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     

Influence of barrier parameters on tunneling in ferromagnet-insulator-ferromagnet contacts

The contribution of electrons moving at large angles to the barrier junction plane to the tunnel current is calculated. This contribution turns out to be small only if the Fermi energy of the electrons equals several electron volts. Otherwise, specifically, when the Fermi energy is no higher than 1–2 eV, this contribution dominates in high and thin potential barriers. It is found that the tunnel magnetic resistance in ferromagnet-insulator-ferromagnet contacts correlates with this contribution. It is this correlation that is responsible for a decrease in this contribution as the potential barriers get lower and thicker.     

Carleman problem for two pairs of functions in a ring

We consider a particular case of the matrix Carleman problem for two pairs of functions in a ring and find a constructive solution of this problem. In addition, we propose an algorithm for the construction of solutions for two infinite systems of smooth transition and for a system of two singular equations of special type. Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 49, No. 5, pp. 662–671, May, 1997     

Control of the molecular characteristics of cationic oligopiperylene using isomeric methylbutenes

Additions of 2-methyl-1-butene or 2-methyl-2-butene to a monomer mixture with piperylene were tested as means for controlling the molecular parameters of cationic oligopiperylene prepared with the TiCl₄-H₂O catalytic system.     

PMR spectra of some five- and six-membered heterocyclic compounds of silicon and germanium

The PMR spectra of various 1-sila- and 1-germacyclopentanes and also those of some substituted disilacyclohexanes are discussed. The influence of the magnetic field of the aryl and vinyl substituents in 1,1-dialkyl-2,5-diaryl(vinyl)-1-sila(germa)cyclopentanes on the chemical shifts of the protons of the individual groups is studied, the differences found in the position of the PMR lines of the methyl and methylene groups showing the existence of cis-trans isomers in these heterocycles. With 1,1-dimethyl-2,5-divinylsilacyclopentane as an example, an increase in screening due to the magnetism of the multiple bonds for the protons of groups not directly connected with the unsaturated groupings and located in a direction perpendicular to the axis of the double bond has been found experimentally.Lecture at the XI-th Scientific Conference of the Institute of High-Molecular-Weight Compounds of the Academy of Sciences of the USSR (Leningrad, March, 1964) and at the All-Union Conference on the Use of Radiospectroscopy in Chemistry (Moscow, January, 1965).The authors express their gratitude to A. V. Kessenikh for taking several of the PMR spectra and for critical observations on the investigation.     

Spin filtering in double tunnel junctions: The two-band model of the electronic structure of magnetic insulators

The effect of the top of the valence band of an insulator on spin filtering in tunnel structures with nanometer magnetic dielectric layers is discussed. It has been shown that the effect disappears completely at a zero bias voltage and is significantly suppressed at finite voltages if the Fermi level lies in the middle of the band gap of the insulator. This is the main cause of the recently observed striking discrepancy between the theoretical values of the magnetoresistance of double tunneling spin filters and the respective experimental data.     

Determination of the molecular weight of polyoxypropylenepolyols by <Superscript>1</Superscript>H NMR spectroscopy

Commercial and laboratory samples of polyoxypropylenepolyols were studied by ¹H NMR spectroscopy at operating frequencies of 100 and 500 MHz. Various methods depending on the solvent used were suggested for determining the equivalent weight (molecular weight of the polyether per terminal hydroxy group). The ¹H NMR data are compared to the data obtained by chemical methods and gel permeation chromatography.     

Fractal scattering of microwaves from soils

Using a combination of laboratory experiments and computer simulation we show that microwaves reflected from and transmitted through soil have a fractal dimension correlated to that of the soil's hierarchic permittivity network. The mathematical model relating the ground-penetrating radar record to the mass fractal dimension of soil structure is also developed. The fractal signature of the scattered microwaves correlates well with some physical and mechanical properties of soils.     

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.