Chemo‐Enzymatic Synthesis and Determination of the Absolute Configuration of Both Enantiomers of Methyl trans‐5‐Oxo‐2‐pentylpyrrolidine‐3‐carboxylate Precursors of the Aza Analogues of (+)‐ and (−)‐Methylenolactocin

Enantiomerically pure methyl esters of (+)‐(2R,3S)‐ and (−)‐(2S,3R)‐5‐oxo‐2‐pentylpyrrolidine‐3‐carboxylic acid with 99% and 98% ee were obtained by enzymatic resolution of the corresponding racemic mixture using α‐chymotrypsin and pig‐liver acetone powder, respectively. Their absolute configurations were established by chemical methods, i.e., conversion of the trans‐γ‐lactam moiety to the corresponding γ‐lactone of known configuration. The favorable interactions between the trans‐γ‐lactam and α‐chymotrypsin were rationalized by molecular‐mechanics calculations, which suggest a different situation for the cis‐diastereoisomer.     

Towards the biosynthesis of the aromatic products of the Mediterranean mollusc Scaphander lignarius: isolation and synthesis of analogues of lignarenones

Secondary metabolites of the Mediterranean mollusc Scaphander lignarius from different collection sites have been investigated, proving the constant presence of a number of minor metabolites correlated to the already known lignarenones. Complete characterization of the new metabolites has been supported by enantioselective synthesis. The data are consistent with the origin of this unique class of ω-phenyloctanoids from a common polyketide pathway.     

The Definition of the Fourier Transform for Weighted Inequalities

Weighted norm inequalities for the Fourier transform have a long history, motivated in part by generalizations of the differentiation formula for Fourier transforms and by applications such as Kolmogorov′s prediction theory and restriction theory. Typically, a norm inequality, || ||L^q_μ ≤ ||f||L^p_v, is established on a subspace of L¹ contained in the weighted space L^p_v, where is the Fourier transform and μ and v are weights. The problem of defining the extension of on all of L^p_v is posed and solved here for several important cases. This definition sometimes results in the ordinary distributional Fourier transform, but there are other situations which are also analyzed. Precise necessary conditions and closure theorems are inextricably related to this program, and these results are established.     

The basis decision problem in λ-calculus

We show that the problem of deciding if a finite set of closed terms in normal form is a basis is recursively unsolvable. The restricted problem concerning one element sets is still recursively unsolvable. MSC: 03B40, 03D35.     

Digital idle speed control of automotive engines: A safety problem for hybrid systems

We address the idle speed control problem in automotive electronics using hybrid methods to derive a digital control law with guaranteed properties. Associating a switching system with the hybrid system that describes the engine operation is crucial to developing a computationally feasible approach. For switching systems with minimum and maximum dwell times and controlled resets, we are able to derive digital control strategies with guaranteed properties that ensure safety. The proposed methodology, while motivated by the idle control problem, is of general interest for hybrid systems for which minimum and maximum dwell times can be established. In our modeling approach, we do not assume synchronization between sampling time and switching time. This is an important technical aspect in general, and in particular for our application, where there is no reason why sampling and switching should be synchronized. Some simulation results are included to demonstrate the effectiveness of the approach.     

Synthesis of optically active α-benzyl paraconic acids and their esters and assignment of their absolute configuration

The cis- and trans-4-benzylparaconic acids and their ethyl esters were synthesized with high enantiomeric excess by hydrolysis of the corresponding diastereomeric lactonic esters using α-chymotrypsin. Thus, at low conversion values, cis- and trans-4-benzyl-5-oxo-3-tetrahydrofurancarboxylic acids were separately isolated with 99% ee and 92% ee, respectively. Both ethyl ester diastereomers were also obtained in enantiopure form. The absolute configuration of the trans-lactonic acid was assigned by ¹H NMR analysis of its ester derivatives with both enantiomers of 1-(9-anthryl)-2,2,2-trifluoroethanol, while that of the cis-lactonic acid was assigned by means of X-ray analysis of a crystalline derivative. The circular dichroism curves of the products obtained are also reported.