Weighted experimental data

Nimura, Y. Carr, M. R. Reduction of the Relative Error in the Standard Additions Method, Analyst 1990, 115, 1589-1595. The following paper discusses the importance of weighting experimental data when using linear regression Karolczak, M. To Weight or Not to Weight An Analyst s Dilemma, Curr. Separations 1995, 13, 98-104. 

Figure 4 shows the k weighted experimental data (solid line), filtered data (dashed line) and fit (squares) for an electrode modified with 50 monolayers of poly-[Ru(v-... 

FIG, 14. (A) Plasma lime course of diazinon (DZN) in rais following intravenou.s (iv) and oral administration of 10 (gray) and 80 (black) mg DZN/kg of body weight, respectively (data from Wu ei ai. 19%). (B) inhibition of plasma ChE, and (C) RBC AChE in rat-s after ip dosing with 100 rag DZN/kg of body weight. Experimental data from Tomokuni and Hasegawa et al. (1985). Adapted with permission from Poet et ai. (2004). 

Figure 14.19 Concentration profiles of Irganox 1076 in LDPE for seven different incubation times at 40 °C expressed as the amount in the polymer at time t relative to the initial amount in the polymer per unit polymer weight. Experimental data are shown by crosses and the best-fitting curve by solid lines. Reproduced with permission from Helmroth and co-workers, Journal of Applied Polymer Science, 2002, 86, 12, 3185 [63], 2002, Wiley)...

At one time, it was thought that this parameter depended only on the solvent and temperature for a given polymer. However, it was later realized that the scaling of the radius with molecular weight is not accoimted for correctly by a constant value of a and that this parameter depends on the molecular weight. Experimental data indicate that the root-mean-square end-to-end vector is in fact proportional to... 

Figure Bl.14.13. Derivation of the droplet size distribution in a cream layer of a decane/water emulsion from PGSE data. The inset shows the signal attenuation as a fiinction of the gradient strength for diflfiision weighting recorded at each position (top trace = bottom of cream). A Stokes-based velocity model (solid lines) was fitted to the experimental data (solid circles). The curious horizontal trace in the centre of the plot is due to partial volume filling at the water/cream interface. The droplet size distribution of the emulsion was calculated as a fiinction of height from these NMR data. The most intense narrowest distribution occurs at the base of the cream and the curves proceed logically up tlirough the cream in steps of 0.041 cm. It is concluded from these data that the biggest droplets are found at the top and the smallest at the bottom of tlie cream.

Polydisperse polymers do not yield sharp peaks in the detector output as indicated in Fig. 9.14. Instead, broad bands are produced which reflect the polydispersity of synthetic polymers. Assuming that suitable calibration data are available, we can construct molecular weight distributions from this kind of experimental data. An indication of how this is done is provided in the following example. 

The quantity of undrainable residual moisture caimot be predicted without the benefit of experimental data. Equation 17 (6) indicates the important parameters where the exponents were determined using limited experimentation. Introducing the approximation that is proportional to 1/d, where s is the specific surface area per weight of solid, the modified equation for undrainable liquid becomes... 

A predictive macromolecular network decomposition model for coal conversion based on results of analytical measurements has been developed called the functional group, depolymerization, vaporization, cross-linking (EG-DVC) model (77). Data are obtained on weight loss on heating (thermogravimetry) and analysis of the evolved species by Eourier transform infrared spectrometry. Separate experimental data on solvent sweUing, solvent extraction, and Gieseler plastometry are also used in the model. 

W1 is Bond work index based on 100 percent passing a 200-mesh sieve, is the sohds feed rate in kg/min, and S is weight percent solids in the feed. This represents experimental data for limestone, feldspar, sulfide ore, and quartz. The influence of Wl is believed to be due to its effect on amount of fines present in the mill. Parameters that did not affect are specific gravity of feed material, and feed size over the narrow range studied. 

The problem of finding conformations of the molecule that satisfy the experimental data is then that of finding conformations that minimize a hybrid energy function i,ybiM, which contains different contributions from experimental data and the force field (see below). These contributions need to be properly weighted with respect to each other. However, if the chosen experimental upper and lower bounds are wide enough to avoid any geometrical inconsistencies between the force field and the data, this relative weight does not play a predominant role. 

Internal dynamics of the macromolecule influences all experimental data that can be measured by NMR. The weighting of the NOE makes the averaging very nonlinear, and the measured distance may appear much shorter than the average distance (see Eig. 9). 

Figures Background-subtracted, normalized, and ili -weighted Mo K-edge EXAFS, versus k (A ), for molybdenum metal foil obtained from the primary experimental data of Figure 2 with Eq = 20,025 eV.

When TPU was the major component (PVC/TPU < 1), the experimental data [11] showed that within a certain range of molecular weight, the strength of the material increased with the increase of PVC molecular weight and the elasticity did not show any significant difference. However, the melt viscosity increased, and this caused difficulties in the processing. 

Figure 2 Orbital magnetic moments in bcc-Fe Coi-a . The triangles pointing up-and downwards represent the theoretical moments of Fe and Co, respectively, while the concentration weighted sum is given by circles. Full and open symbols stand for results obtained with and without the OP-term included (SOPR- and SPR-KKR-CPA, resp.). Experimental data [15] for the average magnetic moment (bottom) stemming from magneto mechanical and spectroscopic g-factors are given by full squares and diamonds.

The situation becomes most complicated in multicomponent systems, for example, if we speak about filling of plasticized polymers and solutions. The viscosity of a dispersion medium may vary here due to different reasons, namely a change in the nature of the solvent, concentration of the solution, molecular weight of the polymer. Naturally, here the interaction between the liquid and the filler changes, for one, a distinct adsorption layer, which modifies the surface and hence the activity (net-formation ability) of the filler, arises. Therefore in such multicomponent systems in the general case we can hardly expect universal values of yield stress, depending only on the concentration of the filler. Experimental data also confirm this conclusion [13],... 

Figure 3.7 shows the growth of R. rubrum in a batch fermentation process using a gaseous carbon source (CO). The data shown follow the logistic model as fitted by (3.14.2.11) with the solid lines, which also represent an unstructured rate model without any lag phase. The software Sigma Plot was used to fit model (3.14.2.11) to the experimental data. An increase in concentration of acetate in the prepared culture media did not improve the cell dry weight at values of 2.5 and 3 gT-1 acetate, as shown in Figure 3.7. However, the exponential growth rates were clearly observed with acetate concentrations of 0.5-2 g-F1 hi the culture media.

Fig. 9. Comparison of Eqs. (144) (solid line) and (145) (dashed line) with the experimental data of Calderbank and Moo-Young (C4) for the absorption of C02 at 25°C in water containing the following percentages by weight of glycerol [after Gal-Or and Walatka (G9)]...

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