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     

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.     

Interaction of the mu-opioid receptor with GPR177 (Wntless) inhibits Wnt secretion: potential implications for opioid dependence

Background  

Opioid agonist drugs produce analgesia. However, long-term exposure to opioid agonists may lead to opioid dependence. The analgesic and addictive properties of opioid agonist drugs are mediated primarily via the mu-opioid receptor (MOR). Opioid agonists appear to alter neuronal morphology in key brain regions implicated in the development of opioid dependence. However, the precise role of the MOR in the development of these neuronal alterations remains elusive. We hypothesize that identifying and characterizing novel MOR interacting proteins (MORIPs) may help to elucidate the underlying mechanisms involved in the development of opioid dependence.     

Two new coumarins from <Emphasis Type="Italic">Euonymus hamiltonianus</Emphasis>

Two new coumarins, euonidiol (1) and euoniside (2), and a known flavone, luteolin 7-methyl ether, were isolated from the aerial parts of the plant Euonymus hamiltanianus Wall. All the compounds were characterized on the basis of spectral analysis viz. ¹H NMR, ¹³C NMR, DEPT, IR, UV, ESI-MS, and elemental analysis. Published in Khimiya Prirodnykh Soedinenii, No. 1, pp. 10–11, January–February, 2008.     

High precision delta(17)O isotope measurements of oxygen from silicates and other oxides: method and applications

The use of infrared laser-assisted fluorination to release oxygen from milligram quantities of silicates or other oxide mineral grains is a well-established technique. However, relatively few studies have reported the optimisation of this procedure for oxygen-17 isotope measurements. We describe here details of an analytical system using infrared (10 μm) laser-assisted fluorination, in conjunction with a dual inlet mass spectrometer of high resolving power ( approximately 250) to provide (17)O and (18)O oxygen isotope measurements from 0.5-2 mg of silicates or other oxide mineral grains. Respective precisions (1) of typically 0.08 and 0.04 per thousand are obtained for the complete analytical procedure. Departures from the mass-dependent oxygen isotope fractionation line are quantified by Delta(17)O; our precision (1) of such measurements on individual samples is shown to be +/-0.024 per thousand. In turn, this permits the offset between parallel, mass-dependent fractionation lines to be characterised to substantially greater precision than has been possible hitherto. Application of this system to investigate the (17)O versus (18)O relationship for numerous terrestrial whole-rock and mineral samples, of diverse geological origins and age, indicates that the complete data set may be described by a single, mass-dependent fractionation line of slope 0.5244+/- 0.00038 (standard error). Copyright 1999 John Wiley & Sons, Ltd.     

Glutinane triterpenes from the stem bark of <Emphasis Type="Italic">Euonymus hamiltonianus</Emphasis>

Three new glutinane-type triterpenes, 19α-glutin-5-en-19-ol (1), 2β,15α,21β-glutin-11-ene-2,15,21-triol (2), and 2β,19α-glutin-7,21-diene-2,19-diol (3), were isolated from the stem bark of Euonymus hamiltonianus. Their structures were determined by 1D and 2D NMR along with MS and IR. Published in Khimiya Prirodnykh Soedinenii, No. 3, pp. 321–323, May–June, 2009.     

Test of bell’s inequality using the one-atom micromaser

We examine a local realist bound in the case of a one-atom micromaser. It is shown that such a bound is violated using a simplified treatment of the micromaser. We consider the effect of dissipation in a proposed experiment with the real micromaser. It is seen that the magnitude of violation of a Bell-type inequality depends significantly on the cavity parameters.     

Evaluation of the precision of drop-size determination in oil/water emulsions by low-resolution NMR spectroscopy

The accuracy of the recently reported low-resolution NMR method (Goudappel, G. J. W.; et al. J. Colloid Interface Sci. 2001, 239, 535) for the determination of drop-size distribution in oil-in-water emulsions is evaluated by comparing the NMR results with precise data from video-enhanced optical microscopy. A series of 27 soybean-oil-in-water emulsions, differing in their mean drop size, polydispersity, oil volume fraction, and emulsifier, is studied. Soybean oil is selected as a typical component of food emulsions. The experimental error of our optical procedure for drop-size determination is estimated to be around 0.3 microm, which allows us to use the microscopy data as a reference for the mean drop-size and distribution width of the studied emulsions, with known experimental error. The main acquisition parameters in the NMR experiment are varied to find their optimal values and to check how the experimental conditions affect the NMR results. Comparison of the results obtained by the two methods shows that the low-resolution NMR method underestimates the mean drop size, d33, by approximately 20%. For most of the samples, NMR measures relatively precisely the distribution width (+/-0.1 to 0.2 dimensionless units), but for approximately 20% of the samples, larger systematic deviation was registered (underestimate by 0.3-0.4 units). No correlation is found between the emulsion properties and the relative difference between the microscopy and NMR data. Possible reasons for the observed discrepancy between NMR and optical microscopy are discussed, and some advantages and limitations of the low-resolution NMR method are considered.     

Preparative high-performance liquid chromatographic separation of naphthodianthrones from St. John's Wort

St. John's Wort (Hypericum perforatum), a perennial flowering plant, has been used medicinally for thousands of years and has most recently been identified as an effective treatment for mild to moderate depression and neuralgic disorders. This work presents a procedure for the isolation of naphthodianthrones from St. John's Wort by an accelerated extraction and separation of marker compounds by preparative high-performance liquid chromatography (HPLC) with photodiode array detection. The accelerated extraction method minimizes the extraction time and increases the yield, and the marker compounds obtained by preparative HPLC are of 98% purity. The compounds are characterized by liquid chromatography-mass spectrometry (electrospray ionization) and NMR spectra.     

Crystallographic analysis of 9-(3-methylbut2-enyloxyfurano)[3,2-g] benzopyran-2-one

This structure of 9-(3-methylbut-2-enyloxyfurano)[3,2-g] benzopyran-2-one has been determined by X-ray diffraction methods. The compound crystallizes in the triclinic (space group P \(bar 1\)) with the unit cell parameters a = 11.1150(10), b = 11.8240(10), c = 11.9290(10) Å, α = 64.90(1)^°, β = 83.53(1)^°, γ = 89.25(1)^° and Z = 4. The structure has been solved by direct methods and refined to reliability index of 0.043. The unit cell contains two crystallographically independent molecules in the asymmetric unit, which exhibit different side-chain conformations. The crystal structure is stabilized by the intra molecular and intermolecular C–H?sO interactions.