We consider the problem of covering the complete r-uniform hypergraphs on n vertices using complete r-partite graphs. We obtain lower bounds on the size of such a covering. For small values of r our result implies a lower bound of Ω( e r r √ r n log n) on the size of any such covering. This improves the previous bound of Ω(rn log n) due to Snir [5]. We also obtain good lower bounds on the size ...

This paper considers totally bounded quasi-uniformities and quasi-proximities for frames and shows that for a given quasi-proximity ⊳ on a frame L there is a totally bounded quasi-uniformity on L that is the coarsest quasi-uniformity, and the only totally bounded quasi-uniformity, that determines ⊳. The constructions due to B. Banaschewski and A. Pultr of the Cauchy spectrum ψL and the compacti...

α-acyclicity is an important notion in database theory. The α-arboricity of a hypergraphH is the minimum number of α-acyclic hypergraphs that partition the edge set of H. The α-arboricity of the complete 3-uniform hypergraph is determined completely.

By K n we denote the complete k-uniform hypergraph of order n, 1 6 k 6 n−1, i.e. the hypergraph with the set Vn = {1, 2, ..., n} of vertices and the set ( Vn k ) of edges. If there exists a permutation σ of the set Vn such that {E, σ(E), ..., σq−1(E)} is a partition of the set ( Vn k ) then we call it cyclic q-partition of K n and σ is said to be a (q, k)-complementing. In the paper, for arbitr...

We generalize a major portion of the classical theory of Cand C embedded subspaces to pointfree topology, where the corresponding notions are frame Cand C -quotients. The central results characterize these quotients and generalize Urysohn’s Extension Theorem, among others. The proofs require calculations in CL, the archimedean f -ring of frame maps from the topology of the reals into the frame ...

A k−uniform hypergraphH is a pair (V, ε), where V = {v1, v2, . . . , vn} is a set of n vertices and ε is a family of k-subset of V called hyperedges. A cycle of length l of H is a sequence of the form (v1, e1, v2, e2, . . . , vl, el, v1), where v1, v2, . . . , vl are distinct vertices, and e1, e2, . . . , el are k-edges of H and vi, vi+1 ∈ ei, 1 ≤ i ≤ l, where addition on the subscripts is modu...

In this paper the earth’s magnetic field is simulated precisely while the intensity and direction of the field are verified with one of the standard references for selected points on the earth and the results are compared with some low-order models. In another simulation, the complete model is compared with a common approximate model. The magnetic field in orbital frame is described and to empl...

Dowling and Rhodes defined different lattices on the set of triples (Subset, Partition, Cross Section) over a fixed finite group G . Although lattice is not geometric lattice, it defines matroid in sense theory boolean representable simplicial complexes. This turns out to be direct sum uniform with lift complete gain link graph As well known, frame similar graph. gives new perspective both matr...

When the existing information does not contain all categories, Generalized Evidence Theory (GET) can deal with fusion. However, question of how to determine number categories through GET is still intriguing. To address this question, a modified k-means clustering, named centers initialized clustering proposed, filling gap identification and complement frame discernment. Based on method, determi...