The relations M(κ, λ, µ) → B [resp. B(σ)] meaning that if A ⊂ [κ] λ with |A| = κ is µ-almost disjoint then A has property B [resp. has a σ-transversal] had been introduced and studied under GCH in [EH]. Our two main results here say the following: Assume GCH and ̺ be any regular cardinal with a supercompact [resp. 2-huge] cardinal above ̺. Then there is a ̺-closed forcing P such that, in V P , we ...

The problem of determining visibility locations (VLs) on/inside a domain bounded by a planar C1-continuous curve (without vertices), such that entire domain is covered, is discussed in this paper. The curved boundary has been used without being approximated into lines or polygons. Initially, a few observations regarding the VLs for a curved boundary have been made. It is proposed that the set o...

Multicamera vehicle tracking is a necessary part of any video-based intelligent transportation system for extracting different traffic parameters such as link travel times and origin/destination counts. In many applications, it is needed to locate traffic cameras disjoint from each other to cover a wide area. This paper presents a method for tracking moving vehicles in such camera networks. The...

A disjoint system of type (∀,∃, k, n) is a collection C = {A1, . . . ,Am} of pairwise disjoint families of k-subsets of an n-element set satisfying the following condition. For every ordered pair Ai and Aj of distinct members of C and for every A ∈ Ai there exists a B ∈ Aj that does not intersect A. Let Dn(∀,∃, k) denote the maximum possible cardinality of a disjoint system of type (∀,∃, k, n)....

A “dijoin” in a digraph is a set of edges meeting every directed cut. D. R. Woodall conjectured in 1976 that if G is a digraph, and every directed cut of G has at least k edges, then there are k pairwise disjoint dijoins. This remains open, but a capacitated version is known to be false. In particular, A. Schrijver gave a digraph G and a subset S of its edge-set, such that every directed cut co...