Integral distribution function

Alternatively, an integral distribution function F may be defined as giving the fraction of surface for which the adsorption energy is greater than or equal to a given Q,... 

Selected entries from Methods in Enzymology [vol, page(s)j Boundary analysis [baseline correction, 240, 479, 485-486, 492, 501 second moment, 240, 482-483 time derivative, 240, 479, 485-486, 492, 501 transport method, 240, 483-486] computation of sedimentation coefficient distribution functions, 240, 492-497 diffusion effects, correction [differential distribution functions, 240, 500-501 integral distribution functions, 240, 501] weight average sedimentation coefficient estimation, 240, 497, 499-500. 

Starting from such frequency distributions one can easily derive cumulative frequencies which can be smoothed by the integrated distribution function F(x). Fig. 2-2 represents the cumulative frequencies of the example depicted in Fig. 2-1, again with a smoothed distribution function. 

The integral distribution function, qn, gives the fraction of total number of particles that represent particles with radius greater than r11 ... 

The use of integral distribution functions is common for two reasons first, these distribution functions have simpler shape and thus are more suitable for curve smoothing second, they allow for an easier determination of the fraction of particles belonging to a particular finite size range, Ar, as a simple difference between corresponding values, q(r + Ar) - q(r). 

This definition of integral distribution function is common in colloid science, while in polymer science the molecular weight distributions are typically evaluated by the summation of molecular weight smaller than the current value... 

An extremely high bubbling velocity results in capture of bubbles in a foam which is subjected to coalescence. However, investigations by Rulyov (1985) show that enlargement of bubbles by coalescence takes place also at small bubbling velocities. Integral distribution functions of bubble diameters in an electroflotation cell, obtained by microphotography, are shown in Fig. 10.11. 

Figure 9. Integral distribution functions of polystyrenes synthesized under Poisson conditions in two solvents (10)...

Figure 11. Integral distribution functions obtained by BW fractionation of anionic poly(methyl methacrylate)s prepared at different reaction temperatures under otherwise identical reaction conditions initiator, cumylcesium in the presence of about 10 3 mole/1 cesium triphenylcyanoborate (19)...

Distribution functions can be classified as discontinuous or continuous. Discontinuous distribution functions are subdivided into frequency distributions and cumulative distributions. Continuous distribution functions are further classified as differential and integral distribution functions. 

If the density function or the mass function is referred to as distribution function, then the real distrihution function is normally called integral distribution function. The reason for the name is clear fromO Eq. (9.5). 

The enforcement of the copolymer fractionation is motivated by the experimental determination of the two-dimensional distribution function of the original polymer. This is normally done by analysis of the fractionation data (ywi. ni) and construction of the integral distribution function. In Fig. 20, the calculated fractionation data are used for this construction. From Fig. 20a it can be seen that the broadness of the original distribution function with respect to the molecular weight can only be obtained by cross-fractionation. This theoretical result agrees with the... 

Sampling without recourse to the Metropolis algorithm has been performed for a limited number of systems. Points are sampled from an integrable distribution function P R), and P- /P is used as a weighting function to obtain averages over Px. For selected systems this approach is competitive with Metropolis sampling and may be especially useful for optimizing atomic and molecular trial functions. ... 

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