On uniform distribution modulo a subdivision

On uniform distribution modulo one

We introduce an elementary argument to the theory of distribution of sequences modulo one.

Analysis of quasi-uniform subdivision

We study the smoothness of quasi-uniform bivariate subdivision. A quasi-uniform bivariate scheme consists of different uniform rules on each side of the y-axis, far enough from the axis, some different rules near the y-axis, and is uniform in the y-direction. For schemes that generate polynomials up to degree m, we derive a sufficient condition for C continuity of the limit function, which is s...

On the Distribution of Inverses Modulo n

Non-uniform interpolatory subdivision via splines

We present a framework for deriving non-uniform interpolatory subdivision algorithms closely related to non-uniform spline interpolants. Families of symmetric non-uniform interpolatory 2n-point schemes of smoothness C are presented for n = 2, 3, 4 and even higher order, as well as a variety of non-uniform 6-point schemes with C continuity.

Uniform Distribution modulo 1 of the Harmonic Prime Factor of an Integer

for the arithmetic mean of the distinct prime factors of n, then pa(n) is uniformly distributed modulo 1. Furthermore, it was also shown that for large x the number of n ≤ x such that pa(n) is an integer of order of magnitude O(x/ log log x). This was made more precise by the first author in [4], who showed that the counting function of the above n is asymptotically equal to (c+o(1))x/ log log ...