Differential distribution function

If the differential distribution function is exponential in Q (Section XVII-14A), the resulting Q(P, T) is that known as the Freundlich isotherm... 

The average size of the surviving particles is obtained by weighting R(t) by the differential distribution function and integrating over the range of possible times ... 

It is normally called the differential distribution function (of residence times). It is also known as the density function or frequency function. It is the analog for a continuous variable (e.g., residence time i) of the probabiUty distribution for a discrete variable (e.g., chain length /). The fraction that appears in Equations (15.2), (15.3), and (15.6) can be interpreted as a probability, but now it is the probability that t will fall within a specified range rather than the probability that t will have some specific value. Compare Equations (13.8) and (15.5). 

Equation (8.11) gave the differential distribution function that corresponds to a parabolic velocity prohle in a tube. This specihc result is now derived in a more general way. 

Thus, the fraction unreacted is the Laplace transform with respect to the transform parameter k of the differential distribution function. 

Finally, the cumulative distribution function G(X) is defined as the integral function of the differential distribution function g(X) ... 

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. 

Equation (15.39) allows moments of a distribution to be calculated from the Laplace transform of the differential distribution function without need for finding f(t). It works for any /(/). The necessary algebra for the present case is formidable, but finally gives the desired relationship ... 

On the same assumptions regarding the limits of cell sizes, the differential distribution function may be approximated by the following exponential formula... 

The dependences of the retention ratio R on the size of the fractionated species (molar mass for the macromolecules or particle diameter for the particulate matter) are presented for various polarization FFF methods in the entry Field-Flow Fractionation Fundamentals. The raw, digitized fractogram, which is a record of the detector response as a function of the retention volume, is represented by a differential distribution function h(y). i can be processed to obtain a series of the height values hi corresponding to the retention volumes as shown in Fig. 1. Subsequently, the retention volumes are converted into the retention ratios Rf. 

According to the cellular model, the structure of curves and response curve shape are described by the differential distribution function ... 

Chain-length distributions are described by their differential distribution function ... 

A probability distribution in which the differential distribution function has two maxima. 

An overall adsorption equation derived within the framework of DFT (Do et al. 2001) improved to be used for different pore models (Gun ko et al. 2007f) and nonlocal DFT (NLDFT Quantachrome Instruments software, version 2.02) with the model of cylindrical pores in silica was applied to calculate the PSDs (PoSD). The differential distribution functions (j/v(l p)6 l p Vp) were converted to incremental PoSDs (IPSDs, 0() p) at EO ( p) Vp) (Figure 1.189). 

---