In this note, we prove the equivalence of two characterizations of hypercomplex structures on Courant algebroids, one in terms of Nijenhuis concomitants and the other in terms of (almost) torsionfree connections for which each of the three complex structures is parallel. A Courant algebroid [4] consists of a vector bundle π : E → M , a nondegenerate symmetric pairing 〈, 〉 on the fibers of π, a ...

2. Write a Matlab script of no more than 10 lines to calculate the Newton-Cotes quadrature weights wj , j = 1, 2, . . . , n, n + 1; go to the end of this handout for more details about wj . For uniformity, we require that the script starts with the four lines n=2; h=1/n; nodes=(0:h:1)’; f=eye(n+1); where the j-th column of the matrix f are needed for the Lagrange interpolation in order to find ...

School finance reform in Michigan involved centralization (at the state level) of spending decisions about schools, a large tax shift (mostly from property to sales), and a small tax cut. The changes came about after two decades of failed attempts to reduce property taxes in the state, and were the immediate result of an unlikely piece of legislation that abolished all funding for public school...

The question of determining for which eigenvalues there exists an eigenfunction has the same number nodal domains as label associated eigenvalue (Courant-sharp property) was motivated by analysis minimal spectral partitions. In previous works, many examples have been analyzed corresponding to squares, rectangles, disks, triangles, tori, M\"obius strips,\ldots . A natural toy model further inves...