Let $\mathbb N$ be the set of nonnegative integers and $\mathbb Z$ the ring of integers. Let $\mathcal B$ be the ring of $N \times N$ matrices over $\mathbb Z$ generated by the following two matrices: one obtained from the identity matrix by shifting the ones one position to the right and the other one position down. This ring plays an important role in the study of directly finite rings. Calculation of invertible and idempotent elements of $\mathcal B$ yields that the subrings generated by them coincide. This subring is the sum of the ideal $\mathcal F$ consisting of all matrices in $\mathcal B$ with only a finite number of nonzero entries and the subring of $\mathcal B$ generated by the identity matrix. Regular elements are also described. We characterize all ideals of $\mathcal B$, show that all ideals are finitely generated and that not all ideals of $\mathcal B$ are principal. Some general ring theoretic properties of $\mathcal B$ are also established.
The increasing availability of computing power in the past two decades has been used to develop new techniques for optimizing the solution of estimation problem. Today's computational capacity and the widespread availability of computers have enabled the development of a new generation of intelligent computing techniques, such as the algorithm of our interest. This paper presents a new member of the class of stochastic search algorithms (known as Canonical Genetic Algorithm "CGA") for optimizing the maximum likelihood function ln (L(θ, σa2 )) of the first order moving average MA(1) model. The presented strategy is composed of three main steps: recombination, mutation, and selection. The experimental design is based on simulating the CGA with different values of (θ), and sample size n. The results are compared with those of moment method. Based on MSE value obtained from both methods, one can conclude that CGA can give estimators (\hat \theta) for MA(1) parameter which are good and more reliable than those estimators obtained by moment method.
The Cantor-Bernstein theorem was extended to $\sigma $-complete boolean algebras by Sikorski and Tarski. Chang’s MV-algebras are a nontrivial generalization of boolean algebras: they stand to the infinite-valued calculus of Łukasiewicz as boolean algebras stand to the classical two-valued calculus. In this paper we further generalize the Cantor-Bernstein theorem to $\sigma $-complete MV-algebras, and compare it to a related result proved by Jakubík for certain complete MV-algebras.
Small bowel obstruction is a common clinical problem presenting with abdominal distention, colicky pain, absolute constipation and bilious vomiting. There are numerous causes, most commonly attributed to an incarcerated hernia, adhesions or obstructing mass secondary to malignancy. Here we present an unusual cause of a small bowel obstruction secondary to an incarcerated incisional hernia in association with an acute organoaxial gastric volvulus. and N. R. Kosai, H. S. Gendeh, M. Noorharisman, P. A. Sutton, S. Das