主题词：Analytic Number Theory Research; Limits and Structures in Graph Theory; Mathematical Dynamics and Fractals; Graph Labeling and Dimension Problems; Algebraic Geometry and Number Theory; semigroups and automata theory; Advanced Mathematical Identities; Advanced Mathematical Theories and Applications; Advanced Graph Theory Research; Finite Group Theory Research; Advanced Numerical Analysis Techniques; Advanced Algebra and Logic; Computability, Logic, AI Algorithms; Mathematics and Applications; Meromorphic and Entire Functions; Geometric and Algebraic Topology; Matrix Theory and Algorithms; Advanced Combinatorial Mathematics; Computational Geometry and Mesh Generation; Rough Sets and Fuzzy Logic; Advanced Topology and Set Theory; Mathematical functions and polynomials; Advanced Banach Space Theory; Advanced Algebra and Geometry; Random Matrices and Applications