This paper describes an empirical investigation into the nature of challenge within the context of flow or effortless attention. An important condition of the flow state is that the challenges of the task are commensurate with the person’s level of skill. However when considering movement interaction those challenges could be composite in the sense that they could comprise physical as well as i...

The blocks of a balanced ternary design, BTD(V,B; ρ1, ρ2, R;K,Λ), can be partitioned into two sets: the b1 blocks that each contain no repeated elements, and the b2 = B − b1 blocks containing repeated elements. In this note, we address, and answer in some particular cases, the following question. For which partitions of the integer B as b1 + b2 does there exist a BTD(V,B; ρ1, ρ2, R;K,Λ)?

Given a set of n black and n white points in general position in the plane, a line l determined by them is said to be balanced if each open half-plane bounded by l contains precisely the same number of black points as white points. It is proved that the number of balanced lines is at least n. This settles a conjecture of George Baloglou.

Let S be a set of r red points and b = r + 2δ blue points in general position in the plane, with δ ≥ 0. A line l determined by them is balanced if in each open half-plane bounded by l the difference between the number of blue points and red points is δ. We show that every set S as above has at least r balanced lines. The main techniques in the proof are rotations and a generalization, sliding r...

The RF power amplifier (PA) is a unit in wireless transmitters that strengthens the signal to combat losses transmission by converting dc electric added output power. Over past decades, with rapid development of communications, high-efficiency PA design has become one most popular topics both academic research and industrial as consumes high portion transmitter energy, thus its efficiency direc...