Complexity of the Gravitational Method for Linear Programming

In the gravitational method for linear programming, a particle is dropped from an interior point of the polyhedron and is allowed to move under the influence of a gravitational field parallel to the objective function direction. Once the particle falls onto the boundary of the polyhedron, its subsequent motion is constrained to be on the surface of the polyhedron with the particle moving along the steepest-descent feasible direction at any instant. Since an optimal vertex minimizes the gravitational potential, computing the trajectory of the particle yields an optimal solution to the linear program.Since the particle is not constrained to move along the edges of the polyhedron, as the simplex method does, the gravitational method seemed to have the promise of being theoretically more efficient than the simplex method. In this paper, we first show that, if the particle has zero diameter, then the worst-case time complexity of the gravitational method is exponential in the size of the input linear program. As a simple corollary of the preceding result, it follows that, even when the particle has a fixed nonzero diameter, the gravitational method has exponential time complexity. The complexity of the version of the gravitational method in which the particle diameter decreases as the algorithm progresses remains an open question.     

Oxygen Sensors Based on a Quenching of Tris-(4,7-diphenyl-1,10-phenanthroline)ruthenium(II) in Fluorinated Polymers

Luminescence quenching of Ru(II) complexes by oxygen has proved a powerful method of quantitative oxygen analysis. It has become clear that the polymer support for the sensor molecule plays a pivotal role in the sensor performance. The current work is devoted to understanding how the physical and photophysical properties of a sensor respond to changes in polymer composition. An oxygen quenching study was conducted on [Ru(Ph₂phen)₃]Cl₂(Ph₂phen=4,7-diphenyl-1,10-phenanthroline), in copolymer supports consisting of GP-163 (a polydimethylsiloxane (PDMS) with varying amounts of pendant acrylate groups) combined with a number of alkyl methacrylates with long chain alkyl or fluorinated alkyl esters. Increasing the chain length or the degree of fluorination on the hydrocarbon chains enhances performance. However, there is an optimal chain length for the fluorinated hydrocarbons for sensitivity, linearity, and physical properties. Too long a chain yields reduced quenching sensitivity and yields cloudy polymers. All systems showed some degree of heterogeneity as indicated by nonlinear Stern-Volmer quenching plots, but their intensity quenching data could be successfully fit with a two-site model.     

Blue‐Light‐Emitting Conjugated Polymers Derived From 2,7‐Carbazoles

Blue‐light‐emitting 2,7‐carbazole‐based conjugated copolymers have been prepared by Yamamoto or Suzuki cross‐coupling reactions. By introducing highly substituted aromatic comonomers, fully soluble high‐molecular‐weight copolymers have been obtained. Moreover, these amorphous polymeric materials exhibit good thermal stability and interesting redox properties. All these features make these new conjugated polymers highly promising for the development of single‐polymer‐layer blue‐light‐emitting diodes.

     

Considerations on Static and Dynamic Sorptive and Adsorptive Sampling to Monitor Volatiles Emitted by Living Plants

Static and dynamic headspace sampling have been applied for the enrichment of volatiles emitted by living plants. For solid phase microextraction (SPME) the sorptive fibers polydimethylsiloxane (PDMS) and polyacrylate (PA) have been compared and, in accordance with the like‐like principle, polar compounds exhibit more affinity for the PA fiber while apolar solutes favor the PDMS fiber. For dynamic sampling, tubes packed with PDMS particles show greater inertness than Tenax; some Tenax decomposition products, e.g. benzaldehyde and acetophenone, interfere with the analyses. With PDMS particles operated in the breakthrough mode, the obtained profiles are similar to those obtained by SPME on the PA fiber. Recoveries relative to a packed PDMS bed are 85% for Tenax, 2.4% for SPME‐PDMS, and 6.2% for SPME‐PA.     

Sorption Tubes Packed with Polydimethylsiloxane: A New and Promising Technique for the Preconcentration of Volatiles and Semi-Volatiles from Air and Gaseous Samples

This paper is concerned with the determination of volatile and semi-volatile organic components in air and gaseous (headspace) samples, focusing primarily on polar analytes. Samples were analyzed by preconcentration on different (ad)sorbents followed by thermal desorption and analysis by capillary gas chromatography. The performance of a cartridge filled with 100% polydimethylsiloxane (PDMS) particles was compared to that of adsorbents like Tenax TA and Carbotrap 300. Though the PDMS phase is non-polar it showed adequate retention for both polar and non-polar components. The blank runs of the PDMS trap were significantly better than those of most adsorbents and did not deteriorate, as was the case with all the conventional adsorbents investigated. With respect to trapping efficiencies, the PDMS phase performed better for most of the analytes under investigation compared to the adsorbents. For a range of analytes including triethylamine, butanone, diacetyl, nicotine, and acetic acid the PDMS phase performed exceptionally well whereas all adsorbents showed unsatisfactory performance. The packed PDMS traps were employed for the determination of organic acids, PAH's and nitro-PAH's in air and for the analysis of the headspace of cacao and hop.     

Experimentation with Chiral CE: The Application of Two Chiral Selectors and Partial Filling with Chiral Selector

Data on the use of two chiral selectors, namely 18-crown-6 tetracarboxylic acid and a negatively charged cyclodextrin derivative (sulfated-β-cyclodextrin or carboxymethyl-β-cyclodextrin), in the same background electrolyte are presented. The use of such dual systems has a considerable influence on the resolution, as illustrated for the separation of tryptophan derivatives. Reduction of the consumption of chiral selector without significant loss in resolution was obtained by only partly filling the capillary and applying a run buffer without selector. This is illustrated for the chiral separation of tryptophan hydroxamate and the diastereomeric and enantiomeric separation of the dipeptide α/b-AspPhe-OMe.