Regularity and relaxed problems of minimizing biharmonic maps into spheres

For n >= 5 and k >= 4, we show that any minimizing biharmonic map from Omega subset of R-n to S-k is smooth off a closed set whose Hausdorff dimension is at most n - 5. When n = 5 and k = 4, for a parameter lambda is an element of [0, 1] we introduce lambda-relaxed energy H-lambda of the Hessian energy for maps in W-2,W-2 (Omega; S-4) so that each minimizer u(lambda) of H-lambda is also a biharmonic map. We also establish the existence and partial regularity of a minimizer of H-lambda for lambda is an element of [0, 1).

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.

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.

Somatotopic organization and cortical projections of the ventrobasal complex of the flying fox: an "inverted" wing representation in the thalamus

The present study investigates the somatotopic representation in the somatosensory thalamus of a megachiropteran bat. Using standard microelectrode mapping techniques, representational maps were generated for the ventrobasal (Vb) and posterior (Po) thalamic complexes of the Grey-headed flying fox. Anatomical tracing from neocortical injections provided additional data confirming the somatotopy found physiologically. A full representation of the body surface innervated by the trigeminal and spinal nerves was found. However, in contrast with other mammals, the representations of the forelimb and adjacent thoracic trunk within the thalamus were inverted. This means that the distal portions of the wing membrane and the tips of the digits were represented dorsally in Vb, and the thoracic trunk was represented ventrally In Po the digit tips were represented in the ventral most portion and the thoracic trunk in the dorsal portion of the nucleus. These results are discussed in relation to similarities of megachiropteran somatosensory thalamic nuclei to those of other mammalian species and in relation to the formation of thalamic somatotopic maps and fiber sorting.

The effects of alanine-substituted conantokin-G and ifenprodil on the human spermine-activated N-methyl-D-aspartate receptor

We evaluated the effects of Ala-7-conantokin-G (Con-G(A7)) and ifenprodil on the modulation by spermine of [H-3]MK801 binding to human cortical membranes. Human cortical tissue was obtained at autopsy and stored at -80 degreesC until assay. Both Con-GA7 and ifenprodil inhibited [H-3]MK801 binding, but spermine affected these inhibitions differently. Con-G(A7) IC50 changed little with spermine concentration, indicative of a non-competitive interaction, whereas the rightward shift in ifenprodil IC50 with increasing spermine concentration suggested partial competition. When the two agents were tested against the biphasic activation of [H-3]MK801 binding by spermine, they again differed in their effects. In the activation phase Con-G(A7) was a non-competitive inhibitor of spermine activation, and may even enhance the spermine EC50, while the ifenprodil data indicated a partially competitive interaction. Both agents were non-competitive in the inhibitory phase. Overall, the data suggest that Con-G(A7) and ifenprodil interact differently with the polyamine modulation of the glutamate-N-methyl-D-aspartate receptor. (C) 2004 IBRO. Published by Elsevier Ltd. All rights reserved.

Modelling pre-clearing vegetation distribution using GIS-integrated statistical, ecological and data models: A case study from the wet tropics of Northeastern Australia

Traditional vegetation mapping methods use high cost, labour-intensive aerial photography interpretation. This approach can be subjective and is limited by factors such as the extent of remnant vegetation, and the differing scale and quality of aerial photography over time. An alternative approach is proposed which integrates a data model, a statistical model and an ecological model using sophisticated Geographic Information Systems (GIS) techniques and rule-based systems to support fine-scale vegetation community modelling. This approach is based on a more realistic representation of vegetation patterns with transitional gradients from one vegetation community to another. Arbitrary, though often unrealistic, sharp boundaries can be imposed on the model by the application of statistical methods. This GIS-integrated multivariate approach is applied to the problem of vegetation mapping in the complex vegetation communities of the Innisfail Lowlands in the Wet Tropics bioregion of Northeastern Australia. The paper presents the full cycle of this vegetation modelling approach including sampling sites, variable selection, model selection, model implementation, internal model assessment, model prediction assessments, models integration of discrete vegetation community models to generate a composite pre-clearing vegetation map, independent data set model validation and model prediction's scale assessments. An accurate pre-clearing vegetation map of the Innisfail Lowlands was generated (0.83r(2)) through GIS integration of 28 separate statistical models. This modelling approach has good potential for wider application, including provision of. vital information for conservation planning and management; a scientific basis for rehabilitation of disturbed and cleared areas; a viable method for the production of adequate vegetation maps for conservation and forestry planning of poorly-studied areas. (c) 2006 Elsevier B.V. All rights reserved.

La Pointe Saint Mathieu, Brittany, France

The "Pointe Saint Mathieu" is one of the most westerly continental landmarks of France. The promontory is located at the entrance of the "Goulet de la Rade de Brest", that is the entrance channel of the harbour of Brest in Brittany (France). It marks also the Southern end of the "Chenal du Four" that is the main navigation channel between the islands of Ouessant, Molène and Béniquet, and Brittany. The "Chenal du Four" is reputed for its dangers. The tidal range is greater than 7 m in spring tides, and the mid-tide current may exceed 5 knots. The Saint Mathieu promontory is equipped with a lighthouse and a semaphore. The former is located in the ruins of an old monastery, founded during the 6th century AD by Saint Tanguy. The present ruins are the remnants of buildings from the 11th to 15th centuries. The first lighthouse was installed in 1689, although the monks of the monastery used to maintain a signal light since the 1250s. Completed in 1835, the present "Phare de la Pointe Saint-Mathieu" is 37 m high and it reaches 58.8 m above sea level During World War 2, the Pointe Saint Mathieu was defended by a series of concrete fortifications built by the Germans. Some were based upon some earlier French bunker systems, like the coastal battery at the Rospects which included 4 main gun bunkers (4*150 mm, or 2*150 mm & 2*105 mm), an observation bunker on the Western side close to sea, and several smaller structures. There was also the large Kéringar Blockhaus system, near Lochrist, located about 1 km inland and designed for 4 guns of 280 mm. Its command bunker remains a landmark along the main road. All this area was very-heavily bombed between 1943 and 1944, and particularly during the battle of Brest in August-September 1944 ("L'Enfer de Brest").