Participants pressed computer keys to keep a moving dot stimulus within a rectangle, either alone or with a partner they could neither see nor hear. Pressing the A-key or L-key caused the dot to move right or left, respectively, for as long as the key was pressed. Switching between the A and L keys (i.e., turning) proved challenging: concurrently pressing both keys made the stimulus move upward...

A straight-line drawing of a plane graph is called an open rectangle-ofinfluence drawing if there is no vertex in the proper inside of the axis-parallel rectangle defined by the two ends of every edge. In an inner triangulated plane graph, every inner face is a triangle although the outer face is not necessarily a triangle. In this paper, we first obtain a sufficient condition for an inner tria...

We solve the problem of decomposing a rectangle R into p rectangles of equal area so that the maximum rectangle perimeter is as small as possible. This work has applications in areas such as flexible object packing and data allocation. Our solution requires only a constant number of arithmetic operations and integer square roots to characterize the decomposition, and linear time to print the de...

Let us consider the interval [0, 1) as a billiard table rectangle with perimeter 1 and a sequence F(m) ∈ [0, 1),m ∈ N ∪ {0}, of successive rebounds of a billiard ball against the sides of a billiard rectangle. We prove that if I is an open segment of a billiard rectangle, then the differences between the successive values of m for which the F(m) lies in I , take at most one even and at most fou...

An effective two-dimensional micromixer named rectangle-square wave micromixer with very simple structure has been presented. The rectangle-square wave micromixer based on split and recombination principle was simulated to analyze the fluid flow and the mixing efficiency. The flow rate, sample concentration, pressure drop at different position in the micromixer was researched. The simulation re...

The topic of this paper is the rectangle-free coloring of grids using four colors which is equivalent to the edge coloring of complete bipartite graphs without complete monochromatic subgraphs K2,2. Despite a strong mathematical background it is not known whether rectangle-free 4-colorable grids exist for five large grid sizes. We present in this paper an approach that solves the most complex p...