Positive solutions of a Neumann problem with competing critical nonlinearities

We present existence results for a Neumann problem involving critical Sobolev nonlinearities both on the right hand side of the equation and at the boundary condition.. Positive solutions are obtained through constrained minimization on the Nehari manifold. Our approach is based on the concentration 'compactness principle of P. L. Lions and M. Struwe.

The status and relevance of Vietnamese journalism education: An empirical analysis

Based primarily on data from indepth interviews with senior journalists and journalism educators as well as a content analysis of journalism curricula, this paper sets out to provide an overview of the demand, overall provision structure, teaching materials and methods of Vietnamese journalism education. It first shows that with a fast expansion in both size and substance, the Vietnamese media system is beginning to feel the urgent need for formal journalism education. However, the country's major journalism programs have been criticised for producing hundreds of unqualified journalism graduates a year. In general, the most deplorable aspects of Vietnamese journalism education include its body of outdated and awkward teaching material, its undue focus on theories and politics at the expense of practical training, its lack of qualified teaching staff and its inadequate teaching resources.

Least energy solutions of a critical Neumann problem with a weight

We investigate the effect of the coefficient of the critical nonlinearity for the Neumann problem on the existence of least energy solutions. As a by-product we establish a Sobolev inequality with interior norm.

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.

Turbulence in Small Sub-Tropical Estuary with Semi-Diurnal Tides

In natural estuaries, contaminant transport is driven by the turbulent momentum mixing. The predictions of scalar dispersion can rarely be predicted accurately because of a lack of fundamental understanding of the turbulence structure in estuaries. Herein detailed turbulence field measurements were conducted at high frequency and continuously for up to 50 hours per investigation in a small subtropical estuary with semi-diurnal tides. Acoustic Doppler velocimetry was deemed the most appropriate measurement technique for such small estuarine systems with shallow water depths (less than 0.5 m at low tides), and a thorough post-processing technique was applied. The estuarine flow is always a fluctuating process. The bulk flow parameters fluctuated with periods comparable to tidal cycles and other large-scale processes. But turbulence properties depended upon the instantaneous local flow properties. They were little affected by the flow history, but their structure and temporal variability were influenced by a variety of mechanisms. This resulted in behaviour which deviated from that for equilibrium turbulent boundary layer induced by velocity shear only. A striking feature of the data sets is the large fluctuations in all turbulence characteristics during the tidal cycle. This feature was rarely documented, but an important difference between the data sets used in this study from earlier reported measurements is that the present data were collected continuously at high frequency during relatively long periods. The findings bring new lights in the fluctuating nature of momentum exchange coefficients and integral time and length scales. These turbulent properties should not be assumed constant.

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.

Nodal solutions for nonlinear eigenvalue problems

We are concerned with determining values of, for which there exist nodal solutions of the boundary value problems u" + ra(t) f(u) = 0, 0 < t < 1, u(O) = u(1) = 0. The proof of our main result is based upon bifurcation techniques.

Periodic or Bounded Solutions of Carathéodory Systems of Ordinary Differential Equations

In this paper we extend the guiding function approach to show that there are periodic or bounded solutions for first order systems of ordinary differential equations of the form x1 =f(t,x), a.e. epsilon[a,b], where f satisfies the Caratheodory conditions. Our results generalize recent ones of Mawhin and Ward.

The Rural Clinical Division: a student journey to rural medicine

Background: The University of Queensland has through an Australian Government initiative, established a Rural Clinical Division (RCD) at four regional sites in the southern and central Queensland. Over the fi rst four years of the existence of the RCD, an integrated package of innovative medical education has been developed. Method: The integrated aspects of the RCD program include: The Rural Medical Rotation: Every medical student undertakes an eight week rural rotation in Year 3. Year 3 and 4 MBBS - 100 students are currently spending one to two years in the rural school and demand is increasing. Interprofessional Education - Medical and Allied Health students attend lectures, seminars and workshops together and often share the same rural clinical placement. Rural health projects - allow students to undertake a project of benefi t to the rural community. Information Technology (IT) - the Clinical Discussion Board (CDB) and Personal Digital Assistants (PDA) demonstrate the importance of IT to medical students in the 21st century. Changing the Model of Medical Education - The Leichhardt Community Attachment Placement (LCAP), is a pilot study that resulted in the addition of three interns to the rural workforce. All aspects of the RCD are evaluated with surveys using both qualitative and quantitative free response questions, completed by all students regularly throughout the academic year. Results: Measures of impact include: Student satisfaction and quality of teaching surveys – 86-91% of students improved their clinical skills and understanding across all rotations. Academic results and progress – RCD students out-perform their urban colleagues. Intent to work in rural areas – 90% of students reported a greater interest in rural medicine. Intern numbers – rural / regional intern placements are increasing. Conclusions: The RCD proves to be a site for innovations all designed to help reach our primary goal of fostering increased recruitment of a rural medical workforce.

A flux ratio theorem for multicomponent linear diffusion equations

Ussing [1] considered the steady flux of a single chemical component diffusing through a membrane under the influence of chemical potentials and derived from his linear model, an expression for the ratio of this flux and that of the complementary experiment in which the boundary conditions were interchanged. Here, an extension of Ussing's flux ratio theorem is obtained for n chemically interacting components governed by a linear system of diffusion-migration equations that may also incorporate linear temporary trapping reactions. The determinants of the output flux matrices for complementary experiments are shown to satisfy an Ussing flux ratio formula for steady state conditions of the same form as for the well-known one-component case. (C) 2000 Elsevier Science Ltd. All rights reserved.