For integers k, l ≥ 0, let D(k, l) denote the family of digraphs in which every vertex has either indegree at most k or outdegree at most l. In this paper we prove that the edges of every digraph in D(3, 3) and D(4, 4) can be covered by at most five directed cuts, and present an example in D(3, 3) which shows that this result is best possible.

Let k ≥ 3 be an integer. We show that if d is a positive integer such that the product of any two distinct elements of the set {k−2, k+2, 4k, d} increased by 4 is a square, then d must be 4k(k2−1).

This paper describes an approach to reconstruct the complete history of a 3-d scene over time from imagery. The proposed approach avoids rebuilding 3-d models of the scene at each time instant. Instead, the approach employs an initial 3-d model which is continuously updated with changes in the environment to form a full 4-d representation. This updating scheme is enabled by a novel algorithm th...

In this note, we establish the formulation of 6D, N = 1 hypermultiplets in terms of 4D chiral-nonminimal (CNM) scalar multiplets. The coupling of these to 6D, N = 1 Yang-Mills multiplets is described. A 6D, N = 1 projective superspace formulation is given in which the above multiplets naturally emerge. The covariant superspace quantization of these multiplets is studied in details. PACS: 04.65....

The (single) black hole solutions of Ba~ nados, Teitelboim and Zanelli (BTZ) in 2+1 dimensional anti-de Sitter space are generalized to an arbitrary number n of such black holes. The resulting multi-black-hole (MBH) spacetime is locally isometric to anti-de Sitter space, and globally it is obtained from the latter as a quotient space by means of suitable identiications. The MBH spacetime has n ...

A simplicial complex is d-collapsible if it can be reduced to an empty complex by repeatedly removing (collapsing) a face of dimension at most d − 1 that is contained in a unique maximal face. We prove that the algorithmic question whether a given simplicial complex is d-collapsible is NP-complete for d ≥ 4 and polynomial time solvable for d ≤ 2. As an intermediate step, we prove that d-collaps...

Prohibitive voice behaviors are employees’ expressions of concern about practices, incidents, or behaviors that may potentially harm the organization. In this study, we examined a potential biological correlate of prohibitive voice: prenatal exposure to testosterone. In a sample of bankers, we used 2D:4D (i.e., the ratio of the length of the index finger to the length of the ring finger) as a m...