The integrally representable trees of norm $3$

Proximity Constraints and Representable Trees

This paper examines an infinite family of proximity drawings of graphs called open and closed ß-drawings, first defined by Kirkpatrick and Radke [15, 21] in the context of computational morphology. Such proximity drawings include as special cases the well-known Gabriel, relative neighborhood and strip drawings. Complete characterizations of those trees that admit open /^-drawings for 0 < ß < iz...

Chains of Integrally Closed Ideals

Let (A, m) be an excellent normal local ring with algebraically closed residue class field. Given integrally closed m-primary ideals I ⊃ J , we show that there is a composition series between I and J , by integrally closed ideals only. Also we show that any given integrally closed m-primary ideal I, the family of integrally closed ideals J ⊂ I, lA(I/J) = 1 forms an algebraic variety with dimens...

some properties of fuzzy hilbert spaces and norm of operators

in this thesis, at first we investigate the bounded inverse theorem on fuzzy normed linear spaces and study the set of all compact operators on these spaces. then we introduce the notions of fuzzy boundedness and investigate a new norm operators and the relationship between continuity and boundedness. and, we show that the space of all fuzzy bounded operators is complete. finally, we define...

On matroids representable over GF(3) and other fields

Orienting Matroids Representable Over Both GF(3) and GF(5)

For matroids representable over both GF 3] and GF 5], we provide a recipe for constructing an orientation.