Asymptotic bifurcation results for quasilinear elliptic operators

We develop results for bifurcation from the principal eigenvalue for certain operators based on the p-Laplacian and containing a superlinear nonlinearity with a critical Sobolev exponent. The main result concerns an asymptotic estimate of the rate at which the solution branch departs from the eigenspace. The method can also be applied for nonpotential operators.

Geogenic sources and sinks of trace metals in the Larsemann Hills, East Antarctica: Natural processes and human impact

To evaluate the extent of human impact on a pristine Antarctic environment, natural baseline levels of trace metals have been established in the basement rocks of the Larsemann Hills, East Antarctica. From a mineralogical and geochemical point of view the Larsemann Hills basement is relatively homogeneous, and contains high levels of Pb, Th and U. These may become soluble during the relatively mild Antarctic summer and be transported to lake waters by surface and subsurface melt water. Melt waters may also be locally enriched in V, Cr, Co, Ni, Zn and Sri derived from weathering of metabasite pods. With a few notable exceptions, the trace metal concentrations measured in the Larsemann Hills lake waters can be entirely accounted for by natural processes such as sea spray and surface melt water input. Thus, the amount of trace metals released by weathering of basement lithologies and dispersed into the Larsemann Hills environment, and presumably in similar Antarctic environments, is, in general, not negligible, and may locally be substantial. The Larsemann Hills sediments are coarse-grained and contain minute amounts of clay-size particles, although human activities have contributed to the generation of fine-grained material at the most impacted sites. Irrespective of their origin, these small amounts of fine-grained clastic sediments have a relatively small surface area and charge, and are not as effective metal sinks as the abundant, thick cyanobacterial algal mats that cover the lake floors. Thus, the concentration of trace metals in the Larsemann Hills lake waters is regulated by biological activity and thawing-freezing cycles, rather than by the type and amount of clastic sediment supply. (c) 2005 Elsevier Ltd. All rights reserved.

Trace metals in Antarctic ecosystems: Results from the Larsemann Hills, East Antarctica

Sediments, mosses and algae, collected from lake catchments of the Larsemann Hills, East Antarctica, were analysed to establish baseline levels of trace metals (Ag, As, Cd, Co, Cr, Cu, Ni, Sb, Pb, Se, V and Zn), and to quantify the extent of trace metal pollution in the area. Both impacted and non-impacted sites were included in the study. Four different leaching solutions (1 M MgCl2, 1 M CH3COONH4, 1 M NH4NO3, and 0.3 N HCl) were tested on the fine fraction (< 63 mu m) of the sediments to extract the mobile fraction of trace metals derived from human impact and from weathering of basement lithologies. Results of these tests indicate that dilute HCl partly dissolves primary minerals present in the sediment, thus leading to an overestimate of the mobile trace metal fraction. Concentrations of trace metals released using the other 3 procedures indicate negligible levels of anthropogenic contribution to the trace metal budget. Data derived from this study and a thorough characterisation of the site allowed the authors to define natural baseline levels of trace metals in sediments, mosses and algae, and their spatial variability across the area. The results show that, with a few notable exceptions, human activities at the research stations have contributed negligible levels (lower than natural variability) of trace metals to the Larsemann Hills ecosystem. This study further demonstrates that anthropogenic sources of trace metals can be correctly identified and quantified only if natural baselines, their variability, and processes controlling the mobility of trace metals in the ecosystem, have been fully characterised. (c) 2006 Elsevier Ltd. All rights reserved.

Mach bands and multiscale models of spatial vision:the role of first, second, and third derivative operators in encoding bars and edges

Ernst Mach observed that light or dark bands could be seen at abrupt changes of luminance gradient in the absence of peaks or troughs in luminance. Many models of feature detection share the idea that bars, lines, and Mach bands are found at peaks and troughs in the output of even-symmetric spatial filters. Our experiments assessed the appearance of Mach bands (position and width) and the probability of seeing them on a novel set of generalized Gaussian edges. Mach band probability was mainly determined by the shape of the luminance profile and increased with the sharpness of its corners, controlled by a single parameter (n). Doubling or halving the size of the images had no significant effect. Variations in contrast (20%-80%) and duration (50-300 ms) had relatively minor effects. These results rule out the idea that Mach bands depend simply on the amplitude of the second derivative, but a multiscale model, based on Gaussian-smoothed first- and second-derivative filtering, can account accurately for the probability and perceived spatial layout of the bands. A key idea is that Mach band visibility depends on the ratio of second- to first-derivative responses at peaks in the second-derivative scale-space map. This ratio is approximately scale-invariant and increases with the sharpness of the corners of the luminance ramp, as observed. The edges of Mach bands pose a surprisingly difficult challenge for models of edge detection, but a nonlinear third-derivative operation is shown to predict the locations of Mach band edges strikingly well. Mach bands thus shed new light on the role of multiscale filtering systems in feature coding. © 2012 ARVO.

An integrated assessment model for cross-country pipelines

The cross-country petroleum pipelines are environmentally sensitive because they traverse through varied terrain covering crop fields, forests, rivers, populated areas, desert, hills and offshore. Any malfunction of these pipelines may cause devastating effect on the environment. Hence, the pipeline operators plan and design pipelines projects with sufficient consideration of environment and social aspects along with the technological alternatives. Traditionally, in project appraisal, optimum technical alternative is selected using financial analysis. Impact assessments (IA) are then carried out to justify the selection and subsequent statutory approval. However, the IAs often suggest alternative sites and/or alternate technology and implementation methodology, resulting in revision of entire technical and financial analysis. This study addresses the above issues by developing an integrated framework for project feasibility analysis with the application of analytic hierarchy process (AHP), a multiple attribute decision-making technique. The model considers technical analysis (TA), socioeconomic IA (SEIA) and environmental IA (EIA) in an integrated framework to select the best project from a few alternative feasible projects. Subsequent financial analysis then justifies the selection. The entire methodology has been explained here through a case application on cross-country petroleum pipeline project in India.

Indirect ties in knowledge networks:a social network analysis with ordered weighted averaging operators

This PhD thesis analyses networks of knowledge flows, focusing on the role of indirect ties in the knowledge transfer, knowledge accumulation and knowledge creation process. It extends and improves existing methods for mapping networks of knowledge flows in two different applications and contributes to two stream of research. To support the underlying idea of this thesis, which is finding an alternative method to rank indirect network ties to shed a new light on the dynamics of knowledge transfer, we apply Ordered Weighted Averaging (OWA) to two different network contexts. Knowledge flows in patent citation networks and a company supply chain network are analysed using Social Network Analysis (SNA) and the OWA operator. The OWA is used here for the first time (i) to rank indirect citations in patent networks, providing new insight into their role in transferring knowledge among network nodes; and to analyse a long chain of patent generations along 13 years; (ii) to rank indirect relations in a company supply chain network, to shed light on the role of indirectly connected individuals involved in the knowledge transfer and creation processes and to contribute to the literature on knowledge management in a supply chain. In doing so, indirect ties are measured and their role as means of knowledge transfer is shown. Thus, this thesis represents a first attempt to bridge the OWA and SNA fields and to show that the two methods can be used together to enrich the understanding of the role of indirectly connected nodes in a network. More specifically, the OWA scores enrich our understanding of knowledge evolution over time within complex networks. Future research can show the usefulness of OWA operator in different complex networks, such as the on-line social networks that consists of thousand of nodes.

Continuity of Pseudo-differential Operators on Bessel And Besov Spaces

We study the continuity of pseudo-differential operators on Bessel potential spaces Hs|p (Rn ), and on the corresponding Besov spaces B^(s,q)p (R ^n). The modulus of continuity ω we use is assumed to satisfy j≥0, ∑ [ω(2−j )Ω(2j )]2 < ∞ where Ω is a suitable positive function.

Compactness in the First Baire Class and Baire-1 Operators

For a polish space M and a Banach space E let B1 (M, E) be the space of first Baire class functions from M to E, endowed with the pointwise weak topology. We study the compact subsets of B1 (M, E) and show that the fundamental results proved by Rosenthal, Bourgain, Fremlin, Talagrand and Godefroy, in case E = R, also hold true in the general case. For instance: a subset of B1 (M, E) is compact iff it is sequentially (resp. countably) compact, the convex hull of a compact bounded subset of B1 (M, E) is relatively compact, etc. We also show that our class includes Gulko compact. In the second part of the paper we examine under which conditions a bounded linear operator T : X ∗ → Y so that T |BX ∗ : (BX ∗ , w∗ ) → Y is a Baire-1 function, is a pointwise limit of a sequence (Tn ) of operators with T |BX ∗ : (BX ∗ , w∗ ) → (Y, · ) continuous for all n ∈ N. Our results in this case are connected with classical results of Choquet, Odell and Rosenthal.

Generalized Variational Inequalities for Upper Hemicontinuous and Demi Operators with Applications to Fixed Point Theorems in Hilbert Spaces

∗ The final version of this paper was sent to the editor when the author was supported by an ARC Small Grant of Dr. E. Tarafdar.

Commuting Nonselfadjoint Operators and their Characteristic Operator-Functions

* Partially supported by Grant MM-428/94 of MESC.