Hyperfields, truncated DVRs, and valued fields

Truncated Signed Distance Fields

This thesis is concerned with topics related to dense mapping of large scale three-dimensional spaces. In particular, the motivating scenario of this work is one in which a mobile robot with limited computational resources explores an unknown environment using a depth-camera. To this end, low-level topics such as sensor noise, map representation, interpolation, bit-rates, compression are invest...

FUZZY HYPERVECTOR SPACES OVER VALUED FIELDS

In this note we first redefine the notion of a fuzzy hypervectorspace (see [1]) and then introduce some further concepts of fuzzy hypervectorspaces, such as fuzzy convex and balance fuzzy subsets in fuzzy hypervectorspaces over valued fields. Finally, we briefly discuss on the convex (balanced)hull of a given fuzzy set of a hypervector space.

Valued Difference Fields and Ntp

We show that the theory of the non-standard Frobenius automorphism, acting on an algebraically closed valued field of equal characteristic 0, is NTP2. More generally, in the contractive as well as in the isometric case, we prove that a σ-Henselian valued difference field of equicharacteristic 0 is NTP2, provided both the residue difference field and the value group (as an ordered difference gro...

Amalgamating valued fields

Dp-Minimal Valued Fields

We show that dp-minimal valued fields are henselian and give classifications of dp-minimal ordered abelian groups and dp-minimal ordered fields without additional structure.