It was conjectured by White in 1980 that the toric ring associated to a matroid is defined symmetric exchange relations. This conjecture extended discrete polymatroids Herzog and Hibi, they prove holds for with so called strong property. In this paper we generalize their result are products of also extends Conca on transversal polymatroids.

We construct an example of a quasi-o-minimal group without the Exchange Property. A structure hM;<;:::i is called quasi-o-minimal 1] if in any structure elementarily equivalent to it the deenable subsets are exactly the Boolean combinations of 0-deenable subsets and intervals. A complete theory T is said to have the Exchange Property if, for any model M of T and for any X M and b; c 2 M, if b 2...

in this paper, we show that every element of a discrete module is a sum of two units if and only if its endomorphism ring has no factor ring isomorphic to $z_{2}$. we also characterize unit sum number equal to two for the endomorphism ring of quasi-discrete modules with finite exchange property.

In this paper we define a property for multi-party protocols called exclusion-freeness. In multi-party protocols respecting the strongest definition of this property, participants are sure that they will not be excluded from a protocol’s execution and, consequently, they do not have to trust each other any more. We study this property on a wellknown multi-party fair exchange protocol with an on...

We study …rms’preferences towards intellectual property rights (IPR) regimes in a North-South context, using a simple duopoly model where a ’North’ and a ’South’ …rm compete in a third market. Unlike other contributions in this …eld, we explicitly introduce the South’s capability to undertake cost-reducing R&D, but maintain the South’s inferiority in utilizing and managing its R&D. In contrast ...