A bisection-extreme point search algorithm for optimizing over the efficient set in the linear dependence case

The algorithms and algorithmic ideas currently available for globally optimizing linear functions over the efficient sets of multiple objective linear programs either use nonstandard subroutines or cannot yet be implemented for lack of sufficient development. In this paper a Bisection-Extreme Point Search Algorithm is presented for globally solving a large class of such problems. The algorithm finds an exact, globally-optimal solution after a finite number of iterations. It can be implemented by using only well-known pivoting and optimization subroutines, and it is adaptable to large scale problems or to problems with many local optima.     

Fast and accurate reflectivity calculations for shaped core optical fibres

A novel scalar (i.e. paraxial) free space radiation mode method is presented for calculating the normal incidence facet reflectivity of the main guided mode of a step-index optical fibre with generally shaped smooth core. Numerical results are presented and discussed for several cases of the Nth order super-elliptical core shape, including the circular, elliptical, rectangular-type and slab limiting cases.     

Asymmetric synthesis of mono- and dinuclear bis(dipyrrinato) complexes

The diastereoselective syntheses of Zn(II) bis(dipyrrinato) helicates is reported, involving ligands templated by the incorporation of homochiral binol within the linker joining the two dipyrrinato units. The most diastereoselective formation of dinuclear bis(dipyrrinato) helicates to date is reported. The formation of either mononuclear or dinuclear helicates can be tuned by varying the length of the linker between the dipyrrinato units and by varying the complexation procedure. The neutral dipyrrinato helicates were readily analyzed by HPLC to ascertain diastereoselectivity, and circular dichroism studies revealed the helical nature of the complexes. The molar ellipticities of the helicates produced by diastereoselective complexation are very large in the visible region and typically correspond to binol moieties in the UV region. Extensive X-ray crystallographic investigations further confirmed the helicity of the mononuclear Zn(II) helicates and identified significant interlayer displacement and bending within crystals.     

Stereoselective synthesis of beta-(chloro)vinylsilanes using a regio- and (E)-stereoselective bis-stannylation of unsymmetrically substituted butadiynes: application to the synthesis of a masked triyne

[reaction: see text] A highly regio- and stereoselective bis-stannylation of unsymmetrically substituted butadiyne 3 provides bis-stannane 4. Selective lithiation of the internal tin residue effects a 1,4-retro-Brook rearrangement to afford vinylsilane 5. This was elaborated into the novel diethynylethene 1, which also functions as a masked triyne.     

Influence of Cyclodextrin Complexation on the in vitro Human Skin Penetration and Retention of the Sunscreen Agent, Oxybenzone

The objective of this study was to investigate the influence of cyclodextrins on the cutaneous availability of the sunscreen oxybenzone. The interaction between oxybenzone and hydrophilic α-, β- and γ-cyclodextrin derivatives was studied in water by phase-solubility analysis. Among the available cyclodextrins, hydroxypropyl-β-cyclodextrin (HP-β-CD) and especially sulfobutylether-β-cyclodextrin (SBE-β-CD) had the greatest solubilizing activity. Ethanol–water solutions containing oxybenzone free or complexed with HP-β-CD or SBE-β-CD were applied to human skin in Franz diffusion cells and the amount of sunscreen permeated into the different cutaneous compartments was determined by HPLC. As much as 20.5% of the oxybenzone applied dose diffused within the skin tissue after 6 h application. Between 39.4% and 54.9% of the penetrated UV filter was localized in the stratum corneum, with no significant difference between uncomplexed oxybenzone or its complex with HP-β-CD. Conversely, the amount retained in the stratum corneum was markedly decreased (ca. 50%) by complexation with SBE-β-CD. Considerable quantities of oxybenzone accumulated into the viable epidermis (5.7% of the applied dose) and dermis (6.2% of the applied dose) from the preparation containing the free UV filter. The sunscreen penetration to the deeper living layers of the skin was remarkably lower (1.0% and 2.0% of applied dose for epidermis and dermis, respectively) upon application of the sunscreen complexed with SBE-β-CD, whereas HP-β-CD had no effect. In addition, photostability experiments demonstrated that SBE-β-CD complexation did not alter the sunscreen photochemical properties.     

Excess molar enthalpies of the ternary mixtures: (diisopropyl ether or 2-methyltetrahydrofuran) + cyclohexane + n-heptane at 298.15 K

Microcalorimetric measurements of excess molar enthalpies, at 298.15 K, are reported for the two ternary systems formed by mixing either diisopropyl ether or 2-methyltetrahydrofuran with binary mixtures of cyclohexane and n-heptane. Smooth representations of the results are presented and used to construct constant excess molar enthalpy contours on Roozeboom diagrams. It is shown that useful estimates of the ternary enthalpies can be obtained from the Liebermann and Fried model, using only the physical properties of the components and their binary mixtures.