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In the coming 5 lectures we consider methods for the random generation of objects from a given combinatorial class C = ∪n≥0Cn indexed by a size parameter n. Examples of classes are permutations (according to the number n of elements permuted), trees (according to the number n of nodes), walks (according to the length n), etc... In general, if not explicitly mentioned, we want uniform generation...

Limit theorems for a random number of independent random variables are frequently called transfer theorems. Investigations into this direction for sums of random variables with independent random sample size have been originated by Gnedenko. We present a widely applicable transfer theorem for random variables on a general metric space with random multiparameters instead of random sample sizes. ...

Experiments suggesting the existence of mind-matter interaction (MMI) effects on the outputs of random number generators (RNG) have been criticized based on the questionable assumption that MMI effects operate uniformly on each random bit, independent of the number of bits used per sample, the rate at which bits are generated, or the psychological conditions of the task. This ‘‘influence-per-bi...

This paper presents a novel approach to generating binary random numbers using d-sequences. We perform various correlation analyses on the new random number generator and provide a new tool to researchers using which the correlation properties of the random sequences can be controlled as desired.

In this paper we show the finite dimensionality of real linear spaces with their carriers equal R n. We also give the standard basis of such spaces. For the set R n we introduce the concepts of linear manifold subsets and orthogonal subsets. The cardinality of orthonormal basis of discussed spaces is proved to equal n. We use the following convention: i, j, n are elements of N, z, B 0 are sets,...

These sums appear in various branches of mathematics: Number Theory, Algebraic Geometry, and Topology; they have consequently been studied extensively in various contexts. These include the quadratic reciprocity law ([13]), random number generators ([12]), group actions on complex manifolds ([9]), and lattice point problems ([14], [5]). Dedekind was the first to show the following reciprocity l...

Article history: Received 17 January 2008 Available online 14 March 2009 Communicated by F. Dehne