Evaluation of integrals and the mellin transform

Translated from Itogi Nauki i Tekhniki, Seriya Matematicheskii Analiz, Vol. 27, pp. 3–146, 1989.     

Comparisons between model equations for long waves

Summary Considered here are model equations for weakly nonlinear and dispersive long waves, which feature general forms of dispersion and pure power nonlinearity. Two variants of such equations are introduced, one of Korteweg-de Vries type and one of regularized long-wave type. It is proven that solutions of the pure initial-value problem for these two types of model equations are the same, to within the order of accuracy attributable to either, on the long time scale during which nonlinear and dispersive effects may accumulate to make an order-one relative difference to the wave profiles.This research was supported in part by the National Science Foundation. A considerable portion of the project was completed while the first author was resident at the Institute for Mathematics and Its Applications, University of Minnesota.     

Buchbesprechungen

Ohne Zusammenfassung

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Book reviews

     

Porosity and typical properties of real-valued continuous functions

Some well-known theorems on typical properties of real-valued continuous functions defined on [0, 1] are improved using the notion of porosity.     

Wechselnde Bindungen in einem Zweikörpersystem mit trockener Reibung

Übersicht Betrachtet wird ein zwangserregtes Zweikörpersystem mit wechselnden Bindungen infolge trockener Reibung. Stationäre Bewegungen werden als Grenzfall instationärer Einschwingvorgänge berechnet. Abhängig von den Systemparametern ergeben sich drei typische Bewegungsformen. Ihnen entsprechen dauernde Haftzustände, wechselnde Haft-Gleitzustände oder dauernde Gleitzustände an der Berührfläche beider Körper.

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Intermittant constraints in a two-body-system with dry friction

Summary An externally excited two-body-system with intermittant constraints due to dry friction is considered. Stationary motions are calculated as limit cases of instationary transients. Depending on the parameters of the system, three typical modes are of interest. These correspond to permanent sticking, slipstick behaviour, or to permanent slipping in the contact surface of the bodies, respectively.

     

Convergent route to the purpuromycin bisphenolic spiroketal: hydrogen bonding control of spiroketalization stereochemistry

A mild and efficient [3+2] nitrile oxide/olefin cycloaddition provided a rapid and convergent entry into precursors of bisphenolic spiroketals, a structural type unique to the rubromycin family of natural products. In addition, implementation of the premise that a hydrogen bond from the C4-OH controls the stereochemistry of the purpuromycin core resulted in moderate diastereocontrol in the spiroketalization. Spectroscopic and X-ray data of these systems have provided the first assignment of the relative configuration of purpuromycin.     

Fluorescence and absorption of polystyrene exposed to UV laser radiation

We show that when polystyrene is exposed (for 15–60 sec) to a UV laser light beam (λ = 248 nm), its absorption and luminescent properties change significantly. In the irradiated polymer, optical centers are formed with absorption bands in the 280–460 nm region and fluorescence bands in the 330–520 nm region. We have established the chemical structure of the optical centers for fluorescence of polystyrene. __________ Translated from Zhurnal Prikladnoi Spektroskopii, Vol. 73, No. 1, pp. 54–58, January–February, 2006.