Dirac operators and spectral triples for some fractal sets built on curves

We construct spectral triples and, in particular, Dirac operators, for the algebra of continuous functions on certain compact metric spaces. The triples are countable sums of triples where each summand is based on a curve in the space. Several fractals, like a finitely summable infinite tree and the Sierpinski gasket, fit naturally within our framework. In these cases, we show that our spectral triples do describe the geodesic distance and the Minkowski dimension as well as, more generally, the complex fractal dimensions of the space. Furthermore, in the case of the Sierpinski gasket, the associated Dixmier-type trace coincides with the normalized Hausdorff measure of dimension log3/log2.     

Nachweis und Bestimmung des Mangans sowie seine Trennung von anderen Elementen

Ohne Zusammenfassung     

Effect of particle size on carburization of Fe-Co alloy catalysts

Bimetallic Fe-Co alloy catalysts supported on silica have been studied by use of combined Mössbauer absorption and emisson spectroscopy. Effects of carburization on samples with different particle size are discussed.     

Optical properties of TiN1-x single crystals

The reflectance spectra of TiN_1–x single crystals were measured at room temperature. The chemical composition of the crystals was varied between TiN_1–0.00 and TiN_1–0.43. The experimental data are analyzed on the basis of a Lorentz-Drude model in order to determine the influence of nitrogen vacancies on the electrical conductivity, on the carrier concentration, and on the collision time.     

New algorithm for optimal parameter estimation with linear constraints

This paper presents a new algorithm for optimal parameter estimation problems with linear constraints. The algorithm developed is based on least absolute-value approximations. The problem is solved first using a least-error-square technique, where we add to the cost function the equality constraints via Lagrange multipliers, to obtain a good estimate for the residuals of the measurements, having gained this information, we choose a number of measurements with the smallest residuals. This number equals the number of parameters to be estimated minus the number of constraints. Using these measurements together with the constraints, we obtain a number of observations equal to the number of parameters to be estimated. By using this technique, we show that there is no need to either iterate or use linear programming to obtain the estimation.This work was supported by the Natural Sciences and Engineering Research Council of Canada, Grant A4146.     

An efficient microwave assisted synthesis of N′-aryl/(alkyl)-substituted N-(4-hydroxy-6-phenylpyrimidin-2-yl)guanidines: Scope and limitations

Treatment of N-[(4-hydroxy-6-phenyl)pyrimidin-2-yl]cyanamide with 1° alkyl or arylamines in isopropyl alcohol for only 10 min at 110–120 °C under microwave conditions gave the corresponding N′-alkyl(aryl)guanidine derivatives in excellent yields (65–84%). Isolated yields were greatest when >1.0 equiv. of amines were employed, but excellent results were also obtained when aryl and alkylamines were reacted with a more atom-economical loading (1.0 equiv.; 70% and 72% ave. yields, respectively). Arylamines with either highly electron withdrawing substituents (e.g. CO₂H) or pi-deficient heterocycles (e.g. variously substituted aminopyridines) did not work well under these conditions, and reaction with ureas and/or amino acids did not give detectable products. Work-up was exceedingly simple, and involved simple collection and washing of product on a sintered glass funnel. Products were obtained in analytically pure form and required approximately 1 h to prepare, start to finish.