Logarithmic mean 1124 INDEX

Most frequently, an aerosol is characterized by its particle size distribution. Usually this distribution is reasonably well approximated by a log-normal frequency function (Fig. 4A). If the distribution is based on the logarithm of the particle size, the skewed log-normal distribution is transferred into the bell-shaped, gaussian error curve (see Fig. 4B). Consequently, two parameters are required to describe the particle size distribution of an aerosol the median particle diameter (MD), and an index of dispersion, the geometric standard deviation (Og). The MD of the log-normal frequency distribution is equivalent to the logarithmic mean and represents the 50% size cut of the distribution. The geometric standard deviation is derived from the cumulative distribution (see Fig. 4C) by... 

A very simple and widely used method, known as the method of cumulants, was described by D. Koppel [45], This method allows one to obtain mean value of T(0) and the width of distribution, characterized by the polydispersity index, PI. In the method of cumulants the natural logarithm of g(l)(xcorr, 0) is expanded into polynomial series, in which usually only the first two terms are retained, i.e. ... 

Fig. 5.6 Double logarithmic plot of the mean-square displacements of monomers versus the time for the scaling law of a long chain in the bulk polymer phase. Reptation chains are slower (half-down indexes) than Rouse chains due to the tube confinement...

Pollard et al O have stated that a linear relationship exists between the logarithm of the retention volume and the carbon number for tetraalkylsilanes belonging to the series R Si-R3SiR 2RSiR 3-SiR . For the corresponding series of tetraalkoxysilanes, an approximately linear relationship between retention index and carbon number will exist only for a series with small values of the product d.k. in the correction term of equation (2). This means that an approximately linear relationship will be found, for example, for the series (PrO) Si(OBu) (n = 4-0), but not for the series (MeO) Si(0Bu) j (n = 4-0), (see Figure 60),... 

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