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...

Abstract. Soil moisture is an important variable linking the atmosphere and terrestrial ecosystems. However, long-term satellite monitoring of surface soil at global scale needs improvement. In this study, we conducted data calibration fusion 11 well-acknowledged microwave remote-sensing products since 2003 through a neural network approach, with Moisture Active Passive (SMAP) applied as primar...

SUMMARY Iris cyst occurs post intraocular -surgery or post penetrating trauma, when corneal epithelial cells or conjunctiva} epithcells gains access to the anterior chamber, with cells may continue to grow & covering all available surface and formed iris cyst. As the cyst grow may caused glaucoma or block pupil area & leads to vision treatment of all form of iris cyst and epithelial down growt...

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 ...