Power exponential

Inverse Laplace transforms have been tabulated for most analytical functions, including power, exponential, trigonometric, hyperbolic and other functions. In this context we require only the inverse Laplace transform which yields a simple exponential ... 

The correlation function R(-, ) in (2) is central to this statistical model. The power-exponential class of correlation functions is a popular choice, for its computational simplicity and because it has been successful in many applications. The power-exponential correlation function is... 

The power-exponential correlation function (3), for example, is of this product form. To computere x), the integral on the right-hand side of (22) is evaluated as... 

A mathematical model using power exponential equations [39] is used to reproduce gastric and ileal deliveries (f = 1 — where / represents... 

Simple Compound symmetry T oeplitz Power Exponential Gaussian... 

The actually observed relaxation function in the fast limit does not alw s follow strictly an exponential decay. In practice a power exponential relaxation is often used... 

Fig. 102. Left Temperature dependence of the near ZF muon spin relaxation rate in i-Tb Mg,2Zn5(i on double logarithmic scales. The vertical dashed line indicates the onset of loss of asymmetry due to instnunental dead time. The inset shows the temperature dependence of power used in the power exponential fit to the relaxation spectra. The spin-glass temperature is near 8K. Right pSR asymmetry spectra of i-Gd Mg42Zn5o at 1.5 K, in the applied longitudinal fields shown. The solid lines are a least-squares fit of a mildly inhomogeneous freezing...

In the paramagnetic regime (T > Tm), the spectra in a weak LF (needed to suppress the depolarization by Cu nuclear dipoles) for x > 0.08 were most easily fitted to a power exponential (exp[—(At) ]) relaxation. Hence the summary label relaxation rate in fig. 113 (left) refers to the static width Aeff (see eq. 74) for T dynamic rate A for r > Tu- The variation of power p was studied in some detail for the 10% sample. A decrease fromp w 1 at high temperatures top w 0.6 close to Tm was found. This is another indication that a disordered spin-glass-like state is approached and 7m might best be considered a spin freezing temperature. This spin-glass-like state, however,... 

Fig. 133. Temperature dependenee of the power in the power-exponential relaxation fit to the ZF speetra of single-erystalline CePt2Snj. From Luke et al. (1997a).

Based on analyses the power-exponential function was selected due to its ability of data approximation. The power-exponential function is the product of the power and exponential function. This function is known to have been used for modelling road safety measures (Kononov et al., 2008), (Elvik, 2004). The generalised form of the function is shown in formula (4). 

To model the measures of normalised risk, the power-exponential function was used described with general formulas (5 and 6) (Jamroz, 2011) ... 

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