Let nand m be integers with n = m 2 + m + 1. Then the projective plane of order m has n points and" lines with each line containing m + 1 ""n 1/2 points. In this paper, we consider the analogous problem for the Euclidean plane and show that there cannot be a comparably large collection of lines each of which contains approximately n 1/ 2 points from a given set of n points. More precisely, we s...

We review the progress in the field of front propagation in recent years. We survey many physical, biophysical and crossdisciplinary applications, including reduced-variable models of combustion flames, Reid’s paradox of rapid forest range expansions, the European colonization of North America during the XIX century, the Neolithic transition in Europe from 13,000 to 5,000 years before present, ...

We present explicit formulae for the eccentric connectivity index and Wiener index of 2-dimensional square and comb lattices with open ends. The formulae for these indices of 2-dimensional square lattices with ends closed at themselves are also derived. The index for closed ends case divided by the same index for open ends case in the limit N →&infin defines a novel quantity we call compression...