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     

Ketene dithioacetal derivatives of 1-phenyl-3,5-dioxopyrazolidine. Synthesis and NMR characterization

1-Phenyl-3,5-dioxopyrazolidine 1 reacts with carbon disufide and alkyl halides in presence of excess of sodium acetate in dimethylformamide to afford the ketene dithioacetals 3a-h . The ¹³C chemical shift assignments of these compounds were made on the basis of two-dimensional nmr studies performed on the N-methylketene dithioacetal derivative 4.     

New cis-clerodane diterpenoids from Croton schiedeanus

The acid fraction of extracts from the aerial part of Croton schiedeanus afforded six cis-clerodane type diterpenoids. Two of them (1 and 4) are new natural compounds. Structural elucidation was achieved on the basis of their spectral data.     

An easy route to pentacyclic terpenylquinones

Cyclisation of terpenylnaphthohydroquinone derivatives or terpenylquinone cycloadducts, obtained from methyl myrcecommunate, was performed in the presence of HI, I₂ or BF₃·OEt₂ and provides efficient synthetic strategies for the preparation of pentacyclic terpenylquinones.     

Chemical constituents of the bark of Dipteryx alata vogel, an active species against Bothrops jararacussu venom

The effect of four sub-extracts prepared from the lyophilized hydroalcoholic bark of Dipteryx alata (Leguminosae-Papilionoideae) dissolved in a methanol-water (80:20) mixture through a liquid-liquid partition procedure has been investigated against the neuromuscular blockade of the venom of the snake Bothrops jararacussu. The active CH?Cl? sub-extract has been extensively analyzed for its chemical constituents, resulting in the isolation of four lupane-type triterpenoids: lupeol, lupenone, 28-hydroxylup-20(29)-en-3-one, betulin, nine isoflavonoids: 8-O-methylretusin, 7-hydroxy-5,6,4'-trimethoxyisoflavone, afrormosin, 7-hydroxy-8,3',4'-trimethoxyisoflavone, 7,3'-dihydroxy-8,4'-dimethoxyisoflavone, odoratin, 7,8,3'-trihydroxy-4'-methoxyisoflavone, 7,8,3'-trihydroxy-6,4'-dimethoxyisoflavone, dipteryxin, one chalcone: isoliquiritigenin, one aurone: sulfuretin and three phenolic compounds: vanillic acid, vanillin, and protocatechuic acid. Their chemical structures were elucidated on the basis of spectroscopic analysis, including HRMS, 1D- and 2D-NMR techniques.     

L 2-Harmonic 1-Forms on Submanifolds with Finite Total Curvature

Let $x:M^{m}\to\bar{M}$ , m≥3, be an isometric immersion of a complete noncompact manifold M in a complete simply connected manifold $\bar{M}$ with sectional curvature satisfying $-k^{2}\leq K_{\bar{M}}\leq0$ , for some constant k. Assume that the immersion has finite total curvature in the sense that the traceless second fundamental form has finite L ^m -norm. If $K_{\bar{M}}\not\equiv0$ , assume further that the first eigenvalue of the Laplacian of M is bounded from below by a suitable constant. We prove that the space of the L ² harmonic 1-forms on M has finite dimension. Moreover, there exists a constant Λ>0, explicitly computed, such that if the total curvature is bounded from above by Λ then there are no nontrivial L ²-harmonic 1-forms on M.     

Velocity renormalization and carrier lifetime in graphene from the electron-phonon interaction

We present a first-principles investigation of the phonon-induced electron self-energy in graphene. The energy dependence of the self-energy reflects the peculiar linear band structure of graphene and deviates substantially from the usual metallic behavior. The effective band velocity of the Dirac fermions is found to be reduced by 4%-8%, depending on doping, by the interaction with lattice vibrations. Our results are consistent with the observed linear dependence of the electronic linewidth on the binding energy in photoemission spectra.     

The Synthesis of Some Fused Pyrazolo‐1,4‐Naphthoquinones

New fused pyrazolo‐1,4‐naphthoquinones were prepared from the reaction of hydrazines with 6‐(4‐methyl‐3‐pentenyl)‐1,4‐naphthoquinone. The reaction was extended to hydroxylamine to afford the corresponding isoxazolo‐1,4‐napthoquinone compound.