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math.NT2026
An elementary proof of the Artin--Springer theorem for generalized quadratic forms over quaternion algebras
Amir Hossein Nokhodkar
We give a short and simple proof that an anisotropic generalized quadratic form over a quaternion division algebra with involution of the first kind, in arbitrary characteristic, r…
math.GM2026
Sharp Bounds on Diminished Sombor Index
Meysam Taheri-Dehkordi, Amir Hossein Nokhodkar, Gholam Hossein Fath-Tabar
The Diminished Sombor index of a simple graph is a recently introduced degree-based topological index, defined as \[ DSO(G)= \sum_{uv\in E(G)} \frac{\sqrt{d_u^2+d_v^2}}…