight line. We consider three cases, when both Hamiltonians systems in each side of the...

Machine learning algorithms are heavily relied on to understand the vast amounts of data from high-energy particle collisions at the CERN Large Hadron Collider (LHC). The data from such collision events can naturally be represented with graph structu...