A Sub-Supersolution Approach for a Quasilinear Kirchhoff Equation

In this paper we establish an existence result for a quasilinear Kirchhoff equation via a sub and supersolution approach, by using the pseudomonotone operators theory

A Survey for Large Separation Lensed FIRST Quasars, II. Magnification Bias and Redshift Distribution

The statistics of large-separation gravitational lensing are a powerful tool to probe mass distributions on the scale of galaxy clusters. In this paper we refine the analysis of our survey for large-separation (>5'') lensed FIRST quasars (Ofek et al. 2001) by estimating the magnification bias and the source redshift distribution. Finding no large separation lens among 8000 likely quasars in that sample, implies an upper bound on the lensed fraction of 3.7 x 10^-4 at 95% CL. From a published deep 1.4 GHz radio survey of the Hubble Deep Field, and corresponding optical searches for faint quasars, we calculate a lower limit to the `double flux magnification bias' affecting our radio-optically selected sample, of B>1.1. From the four-colour information in the SDSS Early Data Release, we calculate the photometric redshift distribution of a sample of FIRST quasar candidates and compare it with the redshift distribution from the FIRST Bright Quasar Survey. We find that the median redshift of the quasars in our sample is about 1.4. With these new results, we find that for all plausible cosmologies, the absence of lensed quasars in our survey is consistent with a model based on an empirical, non-evolving, cluster mass function, where clusters are represented by singular isothermal spheres. On the other hand, comparison of our results to the lensing predictions of published N-body-ray-tracing simulations (Wambsganss et al. 1995, 1998) rejects the COBE normalised \Omega_{0}=1 CDM model at 99.9% confidence.Comment: 6 pages, 3 figures, accepted to MNRA

Stability of a two-sublattice spin-glass model

We study the stability of the replica-symmetric solution of a two-sublattice infinite-range spin-glass model, which can describe the transition from antiferromagnetic to spin glass state. The eigenvalues associated with replica-symmetric perturbations are in general complex. The natural generalization of the usual stability condition is to require the real part of these eigenvalues to be positive. The necessary and sufficient conditions for all the roots of the secular equation to have positive real parts is given by the Hurwitz criterion. The generalized stability condition allows a consistent analysis of the phase diagram within the replica-symmetric approximation.Comment: 21 pages, 5 figure

Valuation of Forest Resources in Watershed Areas: Selected Applications in Makiling Forest Reserve

The valuation of resources found in the watershed area is important in assessing the impacts of changes in the watershed. While the change will have positive impacts which are short-term in nature, there are long-term environmental damages associated with economic benefits. This paper gives a rational judgment on the soundness of such changes through cost and benefit analysis. The watershed approach is utilized to capture the effects that are relevant in the analysis.forestry sector, watershed, uplands