Selection Principles and Sierpinski Sets

We show that a set of real numbers is a Sierpinski set if, and only if, it satisfies a selection property similar to the familiar Menger property.     

Structure of copper-doped tungsten oxide films for solid-state memory

Copper-doped WO₃ films, which are an active media for programmable metallization cell memory devices, are studied. The highlights of this study are the intercalation products forming on the interface between the WO₃ and Cu during thermal evaporation and also after thermal or photothermal diffusion of Cu into WO₃ films. The diffusion profile is established using Auger spectroscopy. Further characterization is provided using Raman spectroscopy which gives evidence for formation of products with a lower valence state related to W and oxidation products related to Cu. The composition of the intercalation products containing Cu is confirmed using X-ray diffraction which shows the formation of copper oxides and tungstates.     

Another look at complete positivity in generalized quantum dynamics: Reply to Raggio and Primas

In this rejoinder to a critique by Raggio and Primas of our paper, On Completely Positive Maps in Generalized Quantum Dynamics, we acknowledge that, contrary to our original assertion, the Bloch equations are indeed completely positive. We then explain briefly why this modification of our analysis does not alter its main conclusions.     

A novel coated-particle design and fluidized-bed chemical vapor deposition preparation method for fuel-element identification in a nuclear reactor

Particle coating is an important method that can be used to expand particle-technology applications. Coated-particle design and preparation for nuclear fuel-element trajectory tracing were focused on in this paper. Particles that contain elemental cobalt were selected because of the characteristic gamma ray spectra of ⁶⁰Co. A novel particle-structure design was proposed by coating particles that contain elemental cobalt with a high-density silicon-carbide (SiC) layer. During the coating process with the high-density SiC layer, cobalt metal was formed and diffused towards the coating, so an inner SiC–Co_xSi layer was designed and obtained by fluidized-bed chemical vapor deposition coupled with in-situ chemical reaction. The coating layers were studied by X-ray diffractometry, scanning electron microscopy, and energy dispersive X-ray spectroscopy techniques. The chemical composition was also determined by inductively coupled plasma optical emission spectrometry. The novel particle design can reduce the formation of metallic cobalt and prevent cobalt diffusion in the coating process, which can maintain safety in a nuclear reactor for an extended period. The experimental results also validated that coated particles maintain their structural integrity at extremely high temperatures (∼1950 °C), which meets the requirements of next-generation nuclear reactors.     

Stability of a Pivoting Strategy for Parallel Gaussian Elimination

Gaussian elimination with partial pivoting achieved by adding the pivot row to the kth row at step k, was introduced by Onaga and Takechi in 1986 as means for reducing communications in parallel implementations. In this paper it is shown that the growth factor of this partial pivoting algorithm is bounded above by _n <#60; 3 ^n–1, as compared to 2 ^n–1 for the standard partial pivoting. This bound _n, close to 3 ^n–2, is attainable for class of near-singular matrices. Moreover, for the same matrices the growth factor is small under partial pivoting.This revised version was published online in October 2005 with corrections to the Cover Date.     

Strongly meager sets of size continuum

We will construct several models where there are no strongly meager sets of size 2⁰. First author partially supported by NSF grant DMS 0200671.Second author partially supported by Israel Science Foundation and NSF grant DMS 0072560. Publication 807. Mathematics Subject Classification (2000):03E15, 03E20     

Measurable cardinals and the cardinality of Lindelöf spaces

We obtain from the consistency of the existence of a measurable cardinal the consistency of “small” upper bounds on the cardinality of a large class of Lindelöf spaces whose singletons are Gδ sets.     

A parallel computational method for simulating two‐phase gel dynamics on a staggered grid

We develop a parallel computational algorithm for simulating models of gel dynamics where the gel is described by two phases, a networked polymer and a fluid solvent. The models consist of transport equations for the two phases, two coupled momentum equations, and a volume‐averaged incompressibility constraint. Multigrid with Vanka‐type box‐relaxation scheme is used as preconditioner for the Krylov subspace solver (GMRES) to solve the momentum and incompressibility equations. Through numerical experiments of a model problem, the efficiency, robustness and scalability of the algorithm are illustrated. Copyright © 2008 John Wiley & Sons, Ltd.