Preventive maintenance for inspected systems with additive subexponential shock magnitudes

We examine the long-run average availability and cost rate of a maintained system which deteriorates according to a random-shock process. Shocks arrive according to a Poisson process. The system fails whenever the cumulative damage exceeds a given threshold. The system's failures are not self-announcing, hence, failures must be detected via inspections. The system is inspected at periodic or exponentially distributed intervals. Systems are replaced by preventive maintenance or after failure (corrective maintenance), whichever occurs first. When the distribution function of the shock magnitudes belongs to the class of subexponential distributions, we obtain simple approximations for the availability and the cost rate. Copyright © 2007 John Wiley & Sons, Ltd.     

Gelfand-Kirillov Dimension and Local Finiteness of Symmetrizations of Associative Superalgebras

In this work we extend to superalgebras a result of Skosyrskii [Algebra and Logic, 18 (1) (1979) 49–57, Lemma 2] relating associative and Jordan structures. As an application, we show that the Gelfand-Kirillov dimension of an associative superalgebra coincides with that of its symmetrization, and that local finiteness is equivalent in associative superalgebras and in their symmetrizations. In this situation we obtain that having zero Gelfand-Kirillov dimension is equivalent to being locally finite.Partially supported by MCYT and Fondos FEDER BFM2001-1938-C02-02, and MEC and Fondos FEDER MTM2004-06580-C02-01.Partially supported by a F.P.I. Grant (Ministerio de Ciencia y Tecnología).     

Reassignment of the Configuration of Several Keto-cyclolignans Prepared from Podophyllotoxin

The configuration of several keto-cyclolignans related to podophyllotoxin has been reviewed. Under basic catalysis, the configuration at the C-atom in α-position to the lactone carbonyl group in podophyllotoxone is inverted instead of the C-atom in α-position to the ketone group, as it has been reported.     

A General Chemistry Experiment to Predict and Measure Functional-Group Stretching Frequencies

An experiment suitable for first-year students is reported. In this activity, students use a molecular modeling program to compute infrared spectra for a series of molecules. From the data obtained, students generate a group frequency chart and use it to identify unknowns. This provides students with an introduction to vibrational spectroscopy and the use of molecular modeling.     

Simultaneous determination of 3,4-dimethoxybenzaldehyde and 3,4-dimethoxyphenylacetone in industrial waste waters by high-performance liquid chromatography-diode array detection

The environmental pollutants 3,4-dimethoxybenzaldehyde (DMB) and 3,4-dimethoxyphenylacetone (DMPA) were separated and quantitatively determined in treated and untreated industrial waste waters on a porous graphitized carbon column using HPLC with diode array detection (DAD). It was established that the detector response is linear in a wide range of injected quantities for both pollutants, and the logarithm of the capacity factor depends linearly on the concentration of acetonitrile in the eluent. The relative standard deviation of the retention time, peak height and peak area was lower than 1% in the normal and lower than 3% in the lowest concentration range. Peak purity tests indicated that the method separates well DMB and DMPA from other impurities present in the waste waters. Both aerobic and anaerobic treatments markedly decreased the concentration of DMB and DMPA in industrial waters and HPLC combined with DAD proved to be an adequate analytical procedure to follow such changes.     

Reactions on solid supports part I: Novel preparation of α-formyl pyrroles from α-methylpyrroles by oxidation with thallium (III) nitrate on clay

Treatment of α-methylpyrroles with thallium (III) nitrate/Montmorillonite clay affords the corresponding α-formylpyrroles in excellent yields.     

Neither even nor odd: Sixth grade students’ dilemmas regarding the parity of zero

This study investigates two sixth grade students’ dilemmas regarding the parity of zero. Both students originally claimed that zero was neither even nor odd. Interviews revealed a conflict between students’ formal definitions of even numbers and their concept images of even numbers, zero, and division. These images were supported by practically based explanations relying on everyday contexts. By using mathematically based explanations that rely solely on mathematical notions, students were able to correctly conclude that zero is an even number. Extending the natural number system in elementary school to include zero can be used as springboard to encourage the use of mathematically based explanations.