Axioms, Volume 14, Issue 11

In this paper, we investigate a fuzzy Hilfer fractional evolution equation of type $0<\beta <1$ and order $1<\alpha <2$ subject to nonlocal conditions. Using the infinitesimal generator of a strongly continuous cosine family, we define a mild...

In this study is introduced a novel generalization of repunit and one-zero numbers through the formulation of the generalized One-kZero. This sequence extends the classical families of repunit and one-zero numbers by establishing a unified framework...

In this paper, a $k/n\left(G\right)$ retrial system with multiple working vacations is considered, and a mathematical model of the system is established by supplementary variable method, and a dynamic analysis of the system is carried out. Firstly, the model is t...

In this manuscript, we study a general incompressible Oldroyd-B system and first establish a new interpretation for the Green’s matrix and then establish the pointwise estimates for the Green’s matrix, especially for the high-frequency pa...

Topological field theories (TFTs) have captured the attention of mathematicians due to their various applications. In categorical terms, an nTFT is defined as a monoidal functor that maps the category of n-dimensional cobordisms to the category of ve...

In this paper, we initiate the study of the asymptotic and oscillatory properties of solutions to third-order functional differential equations. Using the Riccati transformation to eliminate the existence of non-oscillatory solutions, we derive vario...

The transportation problem (TP) is a canonical linear programming model for minimizing the cost of distributing goods from multiple sources to multiple destinations. Classical TPs assume deterministic costs, supplies, and demands, whereas real supply...

This work presents a complete and definitive characterization of all cases where every linear combination of two commuting essentially cubic matrices results in a quadratic matrix, thereby extending existing contributions in the literature. To facili...

This study examines the trapping of linear water waves by an endless structure of stationary, three-dimensional periodic obstacles within a two-layer fluid system. The setup features a lower layer of either limited or unlimited depth, overlaid by an...

We systematically exploit a new generalized hypergeometric identity to obtain new hypergeometric summation formulas. As a consistency test, alternative proofs for some special cases are also provided. As a byproduct, new summation formulas with finit...

We investigate a combined conservative field, in which classical gravitational and electrostatic sources also exhibit mutual interactions. Hitherto neglected, the coupling between mass and charge may be necessary for constructing a unified conservati...

This work explores the dynamics of quantum Fisher information (QFI) in open quantum systems coupled to squeezed reservoirs, providing a mathematical framework for analyzing parameter estimation precision under decoherence. We analyze QFI in two-qubit...

HMLasso (Lasso with High Missing Rate) is a useful technique for sparse regression when a high-dimensional design matrix contains a large number of missing data. To solve HMLasso, an appropriate positive semidefinite symmetric matrix must be obtained...

Let $(M,g)$ be a connected, compact Riemannian manifold of dimensionan n. We demonstrate that, after a suitable normalization, a shrinking gradient Ricci soliton $(M,g,f,\lambda )$ is trivial exactly when the mean value of f is less than or equal to $\frac{n}{2}$....

The geometrical view of the electron as a spinning bivector leads to the partitioning of the electron’s energy into internal and external. The reduced Compton wavelength, ${\overline{\lambda }}_C$, is taken as the radius of the inertial ring (a disc), wh...

In this paper, we study the optimal boundary control of solidification governed by the classical two-phase Stefan problem with a sharp moving interface. The main objective is to formulate an optimal control problem for interface motion using boundary...

This paper presents the first theoretical investigation of the effect of a variable equilibrium coefficient on the steady-state transport of a binary electrolyte in a desalination channel cross-section of the electrodialyzer. To address this problem,...

This paper focuses on the research of the existence of cyclic bases for the quotient ring modulo, a zero-dimensional ideal. Based on the necessary and sufficient condition for the existence of cyclic bases, it further deduces an equivalent condition...

The index-theoretic construction of differential K-theory by Bunke and Schick uses both a geometric family and a differential form as a cocycle data. We prove that geometric families alone can codify the differential K-theory.

This study is devoted to the quasi-optimal convergence analysis of a family of adaptive nonconforming elements with high-order terms, which preserve weak continuities. In contrast with the nonconforming $P_1$ element (Crouzeix–Raviart element) the...

A novel original procedure of encryption/decryption based on the polyadic algebraic structures and on signal processing methods is proposed. First, we use signals with integer amplitudes to send information. Then, we use polyadic techniques to transf...

By using the $C_0$-semigroup theory, we study the asymptotic behavior of the time-dependent solution and the time-dependent indices of the ${\mathrm{M}}^{[\mathrm{X}]}/\mathrm{G}/1$ queuing model with feedback and optional server vacations based on a single vacation policy. This queuing...

In this paper, we study a backward problem for a fractional Rayleigh–Stokes equation by using a quasi-boundary value method. This problem is ill-posed; i.e., the solution (if it exists) does not depend continuously on the data. To overcome its...

In this paper, a Holling–Tanner predator–prey model with generalist predators and Michaelis–Menten-type prey harvesting is investigated. We analyze the existence and stability of equilibria and find the system has at most three posi...

Spacetime singularities, in the sense that curvature invariants are infinite at some point or region, are thought to be impossible to observe, and must be hidden within an event horizon. This conjecture is called Cosmic Censorship (CC), and was formu...

This paper proposes an efficient iteration method for fixed-point approximation in Banach spaces. The method accelerates convergence by incorporating a squared operator term within the iteration process. Analytical proofs verify its convergence and s...

This paper considers the pricing of a subscription service in a heterogeneous market with consumers having different discount rates. We show that in the case of a non-zero enrollment/cancellation cost, solutions of the Hamilton–Jacobi–Bel...

This study presents a comparative analysis of two bio-inspired optimization techniques: the Dragonfly Algorithm (DA) and Cuckoo Search (CS). The DA models the collective behavior of dragonflies, replicating dynamic processes such as foraging, evasion...

This article investigates single-machine group scheduling integrated with resource allocation under different due-window ($DIFDW$) assignment. Three distinct scenarios are examined: one with constant processing times, one with a linear resource consump...

From both theoretical and applied perspectives, the trapezoidal fuzzy numbers are widely relevant fuzzy sets. In this paper, we show that the four kinds of common metrics—the supremum metric, the $L_p$-type $d_p$ metrics, the sendograph metric, and t...

For a connected graph G, let $D^L\left(G\right)$ be its distance Laplacian matrix and ${\lambda }_1\left(G\right)\ge {\lambda }_2\left(G\right)\ge \dots \ge {\lambda }_{n-1}\left(G\right)>{\lambda }_n\left(G\right)=0$ be its $D^L$ eigenvalues. The $D^L$ energy of G is defined as $DLE\left(G\right)={\sum }_{i=1}^n\left|{\lambda }_i\left(G\right)-{\displaystyle \frac{2W\left(G\right)}{n}}\right|$,...

We investigate the relationships between the weak resolution dimensions of subcategories of module categories of Artinian algebras in the present paper. Let $\Lambda$ be an Artinian algebra, and $\mathcal{A}$, $\mathcal{B}$ and $\mathcal{X}$ subcategories of $\Lambda$-modules, such that...

In this paper, we establish a new fractional integral identity linked to the 4-point Lobatto quadrature rule within the Riemann–Liouville fractional calculus framework. Building on this identity, we derive several Lobatto-type inequalities unde...

Fuzzy edge coloring has proven to be a powerful tool for modeling and optimizing complex network systems, owing to its ability to effectively represent and manage the uncertainty in relational strengths and conflicts. It focuses on defining the fuzzy...

This study constructs a Stackelberg differential game model for green technology invest-ment in the food industry under a governmental coordination mechanism. The optimal dynamic strategies for local governments and enterprises are derived using Pont...

This study concerns an online generalized multiscale method for flow in fractured porous media that is based on an embedded discrete fracture model. We first convert a two-point flux-approximation scheme into an equivalent discrete weak formulation t...

The Horadam sequence ${\left\{H_n(a,b;p,q)\right\}}_{n⩾0}$ has been widely studied in combinatorics and number theory. In this paper, we find that the context-free grammar $G=\{x\to px+y,y\to qx\}$ can be used to generate Horadam sequences. Using this grammar, we...

This study focuses on the formulation and analysis of problems that are dual to those defined by convex set-valued mappings. Various important classes of optimization problems—such as the classical problems of mathematical and linear programmin...

This article presents several key findings for fractional-order delay differential equations. First, we establish the existence and uniqueness of solutions using two distinct approaches, the Chebyshev norm and the Bielecki norm, thereby providing a c...

An abstract convexity type is ${\mathbb{B}}^{-1}$–convexity. For ${\mathbb{B}}^{-1}$–convex functions, the Hermite–Hadamard inequality was previously found. Recently, however, new and more popular types of fractional integral operators have been develo...

Real-time control of web traffic is a critical issue for network operators and service providers. It helps ensure robust service and avoid service interruptions, which has an important financial impact. However, due to the high speed and volume of ac...

This work investigates the interplay between the Mellin transform and Lambert transforms to derive several novel results. In particular, we establish new inversion formulae for the Lambert transforms along with a Plancherel-type identity. Additionall...

Shock–accelerated interfaces between fluids of different densities are prone to Richtmyer–Meshkov-type instabilities, whose evolution is strongly influenced by the incident shock Mach number. In this study, we present a systematic numeric...

Multicollinearity among predictor variables is a common challenge in modeling chemical and environmental datasets in physical sciences, often leading to collinearity issues and unreliable parameter estimates when fitting regression models. Ridge regr...

We consider four infinite collections of improper integrals involving the sine and cosine functions and provide explicit values for the integrals in each of the collections. The methods used are elementary and involve the sine integral function and t...

We present a comprehensive quantum field theoretical analysis of graviton self-energy and mass generation in 3+1 dimensional BTZ black hole spacetime, incorporating axion interactions within the framework of dark matter theory. Using a novel mathemat...

In this review, we present a general framework for the construction of Kac–Moody (KM) algebras associated to higher-dimensional manifolds. Starting from the classical case of loop algebras on a circle ${\mathbb{S}}^1$, we extend the approach to compact and n...

The Allen-Cahn equation is a fundamental model in materials science for describing phase separation phenomena. This paper introduces an Energy-Stabilized Scaled Deep Neural Network (ES-ScaDNN) framework to solve the Allen-Cahn equation by energy mini...

This paper presents a novel approach to the controllability of nonlinear dynamic systems using recurrent neural networks (RNNs). We develop a comprehensive theoretical framework that integrates controllability analysis, stability verification via Lya...

The distributivity of implications over fuzzy operators is a desirable property for fuzzy systems and can be employed in the elimination of the explosion of if–then rules. In this paper, we try to explore the relationship between the distributi...