Global Analysis of the Flows of Fluids with Pressure-Dependent Viscosities

 To describe the flows of fluids over a wide range of pressures, it is necessary to take into account the fact that the viscosity of the fluid depends on the pressure. That the viscosity depends on the pressure has been verified by numerous careful experiments. While the existence of solutions local-in-time to the equations governing the flows of such fluids are available for small, special data and rather unrealistic dependence of the viscosity on the pressure, no global existence results are in place. Our interest here is to establish the existence of weak solutions for spatially periodic three-dimensional flows that are global in time, for a large class of physically meaningful viscosity-pressure relationships. (Accepted May 1, 2002) Published online November 15, 2002 Communicated by S. S. ANTMAN     

Stereoselective total syntheses of (±)-warburganal and (±)-isotadeonal

A short, stereoselective synthesis of (±)-warburganal ($\text{1}$), its C-9 epimer ($\text{2}$) and the related sesquiterpene dialdehyde (±)-isotadeonal is presented.     

Liner as the Key of Injection Optimization in Pesticide Analysis

Regulations for pesticide residue analysis in food require very low detection limits; thus requiring maximum sensitivity in the gas chromatographic determination. This is accomplished by an overall method optimisation, which includes optimisation of injector parameters. Here we study the effect of the inlet liner design on the optimisation by comparing five liner designs in splitless and pulsed splitless injection modes, using a test mixture of fifteen pesticides analyzed by GC-ECD. Possible links between the injection parameters and liner types were evaluated, with the result that, accurate choice of inlet liner and injection parameters can reduce detection limits by up to 300%. Revised: 25 October 2005 and 9 January 2006     

Ketopiperazines: Conformationally Constrained Peptidomimetic of Arginine Amides

We have synthesized guanidine‐containing ketopiperazines designed to be conformational mimics of peptidomimetic arginine amides. D‐Allylglycine was converted by an efficient approach to give enantiopure ketopiperazines in which the trans stereochemistry of the C‐substituents resulted from stereospecific enolate alkylation.     

Synthesis of 1-Hydroxyoxindoles

A convenient synthesis of various substituted 1-hydroxyoxindoles is described.     

Trace level triacetone-triperoxide identification with SPME–GC-MS in model systems

Triacetone-triperoxide is a high explosive mainly used by terrorist groups. With the spreading of the recipe on the Internet, increasing number of bomb attacks are being reported worldwide using triacetone-triperoxide. A simple identification method is described using 100 μm polydimethyl siloxane fibre solid phase microextraction and gas chromatography combined with spectrometry. The method was tested on various pre- and post-explosion models that can be collected in a house search or after a bomb attack. Sample preservation and stability was also examined. Identification of triacetone-triperoxide residues in post-explosion models was feasible 24 h after ignition, the detection limit being 5 ng.     

Palladium-mediated transannular cyclizations of medium-ring olefinic enolsilanes

Medium-ring olefinic ketone and lactone enolsilanes were subjected to palladium(II)-mediated cycloalkenylation conditions. Diverse bicyclic ring products were obtained in moderate to good yields. The effect of olefin geometry and ring size is discussed.     

Guided modes of integrated optical guides. A mathematical study

A waveguide in integrated optics is defined by its refractiveindex. The guide is assumed to be invariant in the propagationdirection while in the transverse direction it is supposed tobe a compact perturbation of an unbounded stratified medium.We are interested in the modes guided by this device, whichare waves with a transverse energy confined in a neighbourhoodof the perturbation. Our goal is to analyse the existence of such guided modes. Underthe assumptions of weak guidance the problem reduces to a two-dimensionaleigenvalue problem for a scalar field. The associated operatoris unbounded, selfadjoint, and bounded from below. Its spectrumconsists of the discrete spectrum corresponding to the guidedmodes and of the essential spectrum corresponding to the radiationmodes. We present existence results of guided modes and an asymptoticstudy at high frequencies, which shows that contrarily to thecase of optical fibers, the number of guided modes can remainbounded. The major tools are the min-max principle and comparisonof results between different eigenvalue problems. The originalityof the present study lies in the stratified character of theunbounded reference medium.     

An unusual rearrangement during pyridine synthesis. Anomalous condensation of a β-keto enamine with a tetronic acid.

The condensation of β-keto enamine 1 with 5-methyltetronic acid takes an anomalous course. Single crystal X-ray analysis and chemical evidence establish the rearranged pyridine structure 15 for this condensation product.     

2,3-Dihydrophenalen-2-one and the structure of “blue 342”

Syntheses of the labile ketone $\text{6}$ are described. Bromine rapidly converts $\text{6}$ to a deep blue substance, C₂₆H₂₀O, for which the heptacyclic structure $\text{15}$ is uniquely established.