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 novel genetic locus for low renin hypertension: familial hyperaldosteronism type II maps to chromosome 7 (7p22)

Familial hyperaldosteronism type II (FH-II) is caused by adrenocortical hyperplasia or aldosteronoma or both and is frequently transmitted in an autosomal dominant fashion. Unlike FH type I (FI-I-I), which results from fusion of the CYP11B1 and CYP11B2 genes, hyperaldosteronism in FH-II is not glucocorticoid remediable. A large family with FH-II was used for a genome wide search and its members were evaluated by measuring the aldosterone:renin ratio. In those with an increased ratio, FH-II was confirmed by fludrocortisone suppression testing. After excluding most of the genome, genetic linkage was identified with a maximum two point lod score of 3.26 at theta =0, between FH-II in this family and the polymorphic markers D7S511, D7S517, and GATA24F03 on chromosome 7,a region that corresponds to cytogenetic band 7p22. This is the first identified locus for FH-II; its molecular elucidation may provide further insight into the aetiology of primary aldosteronism.

Disaggregation of polygons of surficial geology and soil maps using spatial modelling and legacy data

Examples from the Murray-Darling basin in Australia are used to illustrate different methods of disaggregation of reconnaissance-scale maps. One approach for disaggregation revolves around the de-convolution of the soil-landscape paradigm elaborated during a soil survey. The descriptions of soil ma units and block diagrams in a soil survey report detail soil-landscape relationships or soil toposequences that can be used to disaggregate map units into component landscape elements. Toposequences can be visualised on a computer by combining soil maps with digital elevation data. Expert knowledge or statistics can be used to implement the disaggregation. Use of a restructuring element and k-means clustering are illustrated. Another approach to disaggregation uses training areas to develop rules to extrapolate detailed mapping into other, larger areas where detailed mapping is unavailable. A two-level decision tree example is presented. At one level, the decision tree method is used to capture mapping rules from the training area; at another level, it is used to define the domain over which those rules can be extrapolated. (C) 2001 Elsevier Science B.V. All rights reserved.

A Century of Change in Coral Reef Status in Southeast and Central Pacific: Polynesia Mana Node, Cook Islands, French Polynesia, Kiribati, Niue, Tokelau, Tonga, Wallis and Futuna

The Polynesia Mana Node of the southeast and central Pacific contains 7 independent or autonomous countries or territories with only 6,000 km2 of land on 347 islands, but surrounded by 12 million km2 of EEZ. These seas contain 13,000 km2 of coral reefs as the main natural ecosystem providing food resources and opportunities for development, especially for tourism and pearl culture for 500,000 inhabitants. During the 19th and first half of the 20th centuries, there was major exploitation by the colonial powers of mother-of-pearl oysters for the button industry, as well as guano, sandalwood and trepang. The Polynesian people were largely involved in a subsistence economy and all coral reefs and lagoons were healthy. During the last two decades of the 20th, all countries experienced rapid development and urbanization, rising populations, and some increased agriculture. These developments were limited to a few islands of each country (i.e. 15 islands amongst the 347) with resulting degradation of the coral reefs around these sites. The other islands remained mostly uninhabited and pristine, and continued with a subsistence economy. Generally, there was more damage to the coral reefs through natural events such as cyclones and coral bleaching, than by human activities. There is however, an urgent need to combat the threats on some islands from increased sedimentation, over-fishing, dredging and nutrient pollution.