Maximal monotonicity, conjugation and the duality product

Recently, the authors studied the connection between each maximal monotone operator and a family of convex functions. Each member of this family characterizes the operator and satisfies two particular inequalities.

The aim of this paper is to establish the converse of the latter fact. Namely, that every convex function satisfying those two particular inequalities is associated to a unique maximal monotone operator.

     

Asymptotic behaviour of the stability parameter for a family of singular-limit Hill's equation

Under some nondegeneracy conditions we give asymptotic formulae for the stability parameter of a family of singular-limit Hill's equation which depends on three parameters. We use the blow-up techniques introduced in [R. Martínez, A. Samà, C. Simó, Analysis of the stability of a family of singular-limit linear periodic systems in R⁴. Applications, J. Differential Equations 226 (2006) 652-686]. The main contribution of this paper concerns the study of the nondegeneracy conditions. We give a geometrical interpretation of them, in terms of heteroclinic orbits for some related systems. In this way one can determine values of the parameters such that the nondegeneracy conditions are satisfied. As a motivation and application we consider the vertical stability of homographic solutions in the three-body problem.     

Fusel oil as precursor for aroma generation by biotransformation using lipase

The feasibility of using mixtures of C4 and C5 chain-length aliphatic alcohols from fusel oil as the bulk organic media for lipase-mediated synthesis of laurate esters was assessed. Reaction mixtures consisted of lauric acid, lipase, solvent (if added), and appropriate amount of fusel oil (previously dehydrated with inorganic salts and molecular sieves). The influence of the reaction conditions such as substrate concentrations and temperature were investigated. Increased molar ratio of acyl donor to acyl acceptor allowed the esterification to proceed with no need for solvent addition.     

An Integrated Plant Design and Scheduling Problem in the Food Industry

An integrated plant design and scheduling problem in the food industry is discussed, and a solution is proposed. This involves the use of two models. The first model is an integer programming model that deals with long-term decisions. The second model deals with decisions that have to be made instantly.     

Flow activation free energy in cholesteric lyotropic liquid crystals

The flow activation free energy ( ΔG *) is the minimum energy necessary to induce a flow in a system that is at rest. It can be calculated from the system viscosity using the Andrade--Eyring theory. In the present work the flow activation free energy of cholesteric lyotropic liquid crystals was studied as a function of D-(+)-mannose concentration added to a nematic mesophase. The results obtained showed that all the systems can be characterized as Newtonian, but a smooth time-dependent effect can be observed mainly in systems with a lower chiral inductor concentration. It has also been observed that an increase of cholestericity leads to a decrease of ΔH * values until a limit is reached at 1 mol % of inductor. From a positive ΔS * variation it was possible to verify the existence of a locally less organized transient state during the process of micellar diffusion. When the cholesterization process was considered, the increase of the inductor concentration leads to a decrease of ΔS * and consequently to a system, as a whole, more orderly, possibly as a result of the restriction of movement caused by the presence of chiral interactions.     

Asymmetric microbial reduction of ketones: absolute configuration of trans-4-ethyl-1-(1S-hydroxyethyl)cyclohexanol

A set of five fungal species, Botrytis cinerea, Trichoderma viride and Eutypa lata, and the endophytic fungi Colletotrichum crassipes and Xylaria sp., was used in screening for microbial biocatalysts to detect monooxygenase and alcohol dehydrogenase activities (for the stereoselective reduction of carbonyl compounds). 4-Ethylcyclohexanone and acetophenone were biotransformed by the fungal set. The main reaction pathways involved reduction and hydroxylations at several positions including tertiary carbons. B. cinerea was very effective in the bioreduction of both substrates leading to the chiral alcohol (S)-1-phenylethanol in up to 90% enantiomeric excess, and the cis–trans ratio for 4-ethylcyclohexanol was 0:100. trans-4-Ethyl-1-(1S-hydroxyethyl)cyclohexanol, obtained from biotransformation by means of an acyloin-type reaction, is reported here for the first time. The absolute configurations of the compounds trans-4-ethyl-1-(1S-hydroxyethyl)cyclohexanol and 4-(1S- and 4-(1R-hydroxyethyl)cyclohexanone were determined by NMR analysis of the corresponding Mosher’s esters.