Aggregation of Malmquist productivity indexes allowing for reallocation of resources

In this paper we consider aggregate Malmquist productivity index measures which allow inputs to be reallocated within the group (when in output orientation). This merges the single period aggregation results allowing input reallocation of Nesterenko and Zelenyuk (2007) with the aggregate Malmquist productivity index results of Zelenyuk (2006) to determine aggregate Malmquist productivity indexes that are justified by economic theory, consistent with previous aggregation results, and which maintain analogous decompositions to the original measures. Such measures are of direct relevance to firms or countries who have merged (making input reallocation possible), allowing them to measure potential productivity gains and how these have been realised (or not) over time.     

Geodesic Webs on a Two-Dimensional Manifold and Euler Equations

We prove that any planar 4-web defines a unique projective structure in the plane in such a way that the leaves of the web foliations are geodesics of this projective structure. We also find conditions for the projective structure mentioned above to contain an affine symmetric connection, and conditions for a planar 4-web to be equivalent to a geodesic 4-web on an affine symmetric surface. Similar results are obtained for planar d-webs, d>4, provided that additional d−4 second-order invariants vanish.     

Consonance and Cantor set-selectors

It is shown that every metrizable consonant space is a Cantor set-selector. Some applications are derived from this fact, also the relationship is discussed in the framework of hyperspaces and Prohorov spaces.     

Bounding sup-norms of cusp forms of large level

Let f be an L ²-normalized weight zero Hecke-Maaß cusp form of square-free level N, character χ and Laplacian eigenvalue λ≥1/4. It is shown that ‖f‖_∞? _λ N ^?1/37, from which the hybrid bound ‖f‖_∞?λ ^1/4(N λ)^?δ (for some δ>0) is derived. The first bound holds also for f=y ^k/2 F where F is a holomorphic cusp form of weight k with the implied constant now depending on k.