An accurate method is presented for the numerical inversion of Laplace transform, which is a natural continuation to Dubner and Abate's method. (Dubner and Abate, 1968). The advantages of this modified procedure are twofold: first, the error bound on the inverse f{t) becomes independent of t, instead of being exponential in t; second, and consequently, the trigonometric series obtained for fit) in terms of F(s) is valid on the whole period 2T of the series. As it is proved, this error bound can be set arbitrarily small, and it is always possible to get good results, even in rather difficult cases. Particular implementations and numerical examples are presented.

This study compared heart rate variability (HRV) in ten male judokas between two types of exercise eliciting the same near-maximal average heart rate (HR): judo wrestling vs. cycloergometric bout. Beat-to-beat RR intervals were recorded during (1) a 4-min judo randori (wrestling); (2) a 4-min cycloergometric exercise eliciting maximal oxygen consumption (VO(2MAX)). Time series were analyzed both by short term Fourier transform (STFT) and Poincaré plot (PP). The main results are as follows. First, despite the fact that the same maximal HR was reached during the two exercises, the spectral energy computed from the judo recordings was significantly higher than that recorded from the cycloergometric exercise. Second, according to the PP index of rapid HRV (SD1), the high-frequency spectral energy (HF) was significantly higher during judo than cycloergometric exercise as well. Third, judo spectra show chaotic harmonics in place of the precise HF peak observed during cycloergometric exercise. Fourth, the respective parts of normalized LFn and HFn are not different between the two exercise modes, suggesting that autonomic control during severe exercise cannot depend on the type of exercise. In conclusion, this study shows that it is possible, according to the observed kind of variability from RR time series, to differentiate between two types of effort: steady-state dynamic exercise or conversely exercise made of both isometric and irregular dynamic efforts (wrestling, collective sports, and others).

Best performances in middle-distance running are characterized by coefficients of variation of the velocity ranging from 1% to 5%. This seems to suggest that running at constant velocity is a strain inducing an increase in physiological variables such as oxygen uptake. This study tested three questions. (l) Does velocity variability during a middle-distance all-out run increase with fatigue? (2) Does velocity variability alter the slow phase of the oxygen kinetic because of small spontaneous recoveries, compared with the same distance run at constant velocity? (3) Is a maintained average velocity over a given distance enhanced by a variable-pace rather than by a constant-pace? Ten long-distance runners performed two series of all-out runs over the distance (previously determined) which they could cover maintaining a velocity equal to 90% of that eliciting maximal oxygen consumption. In the first series ( free-pace) the subjects were asked to run as fast as possible, without any predetermined velocity profile. In the second series, the same distance was covered at a constant velocity (equal to the average in the previous free-pace run), set by a cyclist preceding the runner. Short-term Fourier transform was used to analyse velocity oscillations. Our results show that: (1) for all subjects, the mean energy spectrum did not change throughout the free-pace runs, suggesting that velocity variability did not increase with fatigue (2-way ANOVA, P=0.557); (2) the kinetic of oxygen uptake and its asymptote were not changed during the free-pace runs compared to the constant-velocity run; (3) performance was not significantly improved by free-pace average velocity [mean (SD) 4.22 (0.47) compared to 4.25 (0.52) m x s(-1) for constant and free-pace respectively, t=-0.58, P=0.57]. These results indicate that during middle-distance running, fatigue does not increase variations in velocity, and free-pace changes neither performance nor the oxygen kinetic.

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