The hydrothermal reactions of [A-α-PW9O34](9-) with CuCl2·2H2O in the presence of ethanediamine (en) and acetate afforded a novel poly(polyoxotungstate) containing different lacunary fragments: monolacunary {α-PW11O39}, dilacunary {α-PW10O37}, trilacunary {B-α-PW9O34}, etc. In addition, a cockhorse-like nona-copper {Cu9} slab is incorporated. Magnetic investigation indicates overall antiferroma...

A family of novel lanthanoid-containing polytungstoarsenate(iii) polyanions with interesting structural features has been isolated: six lacunary {alpha-AsW(9)O(33)} building blocks comprising unusual pyramidal WO(5) units are templated by a caesium cation in a central cavity of the structure.

We show how wavelet techniques allow to derive irregularity properties of functions on two particular examples: Lacunary Fourier series and some Gaussian random processes. Then, we work out a general derivation of the multifractal formalism in the sequence setting, and derive some of its properties.

For any lacunary sequence θ = (kr), the aim of the present work is to introduce strong θ-statistical limit and strong θ-statistical cluster points of sequences on probabilistic normed spaces (briefly PN-spaces). Some relations among the sets of ordinary limit points, strong θ-statistical limit and strong θ-statistical cluster points of sequences on PN-spaces are obtained.

An example due to Erdős and Fortet shows that, for a lacunary sequence of integers (qn) and a trigonometric polynomial φ, the asymptotic distribution of 1 √ n ∑n−1 k=0 φ(qkx) can be a mixture of gaussian laws. Here we give a generalization of their example interpreted as the limiting behavior of some modified ergodic sums in the framework of dynamical systems.

An 1876 theorem of Hermite, later extended by Bachmann, gives congruences modulo primes for lacunary sums over the rows of Pascal’s triangle. This paper gives an analogous result for alternating sums over a certain class of rows. The proof makes use of properties of certain linear recurrences.

In this paper we presents three definitions which is a natural combination of the definition of asymptotic equivalence, statistical convergence, lacunary statistical convergence, σ-statistical convergence and Wijsman convergence. In addition, we also present asymptotically equivalent sequences of sets in sense of Wijsman and study some properties of this concept.

We prove a Glivenko-Cantelli type strong law of large numbers for the pair correlation of independent random variables. Except for a few powers of logarithms the results obtained are sharp. Similar estimates hold for the pair correlation of lacunary sequences {nkω} mod 1.

This is a summary of the course Lacunary Polynomials over Finite Fields, given by Simeon Ball, from the University of London, in March 5-8, 2002, at the Universitat Politècnica de Catalunya (Barcelona). Explanations of Dr. Ball have been complemented with some results of [3] and [4].