Locality properties of radial basis function expansion coefficients for equispaced interpolation

Natasha Flyer ^{Many types of radial basis functions (RBFs) are global in termsof having large magnitude across the entire domain. Yet, incontrast, e.g. with expansions in orthogonal polynomials, RBFexpansions exhibit a strong property of locality with regardto their coefficients. That is, changing a single data valuemainly affects the coefficients of the RBFs which are centredin the immediate vicinity of that data location. This localityfeature can be advantageous in the development of fast and well-conditionediterative RBF algorithms. With this motivation, we employ hereboth analytical and numerical techniques to derive the decayrates of the expansion coefficients for cardinal data, in both1D and 2D. Furthermore, we explore how these rates vary in theinteresting high-accuracy limit of increasingly flat RBFs.}     

Oil from the Tropical Marine Benthic-Diatom Navicula sp.

The potential of the tropical marine benthic-diatom Navicula sp. for biodiesel feedstock was investigated. Growth profiles were analyzed by changing nutrient compositions in three different media (Walne, plain seawater, and modified seawater) and irradiance intensities. Navicula sp. cells showed significant growth in Walne and modified seawater medium but not in plain seawater medium. The microalgae grew well in a pH range of 7.8?C8.4, and the cells were very sensitive to the intensity of direct sunlight exposure. The average cell concentration obtained from the cultures in plain seawater, Walne, and modified seawater media at the beginning of the stationary phase was 0.70, 2.17, and 2.54?g/L, respectively. Electron spray ionization-ion trap-mass spectrometry showed that the triacylglycerols of the algae oil were identified as POP (palmitic-oleic-palmitic), POO (palmitic-oleic-oleic), and OOLn (oleic-oleic-linoleic). The oil productivity of Navicula sp. cultivated in Walne and modified seawater media was 90 and 124???L?L^?1 culture d^?1. The Navicula sp. biodiesel exhibited a kinematic viscosity of 1.299?mm²/s, density of 0.8347?g/mL, and internal energy of 0.90?kJ/mL.     

4-Iodo-2-methyl-5-nitro­aniline exhibits neither strong hydrogen bonding nor intermolecular I⃛nitro interactions

In the title compound, C₇H₇IN₂O₂, the O atoms of the nitro group are disordered over two sets of sites and there is evidence that the intramolecular I⃛nitro interaction is repulsive. In the crystal structure, there are neither strong hydrogen bonds, nor intermolecular I⃛nitro interactions, nor aromatic π–π-stacking interactions.     

Prevalent Behavior of Strongly Order Preserving Semiflows

Classical results in the theory of monotone semiflows give sufficient conditions for the generic solution to converge toward an equilibrium or toward the set of equilibria (quasiconvergence). In this paper, we provide new formulations of these results in terms of the measure-theoretic notion of prevalence, developed in Christensen (Israel J. Math., 13, 255–260, 1972) and Hunt et al. (Bull. Am. Math. Soc., 27, 217–238, 1992). For monotone reaction–diffusion systems with Neumann boundary conditions on convex domains, we show the prevalence of the set of continuous initial conditions corresponding to solutions that converge to a spatially homogeneous equilibrium. We also extend a previous generic convergence result to allow its use on Sobolev spaces. Careful attention is given to the measurability of the various sets involved.     

Middle School Students' Conceptual Learning from the Implementation of a New NSF Supported Curriculum: Interactions in Physical Science™

A new National Science Foundation supported curriculum, Interactions in Physical Science?, was evaluated on students’ conceptual change in the twelve concept areas of the national physical science content standard (B) for grades 5–8. Eighth grade students (N=66) were evaluated pre and post on a 31‐item multiple‐choice test of conceptual understanding developed by the Harvard ‐Smithsonian Center for Astrophysics. Significant student gains (p<. 05, t‐test, two‐tailed) occurred in all concept areas in the category of properties and changes in properties of matter; for the force concept areas in the category motions and forces; and for the heat transfer and light interactions areas in the category of transfer of energy. Two of the six concept areas in the category of transfer of energy, chemical and nuclear reactions and the sun as a major source of energy, were not addressed in this study. Significant learning gains as item percent correct were typically close to 20%, though effect sizes were small to medium in magnitude (d = 0.3–0.6). Implications of the study for conceptual change curriculum and teaching are discussed.     

Comtrans algebras, Thomas sums, and bilinear forms

A comtrans algebra is said to decompose as the Thomas sum of two subalgebras if it is a direct sum at the module level, and if its algebra structure is obtained from the subalgebras and their mutual interactions as a sum of the corresponding split extensions. In this paper, we investigate Thomas sums of comtrans algebras of bilinear forms. General necessary and sufficient conditions are given for the decomposition of the comtrans algebra of a bilinear form as a Thomas sum. Over rings in which 2 is not a zero divisor, comtrans algebras of symmetric bilinear forms are identified as Thomas summands of algebras of infinitesimal isometries of extended spaces, the complementary Thomas summand being the algebra of infinitesimal isometries of the original space. The corresponding Thomas duals are also identified. These results represent generalizations of earlier results concerning the comtrans algebras of finite-dimensional Euclidean spaces, which were obtained using known properties of symmetric spaces. By contrast, the methods of the current paper involve only the theory of comtrans algebras.Received: 30 March 2004