Linear stability diagrams for the shear flow of an Oldroyd-B fluid with slip along the fixed wall

We consider the time-dependent shear flow of an Oldroyd-B fluid with slip along the fixed wall. Slip is allowed by means of a generic slip equation predicting that the shear stress is a non-monotonic function of the velocity at the wall. The complete one-dimensional stability analysis to one-dimensional disturbances is carried out and the corresponding neutral stability diagrams are constructed. Asymptotic results for large values of the elasticity number and finite element calculations are also presented. The instability regimes are within or coincide with the negative-slope regime of the slip equation. The numerical calculations agree with the linear stability results when the size of the initial perturbation is small. Large perturbations may destabilize a linearly stable steady state, leading to a periodic solution. The period and the amplitude of the periodic solutions increase with elasticity. Received: 19 June 1997 Accepted: 22 September 1997     

Formation of eight-membered ring β-keto lactones via the intramolecular trapping of hydroxy acylketenes

Eight-membered ring β-keto lactones were prepared from 2,2,6-trimethyl-4H-1,3-dioxin-4-one in three steps involving conjugate addition to α,β-unsaturated aldehydes or ketones, followed by conversion to an alcohol and thermolysis. The formation of these eight-membered rings involves the intramolecular trapping of a hydroxy acyl ketene intermediate and is facilitated by a suppressed ring strain and an unfavorable intramolecular hydrogen bond, which is suggested to favor the formation of oligomers. These aspects of the reaction were supported by molecular mechanics calculations.     

A new exact algorithm for the vehicle routing problem based onq-paths andk-shortest paths relaxations

We consider the basic Vehicle Routing Problem (VRP) in which a fleet ofM identical vehicles stationed at a central depot is to be optimally routed to supply customers with known demands subject only to vehicle capacity constraints. In this paper, we present an exact algorithm for solving the VRP that uses lower bounds obtained from a combination of two relaxations of the original problem which are based on the computation ofq-paths andk-shortest paths. A set of reduction tests derived from the computation of these bounds is applied to reduce the size of the problem and to improve the quality of the bounds. The resulting lower bounds are then embedded into a tree-search procedure to solve the problem optimally. Computational results are presented for a number of problems taken from the literature. The results demonstrate the effectiveness of the proposed method in solving problems involving up to about 50 customers and in providing tight lower bounds for problems up to about 150 customers.     

Determination of malathion, coumaphos, and fluvalinate residues in honey by gas chromatography with nitrogen-phosphorus or electron capture detectors

A rapid, reliable, and inexpensive extraction method was developed to determine acaricide residues in honey by gas chromatography (GC) with nitrogen-phosphorus (NP) or electron capture (EC) detectors. Because of the high selectivity of the NP detector, no interfering peaks were present and no cleanup was necessary. A simple cleanup step is proposed for the GC-ECD analysis. Recoveries from spiked honey samples ranged from 79 to 94.4%, with coefficients of variation of 0.3-18.5%. The quantitation limit obtained was 0.015 mg/kg for malathion, 0.020 mg/kg for coumaphos, and 0.005 mg/kg for fluvalinate. The method was used to determine the disappearance of malathion and coumaphos residues from honey samples collected from beehives treated with these acaricides. The disappearance of both acaricides was rapid and followed a first-order model for the duration of the experiment.     

Automated flow injection spectrophotometric determination of para- and meta-substituted phenols of pharmaceutical interest based on their oxidative condensation with 1-nitroso-2-naphthol

The reaction of para- and meta-substituted phenols with 1-nitroso-2-naphthol in the presence of either CeIV or PbIV as an oxidant has been used to develop a fast automated flow injection (Fl) method. A stopped-flow kinetic study of the reaction revealed the optimum conditions for the proposed Fl method. Acetaminophen, amoxicillin, cefadroxil, isoxsuprine, nylidrin, propylparaben, tyrosine and metaraminol can be determined in the range 1 x 10(-4)-8 x 10(-4) M, with relative standard deviations of less than 2%, and a measurement throughput of 40 measurements h-1. The method was evaluated by performing interference studies of common excipients and assaying commercial formulations of acetaminophen and isoxsuprine. The results were in good agreement with those obtained by acceptable spectrophotometric or high-performance liquid chromatographic methods (mean difference 2.1%). The high sample throughput of the Fl method was exploited by performing a content uniformity test of isoxsuprine tablets.     

Flow-injection stopped-flow kinetic spectrophotometric determination of drugs, based on micellar-catalysed reaction with 1-fluoro-2,4-dinitrobenzene

A flow-injection stopped-flow kinetic spectrophotometric method for the determination of hydrazines, hydrazides, amines and amino-acids, based on the cetyltrimethylammonium bromide catalysed reaction with 1-fluoro-2,4-dinitrobenzene is described. With the proposed method dihydralazine, isoniazid, levodopa and aspartame can be determined at concentrations of 0.1-6 x 10(-4)M. The calibration ranges can be varied by adjusting the pH and surfactant concentration. The determination of amphetamine, cysteine, s-carboxymethylcysteine, cephalexin, tobramycin and gentamicin is also feasible. The method has been applied to the determination of levodopa, isoniazid and aspartame in commercial pharmaceutical formulations. The determination of isoniazid in formulations containing the highly coloured antibiotic rifamycin, and of aspartame in coloured beverages was also accomplished. The results were in good agreement with those obtained by reference methods and the throughput was 40 measurements per hour with 0.4-3.9% RSD.     

Stereoselective synthesis of anti-alpha-(difluoromethyl)-beta-amino alcohols by boronic acid based three-component condensation. Stereoselective preparation of (2S,3R)-difluorothreonine

Starting from optically active 3,3-difluorolactaldehyde, an alkenyl or aryl boronic acid, and an amine, a one-step three-component methodology was developed for the stereoselective preparation of anti-alpha-(difluoromethyl)-beta-amino alcohols. beta-Furyl-substituted anti-alpha-(difluoromethyl)-beta-amino alcohol was further elaborated to form (2S,3R)-difluorothreonine in high yield and ee.     

Lipoxins and Related Eicosanoids: Biosynthesis,Biological Properties,and Chemical Synthesis

Among the various enzymes found in human tissues that act on arachidonic acid, there are three major types of lipoxygenases (LO), operating at the 5-, 12-, and 15-positions. The 5-LO is a key enzyme and plays a central role in the biosynthesis of leukotrienes, which are potent arachidonate-derived mediators of allergy and inflammation. Because of the importance of the 5-LO-derived products in human pathophysiology, studies were initiated to examine the consequences of initial lipoxygenation at C15 of arachidonic acid as well as to probe interactions between the major LO pathways. These studies led to the identification of a new series of biologically active tetraene-containing eicosanoids termed lipoxins. This article summarizes the isolation, biosynthesis, and chemical synthesis of lipoxins and related systems, and reviews recent results concerning their formation and biological activities. The total synthesis of these molecules based on a new and general synthetic strategy involving palladium catalysis is reviewed. This synthetic approach has allowed the preparation of several types of acyclic eicosanoids in their naturally occurring forms which, in turn, allowed comparisons with naturally derived materials and enabled detailed studies of the biological actions of these biomolecules. Structure–activity relationships were also derived by combining chemical synthesis and biological investigations.     

Variational Formulas and Cocycle solutions for Directed Polymer and Percolation Models

We discuss variational formulas for the law of large numbers limits of certain models of motion in a random medium: namely, the limiting time constant for last-passage percolation and the limiting free energy for directed polymers. The results are valid for models in arbitrary dimension, steps of the admissible paths can be general, the environment process is ergodic under spatial translations, and the potential accumulated along a path can depend on the environment and the next step of the path. The variational formulas come in two types: one minimizes over gradient-like cocycles, and another one maximizes over invariant measures on the space of environments and paths. Minimizing cocycles can be obtained from Busemann functions when these can be proved to exist. The results are illustrated through 1+1 dimensional exactly solvable examples, periodic examples, and polymers in weak disorder.