A boundary layer problem in nonflat domains with measurable viscous coefficients

We study the convergence of weak solutions of the Navier–Stokes equations with vanishing measurable viscous coefficients in domains with nonflat boundaries. Sufficient anisotropic conditions on the vanishing rates of the viscous coefficients are found to prove the convergence of Leray–Hopf weak solutions of the Navier–Stokes equations to solutions of the corresponding Euler equations. As the domains are not flat, we apply a change of variables to flatten the domains. We then construct explicit boundary layers for the system of Navier–Stokes equations in the upper-half space with measurable viscous coefficients. The result is new even when the viscous coefficients are constant, and it recovers the classical results when domains are flat and with constant viscous coefficients.     

Sulfated Triterpenes from Lemon Balm

The hydroalcoholic (EtOH/H₂O) extract of matured leaf margins of lemon balm (Melissa officinalis L.) afforded a new 3,23‐disulfate of 2α,3β‐23,29‐tetrahydroxyolean‐12‐en‐28‐oic acid 28‐O‐β‐D ‐glucopyranoside ( 1 ) and a new 23‐monosulfate of 2α,23‐dihydroxyurs‐12‐en‐28‐oic acid 3‐O‐β‐D ‐glucopyranoside ( 2 ), along with six known compounds, i.e., 23‐monosulfate of 2α,3β,19α,23‐tetrahydroxyurs‐12‐ene‐28‐oic acid 28‐O‐β‐D ‐glucopyranoside ( 3 ), 3,5,6‐trihydroxydehydro‐α‐ionol 9‐O‐β‐D ‐glucopyranoside ( 4 ), quadranoside III ( 5 ), rosmarinic acid ( 6 ), caffeic acid ( 7 ), and luteolin ( 8 ). All the isolated compounds were evaluated for their antioxidant, antimicrobial, antimalarial, and cytotoxic activities. Only rosmarinic acid exhibited substantial antioxidant and antimicrobial activities, whereas sulfated terpenes showed considerably lower or no antimicrobial activity.     

Heterogeneous reusable catalyst,ultrasound energy,and no solvent: a quick and green recipe for one-pot synthesis of β-phosphonomalononitriles at room temperature

Clay-supported heteropolyacid catalyst has been prepared and investigated as a novel heterogeneous, reusable and efficient catalyst for the one-pot synthesis of β-phosphonomalononitriles under ultrasound irradiation at room temperature. Compared with traditional methods, the present method is solvent-free, works under milder and cleaner conditions, furnishes products with higher purity and yields, needs shorter reaction time, easier work-up procedure, and generates less waste. No column purification is required and the products can be purified by simple crystallization. The catalyst can be easily recovered and reused several times without significant loss of its catalytic activity. The catalyst was characterized by scanning electron microscopy, X-ray powder diffraction, and thermal gravimetric, surface area, and elemental analyses.     

Intermolecular Interactions in Mixed Self‐Assembled Monolayers of Ferrocene

Electrochemical characterization of mixed self‐assembled monolayers (SAMs) of 6‐ferrocenyl‐1‐hexanethiol (FcH) and mercaptoundecanoic acid tyrosinamide (MUATyr) on gold is reported. Single‐component SAMs of FcH presented repulsive intermolecular interactions (vGθ_T=?1.12), while mixed SAMs of FcH/MUATyr (1 : 1) exhibited attractive interactions (vGθ_T=+0.20), with a homogeneous distribution of both components. Electrochemical kinetic determinations on mixed SAMs of FcH/MUATyr, indicated a secondary electron transfer pathway between the redox centers of both components. Higher amounts of FcH in the mixed SAMs lowered the observed rate of electron transfer of MUATyr. The oxidation of FcH caused an anodic shift of 160 mV in the voltammetric wave of MUATyr.     

Scanning X-ray microanalysis of bottom sediments using synchrotron radiation from the BINP VEPP-3 storage ring

Combining the features of synchrotron radiation (low angular divergence and continuous spectrum, natural polarization, and high intensity) with the use of modern X-ray optics (polycapillary lenses) and registering devices results in a new quality of analysis: measuring picogram concentrations of a broad set of elements with micron spatial resolution. Using a dedicated experimental station and developed methodologies, numerous scanning microanalyses of bottom sediments is performed to obtain a time series of geochemical indicators of paleoclimate in the Central Asian region. The detection limit under optimum conditions is 5 × 10^?5% with a spatial resolution of ～100 μm.     

Fine structure and formation mechanism of particulate phase‐inversion poly(vinylidene fluoride) membranes

The structure and formation mechanism of a microporous phase‐inversion poly(vinylidene fluoride) (PVDF) membrane exhibiting a relatively loosely packed agglomerate of semicrystalline globules are explored. The membrane has been prepared by the coagulation of a solution of PVDF in dimethylformamide by the action of 1‐octanol, which is a soft nonsolvent. Experimental observations pertain to the globule surface, which is dominated by a grainy nanostructure; the globular interior, which exhibits a range of fine structures (e.g., twisted sheets and treelike branches); and the globule–globule connections, which exhibit a sheetlike or ropelike structure. On the basis of the observed structural details and phase diagram considerations, it is proposed that the membrane structure is the result of a unique combination of a polymer crystallization and a liquid–liquid phase‐separation process, with end‐result globular structural features of remarkable uniformity. © 2003 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 41: 1578–1588, 2003     

The Matkowski–Sutő problem for weighted quasi-arithmetic means

In this paper the so-called invariance equation is studied for weighted nonsymmetric quasi-arithmetic means and solved under continuous differentiability assumptions with respect to the generating functions of the quasi-arithmetic means. This revised version was published online in June 2006 with corrections to the Cover Date.