we call a module  essentially retractable if homr for all essential submodules n of m. for a right fbn ring r, it is shown that: (i)  a non-zero module  is retractable (in the sense that homr for all non-zero ) if and only if certain factor modules of m are essentially retractable nonsingular modules over r modulo their annihilators. (ii)  a non-zero module  is essentially retractable if and on...

We show that the hereditary discrepancy of a hypergraph F on n points increases by a factor of at most O(log n) when one adds a new edge to F . Let X be a set of n points. We say that a hypergraph F on X has discrepancy h if h is the smallest integer satisfying the following: There is a coloring χ: X → {−1, +1} such that for every edge S ∈ F , |χ(S)| ≤ h, where we write χ(S) for ∑ x∈S χ(x). The...

Objective(s) The aim of this study was to investigate the overall effect of cardiac vasoactive factors during coronary occlusion and reperfusion on peripheral vascular tone, using a sequential isolated rabbit heart-ear perfusion model. Materials and Methods Isolated ears were perfused with the effluent of isolated hearts subjected to ischemia (30 min) and reperfusion (180 min, n=6). The comp...

In this paper, we introduce the notion of “(n, d)-perfect rings” which is in some way a generalization of the notion of “S-rings”. After we give some basic results of this rings and we survey the relationship between “A(n) property” and “(n, d)-perfect property”. Finally, we investigate the “(n, d)-perfect property” in pullback rings.