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     

Precursor decomposition and nucleation kinetics during platelike apatite synthesis

Self-organization of calcium and phosphorus precursors in solution containing acetic acid and ethylene glycol produces a nanosized lamellar acetate-phosphonate hybrid containing two acetate and one phosphonate components. The lamellar morphology of the hybrid precursor is responsible the formation of platelike apatite product after thermal treatment at or above 400 degrees C. However a preliminary preheating stage (300 degrees C, 24 h) is crucial in determining the morphology of the apatite. Activation energy measurements by nonisothermal thermogravimetric analysis show that decomposition of the hybrid precursor involves at least two steps. Among the three components, it appears that the calcium acetate bidentate chelate component is stable below or at 300 degrees C. However, the calcium phosphonate and calcium acetate monodentate components are decomposed at this temperature. Above 360 degrees C, nuclear magnetic resonance and infrared spectroscopic data reveal the decomposition of more stable calcium acetate bidentate chelate. It is evident that the bond rupture of the bidentate calcium acetate species in the precursor results in the start of crystalline apatite formation but the other components must be decomposed by heating prior to this critical step in order to produce platelike apatite.     

Stability of linear systems of differential equations with variable structure and impulse effect

In the present paper sufficient conditions for stability of the solutions of linear systems of differential equations with variable structure and impulse effect are found.     

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.     

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.     

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.     

Surfactant-Mediated and Morphology-Controlled Nanostructured LiFePO4/Carbon Composite as a Promising Cathode Material for Li-Ion Batteries

The synthesis of morphology-controlled carbon-coated nanostructured LiFePO₄ (LFP/Carbon) cathode materials by surfactant-assisted hydrothermal method using block copolymers is reported. The resulting nanocrystalline high surface area materials were coated with carbon and designated as LFP/C123 and LFP/C311. All the materials were systematically characterized by various analytical, spectroscopic and imaging techniques. The reverse structure of the surfactant Pluronic® 31R1 (PPO-PEO-PPO) in comparison to Pluronic® P123 (PEO-PPO-PEO) played a vital role in controlling the particle size and morphology which in turn ameliorate the electrochemical performance in terms of reversible specific capacity (163 mAh g⁻¹ and 140 mAh g⁻¹ at 0.1 C for LFP/C311 and LFP/C123, respectively). In addition, LFP/C311 demonstrated excellent electrochemical performance including lower charge transfer resistance (146.3 Ω) and excellent cycling stability (95 % capacity retention at 1 C after 100 cycles) and high rate capability (163.2 mAh g⁻¹ at 0.1 C; 147.1 mAh g⁻¹ at 1 C). The better performance of the former is attributed to LFP nanoparticles (<50 nm) with a specific spindle-shaped morphology. Further, we have also evaluated the electrode performance with the use of both PVDF and CMC binders employed for the electrode fabrication.     

Discovering New Classes of <Emphasis Type="Italic">Brugia malayi</Emphasis> Asparaginyl-tRNA Synthetase Inhibitors and Relating Specificity to Conformational Change

SLIDE software, which models the flexibility of protein and ligand side chains while docking, was used to screen several large databases to identify inhibitors of Brugia malayi asparaginyl-tRNA synthetase (AsnRS), a target for anti-parasitic drug design. Seven classes of compounds identified by SLIDE were confirmed as micromolar inhibitors of the enzyme. Analogs of one of these classes of inhibitors, the long side-chain variolins, cannot bind to the adenosyl pocket of the closed conformation of AsnRS due to steric clashes, though the short side-chain variolins identified by SLIDE␣apparently bind isosterically with adenosine. We hypothesized that an open conformation of the motif 2 loop also permits the long side-chain variolins to bind in the adenosine pocket and that their selectivity for Brugia relative to human AsnRS can be explained by differences in the sequence and conformation of this loop. Loop flexibility sampling using Rigidity Optimized Conformational Kinetics (ROCK) confirms this possibility, while scoring of the relative affinities of the different ligands by SLIDE correlates well with the compounds’ ranks in inhibition assays. Combining ROCK and SLIDE provides a promising approach for exploiting conformational flexibility in structure-based screening and design of species selective inhibitors.     

An inequality of Schur's type

It is proved that the Chebyshev polynomial , has the greatest uniform norm on [−1, 1] of its third derivative among the real polynomials of degree at most n, which are bounded by 1 in [−1, 1] and vanish in −1 and 1. Research Supported by the Sofia University Science Foundation under Project No. 153/95.