Journal ArticleDOI
An eigenfunction expansion method for the analysis of exponential decay curves
Reads0
Chats0
TLDR
In this article, a method is developed for the analysis of data composed of random noise, plus an unknown constant "baseline", plus a sum (or an integral over a continuous distribution) of exponential decay functions.Abstract:
A method is developed for the analysis of data composed of random noise, plus an unknown constant ’’baseline,’’ plus a sum (or an integral over a continuous distribution) of exponential decay functions. It is based on the expansion of the solution of a Fredholm integral equation of the first kind in the eigenfunctions of the kernel. In contrast to the Fourier transform solution [Gardner et al., J. Chem. Phys. 31, 978 (1959)], the finite time range of the data is exactly accounted for, and no extrapolation or iteration is necessary. A computer program is available for the analysis of sums of exponentials. It is completely automatic in that the only input are the data (not necessarily in equal intervals of time); no potentially biased initial estimates of either the number or values of the amplitudes and decay constants are needed. These parameters and their standard deviations are decided with a linear hypothesis test corrected approximately for nonlinearity. Tests with simulated two‐, three‐, and four‐com...read more
Citations
More filters
Journal ArticleDOI
Investigation of dynamic equilibria using NMR-spectroscopy III. Saturation transfer experiments on the hydration of pyridine-4-carbaldehyde
TL;DR: Spin saturation experiments can be performed by pulse techniques and are very useful for the estimation of rate constants of chemical reactions in the time range of 0.1 to 1 seconds, where classical methods as well as relaxation kinetics are unfavourable as mentioned in this paper.
Journal ArticleDOI
Fit of a sum of exponential functions to experimental data points
F.S. Monjoie,Henri-Pierre Garnir +1 more
TL;DR: Expfit as discussed by the authors is a program aimed at the analysis of light decay curves in beam-foil spectroscopy experiments, which fits, using the least-squares method, a sum of exponential functions to experimental data points.
Book ChapterDOI
The interpretation of fission track annealing behaviour in apatite and other minerals
E. Bertel,T.D. Märk,M. Pahl +2 more
TL;DR: In this paper, a new mathematical representation for the isothermal annealing function of fission tracks in apatite (and other minerals) is given, and it is shown that this analysis suggests the FT-annealing to be governed by monomolecular recombination or by anneal of dislocation loops.
Journal ArticleDOI
Cascade corrected lifetimes of the 4p4DJ0 excited states in Ar II using the beam—foil technique
TL;DR: In this paper, the beamfoil and ANDC method was used to determine the lifetimes of the 4p4D7/2, 5/2 and 3/2 levels in Ar II.
Book ChapterDOI
Beam-Foil Spectroscopy
TL;DR: The energy levels and spectra of free atoms and ions have been studied for many years as mentioned in this paper, and the physical quantities of interest include transition wavelengths, excitation and ionization energies, as well as fine-and hyperfine structure separations.
References
More filters
Journal ArticleDOI
Handbook of Mathematical Functions
Journal ArticleDOI
A Fourier method for the analysis of exponential decay curves
TL;DR: A method based on the Fourier convolution theorem is developed for the analysis of data composed of random noise, plus an unknown constant "base line," plus a sum of (or an integral over a continuous spectrum of) exponential decay functions.
Journal ArticleDOI
Method for the Analysis of Multicomponent Exponential Decay Curves
TL;DR: In this article, a mathematical approach based on the inversion of the Laplace integral equation by a method of Fourier transforms was proposed to estimate the physically significant parameters Ni and λi. The results of the analysis appeared in the form of a frequency spectrum.