Lower rim mono-functionalization of resorcinarenes

A versatile, scaleable, one step synthesis of a lower rim mono-functionalized resorcinarene is described.     

Free interfacial vibrations in cylindrical shells

The 2D equations in the Kirchhoff-Love theory are subjected to asymptotic analysis in the case of free interfacial vibrations of a longitudinally inhomogeneous infinite cylindrical shell. Three types of interfacial vibrations, associated with bending, super low-frequency semi-membrane, and extensional motions, are investigated. It is remarkable that for extensional modes natural frequencies have asymptotically small imaginary parts caused by a weak coupling with propagating bending waves. Bending and extensional vibrations correspond to Stonely-type plate waves, while semi-membrane ones are strongly dependent on shell curvature and do not allow flat plate interpretation. The paper represents generalization of the recent authors' publication [Kaplunov et al., J. Acoust. Soc. Am. 107, 1383-1393 (2000)] dealing with edge vibrations of a semi-infinite cylindrical shell.     

Noncommutative Line Bundle and Morita Equivalence

Global properties of Abelian noncommutative gauge theories based on -products which are deformation quantizations of arbitrary Poisson structures are studied. The consistency condition for finite noncommutative gauge transformations and its explicit solution in the Abelian case are given. It is shown that the local existence of invertible covariantizing maps (which are closely related to the Seiberg–Witten map) leads naturally to the notion of a noncommutative line bundle with noncommutative transition functions. We introduce the space of sections of such a line bundle and explicitly show that it is a projective module. The local covariantizing maps define a new star product which is shown to be Morita equivalent to .     

Über das fettspaltende Ferment der höheren Pilze

Ohne Zusammenfassung     

The calculation of the thermal laminar boundary layer on a rotating sphere

Sommaire La communication expose une méthode permettant de déterminer la couche limite thermique d'une sphère en rotation dans un fluide incompressible à écoulement uniforme. La méthode se base sur l'idée deFrössling, selon laquelle la répartition des températures s'exprime en tant que développement en série de puissances, et utilise les résultats déjà obtenus parHoskin pour la répartition des vitesses dans la couche limite d'une sphère en rotation. L'auteur donne des résultats numériques obtenus sur une machine à calculer IBM 704.

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Nomenclature x distance along surface of body in a meridian plane from forward stagnation point - y distance measured normal to surface - U velocity of main flow - U velocity of undisturbed stream - u component of velocity inx-direction - v component of velocity iny-direction - w transverse component of velocity due to spin - p pressure - density - T temperature - R distance of surface from axis of symmetry measured normal to axis of symmetry - coefficient of viscosity - kinematic viscosity - a radius of sphere - k thermal conductivity - angular velocity about axis of symmetry - Re Reynolds number - Pr Prandtl number - Nu Nusselt number - a constant - S area - Q quantity of heat transferred in unit time across areaS - d a characteristic length     

Note on a Riegels-type integral

Zusammenfassung Die vorliegende Arbeit befasst sich mit einer Klasse von Integralen, die bei der Untersuchung der Strömung um Ringflügel von elliptischem Querschnitt auftreten. Es wird gezeigt, dass sich die fraglichen Integrale mittels Riegels'scher und vollständiger elliptischer Integrale darstellen lassen, ferner werden Reihenentwicklung nach Potenzen des Moduls angegeben und Rekursionsformeln für die numerische Berechnung der Integrale mitgeteilt.     

Grafting of single, stimuli-responsive poly(ferrocenylsilane) polymer chains to gold surfaces

Redox-responsive poly(ferrocenylsilane) (PFS) polymer molecules were attached individually to gold surfaces for force spectroscopy experiments on the single molecule level. By grafting ethylenesulfide-functionalized PFS into the defects of preformed self-assembled monolayers (SAMs) of different omega-mercaptoalkanols on Au(111), the surface coverage of PFS macromolecules could be conveniently controlled. Atomic force microscopy (AFM), contact angle, as well as cyclic and differential pulse voltammetry measurements were carried out to characterize the morphology, wettability, and surface coverage of the grafted layers. The values of the PFS surface coverage were found to depend on the chain length of the omega-mercaptoalkanol molecules and on the concentration of the PFS solution but not on the insertion time or on the molar mass of PFS. The equilibrium surface coverages were successfully described by Langmuir adsorption isotherms. For low-surface coverage values (< 6.2 x 10(-4) chain/nm2), achieved by PFS insertion from very dilute solutions (8 x 10(-6) M) into long-chain SAMs, AFM and differential pulse voltammetry showed that surfaces exposing isolated individual polymer chains were obtained. The isolated PFS macromolecules were subjected to in situ AFM-based single molecule force spectroscopy (SMFS) measurements. The single chain elasticity of PFS in isopropanol (and ethanol) was fitted with the modified freely jointed chain (m-FJC) model. This procedure yielded a Kuhn segment length of 0.33 +/- 0.05 nm and a segment elasticity of 32 +/- 5 nN/nm.