Axioms, Volume 15, Issue 5

In this paper, we introduce topological information systems between objects with a distance and attributes with a distance based on a complete co-residuated lattice. We can obtain two distances and Alexandrov topologies for objects and attributes fro...

In terms of order, lower order, type, lower type and two-member power asymptotic for the function $A\left(z\right)={\displaystyle \sum _{n=1}^{\infty }}{a}_{n}f\left({\lambda }_{n}z\right)$, analytic in a finite disk, where f is an entire transcendental function and $\left({\lambda }_n\right)$ is sequence of positive num...

This article investigates the lower bounds of analytic functions defined by absolutely convergent Dirichlet series in the left half-plane and establishes conditions under which such functions exhibit the pits property. The study extends classical res...

Ordinary differential equations are fundamental tools for modeling dynamic systems in science, engineering, and applied mathematics. Solving these equations accurately and efficiently is crucial, particularly in cases where analytical solutions are c...

The possible existence of a regular Moore graph of diameter 2 and degree 57 with the maximum number 3250 of vertices has been an open question for over 65 years. One approach to a construction focuses on the set of permutations that describe the 1-fa...

In 2003 W. Takahashi and M. Toyodaestablished the weak convergence of an iteration process to solve a variational inequality problem induced by an inverse strongly-monotone mapping. Recently we proved that for the same iterative process, most of its...

Some equivalent statements and basic properties for the generalized convexity assumption $p\left(x\right)f\left(x\right)+q\left(x\right)f^{\prime }\left(x\right)+f^{″}\left(x\right)\ge 0$ are proved. Then based on these conclusions, various Jensen type inequalities under the generalized convexity are estab...

This paper studies the algebraic properties of little Hankel operators on Hardy–Sobolev spaces $H_s^2$, focusing on a notion of commutativity defined via adjoint products. For symbols $\phi$ and $\psi$, whose co-analytic parts are trigonometric polyn...

This study presents an extended cubic B-spline Galerkin scheme for the numerical solution of multi-term time-fractional differential equations. The proposed formulation employs extended cubic B-splines together with the Caputo fractional derivative t...

Many authors consider modified SIQR (susceptible, infected, isolated (quarantined), and recovered individuals) models for childhood diseases. In this paper, we examine a modified differential system with N free parameters that may be of interest to e...

Let $G\subset \mathbb{C}$ be a bounded simply connected domain with rectifiable Jordan boundary. Denote by $\varphi$ the conformal map of the exterior of G onto the exterior of the unit disk. For $R>1$, let ${\mathsf{\Gamma }}_R$ be the level curve defined by $\left|\varphi \left(z\right)\right|=R$, and let...

The Gielis superformula is a powerful parametric tool that generates an infinite variety of natural and organic curves and surfaces through a compact set of parameters. However, classical differential geometry has lacked a unified framework for analy...

Accurate mortality prediction is essential to actuarial practice as it is directly linked to insurance pricing, reserving, and the management of longevity risk. This study proposes a deep neural network (DNN) model for the mortality rates of multiple...

The harmonic structure of a chord C composed of rational frequency ratios is studied from its tonal graph. The graph describes harmoncity/periodicity properties of the chord allowing to characterize the chord from several parameters, which are easily...

This research focuses on the following equation: $(\overline{g}g-1)(g\underline{g}-1)+B\left(z\right){\displaystyle \frac{g^{\prime }\left(z\right)}{g\left(z\right)}}=R(z,g)={\displaystyle \frac{P(z,g)}{Q(z,g)}},$ where $P(z,g)$ and $Q(z,g)$ represent polynomials in g, possessing rational coefficients in z and lacking shared roots, $B\left(z\right)$ is...

We study finite-horizon first-passage time and boundary non-crossing probabilities for Gaussian martingales, viewed as continuous local martingales obtained by running Brownian motion on a deterministic variance clock associated with deterministic vo...

This paper introduces a rank-based panel kink threshold regression model with a covariate-dependent threshold, where the threshold is specified as a function of informative covariates. To estimate the model parameters, we propose a profile estimation...

We prove that a self-mapping T on a complete metric space $(X,D)$, satisfying a generalized contractive condition involving its $\rho$-th iterate $T^{\rho }$ ($\rho \in \mathbb{N},\rho \ge 2$) and a uniform coefficient bound $L<1$, possesses a unique fixed point. Th...

Distance measures play a crucial role in fuzzy decision-making, pattern recognition, and uncertainty modeling. However, some existing distance measures for Complex Picture Fuzzy Sets (CPiFSs) have shown limitations and may produce counterintuitive re...

We investigate Ricci–Bourguignon solitons on mixed doubly sequential warped product manifolds. Necessary and sufficient conditions for the existence of such solitons are established, and their implications for Einstein manifolds are analyzed. T...

Uncertain fractional differential equations model complex systems that exhibit memory effects and are influenced by human-based uncertainty. These equations provide a flexible and accurate framework for representing real-world phenomena, particularly...

To resolve the inherent conflict between high robustness and strict reversibility in frequency-domain image encryption, as well as to eliminate data expansion caused by floating-point errors, this paper presents a novel lossless frequency-domain imag...

In quantitative logic, the $\mathrm{\Delta }$ operator plays a crucial role in defuzzification by mapping multi-valued truth values to classical two-valued ones. This paper introduces and investigates the $\mathrm{\Delta }$-randomized divergent degree and consistent degre...

Recent developments in algebra, coding theory, and cryptography have shown that algebraic structures play an important role in both theoretical research and practical applications, with modern communication systems, reliable data transmission, and se...

This paper investigates the solution theory of a class of prescribed positive Q-curvature equations with power-law singularity at the origin and polynomial growth at infinity in the four-dimensional Euclidean space. We focus on the equation involving...

In modern reliability and survival analysis, modeling bounded-lifetime data under complex sampling mechanisms remains a challenging yet practically significant problem, particularly in biomedical and engineering applications where experimental time a...

We investigate the infeasibility of rank reversal in the Analytic Hierarchy Process under the Saaty and Belton–Gear frameworks. In the Saaty framework, we propose an algebraic characterization and show that it is equivalent to the geometric cha...

We introduce a minimal relational network model in which superconducting-like behavior emerges as a collective phase of constrained connectivity and phase coherence, without assuming microscopic electrons, phonons, or material-specific interactions....

Giving the definitions of one-parameter family of frontals in lightcone and one-parameter family of spacelike Legendrian curves in ${\Delta }_2$ and ${\Delta }_3$, and further using the variability condition and the tangency condition, the definitions of envel...

We study the long-time behavior of nonlinear stochastic evolution equations in a separable Hilbert space driven by a Q-Wiener process. The linear part of the equation is generated by a strongly continuous semigroup with an exponential dichotomy, whic...

In this paper, we give a characterization of the closed Jordan ideals of vector-valued Beurling algebras $L^1(G,\mathcal{A},\omega )$ and the direct sum of Banach algebras. We also investigate Jordan ideals of the $\theta$-Lau product of Banach algebras and give s...

This study presents findings on the existence, uniqueness, averaging principle, and numerical solutions for fractional stochastic systems influenced by both Brownian motion and Poisson jumps within the pth-moment framework. While most existing result...

This study proposes a novel image encryption algorithm based on a two-dimensional discrete chaotic system that integrates cellular automata (CA) with a tent map. The algorithm addresses security vulnerabilities in digital image transmission and stora...

Reusing separate, pre-filled Key-Value (KV) Caches for multiple contexts has become a common practice in handling multi-context scenarios with Large Language Models. However, this leads to a lack of cross-attention mechanisms between contexts. To add...

This paper introduces a rigorous class of two-dimensional Markov-switching autoregressive moving-average (2D MS-ARMA) models for spatial lattice data exhibiting regime-dependent dynamics. The switching mechanism is governed by a latent causal Markov...

In recent years, the study of generalized fuzzy structures in algebraic systems has attracted considerable attention due to their ability to represent uncertainty and bipolar information. In this paper, we introduce the notion of cubic bipolar ideals...