On orderings induced by the Loewner partial ordering

Mathematical Morphology for Tensor Data Induced by the Loewner Ordering in Higher Dimensions

Positive semidefinite matrix fields are becoming increasingly important in digital imaging. One reason for this tendency consists of the introduction of diffusion tensor magnetic resonance imaging (DTMRI). In order to perform shape analysis, enhancement or segmentation of such tensor fields, appropriate image processing tools must be developed. This paper extends fundamental morphological opera...

A Game on Partial Orderings

We study the determinacy of the game Gκ(A) introduced in [FuKoShe] for uncountable regular κ and several classes of partial orderings A. Among trees or Boolean algebras, we can always find an A such that Gκ(A) is undetermined. For the class of linear orders, the existence of such A depends on the size of κ. In particular we obtain a characterization of κ = κ in terms of determinacy of the game ...

On the Property “sep” of Partial Orderings

A partial ordering P has the property SEP (or SEP(P )), if, for a sufficiently large regular cardinal χ, the family of elementary submodels of H(χ) of cardinality א1 with the property that [M ]א0 ∩M is cofinal subset (with respect to ⊆) of [M ]א0 and P ∩M ≤σ P , is cofinal (also with respect to ⊆) in [H(χ)]א1 (see Proposition 2 below). We describe, in section 1, against which historical backgro...

Loewner matrix ordering in estimation of the smallest singular value

Herrmann's Beautiful Theorem on Computable Partial Orderings

We give an exposition of Herrmann’s proof that there is an infinite computable partial ordering with no infinite Σ 2 chains or