This paper and its companion (Part II) are devoted to the analysis of the application of a chaotic piecewise-linear onedimensional (PL1D) map as random number generator (RNG). Piecewise linearity of the map enables us to mathematically find parameter values for which a generating partition is Markov and the RNG behaves as a Markov information source, and then to mathematically analyze the infor...

This problem belongs to an ever-increasing list of problems known to be unsolvable from the (usual) axioms of set theory. However, some of these problems have now been solved. But what does this actually mean? Could the Continuum Hypothesis be similarly solved? These questions are the subject of this article, and the discussion will involve ingredients from many of the current areas of set theo...

The series constitute ‘ideas in progress,’ after the notion described by I.J. Good in ‘The Scientist Speculates.’ Good also describes ideas about ideas as ‘partly baked ideas’ believing that “ ... it is often better to be stimulating and wrong than boring and right.” While the papers do not take this tenet as an excuse for licence at the expense of rigour, they are exploratory and the ideas may...

Residue Number System is a kind of numerical systems that uses the remainder of division in several different moduli. Conversion of a number to smaller ones and carrying out parallel calculations on these numbers will increase the speed of the arithmetic operations in this system. However, the main factor that affects performance of system is hardware complexity of reverse converter. Reverse co...