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     

The Orbit Rigidity Matrix of a Symmetric Framework

A number of recent papers have studied when symmetry causes frameworks on a graph to become infinitesimally flexible, or stressed, and when it has no impact. A number of other recent papers have studied special classes of frameworks on generically rigid graphs which are finite mechanisms. Here we introduce a new tool, the orbit matrix, which connects these two areas and provides a matrix representation for fully symmetric infinitesimal flexes, and fully symmetric stresses of symmetric frameworks. The orbit matrix is a true analog of the standard rigidity matrix for general frameworks, and its analysis gives important insights into questions about the flexibility and rigidity of classes of symmetric frameworks, in all dimensions.     

Development and reproducibility of a novel high‐performance liquid‐chromatography monolithic column method for the detection and quantification of trans‐indolyl‐3‐acryloylglycine in human urine

Elevated levels of trans‐indolyl‐3‐acryloylglycine (IAcrGly) have been reported in the urine of people with various conditions including pervasive developmental disorders (PDDs) such as autism and Asperger syndrome. Reversed‐phase high‐performance liquid chromatography with ultra‐violet detection using traditional particle silica‐based columns subsequent to solid‐phase extraction (SPE) has been the preferred assay method; requiring long analytical run times, high flow rates and high solvent usage. Recent developments in monolithic HPLC column technology facilitated the development of a novel analytical method, for the detection and quantification of urinary IAcrGly. The revised method eliminates the requirement for SPE pre‐treatment, reduces sample run‐time and decreases solvent volumes. Five urine samples from people diagnosed with PDD were run in quadruplicate to test the intra‐ and inter‐day reliability of the new method based on retention time, peak area and peak height for IAcrGly. Detection was by UV with IAcrGly confirmation by MS/MS‐MS. Relative standard deviations showed significant improvement with the new method for all parameters. The new method represents a major advancement in the detection and quantification of IAcrGly by reducing time and cost of analysis whilst improving detection limits and reproducibility. Copyright © 2009 John Wiley & Sons, Ltd.     

Ueber die Bestimmung von Gerbs?ure

Ohne Zusammenfassung     

Rigidity and polarity

Any projective polarity in 3-space transforms a statically (or equivalently, infinitesimally) rigid bar-and-joint framework into a statically rigid hinged sheetwork — a set of plane-statically rigid sheets, joined in pairs along hinge lines. In the more general class of jointed sheetworks, which is closed under polarity, static rigidity is also preserved by the polarities. In particular, the class of infinitesimally (or statically) rigid polyhedra, built with joints at the vertices and bars triangulating the faces, is closed under polarity.Work supported, in part, by grants from N.S.E.R.C. (Canada) and F.C.A.C. (Quebec), and a visiting appointment at McGill University.     

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.     

Analysis of chromates for traces of Cr(III) by solvent extraction and inductively coupled plasma atomic emission spectrometry

Summary A method for the determination of quantities of 0.5–500 g of Cr(III) in the presence of chromates and dichromates is described. The samples are dissolved in an aqueous solution buffered at pH 7.0; the Cr(III) is selectively chelated with 2-thenoyltrifluoroacetone and extracted into xylene. The extracted chromium is analyzed using inductively coupled plasma emission spectrometry. Extraction of 1.0 g Cr(III) from 5.0 mg K₂Cr₂O₇ was accomplished and easily determined in a volume of 25 ml of xylene. The relative standard deviation for the determination of Cr(III) contents ranging from 4.0 × 10^–8 g/ml to 2.0 × 10^–8 g/ml was ± 0.079. Using a minimum signal to noise ratio of 101, the detection limits of the method were determined to be approximately 2.0 × 10^–8 g/ml xylene. Chloride, high surface area silica, and easily oxidized amorphous boron give rise to only minor interferences.

---

Analyse von Cr(III)-Spuren in Chromaten durch Extraktion und ICP-Atomemissionsspektrometrie

Zusammenfassung Ein Verfahren wird beschrieben zur Bestimmung von 0,5–500 g Cr(III) in Gegenwart von Chromaten und Dichromaten. Die Proben werden in Pufferlösung pH 7,0 gelöst, und 2-Thenoyltrifluoraceton behandelt und Cr(III) selektiv mit Xylol extrahiert. Die Bestimmung erfolgt durch ICP-Spektrometrie. 1,0 g Cr(III) konnte von 5,0 mg K₂Cr₂O₇ getrennt und in einen Volumen von 25 ml Xylol bestimmt werden. Die relative Standardabweichung im Bereich von 4,0 · 10^–8 bis 2,0 · 10^–7 g Cr(III)/ml betrug ± 0,079. Bei einem Verhältnis SignalUntergrund = 101 wurden Nachweisgrenzen um 2,0 · 10^–8 g/ml gefunden. Störungen durch Chlorid, Siliciumdioxid und amorphes Bor sind gering.

---

---

This work was supported by the U.S. Department of Energy (DOE) under contract number DE-AC04-76-DP00789

---

A U.S. DOE facility     

Transition metal derivatives of 1,1′-dichloroferrocene

Complexes of the general formula [Cl₂Fc] _nML, (Cl₂Fc = C1C₅H₄FeC₅H₃Cl; ML = Fe(CO)₂C₅H₅, AuP(C₆H₅)₃, Mn(CO)₅ or Ir(CO)[P(C₆H₅)₃]₂ when n = 1; ML = Ti(C₅H₅)₂ when n = 2) have been prepared from a salt elimination reaction between 1,1′-dichloro-2-lithioferrocene and transition metal halide complexes. Spectroscopic properties of the compounds are reported. The titanium complex exists in meso and dl forms.     

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.