On the nonlinear Neumann problem with critical and supercritical nonlinearities

We investigate the solvability of the Neumann problem (1.1) involving a critical Sobolev exponent. In the first part of this work it is assumed that the coeffcients Q and h are at least continuous. Moreover Q is positive on overline Omega and lambda > 0 is a parameter. We examine the common effect of the mean curvature and the shape of the graphs of the coeffcients Q and h on the existence of low energy solutions. In the second part of this work we consider the same problem with Q replaced by - Q. In this case the problem can be supercritical and the existence results depend on integrability conditions on Q and h.

The meeting place problem: Salience and search.

The notion of salience was developed by Schelling in the context of the meeting-place problem of locating a partner in the absence of a pre-agreed meeting place. In this paper, we argue that a realistic specification of the meeting place problem involves allowing a strategy of active search over a range of possible meeting places. We solve this extended problem, allowing for extensions such as repeated play, search costs and asymmetric payoffs. The result is a considerably richer, but more complex, notion of salience. (C) 1998 Elsevier Science B.V.

Novel guidance cues during neuronal pathfinding in the early scaffold of axon tracts in the rostral brain

A scaffold of axons consisting of a pair of longitudinal tracts and several commissures is established during early development of the vertebrate brain. We report here that NOC-2, a cell surface carbohydrate, is selectively expressed by a subpopulation of growing axons in this scaffold in Xenopus. NOC-2 is present on two glycoproteins, one of which is a novel glycoform of the neural cell adhesion molecule N-CAM. When the function of NOC-2 was perturbed using either soluble carbohydrates or anti-NOC-2 antibodies, axons expressing NOC-2 exhibited aberrant growth at specific points in their pathway. NOC-2 is the first-identified axon guidance molecule essential for development of the axon scaffold in the embryonic vertebrate brain.

Detection of dimethyl sulfone in the human brain by in vivo proton magnetic resonance spectroscopy

We wish to report the detection of dimethyl sulfone (methylsulfonylmethane, C2H6O2S) in the brain of a normal 62-year-old male using in vivo proton magnetic resonance spectroscopy. The presence of this exogenous metabolite resulted from ingestion of a dietary supplement containing dimethyl sulfone. The concentration of this compound in the brain was measured to be 2.4 mmol, with a washout half life of approximately 7.5 days. The in vivo T-1 and T-2 relaxation times of dimethyl sulfone were measured to be 2180 ms and 385 ms, respectively. The concentration of major brain metabolites, namely N-acetylaspartate, total Creatine and Choline, and myo-Inositol were within normal limits. (C) 2000 Elsevier Science Inc. All rights reserved.

Chronic ethanol has region-selective effects on Egr-1 and Egr-3 DNA-binding activity and protein expression in the rat brain

This study focused on the DNA-binding activity and protein expression of the transcription factors Egr-1 and Egr-3 in the rat brain cortex and hippocampus after chronic or acute ethanol exposure. DNA-binding activity was reduced in both regions after chronic ethanol exposure and was restored to the level of the pair-fed group at 16 h of withdrawal. Cortical Egr-1 protein levels were not altered by chronic ethanol exposure but increased 16 h after withdrawal, thus mirroring DNA-binding activity. In contrast, Egr-3 protein levels did not undergo any change. There was no change in the level of either protein in the hippocampus. Immunohistochemistry revealed a region-selective change in immunopositive cells in the cortex and hippocampus. Finally, an acute bolus dose of ethanol did not affect Egr DNA-binding activity and ethanol treatment did not alter the DNA-binding activity or protein levels of the transcription factor Spl. These observations suggest that chronic exposure to ethanol has region-selective effects on the DNA-binding activity and protein expression of Egr-1 and Egr-3 transcription factors in the rat brain. These changes occur after prolonged ethanol exposure and may thus reflect neuroadaptive changes associated with physical dependency and withdrawal. These effects are also transcription factor-selective. Clearly, protein expression is not the sole mediator of the changes in DNA-binding activity and chronic ethanol exposure must have effects on modulatory agents of Egr DNA-binding activity. (C) 2000 Elsevier Science Ltd, All rights reserved.

Ischaemic preconditioning in the rat brain: a longitudinal magnetic resonance imaging (MRI) study

Ischaemic preconditioning in rats was studied using MRI. Ischaemic preconditioning was induced, using an intraluminal filament method, by 30 min middle cerebral artery occlusion (MCAO), and imaged 24 h later. The secondary insult of 100 min MCAO was induced 3 days following preconditioning and imaged 24 and 72 h later. Twenty four hours following ischaemic preconditioning most rats showed small sub-cortical hyperintense regions not seen in sham-preconditioned rats. Twenty-four hours and 72 h following the secondary insult preconditioned animals showed significantly smaller lesions (24 h = 112 +/- 31 mm(3), mean +/- standard error; 72 h = 80 +/- 35 mm(3)) which were confined to the striatum, than controls (24 h = 234 +/- 32 mm(3), p = 0.026; 72 h = 275 +/- 37 mm(3), p = 0.003). In addition during Lesion maturation from 24 to 72 h post-secondary MCAO, preconditioned rats displayed an average reduction in lesion size as measured by MRI whereas sham-preconditioned rats displayed increases in lesion size; this is the first report of such differential lesion volume evolution in cerebral ischaemic preconditioning. Copyright (C) 2001 John Wiley & Sons, Ltd.

Analytical solution to the zero-inertia problem for surge flow phenomena in nonprismatic channels

Surge flow phenomena. e.g.. as a consequence of a dam failure or a flash flood, represent free boundary problems. ne extending computational domain together with the discontinuities involved renders their numerical solution a cumbersome procedure. This contribution proposes an analytical solution to the problem, It is based on the slightly modified zero-inertia (ZI) differential equations for nonprismatic channels and uses exclusively physical parameters. Employing the concept of a momentum-representative cross section of the moving water body together with a specific relationship for describing the cross sectional geometry leads, after considerable mathematical calculus. to the analytical solution. The hydrodynamic analytical model is free of numerical troubles, easy to run, computationally efficient. and fully satisfies the law of volume conservation. In a first test series, the hydrodynamic analytical ZI model compares very favorably with a full hydrodynamic numerical model in respect to published results of surge flow simulations in different types of prismatic channels. In order to extend these considerations to natural rivers, the accuracy of the analytical model in describing an irregular cross section is investigated and tested successfully. A sensitivity and error analysis reveals the important impact of the hydraulic radius on the velocity of the surge, and this underlines the importance of an adequate description of the topography, The new approach is finally applied to simulate a surge propagating down the irregularly shaped Isar Valley in the Bavarian Alps after a hypothetical dam failure. The straightforward and fully stable computation of the flood hydrograph along the Isar Valley clearly reflects the impact of the strongly varying topographic characteristics on the How phenomenon. Apart from treating surge flow phenomena as a whole, the analytical solution also offers a rigorous alternative to both (a) the approximate Whitham solution, for generating initial values, and (b) the rough volume balance techniques used to model the wave tip in numerical surge flow computations.

Heroin-assisted treatment as a response to the public health problem of opiate dependence

Injection drug use (involving the injection of illicit opiates) poses serious public health problems in many countries. Research has indicated that injection drug users are at higher risk for morbidity in the form of HIV/AIDS and Hepatitis B and C, and drug-related mortality, as well as increased criminal activity. Methadone maintenance treatment is the most prominent form of pharmacotherapy treatment for illicit opiate dependence in several countries, and its application varies internationally with respect to treatment regulations and delivery modes. In order to effectively treat those patients who have previously been resistant to methadone maintenance treatment, several countries have been studying and/or considering heroin-assisted treatment as a complementary form of opiate pharmacotherapy treatment. This paper provides an overview of the prevalence of injection drug use and the opiate dependence problem internationally, the current opiate dependence treatment landscape in several countries, and the status of ongoing or planned heroin-assisted treatment trials in Australia, Canada and certain European countries.

The land assembly problem revisited

As in the standard land assembly problem, a developer wants to buy two adjacent blocks of land belonging to two different owners. The value of the two blocks of land to the developer is greater than the sum of the individual values of the blocks for each owner. Unlike the land assembly literature, however, our focus is on the incentive that each lot owner has to delay the start of negotiations, rather than on the public goods nature of the problem. An incentive for delay exists, for example, when owners perceive that being last to sell will allow them to capture a larger share of the joint surplus from the development. We show that competition at point of sale can cause equilibrium delay, and that cooperation at point of sale will eliminate delay. This suggests that strategic delay is another source for the inefficient allocation of land, in addition to the public-good type externality pointed out by Grossman and Hart [Bell Journal of Economics 11 (1980) 42] and O'Flaherty [Regional Science and Urban Economics 24 (1994) 287]. (C) 2004 Elsevier B.V. All rights reserved.

Immediate early gene expression and delayed cell death in limbic areas of the rat brain after kainic acid treatment and recovery in the cold

Systemic injection of kainic acid (KA) results in characteristic behaviors and programmed cell death in some regions of the rat brain. We used KA followed by recovery at 4 degrees C to restrict damage to limbic structures and compared patterns of immediate early gene (IEG) expression and associated DNA binding activity in these damaged areas with that in spared brain regions. Male Wistar rats were injected with BA (12 mg/kg, ip) and kept at 4 degrees C for 5 h. This treatment reduced the severity of behaviors and restricted damage (observed by Nissl staining) to the CA1 and CA3 regions of the hippocampus and an area including the entorhinal cortex. DNA laddering, characteristic of apoptosis, was first evident in the hippocampus and the entorhinal cortex 18 and 22 h after RA, respectively. The pattern of IEG mRNA induction fell into three classes: IEGs that were induced in both damaged and spared areas (c-fos, fos B, jun B, and egr-1), IEGs that were induced specifically in the damaged areas (fra-2 and c-jun), and an IEG that was significantly induced by saline injection and/or the cold treatment (jun D). The pattern of immunoreactivity closely followed that of mRNA expression. Binding to the AP-1 and EGR DNA consensus sequences increased in all three regions studied. This study describes a unique modification of the animal model of ICA-induced neurotoxicity which may prove a useful tool for dissecting the molecular cascade that ultimately results in programmed cell death. (C) 1997 Academic Press.

Are pioneer axons guided by regulatory gene expression domains in the zebrafish forebrain? High-resolution analysis of the patterning of the zebrafish brain during axon tract formation

Although the principles of axon growth are well understood in vitro the mechanisms guiding axons in vivo are less clear. It has been postulated that growing axons in the vertebrate brain follow borders of neuroepithelial cells expressing specific regulatory genes. In the present study we reexamined this hypothesis by analysing the earliest growing axons in the forebrain of embryonic zebrafish. Confocal laser scanning microscopy was used to determine the spatiotemporal relationship between growing axons and the expression pattern of eight regulatory genes in zebrafish brain. Pioneer axons project either longitudinally or dorsoventrally to establish a scaffold of axon tracts during this developmental period. Each of the regulatory genes was expressed in stereotypical domains and the borders of some were oriented along dorsoventral and longitudinal planes. However, none of these borders clearly defined the trajectories of pioneer axons. In two cases axons coursed in proximity to the borders of shh and pax6, but only for a relatively short portion of their pathway. Only later growing axons were closely apposed to the borders of some gene expression domains. These results suggest that pioneer axons in the embryonic forebrain do not follow continuous pathways defined by the borders of regulatory gene expression domains, (C) 2000 Academic Press.

A zebrafish homologue of deleted in colorectal cancer (zdcc) is expressed in the first neuronal clusters of the developing brain

DCC (deleted in colon cancer), Neogenin and UNC-5 are all members of the immunoglobulin superfamily of transmembrane receptors which are believed to play a role in axon guidance by binding to their ligands, the Netrin/UNC-40 family of secreted molecules (Cell. Mol. Life Sci. 56 (1999) 62; Curr. Opin. Genet. Dev. 7 (1997) 87). Although zebrafish homologues of the Netrin family of secreted molecules have been reported, to date there has been no published description of zebrafish DCC homologues (Mol. Cell. Neurosci. 9 (1997) 293., Mol. Cell. Neurosci. I I ( 1998) 194; Mech. Dev. 62 (1997) 147). We report here the expression pattern of a zebrafish dcc (zdcc) homologue during the initial period of neurogenesis and axon tract formation within the developing central nervous system. Between 12 and 33 h post-fertilisation zdcc is expressed in a dynamic spatiotemporal pattern in all major subdivisions of the central nervous system. Double-labelling for zdcc and the post-mitotic neuronal marker HNK-1 revealed that subpopulations of neurons within the first nuclei of the zebrafish brain express zdcc. These results support our previous observation that patterning of neuronal clusters in the zebrafish brain occurs early in development (Dev. Bioi, 229 (2001) 271). (C) 2001 Elsevier Science Ireland Ltd. All rights reserved.