This paper proposes a novel stochastic process that represents the arbitrary rectangular partitioning of an infinite-dimensional matrix as the conditional projective limit. Rectangular partitioning is used in relational data analysis, and is classified into three types: regular grid, hierarchical, and arbitrary. Conventionally, a variety of probabilistic models have been advanced for the first ...

We discuss several two-dimensional generalizations of the familiar Lyndon-Schützenberger periodicity theorem for words. We consider the notion of primitive array (as one that cannot be expressed as the repetition of smaller arrays). We count the number of m×n arrays that are primitive. Finally, we show that one can test primitivity and compute the primitive root of an array in linear time.

The paper deals with m by n rectangular arrays whose mn cells are filled with symbols. A section of the array consists of m cells, one from each row and no two from the same column. The paper focuses on the existence of sections that do contain symbols with high multiplicity.

The practical problem we are trying to model is: we have to cover a room with a material(carpet or linolleum). This material is in a roll of fixed width. We want to cover the room with a minimum number of pieces and to waste a minimum amount of material. We present in this paper a synthesis of our works. We can easily see that the two criteria, the minimum loss of material and the minimumnumber...

In this paper, we have investigated printed rectangular monopole antennas, which is basically a printed microstrip antenna with etched ground plane for multi-band applications. In particular, we have fabricated and tested printed rectangular monopole antennas for dual-band and penta-band applications. It has been observed that printed rectangular monopole antennas are small in size and simple i...

In this article, we consider rectangular finite element methods for fourth order elliptic singular perturbation problems. We show that the non-C0 rectangular Morley element is uniformly convergent in the energy norm with respect to the perturbation parameter. We also propose a C0 extended high order rectangular Morley element and prove the uniform convergence. Finally, we do some numerical expe...

We compare the resolution of the hologram reconstruction synthesis methods based on integral imaging using rectangular and hexagonal lens arrays. By using a hexagonal lens array instead of conventional rectangular lens array, the three-dimensional objects are sampled with hexagonal grids. Due to more efficient sampling of the hexagonal grid, the resolution of the reconstructed object is higher ...

A rectangular rod is placed in a flow field flowing parallel to a flat plate. Effect of chord-thickness ratio of rectangular rod on developing vortex shedding downstream to the rod is studied. Then, for each one of the aspect ratios, the distance of the rod from the neighboring flat plate is reduced until the rod sticks to the flat plate. In each case, the effect of the flat plate boundary laye...

In this paper, the notion of rank−k numerical range of rectangular complex matrix polynomials are introduced. Some algebraic and geometrical properties are investigated. Moreover, for > 0, the notion of Birkhoff-James approximate orthogonality sets for −higher rank numerical ranges of rectangular matrix polynomials is also introduced and studied. The proposed definitions yield a natural general...