Scaling range

An alternative to autoscaling is range scaling, where the denominator in Equation (12.20] equals the range (the difference between the maximum and minimum values). Range scaling gives a set of new values between —0.5 and +0.5. 

Other possibilities are range scaling and logarithmic transformation. In range scaling one does not divide by Sj as in eq. (30.6), but by the range rj of vmable j. 

In some cases, one needs to combine variables of mixed types (binary, ordinal or continuous). The usual way to do this is to eliminate the effect of varying ranges by scaling. All variables are transformed, so that they take values from 0 to 1 using range scaling for the continuous variables or the procedure for scaling described... 

The scalar-dissipation wavenumber /cd is defined in terms of /cdi by /cd = Sc1/2kdi-Like the fraction of the turbulent kinetic energy in the dissipation range kn ((2.139), p. 54), for a fully developed scalar spectrum the fraction of scalar variance in the scalar dissipation range scales with Reynolds number as... 

The mixing parameter Q must be chosen to yield the correct mixture-fraction-variance dissipation rate. However, inertial-range scaling arguments suggest that its value should be near unity.165... 

MLF are composed of a number of computational elements, called neurons, generally organized in three layers (Marini, 2009). In the first one, the input layer, there are usually N neurons which correspond to the original predictor. The predictors are scaled (generally range scaled). When the number of original predictors is very high, the PCs may be used, in order to reduce the data amount and the computational time. 

On the other hand, WAXS measurements of PE melt clearly indicate a range of intermolecular distance correlations of about 25 A [3]. Together with the relatively high density of polymer melts, the fact that the first interchain halo in WAXS patterns of oriented amorphous polymers tends to lie in the equatorial direction and the relatively high WAXS intensity of the interchain halo support the idea of parallel chain segments on the short range scale. 

The flexibility index determines the largest uncertainty range (scaled hyperrectangle) for which the HEN is resilient. The flexibility index is scaled in terms of an expected uncertainty range (0N - F Afl <0<0N + F A0+). 

CSM has coupled the FBRM with a second probe, the particle video microscope, PVM (Lasentec/Mettler Toledo), which consists of six illuminating near-infrared lasers (850 nm) that are transmitted into the sample. While the FBRM provides precise quantitative tracking of the chord lengths, the PVM probe provides qualitative images of the hydrate particle size and degree of agglomeration. The size range scale of hydrate particles that can be measured with the PVM probe is 10-300 i,m. 

An automatic or manual titration device may be used. For the latter, the burette is graduated in UJUU5 mi, and the pH meter is provided with a wide-range scale and glass-calomel electrodes. 

Here 3/, = Ex — av = tuox — (Ek + ))/2. The second term in Eq. (5.47), in brackets, is a function of TxSEfi. If two bound state levels dominate the pump excitation, then this term contributes a scaling characteristic to control plots. That is, if we plot contours of constant dissociation probability as a function of A, and 5E.k then, barring the first term, plots with different Tx will appear similar, with a new range scaled by 5E, = (Tx/T )2SEjt. >... 

The long-range order which is stabilized at low temperature depends on the nature of the incipient instabilities that develop at high temperature along each stack on a short-range scale without any transverse correlation (i.e., one-dimensional fluctuations). It is therefore more illustrative to present the physical properties versus temperature for a few representative... 

TABLE I. Permeabilities, Pore Size Ranges, Scale, ... 

A typical situation is realized in such cases - fractal structure properties appear on a range scale which is limited by the dimensions of the particles forming the aggregate at the beginning, and at the end, by the dimensions of the initial fractal clusters. Typical particle dimensions are 1-10 nm aggregate dimensions are 10-1000 nm. The fractal dimension, df, depends on the conditions of aggregate formation and, as a rule, lies within a range of df = 2 — 2.9. 

Work carried out at the University of Birmingham (11), in England, by Dr. Emmott on middle distillates has revealed the presence of large amounts of sulfides in virgin stocks. As one ascends the boiling range scale the information on the types of sulfur compounds present becomes more limited. Hoog (26) has examined some Middle East gas oil and has deduced from the results of the several experimental techniques employed that essentially no sulfides, di- or polysulfides, or mercaptans were present and that the sulfur compounds of that specific gas oil were preponderantly of the thiophene and thiophane type. 

FIGURE 8.7. (a) 3D plot after SIMCA analysis using mean-centered preprocessing with five factors and a probability threshold of 0.95 for the opium samples from different locations, (b) 3D plot after SIMCA analysis using range scale preprocessing with three factors at a probability threshold of 0.95 for the poppy straw samples. See color insert. 

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