Pairs of theories satisfying a Mordell–Lang condition

Group connectivity of graphs satisfying Ore-condition

In this paper, we show that a simple graph G satisfying Ore-condition with |V (G)| ≥ 3 is A-connected if and only if G is not a 4-cycle, where A is an abelian group of order at least 4.

Inclusion Pairs Satisfying Eshelby's Uniformity Property

Eshelby conjectured that if for a given uniform loading the field inside an inclusion is uniform, then the inclusion must be an ellipse or an ellipsoid. This conjecture has been proved to be true in two and three dimensions provided that the inclusion is simply connected. In this paper we provide an alternative proof of Cherepanov’s result that an inclusion with two components can be constructe...

Approximation of o-minimal maps satisfying a Lipschitz condition

Consider an o-minimal expansion of the real field. We show that definable Lipschitz continuous maps can be definably fine approximated by definable continuously differentiable Lipschitz maps whose Lipschitz constant is close to that of the original map.

On ℤ4 codes satisfying the chain condition

On Regular Rings Satisfying Weak Chain Condition

In this paper, we shall study regular rings satisfying weak chain condition. As main results, we show that regular rings satisfying weak chain condition are unit-regular, and show that these rings have the unperforation and power cancellation properties for the family of finitely generated projective modules.