In 1928 H. Cartan proved an extension of Montel’s normality criterion to holomorphic curves in complex projective plane P2. He also conjectured that a similar result is true for holomorphic curves in P for any n. Recently the author constructed a counterexample to this conjecture for any n ≥ 3. In this paper we show how to modify Cartan’s conjecture so that it becomes true, at least for n = 3.

Proving a normality criterion for a family of meromorphic functions we exhibit a counterexample to the general converse of Bloch principle.

A number is normal to the base r if, in its expansion to that base, all possible digit strings of length t are equally frequent for each t. While it is generally believed that many familiar irrational constants are normal, normality has only been proven for numbers expressly invented for the purpose of proving their normality. In this study we give an overview of the main results to date. We th...

Let F be a family of meromorphic functions on a domain D. We present a quite general sufficient condition for F to be a normal family. This criterion contains many known results as special cases. The overall idea is that certain comparatively weak conditions on F locally lead to somewhat stronger conditions, which in turn lead to even stronger conditions on the limit function g in the famous Za...

Standard control chart practice assumes normality and uses estimated parameters. Because of the extreme quantiles involved, large relative errors result. Here simple corrections are derived to bring such estimated charts under control. As a criterion, suitable exceedance probabilities are used.

False positives arise when people without disorders are diagnosed as having disorders. Various approaches for avoiding false positives have been suggested. This review critically assesses the roles of zones of rarity, the threshold problem (the problem of determining the boundary of disorder in cases that shade into normality), and the Diagnostic and Statistical Manual of Mental Disorders (DSM)...