The Schnorr-Stimm dichotomy theorem (Schnorr and Stimm, 1972) concerns finite-state gamblers that bet on infinite sequences of symbols taken from a finite alphabet Σ. asserts that, for any such sequence S, the following two things are true. (1) If S is not normal in sense Borel (meaning every strings equal length appear with asymptotic frequency S), then there gambler wins money at an infinitel...

Let R be a ring equipped with proper norm. We show that under suitable conditions on R, there is natural basis continuous linear injection for the set of Polish R-modules which are not countably generated. When division ring, this can taken to singleton.

Given the important role of family environment in children's psychological development, the objective of this study was to examine the linkages between family factors at the whole, dyadic, and individual levels and two dimensions (affective and behavioral) of Oppositional Defiant Disorder (ODD) symptoms in Chinese children. Participants comprised of 80 father-child dyads and 169 mother-child dy...

A case of pediatric oppositional defiant disorder (ODD) with concomitant emotional dysregulation and secondary behavioral disruptiveness was treated with hypnosis by means of the hypnotic hold, a method adapted by the authors. An A-B-A-B time-series design with multiple replications was employed to measure the relationship of the hypnotic treatment to the dependent measure: episodes of emotiona...

The Global Diffusion of the Internet (GDI) framework was used to study the progress in the adoption of the Internet in close to 30 countries since 1997. A new methodology in data mining is presented to extend the use of Kiviat diagrams to visualize the framework cast in a supplydemand dichotomy. A maximum resolution topology is derived as an additional tool for exploratory data analysis of such...

The topography on Mars is dominated by the crustal dichotomy between the northern and southern hemispheres and the Tharsis rise on the equator[1]. No explanation has been offered so far as to why the dichotomy should be in its current orientation rather than another. The geoid is currently dominated by Tharsis [2] and rotational stability suggests that a Tharsis-sized load would induce polar wa...