Orderings of filters in terms of reloids ∗ Extensions of
Orderings of filters which extend Rudin-Keisler preorder of ultrafilters are described in terms of reloids that (roughly speaking) is filters on sets of binary relations between some sets. Also it is defined isomorphism of filters which extends Rudin-Keisler equivalence of ultrafilters.
Funcoids and Reloids
It is a part of my Algebraic General Topology research. In this article I introduce the concepts of funcoids which generalize proximity spaces and reloids which generalize uniform spaces. The concept of funcoid is generalized concept of proximity, the concept of reloid is cleared from superfluous details (generalized) concept of uniformity. Also funcoids and reloids are generalizations of binary relations whose domains and ranges are filters (instead of sets). Also funcoids and reloids can be considered as a generalization of (oriented) graphs, this provides us with a common generalization of analysis and discrete mathematics. The concept of continuity is defined by an algebraic formula (instead of old messy epsilon-delta notation) for arbitrary morphisms (including funcoids and reloids) of a partially ordered category. In one formula are generalized continuity, proximity continuity, and uniform continuity.
Review of Literature on Probability of Detection for Magnetic Particle Nondestructive Testing
Abstract : A critical review of the available literature concerning the minimum reliably detectable defect size aNDI for magnetic particle testing (MPT) in aerospace applications is presented. Four probability of detection (POD) studies relevant to detection of fatigue cracks in aircraft components were found over the period 1968 to 2011. As the statistical methods used in these four previous studies were either outdated or otherwise deficient, the original data were reanalysed using currently accepted techniques. A meta-analysis of the results is presented, with emphasis on statistical inferences for the defect size expected to be detected with 90% POD. It is shown that the minimum reliably detectable defect size aNDI = 2.0 mm currently specified by the Royal Australian Air Force for wet fluorescent magnetic particle inspection using the continuous method is consistent with estimates of the average performance of MPT derived from the reanalysis of the literature.