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This article develops a comprehensive theory of multiary graded polyadic algebras, extending the classical concept of group-graded algebras to higher-arity structures. We introduce the notion of grading by multiary groups and investigate various comp...

This study examines a nonlinear partial differential equation, namely the (3+1)-dimensional Boussinesq-type equation. To explore this model, three versatile analytical approaches are applied: the Exp-function method, the Kudryashov method, and the Ri...

In this study, we investigate the upper- and lower-bound approximations of numerical eigenvalues derived by weak Galerkin spectral element methods on arbitrary convex quadrilateral meshes for the Laplace eigenvalue problem. Firstly, the Piola transfo...

Provided that the initial data $({\rho }_0,v_0,{\eta }_0)$ is of small energy around steady state $({\rho }^{▵},0,0)$, in this work we obtain the global-in-time existence of weak solutions to a fluid particle interaction system. It should be pointed out that v...

The Fourier transform is continuous in the weak sense of tempered distribution; this ensures the weak stability of Fourier pairs. This article investigates a stronger form of stability of the pair of homogeneous profiles $\left(\right|x{|}^{-\alpha },c_d|\xi {|}^{d\&}$...

The Energy-Efficient Hybrid Flow Shop Scheduling Problem poses a significant multi-objective optimization challenge, necessitating the simultaneous minimization of conflicting objectives: Total Tardiness, Total Energy Cost, and Carbon Trading Cost. T...

We present Hyperbolic Symmetric Hypermodular Neural Operators (ONHSH), a novel operator learning framework for solving partial differential equations (PDEs) in curved, anisotropic, and modularly structured domains. The architecture integrates three c...

The efficient minus domination problem (EMDP) and the efficient signed domination problem (ESDP) are domination-type problems in graphs. These problems are known to be NP-complete on chordal graphs and polynomially solvable on chain interval graphs,...

We consider two steady-state heat conduction systems called, S and $S_{\alpha }$, in a multidimensional bounded domain D for the Poisson equation with source energy g. In one system, we impose mixed boundary conditions (temperature b on the boundary ${\mathsf{\&Gamm}}_{}$...

An odd right-end semigroup (hereinafter Ore semigroup) is a numerical semigroup S verifying that $x+1\in S$ for every $x\in S\setminus \left\{0\right\}$ such that x is even. The introduction and study of these semigroups is the purpose of the present work. In partic...

In this paper, we present approximation results for a generalized $\alpha$-non-expansive multi-valued mapping using a four-step iteration scheme introduced in the context of a convex metric space. We extend some recent results about generalized $\mathrm{\&alpha}$...

This paper investigates a fractional-order mathematical model for the co-infection dynamics of pneumonia and typhoid fever using the Liouville–Caputo derivative. We establish the existence, uniqueness, non-negativity, and boundedness of solutio...

In this work, we revisit the two-step Jarratt method from the perspective of numerical stability. While high-order iterative schemes are often examined in terms of convergence rate and computational efficiency, their backward stability properties hav...

Asymptotic synchronization is one of the essential differences between artificial neural networks and biologically inspired neural networks due to mismatches from the dynamical update of weight parameters and heterogeneous activations. In this paper,...

This review develops a unified geometric framework for synthesizing global asymptotic laws, termed classical entanglement. The central tool is the entanglement operator, a Minkowski–$L_a$ metric blend that couples asymptotic regimes through an ind...

Using some new techniques, criteria for strongly exposed points of Orlicz sequence spaces generated by arbitrary Orlicz function and equipped with the p-Amemiya $(1 < p < \infty )$ norm are obtained. Next, strongly exposed pro...

This study analyzes network coherence in two-layer and three-layer networks with positive and negative inter-layer correlation patterns. Using algebraic graph theory, we construct the Laplacian matrices for different correlated graph structures and c...

This paper investigates the conservation of mass and energy in the space-fractional Klein-Gordon-Schrödinger system with fractional Laplacian operators. Firstly, the invariant energy quadratization method is applied to transform the original sys...

This article develops a combinatorial and graph-theoretic framework for the study of finite-dimensional anticommutative algebras. Given a fixed basis, we associate to each algebra a directed graph that may contain filled oriented triangles, encoding...

Latent growth modeling (LGM) is widely used to examine group differences in developmental trajectories in educational research. With multiple outcomes of interest, a multiple-domain latent growth model (MDLGM) can be applied to account for associatio...

This paper investigates the event-triggered secure consensus problem for stochastic multi-agent systems (MASs) subject to bilateral false data injection attacks (FDIAs). To achieve reliable secure consensus while reducing resource consumption, an eve...

This paper investigates an abstract fractional Cauchy problem with damping formulated in the sense of the Caputo derivative, where the derivative orders satisfy $0<\delta <\gamma \le 1$. By introducing the concept of a Caputo fractional $(\gamma ,$...

Increasing turbulence in contemporary business environments has made the quantitative analysis of unstructured textual data a central methodological challenge for researchers and decision-makers. The increasing availability of large-scale textual dat...

This work addresses the numerical solution of fourth-order initial value problems of the form $y^{\left(4\right)}=f(x,y,y^{\prime })$, extending the capabilities of standard Runge–Kutta–Nyström (RKN) methods which are typically limited to $y^{\left(4\right)}=f(x,y)$....

This paper mainly studies the equivariant Hopf bifurcation of a delayed reaction–diffusion predator–prey model with stage structures on a two-dimensional circular domain. Firstly, we calculate the existence of steady-state solutions, and...

This paper investigates the optical solitons to the M-truncated fractional $(1+1)$-dimensional nonlinear generalized Bretherton model with arbitrary constants. It is employed to forecast the movement of liquid droplets or gas bubbles in microchannels,...

The coupled nonlinear system of fractional Boussinesq–Burger equations that may be utilized to model the propagation of shallow water waves is solved in this study using a novel numerical approach. The fractional derivatives in Caputo–Fab...

This paper introduces coefficient functionals for a new subclass (${\mathcal{S}}_{tanh}^{*})$ of starlike functions associated with the tangent hyperbolic function, including the first four sharp coefficient bounds, the Fekete-Szegő problem, Zalcman inequalities, a...

Functional data analysis (FDA) provides a framework for representing high-frequency or longitudinal observations as smooth functions, enabling principled dimension reduction and feature extraction. We develop a B-spline-based FDA approach with a tota...

Maximizing the expected value of a concave and strictly increasing utility function defines a fundamental class of discrete optimization problems. Among them, coverage decision problems with diminishing marginal returns under uncertainty, typically m...

In this paper, we establish sharp pinching inequalities that relate the generalized $\delta$-Casorati curvatures to the normalized scalar curvature of submanifolds immersed in Kähler product manifolds endowed with a quarter-symmetric metric conne...

In order to overcome the computational challenges associated with block preconditioners for Krylov subspace methods, particularly those arising from Schur complement systems, this paper proposes an improved new block (INB) preconditioner for solving...

This paper proposes a continuous-time dynamic clearing model on a multilayer financial network to study systemic risk propagation and optimal intervention. The model incorporates interbank credit, equity crossholdings, and overlapping portfolios, and...

Dynamical systems with chaotic attractors are an interesting topic not only for their complex behavior but also due to their potential applications. Along with the chaos, systems can also present interesting features such as multistability, global ba...

This work presents a pair of sharp geometric inequalities that connect the normalized scalar curvature with the generalized normalized $\delta$-Casorati curvature for $\theta$-slant submanifolds immersed in quaternionic space forms endowed with a quart...

Integral inclusion systems play a significant role in applied analysis and modeling, providing an effective framework for studying various physical, engineering, and dynamical processes. In this work, the solvability of a multidimensional integral in...

The bichromatic triangle polynomial $P_G\left(k\right)$ counts vertex k-colorings in which every triangle uses exactly two colors. We develop a transfer matrix framework for three canonical families of 2-trees: book graphs $B_n$, 1-fans $F_n^1$, and triangulated ladders...

Let $(M_1,F_1)$ and $(M_2,F_2)$ be two Finsler manifolds. A Minkowskian product Finsler manifold is defined to be the product manifold $M_1\times M_2$, which is endowed with a Finsler metric F. This metric F is constructed by taking the square root of a product...

The purpose of this research article is to establish common fixed point results for generalized contractions defined with control functions in the framework of elliptic-valued suprametric spaces. By utilizing the structure and properties of these spa...

This study presents a higher-order uniformly convergent numerical method for a singularly perturbed nonlinear reaction–diffusion equation. The quasilinearization technique is used to transform a nonlinear term into a linear boundary value probl...

The Burgers–Huxley equation is a nonlinear partial differential equation that incorporates convective, diffusive and reactive effects and arises in various reaction–diffusion and fluid flow models. In this paper, a numerical method based...

Let $(X,\mathfrak{A},P)$ and $(Y,\mathfrak{B},Q)$ be two probability spaces, R be their skew product on the product $\sigma$-algebra $\mathfrak{A}\otimes \mathfrak{B}$ and $\{({\mathfrak{A}}_y,S_y):y\in Y\}$ be a Q-disintegration of R. Then, let $\mathfrak{A}\divideontimes \mathfrak{B}$ be the $\sigma$-algebra generated $\mathfrak{A}\otimes \mathfrak{B}$ and by the family...

The (3+1)-dimensional B-type Kadomtsev–Petviashvili (BKP) problem was examined in this paper using the developed Exp-function method (DEFM) and Lie symmetry analysis. The objective of this research is studying the BKP equation to get novel exac...

This work is axiomatic and structural in nature and is not intended as a phenomenological physical theory, but as a framework clarifying minimal informational primitives from which geometric and dynamical descriptions may emerge. We present a backgro...

In clinical studies such as ophthalmologic or otolaryngologic research, bilateral correlated data frequently arise when outcomes are collected from paired organs or body parts. Since the measurements from such paired observations are usually highly c...

The second immanantal polynomial is one of the important directions in algebraic theory. Let $M=\left[m_{ij}\right]$ be an $n\times n$ matrix. The second immanant of matrix M is defined as $d_2\left(M\right)={\sum }_{\sigma \in S_n}\chi \left(\sigma \right){\prod }_{i=1}^n{m}_{i\sigma \left(i\right)}$, where $\chi$ is...

Closed-form analytic inverses allow explicit tracking of parameter effects, facilitate interpretation of experimental signals, and support solving inverse problems. Here, we derive a rigorous closed-form expression for the inverse Laplace transform o...

We study ratio-induced mismatch cost functions of the form $c(s,o)=J\left({\iota }_S\left(s\right)/{\iota }_O\left(o\right)\right)$ built from positive scale maps ${\iota }_S:S\to {\mathbb{R}}_{>0}$ and ${\iota }_O:O\to {\mathbb{R}}_{>0}$ and a penalty $J:(0,\infty )\to [0,\infty )$. Assuming inversion symmetry, strict...

In many scientific fields (e.g., statistics, data science, machine learning, and image processing), effectively quantifying the statistical difference between two probability distributions is an important task. Although a wide variety of measures hav...

Parallel–series systems are fundamental in many industrial and engineering applications, yet their reliability assessment and improvement remain challenging, particularly when components exhibit non-constant failure rates. This study addresses...