The class of completely regular codes includes not only some of the most important error-correcting codes, such as perfect codes and uniformly packed codes, but also a number of substructures fundamental to the study of distance-regular graphs themselves. In a companion paper, we study products of completely regular codes and codes whose parameters form arithmetic progressions. This family of c...

There is a concept in linear algebra called tridiagonal pair. The was motivated by the theory of $Q$-polynomial distance-regular graphs. We give tutorial introduction to pairs, working with special case as concrete example. totally bipartite, or bipartite (TB). Starting from first principles, we an elementary but comprehensive account TB pairs. following topics are discussed: (i) notion system;...

let $r$ be an associative ring with identity. an element $x in r$ is called $mathbb{z}g$-regular (resp. strongly $mathbb{z}g$-regular) if there exist $g in g$, $n in mathbb{z}$ and $r in r$ such that $x^{ng}=x^{ng}rx^{ng}$ (resp. $x^{ng}=x^{(n+1)g}$). a ring $r$ is called $mathbb{z}g$-regular (resp. strongly $mathbb{z}g$-regular) if every element of $r$ is $mathbb{z}g$-regular (resp. strongly $...

By a multi-pointed category we mean a category C equipped with a so called ideal of null morphisms, i.e. a class N of morphisms satisfying f ∈ N ∨ g ∈ N ⇒ fg ∈ N for any composable pair f, g of morphisms. Such categories are precisely the categories enriched in the category of pairs X = (X,N) where X is a set and N is a subset of X, whereas a pointed category has the same enrichment, but restri...

Description of the pairs 〈low approximation, upper approximation〉 of rough sets is an important aspect in the research of rough set theory by algebraic method. By defining some basic operators on the approximation pairs, rough algebras can be constructed. Then some general algebras can be selected to describe the pairs of rough sets. The most famous rough algebras are Rough Double Stone Algebra...

In this paper, we have developed a new general distance measure that not only can be used in a vector quantization (VQ) of the line spectrum frequency (LSF) parameters but performes well in the LSF transformed domain. The new distance is based on the spectral sensitivity of LSF and their transformed coe cients. In addition, the x scaling factor is used to decrease the sensitivity of spectral er...

Voice adaptation describes the process of converting the output of a text-to-speech synthesizer voice to sound like a different voice after a training process in which only a small amount of the desired target speaker’s speech is seen. We employ a locally linear conversion function based on Gaussian mixture models to map bark-scaled line spectral frequencies. We compare performance for three di...

The Regularity Lemma [16] is a powerful tool in Graph Theory and its applications. It basically says that every graph can be well approximated by the union of a constant number of random-looking bipartite graphs called regular pairs (see the definitions below). These bipartite graphs share many local properties with random bipartite graphs, e.g. most degrees are about the same, most pairs of ve...