主题词：Algebraic Geometry and Number Theory; Advanced Algebra and Geometry; Analytic Number Theory Research; Advanced Mathematical Identities; Algebraic structures and combinatorial models; Advanced Combinatorial Mathematics; Polynomial and algebraic computation; Homotopy and Cohomology in Algebraic Topology; Geometric and Algebraic Topology; Commutative Algebra and Its Applications; Advanced Mathematical Modeling in Engineering; Numerical methods in inverse problems; Model Reduction and Neural Networks; Geometric Analysis and Curvature Flows; Finite Group Theory Research; Mathematical functions and polynomials; Mathematical Dynamics and Fractals; Advanced Topics in Algebra; Geometry and complex manifolds; Advanced Differential Equations and Dynamical Systems; Nonlinear Waves and Solitons; Advanced Numerical Methods in Computational Mathematics; Navier-Stokes equation solutions; Advanced Numerical Analysis Techniques; Limits and Structures in Graph Theory