Zur Theorie der Gammafunction

Ohne Zusammenfassung Vergl. meine Abhandlung:Om en ny klass af transcendenta functioner, hvilka ?ro n?ra besl?gtade med gammafunktionen, Acta soc. scient. Fennic?, Tom. XIV, XV; 1885, 1886.     

An efficient step size control for continuation methods

In solving a nonlinear equation by the use of a continuation method one of the crucial problems is the choice of the step sizes. We present a model for the total computational cost of a standard numerical continuation process and solve the problem of optimal step size control for this model. Using the theoretical results as a basis, we develop an adaptive step size algorithm for Newton's method. This procedure is computationally inexpensive and it gives quite satisfactory results compared to some other numerical experiments found in the literature.     

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.