Let H denote the set {f1, f2, ..., fn}, 2 the collection of all subsets of H and F ⊆ 2 be a family. The maximum of |F| is studied if any k subsets have a non-empty intersection and the intersection of any l distinct subsets (1 ≤ k < l) is empty. This problem is reduced to a covering problem. If we have the conditions that any two subsets have a non-empty intersection and the intersection of any...

In this paper, locally 3-arc-transitive regular covers of complete bipartite graphs are studied, and results are obtained that apply to arbitrary covering transformation groups. In particular, methods are obtained for classifying the locally 3-arctransitive graphs with a prescribed covering transformation group, and these results are applied to classify the locally 3-arc-transitive regular cove...

Let T be a unit equilateral triangle, and T1, . . . , Tn be n equilateral triangles that cover T and satisfy the following two conditions: (i) Ti has side length ti (0 < ti < 1); (ii) Ti is placed with each side parallel to a side of T . We prove a conjecture of Zhang and Fan asserting that any covering that meets the above two conditions (i) and (ii) satisfies ∑n i=1 ti ≥ 2. We also show that ...

This paper gives a proof that the universal cover of a closed 3-manifolds built from three π1-injective handlebodies is homeomorphic to R .

We prove that the set of homotopy classes of the paths in a topological ring is a ring object (called ring groupoid). Using this concept we show that the ring structure of a topological ring lifts to a simply connected covering space.

The purpose of this note is to use covering space theory to construct new examples of buildings. On the level of Coxeter systems, this contsruction was described previously in Davis [4]. It goes as follows. Start with a Coxeter system (W ′, S). Change some m(s, t)’s in its Coxeter matrix from integers ≥ 2 to the symbol ∞ . This defines a new Coxeter system (W, S). Suppose C′ is a building of ty...

This article contains a new argument which proves vanishing of the first cohomology for negative vector bundles over a complex projective variety if the rank of the bundle is smaller than the dimension of the base. Similar argument is applied to the construction of holomorphic functions on the universal covering of the complex projective variety .

This paper describes certain properties of the fundamental group of the shrinking wedge of circles. Covering space theory is an inadequate tool since the shrinking wedge of circles is not semi-locally simply connected. We conclude with the fact that the shrinking wedge of circles is not homotopy equivalent to the wedge product of a countable number of circles.

BACKGROUND AND PURPOSE Estimation of the stability of fusiform aneurysms of the basilar artery requires precise monitoring of the luminal and outer wall volumes. In this report we describe the use of MR imaging and 3D postprocessing methods to study the evolution of those aneurysms. MATERIALS AND METHODS Nine patients with fusiform basilar artery aneurysms underwent MR imaging studies coverin...

This study is aimed to examine which configurations of mortar covering give the best fire protection for bamboo-plaster wall system. The research done in two stages, first non-standardized pre-test stage results will become basis determining specimen specification. In second stage, with resistance level tested a standardized test referred SNI 1741-2008 and ISO 834-1-1999. Fire performance was m...