In this paper, we propose the definition of a measure for sets of strings of length not greater than a given number. This measure leads to an instanciation of the uniform distribution definition in sets of such limited-size strings, for which we provide a linear time complexity generative algorithm. Some ideas could rather easily be extended to other ordered structure types.

A sequence s1, s2, . . . in U = [0, 1) is said to be uniformly distributed if, in the limit, the number of sj falling in any given subinterval is proportional to its length. Equivalently, s1, s2, . . . is uniformly distributed if the sequence of equiweighted atomic probability measures μN (sj) = 1/N , supported by the initial N -segments s1, s2, . . . , sN , converges weakly to Lebesgue measure...

The book Uniform distribution of sequences by Kuipers and Niederreiter, long out of print, has recently been made available again by Dover books. I came across a copy at the Borders bookstore in San Francisco and decided to give it a try (the price, as they say, was right). It turned out to be full of interesting results, so I decided to take some notes on what seemed to me to be the parts most...

The reuseability and accessibility of lexical and linguistic resources often requires substantial programming overhead and detailed knowledge of the structure and nature of resource-specific information. Each resource has its own representation syntax and covers a particular subset of linguistic phenomena. This paper will discuss ways to overcome these barriers to resource reuse and presents a ...

A sequence s1, s2, . . . in U = [0, 1) is said to be uniformly distributed if, in the limit, the number of sj falling in any given subinterval is proportional to its length. Equivalently, s1, s2, . . . is uniformly distributed if the sequence of equiweighted atomic probability measures μN (sj) = 1/N , supported by the initial N -segments s1, s2, . . . , sN , converges weakly to Lebesgue measure...

Wemodify the recent method of J.-M. Deshouillers and H. Iwaniec in the theory of uniform distribution to show that the sequence with general term an = 1 n ∑ m≤n σ(m) is uniformly distributed modulo 1. We also study uniform distribution modulo 1 of some sequences related by the functions σ and φ. AMS subject classifications: 11K65, 11K31, 11J71, 11N36, 11N64

We consider a class of Dirichlet series which is more general than the Selberg class. Dirichlet series in this class, have meromorphic continuation to the whole plane and satisfy a certain functional equation. We prove, under the assumption of a certain hypothesis concerning the density of zeros on average, that the sequence formed by the imaginary parts of the zeros of a Dirichlet series in th...

Automatic sequences and their number theoretic properties have been intensively studied during the last 20 or 30 years. Since automatic sequences are quite regular (they just have linear subword complexity) they cannot be used as quasi-random sequences. However, the situation changes drastically when one uses proper subsequences, for example the subsequence along primes or squares. It is conjec...

The note explores a vertical differentiation model with a continuous nonuniform consumers’ distribution. First a result concerning the finiteness property obtained with uniform consumers’ distribution is generalized. Second we prove an existence result of price equilibrium when the distribution is concave. Finally we exhibit a counter-example to the existence of price equilibrium to show that t...