We introduce an extension of the Parikh mapping called the Parikh -matrix mapping, which takes its values in matrices with polynomial entries. The morphism constructed represents a word over a -letter alphabet as a -dimensional upper-triangular matrix with entries that are nonnegative integral polynomials in variable . We show that by appropriately embedding the -letter alphabet into the -lette...

We develop and test a new mapping that can be applied to directed unweighted networks. Although not a “matrix function” in the classical matrix theory sense, this mapping converts an unsymmetric matrix with entries of zero or one into a symmetric real-valued matrix of the same dimension that generally has both positive and negative entries. The mapping is designed to reveal approximate directed...

Abstract: In this study Al-5 (Vol) % SiCp nanocomposite powder has been successfully synthesized by high-energy planetary milling of Al and SiC powders for a period of 25 h at a ball-to-powder ratio of 15:1. The changes of the lattice strain, the crystallite size of the matrix phase, and the nanocomposite powder microstructure with time have been investigated by X-ray diffraction (XRD), X-ray m...

today, extensive improvements in fields of soil mapping have increased the purity and accuracy ofsoil maps. usual mapping methods moreover depend on skills and experience of surveyor inidentifying and delineating the boundaries, also need the high cost and time consuming that face thesoil mapping with restrictions. in this study, aerial photographs with 1/40000 scale were used in orderto prepar...

We introduce a generalization of the Parikh mapping called the Parikh q-matrix encoding, which takes its values in matrices with polynomial entries. The encoding represents a word w over a k-letter alphabet as a (k + 1)-dimensional upper-triangular matrix with entries that are nonnegative integral polynomials in variable q. Putting q = 1, we obtain the morphism introduced by Mateescu, Salomaa, ...