Virtual extrema

The direction of the differentiation determines the sign of the function. A positive slope of the curve always gives a positive value of the derivative and a negative slope results in a negative value of the derivative. In Fig. 2-8 the direction is from left to right if differentiation proceeds from right to left, then the curves are inverted. Statements c) and d) are especially important and thus need to be discussed in more detail. 

With virtual extrema, inflections are more readily determined, and therefore the spectrum is easier to resolve. On the other hand, with increasing derivative order, simplicity is lost and satellites may sometimes superpose extrema of neighboring analytical peaks. For this reason, with increasing differentiation order, a maximum amount of information will be run through, depending on the complexity of the signals. 

Fortunately, the ratio (i ) of the satellite height to the height of the main peak Aq does not increase linearly. In the value for Ri is 45in it is not approximately 120 0 (extrapolated) but only (Fig. 2-9a and 2-9b) [34, 35]. 

Fell [36] studies the satellites of Gaussian and Lorentzian functions of even orders up to He used a more common but also more complex expression of the Gaussian distribution function. 

The other signs are identical to those in Eq. (2-35) (see Table 2-2). By comparing the derivatives of a Gaussian-shaped analytical peak with a Lorentzian peak (Fig. 2-10), it is remarkable that the outlying satellites of the latter interfere less than 

---

If the amount of heat transferred is infinitesimally small, the extremum principle dictates that the entropy of the system in virtual equilibrium does not change, dS = 0. Since dU0) 0, it is implied that, at equilibrium... 

There are various strategies for avoiding these effects, some of which are common to bulk and non-environmental EXAFS. For instance, if the beamline is capable of quick-EXAFS, then each scan will be taken so quickly that slow drifts will not cause artifacts (Gaillard et al. 2001). Some beamlines (MacDowell et al. 2001) create an image of the source on a set of slits, which in turn becomes a fixed virtual source. Attention to mechanics and temperature stability can pay off in terms of beam-position stability. If one is looking at a particle whose fluorescent yield or transmission is very different from that of its surroundings, then it pays to put the beam accurately on an extremum of yield or transmission. That way, small motions only cause second-order perturbations in the signal. This procedure also minimizes the effect of vibrations. 

---