Products of mixed covering arrays of strength two

A covering array CA(N;t,k, v is an N × k array such that every N × t subarray contains all t‐tuples from v symbols at least once, where t is the strength of the array. Covering arrays are used to generate software test suites to cover all t‐sets of component interactions. The particular case when t = 2 (pairwise coverage) has been extensively studied, both to develop combinatorial constructions and to provide effective algorithmic search techniques. In this paper, a simple “cut‐and‐paste” construction is extended to covering arrays in which different columns (factors) admit different numbers of symbols (values); in the process an improved recursive construction for covering arrays with t = 2 is derived. © 2005 Wiley Periodicals, Inc. J Combin Designs 14: 124–138, 2006     

The vacancy formation energy in crystalline adamantane determined by position annihilation techiniques

The injection of positrons into crystalline adamantane results in the formation of positronium (Ps). At temperatures T> 400 K the mean lifetime of the long-lived ortho-positronium exhibits a sigmoidal increase with temperature characteristic of the trapping of this species in thermally created defects. The variation is well described by the trapping model usually applied to the trapping of positrons in defects in metals. The formation energy of the defects which trap ortho-Ps is estimated at E_f^v = 70 ± 10 kJ mol^-1 (0.73 ± 0.1 eV). This value is in good agreement with estimates of the formation energy of lattice vacancies in adamantane derived from self-diffusion studies.     

On the feasibility of antideuteron production and storage at CERN

The new Antiproton Accumulator Complex is now in operation at CERN. We consider the possibility of using this facility to create and store antideuterons and conclude that we could achieve an accumulation rate of about 2·10⁶ particles/day. No major rebuild of the rings is envisaged, but it is thought that modification to existing components and becoming operational would take about 5 to 6 months. We stress, however, that the operation of such a facility and the use of any stack of antideuterons for particle physics would be extremely taxing.     

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