For any affine variety equipped with coordinates, there is a surjective, continuous map from its Berkovich space to its tropicalisation. Exploiting torus actions, we develop techniques for finding an explicit, continuous section of this map. In particular, we prove that such a section exists for linear spaces, Grassmannians of planes (reproving a result due to Cueto, Häbich, and Werner), matrix...

Applying machine translation (MT) to literary texts involves the same domain shift challenges that arise for any sublanguage (e.g. medical or scientific). However, it also introduces additional challenges. One focus in the discussion of translation theory in the humanities has been on the human translator’s role in staying faithful to an original text versus adapting it to make it more familiar...

The aim of this note is to study the submajorization inequalities for $tau$-measurable operators in a semi-finite von Neumann algebra on a Hilbert space with a normal faithful semi-finite trace $tau$. The submajorization inequalities generalize some results due to Zhang, Furuichi and Lin, etc..

In this paper, a commutative semigroup will be written as a disjoint union of its cancellative subsemigroups. Based on this fact we will define the left regular representation of a commutative separative semigroup and show that this representation is faithful. Finally concrete examples of commutative separative semigroups, their decompositions and their left regular representations are given.

Research on imitation in infancy has primarily focused on what and when infants imitate. More recently, however, the question why infants imitate has received renewed attention, partly motivated by the finding that infants sometimes selectively imitate the actions of others and sometimes faithfully imitate, or overimitate, the actions of others. The present study evaluates the hypothesis that t...