The least element property of center location on tree networks with applications to distance and precedence constrained problems

In the classicalp-center location model on a network there is a set of customers, and the primary objective is to selectp service centers that will minimize the maximum distance of a customer to a closest center. Suppose that thep centers receive their supplies from an existing central depot on the network, e.g. a warehouse. Thus, a secondary objective is to locate the centers that optimize the primary objective as close as possible to the central depot. We consider tree networks and twop-center models. We show that the set of optimal solutions to the primary objective has a semilattice structure with respect to some natural ordering. Using this property we prove that there is ap-center solution to the primary objective that simultaneously minimizes every secondary objective function which is monotone nondecreasing in the distances of thep centers from the existing central depot.Restricting the location models to a rooted path network (real line) we prove that the above results hold for the respective classicalp-median problems as well.     

Calorimetric study on the temperature dependence of the formation of mixed ionic/nonionic micelles

The differential excess enthalpy of mixed micelle formation was measured at different temperatures by mixing nonionic hexa(ethylene glycol) mono n-dodecyl ether with anionic sodium dodecyl sulfate or cationic dodecylpyridinium chloride. The experimental data were obtained calorimetrically by titrating a concentrated surfactant solution into a micellar solution of nonionic surfactant. The composition and the size of the mixed nonionic/ionic micelles at different surfactant concentrations were also determined. Pronounced differences in both composition and excess enthalpy were found between the anionic and the cationic mixed system. For both systems, the excess enthalpies become more exothermic with increasing temperature, but for the anionic mixed system an additional exothermic contribution was found which was much less temperature dependent. Temperature dependence of the excess enthalpy was attributed to the effect of the ionic headgroup on the hydration of the ethylene oxide (EO) groups in the mixed corona. Ionic headgroups located in the ethylene oxide layer cause the dehydration of the EO chains resulting in an additional hydrophobic contribution to the enthalpy of mixing. A high affinity of sodium dodecyl sulfate for nonionic micelles and an extra exothermic and less temperature dependent contribution to the excess enthalpy found for the SDS-C(12)E(6) system might be attributed to specific interactions (hydrogen bonds) between the sulfate headgroup and the partly dehydrated EO chain.     

Enzymatic polyesterification in organic media. Enzyme-catalyzed synthesis of linear polyesters. I. Condensation polymerization of linear hydroxyesters. II. Ring-opening polymerization of ϵ-caprolactone

With the object to synthesize polyesters by enzymatic catalysis in organic media, two directions have been investigated: (1) the condensation polymerization of linear ω-hydroxyesters and (2) the ring-opening polymerization of lactones. The commercially-available crude porcine pancreatic lipase (PPL), suspended in organic solvents, was the preferred enzyme for the reactions. In order to determine the optimal conditions for the condensation polymerization, the bifunctional methyl 6-hydroxyhexanoate was used as a model compound to study the influence of the following parameters: type of the enzymecatalyst, kind of solvent, concentration, temperature, duration, size of the reaction mixture, and stirring. Film-forming polyesters with a degree of polymerization (DP) up to about 100 were obtained from linear aliphatic hydroxyesters in n-hexane at reflux temperature (69°C). Yet concurrently with the intermolecular condensation polymerization, macrolactones were also formed by intramolecular reaction. Two aromatic hydroxyesters did not react under these conditions. For the ring-opening polymerization of lactones the reaction of ?-caprolactone with methanol as the preferred nucleophile, was studied. Polyesters with a DP of up to 35 were obtained in n-hexane at temperatures between 25 and 40°C. The degrees of polymerization of the polyesters were determined by comparative analyses of the end groups in the ¹H-NMR spectra and by determination of molecular weights either by vapor phase osmometry, gel permeation chromatography, or intrinsic viscosity. © 1993 John Wiley & Sons, Inc.     

Time-resolved fluorescence analysis of the mobile flavin cofactor in p -hydroxybenzoate hydroxylase

Conformational heterogeneity of the FAD cofactor in p-hydroxybenzoate hydroxylase (PHBH) was investigated with time-resolved polarized flavin fluorescence. For binary enzyme/substrate (analogue) complexes of wild-type PHBH and Tyr222 mutants, crystallographic studies have revealed two distinct flavin conformations; the ‘in’ conformation with the isoalloxazine ring located in the active site, and the ‘out’ conformation with the isoalloxazine ring disposed towards the protein surface. Fluorescence-lifetime analysis of these complexes revealed similar lifetime distributions for the ‘in’ and ‘out’ conformations. The reason for this is twofold. First, the active site of PHBH contains various potential fluorescence-quenching sites close to the flavin. Fluorescence analysis of uncomplexed PHBH Y222V and Y222A showed that Tyr222 is responsible for picosecond fluorescence quenching free enzyme. In addition, other potential quenching sites, including a tryptophan and two tyrosines involved in substrate binding, are located nearby. Since the shortest distance between these quenching sites and the isoalloxazine ring differs only little on average, these aromatic residues are likely to contribute to fluorescence quenching. Second, the effect of flavin conformation on the fluorescence lifetime distribution is blurred by binding of the aromatic substrates: saturation with aromatic substrates induces highly efficient fluorescence quenching. The flavin conformation is therefore only reflected in the small relative contributions of the longer lifetimes.     

Non‐symmetric bent‐core mesogens with one terminal vinyl group

Two series of non‐symmetric banana‐shaped compounds, both with one alkyl and one alkenyl terminal tail, have been synthesized and studied. Both series were compared with the corresponding series with two saturated terminal alkyl tails. All the compounds have a bent central 1,3‐phenylene bis(4‐benzoyloxy)benzoate core; their mesophases were characterized by polarizing optical microscopy, differential scanning calorimetry, X‐ray diffraction and switching current response experiments. In all four series one of the terminal tails is varied from OC₈H₁₇ to OC₁₆H₃₃. The other terminal tails are OC₁₁H₂₃, O(CH₂)₉CH?=?CH₂, OC₁₀H₂₁ and O(CH₂)₈CH?=?CH₂. The short‐tailed compounds show monotropic or enantiotropic B₁ phases and the long‐tailed compounds the B₂ phase. The introduction of one terminal vinyl group slightly lowers the transition temperatures. The introduction of a second terminal vinyl group further suppresses the liquid crystalline properties. All compounds with B₂ phases have layer spacings that suggest a tilt of ～45° of the bent molecules in the layers, and their switching behaviour is antiferroelectric.     

A note on medieval microfabrication: the visualization of a prayer nut by synchrotron‐based computer X‐ray tomography

One of the most fascinating objects in the Rijksmuseum (Amsterdam, The Netherlands) is an early 16th century prayer nut. This spherical wooden object measures 4 cm in diameter and consists of two hemispheres connected with a small hinge so that it can be opened. The interior of the nut holds wood carvings with scenes from the life of Christ. These miniature reliefs show an incredible degree of finish with carving details well beyond the millimetre scale. In the present paper it is shown how synchrotron‐based computer X‐ray tomography revealed the structure and fabrication method of the bead. The central part of the relief was cut from a single piece of wood, rather than assembled from multiple components, underlining the extraordinary manual dexterity of its maker. In addition, a piece of fibrous material contained in the inner structure of the bead is revealed. This may have served as a carrier for an odorous compound, which would be in line with the religious function of the prayer nut.     

On the Order Reduction Approach for Singularly Perturbed Optimal Control Systems

The order reduction method for singularly perturbed optimal control systems consists of employing the system obtained while setting the small parameter to be zero. In many situations the differential-algebraic system thus obtained indeed provides an appropriate approximation to the singularly perturbed problem with a small parameter. In this paper we establish that if relaxed controls are allowed then the answer to the question whether or not this method is valid depends essentially on one simple parameter: the dimension of the fast variable, denoted n. More specifically, if n=1 then the order reduction method is indeed applicable, while if n>1 then the set of singularly perturbed optimal control systems for which it is not applicable is dense (in the L norm).