The combination generator, first proposed by Wichmann and Hill (1982), is constructed by taking the fractional part of the sum of several random number generators. It is probably one of the most popular random number generators used. Its empirical performance is superior to the classical Lehmer congruential generator. However, its theoretical justification is somewhat primitive. In this paper, ...

Arabic Numerals are one of the major aspects to be considered in Arabic language processing. In this paper, we present an approach for developing a numeral checker application for the Arabic language, called “Arabic Numerals Checker”. Arabic Numerals Checker is intended to help users achieve competence in writing according to the Arabic numeral rules. It is supported by an explanation facility ...

We adopt the following convention: i, j, m, n denote natural numbers, K denotes a field, and a denotes an element of K. Next we state several propositions: (1) Let A, B be matrices over K, n1 be an element of Nn, and m1 be an element of Nm. If rng n1 × rngm1 ⊆ the indices of A, then Segm(A + B,n1,m1) = Segm(A,n1,m1) + Segm(B,n1,m1). (2) For every without zero finite subset P of N such that P ⊆ ...

Random numbers are arranged in a circle. At each time step, the lowest number, and the numbers at its two neighbors, are each replaced by new random numbers. That’s all! This step is repeated again and again. What could be simpler than replacing some random numbers with some other random numbers? Who says that complexity cannot be simple? This simple scheme leads to rich behavior beyond what we...

Suppose that a geometrically distributed number of observations are available from an absolutely continuous distribution function F , within this set of observations denote the random number of records by M . This is called geometric random record model. In this paper, characterizations of F are provided in terms of the subsequences entropies of records conditional on events {M ≥ n} or {M = n} ...

For simplicity, we adopt the following rules: n denotes an element of N, X, X1 denote sets, r, p denote real numbers, s, x0, x1, x2 denote real numbers, S, T denote real normed spaces, f , f1, f2 denote partial functions from R to the carrier of S, s1 denotes a sequence of real numbers, and Y denotes a subset of R. The following propositions are true: (1) Let s2 be a sequence of real numbers an...

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

We consider a generalized version of Knuth’s parking problem, in which caravans consisting of a random number of cars arrive at random on the unit circle. Then each car turns clockwise until it finds a free lot to park. Extending a recent work by Chassaing and Louchard [9], we relate the asymptotics for the sizes of blocks formed by occupied lots with the dynamics of the additive coalescent. Ac...