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.

     

关于具有负系数和缺系数的单叶函数

Let P_k(A,B) be the class of functions(?), regu-lar in the unit disc U={z:|z|<1} and satisfying |[f′(z)-1]/[A-Bf′(z)]|<1 for z∈U, where -1≤Bk(A,B) under the assumption -1≤B≤0. We also obtain class preserving integral operators of the form.     

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.     

Differential refractometry of molecular complexes: A reinvestigation

A modified plot method is used to calculate equilibrium constants of molecular complexes. This method (Sahai andSingh's plot) is compared with the method ofYoshida andOsawa.

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Differentielle Refraktometrie von Molekülkomplexen: Eine Neuuntersuchung (Kurze Mitteilung)

Zusammenfassung Eine modifizierte refraktometrische Methode zur Berechnung von Gleichgewichtskonstanten von Molekülkomplexen wird verwendet und diese mit der Methode vonYoshida undOsawa verglichen.

     

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.     

Aziridine carboxylate from D-glucose: synthesis of polyhydroxylated piperidine, pyrrolidine alkaloids and study of their glycosidase inhibition

The D-glucose derived aziridine carboxylate 5 was obtained from (E)-ethyl-6-bromo-1,2-O-isopropylidene-3-O-benzyl-5-deoxy-alpha-D-xylo-5-eno-heptofuranuronate 4 through conjugate addition of benzylamine and in situ intramolecular nucleophilic expulsion of bromine. The regioselective aziridine ring-opening, using water as a nucleophile, resulted in the alpha-hydroxy-beta-aminoester 6, which was exploited in the synthesis of six and five membered azasugars 1b/1c and 2b/2c, respectively. The glycosidase inhibitory activity of the title compounds was evaluated.