We study directed sets definable in o-minimal structures, showing that expansions of ordered fields these admit cofinal curves, as well a suitable analogue groups, and furthermore no holds full generality. use the theory tame pairs to extend results field case families with finite intersection property. then apply our topologies. prove all topological spaces display properties akin first counta...

Introduction The use of multi-dimensional spatially-selective excitation (SSE) pulses for MR-spectroscopy (MRS) offers great potential for solving several problems generally occuring in classical volume-selective MRS with single rectangular voxels. On the one hand, the possibility of exciting arbitrarily shaped voxels, adapted to anatomical structures, can help maximizing the target-volume whil...

Anatomy of the differential gluon structure function of the proton from the experimental data on F 2p (x, Q 2) Abstract The use of the differential gluon structure function of the proton F(x, Q 2) introduced by Fadin, Kuraev and Lipatov in 1975 is called upon in many applications of small-x QCD. We report here the first determination of F(x, Q 2) from the experimental data on the small-x proton...

The aim of this note is to determine whether certain non-o-minimal expansions of o-minimal theories which are known to be NIP, are also distal. We observe that while tame pairs of o-minimal structures and the real field with a discrete multiplicative subgroup have distal theories, dense pairs of o-minimal structures and related examples do not.

There are several methods for constructing secret sharing schemes, one of which is based on coding theory. Theoretically, every linear code can be used to construct secret sharing schemes. However, in general, determining the access structures of the schemes based on linear codes is very hard. This paper proposed the concept of minimal linear code, which makes the determination of the access st...

An intermediate stage in Hrushovski’s construction of flat strongly minimal structures produces ω-stable structures of rank ω. We analyze the pregeometries given by forking on the regular type of rank ω in these structures. A sequel will compare these to the pregeometries of the strongly minimal structures.