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     

1-Dibutylboryl-2-diphenylphosphinoethene and its derivatives

1-Butyl-1-dibutylboryl-2-diphenylphosphino-2-phenylethene, which exists in the form 1,1,2-tributyl-3,4,4-triphenyT-1-borata-4-phosphoniacyclobut-2-ene, reacts with sulfur, selenium, methyl iodide, and pyridine under mild conditions with ring cleavage. In (2-butyl-2-dibutylboryl-1-phenylethenyl) diphenylphosphine sulfide and selenide, there is a coordinate bond between the thio-or selenophosphoryl group and the boron atom.Translated from Izvestiya Akademii Nauk SSSR, Seriya Khimicheskaya, No. 12, pp. 2793–2796, December, 1989.     

Synthesis and some properties of planar 4-diphenylphosphino-1,3,2-dioxaborinanes

Fused 1,3,2-dioxaborinanes, derivatives of 4-diphenylphosphino- and 4-diphenylphosphoryl-4H-1, 3-dioxa-2-boraphenanthrenes, and their complexes with amines have been synthesized. According to X-ray diffraction data, the complex of 2-phenyl-4-diphenylphosphoryl-4H-1, 3-dioxa-2-boraphenanthrene with butylamine exists as a dimer due to the formation of intermolecular hydrogen bonds.Translated fromIzvestiya Akademii Nauk. Seriya Khimicheskaya, No. 9, pp. 1649–1655, September, 1994.The present work was financially supported by the International Science Foundation (grant No. RHBOOO).     

Synthesis of new macrocyclic aminomethylphosphines based on 4,4"-diaminodiphenylmethane and its derivatives

The reaction of bis(hydroxymethyl)phenylphosphine with 4,4"-diaminodiphenylmethane in DMF afforded 1,1",5,5"-bis[methylenedi(p-phenylene)]di(3,7-diphenyl-1,5-diaza-3,7-diphosphacyclooctane) (1) whose structure was established by X-ray diffraction analysis. Sulfurization and oxidation of macrocyclic tetraphosphine 1 gave rise to products 2 and 3, respectively, compound 3 being obtained as a stable hexahydrate. The reaction of bis(hydroxymethyl)phenylphosphine with bis(4-N-methylaminophenyl)methane in DMF followed by sulfurization yielded monocyclic bis{methylenedi[p-phenylene(N-methyl)aminomethyl]}di(P-phenyl)phosphine sulfide (4).     

Molecular structure of (3,5-diallylisocyanuratomethyl)bis(chloromethyl)phosphine oxide. Synthesis of (3,5-diallylisocyanuratomethyl)phosphine sulfides

X-Ray study of the (3,5-diallylisocyanuratomethyl)bis(chloromethyl)phosphine oxide showed that the phosphorylmethyl group is bonded to the nitrogen atom of the cycle. Reaction of the tris(chloromethyl)phosphine sulfide with sodium diallylisocyanurate gave (3,5-diallylisocyanuratomethyl)bis(chloromethyl)phosphine sulfide, and treatment of the tris(3,5-diallylisocyanuratomethyl)phosphine oxide with phosphorus pentasulfide gave a tris(3,5-diallylisocyanuratomethyl)bis(chloromethyl)phosphine sulfide.Translated fromIzvestiya Akademii Nauk. Seriya Khimicheskaya, No. 8, pp. 1446–1448, August, 1993.     

New aminomethylphosphines with cyanophenyl substituents at the nitrogen atoms

A condensation of bis(hydroxymethyl)arylphosphines with 3- and 4-aminobenzonitriles leads to the corresponding 3,7-diaryl-1,5-bis(cyanophenyl)-1,5-diaza-3,7-diphosphacyclooctanes. Acyclic (aryl)bis[N-(2-cyanophenyl)aminomethyl]phosphines are formed in the case of 2-aminobenzonitrile. Molecular and crystalline structure of the compounds obtained was studied by X-ray diffraction analysis.     

Stacking-Conformations in Functionally Substituted Phosphines

The methods of synthesis and space structure of phosphorus-containing compounds, in which stacking conformation is realized, are considered. It is shown that intramolecular stacking can be observed in monoheterocyclic compounds, bi-and polycyclic compounds, complexes of metals and acyclic compounds.     

Structure and reactions of benzo-4-diphenylphosphino-2-phenyl-1,3,2-dioxaborinane

The crystal structure of 5,6-benzo-4-diphenylphosphino-2-phenyl-1,3,2-dioxaborinane 1 indicates the occurrence of an interaction between the π-systems of the 1,3,2-dioxaborinane ring and the appropriate phenyl group of the diphenylphosphino group. Complexes of compound 1 with PtCl₂, PdCl₂, and Cul were synthesized. Compound 1 and its complexes are readily hydrolyzed in solution to give diphenylphosphine and its corresponding complexes (NMR).     

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.