Abstract
Classes of an equivalence relation on a module V over a supertropical semiring, called rays, carry the underlying structure of 'sup ertropical trigonometry' and thereby a version of convex geometry which is compatible with quasilinearity. In this theory, the traditional Cauchy-Schwarz inequality is replaced by the CS-ratio, which gives rise to special characteristic functions, called ...
Abstract
Classes of an equivalence relation on a module V over a supertropical semiring, called rays, carry the underlying structure of 'sup ertropical trigonometry' and thereby a version of convex geometry which is compatible with quasilinearity. In this theory, the traditional Cauchy-Schwarz inequality is replaced by the CS-ratio, which gives rise to special characteristic functions, called CS-functions. These functions partite the ray space Ray(V) into convex sets and establish the main tool for analyzing varieties of quasilinear stars in Ray(V ). They provide stratifications of Ray(V) and, therefore, a finer convex analysis that helps better understand geometric properties.
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