Let f(n) be a totally multiplicative function such that |f(n)| ≤ 1 for all n, and let F (s) = ∑∞ n=1 f(n)n−s be the associated Dirichlet series. A variant of Halász’s method is developed, by means of which estimates for ∑N n=1 f(n)/n are obtained in terms of the size of |F (s)| for s near 1 with 1. The result obtained has a number of consequences, particularly concerning the zeros of the p...

The complexity of the present data-centric world finds its expression in the increasing number of multi-indicator systems. This has led to the development of multicriteria ranking systems based on partial order. Partial order is a main pillar of structural mathematics. Partial order helps reveal why an object of interest holds a certain ranking position and how much it is subject to change if a...

the positions 0 = B0 ≤ B1 ≤ B2 ≤ ... ≤ Bn ≤ ... In this last case it moves necessarily up : Bn denotes the position of the nth reflecting barrier. The barriers are assumed to be thrown at random on N, and more precisely the intervals Xn between the barriers are assumed to be i.i.d.. We prove, giving thus a complete answer to a question of Molchanov, that there is homogeneization for xt iff (q/p...

The notion of functionality is not cast in stone, but depends upon what we have as types in our language. With partial equivalence relations (pers) as types we show that the functional relations are precisely those satisfying the simple equation f = f ◦ f∪ ◦ f , where “∪” is the relation converse operator. This article forms part of “A calculational theory of pers as types” [1].

We describe a distributed partial order reduction algorithm for security protocols. Some experimental results using an implementation of the algorithm in the distributed μCRL toolset are also reported.

In this essay I present a general characterization of qualitative probability, including a partial taxonomy of possible approaches. I discuss some of these in further depth, identify central issues, and suggest some general comparisons.

Artificial intelligent techniques have been widely used in high voltage insulation technology application. In this paper, the effectiveness of artificial intelligent technique to apply for pattern recognition and classification of Partial Discharge (PD) is presented. Partial discharge signal was generated and measured by using an artificial partial discharge source. Characteristics of PD signal...