Immobilized microorganisms in the reduction of ethyl benzoylacetate

The enantioselective reduction of ethyl benzoylacetate (EBA) into ethyl (S)-3-hydroxy-3-phenylpropanoate (S-HPPE) by nine yeast strains and three filamentous fungi strains is described. The conversion obtained was in the range 0-89% and the enantiomeric excess was 100% in many cases. Conversion levels were higher when the reduction was performed with microorganisms immobilized in calcium alginate and enantioselectivity remained excellent. Some reaction’s conditions of bioreduction by immobilized cells of Rhodotorula rubra were studied using a 2^5-2 fractional factorial design.     

Mathematical Aspects of the Periodic Law

We review different studies of the Periodic Law and the set of chemical elements from a mathematical point of view. This discussion covers the first attempts made in the 19th century up to the present day. Mathematics employed to study the periodic system includes number theory, information theory, order theory, set theory and topology. Each theory used shows that it is possible to provide the Periodic Law with a mathematical structure. We also show that it is possible to study the chemical elements taking advantage of their phenomenological properties, and that it is not always necessary to reduce the concept of chemical elements to the quantum atomic concept to be able to find interpretations for the Periodic Law. Finally, a connection is noted between the lengths of the periods of the Periodic Law and the philosophical Pythagorean doctrine.     

Headspace single drop microextraction of methylcyclopentadienyl-manganese tricarbonyl from water samples followed by gas chromatography-mass spectrometry

Headspace single drop microextraction coupled to gas chromatography-mass spectrometry yielded a simple, fast and virtually solventless analytical protocol used for the headspace analysis of aqueous samples contaminated with methylcyclopentadienyl-manganese tricarbonyl (MMT). Initially, several experimental parameters were controlled and optimized and the optimum conditions found were 2.5 μl octane microdrop exposed for 20 min to the headspace of a 10 ml aqueous sample (15 ml vial) containing 20% (w/v) NaCl and stirred at 1250 rpm. The calculated calibration curves gave a high level of linearity for MMT with correlation coefficients >0.9995 after conducting a 3-day study. The limit of detection was calculated to be 0.21 μg l⁻¹. The proposed method achieved an enrichment factor of the order of 2100 and a 53% recovery after extracting the spiked aqueous solution for 20 min under the optimized experimental conditions. The repeatability and intra-day reproducibility of the proposed method, expressed as relative standard deviation were 8.4 and 6.4%, respectively. Finally, analysis of spiked tap and wastewater samples revealed that matrix had little effect upon extraction.     

Asymptotic stability of Riemann solutions in BGK approximations to certain multidimensional systems of conservation laws

We prove the asymptotic stability of nonplanar two-states Riemann solutions in BGK approximations of a class of multidimensional systems of conservation laws. The latter consists of systems whose flux-functions in different directions share a common complete system of Riemann invariants, the level surfaces of which are hyperplanes. The asymptotic stability to which the main result refers is in the sense of the convergence as t→∞ in of the space of directions ζ=x/t. That is, the solution z(t,x,ξ) of the perturbed Cauchy problem for the corresponding BGK system satisfies as t→∞, in , where R(ζ) is the self-similar entropy solution of the two-states nonplanar Riemann problem for the system of conservation laws.     

Efficient simulation of tail probabilities of sums of correlated lognormals

We consider the problem of efficient estimation of tail probabilities of sums of correlated lognormals via simulation. This problem is motivated by the tail analysis of portfolios of assets driven by correlated Black-Scholes models. We propose two estimators that can be rigorously shown to be efficient as the tail probability of interest decreases to zero. The first estimator, based on importance sampling, involves a scaling of the whole covariance matrix and can be shown to be asymptotically optimal. A further study, based on the Cross-Entropy algorithm, is also performed in order to adaptively optimize the scaling parameter of the covariance. The second estimator decomposes the probability of interest in two contributions and takes advantage of the fact that large deviations for a sum of correlated lognormals are (asymptotically) caused by the largest increment. Importance sampling is then applied to each of these contributions to obtain a combined estimator with asymptotically vanishing relative error.     

Synthesis of N,N-dialkylaminobenzonitriles and halo-(N,N-dialkyl)benzamidines by reaction of halobenzonitriles with lithium amides

3- and 4-N,N-Dialkylaminobenzonitriles and 4-chloro-(N,N-dialkyl)benzamidines were isolated by reacting 4-chlorobenzonitrile with hindered lithium amides under thermodynamic (0 °C) and kinetic control conditions (−78 °C), respectively. As previously reported, a benzyne mechanism seems to be confirmed since N,N-dialkylaminobenzonitriles are formed. Only benzamidines were isolated in fair to high yields at both 0 °C and −78 °C with non-hindered lithium amides. Exploitation and mechanistic rationale of the reaction of different halobenzonitriles are also reported.