December 2025 - 75 articles
The Horadam sequence Hn(a,b;p,q) unifies a number of well-known sequences, such as Fibonacci and Lucas sequences. We use the context-free grammars as a new tool to study Horadam sequences. By introducing a set of auxiliary basis polynomials (v1,v2,v3...
This study examines the synchronization of Markovian switching stochastic delayed complex dynamical networks (MSSDCDNs). MSSDCDNs have general structures and coupling forms, which are influenced by Markovian switching, random disturbances, and time d...
Let G=(V,E) be a simple graph with the vertex set V and the edge set E|V|=n,|E|=m. An example of a vertex-decorated graph DG is a vertex-quadrangulated graph QG. The vertex quadrangulation QG of 4-regular graph G visually looks like a graph whose ver...
This work presents a comprehensive study of quantum correlations and their degradation under environmental dephasing within the atomic hydrogen system. By analyzing the magnetic coupling between the electron and proton spins in the 1s hyperfine state...
This paper develops the theory of strongly continuous semigroups and abstract evolution equations in modular function spaces. We study the autonomous problem u˙(t)=Bu(t) with initial condition u(0)=u0∈Lρ, where B is the infinitesimal ge...
We present a mathematical analysis of the sterol regulatory element-binding protein 2 (SREBP-2) pathway, a key regulator of intracellular cholesterol homeostasis. Using a compartment model formulated as a nonlinear system of ordinary differential equ...
A graph G is said to be singular if its adjacency matrix is a singular matrix. In this paper, by analyzing the structure of Sachs subgraphs on three types of tricyclic graphs ϖ(a1,a2,b1,b2,c1,c2), σ(a1,a2,b1,b2,c), and τ(a1,a2,a3,a4) an...
We analyze the population dynamics of a microbial cross-protection model and derive the exact conditions under which a Fold–Hopf bifurcation emerges. By applying center-manifold reduction and normal-form theory, we reduce the infinite-dimension...
In this paper, we propose a novel sparse clustering method designed for high-dimensional mixed-type data, integrating Azzalini’s score-based encoding for ordinal variables. Our approach aims to retain the inherent nature of each variable type&m...
As digital images proliferate across open networks, securing them against unauthorized access has become imperative. However, many recent image encryption algorithms are limited by weak chaotic dynamics and inadequate cryptographic design. To overcom...
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