The abstract (or sem antic) syntax of the Pascal language is identi­ fied. and a linea r representation fo r the trees so formed within the framework of the concrete syntax fo r that language is imposed. The indentation schem e so form ed, augm ented with a sm all numDer of pragm atic considera tions, is com pared with several previously proposed formatting schem es for Pascal and an example of...

This paper is about counting the number of distinct (scattered) subwords occurring in a given word. More precisely, we consider the generalization of the Pascal triangle to binomial coefficients of words and the sequence (S(n))n≥0 counting the number of positive entries on each row. By introducing a convenient tree structure, we provide a recurrence relation for (S(n))n≥0. This leads to a conne...

The self similar (fractal) structure of the Pascal triangle of binomial coefficients modulo some fixed prime has been known for some time and explored in detail. It turns out that such a fractal structure is the common property arithmetical functions of two variables possessing a more general recursive relation (R) f(i,j) = af(i-l,j) + bf(i 1,j-1) where a and b are fixed integers. 'When a, b ar...

A central problem in matroid theory—and by extension coding theory and finite geometry— is the problem of constructing matrices with a maximal number of columns such that every square submatrix formed by a subset of the columns is nonsingular. In this project, we apply the tools of analysis to this problem and demonstrate the value of such an approach. First, we introduce various quantities tha...

Copyright: © 2015 Pereira D, et al. This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. *Corresponding author: Daniel Pereira, Internal Medicine resident, Serviço de Medicina, Centro Hospitalar do Porto, Largo Pro...

In this paper we introduce new Tauberian conditions for Abel summability method that include Hardy Littlewood Tauberian condition [4] as a special case. Mathematics Subject Classification: 40E05

1 Egas Moniz, Health Sciences Institute, Quinta da Granja, Monte de Caparica, 2829-511 Caparica, Portugal 2 Serviço de Hematologia, Instituto Português de Oncologia de Lisboa Francisco Gentil EPE, Rua Professor Lima Basto, 1099-023 Lisboa, Portugal 3 Serviço de Anatomia Patológica, Instituto Português de Oncologia de Lisboa Francisco Gentil EPE, Rua Professor Lima Basto, 1099-023 Lisboa, Portug...