In this paper it is proved that the volumes of the moduli spaces of polarized Calabi-Yau manifolds with respect to Weil-Petersson metrics are rational numbers. Mumford introduce the notion of a good metric on vector bundle over a quasi-projective variety in [10]. He proved that the Chern forms of good metrics define classes of cohomology with integer coefficients on the compactified quasi-proje...

Householder orthogonalization plays an important role in numerical linear algebra. It attains perfect orthogonality regardless of the conditioning input. However, context a non-standard inner product, it becomes difficult to apply due lack initial orthonormal basis. We propose strategies overcome this obstacle and discuss algorithms variants with product. Theoretical analysis experiments demons...