Associativity of the <Emphasis Type="Italic">∇</Emphasis>-operation on bands in rings

Given a multiplicative band of idempotents S in a ring R, for all e,f∈S the ∇-product e ∇ f=e+f+fe−efe−fef is an idempotent that lies roughly above e and f in R just as ef and fe lie roughly below e and f. In this paper we study ∇-bands in rings, that is, bands in rings that are closed under ∇, giving various criteria for ∇ to be associative, thus making the band a skew lattice. We also consider when a given band S in R generates a ∇-band.     

General-Dimensional Constrained Delaunay and Constrained Regular Triangulations, I: Combinatorial Properties

Two-dimensional constrained Delaunay triangulations are geometric structures that are popular for interpolation and mesh generation because they respect the shapes of planar domains, they have “nicely shaped” triangles that optimize several criteria, and they are easy to construct and update. The present work generalizes constrained Delaunay triangulations (CDTs) to higher dimensions and describes constrained variants of regular triangulations, here christened weighted CDTs and constrained regular triangulations. CDTs and weighted CDTs are powerful and practical models of geometric domains, especially in two and three dimensions. The main contributions are rigorous, theory-tested definitions of CDTs and piecewise linear complexes (geometric domains that incorporate nonconvex faces with “internal” boundaries), a characterization of the combinatorial properties of CDTs and weighted CDTs (including a generalization of the Delaunay Lemma), the proof of several optimality properties of CDTs when they are used for piecewise linear interpolation, and a simple and useful condition that guarantees that a domain has a CDT. These results provide foundations for reasoning about CDTs and proving the correctness of algorithms. Later articles in this series discuss algorithms for constructing and updating CDTs. Supported in part by the National Science Foundation under Awards CMS-9318163, ACI-9875170, CMS-9980063, CCR-0204377, CCF-0430065, and EIA-9802069, in part by the Advanced Research Projects Agency and Rome Laboratory, Air Force Materiel Command, USAF under agreement number F30602-96-1-0287, in part by an Alfred P. Sloan Research Fellowship, and in part by gifts from the Okawa Foundation and Intel. The views in this document are those of the author. They are not endorsed by the sponsors or the U.S. Government.     

Self-consistent Monte Carlo simulations of the electron and ion distributions of inhomogeneous liquid alkali metals. II. Longitudinal and transverse density distributions in the liquid-vapor interface of binary metallic alloys

We present the results of Monte Carlo simulations of the liquid-vapor interface of sodium-cesium alloys. The longitudinal density profile of each alloy shows that the liquid-vapor interface consists of a well-defined monolayer of cesium sitting on top of a slab of the bulk alloy. Underneath the monolayer there is a slight excess of sodium. A comparison with a van der Waals analog of one of the alloys shows that the presence of the well-defined monolayer of cesium on the outside of the liquid-vapor interface is a feature peculiar to metallic mixtures. The transverse pair correlation functions of the cesium monolayer are insensitive to the composition of the bulk of the slab.     

The photodegradation of cadmium yellow paints in Henri Matisse’s Le Bonheur de vivre (1905–1906)

Evidence for the alteration of the yellow paints in Henri Matisse’s Le Bonheur de vivre (1905–1906, The Barnes Foundation) has been observed since the 1990s. The changes in this iconic work of Matisse’s Fauvist period include lightening, darkening, and flaking of the yellow paints. Handheld X-ray fluorescence (XRF) and multispectral imaging surveys reveal that the degradation is confined to cadmium yellow (CdS) paints. The discoloration of cadmium yellow paints in Impressionist, Post-Impressionist and early modernist work from the 1880s through the 1920s has been ascribed to the photo-oxidative degradation of CdS. Preliminary investigations of the degraded yellow paints in this work involved Cd L_III-edge X-ray Absorption Near Edge Spectroscopy (XANES) at the Stanford Synchrotron Radiation Light Source (SSRL Menlo Park, California) and Scanning Electron Microscopy-energy dispersive X-ray analysis (SEM-EDS) at the Winterthur Museum Scientific Research and Analysis Laboratory. To determine if the visual changes in the paints did in fact indicate photo-oxidative degradation and if different chemistries could be observed for the lightened versus darkened regions, synchrotron radiation-micro Fourier Transform InfraRed (SR-μFTIR) spectroscopy, X-ray Fluorescence (SR-μXRF) mapping and micro X-ray Absorption Near Edge Spectroscopy (μXANES) mapping at the Cd L_III-edge of the altered paint cross-sections were carried out at the European synchrotron radiation facility (ESRF, Grenoble, France) beamline ID-21. The goal is to elucidate the discoloration mechanisms observed in the paint using elemental and speciation mapping. The μXANES mapping and SR-FTIR imaging showed a substantial enrichment of CdCO₃ in the off-white surface crust of the faded/discolored CdS paint. This suggests that the CdCO₃ is present as an insoluble photodegradation product rather than solely a paint filler or starting reagent. Additionally, oxalates and sulfates were found to be concentrated at the alteration surface.