Cumulative properties definition

There is a definite need for a good, long-acting sedative which will have no cumulative properties—perhaps a long-acting chloral hydrate or an agent with slow onset of action but which is rapidly eliminated. 

By definition, biocides are toxicologically active. It is therefore important to ensure that they are not harmful, in the doses used, to humans and other warm blooded animals. In particular, no cumulative properties... 

It is possible to determine the cumulative residence time distribution function F(t) from either a tracer step-change or a tracer impulse response. From its definition, the properties of F(t) are ... 

Before discussing our method for determining particle size, it is necessary to briefly review the definition of size distribution. If all particles of a given system were spherical in shape, the only size parameter would be the diameter. In most real cases of irregular particles, however, the size is usually expressed in terms of a sphere equivalent to the particle with regard to some property. Particles of a dispersed system are never of either perfectly identical size or shape A spread around the mean distribution) is found. Such a spread is often described in terms of standard deviation. However, a frequency function, or its integrated (cumulative) distribution function, more properly defines not only the spread but also the shape of such a spread around the mean value. This is commonly referred to as the particle size distribution (PSD) profile of the dispersed sample. 

In Fig. 16.2(A-D) we present the spectra as a function of energy for all four cases. In Fig. 16.2A we show the exact 24-mode result and for the sake of comparison the remaining Fig. 16.2(B-D) also display this curve. It was already mentioned in the theory section that the 3(QVC)-mode model reproduces the zeroth- to second-order cumulants of the molecule, connected to observable properties of the spectrum in such experiments. These are the total intensity, the position of the maximum and the with of the spectrum. Due to the absence of theoretical proof concerning the conservation of the third cumulant, which is related to the major asymmetry of the spectra, we can not discuss this feature with certainty. As expected the spectra obtained by the 6-mode model (see Fig. 16.2B) is most similar to the exact one. However the global shape of the exact spectrum is more or less reproduced by our 3(QVC)-mode formulas too. Some oscillations appear in particular within the (0-0.3 eV) interval, but the picture is definitely closer to the exact one than that obtained by the 3(LVC)-mode approach. Apart from these oscillations one can see that the position of the maximum, the width and even the main asymmetry of the spectrum are satisfactorily reproduced by our present method. 

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