In this work, we study a class of generalized quasi-cyclic (GQC) codes called skew GQC codes. By the factorization theory of ideals, we give the Chinese Remainder Theorem over the skew polynomial ring, which leads to a canonical decomposition of skew GQC codes. We also focus on some characteristics of skew GQC codes in details. For a 1-generator skew GQC code, we define the parity-check polynom...

In this paper, we build the unfolding approach from acyclic sign-skew-symmetric matrices of finite rank to skew-symmetric matrices of infinite rank, which can be regard as an improvement of that in the skew-symmetrizable case. Using this approach, we give a positive answer to the problem by Berenstein, Fomin and Zelevinsky in [6] which asks whether an acyclic signskew-symmetric matrix is always...

A skew edge coloring of a graph G is defined to be a set of two edge colorings such that no two edges are assigned the same unordered pair of colors. The skew chromatic index s(G) is the minimum number of colors required for a skew edge coloring of G. In this paper, skew edge coloring of certain classes of graphs are determined. Furthermore, the skew chromatic index of those graphs is obtained ...

Despite occupancy-based switching and daylight-based dimming controls being widely believed to have tremendous energy saving potential, there is often a lot of variability in the actual savings across customer sites. A major challenge in a reliable, site-specific assessment of these advanced lighting controls is the skew associated with time-logging using a low-power clock. We develop a robust ...

Two canonical forms for skew-symmetric matrix polynomials over arbitrary fields are characterized — the Smith form, and its skew-symmetric variant obtained via unimodular congruences. Applications include the analysis of the eigenvalue and elementary divisor structure of products of two skew-symmetric matrices, the derivation of a Smith-McMillan-like canonical form for skew-symmetric rational m...

We provide a new definition for the concept of skew in parallel asynchronous communications introduced in [2]. The new definition extends and strengthens previously known results on skew. We give necessary and sufficient conditions for codes that can tolerate a certain amount of skew under the new definition. We also extend the results to codes that can tolerate a certain amount of skew and det...

We mainly investigate the structures of skew cyclic and skew quasicyclic codes of arbitrary length over Galois rings. Similar to [5], our results show that the skew cyclic codes are equivalent to either cyclic and quasi-cyclic codes over Galois rings. Moreover, we give a necessary and sufficient condition for skew cyclic codes over Galois rings to be free. A sufficient condition for 1-generator...

In this article, we study skew cyclic codes over ring R = Fq + vFq + v 2 Fq, where q = p, p is an odd prime and v3 = v. We describe generator polynomials of skew cyclic codes over this ring and investigate the structural properties of skew cyclic codes over R by a decomposition theorem. We also describe the generator polynomials of the duals of skew cyclic codes. Moreover, the idempotent genera...

This paper considers Schrödinger operators, and presents a probabilistic interpretation of the variation (or shape derivative) of the Dirichlet groundstate energy when the associated domain is perturbed. This interpretation relies on the distribution on the boundary of a stopped random process with Feynman-Kac weights. Practical computations require in addition the explicit approximation of the...

In this paper , an improved skew angle estimation technique is presented. Skew angle detection is an important part of any Optical Character Recognition (OCR) and document analysis system. The method considers the lowermost pixels of some selected characters of the text, which maybe subject to Hough transform for skew angle detection. A fast approach is also proposed which works almost as accur...