Here, we propose an optical filter and an optical power splitter based on two-dimensionalphotonic crystal all circular ring resonators. These structures are made of a square lattice ofsilicon rods with the refractive index n1=3.464 surrounded by air (with refractive indexn2=1). First, we have designed the filter and by using that, we designed a power splitter. Thetransmission efficiency and Qua...

a ring $r$ is a strongly clean ring if every element in $r$ is the sum of an idempotent and a unit that commutate. we construct some classes of strongly clean rings which have stable range one. it is shown that such cleanness of $2 imes 2$ matrices over commutative local rings is completely determined in terms of solvability of quadratic equations.

Using the concept of the λ-lattice introduced recently by V. Snášel we define λ-lattices with antitone involutions. For them we establish a correspondence to ring-like structures similarly as it was done for ortholattices and pseudorings, for Boolean algebras and Boolean rings or for lattices with an antitone involution and the so-called Boolean quasirings.

In this paper we present the reliability analysis of ring-based hierarchical directed networks in the context of large-scale multiprocessors. A wide range of hierarchical structures based on the basic, dual counter-rotating, and braided (skip-a-node) rings are analyzed and compared in thispaper. We have adopted the two-processor (two-temzinal) reliability criteria for our analysis. The results ...