Axioms, Volume 14, Issue 10

In this paper we will be concerned with zeta-symmetry—the functional equation for the (Riemann) zeta-function (equivalents to which are called modular relations)—and reveal the reason why so many results are intrinsic to PFE (Partial Frac...

Honey bee colonies are important to worldwide agriculture and the health of natural ecosystems. Understanding the factors behind colony persistence and failure has been a major challenge for both ecologists and mathematicians. In this paper, we prese...

This paper presents soliton solutions of the fractional (2+1)-dimensional Davey–Stewartson equation based on a local fractional derivative to represent wave packet propagation in dispersive media under both spatial and temporal effects. The imp...

We interpret the Narayana numbers combinatorially by having them count the number of tilings of an n-strip using squares and triominoes. Using this interpretation, we develop a collection of identities satisfied by the sequence of Narayana numbers. A...

In this paper, the uniqueness of steady Schwarzschild gradient Ricci solitons is studied. The role of the weight functions is analyzed. The generalized steady Schwarzschild gradient Ricci solitons are investigated; the implications of the rotational...

The analysis of lifetime data under censoring schemes plays a vital role in reliability studies and survival analysis, where complete information is often difficult to obtain. This work focuses on the estimation of the parameters of the recently prop...

We study stochastic production planning in capacity-constrained manufacturing systems, where feasible operating states are restricted to a convex safe-operating region. The objective is to minimize the total cost that combines a quadratic production...

Artificial intelligence is playing an increasingly important role in education. Learning path recommendation is one of the key technologies in artificial intelligence education applications. This paper applies knowledge space theory and fuzzy set the...

In real-world applications, finite time convergence to a desired Lyapunov stable equilibrium is often necessary. This notion of stability is known as finite time stability and refers to systems in which the state trajectory reaches an equilibrium in...

This note adds to the investigation of Abbott algebras in relation to quantum logics (see the references below). We introduce a variety of modular Abbott algebras and show that they are isomorphic to the variety of modular quantum logics. We extend t...

The goal of the current study is to introduce a new class of proximal-point mappings that are associated with a new class of ${\mathcal{B}}^l$-co-monotone mappings that are being defined. The ${\mathcal{B}}^l$-co-monotone mapping is the sum of co-coercive and symmetric monotone m...

In this paper, we investigate the generalized coupled Zakharov system (GCZS), a fundamental model in plasma physics that describes the nonlinear interaction between high-frequency Langmuir waves and low-frequency ion-acoustic waves, including the inf...

We show how the Brooks–Chacon Biting Lemma can be combined with the Castaing–Saadoune procedure to provide the complete rate of convergence along subsequences when the uniformly boundedness condition is violated.

This paper studies discontinuous quasilinear sub-elliptic systems associated with Hörmander’s vector fields under controllable and natural growth conditions. By a new $\mathcal{A}$-harmonic approximation reformulation for bilinear forms $\mathcal{A}\in \mathrm{Bil}({\mathbb{R}}^{kN}$...

In this article, we establish the existence of global mild solutions to the Vlasov–Fokker–Planck equation with local alignment forces under specular reflection boundary conditions in the low-regularity function space $L_k^1{L}_T^{\infty }{L}_v^2$. A ke...

In this paper, we study Z-solitons and gradient Z-solitons on $\alpha$-cosymplectic manifolds. The soliton structure is defined by the generalized tensor $Z=S+\beta g$, where S denotes the Ricci tensor, g the metric tensor, and $\beta$ a smooth function....

Through transformation and utilizing a novel extended complex method combining with the Weierstrass factorization theorem, Wiman–Valiron theory and the Painlevé test, new non-constant meromorphic solutions were constructed for the predat...

We address a fractional spatial Stefan problem derived from a non-Fourier heat flux model with a convective boundary condition at the fixed boundary. An explicit solution is obtained in terms of a three-parameter Mittag–Leffler function. A dime...

In this paper, we investigate the non-uniform m-dimensional Moran walk $(Z_n^{\left(1\right)},\dots ,Z_n^{\left(m\right)})$, where each component process ${(Z_n^{\left(j\right)})}_{1\le j\le m}$, either increases by one unit or resets to zero at each step. Using probability generating functions, we an...

By using the construction theorem of semi-discrete Hilbert-type inequalities with quasi-homogeneous kernels and real analysis techniques, this paper establishes a semi-discrete Hilbert-type inequality involving partial sums and variable upper limit i...

This paper aims to introduce a new interval approach called the Semi-Type-2 interval to represent imprecise parameters in uncertain decision-making. The proposed work establishes arithmetic operations of Semi-Type-2 intervals with algebraic propertie...

This paper introduces Exponentiated Inverse Exponential Distribution (EIED), a novel probability model developed within the power inverse exponential distribution framework. A distinctive feature of EIED is its highly flexible hazard rate function, w...

In this work, the discontinuous Dirac operator with weight is studied. We prove the completeness theorems of the system of eigenfunctions for the discontinuous Dirac operator.

The quasisymmetric minimality for fractal sets is a hot research topic for scholars focused on the fractal geometry and quasisymmetric mappings. In this paper, we study the quasisymmetric minimality on packing dimension for homogeneous perfect sets....

The Kronecker product has been commonly seen in various scientific fields to formulate higher-dimensional spaces from lower-dimensional ones. This paper presents a generalization of the Cannon–Kronecker product bases by introducing generalized...

This work presents a comprehensive study of weakly B-symmetric warped product manifolds ${\left(WBS\right)}_n$, a natural extension of several classical curvature-restricted geometries including B-flat, B-parallel, and B-recurrent manifolds. We begin by formulating...

This article introduces a new type of contractions via $\phi$-admissibility and ${\omega }_b$-distance called generalized ${\omega }_b^{\phi }$-contractions. We prove the existence of fixed points for this type of contractions under some conditions. Moreover, we g...

This paper establishes two novel recurrence relations for Stirling numbers of the second kind—an L recurrence and a vertical recurrence—discovered through a probabilistic analysis of Poisson higher-order origin moments. While the link bet...

In this paper, we derive novel formulas and identities connecting Cauchy numbers and polynomials with both ordinary and generalized Stirling numbers, binomial coefficients, central factorial numbers, Euler polynomials, r-Whitney numbers, and hyperhar...

In this paper, we aim to investigate a type of lattice-valued fuzzy metric within the framework of L-topology. Firstly, we present a comprehensive construction theorem for this type of metric, utilizing the concept of L-quasi metric. Secondly, we pro...

Amid intensifying global competition, industrial product quality has become a critical determinant of competitive advantage. However, persistent quality-related faults in production environments threaten product integrity. To address this challenge,...

Spherical distributions, in particular, the von Mises–Fisher distribution, are often used to analyze directional data. The first and second moments of these distributions are of central interest, as they describe mean orientations as well as an...

According to the World Health Organization (WHO), globally, cervical cancer ranks as the fourth most common cancer in women, with around 660,000 new cases in 2022. In the same year, about 94 percent of the 350,000 deaths caused by cervical cancer occ...

This paper investigates nonparametric estimations of a density function within a mixed density model. A linear wavelet density estimator and an adaptive nonlinear wavelet estimator are proposed using wavelet method and hard thresholding algorithm. Un...

By combining modular invariance of characteristic forms and the family index theory, we obtain some new anomaly cancellation formulas for any dimension under the not top degree component. For a fiber bundle of dimension $(4l-2)$, we obtain the an...

This study focuses on a class of perturbed Dirichlet–Neumann tridiagonal (PDNT) Toeplitz matrices, mainly exploring their eigenvalue sensitivity and inverse problems. By the explicit expressions for eigenvalues and eigenvectors of PDNT Toeplitz...

Recent developments in fixed-point theory have focused on iterative techniques for approximating solutions, yet there remain important questions about whether different methods are equivalent and how well they resist perturbations. In this study, two...

This study develops an improved family of estimators for estimating the finite population median within a two-phase sampling method. The proposed estimators, which use transformation techniques to reduce survey costs when full auxiliary information i...

The solution of a nonhomogeneous linear Caputo fractional differential equation of order $nq,(n-1)<nq<n$ with Caputo fractional initial conditions can be expressed using suitable Mittag–Leffler functions. In order to extend this resul...

The contraction method is a procedure that allows to establish non-trivial relations between Lie algebras and has had successful applications in both mathematics and theoretical physics. This work deals with generalizations of the contraction procedu...

The local convergence analysis of the $m+1$-step Newton-Jarratt composite scheme with order $2m+1$ has been shown previously. But the convergence order $2m+1$ is obtained using Taylor series and assumptions on the existence of at least the fifth derivative...

This study develops a stochastic SIQR epidemic model with mean-reverting Ornstein–Uhlenbeck (OU) processes for both transmission rate $\beta \left(t\right)$ and quarantine release rate $k\left(t\right)$; this is distinct from existing non-white-noise stochastic epidemic...

Developing classical three-dimensional consolidation theories considers the small-strain assumption. This small-strain assumption is inappropriate when studying the consolidation process of soft or very soft clay layers. Instead, this study derives a...

In recent years, special functions have played a significant role in the investigation of different subclasses within the class of bi-univalent functions. In this work, we present and investigate two new subclasses of bi-univalent functions defined i...

In the present paper, we introduce and investigate the concepts of Wijsman $f_{\rho }$-statistical convergence of order $\alpha$ and Wijsman strong $f_{\rho }$-convergence of order $\alpha$. These notions are defined as natural generalizations of classical stati...

According to a clever but rarely quoted or acknowledged work of E. Vessiot that won the prize of the Académie des Sciences in 1904, “Differential Galois Theory” (DGT) has mainly to do with the study of “Principal Homogeneous...

We introduce the generalized fractional-order Dirac delta distribution ${\delta }_{\mathrm{GFODDF}}$, defined by applying the generalized fractional derivative (GFD) operator to the Heaviside function. This construction extends the classical Dirac delta to non-integ...

This study proposes a dimensionality reduction method based on proper orthogonal decomposition (POD) for numerically solving the Schrödinger equation by optimizing the coefficient vectors of the Crank–Nicolson finite element (CNFE) solutio...

This paper addresses first- and second-kind Volterra integral equations (VIEs) with discontinuous kernels. A hybrid method combining the Homotopy Analysis Method (HAM) and Physics-Informed Neural Networks (PINNs) is developed. The convergence of the...

We present a unified framework for fuzzy statistical convergence of Grünwald–Letnikov (GL) fractional differences in Bag–Samanta fuzzy normed linear spaces, addressing memory effects and nonlocality inherent to fractional-order model...