The notions of quasi-prime submodules and developed  Zariski topology was introduced by the present authors in cite{ah10}. In this paper we use these notions to define a scheme. For an $R$-module $M$, let $X:={Qin qSpec(M) mid (Q:_R M)inSpec(R)}$. It is proved that $(X, mathcal{O}_X)$ is a locally ringed space. We study the morphism of locally ringed spaces induced by $R$-homomorphism $Mrightar...

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 Many efficient interior-point methods (IPMs) are based on the use of a self-concordant barrier function for the domain of the problem that has to be solved. Recently, a wide class of new barrier functions has been introduced in which the functions are not self-concordant, but despite this fact give rise to efficient IPMs. Here, we introduce the notion of locally self-concordant barrier functio...

The lack of proven mechanisms for transferring data between multiple synchronous islands has been a major impediment for applying globally asynchronous locally synchronous (GALS) techniques to SoC design. We have implemented on a VLSI test chip three alternative solutions to fill the gap: an arbitrated bus, a switch, and a self-timed ring. Circuit details and various extensions of the basic rin...

We consider a class of encoders for constrained systems, which we call block-typedecodable encoders. For a constrained system presented by a deterministic graph, we design a blocktype-decodable encoder by selecting a subset of states of the graph to be used as encoder states. Such a subset is known as a set of principal states. Our goal is to find an optimal set of principal states, i.e., a set...

In this paper we describe a complete design methodology for a globally asynchronous onchip communication network connecting both locally-synchronous and asynchronous modules. Synchronous modules are equipped with asynchronous wrappers which adapt their interfaces to the self-timed environment and prevent metastability. These wrappers are assembled from a concise library of predesigned technolog...