On the Schrodinger equation involving a critical Sobolev exponent and magnetic field

We consider the semilinear Schrodinger equation -Delta(A)u + V(x)u = Q(x)vertical bar u vertical bar(2* -2) u. Assuming that V changes sign, we establish the existence of a solution u not equal 0 in the Sobolev space H-A,V(1) + (R-N). The solution is obtained by a min-max type argument based on a topological linking. We also establish certain regularity properties of solutions for a rather general class of equations involving the operator -Delta(A).

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.

Linking Agentive Objects in Mandarin Chinese

This paper is concerned with the problem of argument-function mismatch observed in the apparent subject-object inversion in Chinese consumption verbs, e.g., chi 'eat' and he 'drink', and accommodation verbs, e.g., zhu 'live' and shui 'sleep'. These verbs seem to allow the linking of [agent-SUBJ theme-OBJ] as well as [agent-OBJ theme-SUBJ], but only when the agent is also the semantic role denoting the measure or extent of the action. The account offered is formulated within LFG's lexical mapping theory. Under the simplest and also the strictest interpretation of the one-to-one argument-function mapping principle (or the theta-criterion), a composite role such as ag-ext receives syntactic assignment via one composing role only. One-to-one linking thus entails the suppression of the other composing role. Apparent subject-object inversion occurs when the more prominent agent role is suppressed and thus allows the less prominent extent role to dictate the linking of the entire ag-ext composite role. This LMT account also potentially facilitates a natural explanation of markedness among the competing syntactic structures.

NMR study of the radiation-induced cross-linking of poly(tetrafluoroethylene-co-perfluoromethyl vinyl ether)

The gamma-radiolysis of poly(tetrafluoroethylene-co-perfuoromethyl vinyl ether) (TFE/PMVE) was investigated using solid state F-19 and C-13 NMR spectroscopy. Chain scission products identified in the polymer were saturated chain ends -CF2CF3 (G = 1.0), methyl ether end groups -CF2OCF3 (G = 0.9), acid end groups -CF2COOH (G = 0.5), and a small amount of terminal unsaturation -CF=CF2 (G = 0.2). A mechanism for the formation of these scission products was proposed and the G value for main chain scission, G(S), was determined to be 1.4. Cross-linking of TFE/PMVE was found to proceed via a Y-linking mechanism. The G value for cross-linking, G(X), was determined to be 0.9. A maximum of 0.2 mol % cross-links were formed under the experimental conditions.

Linking client and employee perceptions of the organization: A study of client satisfaction with health care services

Client satisfaction with health care sen ices has usually been researched in terms of socio-demographic and predispositional characteristics associated with the client. The present study included organizational characteristics as predictors of client satisfaction with health care services. Participants in the research were clients and employees of an Australian public-sector health care organization who responded to separate client and employee questionnaires. Hierarchical regression analyses indicated that, after controlling for a number of client characteristics, organizational characteristics, as perceived by employees, accounted for a significant proportion of additional variance in client satisfaction with health care services. Results of the present study provided some support for the proposition that employee perceptions of the working environment should be considered in a more comprehensive understanding of client satisfaction with health care services. Limitations of the study highlight practical difficulties in the assessment of client outcomes and methodological complexities in linking individual and organizational processes.

The relationship between hetero-oligomer formation and function of the topological specificity domain of the Escherichia coli MinE protein

MinE is an oligomeric protein that, in conjunction with other Min proteins, is required for the proper placement of the cell division site of Escherichia coli. We have examined the self-association properties of MinE by analytical ultracentrifugation and by studies of hetero-oligomer formation in non-denaturing polyacrylamide gets. The self-association properties of purified MinE predict that cytoplasmic MinE is likely to exist as a mixture of monomers and dimers. Consistent with this prediction, the C-terminal MinE(22-88) fragment forms hetero-oligomers with MinE(+) when the proteins are co-expressed. In contrast, the MinE(36-88) fragment does not form MinE(+)/MinE(36-88) hetero-oligomers, although MinE36-88 affects the topological specificity of septum placement as shown by its ability to induce minicell formation when co-expressed with MinE(+) in wild-type cells. Therefore, hetero-oligomer formation is not necessary for the induction of mini-celling by expression of MinE(36-88) in wild-type cells. The interference with normal septal placement is ascribed to competition between MinE(36-88),nd the corresponding domain in the complete MinE protein for a component required for the topological specificity of septal placement.

The dimerization and topological specificity functions of MinE reside in a structurally autonomous C-terminal domain

Correct placement of the division septum in Escherichia coli requires the co-ordinated action of three proteins, MinC, MinD and MinE. MinC and MinD interact to form a non-specific division inhibitor that blocks septation at all potential division sites. MinE is able to antagonize MinCD in a topologically sensitive manner, as it restricts MinCD activity to the unwanted division sites at the cell poles, Here, we show that the topological specificity function of MinE residues in a structurally autonomous, trypsin-resistant domain comprising residues 31-88, Nuclear magnetic resonance (NMR) and circular dichroic spectroscopy indicate that this domain includes both alpha and beta secondary structure, while analytical ultracentrifugation reveals that it also contains a region responsible for MinE homodimerization. While trypsin digestion indicates that the anti-MinCD domain of MinE (residues 1-22) does not form a tightly folded structural domain, NMR analysis of a peptide corresponding to MinE(1-22) indicates that this region forms a nascent helix in which the peptide rapidly interconverts between disordered (random coil) and alpha-helical conformations, This suggests that the N-terminal region of MinE may be poised to adopt an alpha-helical conformation when it interacts with the target of its anti-MinCD activity, presumably MinD.

Unitary R-matrices for topological quantum computing

The main problem with current approaches to quantum computing is the difficulty of establishing and maintaining entanglement. A Topological Quantum Computer (TQC) aims to overcome this by using different physical processes that are topological in nature and which are less susceptible to disturbance by the environment. In a (2+1)-dimensional system, pseudoparticles called anyons have statistics that fall somewhere between bosons and fermions. The exchange of two anyons, an effect called braiding from knot theory, can occur in two different ways. The quantum states corresponding to the two elementary braids constitute a two-state system allowing the definition of a computational basis. Quantum gates can be built up from patterns of braids and for quantum computing it is essential that the operator describing the braiding-the R-matrix-be described by a unitary operator. The physics of anyonic systems is governed by quantum groups, in particular the quasi-triangular Hopf algebras obtained from finite groups by the application of the Drinfeld quantum double construction. Their representation theory has been described in detail by Gould and Tsohantjis, and in this review article we relate the work of Gould to TQC schemes, particularly that of Kauffman.

Cross-linking studies and membrane localization and assembly of radiolabelled large mechanosensitive ion channel (MscL) of Escherichia coli

The gene encoding the large conductance mechanosensitive ion channel (MscL) of Escherichia coli and several deletion mutants of mscL were cloned under the control of the T7 RNA polymerase promoter. Transformation of these constructs into an E. coli strain carrying an inducible T7 RNA polymerase gene allowed the specific production and labelling of MscL with [S-35]methionine. Preparation of membrane fractions of E. coli cells by sucrose gradient centrifugation indicated that the radiolabelled MscL was present in the inner cytoplasmic membrane in agreement with results of several studies. However, treatment of the labelled cells and cell membrane vesicles with various cross-linkers resulted in the majority of labelled protein migrating as a monomer with a small proportion of molecules (approximate to 25%) migrating as dimers and higher order multimers. This result is in contrast with a finding of a study suggesting that the channel exclusively forms hexamers in the cell membrane off. coli (1) and therefore may have profound implication for the activation and/or ''multimerization'' of the channel by mechanical stress exerted to the membrane. In addition, from the specific activity of the radiolabelled protein and the amount of protein in the cytoplasmic membrane fraction we estimated the number of MscL ion channels expressed under these conditions to be approximately 50 channels per single bacterium. (C) 1997 Academic Press.

Topological charge and angular momentum of light beams carrying optical vortices

We analyze the properties of light beams carrying phase singularities, or optical vortices. The transformations of topological charge during free-space propagation of a light wave, which is a combination of a Gaussian beam and a multiple charged optical vortex within a Gaussian envelope, are studied both in theory and experiment. We revise the existing knowledge about topological charge conservation, and demonstrate possible scenarios where additional vortices appear or annihilate during free propagation of such a combined beam. Coaxial interference of optical vortices is also analyzed, and the general rule for angular-momentum density distribution in a combined beam is established. We show that, in spite of any variation in the number of vortices in a combined beam, the total angular momentum is constant during the propagation. [S1050-2947(97)09910-1].

Linking policies for biodiversity conservation with advances in behavioural economics

Global biodiversity loss and its consequences for human welfare and sustainable development have become major concerns. Economists have, therefore, given increasing attention to the policy issues involved in the management of genetic resources. To do so, they often apply empirical methods developed in behavioral and experimental economics to estimate economic values placed on genetic resources. This trend away from almost exclusive dependence on axiomatic methods is welcomed. However, major valuation methods used in behavioral economics raise new scientific challenges. Possibly the most important of these include deficiencies in the knowledge of the public (and researchers) about genetic resources, implications for the formation of values of supplying information to focal individuals, and limits to rationality. These issues are explored for stated-preference techniques of valuation (e.g., contingent valuation) as well as revealed preference techniques, especially the travel cost method. They are illustrated by Australian and Asian examples. Taking into account behavioral and psychological models and empirical evidence, particular attention is given to how elicitation of preferences, and supply of information to individuals, influences their preferences about biodiversity. Policy consequences are outlined.

Topological methods for some boundary value problems

We establish existence of solutions for a finite difference approximation to y = f(x, y, y ') on [0, 1], subject to nonlinear two-point Sturm-Liouville boundary conditions of the form g(i)(y(i),y ' (i)) = 0, i = 0, 1, assuming S satisfies one-sided growth bounds with respect to y '. (C) 2001 Elsevier Science Ltd. All rights reserved.