It is often the case that the exact moments of a statistic of the continuous type can be explicitly determined, while its density function either does not lend itself to numerical evaluation or proves to be mathematically intractable. The density approximants discussed in this article are based on the first n exact moments of the corresponding distributions. A unified semiparametric approach to...

In the paper ‘The symbolization of central approximants in the IPA’, Martin Ball and Joan Rahilly approach an interesting problem – the phonetic transcription of approximants other than the so-called semivowels. In the absence of special symbols in the IPA chart, they suggest that special characters should be used for the notation of approximant realizations made at the bilabial, dental, alveol...

Bisimilarity ∼ and weak bisimilarity ≈ are canonical notions of equivalence between processes, which are defined co-inductively, but may be approached – and even reached – by their (transfinite) inductively-defined approximants ∼α and ≈α. For arbitrary processes this approximation may need to climb arbitrarily high through the infinite ordinals before stabilising. In this paper we consider a si...

polynomial if for j = O,..., m the Aj are symmetric j-linear bounded operators: (lR”y’+ IR, in other words, if Ajxj= 1 aj,...j,xil...xi, with ail.. .j in iR. II j,+. . . +j,=j (b) a,P=m, is the order of the abstract polynomial P if for 0 < k <.m, : A,xk = 0 and A,,x”‘l& 0. (c) aP= m2 is the exact degree of the abstract polynomial P if for m,(k<m:Akxk=OandA,,,ZxmZ&O. We say that J(x) = 0(x’) if ...