主题词：Algebraic Geometry and Number Theory; Advanced Algebra and Geometry; Advanced Mathematical Identities; Analytic Number Theory Research; Algebraic structures and combinatorial models; Commutative Algebra and Its Applications; Finite Group Theory Research; Polynomial and algebraic computation; Advanced Topics in Algebra; Advanced Differential Equations and Dynamical Systems; Meromorphic and Entire Functions; Homotopy and Cohomology in Algebraic Topology; Coding theory and cryptography; Mathematics and Applications; advanced mathematical theories; Geometric Analysis and Curvature Flows; Advanced Combinatorial Mathematics; Rings, Modules, and Algebras; Geometry and complex manifolds; Functional Equations Stability Results; Matrix Theory and Algorithms; Mathematical functions and polynomials; Advanced Numerical Analysis Techniques; Graph theory and applications; Cryptography and Residue Arithmetic