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.     

On Some Conditions for Complete Convergence for Arrays of Rowwise Negatively Dependent Random Variables

Abstract

This note contains some sufficient conditions for the complete convergence in the strong law of large numbers for arrays of rowwise negatively dependent random variables. Moreover, the rowwise sums are randomly indexed.