To conserve energy, a design which utilizes different power modes has been widely adopted. However, when a design has many different power modes, clock tree optimization (CTO) becomes very difficult. In this paper, we propose a two-level power-mode-aware CTO methodology. Among all different power modes, the chip-level CTO globally reduces clock skew among modules, whereas the module-level CTO r...

let $alpha$ be an endomorphism and $delta$ an $alpha$-derivationof a ring $r$.  in this paper we  study the relationship between an$r$-module $m_r$ and the  general polynomial module  $m[x]$ over theskew polynomial ring $r[x;alpha,delta]$. we introduce the notionsof skew-armendariz modules and skew quasi-armendariz modules whichare generalizations of $alpha$-armendariz modules and extend thecla...

for a ring endomorphism $alpha$ and an $alpha$-derivation $delta$, we introduce a concept, so called skew $pi$-armendariz ring, that is a generalization of both $pi$-armendariz rings, and $(alpha,delta)$-compatible skew armendariz rings. we first observe the basic properties of skew $pi$-armendariz rings, and extend the class of skew $pi$-armendariz rings through various ring extensions. we nex...

In this paper, some properties of $alpha$-skew Armendariz and central Armendariz rings have been studied by variety of others. We generalize the notions to central $alpha$-skew Armendariz rings and investigate their properties. Also, we show that if $alpha(e)=e$ for each idempotent $e^{2}=e in R$ and $R$ is $alpha$-skew Armendariz, then $R$ is abelian. Moreover, if $R$ is central $alpha$-skew A...

An oriented graph G is a simple undirected graph G with an orientation σ, which assigns to each edge of G a direction so that G becomes a directed graph. G is called the underlying graph of G and we denote by S(G) the skew-adjacency matrix of G and its spectrum Sp(G) is called the skew-spectrum of G. In this paper, the skew spectra of two orientations of the Cartesian product of two graphs are ...

Topological indices are the numerical value associated with chemical constitution purporting for correlation of chemical structure with various physical properties, chemical reactivity or biological activity. Graph theory is a delightful playground for the exploration of proof techniques in Discrete Mathematics and its results have applications in many areas of sciences. One of the useful indic...

Two digraphs of same order are said to be skew-equienergetic if their skew energies are equal. One of the open problems proposed by Li and Lian was to construct non-cospectral skew-equienergetic digraphs on n vertices. Recently this problem was solved by Ramane et al. In this  paper, we give some new methods to construct new skew-equienergetic digraphs.