Asymmetric Singular Coordinate System (ASCS): A Structural Reformulation of the Number Line via Boundary Singularity and Non-Linear Asymptotics
Year: 2026
Type: preprint
Abstract: The traditional Cartesian coordinate system exhibits limitations when modeling systems with phase discontinuities or boundary shocks. This paper proposes the Asymmetric Singular Coordinate System (ASCS) featuring three core characteristics: the origin acts as a boundary singularity severing symmetry, the positive domain expands linearly toward infinity, and the negative domain initiates from negative infinity adjacent to the boundary before increasing non-linearly to asymptotically approach a saturation bound at extreme distances. The study establishes custom algebraic operations, analyzes differential behaviors, and demonstrates its application as a threshold-sensitive activation function for artificial neural networks.
Author: DONG PHAM, HOANG ANH
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7223666176