On the exceptional zeros of cross-products of derivatives of spherical Bessel functions

The lowest zeros of the cross-products of derivatives of spherical Bessel functions are not obtainable from a McMahon-type formula. This paper derives an analytical approximation for these lowest, exceptional, zeros, through to 4th order in a parameter specifying the thinness of the corresponding concentric spherical region.

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Zusammenfassung Die kleinsten Nullstellen der Kreuzprodukte der Ableitungen von spherischen Bessel-funktionen können nicht durch eine Formel von McMahon Typ erhalten werden. Durch eine Entwicklung bis zu vierter Ordnung in einem Parameter proportional zur Dicke des zugeordneten spherischen Gebietes berechnen wir eine analytische Näherung für diese kleinsten, außergewöhnlichen, Nullstellen.

     

A hydrogenation product derived from the diterpenoid barbatusin:A revised structure

The structure of the hydrogenation product of barbatusin, a diterpenoid from Coleus barbatus Bentham has been revised on the basis of NMR and X-ray data. A geminal coupling of unusually high magnitude has been observed and analysed.     

Gauge theory of fermions onR × S 3 spacetime

A Lorentz-invariant gauge theory for massive fermions on R × S ³ spacetime is built up. Using the symmetry of S ³,we obtain Dirac-type equation and derive the expression of the fermionic propagator. Finally, starting from the SU(N) gauge-invariant Lagrangian, we obtain the set of Dirac-Yang-Mills equations on R × S ³ spacetime, pointing out major differences from the Minkowskian case.     

Virus Particles Monitored by Fluorescence Spectroscopy: A Potential Detection Assay for Macromolecular Assembly¶

Native fluorescence spectroscopy was used for in situ investigations of two lipid‐containing bacteriophages from the cystovirus family as well as their Pseudomonad host cells. Both the viruses φ6 and φ12 and their bacterial host proteins contain the amino acid tryptophan (trp), which is the predominant fluorophore in UV. Within proteins, trp's structural environment differs, and the differences are reflected in their spectroscopic signatures. It was observed that the peak of the trp emission from both viruses was at 330 nm, a significantly shorter wavelength than trp in either the Pseudomonad host cells or the amino acid's chemical form. This allowed us to monitor the viral attachment process and subsequent lytic release of progeny virus particles by measurement of the trp emission spectra during the infection process. This work demonstrates that fluorescence may offer a novel tool to detect viruses and monitor viral infection of cells and may be part of a biodefense application.     

Simple instrument for titrimetry without visual indicators. gasometric titrations: Cerimetry,chlorometry, nitrate,nitrite, hydroxide and carbonate determination

It was shown in previous papers, that many titrimetric problems can be solved by observing the pressure change of a closed system above the solution titrated at the equivalence point. This principle was made the basis of a gasometric titration method in which the end-point is found graphically. The titrant is added to the sample solution in measured increments at fixed intervals of time and the corresponding gas pressure or volume of the system is recorded and then plotted against the volume of added titrant. Half a dozen readings are sufficient to establish the end-point of a titration, which is found at the intersection of two straight lines. This graphical method was applied to cerimetry and chlorometry, as well as to some other analytical reactions (determination of nitrite, nitrate, hydroxide and carbonate) already described in previous papers on the gas pressure end-point technique. The results are comparable in precision and accuracy to the values obtained by the conventional visual end-point titrations. A gasometric titration takes about 10 minutes. The presence of other substances in the sample capable of reacting with the titrant does not necessarily cause interference.