Optimal partitions having disjoint convex and conic hulls

LetA ¹,,A ⁿ be distinctk-dimensional vectors. We consider the problem of partitioning these vectors intom sets so as to maximize an objective which is a quasi-convex function of the sum of vectors in each set. We show that there exists an optimal partition whose sets have (pairwise) disjoint conic hulls. We also show that if the number of vectors in each of the sets is constrained, then a weaker conclusion holds, namely, there exists an optimal partition whose sets have (pairwise) disjoint convex hulls. The results rely on deriving necessary and sufficient conditions for a point to be an extreme point of a corresponding polytope.Research of this author was partially supported by NSF Grant ECS-83-10213 and by a Grant for the Promotion of Research at the Technion.     

Synthesis and characterisation of transition metal halide complexes of the xylyl-distibine, 1,2-bis(dimethylstibanylmethyl)benzene

Complexes of the title ligand with Cu(I), Ag(I), Au(I), Pd(II), Pt(II), Rh(III), and rare examples with Ni(II) and Co(III) have been prepared and characterised by analysis, IR, UV-vis, 1H, 63Cu and 59Co NMR spectroscopy and ES+ mass spectrometry as appropriate. The structures of [Cu[1,2-C6H4(CH2SbMe2)2]2]BF4, [PtCl2[1,2-C6H4(CH2SbMe2)2]], [M[1,2-C6H4(CH2SbMe2)2]2][PF6]2 (M = Pd or Pt), and [NiI[1,2-C6H4(CH2SbMe2)2]2]ClO4 have been determined, and the varying chelate bite and conformations of the xylyl backbone in these structures are discussed. Despite the unfavourable seven-membered chelate ring and the large soft antimony donors, 1,2-C6H4(CH2SbMe2)2 proves to be a surprisingly good ligand for late transition metals in medium oxidation states.     

Electrically actuated, pressure-driven microfluidic pumps

In order to make the lab-on-a-chip concept a reality, it is desirable to have an integrated component capable of pumping fluids through microchannels. We have developed novel, electrically actuated micropumps and have integrated them with microfluidic systems. These devices utilize the build-up of electrolysis gases to achieve pressure-driven pumping, only require small voltages (approximately 10 V), and have approximate dimensions of 5 cm x 3 cm x 2 cm. Furthermore, these micropumps are composed of relatively inexpensive materials, and the reversible sealability of their poly(dimethylsiloxane) body to different microfluidic arrays enables repeated uses of the same pump. Under an applied potential of 10 V, three different micropumps had average flow rates of 8-13 microL min(-1) for water being pumped through five different 2 cm-long, 5500 microm(2) cross-sectional-area channels in poly(methyl methacrylate), in approximate agreement with predicted pump rates. We have also evaluated pump operation at the lower applied potential of 8 V and observed an average flow rate of 6.1 microL min(-1) for a pump-channel system. The current micropump design is capable of sustaining pumping pressures in the range of 300 kPa. The various advantages of these micropumps make them well suited for use in lab-on-a-chip analysis techniques.     

Benzothiazines in synthesis. Toward the synthesis of pseudopteroxazole

[reaction: see text] The tricyclic benzothiazine 15 was prepared in a straightforward fashion via a completely stereoselective intramolecular Friedel-Crafts alkylation. This compound represents a potential precursor to the antitubercular agent, pseudopteroxazole. Its synthesis proceeded via a completely selective, intramolecular addition of a sulfoximine-stabilized carbanion to an alpha,beta-unsaturated ester, followed by functional group manipulations.     

Development, validation and transfer of a hydrophilic interaction liquid chromatography/tandem mass spectrometric method for the analysis of the tobacco-specific nitrosamine metabolite NNAL in human plasma at low picogram per milliliter concentrations

A highly sensitive bioanalytical method based on a simple liquid/liquid extraction and hydrophilic interaction liquid chromatography with tandem mass spectrometry (HILIC/MS/MS) analysis has been developed, validated and transferred for the determination of 4-(methylnitrosamino)-1-(3-pyridyl)-1-butanol (NNAL), a tobacco-specific nitrosamine metabolite. Deuterated NNAL (NNAL-d(4)) was synthesized and used as the internal standard. This method can be used for the analysis of free and total NNAL (free NNAL plus NNAL-gluc) in K(3)-EDTA human plasma. Free NNAL and NNAL-d(4) are extracted from human plasma by liquid/liquid extraction. To analyze for total NNAL and the internal standard, a separate aliquot of the K(3)-EDTA human plasma is treated with beta-glucuronidase to deconjugate the NNAL-gluc; the total NNAL and internal standard are then extracted using liquid/liquid extraction. After drying down under nitrogen, the residue is reconstituted with acetonitrile and analyzed using positive ion electrospray and HILIC/MS/MS at a flow rate of 1.0 mL/min. The chromatographic run time is 1.0 min per injection, with retention time for both NNAL and NNAL-d(4) of 0.75 min with a capacity factor (k') of 2. The standard curve range for this assay is from 5.00-1000 pg/mL for both free and total NNAL, using a total plasma sample volume of 1.0 mL. The interday precision and accuracy of the quality control (QC) samples demonstrated <7.6% relative standard deviation (RSD) and <3.3% relative error (RE) for free NNAL. For total NNAL, the interday precision and accuracy of the QC samples demonstrated <11.7% RSD and <2.8% RE. Optimization of enzyme hydrolysis of NNAL-gluc is discussed in detail. The overall recoveries for free and total NNAL and IS were 68.2 and 71.5% (free) and 70.7 and 65.5% (total). No adverse matrix effects were noticed for this assay.     

The use of inverse gas chromatography to study surface thermal oxidation of polypropylene

Thermo-oxidative effects on the surface energy of polypropylene were measured by inverse gas chromatography as a function of exposure time and temperature. Unaltered polypropylene had a surface energy of 33 mJ/m². Oxidized polypropylene, after exposure to air at temperatures of 100 °C and 110 °C, had a range of maximum surface energies from 38 to 41 mJ/m². Comparisons between FTIR carbonyl peak growth and the surface energy showed that both methods detect oxidation, though the increase in surface energy is detected before the carbonyl peak growth is noticeable. The work of adhesion predicted by the surface free energies obtained in this work between a coated calcium carbonate and polypropylene changes by 10% due to the oxidation of the polymer at 110 °C.