One of the main predictions of principal-agent theory, the “informativeness principle”, is often violated in practice. We propose an explanation that emphasizes the role played by the change in the form of the optimal contract that follows an improvement in informativeness. We show that the overall gains from a less noisy performance measure emanate from two sources: the direct effect of a chan...

We study Farrell Nil-groups associated to a finite order automorphism of a ring R. We show that any such Farrell Nil-group is either trivial, or infinitely generated (as an abelian group). Building on this first result, we then show that any finite group that occurs in such a Farrell Nil-group occurs with infinite multiplicity. If the original finite group is a direct summand, then the countabl...

Generalizing the idea of viewing a digraph as a model of a linear map, we suggest a multi-variable analogue of a digraph, called a hydra, as a model of a multi-linear map. Walks in digraphs correspond to usual matrix multiplication while walks in hydras correspond to the tensor multiplication introduced by Robert Grone in 1987. By viewing matrix multiplication as a special case of this tensor m...

The Hankel matrix has various applications. In this paper we prove that Hankel matrix is strongly regular and apply to obtain the necessary and sufficient conditions to sum the Walsh–Fourier series of a function of bounded variation. 2013 Elsevier Inc. All rights reserved.

Let G be a strongly connected, weighted directed graph. We define a product distance η(i, j) for pairs i, j of vertices and form the corresponding product distance matrix. We obtain a formula for the determinant and the inverse of the product distance matrix. The edge orientation matrix of a directed tree is defined and a formula for its determinant and its inverse, when it exists, is obtained....