A number theoretic estimate of Davenport from a functional analytic viewpoint

We consider the problem of the identification of continuous functionsf∶[0, 1]→R, by means of the sums . This is not possible, in general, but we prove that it may be the case under auxiliary conditions. We also study the behaviour of a well known exceptional function.

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Sunto Consideriamo il problema dell’identificazione delle funzioni continuef:[0,1]→ →R, mediante le somme . Ciò non è, in generale, possibile: dimostriamo però tale possibilità sotto condizioni ausiliarie. Studiamo inoltre il comportamento di una ben nota funzione eccezionale.

     

Use of zeo-karb 226 and dowex a-l in the analysis of high-purity zinc and zinc-base alloys for Tl and In

Utility of Zeo-Karb 226 and Dowex A-l for the separation of Tl and In at 5-ppm level from high-purity zinc and zinc-base alloys has been investigated. With Zeo-Karb 226 (NH(4)(+)), T1(+) is conveniently separated from these materials and also from many other cations, with l.0M ammonium nitrate as the eluent. It is subsequently determined with Rhodamine B. This separation principle is also applied to the analysis of Pb-Tl alloys. Both Tl and In (along with Fe) are preconcentrated on Zeo-Karb 226(H(+)) from a solution of the sample at pH 3.0. Suitable methods of subsequent determination of Tl and In are described. In the case of Dowex A-1(H(+)), Tl(+), In(3+), Fe(3+) and Cu(2+) are retained from a solution of the sample at pH 2.0. An o-phenanthroline solution at pH 2.0 elutes all but traces of Cu(2+). In(3+) along with Fe(3+) is eluted with l.0M hydrochloric acid. Finally, Tl is eluted with 2.0M hydrochloric acid containing sulphurous acid.     

Dynamic stability of a curved rail under a moving load

The stability of a curved rail under a constant moving load has been investigated using a linear theory; critical speeds of the moving load, and the dynamic rail deflections and rotation were calculated. The effect of the foundation was included through distributed linear springs. It was assumed that the moving load remains in constant contact with the rail and travels along a fixed path on the rail head.     

Engaging the pyridine-DMAD zwitterion in a novel strategy for the selective synthesis of highly substituted benzene and cyclopentenedione derivatives

[reaction: see text] The pyridine-mediated reaction of dimethyl acetylenedicarboxylate and cyclobutene-1,2-diones affords selective access to either hexasubstituted benzene derivatives or cyclopentenedione derivatives depending on the concentration of pyridine.     

Pyridine-catalyzed addition of diaryl-1,2-diones to dimethyl butynedioate leading to the formation of 1,2-diaroyl dimethyl maleates via an unprecedented rearrangement

[reaction: see text] Pyridine catalyzes the reaction of 1,2-diaryl diones with dimethyl butynedioate to afford diaroyl maleates. This unprecedented rearrangement involves a unique benzoyl migration and proceeds with complete stereoselectivity.     

Practical synthesis of triaryl- and triheteroarylmethanes by reaction of aldehydes and activated arenes promoted by gold(III) chloride

[reaction: see text] Electron-rich arenes condense efficiently with various aldehydes under the influence of AuCl3, thus opening up a practical route to triarylmethanes, which have important applications. The mild conditions employed are especially noteworthy.     

Coalescence suppression in model immiscible polymer blends by nano-sized colloidal particles

The effect of nanometer sized silica particles (R16 nm) on the flow-induced morphology of immiscible polymer blends is studied. Polydimethylsiloxane (PDMS) and polyisobutylene (PIB) are chosen as model components. A stable droplet/matrix microstructure is obtained for blends of 30% PIB in 70% PDMS or vice versa. Rheological measurements are used to show that the silica particles alter the sensitivity of the of dispersed phase/matrix microstructure to shear flow. Coalescence is suppressed or at least slowed down on a practical time scale, especially when PDMS is the matrix phase. The effect of mixing conditions, pre-shear rate and particle concentration on the blend morphology are studied. Cryo-SEM is used to observe the accumulation of the particles at the interface. Blends stabilized by solid particles could provide an interesting alternative to blends compatibilized by block-copolymers.This paper was presented at the first Annual European Rheology Conference (AERC) held in Guimarães, Portugal, September 11-13, 2003.     

Synthesis of novel iodo derived bicalutamide analogs

A series of optically active nonsteroidal selective androgen receptor modulators with structures analogous to bicalutamide was prepared by replacing the trifluoromethyl group with iodine and the sulfonyl linker by oxygen.     

Lewis acid-promoted annulation of O-quinonediimines by allylstannane: a facile synthesis of quinoxaline derivatives

[reaction: see text] Lewis acid-promoted addition of allyltri-n-butylstannane to o-quinonediimines afforded tetrahydroquinoxaline derivatives or allylated amides depending on the nature of the substituent on imine nitrogen.