%0 Journal Article %1 gardner1959method %A Gardner, Donald G. %A Gardner, Jeanne C. %A Laush, George %A Meinke, W. Wayne %D 1959 %J The Journal of Chemical Physics %K Laplace_inversion %N 4 %P 978-986 %T Method for the Analysis of Multicomponent Exponential Decay Curves %U http://deepblue.lib.umich.edu/handle/2027.42/70060 %V 31 %X A frequently encountered problem in many branches of science involves the resolution of experimental data into a sum of independent exponential curves of the form $f(t)=\sum_i=1^N N_i \exp(-łambda_i t)$ in order to estimate the physically significant parameters N, and $łambda_i$. Such problems arise, for example, in the analysis of multicomponent radioactive decay curves, and in the study of the dielectric properties of certain compounds. This paper is concerned with the numerical evaluation of a mathematical approach to the problem. The approach is based on the inversion of the Laplace integral equation by a method of Fourier transforms. The results of the analysis appear in the form of a frequency spectrum. Each true peak in the spectrum indicates a component, the abscissa value at the center of the peak is the decay constant Ai, while the height of the peak is directly proportional to Ni/A ·. Results obtained on an IBM 650 computer indicate that the method may possess certain advantages over previous methods of analysis.

@article{gardner1959method, abstract = { A frequently encountered problem in many branches of science involves the resolution of experimental data into a sum of independent exponential curves of the form $f(t)=\sum_{i=1}^N N_i \exp(-\lambda_i t)$ in order to estimate the physically significant parameters N, and $\lambda_i$. Such problems arise, for example, in the analysis of multicomponent radioactive decay curves, and in the study of the dielectric properties of certain compounds. This paper is concerned with the numerical evaluation of a mathematical approach to the problem. The approach is based on the inversion of the Laplace integral equation by a method of Fourier transforms. The results of the analysis appear in the form of a frequency spectrum. Each true peak in the spectrum indicates a component, the abscissa value at the center of the peak is the decay constant Ai, while the height of the peak is directly proportional to Ni/A ·. Results obtained on an IBM 650 computer indicate that the method may possess certain advantages over previous methods of analysis. }, added-at = {2011-08-15T04:48:01.000+0200}, author = {Gardner, Donald G. and Gardner, Jeanne C. and Laush, George and Meinke, W. Wayne}, biburl = {https://www.bibsonomy.org/bibtex/2b1babb0e972f48cc492ae5e71c9fc104/peter.ralph}, description = {Method for the Analysis of Multicomponent Exponential Decay Curves : Deep Blue at the University of Michigan}, interhash = {e2d6809f341e83145f260c54af8927f5}, intrahash = {b1babb0e972f48cc492ae5e71c9fc104}, journal = {The Journal of Chemical Physics}, keywords = {Laplace_inversion}, month = oct, number = 4, pages = {978-986}, timestamp = {2012-03-23T20:17:13.000+0100}, title = {Method for the Analysis of Multicomponent Exponential Decay Curves}, url = {http://deepblue.lib.umich.edu/handle/2027.42/70060}, volume = 31, year = 1959 }