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 ...

Evidence-based treatments and preventive interventions in the child and family area have not met with widespread adoption by practitioners. Despite the high prevalence of child behavioral and emotional problems, many parents and families in need are not receiving or participating in services, and when they do, the most efficacious interventions are not what is usually provided. Simultaneously a...

While a large proportion of Aboriginal Australians do not consume alcohol, those who do frequently show severe alcohol problems. In European-derived samples, heavy alcohol use is associated with relationship distress, conflict, and violence. Because Aboriginal groups commonly have very different family structures, values, and obligations to European-derived families, the association of family a...

OBJECTIVE This study examined associations among family environment, coping, and emotional and conduct problems in adolescents attending therapeutic day schools due to mental health problems. METHODS Adolescents (N = 417; 30.2% female) ages 13-20 (M = 15.25) reported on their family environment (affective involvement and functioning), coping (emotion-focused support-seeking, cognitive restruc...

Article history: Received 15 April 2014 Received in revised form 29 September 2014 Accepted 28 October 2014 Available online 4 November 2014

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...