Impacts of Wheat Export Strategies on Market Shares

Marketing, International Relations/Trade,

Comparison of Computational and Experimental Aerodynamics: Results for a WMU Solar Car Model

Three-dimensional numerical simulations using FLUENT [1] were performed to model the airflow over the Sunseeker, an award-winning solar car that was designed and built at Western Michigan University. Converged numerical solutions on three different grids are reported and compared with the available experimental data, which include the lift and the drag coefficients. Also reported are the results obtained by using the second-order upwinding discretization on one of the grids. The comparison shows that the computed lift coefficients agree well with the experimental data for all the three grids and the different orders of numerical methods, indicating that the pressure field is well captured. The agreement with the data for drag coefficient varies, which appears to suggest a higher degree of dependency on the grid distributions than that for the lift coefficient. These results are discussed in terms of their implications for the simulations of similar low-drag vehicles

Parity Reversing Involutions on Plane Trees and 2-Motzkin Paths

The problem of counting plane trees with $n$ edges and an even or an odd number of leaves was studied by Eu, Liu and Yeh, in connection with an identity on coloring nets due to Stanley. This identity was also obtained by Bonin, Shapiro and Simion in their study of Schr\"oder paths, and it was recently derived by Coker using the Lagrange inversion formula. An equivalent problem for partitions was independently studied by Klazar. We present three parity reversing involutions, one for unlabelled plane trees, the other for labelled plane trees and one for 2-Motzkin paths which are in one-to-one correspondence with Dyck paths.Comment: 8 pages, 4 figure