2025/09/24 by Martin Himmel, Himmel, Martin
Mathematics · Physics and Astronomy · #Mathematical and Theoretical Analysis #Advanced Optimization Algorithms Research #Theoretical and Computational Physics
paper · pdf · doi:10.48550/arxiv.2509.25227
The four types of homogeneity -- additive, multiplicative, exponential, and logarithmic -- are generalized as transformations describing how a function f changes under scaling or shifting of its arguments. These generalized homogeneity functions capture different scaling behaviors and establish fundamental properties. Such properties include how homogeneity is preserved under function operations and how it determines the transformation behavior of related constructions like quotient functions. This framework extends the classical concept of homogeneity to a wider class of functional symmetries, providing a unified approach to analyzing scaling properties in various mathematical contexts.