Axioms, Volume 15, Issue 4

The aim of the present work is to give a mathematical underpinning for the use of quasi-probabilities and pseudo-metrics in infinite-dimensional Banach manifolds. The notion of a continuous binary structure is introduced. It is a triple consisting of...

Let $\epsilon >0$ and $\mathcal{TB}(\mathcal{X}\times \mathcal{X})$ be the Banach algebra of all $2\times 2$ bounded upper triangular operator matrices on a separable Hilbert space $\mathcal{X}\times \mathcal{X}$. In this paper, we first establish the spectrum equalities for special cases of upper triang...

Along with some known and less known results, we discuss new insights relating combinatorics of words and the ordering of rationals from a dynamical systems point of view, somehow continuing along the path started in previous works of the first autho...

This work addresses the integrability of four-dimensional quadratic Lotka–Volterra systems exhibiting (1:−1:i:−i) resonance by identifying the parameter constraints required for such properties to exist. Our results show that, withi...

The support functions of crisp sets have been widely used in the topic of nonlinear analysis. This observation inspires to introduce the support functions of fuzzy sets. Two different support functions of fuzzy sets were introduced in the literature...

We investigate gradient Einstein solitons admitting closed conformal vector fields. Under constant scalar curvature, we establish rigidity results showing that complete solitons with non-parallel closed conformal vector fields are isometric to Euclid...

In this paper, we investigate controllability for both linear and nonlinear Hahn difference equations, whose nonlinear terms are given by involving maxima. Introducing a Grammian matrix, we derive a necessary and sufficient condition characterizing c...

Let ${\mathcal{Z}}_2\left(s\right)$ denote the modified Mellin transforms of the modulus of the fourth power of the Riemann zeta-function. This paper is devoted to the probabilistic properties of generalized discrete shifts ${\mathcal{Z}}_2(s+i\psi \left(k\right))$, $k\in \mathbb{N}$, with a certain differenti...

In this paper, we present a novel identity for twice partially differentiable mappings. Based on this identity, new fractional Bullen-type inequalities for differentiable functions of two variables, which are convex on the coordinate via Riemann&ndas...

Zagreb-type indices are topological indices derived from the degrees of nodes. The first Zagreb index, the F-index, and the Y-index represent the sum of the squares, cubes, and fourth powers of all node degrees, respectively. These indices are valuab...

Oscillatory motions in stratified atmospheric fluid layers significantly influence weather and climate dynamics. Shallow-water equations effectively describe these motions. This study extends the shallow-water model to the time-fractional domain usin...

The arbitrary-order hidden Markov model ($\alpha$-HMM) is a nontrivial generalization of the standard HMM, designed to model stochastic processes with higher-order dependences among arbitrarily distant random events. The $\alpha$-HMM admits an efficien...

The Mittag-Leffler function holds significant importance in fractional calculus due to its extensive applications in addressing challenges across science, engineering, biology, hydrology, and earth sciences. Notably, the closed-form solution of a tim...

This work investigates a sophisticated class of neutral fuzzy fractional functional differential equations (N3FDEs), where the fractional order $\alpha$ satisfies $0<\alpha \le 1$. We present a comprehensive analysis of the existence, uniqueness, and...

In this paper, we present the spinor structure associated with the Hyperbolic Clifford algebra of a real n-dimensional vector space V, which is denoted by $\mathcal{C}l\left(H_V\right)$. Unlike the standard Clifford algebra, the Hyperbolic Clifford algebra $\mathcal{C}l\left(H_V\right)$ simultaneous...

A new approach in constructing a univariate absolutely continuous probability model via power transformation is adopted. The proposed distribution appears to subsume several popular univariate continuous probability models that are already existent i...

C. F. Hansen’s NASA TR R-50 published in 1959 remains one of the most widely used analytic approximations for the thermodynamic and transport properties of high-temperature air. Although modern equilibrium and nonequilibrium models extend the t...

We investigate whether the geometric parameters of a three-dimensional domain can be recovered from the Dirichlet spectrum of the Laplacian. As a controlled benchmark, we consider rectangular boxes, about which the eigenvalues are explicitly known an...

Detonation phenomena in reactive flow systems continue to pose significant challenges for accurate simulation, particularly in 3D validation against experiments and achieving community standardization for schemes. Among the primary difficulties is th...

This paper gives expansions for the distribution, density and quantiles of any estimate that is a smooth function of the sample cross-moments of a stationary process. Three versions of these are given, depending on whether an exact, approximate, or a...

The goal of this study is to establish a new type of Milne-type inequality in the scope of fractional calculus with the aid of proportional Caputo-hybrid operators. We will focus on two different scopes of regularity, which contain functions whose fi...

Assouad-type dimensions primarily describe the local structure of sets and have attracted significant attention in recent years within the field of fractal geometry. In this paper, we derive a formula for the Assouad dimension and establish an upper...

We investigate a generalization of complement reducible graphs, called co-graphs, for r-uniform hypergraphs. The operations of r-co-hypergraphs are the disjoint union of two given r-co-hypergraphs and the join operation, which inserts all hyperedges...

The most well-known perturbed Dirichlet series is the Hurwitz zeta-function. Its analytic continuation via the binomial expansion has been studied extensively, beginning with Wilton’s work. In this paper, we shall provide, above all things, two...

In 2024, Kimura proposed the modified shrinking method without assuming the existence of a common fixed point for a family of nonexpansive mappings defined on a complete geodesic space with a nonpositive upper curvature bound. In this paper, we discu...

This article proposes a novel time-space two-grid high-order compact difference scheme for the one-dimensional nonlinear Schrödinger equation subject to Dirichlet boundary conditions. In comparison with the fully nonlinear compact difference sch...

The paper proposes a new mathematical framework in explaining the effect of periodic electric fields on the nonlinear interfacial instability emerging between two Walters’ B/Rivlin–Ericksen of non-Newtonian fluids. The suggested approach...

Modeling and forecasting nonstationary and nonlinear economic time series remain fundamentally challenging due to structural breaks, volatility clustering, and noise contamination that distort the intrinsic stochastic structure. To address these limi...

Following Bauer’s 1985 question on how a graph’s minimum degree relates to it being supereulerian, Catlin solved the problem for graphs with a minimum degree of at least ${\displaystyle \frac{n}{5}}$. Subsequently, Lai solved it for the case where the minimum degre...

Some inequalities for products of Struve functions $H_{\nu }\left(x\right)$ when $\left|\nu \right|\le {\displaystyle \frac{1}{2}}$ are established using their infinite product formula as well as the arithmetic–geometric mean inequality. When these results are combined with some previously establi...

The Dedekind $\eta$-function plays an important role in number theory, particularly in the study of modular forms, q-series, and partition identities. In this paper, we investigate several level-12 $\eta$-function identities and examine their combinato...

This paper investigates fundamental concepts of statistical convergence for double sequences of time-scale functions via the deferred Cesàro summability mean. Several limit properties and inclusion relations between the newly-introduced conver...

The present paper is aimed at studying the convergence of the Yamabe flow in the case of noncompact solitons. The more specified example of locally conformally flat noncompact solitons is addressed with the aim to newly analyse the qualities of the R...

In clinical research, unilateral data and bilateral data are commonly collected when paired organs or body parts of people receive treatment. Existing models are often inadequate for the research of combined unilateral and bilateral data. Considering...

We develop the Sawyer duality principle for non-increasing functions where, in the denominator, the function g is replaced by ${\int }_x^{\infty }{\displaystyle \frac{g\left(t\right)}{t}}dt$. This result complements Stepanov’s result in which g was replaced by ${\displaystyle \frac{1}{x}}{\int }_0^{x}g\left(t\right)dt$. We use our...

This paper synthesizes classical results in Hodge theory, curvature positivity, and vanishing theorems to give a concise curvature–cohomology criterion for the projectivity of compact Kähler manifolds. While each analytic component—Y...

While the standard Schwarzschild metric is overwhelmingly employed in general relativity (GR) as the starting point for various spherical spacetime metric calculations, its isotropic (ISO) form is mentioned in more specialized contexts and its deriva...

This work investigates stability under Hyers–Ulam criteria for a class of Hadamard Neutral fractional stochastic differential equations (HNFSDE). The analysis applies a fixed-point theorem (FPT) combined with principles of stochastic integratio...

This study presents results on the well-posedness, Ulam–Hyers stability, and $\mathrm{m}$th moment averaging principle for the Itô–Doob fractional stochastic system within the framework of $\eta$-Caputo fractional derivatives. We demonstrate we...

We study equilibrium and stability properties of self-gravitating bosonic configurations in the nonrelativistic regime by numerically solving the nonlinear Gross–Pitaevskii–Poisson (GPP) equations system. Using an appropriate coordinate t...

Let $\mathcal{N}$ be a nest on a Banach space, and let $Alg\left(\mathcal{N}\right)$ denote the associated nest algebra equipped with the operator norm. In this paper, we develop a Banach–Lie framework for bounded triple derivations and triple automorphisms on $Alg\left(\mathcal{N}\right)$. We prove t...

Let $\mathcal{A}$ be a unital ∗-algebra containing a nontrivial projection P. In this paper, we introduce the notion of a nonlinear mixed skew Jordan-type derivation (that is, $p_n\left(S_1,S_2,S_3,\cdots ,S_n\right)=S_1\diamond S_2•S_3•\cdots •S_n$, where $S\diamond K$...

Let $0,1\ne m\in \mathbb{Z}$ and $\alpha =\sqrt[8]{m}$. According to the results of Gaál and El Fadil, $\alpha$ generates a power integral basis in $K=\mathbb{Q}\left(\alpha \right)$, if and only if m is square-free and $m\not\equiv 1\left(\mathrm{mod}4\right)$. In the present paper, we consider totally complex...

This paper studies prescribed-time (PT) stabilization for a heat equation with an unstable term at the uncontrolled boundary, subject to external disturbances and internal unknown mode uncertainties at the controlled boundary. A boundary time-varying...

In order to solve linear systems of Fredholm integral equations, this paper proposes a novel hybrid numerical method that combines improved block-pulse functions with Legendre polynomials. By utilizing the orthogonality and strong approximation prope...

We provide a combinatorial proof for the fact that the numbers of derangements of length n form a log-convex sequence for $n\ge 3$. A minor modification of our proof yields the same result for permutations of length $n\ge 4$ that have exactly one fixed p...

This study aims to advance the understanding of laminar magnetohydrodynamic (MHD) fluid flow between two parallel plates subjected to a uniform transverse magnetic field, motivated by its significant applications in engineering and industrial systems...

We study the predictability and cross-market structural similarity of Brent, WTI, and Dubai crude oil futures by means of a wavelet-based Sharma–Mittal energy entropy measure. The proposed framework combines multiresolution wavelet decompositio...

Fix $m\ge 3$. The choice number $ch\left(K_{m,n}\right)$ of the complete bipartite graph $K_{m,n}$ has two sharp thresholds as n grows. We give complete proofs of the Hoffman–Johnson values at levels $m+1$ and m, and we pin down the extremal list assignments at the low...

In this paper, a cold standby repairable system comprising two heterogeneous components, each characterized by multiple types of mutually independent failure modes, is investigated. The operational lifetimes of the components follow exponential distr...