Conjugate points in

An example of a geodesic in with conjugate points is given, thus providing an affirmative answer to a question of V.I. Arnold.

     

Isotope ratio monitoring gas chromatography/Mass spectrometry of D/H by high temperature conversion isotope ratio mass spectrometry

Of all the elements, hydrogen has the largest naturally occurring variations in the ratio of its stable isotopes (D/H). It is for this reason that there has been a strong desire to add hydrogen to the list of elements amenable to isotope ratio monitoring gas chromatography/mass spectrometry (irm-GC/MS). In irm-GC/MS the sample is entrained in helium as the carrier gas, which is also ionized and separated in the isotope ratio mass spectrometer (IRMS). Because of the low abundance of deuterium in nature, precise and accurate on-line monitoring of D/H ratios with an IRMS requires that low energy helium ions be kept out of the m/z 3 collector, which requires the use of an energy filter. A clean mass 3 (HD(+.)) signal which is independent of a large helium load in the electron impact ion source is essential in order to reach the sensitivity required for D/H analysis of capillary GC peaks. A new IRMS system, the DELTA(plus)XL(trade mark), has been designed for high precision, high accuracy measurements of transient signals of hydrogen gas. It incorporates a retardation lens integrated into the m/z 3 Faraday cup collector. Following GC separation, the hydrogen bound in organic compounds must be quantitatively converted into H(2) gas prior to analysis in the IRMS. Quantitative conversion is achieved by high temperature conversion (TC) at temperatures >1400 degrees C. Measurements of D/H ratios of individual organic compounds in complicated natural mixtures can now be made to a precision of 2 per thousand (delta notation) or, better, with typical sample amounts of approximately 200 ng per compound. Initial applications have focused on compounds of interest to petroleum research (biomarkers and natural gas components), food and flavor control (vanillin and ethanol), and metabolic studies (fatty acids and steroids). Copyright 1999 John Wiley & Sons, Ltd.     

Extended-ion approximation and pressure shifts inF-band energies

Pressure variation of maximumF-band absorption energies in the halides of lithium, sodium and potassium has been investigated employing the extended-ion approximation for the calculation of theF-electron energy eigenvalues and using values of local compressibility in the neighbourhood of theF-centres which include the effect of vacancy and pressure. The results obtained agree with the experimental results.     

"Inverse sodium hydride": a crystalline salt that contains H(+) and Na(-)

A crystalline salt has been synthesized that contains H(+) and Na(-) rather than the usual hydride oxidation states of H(-) and Na(+). The key is irreversible encapsulation of H(+) within the cage of 3(6)adamanzane (Adz). The internal proton is kinetically inert to reduction by Na(-) in solution in NH(3)-MeNH(2) mixtures. Synthesis of the sodide is accomplished by a metathesis reaction between Na and AdzH(+)X(-) in which X(-) is a sacrificial anion such as glycolate, isethionate, or nitrate. Reduction or deprotonation of the sacrificial anion forms insoluble byproducts and AdzH(+)Na(-) in solution. After solvent removal, the sodide is dissolved in dimethyl ether and transferred through a frit into a separate chamber for crystallization. The compound was characterized as the sodide by analysis, NMR spectra, and optical absorption spectroscopy.     

Exponential maps of Sobolev metrics on loop groups

We find conditions for the exponential map on a weak riemannian Hilbert manifold to be a nonlinear Fredholm map of index zero and apply the result to left-invariant Sobolev metrics on loop groups.