On the nonlinear Neumann problem involving the critical Sobolev exponent on the boundary

in this paper we investigate the solvability of the Neumann problem (1.1) involving the critical Sobolev exponents on the right-hand side of the equation and in the boundary condition. It is assumed that the coefficients Q and P are smooth. We examine the common effect of the mean curvature of the boundary a deltaOhm and the shape of the graph of the coefficients Q and P on the existence of solutions of problem (1.1). (C) 2003 Published by Elsevier Inc.

On the possibility of elastic strain localisation in a fault

The phenomenon of strain localisation is often observed in shear deformation of particulate materials, e.g., fault gouge. This phenomenon is usually attributed to special types of plastic behaviour of the material (e.g., strain softening or mismatch between dilatancy and pressure sensitivity or both). Observations of strain localisation in situ or in experiments are usually based on displacement measurements and subsequent computation of the displacement gradient. While in conventional continua the symmetric part of the displacement gradient is equal to the strain, it is no longer the case in the more realistic descriptions within the framework of generalised continua. In such models the rotations of the gouge particles are considered as independent degrees of freedom the values of which usually differ from the rotation of an infinitesimal volume element of the continuum, the latter being described for infinitesimal deformations by the non-symmetric part of the displacement gradient. As a model for gouge material we propose a continuum description for an assembly of spherical particles of equal radius in which the particle rotation is treated as an independent degree of freedom. Based on this model we consider simple shear deformations of the fault gouge. We show that there exist values of the model parameters for which the displacement gradient exhibits a pronounced localisation at the mid-layers of the fault, even in the absence of inelasticity. Inelastic effects are neglected in order to highlight the role of the independent rotations and the associated additional parameters. The localisation-like behaviour occurs if (a) the particle rotations on the boundary of the shear layer are constrained (this type of boundary condition does not exist in a standard continuum) and (b) the contact moment-or bending stiffness is much smaller than the product of the effective shear modulus of the granulate and the square of the width of the gouge layer. It should be noted however that the virtual work functional is positive definite over the range of physically meaningful parameters (here: contact stiffnesses, solid volume fraction and coordination number) so that strictly speaking we are not dealing with a material instability.

The impact of breast cancer on the lives of middle-aged women: Results from the Australian longitudinal study of women's health

This article investigated the impact of breast cancer (BC) in middle-aged Australian women (45-50 years). Two waves of data collected 2 years apart from a longitudinal survey of 12,177 women identified 3 groups: (a) 11,933 (98%) who reported never having had BC, (b) 181 (1.5%) who reported a diagnosis of BC at Time 1, and (c) 63 (0.5%) who reported onset of BC between Time I and Time 2. Repeated measures analysis of variance was used to compare the 3 groups. Women with recent onset of BC experienced significant changes across a range of functioning compared with the other 2 groups. Compared with women with no BC, women with longer established onset of BC had significantly worse health and social outcomes, but these were associated with small effect sizes. Both groups of women with BC reported less impact on mental and emotional health than on other areas of functioning.

On the existence of solutions to boundary value problems on time scales

This work formulates existence theorems for solutions to two-point boundary value problems on time scales. The methods used include maximum principles, a priori bounds and topological degree theory.

Boundary element method predictions of the influence of the electrolyte on the galvanic corrosion of AZ91D coupled to steel

This research investigated the galvanic corrosion of the magnesium alloy AZ91D coupled to steel. The galvanic current distribution was measured in 5% NaCl solution, corrosive water and an auto coolant. The experimental measurements were compared with predictions from a Boundary Element Method (BEM) model. The boundary condition, required as an input into the BEM model, needs to be a polarization curve that accurately reflects the corrosion process. Provided that the polarization curve does reflect steady state, the BEM model is expected to be able to reflect steady state galvanic corrosion.

Dinosaur sanctuary on the Chatham Islands, Southwest Pacific: First record of theropods from the K-T boundary Takatika Grit

Cretaceous-Tertiaty (K-T) boundary (ca. 65 Ma) sections on a Southwest Pacific island containing dinosaurs were unknown until March 2003 when theropod bones were recovered from the Takatika Grit on the remote Chatham Islands (latitude 44 degrees S, longitude 176 degrees W), along the Chatham Rise. Tectonic and palaeontologic evidence support the eastward extension of a ca. 900 km land bridge that connected the islands to what is now New Zealand prior to the K-T boundary. The Chathams terrestrial fauna inhabited coastal, temperate environments along a low-lying, narrow, crustal extension of the New Zealand subcontinent, characterised by a tectonically dynamic, volcanic landscape with eroding hills (horsts) adjacent to flood plains and deltas, all sediments accumulating in grabens. This finger-like tract was blanketed with a conifer and clubmoss (Lycopodiopsida) dominated forest. The Chatham Islands region would have, along with New Zealand, provided a dinosaur island sanctuary after separating from the Gondwana margin ca. 80 Ma. (c) 2005 Elsevier B.V. All rights reserved.

The effect of box shape on the dynamic properties of proteins simulated under periodic boundary conditions

The effect of the box shape on the dynamic behavior of proteins simulated under periodic boundary conditions is evaluated. In particular, the influence of simulation boxes defined by the near-densest lattice packing (NDLP) in conjunction with rotational constraints is compared to that of standard box types without these constraints. Three different proteins of varying size, shape, and secondary structure content were examined in the study. The statistical significance of differences in RMSD, radius of gyration, solvent-accessible surface, number of hydrogen bonds, and secondary structure content between proteins, box types, and the application or not of rotational constraints has been assessed. Furthermore, the differences in the collective modes for each protein between different boxes and the application or not of rotational constraints have been examined. In total 105 simulations were performed, and the results compared using a three-way multivariate analysis of variance (MANOVA) for properties derived from the trajectories and a three-way univariate analysis of variance (ANOVA) for collective modes. It is shown that application of roto-translational constraints does not have a statistically significant effect on the results obtained from the different simulations. However, the choice of simulation box was found to have a small (5-10%), but statistically significant effect on the behavior of two of the three proteins included in the study. (c) 2005 Wiley Periodicals, Inc.

Effects of marine reserve protection on the mud crap Scylla serrata in a sex-biased fishery in subtropical Australia

The impact of sex-biased fishing and marine reserve protection on the mud crab Scylla serrata was examined by comparing the catch rates (catch-per-unit-effort, CPUE), mean size, sex ratios and movement of crabs in 2 coastal marine reserves (1.9 and 5.7 km(2)) and 4 fished non-reserve sites in subtropical Australia. Five years after closure, both marine reserves supported higher catch rates and a larger mean size of S. serrata than non-reserve sites. Males dominated catches of S. serrata in both marine reserves, where CPUE was at least twice as high within the reserves compared to non-reserve sites. Male crabs were also 10% larger in the reserves compared to adjacent fished areas, and of the total male catch, over 70% were equal to or greater than legal size compared to less than 50% outside the reserves. The sex ratio of S. serrata was skewed towards females in all nonreserve sites, which was most likely a result of the ban on taking female S. serrata in Moreton Bay. As only male crabs of >= 15 cm CW made up the S. serrata fishery in Moreton Bay, sex ratios of mature male and female crabs were examined, revealing a strong skew (2:1) towards mature males in both marine reserves. Of the 472 S. serrata captured in this study, 338 were tagged in the reserves in order to document movement of the crabs between the reserve and non-reserve sites. Of the 37 recaptured crabs, 73% were recorded inside the reserves, with some spillover (i.e. cross-boundary movement) of crabs recorded in fished areas. This study demonstrates the effectiveness of small (< 6 km(2)) marine reserves for sex-biased exploited fisheries species.

Effect of moisture content on the R-70 self-heating rate of Callide coal

Strip samples from the Boundary Hill pit at Callide have been tested in an adiabatic oven to assess the effect of moisture on the R-70 self-heating rate of coal. The two strip samples tested had R-70 self-heating rate values of 10.23 and 8.61 degrees C/h. As the moisture content of the coal was progressively increased, from the dry state of the test, the R-70 value decreased dramatically. At approximately 40-50% of the moisture holding capacity of the coal, the self-heating rate becomes measurable. Above this critical level of moisture content, the heat produced by oxidation is dissipated by moisture evaporation and coal self-heating is significantly delayed. (c) 2005 Elsevier B.V All rights reserved.

Sharp Sobolev inequality involving a critical nonlinearity on a boundary

We consider the solvability of the Neumann problem for the equation -Delta u + lambda u = 0, partial derivative u/partial derivative v = Q(x)vertical bar u vertical bar(q-2)u on partial derivative Omega, where Q is a positive and continuous coefficient on partial derivative Omega, lambda is a parameter and q = 2(N - 1)/(N - 2) is a critical Sobolev exponent for the trace embedding of H-1(Omega) into L-q(partial derivative Omega). We investigate the joint effect of the mean curvature of partial derivative Omega and the shape of the graph of Q on the existence of solutions. As a by product we establish a sharp Sobolev inequality for the trace embedding. In Section 6 we establish the existence of solutions when a parameter lambda interferes with the spectrum of -Delta with the Neumann boundary conditions. We apply a min-max principle based on the topological linking.

Segregation of particles and its influence on the morphology of the eutectic silicon phase in Al-7 wt.% Si alloys

A new modification phenomenon is reported for Al-Si alloys, where the Al-Si eutectic is refined by segregated TiB2 particles. The TiB2 particles are pushed to the Al-Si phase boundary during solidification of the eutectic and it is believed that at high concentrations the TiB2 particles restrict solute redistribution causing refinement of the Si. (c) 2005 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved.

Quantifying aphasic people's social lives in the context of non-aphasic peers

Background: Developing the knowledge base on the impact of aphasia on people's social lives has become increasingly important in recent times to further our understanding of the broad consequences of communication disability and thus provide appropriate services. Past research clearly indicates that relationships and social activities with family members and others undergo change with the onset of aphasia in an individual, however more evidence of a quantitative nature would be beneficial. Aims: The current research furthers our knowledge by quantifying chronically aphasic older people's regular social contacts and social activities, and places them in context by comparing them with healthy older people of similar age and education. Methods & Procedures: A total of 30 aphasic participants aged 57 to 88 years, and 71 non-aphasic controls aged 62 to 98 years were interviewed by a speech and language therapist using self-report measures of Social Network Analysis (Antonucci & Akiyama, 1987) and Social Activities Checklist (Cruice, 2001, in Worrall & Hickson, 2003). Demographic information was also collected. Descriptive statistics are presented and independent samples t tests were used to examine differences between the groups. Outcomes & Results: Participants with primarily mild to moderate aphasic impairment reported a considerable range of social contacts (5-51) and social activities (8-18). Many significant differences were evident between the two groups' social contacts and activities. On average, aphasic participants had nine fewer social contacts (mainly friend'' relationships) and three fewer social activities (mainly leisure'' activities) than their non-aphasic peers. The majority of controls were satisfied with their social activities, whereas the majority of aphasic participants were not and wanted to be doing more. There were some general similarities between the groups, in terms of range of social contacts, overall pattern of social relationships, and core social activities. Conclusions: Older people with chronic aphasia had significantly fewer social contacts and social activities than their peers. People with aphasia expressed a desire to increase the social activity of their lives. Given the importance of leisure activity and relationships with friends as well as family for positive well-being, speech and language therapists may direct their rehabilitation efforts towards two areas: (1) conversational partner programmes training friends to maintain these relationships; and (2) encouraging and supporting aphasic clients in leisure activities of their choice.