The problem of existence of closed knight tours for rectangular chessboards was solved by Schwenk in 1991. Last year, in 2011, DeMaio and Mathew provide an extension of this result for 3-dimensional rectangular boards. In this article, we give the solution for n-dimensional rectangular boards, for n > 4.

A plane graph is a planar graph with a fixed planar embedding in the plane. In a boxrectangular drawing of a plane graph, every vertex is drawn as a rectangle, called a box, each edge is drawn as either a horizontal line segment or a vertical line segment, and the contour of each face is drawn as a rectangle. A planar graph is said to have a box-rectangular drawing if at least one of its plane ...

DS-CDMA is evaluated for rectangular pulse shaping and square root raised cosine pulses with different roll off factors. Rectangular pulses are found to be better even with close adjacent channels. With synchronization error in the order of 10% of a chip interval, square root raised cosine pulses outperform the rectangular pulse.

Some methods of construction of rectangular designs with unequal replications number ri (i=1, 2) of treatments are described. Such designs are labeled as rectangular designs with varying replicates (RDVR) in literature. In this paper, rectangular designs with two replications r1 and r2 are discussed. AMS subject classifications: primary 62 K05, secondary 62 K 10; 05B10.

We present a new linear time algorithm for nding rectangular duals of planar triangular graphs. The algorithm is conceptually simpler than the previous known algorithm. The coordinates of the rectangular dual constructed by our algorithm are integers and have pure combinatorial meaning. This allows us to discuss the heuristics for minimizing the size of the rectangular duals.

A regular edge labeling (REL) of an irreducible triangulation G uniquely defines a rectangular dual of G. Rectangular duals find applications in various areas: as floor plans of electronic chips, in architectural designs, as rectangular cartograms, or as treemaps. An irreducible triangulation can have many RELs and hence many rectangular duals. Depending on the specific application different du...

We consider zeros of two-dimensional sums over rectangular lattices, and in particular a sum first studied by Potter and Titchmarsh in 1935. They proved several properties of the zeros of sums over the rectangular lattice, and commented on the fact that a particular sum had zeros off the critical line. We investigate the behaviour of one such zero as a function of the ratio of the periods of th...

We prove some common fixed-point theorems for the ordered g-weak contractions in cone rectangular metric spaces without assuming the normality of cone. Our results generalize some recent results from cone metric and cone rectangular metric spaces into ordered cone rectangular metric spaces. Examples are provided which illustrate the results.

In this paper, we propose a variation of honeycomb meshes. A honeycomb rectangular disk HReD(m,n) is obtained from the honeycomb rectangular mesh HReM(m,n) by adding a boundary cycle. A honeycomb rectangular disk HReD(m,n) is a 3-regular planar graph. It is obvious that the honeycomb rectangular mesh HReM(m,n) is a subgraph of HReD(m,n). We also prove that HReD(m,n) is hamiltonian. Moreover, HR...