Axioms, Volume 13, Issue 8

In this study, to approximate nabla sequential differential equations of fractional order, a class of discrete Liouville–Caputo fractional operators is discussed. First, some special functions are re-called that will be useful to make a connect...

For the set $\mathsf{I}\left(X\right)$ of probability measures on a compact Hausdorff space X, we propose a new way to introduce the topology by using the open subsets of the space X. Then, among other things, we give a new proof that for a compact Hausdorff space X, the...

The advances in science and technology have led to vast amounts of complex and heterogeneous data from multiple sources of random sample length. This paper aims to investigate the extreme behavior of competing risks with random sample sizes. Two acce...

We study certain Volterra integral equations that extend and recover first order ordinary differential equations (ODEs). We formulate the former equations from the latter by replacing classical derivatives with nonlocal integral operators with anti-s...

In the study of algebraic structures related to logical systems, ideals and filters have different meanings and are algebraic notions related to logical provable formulas. Unlike the classical Boolean lattice theory, ideals and filters are not dual n...

A signed graph $\Sigma =(G,\sigma )$ consists of an underlying graph $G=(V,E)$ with a sign function $\sigma :E\to \{-1,1\}$. Let $A(\Sigma )$ be the adjacency matrix of $\Sigma$ and ${\lambda }_1(\Sigma )$ denote the largest eigenvalue (index) of $\Sigma$. De...

Following Dirac’s notation in Quantum Mechanics (QM), we propose the Probability Bracket Notation (PBN), by defining a probability-bra (P-bra), P-ket, P-bracket, P-identity, etc. Using the PBN, many formulae, such as normalizations and expectat...

In this manuscript, we initiate a large class of enriched $(\mathrm{d},\mathfrak{Z})$-$\mathcal{Z}$-contractions defined on Banach spaces and prove the existence and uniqueness of the fixed point of these contractions. We also provide an example to support our results and give an exi...

This study introduces a $4\times 4$ matrix eigenvalue problem and develops an integrable hierarchy with a bi-Hamiltonian structure. Integrability is ensured by the zero-curvature condition, while the Hamiltonian structure is supported by the trace iden...

With this Editorial, we present a Special Issue of Axioms entitled ‘Differential Geometry and Its Application, 2nd edition’ [...]

Planetary gear transmission mechanisms (PGTMs) are widely used in mechanical transmission systems due to their compact structure and high transmission efficiency. To implement the reliability design and optimization of a PGTM, a novel multi-objective...

Experimental designs are commonly used to produce valid, defensible, and supportable conclusions. Among commonly used block designs, the class of Latin square designs is used to study factors or treatment levels expressed as Latin letters and applyin...

Recently, k -fuzzy metric spaces were introduced by connecting the degree of nearness of two points with k parameters $(t_1,t_2,t_3,\cdots ,t_k)$ and the authors presented an analogue of Grabiec’s fixed-point result in k-fuzzy metric spaces along wit...

The concept of summability is crucial in deriving formal solutions to partial differential equations. This paper explores the connection between the methods of statistical convergence of sequences and statistical Cesàro summability in intuitio...

In this work, we consider De Luca and Termini’s notion of non-probabilistic entropy, and we extend some entropy-like measures of the degree of fuzziness to type-2 fuzzy sets. With this aim, we first study different entropy measures proposed in...

The rapid progression of emerging technologies like the Internet of Things (IoT) and Big Data analytics for manufacturing has driven innovation across various industries worldwide. Production data are utilized to construct a model for quality evaluat...

The coronavirus pandemic has raised concerns about the emergence of other viral infections, such as monkeypox, which has become a significant hazard to public health. Thus, this work proposes a novel time series ensemble technique for analyzing and f...

In this paper, we use the generalized version of convex functions, known as strongly convex functions, to derive improvements to the Jensen–Mercer inequality. We achieve these improvements through the newly discovered characterizations of stron...

Suppose that $R={\mathbb{Z}}_{p^4}\left[u\right]$ with $u^2=p^3\beta$ and $pu=0,$ where p is a prime and $\beta$ is a unit in $R.$ Then, R is a local non-chain ring of order $p^5$ with a unique maximal ideal $J=(p,u)$ and a residue field of order $p.$ A linear code C of length N over R is an...

In this study, we present a numerical method named the logarithmic non-polynomial spline method. This method combines conformable derivative, finite difference, and non-polynomial spline techniques to solve the nonlinear inhomogeneous time-fractional...

We undertake this study with the objective of introducing certain control functions in the contractive condition to prove fixed-point theorems in the framework of complex-valued bipolar metric spaces. The incorporation of control functions broadens t...

We deal with two apparently disparate theories. One of them studies extensions of orderings from a set to its power set. The other one defines suitable scores on hesitant fuzzy elements. We show that both theories have the same mathematical substrate...

In this paper, we mainly study the p-Kirchhoff type equations with logarithmic nonlinear terms and critical growth: $\left\{\begin{array}{c}-M\left({\displaystyle {\int }_{\mathsf{\Omega }}{\left|\nabla u\right|}^{p}dx}\right){\Delta }_{p}u={\left|u\right|}^{p^{\ast }-2}u+\lambda {\left|u\right|}^{p-2}u-{\left|u\right|}^{p-2}u\ln {\left|u\right|}^2\hspace{0.33em}\hspace{0.33em}\hspace{0.33em}\hspace{0.33em}Q\end{array}\right.$...

Special calculation methods are presented for critical indices and amplitudes for the permeability of thin wavy channels dependent on the waviness. The effective permeability and wetted perimeter of the two-dimensional random percolating media are co...

In this paper, the pathway model for the real scalar variable case is re-explored and its connections to fractional integrals, solutions of fractional differential equations, Tsallis statistics and superstatistics in statistical mechanics, the reacti...

Mathematical models play a crucial role in evaluating real-life processes qualitatively and quantitatively. They have been extensively employed to study the spread of diseases such as hepatitis B, COVID-19, influenza, and other epidemics. Many resear...

Let $n,m,p,r\in N$ with $p\ge n\ge r$. For a hypergraph, if each edge has r vertices, then the hypergraph is called an r-graph. Define $e_r(n,m;p)$ to be the maximum number of edges of an r-graph with p vertices in which every subgraph of n vertices has a...

This paper studies the optimal asset allocation problem of a defined contribution (DC) pension plan with a stochastic salary and value under a constraint within a stochastic volatility model. It is assumed that the financial market contains a risk-fr...

This paper investigates a quantum system described by the Schrödinger equation, utilizing the concept of the quantum Lyapunov function. The Lyapunov function is chosen based on the mean value of a virtual mechanical quantity, where different val...

An m-consecutive-k-out-of-n: F ($m/C/k/n: F$) system consists of n linearly ordered components such that the system fails if and only if there are at least m nonoverlapping runs of k consecutive failed components. Our motivation in this work is to...

The Time-Varying Matrix Inversion (TVMI) problem is integral to various fields in science and engineering. Countless studies have highlighted the effectiveness of Zeroing Neural Networks (ZNNs) as a dependable approach for addressing this challenge....

This paper addresses the weighted composition operators ${}_{\psi }C_{\varphi }$ from the $(\alpha ,k)$-Bloch spaces to the ${\mathcal{A}}_{(\beta ,k)}$ spaces of bounded holomorphic functions on W, where W is a generalized Hua domain of the fourth kind. Additionally, we obtain so...

In this paper, we scrutinize a collection of meromorphic functions known as normal families, prove the theorem that normal families share a holomorphic function, and present several illustrative counterexamples.

The mean first-passage time represents the average time for a migrating cell within its environment, starting from a certain position, to reach a specific location or target for the first time. In this feature article, we provide an overview of the c...

We consider the concept of fuzzy $\mathcal{H}$-quasi-contraction ($\mathcal{F}\mathcal{H}$-$\mathcal{Q}\mathcal{C}$ for short) initiated by Ćirić in tripled fuzzy metric spaces ($\mathcal{T}$-$\mathcal{F}\mathcal{M}\mathcal{S}$s for short) and present a new fixed point theorem ($\mathcal{F}\mathcal{P}\mathcal{T}$ for short) for $\mathcal{F}\mathcal{H}$-$\mathcal{Q}\mathcal{C}$ in complete $\mathcal{T}$-$\mathcal{F}\mathcal{M}\mathcal{S}$s. As an applicatio...

We formulate a data-independent latent space regularization constraint for general unsupervised autoencoders. The regularization relies on sampling the autoencoder Jacobian at Legendre nodes, which are the centers of the Gauss–Legendre quadratu...

The principal aim of this paper is to introduce the extended Voigt-type function ${\mathbb{V}}_{\mu ,\nu }(x,y)$ and its counterpart extension ${\mathbb{W}}_{\mu ,\nu }(x,y)$, involving the Neumann function $Y_{\nu }$ in the kernel of the representing integral. The newly defined integra...

In this paper, we derive a new generic equality for the first-order differentiable functions. Through the utilization of the general identity and convex functions, we produce a family of upper bounds for numerous integral inequalities like Ostrowski&...

Needed for cosmological and stellar nucleosynthesis, we are studying the closed-form analytic evaluation of thermonuclear reaction rates. In this context, we undertake a comprehensive analysis of three largely distinct velocity distributions, namely...

In this paper Chen-Burr XII distribution is constructed and graphical description of the probability density function, hazard rate and reversed hazard rate functions of the proposed model is obtained. Also, some statistical characteristics of the Che...

The single generalized weighted composition operator $D_{u,\psi }^n$ on various spaces of analytic functions has been investigated for decades, i.e., $D_{u,\psi }^{n}f=u·(f^{\left(n\right)}\circ \psi )$, where $f\in H\left(\mathbb{D}\right)$. However, the study of the finite sum of general...

In this paper, we implement the finite detail technique primarily based on T-Splines for approximating solutions to the linear elasticity equations in the connected and bounded Lipschitz domain. Both theoretical and numerical analyses of the Dirichle...

In this paper, quasi-canonical biholomorphically projective and equitorsion quasi-canonical biholomorphically projective mappings are defined. Some relations between the corresponding curvature tensors of the generalized Riemannian spaces $G{R}_N$ and $G{\stackrel{\&}{R}}_{}$...

Our goal in this work is to solve the fractional Bratu equation, where the fractional derivative is of the Caputo type. As we know, the nonlinearity and derivative of the fractional type are two challenging subjects in solving various equations. In t...

A new form of the mathematical expression for the co-moving volume element of a flat universe with cosmological constant, cold matter, and stiff matter is presented. It is used to determine the constraints from the Planck measurements of the Hubble p...

The objective of this research is to present a novel approach to enhance the extragradient algorithm’s efficiency for finding an element within a set of fixed points of nonexpansive mapping and the set of solutions for equilibrium problems. Spe...

This paper explores the linearized stability of nonlinear delay differential equations (DDEs) with impulses. The classical results on the existence of periodic solutions are extended from ordinary differential equations (ODEs) to DDEs with impulses....

In this work, supercobalancing numbers are considered and some properties of these numbers are investigated. In the first part of this work, it is shown that every supercobalancing number is also a subbalancer. More specifically, $B_3$-supercobalancing...

By using the most generalized gamma function (parametric gamma function, or p-gamma function), we present the most generalized Rabotnov function, called the p-Rabotnov function. Consequently, new fractal–fractional differential and integral ope...

In the present paper, we define and study a new family of holomorphic functions which involve the Bazilevič functions and the $\lambda$-pseudo-starlike functions. We establish coefficient estimates for the first four determinants of the symmetric...