Journal of Computational Mathematica

A Systematic Review of Meta-Analysis for Refractive Errors

G. Gopi — 2025-12-31

Refractive errors make for 43% of vision impairments worldwide, consequently being the most common eye disorders. With a focus on the public health consequences, this work attempts to conduct a comprehensive investigation and systematic review of the overall incidence of astigmatism, hyperopia, and myopia. A comprehensive search for original English-language research published between 2008 and 2024 was carried out using PubMed, Google Scholar, and Research Gate. Studies with human participants and published averages and standard deviations (SDs) of refractive errors were included in the inclusion criteria. Reviews, non-English publications, and case reports were not accepted. Of the 47 publications found, 26 satisfied the criteria, examining568,560 eyes. The Meta analysis revealed a high prevalence of refractive errors, particularly myopia, which is more common in children and younger populations. Astigmatism also emerged as a significant concern. While hyperopia decreases with age, myopia increases with inconsistent gender differences in prevalence. The findings highlight a troubling in refractive errors, especially myopia and astigmatism among children and adolescents. To mitigate their impact on visual health and quality of life, regular vision screenings, awareness campaigns and improved access to eye care services are crucial.

Applications of Solutions of Difference Equations in Graph Theory

Iruthayaraj S — 2025-08-31

Graph labeling, which assigns values to the vertices and edges of a graph under specific conditions, has significant applications in real-world problems such as coding theory, radar code design, synch-set codes, missile guidance, and convolution codes with optimal error-correction properties. This study explores the connections between graph labeling and solutions of difference equations by constructing infinite graphs from sequences of real or complex numbers. Each solution of a difference equation induces a labeled graph in the complex plane, where vertex functions extend naturally to edge functions through binary operations over the complex field. Furthermore, the use of complex plane labeling provides a framework for visualizing higher-dimensional relationships in two-dimensional settings, enriching the structural understanding of labeled graphs and their diverse applications.

Tensor Product of Solution Graphs of Generalized Difference Equation

Iruthayaraj S — 2025-08-31

The tensor product is a fundamental mathematical concept with applications spanning linear algebra, graph theory, quantum computing, and representation theory. In graph theory, the tensor product provides a framework for analyzing structural relationships, particularly through the study of complete graphs, which yield complex networks from simple structures. Closely related is the Kronecker product of matrices, an essential tool for investigating tensor products via adjacency matrices. The Kronecker product preserves key algebraic properties, including linearity, distributivity, and associativity, and has played a central role in matrix analysis, systems theory, and signal processing. This work presents the definitions and core properties of the tensor product, supported by illustrative examples with complete graphs, and explores the Kronecker product along with its fundamental properties and theorems. By combining theoretical foundations with applications, the study offers both conceptual insights and practical perspectives on these algebraic constructions.