A recursion for the Pólya polynomial of the symmetric group is proved. This recursion will be used to compute the Pólya polynomial of the Young group. In turn, a theorem by George Pólya, generalized by deBruijn, will be used to compute the double cosets of Young groups embedded in an overall...

The length of the Spanish broad gauge network has decreased in the 1956–2006 period. When looking at different railway maps through this period, it seems that the network is offering fewer and fewer alternatives when a line is cut, that is, the network is becoming less and less flexible. The...

Using standard calculus, explicit formulas for the one-dimensional continuous and discrete homotopy operators are derived. It is shown that these formulas are equivalent to those in terms of Euler operators obtained from the variational complex.

Currently, the variable-coefficient nonlinear Schrödinger (NLS)-typed models have attracted considerable attention in such fields as plasma physics, nonlinear optics, arterial mechanics and Bose-Einstein condensates. Motivated by the recent work of Tian et al. [Eur. Phys. J. B <Emphasis Type="Bold">47, 329 (2005)],...</emphasis>

We discuss using computer algebras systems (CAS) in an undergraduate intermediate macroeconomics class. The criteria used in choosing a CAS are considered. One criterion was that students would bear little or no financial. The lessons learned in implementing a CAS – things that worked well and...