On a semilinear Schrodinger equation with critical Sobolev exponent

We consider the semilinear Schrodinger equation -Deltau+V(x)u= K(x) \u \ (2*-2 u) + g(x; u), u is an element of W-1,W-2 (R-N), where N greater than or equal to4, V, K, g are periodic in x(j) for 1 less than or equal toj less than or equal toN, K>0, g is of subcritical growth and 0 is in a gap of the spectrum of -Delta +V. We show that under suitable hypotheses this equation has a solution u not equal 0. In particular, such a solution exists if K equivalent to 1 and g equivalent to 0.

Tram at South Brisbane station, Brisbane Australia

Three men inspecting tram at South Brisbane station, Brisbane Australia, during No War Toys outing. WILPF (Womens International League for Peace and Freedom) banner can be seen on the front of the tram. The Women's International League for Peace and Freedom was founded in 1915. It works towards disarmament, political solutions to international conflicts, equal participation of women in activities, economic justice and the elimination of racism and discrimination. To achieve these goals, the Women's International League for Peace and Freedom organises meetings, conferences and campaigns.

Spectral properties of the tandem Jackson network, seen as a quasi-birth-and-death process

Quasi-birth-and-death (QBD) processes with infinite “phase spaces” can exhibit unusual and interesting behavior. One of the simplest examples of such a process is the two-node tandem Jackson network, with the “phase” giving the state of the first queue and the “level” giving the state of the second queue. In this paper, we undertake an extensive analysis of the properties of this QBD. In particular, we investigate the spectral properties of Neuts’s R-matrix and show that the decay rate of the stationary distribution of the “level” process is not always equal to the convergence norm of R. In fact, we show that we can obtain any decay rate from a certain range by controlling only the transition structure at level zero, which is independent of R. We also consider the sequence of tandem queues that is constructed by restricting the waiting room of the first queue to some finite capacity, and then allowing this capacity to increase to infinity. We show that the decay rates for the finite truncations converge to a value, which is not necessarily the decay rate in the infinite waiting room case. Finally, we show that the probability that the process hits level n before level 0 given that it starts in level 1 decays at a rate which is not necessarily the same as the decay rate for the stationary distribution.

On the threshold of forgetting: Amnesiac identities and the Brazilian capital

Centuries after Locke asserted the importance of memory to identity, Freudian psychology argued that what was forgotten was of equal importance as to what was remembered. The closing decades of the nineteenth century saw a rising interest in the nature of forgetting, resulting in a reassessment and newfound distrust of the long revered faculty of memory. The relationship between memory and identity was inverted, seeing forgetting also become a means for forging identity. This newfound distrust of memory manifested in the writings of Nietzsche who in 1874 called for society to learn to feel unhistorically and distance itself from the past - in what was essentially tantamount to a cultural forgetting. Following the Nietzschean call, the architecture of Modernism was also compelled by the need to 'overcome' the limits imposed by history. This paper examines notions of identity through the shifting boundaries of remembering and forgetting, with particular reference to the construction of Brazilian identity through the ‘repression’ of history and memory in the design of the Brazilian capital. Designed as a forward-looking modernist utopia, transcending the limits imposed by the country's colonial heritage, the design for Brasilia exploited the anti-historicist agenda of modernism to emancipate the country from cultural and political associations with the Portuguese Empire. This paper examines the relationship between place, memory and forgetting through a discussion of the design for Brasilia.

Integrability of the Russian doll BCS model

We show that integrability of the BCS model extends beyond Richardson's model (where all Cooper pair scatterings have equal coupling) to that of the Russian doll BCS model for which the couplings have a particular phase dependence that breaks time-reversal symmetry. This model is shown to be integrable using the quantum inverse scattering method, and the exact solution is obtained by means of the algebraic Bethe ansatz. The inverse problem of expressing local operators in terms of the global operators of the monodromy matrix is solved. This result is used to find a determinant formulation of a correlation function for fluctuations in the Cooper pair occupation numbers. These results are used to undertake exact numerical analysis for small systems at half-filling.

Existence of Multiple Solutions for Second Order Boundary Value Problems

We give conditions on f involving pairs of lower and upper solutions which lead to the existence of at least three solutions of the two point boundary value problem y" + f(x, y, y') = 0, x epsilon [0, 1], y(0) = 0 = y(1). In the special case f(x, y, y') = f(y) greater than or equal to 0 we give growth conditions on f and apply our general result to show the existence of three positive solutions. We give an example showing this latter result is sharp. Our results extend those of Avery and of Lakshmikantham et al.

High-Frequency Suspended Sediment Flux Measurements in a Small Estuary

In small estuaries, the predictions of scalar dispersion can rarely be predicted accurately because of a lack of fundamental understanding of the turbulence structure. Herein detailed turbulence measurements and suspended sediment concentrations were conducted simultaneously and continuously at high-frequency for 50 hours per investigation in a small subtropical estuary with semi-diurnal tides. The data analyses provided an unique characterisation of the turbulent mixing processes and suspended sediment fluxes. The turbulence was neither homogeneous nor isotropic, and it was not a Gaussian process. The integral time scales for turbulence and suspended sediment concentration were about equal during flood tides, but differed significantly during ebb tides. The field experiences showed that the turbulence measurements must be conducted at high-frequency to characterise the small eddies and the viscous dissipation process, while a continuous sampling was necessary to characterise the time-variations of the instantaneous velocity field, Reynolds stress tensor and suspended sediment flux during the tidal cycles.

Sequence and tissue distribution of chicken cellular nucleic acid binding protein cDNA

We sequenced cDNAs coding for chicken cellular nucleic acid binding protein (CNBP). Two slightly different variations of the open reading frame were found, each of which translates into a protein with seven zinc finger domains. The longest transcript contains an in-frame insert of 3 bp. The sequence conservation between chick CNBP cDNAs with human, rat and mouse CNBP cDNAs is extreme, especially in the coding region, where the deduced amino acid sequence identity with human, rat and mouse CNBP is 99%. CNBP-like transcripts were also found in various tissues from insect, shrimp, fish and lizard. Regions with remarkable nucleotide conservation were also found in the 3' untranslated region, indicating important functions for these regions. Quantitative reverse transcription polymerase chain reaction (RT-PCR) indicated that in the chick, CNBP is present in all tissues examined in approximately equal ratios to total RNA. RT-PCR of total RNA isolated from different phyla indicate CNBP-like proteins art widespread throughout the animal kingdom. The extraordinary level of conservation suggests an important physiological role for CNBP. (C) 1997 Elsevier Science Inc.

Matrix elements of U(2n) generators in a multishell spin-orbit basis. I. The del-operator MEs in a two-shell composite Gelfand-Paldus basis

This is the first in a series of three articles which aimed to derive the matrix elements of the U(2n) generators in a multishell spin-orbit basis. This is a basis appropriate to many-electron systems which have a natural partitioning of the orbital space and where also spin-dependent terms are included in the Hamiltonian. The method is based on a new spin-dependent unitary group approach to the many-electron correlation problem due to Gould and Paldus [M. D. Gould and J. Paldus, J. Chem. Phys. 92, 7394, (1990)]. In this approach, the matrix elements of the U(2n) generators in the U(n) x U(2)-adapted electronic Gelfand basis are determined by the matrix elements of a single Ll(n) adjoint tensor operator called the del-operator, denoted by Delta(j)(i) (1 less than or equal to i, j less than or equal to n). Delta or del is a polynomial of degree two in the U(n) matrix E = [E-j(i)]. The approach of Gould and Paldus is based on the transformation properties of the U(2n) generators as an adjoint tensor operator of U(n) x U(2) and application of the Wigner-Eckart theorem. Hence, to generalize this approach, we need to obtain formulas for the complete set of adjoint coupling coefficients for the two-shell composite Gelfand-Paldus basis. The nonzero shift coefficients are uniquely determined and may he evaluated by the methods of Gould et al. [see the above reference]. In this article, we define zero-shift adjoint coupling coefficients for the two-shell composite Gelfand-Paldus basis which are appropriate to the many-electron problem. By definition, these are proportional to the corresponding two-shell del-operator matrix elements, and it is shown that the Racah factorization lemma applies. Formulas for these coefficients are then obtained by application of the Racah factorization lemma. The zero-shift adjoint reduced Wigner coefficients required for this procedure are evaluated first. All these coefficients are needed later for the multishell case, which leads directly to the two-shell del-operator matrix elements. Finally, we discuss an application to charge and spin densities in a two-shell molecular system. (C) 1998 John Wiley & Sons.

Flow and axial dispersion simulation for traveling axisymmetric Taylor vortices

Numerical experiments using a finite difference method were carried out to determine the motion of axisymmetric Taylor vortices for narrow-gap Taylor vortex flow. When a pressure gradient is imposed on the flow the vortices are observed to move with an axial speed of 1.16 +/- 0.005 times the mean axial flow velocity. The method of Brenner was used to calculate the long-time axial spread of material in the flow. For flows where there is no pressure gradient, the axial dispersion scales with the square root of the molecular diffusion, in agreement with the results of Rosen-bluth et al. for high Peclet number dispersion in spatially periodic flows with a roll structure. When a pressure gradient is imposed the dispersion increases by an amount approximately equal to 6.5 x 10(-4) (W) over bar(2)d(2)/D-m, where (W) over bar is the average axial velocity in the annulus, analogous to Taylor dispersion for laminar flow in an empty tube.

Use of otoliths and eye lenses for measuring trace-metal incorporation in fishes: a biogeographic study

The otoliths and lenses of the temperate damselfish Parma microlepis (Gunther) (Pomacentridae) showed similar differences in trace-metal profile for selected locations along the coast of New South Wales, Australia. Otoliths and lenses displayed a differential ability to accumulate metals. Metal concentrations were ranked differently in the two structures (e.g. Sr > Ba > Pb > Rb > Hg in otoliths, and Hg > Sr similar or equal to Rb > Pb > Ba in lenses), and where similar metals were accumulated, they were accumulated at vastly different concentrations (e.g. Ba concentrations in otoliths are a thousand-fold greater than in lenses). Analyses of the otoliths and lenses of P. microlepis from locations close to Sydney and up to 100 kill from the city were able to distinguish amongst these locations with respect to a number of metals, namely Ba, Mn and Hg. Multivariate analyses of otolith and lens data gave similar results among locations (agreement was obtained for Ii out of 15 pair-wise comparisons), and differences were attributable to the differential ability of the two structures to accumulate metals such as Mn and Hg. Trace-metal differences between locations were found to coincide with the proximity of sewage (including industrial waste) and petroleum storage facilities to the different locations.

Improving wheat simulation capabilities in Australia from a cropping systems perspective - III. The integrated wheat model (I_WHEAT)

Previous work has identified several short-comings in the ability of four spring wheat and one barley model to simulate crop processes and resource utilization. This can have important implications when such models are used within systems models where final soil water and nitrogen conditions of one crop define the starting conditions of the following crop. In an attempt to overcome these limitations and to reconcile a range of modelling approaches, existing model components that worked demonstrably well were combined with new components for aspects where existing capabilities were inadequate. This resulted in the Integrated Wheat Model (I_WHEAT), which was developed as a module of the cropping systems model APSIM. To increase predictive capability of the model, process detail was reduced, where possible, by replacing groups of processes with conservative, biologically meaningful parameters. I_WHEAT does not contain a soil water or soil nitrogen balance. These are present as other modules of APSIM. In I_WHEAT, yield is simulated using a linear increase in harvest index whereby nitrogen or water limitations can lead to early termination of grainfilling and hence cessation of harvest index increase. Dry matter increase is calculated either from the amount of intercepted radiation and radiation conversion efficiency or from the amount of water transpired and transpiration efficiency, depending on the most limiting resource. Leaf area and tiller formation are calculated from thermal time and a cultivar specific phyllochron interval. Nitrogen limitation first reduces leaf area and then affects radiation conversion efficiency as it becomes more severe. Water or nitrogen limitations result in reduced leaf expansion, accelerated leaf senescence or tiller death. This reduces the radiation load on the crop canopy (i.e. demand for water) and can make nitrogen available for translocation to other organs. Sensitive feedbacks between light interception and dry matter accumulation are avoided by having environmental effects acting directly on leaf area development, rather than via biomass production. This makes the model more stable across environments without losing the interactions between the different external influences. When comparing model output with models tested previously using data from a wide range of agro-climatic conditions, yield and biomass predictions were equal to the best of those models, but improvements could be demonstrated for simulating leaf area dynamics in response to water and nitrogen supply, kernel nitrogen content, and total water and nitrogen use. I_WHEAT does not require calibration for any of the environments tested. Further model improvement should concentrate on improving phenology simulations, a more thorough derivation of coefficients to describe leaf area development and a better quantification of some processes related to nitrogen dynamics. (C) 1998 Elsevier Science B.V.

Distribution of transferrin saturation in an Australian population: Relevance to the early diagnosis of hemochromatosis

Background & Aims: An elevated transferrin saturation is the earliest phenotypic abnormality in hereditary hemochromatosis. Determination of transferrin saturation remains the most useful noninvasive screening test for affected individuals, but there is debate as to the appropriate screening level. The aims of this study were to estimate the mean transferrin saturation in hemochromatosis heterozygotes and normal individuals and to evaluate potential transferrin saturation screening levels. Methods: Statistical mixture modeling was applied to data from a survey of asymptomatic Australians to estimate the mean transferrin saturation in hemochromatosis heterozygotes and normal individuals. To evaluate potential transferrin saturation screening levels, modeling results were compared with data from identified hemochromatosis heterozygotes and homozygotes. Results: After removal of hemochromatosis homozygotes, two populations of transferrin saturation were identified in asymptomatic Australians (P < 0.01). In men, 88.2% of the truncated sample had a lower mean transferrin saturation of 24.1%, whereas 11.8% had an increased mean transferrin saturation of 37.3%. Similar results were found in women, A transferrin saturation threshold of 45% identified 98% of homozygotes without misidentifying any normal individuals. Conclusions: The results confirm that hemochromatosis heterozygotes form a distinct transferrin saturation subpopulation and support the use of transferrin saturation as an inexpensive screening test for hemochromatosis. In practice, a fasting transferrin saturation of greater than or equal to 45% identifies virtually all affected homozygous subjects without necessitating further investigation of unaffected normal individuals.

Metabolite mean transit times in the liver as predicted by various models of hepatic elimination

Predicted area under curve (AUC), mean transit time (MTT) and normalized variance (CV2) data have been compared for parent compound and generated metabolite following an impulse input into the liver, Models studied were the well-stirred (tank) model, tube model, a distributed tube model, dispersion model (Danckwerts and mixed boundary conditions) and tanks-in-series model. It is well known that discrimination between models for a parent solute is greatest when the parent solute is highly extracted by the liver. With the metabolite, greatest model differences for MTT and CV2 occur when parent solute is poorly extracted. In all cases the predictions of the distributed tube, dispersion, and tasks-in-series models are between the predictions of the rank and tube models. The dispersion model with mixed boundary conditions yields identical predictions to those for the distributed tube model (assuming an inverse gaussian distribution of tube transit times). The dispersion model with Danckwerts boundary conditions and the tanks-in series models give similar predictions to the dispersion (mixed boundary conditions) and the distributed tube. The normalized variance for parent compound is dependent upon hepatocyte permeability only within a distinct range of permeability values. This range is similar for each model but the order of magnitude predicted for normalized variance is model dependent. Only for a one-compartment system is the MIT for generated metabolite equal to the sum of MTTs for the parent compound and preformed metabolite administered as parent.

Analytical solution for the Mollow and Autler-Townes probe absorption spectra of a three-level atom in a squeezed vacuum

The Mellow and Autler-Townes probe absorption spectra of a three-level atom in a cascade configuration with the lower transition coherently driven and also coupled to a narrow bandwidth squeezed-vacuum field are studied. Analytical studies of the modifications caused by the finite squeezed-vacuum bandwidth to the spectra are made for the case when the Rabi frequency of the driving field is much larger than the natural linewidth. The squeezed vacuum center frequency and the driving laser frequency are assumed equal. We show that the spectral features depend on the bandwidth of a squeezed vacuum field and whether the sources of the squeezing field are degenerate (DPA) or nondegenerate (NDPA) parametric amplifiers. In a broadband or narrow bandwidth squeezed vacuum generated by a NDPA, the central component of the Mellow spectrum can be significantly narrower than that in the normal vacuum. When the source of the squeezed vacuum is a DPA, the central feature is insensitive to squeezing. The Rabi sidebands, however, can be significantly narrowed only in the squeezed vacuum produced by the DPA. The two lines of the Autler-Townes absorption spectrum can be narrowed only in a narrow bandwidth squeezed vacuum, whereas they are independent of the phase and are always broadened in a broadband squeezed vacuum.