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...