Axioms, Volume 15, Issue 5

Let X be a compact connected Riemann surface of genus $g\ge 2$ and let E be a holomorphic vector bundle of rank n over X. The compactness and connectedness of X imply that the characteristic polynomial of any holomorphic endomorphism $\phi \in H^0(X,\mathcal{E}n$...

Standard Bayesian autoregressive changepoint models can become unstable near sample boundaries. As a candidate changepoint approaches either edge of the series, the local residual degrees of freedom shrink, producing a Gamma-function singularity in t...

Tanner quasi-cyclic low-density parity-check (QC-LDPC) codes form an important family of structured LDPC codes with favorable girth properties. This paper studies the girth of Tanner $(2, L)$-regular QC-LDPC codes (referred to as Tanner QC-LDPC cy...

Roman-type domination parameters form an important class of graph invariants that model protection and resource allocation problems on networks. Among them, $\left[k\right]$-Roman domination provides a unified framework that generalizes Roman, double Roman, and h...

In this paper, certain subclasses of meromorphic harmonic functions which are formulated using a q-differential operator are meticulously analyzed. Initially, two new subclasses $W_H^q(k;E,F)$ and $W_{\eta }^q(k;E,F)$ associated with the Janowski function with...

With this Editorial, we present a Special Issue of Axioms entitled “Trends in Differential Geometry and Algebraic Topology [...]

This research paper investigates the solution of diffusion equations characterized by Third-Kind (Robin) boundary conditions within n-dimensional complex domains. The analysis is conducted in the $L_2$ Hilbert space, which facilitates the substantiation...

One of the main tasks in the field of directional statistics is to build goodness-of-fit tests for uniformity on circles, spheres or more abstract manifolds. We discuss a goodness-of-fit test for uniformity on a distance-regular graph. Our main tool...

In this paper, we study the geometric structure induced by the canonical reciprocal cost function and its natural n-dimensional extension. In logarithmic coordinates, the potential depends only on the linear combination $S=\alpha ·t$, and the as...

This paper extends Loomis’s classical spectral criterion for almost periodic functions to bounded sequences in discrete settings. We first establish a discrete Kadets-type theorem for bounded sequences by regarding almost periodic functions as...

Traditional DEA models can neither effectively handle fuzzy random variables nor achieve a complete ranking of decision-making units (DMUs). Based on the conventional fuzzy stochastic DEA model, this study introduces an exponential distribution exten...

We introduce the abstract weighted Morrey spaces $M_{p,u}^{\kappa }(X,\mathfrak{M},\mu )$, where $\mu$ is a general measure; investigate the properties of their predual spaces; and prove the boundedness of the Hardy–Littlewood maximal operator. Furthermore, we obt...

This paper presents two analytic mappings defined on probability measures that extend and unify the $(a,b)$- and $(s,t)$-deformations arising in free probability for s, $b>0$ and a, $t\in \mathbb{R}$. These unified operators, denoted ${\mathbf{U}}_{(a,b,s,t)}^{\prime }$ and ${\mathbf{U}}_{(a,b,}^{}$...

This manuscript investigates conformal $\eta$-Ricci–Yamabe solitons of type $(\kappa ,l)$ on Kählerian Norden space-time admitting a Kählerian Norden torse-forming vector field. Necessary conditions are obtained under which the soliton e...

We study the incompressible fractional viscous–resistive magnetohydrodynamic system on ${\mathbb{R}}^n$ with fractional diffusion ${(-\Delta )}^{\alpha }$, where $\alpha \in (1/2,1]$, and with positive viscosity and resistivity coefficients $\mu ,\nu >0$. Th...

This paper introduces and systematically develops the theory of polyadic group rings, a higher arity generalization of classical group rings. We construct the fundamental operations of these structures, defining the m-ary addition and n-ary multiplic...

We study the center problem for polynomial maps $y=f\left(x\right)=-x-{\displaystyle \sum _{n=1}^{\infty }}{a}_n{x}^{n+1},$ arising from homogeneous algebraic curves $x+y+{\displaystyle \sum _{i=0}^n}{\alpha }_{n-i,i}{x}^{n-i}{y}^i=x+y+H_n(x,y)=0.$ While explicit conditions were previously known only for...

In this paper, we consider the existence of normalized solutions for the fractional Kirchhoff system with Hardy critical nonlinearities. The problem combines the challenges of nonlocal operators, singular critical effects, and a variational framework...

The three-way decision paradigm is a new and auspicious paradigm approach to classification. It introduces a non-commitment region, allowing classifiers to abstain from (defer) uncertain predictions. This is a key mechanism in cascade classification...

An investigation is presented into the coupled thermo-mechanical behavior of a fiber-reinforced composite solid, with specific consideration given to the influences of gravity and thermal preconditions under inclined loading. The theoretical foundati...

Cluster Validity Indices (CVIs) act as a pivotal tool in machine learning for assisting in the determination of the optimal number of clusters. Nevertheless, traditional CVIs often exhibit subpar performance when confronted with the complex character...

This study investigates the robustness of Frenet–Serret curvature ($\kappa$) and torsion ($\tau$) estimates derived from noisy discretely-sampled three-dimensional space curves, with emphasis on the comparative performance of cubic spline and cub...

We investigate the nonlinear dynamics of a linearly coupled van der Pol–Duffing system using numerical continuation, time-domain simulations, stochastic analysis, and analog circuit experiments. The model exhibits a rich variety of dynamical re...

This paper proposes an outer space branch-and-search method for a class of linear fractional programming problems over a polytope. First, the original problem is reformulated in an equivalent problem by applying the equivalent transformation. Second,...

Connectivity is a classic measure that evaluates the fault tolerance of multiprocessor systems when processor failures occur. To better evaluate the reliability of multiprocessor systems, researchers have proposed many indicators based on connectivit...

The paper provides a new approach to estimating the coefficients of arbitrary holomorphic functions, which still remains an important problem of complex analysis. This approach is intrinsically connected with the features of univalent functions and w...

We extend the classical Euler-type integral representations for the Appell functions $F_1$, $F_2$, and $F_3$, to the appropriate Kampé de Fériet functions by using integration against the Meijer–Nørlund G-function. In particular, th...

This paper introduces a novel continuous probability distribution on the unit interval called the unit Jamal distribution and explores its properties. The proposed distribution performs well in modeling bathtub-shaped data, effectively capturing its...

This study presents some novel sharp estimates of the Euler–Maclaurin inequality using a new higher-order derivative Maclaurin identity. By utilizing the properties of convexity and classical inequalities, we exploit various novel tight boundar...

This paper focuses on optimizing machine learning-based time-series forecasting models by constructing compact data. Compact Data Learning for Time Series (CDL-TS) is a novel framework aimed at minimizing forecasting model errors. By utilizing reduce...

This work presents a new family of distributions (FoDs) called the exponentiated half logistic-generalized-Topp-Leone-G (EHL-GEN-TL-G) family. This family can be expressed as an infinite linear combination of exponentiated-G densities, which facilita...

An endogenous extension of the classical logistic equation, in which the carrying capacity $\kappa \left(t\right)$ varies in a periodic manner, is developed within this study. Existing theoretical results characterize the behavior of models of this nature. Nevert...

Singular behavior near the initial times, arising from the presence of fractional-order derivatives in fractional differential equations, often leads to the deterioration of solutions obtained using spectral methods when applied based on classical or...

The notion of 2-conformal vector fields on pseudo-Riemannian manifolds, which arose naturally in the study of hyperbolic solitons, is introduced by Fasihi-Ramandi, De, and Shamkhali. In this paper, we study invariant 2-conformal vector fields on four...

Mobi spaces were introduced by the authors as a possible algebraic axiomatization of spaces in which any two points are connected by a geodesic path. Previous work has focused primarily on the algebraic properties of these structures; here, we return...

We propose a novel subspace derivative-free conjugate gradient method for solving large-scale nonlinear monotone equations with convex constraints. At each iteration, the search direction is constructed by minimizing a quadratic model within a subspa...

We investigate the local well-posedness of semilinear fractional integro-differential equations in Banach spaces with the Hadamard fractional derivative. The equation is ${}^{H}D_t^{\beta }u\left(t\right)=Au\left(t\right)+\phi \left(t,u\left(t\right),{\int }_1^{t}K(t,s)\rho (s,u\left(s\right))ds\right),u\left(1\right)=u_0,$ where A ge...

Z.K. Li established the first explicit decoupling estimate for the parabola in the range $4<p<6$. Such explicit bounds are essential in number theory applications. Following the approach of J. Bourgain and C. Demeter, we derive an explicit bound...

This work introduces Fuzzy Implication Modeling Theory, a connective-centered framework that supplies an intermediate structural layer between the class and family levels in the subset of fuzzy implications generated by compositions of the three basi...

A new RSA variant based on the cubic Pell curve operates with a modulus $N=pq$ where the encryption and the decryption exponents e and d are linked by the congruence $ed\equiv 1 \left(\mathrm{mod}{(p-1)}^2{(q-1)}^2\right).$ At Africacrypt 2025, Rahmani and Nitaj...

Let $\mathcal{P}$ be a system of generalized prime numbers, and ${\mathcal{N}}_{\mathcal{P}}$ the corresponding system of generalized integers. Assuming that ${\displaystyle \underset{m\in {\mathcal{N}}_{\mathcal{P}}}{{\displaystyle \sum _{m⩽x}}}}1-ax\ll x^{\beta }$ with $a>0$ and $0⩽\beta <1$, we consider the Beurling zeta-function ${\mathrm{\&zeta}}_{}$...

We first study the f-biharmonicity of totally umbilical hypersurfaces in a Riemannian manifold of dimension $n\ge 3$ and prove that any totally umbilical proper f-biharmonic hypersurface without boundaries in a nonpositively curved manifold must be non...

This paper revisits the use of the Laplace transform in the study of Bessel and modified Bessel differential equations. Rather than presenting the method as a new alternative to the classical Frobenius approach, the paper is organized as a pedagogica...

The paper links Stevenson’s formally complex hypergeometric polynomials to the real-by-definition Romanovski-Routh (R-Routh) polynomials. The spectral problem for Stevenson’s second-order normal ordinary differential equation (NODE) was f...

This survey presents an overview of recent developments in the analysis and numerical treatment of spectral fractional diffusion equations. Particular attention is devoted to efficient strategies for solving spectral fractional diffusion problems, in...

This survey provides a systematic review of delayed matrix functions and their role in deriving explicit solutions for linear discrete delay systems. Tracing the evolution from foundational single-delay first-order systems to sophisticated multi-dela...

Complex metrics play a fundamental role in applied mathematical analysis and in the study of physical phenomena. In this work, two complex Minkowski spacetime metrics are examined in detail. The investigation centers on the spin matrices that generat...

In this paper, we investigate Chen’s $\delta$-invariant for partially slant (PS) submanifolds of complex space forms. A PS-submanifold admits an orthogonal decomposition of the tangent bundle into a proper slant distribution and an arbitrary amb...

We investigate biased and unbiased Monte Carlo algorithms for solving Fredholm integral equations of the second kind and for estimating linear functionals of their solutions. Fredholm integral equations provide a common mathematical framework in unce...

The score set of a tournament is defined as the set of its distinct out-degrees. In 1978, Reid proposed the conjecture that for any set of nonnegative integers D, there exists a tournament T with a score set D. In 1989, Yao presented an arithmetic pr...