The goal of this thesis is to describe certain algebraic invariants of links, and try to modify them to obtain invariants of 3-manifolds. Racks and quandles are algebraic structures that were invented to give invariants ...

Aromatic B-series are a generalization of B-series. Some of the algebraic structures on B-series can be defined analogically for aromatic B-series. This paper derives combinatorial formulas for the composition and substitution ...

In this thesis we are considering finite dimensional algebras. We prove that any basic and indecomposable finite dimensional algebra A over an algebraically closed field k is isomorphic to a bound quiver algebra. Furthermore, ...

We show that Cantor minimal Z⋊Z2\mathbb{Z}\rtimes\mathbb{Z}_2Z⋊Z2​-systems and essentially free amenable odometers are almost finite. We also compute the homology groups of Cantor minimal Z⋊Z2\mathbb{Z}\rtimes\mathbb{Z}_ ...

We discuss an Abel-Jacobi invariant for algebraic cobordism cycles whose image in topological cobordism vanishes. The existence of this invariant follows by abstract arguments from the construction of Hodge filtered ...

We have considered a cryptographic communication protocol and given a proof for its security.

I denne masteroppgaven ble det utført en komparativ analyse av de tre ulike modelleringsmetodene: multippel lineær regresjon, gradient boosting metoden XGBoost og det nevrale nettverket Long Short-Term Memory (LSTM). For ...