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...

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...

background: with the rapid development of health services, the progress of medical science and technology, and the improvement of materials research, the consumption of medical consumables (mcs) in medical activities has increased in recent years. however, owing to the lack of effective management methods and the complexity of mcs, there are several management problems including mc waste, low m...

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...