James Warner

Coordination Capacity Paul Warner

We develop elements of a theory of cooperation and coordination in networks. Rather than considering a communication network as a means of distributing information, or of reconstructing random processes at remote nodes, we ask what dependence can be established among the nodes given the communication constraints. Specifically, in a network with communication rates between the nodes, we ask what...

E. H. Warner

Homer Richards Warner, 1922–2012

Homer, the ancient Greek poet (8th or 7th century BC) was the reator of the Iliad, an epic poem of dactylic hexameters that tells s the history of the Trojan, and also – as a kind of sequel – the dyssey that tells us about the hero Odysseus’ journey home after he fall of Troy in dactylic hexameters. Homer Richards Warner (1922–2012), the US-American cardilogist was the creator of ILIAD and ODYS...

Kazdan-Warner equation on graph

Let G = (V, E) be a connected finite graph and ∆ be the usual graph Laplacian. Using the calculus of variations and a method of upper and lower solutions, we give various conditions such that the Kazdan-Warner equation ∆u = c− heu has a solution on V , where c is a constant, and h : V → R is a function. We also consider similar equations involving higher order derivatives on graph. Our results ...

The Late Dr. Francis Warner

The recent death of Dr. Warner in his eightieth year, is an event which must command the sympathy and regret of the readers of Mental Welfare. For many years past he had been retired from active work, but in the l'atter part of last century his name was one of the best known among those working in the field to which this journal is devoted. He was, indeed, a leader in the way in which he approa...