Reply to Nathan: How to reconstruct the causal argument

Nicholas Nathan tries to resist the current version of the causal argument for sense-data in two ways. First he suggests that, on what he considers to be the correct re-construction of the argument, it equivocates on the sense of proximate cause. Second he defends a form of disjunctivism, by claiming that there might be an extra mechanism involved in producing veridical hallucination, that is not present in perception. I argue that Nathan’s reconstruction of the argument is not the appropriate one, and that, properly interpreted, the argument does not equivocate on proximate cause. Furthermore, I claim that his postulation of a modified mechanism for hallucinations is implausibly ad hoc.     

Sub-bundles of the complexified tangent bundle

We study embeddings of complex vector bundles, especially line bundles, in the complexification of the tangent bundle of a manifold. The aim is to understand implications of properties of interest in partial differential equations.

     

Bases,spanning sets,and the axiom of choice

Two theorems are proved: First that the statement “there exists a field F such that for every vector space over F, every generating set contains a basis” implies the axiom of choice. This generalizes theorems of Halpern, Blass, and Keremedis. Secondly, we prove that the assertion that every vector space over ?₂ has a basis implies that every well‐ordered collection of two‐element sets has a choice function. (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Performance and analysis of saddle point preconditioners for the discrete steady-state Navier-Stokes equations

Summary. We examine the convergence characteristics of iterative methods based on a new preconditioning operator for solving the linear systems arising from discretization and linearization of the steady-state Navier-Stokes equations. With a combination of analytic and empirical results, we study the effects of fundamental parameters on convergence. We demonstrate that the preconditioned problem has an eigenvalue distribution consisting of a tightly clustered set together with a small number of outliers. The structure of these distributions is independent of the discretization mesh size, but the cardinality of the set of outliers increases slowly as the viscosity becomes smaller. These characteristics are directly correlated with the convergence properties of iterative solvers. Received August 5, 2000 / Published online June 20, 2001     

Dark matter searches by the Boulby Collaboration and liquid xenon prototype development

The current status of direct dark matter searches by the Boulby Dark Matter Collaboration is presented with the latest result from the ZePLiN I liquid xenon detector. An upper limit in the interaction cross section per nucleon of ～1×10^?6 pb for a WIMP mass of 100 GeV is found. Details of ZePLiN’s II and III—two future liquid xenon dark matter are presented. Extensive two-phase liquid-gas xenon prototype work has been undertaken and results of characterization studies are presented. The detector response to internal alpha and external gamma and neutron sources is shown. The potential discrimination power of the two-phase technique is displayed. Finally, prospects for the future dark matter search program are discussed.     

Correlation between luminescent properties and structure organization in AlGaN/GaN superlattices annealed after erbium ion implantation

The evolution of the structure organization of MOCVD-grown AlGaN/GaN superlattices subjected to erbium ion implantation with an energy of 1 MeV and dose of 3 × 10¹⁵ cm^?2 and subsequent annealing is correlated with their photoluminescent properties. The structure organization is quantitatively estimated using parameter Δ (degree of violation of local symmetry), which is found via multifractal analysis of surface morphology patterns obtained with atomic force microscopy. It is shown that the implantation not only causes Ga segregation on the surface, but also changes the structure organization, which shows up in the finer grain structure compared with the starting one and disordering, as well as in an increase in Δ. As the annealing temperature rises from 700 to 800°C, Δ declines, indicating that the structure organization is improved, and the intensity of the dominating photoluminescence peak due to Er³⁺ ions (1.542 μm) grows. With a further increase in the annealing temperature to 1050°C, the structure organization degrades, domains get larger, voids 100–200 nm deep form, and the photoluminescence intensity drops. The formation of voids during high-temperature annealing is also substantiated by data for 230-keV proton scattering. It is thus established that the improvement of the superlattice structure organization activates erbium and causes the erbium-ion-related luminescence intensity to grow.