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     

(2,4-Di-(tert-butyl)-6-methylphenyl)dithiophosphorane

Use of the 2,4-di-(tert-butyl)-6-methylphenyl radical permits stabilization of the corresponding dithiophosphorane (I). The analogous diselenophosphorane could not be detected as the monomer. This compound undergoes intramolecular addition of the C-H bond of the ortho-tert-butyl group at the P=Se bond with formation of the corresponding diselenophosphonic acid (III). Intermediate selenophosphine oxide (IV) was trapped as its salt with triethylamine (V).Translated from Izvestiya Akademii Nauk SSSR, Seriya Khimicheskaya, No. 7, pp. 1654–1656, July, 1991.     

Synthesis and structural characterization of η-allyl(α-diimine)nickel(II) complexes bearing trimethylsilyl groups

A set of isomeric para- and meta-trimethylsilylphenyl ortho-substituted N,N-phenyl α-diimine ligands [(Ar-NC(Me)-(Me)CN-Ar) Ar=2,6-di(4-trimethylsilylphenyl)phenyl (16); Ar=2,6-di(3-trimethylsilylphenyl)phenyl (17)] have been synthesized through a two-step procedure. The palladium-catalysed cross-coupling reaction between 2,6-dibromophenylamine (7) and 4-trimethylsilylphenylboronic acid (8), 3-trimethylsilylphenylboronic acid (9) was used to prepare 4,4^′-bis(trimethylsilyl)-[1,1^′;3^′,1″]terphenyl-2^′-ylamine (10) and 3,3^′-bis(trimethylsilyl)-[1,1^′;3^′,1″]terphenyl-2^′-ylamine (11). The di-1-adamantylphosphine oxide Ad₂P(O)H (13) and di-tert-butyl-trimethylsilylanylmethylphosphine tert-Bu₂P-CH₂-SiMe₃ (14) were used for the first time as ligands for the Suzuki coupling. The condensation of 2,2,3,3-tetramethoxybutane (15) with anilines 10 and 11 afforded α-diimines 16 and 17. The reaction of π-allylnickel chloride dimer (18), α-diimines (16), (17) and sodium tetrakis[3,5-bis(trifluoromethyl)phenyl]borate (BAF) (19) or silver hexafluoroantimonate (20) led to two sets of isomeric complexes [η³-allyl(Ar-NC(Me)-(Me)CN-Ar)Ni]⁺ X⁻, [Ar=2,6-di(4-trimethylsilylphenyl)phenyl, X=BAF (3), X=SbF₆ (4); Ar=2,6-di(3-trimethylsilylphenyl)phenyl, X=BAF (5), X=SbF₆ (6)]. The steric repulsion of closely positioned trimethylsilyl groups in 4 caused the distortion of the nickel square planar coordination by 17.6° according to X-ray analysis.     

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.     

PMR spectra and three-dimensional structure of stereoisomers of 4,6-disubstituted 2,5-diphenyl-1,3,2,5-dioxaboraphosphorinanes

Conclusions Stereospecificity was demonstrated for the²J_PH coupling constants of 4,6-disubstituted 2,5-diphenyl-1,3,2,5-dioxaboraphosphorinanes and possibilities for their use for the determination of the three-dimensional structure of stereoisomers was shown.Translated from Izvestiya Akademii Nauk SSSR, Seriya Khimicheskaya, No. 11, pp. 2501–2507, November, 1984.     

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.