主题词：Homotopy and Cohomology in Algebraic Topology; Advanced Algebra and Geometry; Advanced Topics in Algebra; Algebraic Geometry and Number Theory; Geometric and Algebraic Topology; Holomorphic and Operator Theory; Polynomial and algebraic computation; Geometry and complex manifolds; Topological and Geometric Data Analysis; advanced mathematical theories; Algebraic structures and combinatorial models; Liquid Crystal Research Advancements; Surfactants and Colloidal Systems; Advanced Topology and Set Theory; Quantum chaos and dynamical systems; Advanced Mathematical Identities; Advanced Mathematical Physics Problems; Fuzzy and Soft Set Theory; Rings, Modules, and Algebras; Advanced Algebra and Logic; Algebraic and Geometric Analysis; Commutative Algebra and Its Applications; Mathematics and Applications; Legal and Regulatory Analysis; Linguistic, Cultural, and Literary Studies