Multiple-Output Fiber-Ring Lasers and Amplifiers in a Hybrid CATV and ADSL Broadcasting Optical Fiber Communication System

In this article we propose two kinds of new fiber ring structure with a semiconductor optical amplifier. The first structure is a one-fiber-ring amplifier with an 8 × 8 fiber coupler and a semiconductor optical amplifier (SOA). The second fiber ring structure is a two-fiber-ring laser including an 8 × 8 fiber coupler, a 2 × 2 E/O modulator, and an SOA. The 14-output spectra of the fiber laser are measured. The gain coefficients of each port of the multiple-output-fiber-ring amplifiers are also measured. We apply these two kinds of fiber ring structures in a hybrid CATV and ADSL broadcasting optical fiber communication system. This application can develop a broadcasting system with large coverage area without using many laser diodes and optical amplifiers. The performance of such a system is also analyzed in this article.     

Engel conditions and symmetric tensors

In a recent study of Engel Lie rings, Serena Cicalò and Willem de Graaf have given a practical set of conditions for an additively finitely generated Lie ring L to satisfy an Engel condition. We present a simpler and more direct proof of this fact. Our main result generalizes this in the language of tensor algebra, and describes a relatively small generating set for the module generated by all n-th tensor powers of elements of a finitely generated ?-module M, in terms of a generating set for M.     

Jordan isomorphisms of generalized structural matrix rings

We describe the sub-bimodules of matrix bimodules over two structural matrix rings. Structural matrix bimodules arise as particular such sub-bimodules, and we discuss when such a bimodule is faithful or indecomposable. As an application, we obtain a large class of rings whose Jordan isomorphisms are either ring isomorphisms or ring anti-isomorphisms. Complete upper block triangular matrix rings over 2-torsion-free indecomposable rings are elements of this class.     

Constructing Almost Excellent Unique Factorization Domains

Abstract

Let (T, M) be a complete local normal integral domain containing the rationals such that |T/M | ≥ c where c is the cardinality of the real numbers. Let p be a non-maximal prime ideal of T such that _{T p} is a regular local ring. We construct a local Unique Factorization Domain (UFD) A such that the M-adic completion of A is T, p is maximal in the generic formal fiber and all fibers of A are geometrically regular except for those over some height one prime ideals.