Multiplicative processes and multifractals proved useful in various applications ranging from hydrodynamic turbulence to computer network traffic, to name but two. It was recently shown and explained how and why multifractal analysis could be interestingly and fruitfully placed in the more general framework of infinitely divisible cascades. The aim of this contribution is to design processes, c...

Electronic voting is a prime application of cryptographic tools. Many researches are addressing election or confidence voting in this area. We address a new type of voting scheme “Divisible Voting Scheme,” in which each voter has multiple ballots where the number of ballots can be different among the voters. This type of voting is popular, however there is no secure protocol which achieves this...

We give an estimate for the Kolmogorov distance between an infinitely divisible distribution (with mean zero and variance one) and the standard Gaussian distribution in terms of the difference between the fourth moment and 3. In a similar fashion we give an estimate for the Kolmogorov distance between a freely infinitely divisible distribution and the Semicircle distribution in terms of the dif...

A product form solution for the optimal fractions of divisible load to distribute to processors in a multi-level tree network is described. Here optimality involves parallel processing the load in a minimal amount of time. This tractable solution is similar to the product form solution for equilibrium state probabilities arising in Markovian queueing networks. The existence of this product form...

Chen, D., CC. Lindner and D.R. Stinson, Further results on large sets of disjoint group-divisible designs, Discrete Mathematics 110 (1992) 35-42. This paper is a continuation of a recent paper by Chen and Stinson, where some recursive constructions for large sets of group-divisible design with block size 3 arc presented. In this paper, we give two new recursive constructions. In particular, we ...

We give a complete solution for the existence problem of group divisible designs (or PBIBDs) with blocks of size k = 3, four groups of size (n, n, n, 1), and any two indices (λ1, λ2). Moreover, we introduce a construction of infinitely many group divisible designs with t groups of size n and one group of size 1. The construction technique utilizes our main result, together with some other known...