A note on rank additivity and range additivity

A Note on Additivity of Polygamma Functions

In the note, the functions ̨ ̨ψ(i)(ex) ̨ ̨ for i ∈ N are proved to be sub-additive on (ln θi,∞) and super-additive on (−∞, ln θi), where θi ∈ (0, 1) is the unique root of equation 2 ̨ ̨ψ(i)(θ) ̨

Additivity of the Dp-rank

The main result is the prove of the linearity of the dp-rank. We also prove that the study of theories of finite dp-rank cannot be reduced to the study of its dp-minimal types and discuss the possible relations between dp-rank and VC-density.

Additivity and non-additivity for perverse signatures

A well-known property of the signature of closed oriented 4n-dimensional manifolds is Novikov additivity, which states that if a manifold is split into two manifolds with boundary along an oriented smooth hypersurface, then the signature of the original manifold equals the sum of the signatures of the resulting manifolds with boundary. Wall showed that this property is not true of signatures on...

Remarks on Cyclic Additivity

Additivity and non-additivity of multipartite entanglement measures

We study the additivity property of three multipartite entanglement measures, i.e. the geometric measure of entanglement (GM), the relative entropy of entanglement and the logarithmic global robustness. Firstly, we show the additivity of GM of multipartite states with real and non-negative entries in the computational basis. Many states of experimental and theoretical interest have this propert...