Combining V. Koziarz’s observation about the regularity of some modified section related to initial extension with J. McNeal–D. Varolin’s argument, we generalize two theorems McNeal–Varolin for \(L^2\) of\({{\bar{\partial }}}\)-closed high-degree forms on a Stein manifold weakly pseudoconvex Kähler case under mixed positivity conditions.

We show that a typical interval exchange transformation is either weakly mixing or it is an irrational rotation. We also conclude that a typical translation flow on a surface of genus g ≥ 2 (with prescribed singularity types) is weakly mixing.

A combinatorial 2-manifold is called weakly regular if the action of its automorphism group on its vertices is transitive. A combinatorial 2-manifold is called degree-regular if each of its vertices have the same degree. Clearly, a weakly regular combinatorial 2-manifold is degree-regular. In [5], Lutz has classified all the weakly-regular combinatorial 2-manifolds on at most 15 vertices, among...

Given two non-weakly k-normal Boolean functions on n variables a method is proposed to construct a non-weakly (k + 1)-normal Boolean function on (n + 2)variables.

A graph G = (V,E) is said to be weakly four-connected if G is 4-edgeconnected and G− x is 2-edge-connected for every x ∈ V . We prove that every weakly four-connected Eulerian graph has a 2-connected Eulerian orientation. This verifies a special case of a conjecture of A. Frank.

We introduce the notion of weakly globular double categories, a particular class of strict double categories, as a way to model weak 2-categories. We show that this model is suitably equivalent to bicategories and give an explicit description of the functors involved in this biequivalence. As an application we show that groupoidal weakly globular double categories model homotopy 2-types.

Suzuki (2004) classified thin weakly distance-regular digraphs and proposed the project to classify weakly distance-regular digraphs of valency 3. The case of girth 2 was classified by the third author (2004) under the assumption of the commutativity. In this paper, we continue this project and classify these digraphs with girth more than 2 and two types of arcs.