Diophantine approach to isotopic abundance calculations. Hsu, C. S. *Anal Chem*, 56(8):1356–1361, 1984. doi abstract bibtex Polynomial approaches have been used in the literature for calculating the Isotopic abundance of a given formula containing polyisotopic elements. These approaches limit the number of elements In the formula being calculated. A more general and flexible computer program based on a Diophantine algorithm has been developed. The equation used for calculating the fractional abundances is converted into a logarithmic form to avoid the use of a Gamma function, which limits the number of occurrences of an element one may calculate by a computer program. To reduce computation time and error for heavy isotopic clusters, a method similar to that described by Yergey is used. In the program, the formula weight is defined and calculated. The mass assignment of the isotopic cluster is corrected for the mass defect of the elements so that the calculated output can be dlrectly compared with low-resolution mass spectrometric measurements.

@Article{hsu84diophantine,
author = {Chang S. Hsu},
title = {Diophantine approach to isotopic abundance calculations},
journal = {Anal Chem},
year = {1984},
volume = {56},
number = {8},
pages = {1356--1361},
abstract = {Polynomial approaches have been used in the literature for calculating the Isotopic abundance of a given formula containing polyisotopic elements. These approaches limit the number of elements In the formula being calculated. A more general and flexible computer program based on a Diophantine algorithm has been developed. The equation used for calculating the fractional abundances is converted into a logarithmic form to avoid the use of a Gamma function, which limits the number of occurrences of an element one may calculate by a computer program. To reduce computation time and error for heavy isotopic clusters, a method similar to that described by Yergey is used. In the program, the formula weight is defined and calculated. The mass assignment of the isotopic cluster is corrected for the mass defect of the elements so that the calculated output can be dlrectly compared with low-resolution mass spectrometric measurements.},
doi = {10.1021/ac00272a035},
file = {Hsu_DiophantineApproachIsotopic_AnalChem_1984.pdf:1984/Hsu_DiophantineApproachIsotopic_AnalChem_1984.pdf:PDF},
keywords = {isotope distribution, frobenius, TrACReview},
owner = {Sebastian},
timestamp = {2006.01.18},
}

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