Let F denote the class of all functions univalent in the unit disk and convex in the direction of the real axis. In the paper we discuss the functions of the class F which are n-fold symmetric, where n is positive even integer. For the class of such functions we find the Koebe set as well as the covering set, i.e. T f2F f ðDÞ and S f2F f ðDÞ. Moreover, the Koebe constant and the covering consta...

For every fixed graph H, we determine the H-covering number of Kn, for all n > n0(H). We prove that if h is the number of edges of H, and gcd(H) = d is the greatest common divisor of the degrees of H, then there exists n0 = n0(H), such that for all n > n0, C(H,Kn) = d dn 2h dn− 1 d ee, unless d is even, n = 1 mod d and n(n− 1)/d+ 1 = 0 mod (2h/d), in which case C(H,Kn) = d ( n 2 ) h e+ 1. Our m...

CMAJ • NOVEMBER 23, 2010 • 182(17) © 2010 Canadian Medical Association or its licensors 1831 We have intuitively known for a long time that poor nutritional status in disease is associated with mor bidity and mortality. Only recently, however, have studies provided evidence of an association between poor nutritional status and prolonged hospital stay, decreased quality of life, and increased mo...

Adolescence is a time of dramatic physical, cognitive, emotional, and social changes as well as a time for the development of many social-emotional problems. These characteristics raise compelling questions about accompanying neural changes that are unique to this period of development. Here, we propose that studying adolescent-specific changes in face processing and its underlying neural circu...

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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...