Multi-exponential behaviour

Two principal explanations have been put forward to account for this multi-exponential behaviour, which have turned out to be very difficult to distinguish experimentally (and anyway are not mutually exclusive). However this topic has attracted considerable interest because regardless of which explanation is correct, both originate from fundamental properties of protein systems which are difficult to access through experiment. A number of the papers cited above have discussions on the possible origins of multi-exponential P decay, as do recent reviews and articles (Parson, 1996 Bixon et al., 1995 Woodbury and Allen, 1995 Gehlen et al., 1994 Gudowska-Nowak et al., 1994 Kolaczkowski et al., 1994 Small et al.,... 

Knowledge of is essential if production of a state of thermal equilibrium is required. Various schemes have been proposed to measure rapidly, but these are always approximate and usually unable to detect any complex, multi-exponential behaviour. The two accurate methods in common use are inversion recovery and saturation recovery. Both of these techniques involve the establishment of a known non-equilibrium population state, evolution, and sampling of the magnetisation as a function of the evolution time. 

In particular, the application of multi-exponential decay kinetics anticipated from models that assume distinct photophysical species within polymer chains may be inappropriate in some cases. The possibility of non-exponential fluorescence decay behaviour arising from energy migration and trapping (11) should also be considered. Additional studies of the mobilities of fluorescent probes incorporated in PMA using time-resolved fluorescence anisotropy measurements provide further support for a "connected cluster" model to describe the conformation of this polyelectrolyte in aqueous solution at low pH. 

At all but the simplest level, treatment of the results from a time-domain experiment involves some mathematical procedure such as non-linear least squares analysis. Least squares analysis is generally carried out by some modification of the Newton-Raphson method, that proposed by Marquardt currently being popular [21, 22]. There is a fundamental difficulty in that the normal equations that must be solved as part of the procedure are often ill-conditioned. This means that rather than having a single well-defined solution, there is a group of solutions all of which are equally valid. This is particularly troublesome where there are exponential components whose time constants differ by less than a factor of about three. It is easy to demonstrate that the behaviour is multi-exponential, but much more difficult to extract reliable parameters. The fitting procedure is also dependent on the model used and it is often quite difficult to determine the number of exponentials needed to adequately represent the data. Various procedures have been suggested to overcome these difficulties, but none has yet received wide acceptance in solid-state NMR [23-26]. 

To provide an answer to the question, how the SPF depends on the application amount, a multi-centre study involving three test centres has been conducted by the task force sun protection of the DGK (German society of scientific and applied cosmetics). Employing the SPF in vivo test, three commercial sunscreens were applied at rates of 0.5, 1.0, and 2.0 mg/cm, and a linear dependence of the SPF on application amount was observed. Thus, the exponential behaviour expected from the oversimplified consideration of equation (7) was not confirmed. 

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