Some new examples for nonuniqueness of the evolution problem of harmonic maps

We find some new examples to show nonuniquence for the heat flow of harmonic maps where weak solutions satisfy the same monotonicity property.

On the Jager-Kaul theorem concerning harmonic maps

In 1983, Jager and Kaul proved that the equator map u*(x) = (x/\x\,0) : B-n --> S-n is unstable for 3 less than or equal to n less than or equal to 6 and a minimizer for the energy functional E(u, B-n) = integral B-n \del u\(2) dx in the class H-1,H-2(B-n, S-n) with u = u* on partial derivative B-n when n greater than or equal to 7. In this paper, we give a new and elementary proof of this Jager-Kaul result. We also generalize the Jager-Kaul result to the case of p-harmonic maps.

A new approach for detecting and mapping sewage impacts

Increased nitrogen loading has been implicated in eutrophication occurrences worldwide. Much of this loading is attributable to the growing human population along the world's coastlines. A significant component of this nitrogen input is from sewage effluent, and delineation of the distribution and biological impact of sewage-derived nitrogen is becoming increasingly important. Here, we show a technique that identifies the source, extent and fate of biologically available sewage nitrogen in coastal marine ecosystem. This method is based on the uptake of sewage nitrogen by marine plants and subsequent analysis of the sewage signature (elevated delta N-15) in plant tissues. Spatial analysis is used to create maps of delta N-15 and establish coefficient of variation estimates of the mapped values. We show elevated delta N-15 levels in marine plants near sewage outfalls in Moreton Bay, Australia, a semi-enclosed bay receiving multiple sewage inputs. These maps of sewage nitrogen distribution are being used to direct nutrient reduction strategies in the region and will assist in monitoring the effectiveness of environmental protection measures. (C) 2001 Elsevier Science Ltd. All rights reserved.

Brain maps, great and small: lessons from comparative studies of primate visual cortical organization

In this paper, we review evidence from comparative studies of primate cortical organization, highlighting recent findings and hypotheses that may help us to understand the rules governing evolutionary changes of the cortical map and the process of formation of areas during development. We argue that clear unequivocal views of cortical areas and their homologies are more likely to emerge for 'core' fields, including the primary sensory areas, which are specified early in development by precise molecular identification steps. In primates, the middle temporal area is probably one of these primordial cortical fields. Areas that form at progressively later stages of development correspond to progressively more recent evolutionary events, their development being less firmly anchored in molecular specification. The certainty with which areal boundaries can be delimited, and likely homologies can be assigned, becomes increasingly blurred in parallel with this evolutionary/developmental sequence. For example, while current concepts for the definition of cortical areas have been vindicated in allowing a clarification of the organization of the New World monkey 'third tier' visual cortex (the third and dorsomedial areas, V3 and DM), our analyses suggest that more flexible mapping criteria may be needed to unravel the organization of higher-order visual association and polysensory areas.