We consider input deterministic finite state transducers with infinite inputs and outputs, we the property of Borel normality on words. When these are given by a strongly connected set states, when is normal sequence, output an word such that every has frequency weighted automaton over rationals. prove there algorithm decides in cubic time whether transducer preserves normality.

Functional mapping has been a powerful tool in mapping quantitative trait loci (QTL) underlying dynamic traits of agricultural or biomedical interest. In functional mapping, multivariate normality is often assumed for the underlying data distribution, partially due to the ease of parameter estimation. The normality assumption however could be easily violated in real applications due to various ...

Various parametric tests make assumptions of the normal distribution, including t-test, analysis of variance (ANOVA), correlation, and regression. Different from some researcher’s understanding, tests of normality are not for the normality of observed data but for normality of the population distribution of a random characteristic; e.g. assuming normality for the population distribution of the ...

The aim of this paper is to study the normality of fuzzy topological spaces in Kubiak-Šostak’s sense. Also, some characterizations and the effects of some types of functions on these types of normality are

The projective normality of smooth, linearly normal surfaces of degree 9 in P is studied. All non projectively normal surfaces which are not scrolls over a curve are classified. Results on the projective normality of surface scrolls are also given.

I survey some problems and techniques that have interested me over the years, e.g. normality vs. collectionwise normality, reflection, preservation by forcing, forcing with Souslin trees, and Lindelöf problems.