(nil) = nil sigperm(x :: xs) = append(sigrot(x; x); sigperm(xs)) sigrot(x; nil) = nil sigrot(u; x :: xs)) = cond(issig(u); u :: sigrot(rotate(u); xs); sigrot(rotate(u); xs)) 4.4 Third transformation step Our objective is to get rid of the costly occurrences of append in sigperm. We introduce the new denition: sr(x; y; u) = append(sigrot(x; y); u) and the theorem: The complete denition of sigper...

It is shown that a commutative Bézout ring R with compact minimal prime spectrum is an elementary divisor ring if and only if so is R/L for each minimal prime ideal L. This result is obtained by using the quotient space pSpec R of the prime spectrum of the ring R modulo the equivalence generated by the inclusion. When every prime ideal contains only one minimal prime, for instance if R is arith...

Let R be a commutative ring and G(R) be a graph with vertices as proper andnon-trivial ideals of R. Two distinct vertices I and J are said to be adjacentif and only if I + J = R. In this paper we study a graph constructed froma subgraph G(R)Δ(R) of G(R) which consists of all ideals I of R such thatI Δ J(R), where J(R) denotes the Jacobson radical of R. In this paper westudy about the relation b...

Introduction: Ischemia/reperfusion (IR) injury involves a complex interrelated sequence of events. High levels of nitric oxide (NO) are generated with inducible form of nitric oxide synthase (iNOS) leading to the renal IR injury and glutathione (GSH) depletion. The present study was designed to investigate the effect of L-Nil (N6- (1-Iminoethyl)-L- lysine.hydrochloride), a selective inhibito...

We experimentally demonstrate cascaded silicon micro-ring modulators as the key component of a WDM interconnection system. We show clean eye-diagrams when each of the four micro-ring modulators is modulated at 4 Gbit/s. We show that optical inter-channel crosstalk is negligible with 1.3-nm channel spacing.

We show that a Dedekind-finite, semi-π-regular ring with a “nice” topology is an א0-exchange ring, and the same holds true for a strongly clean ring with a “nice” topology. We generalize the argument to show that a Dedekind-finite, semi-regular ring with a “nice” topology is a full exchange ring. Putting these results in the language of modules, we show that a cohopfian module with finite excha...

A new class of rings are introduced which every element in the ring sum involution and tripotent elements. This called t-clean is a generalization invo-clean subclass clean rings. Some properties this investigate. For an application graph theory, defined set vertices order pairs them element. The two adjacent if only elements zero or product zero. graphs connecting, has diameter one girth three.