Optimum deviation parameters

Table VII. Root Mean Square Deviations (GPa-1) between Calculated Mixture Isothermal Compressibilities and Experimental Values from Reference 11, pp. 166—184, and Optimum Deviation Parameters (j) for Equation 26...

A comparison of columns 4 and 8 reveals no clear pattern, which is perhaps of greater significance. The use of raw data yields smaller values of the vapor composition sample deviations in four out of six cases, but the effects are small and could be masked by errors in the vapor compositions themselves. It seems likely that the greatest source of error lies in determination of vapor composition. Thus there is very little difference in using raw or smoothed data. A typical example of the fit is shown in Figure 2. The optimum smoothing parameters used in run 1 were found to be the same as required for run 2, and are listed in columns 11 and 12 of Table II. 

Figure 1. Optimum binary deviation parameters (k and ji j) and confidence ellipses for the fit of the LHW equation of state to the Nz + Ar VE data of Ref. 11, pp. 166-168...

Optimum transport parameters obtained from diffusion and pomeation measurements are summarized in Table 2 and visualized in Fig. 4. The Cherox 42-00 and F12(K) samples show an excellent agreement between transit parameters iif)A and (ip)p (deviation less than 5% index d stands for diffiision and V for permeation). For the other pellets the agreement is slightly worse. 

The maximum number of latent variables is the smaller of the number of x values or the number of molecules. However, there is an optimum number of latent variables in the model beyond which the predictive ability of the model does not increase. A number of methods have been proposed to decide how many latent variables to use. One approach is to use a cross-validation method, which involves adding successive latent variables. Both leave-one-out and the group-based methods can be applied. As the number of latent variables increases, the cross-validated will first increase and then either reach a plateau or even decrease. Another parameter that can be used to choose the appropriate number of latent variables is the standard deviation of the error of the predictions, SpREss ... 

Fig. 5.17. Time domain CARS of nitrogen under normal conditions. Points designate experimental data, solid line calculation with a = 6.0 A, b = 0.024, c = 0.0015. The insert depicts the dependences of the relative mean-square deviation on each of the parameters , b and c, the other two being fixed at their optimum values. The deviations are expressed as percentage of optimum parameters.

Estimates have been made of the amount of strain energy associated with the deviation from the optimum values of the structural parameters caused by steric factors.112 These estimates can be expressed by... 

The variability of the process parameters with flow causes variability in load response, as shown in Fig. 8-50. The PID controller was tuned for optimum (minimum-IAE) load response at 50 percent flow. Each curve represents the response of exit temperature to a 10 percent step in liquid flow, culminating at the stated flow. The 60 percent curve is overdamped and the 40 percent curve is underdamped. The differences in gain are reflected in the amplitude of the deviation, and the differences in dynamics are reflected in the period of oscillation. 

A closer relationship between foam stability and HLB has been reported for two- or three-phase systems surfactant solution-oil or oil-surfactant phase-water [60,109-111]. The effect of various parameters changing HLB on the stability of foams and emulsions has been studied in [111]. These were the concentration of amyl alcohol and sodium chloride, the number of the ethylene oxide groups in the molecule of the oxyethylated octylphenol. As a general parameter of HLB the authors used the surfactant affinity difference concept (SAD) which is an empirical generalised formulation. It measures the deviation from the optimum formulation for three phase behaviour. For anionic surfactants... 

With the present feasibility of evaluating experimental data with the aid of a computer, more refined or optimum values of the ion-size parameter can be obtained. For example, Paabo and Bates, in a study of the dissociation of deuteriophosphoric acid or deuteriocarbonate ion, selected the ion-size parameter as that which gave the smallest standard deviation for the least-squares intercept for the ionization constant. 

To determine the optimum process condition(s) and formulation that minimize the effects of ageing requires 1) an acceptable value for the parameter being investigated and 2) consistency in the parameter as a function of measurements taken over time. The Nike specification is taken as the acceptable value. The percent standard deviation (%SD) is used as a measure of consistency. 

In this case the initial guess was fairly close the optimum, k. As the initial guess is further away from k, the number of iterations increases. For example, if we use as initial guess k ° l, 1000000), convergence is achieved in eight iterations. At the optimum, the following parameter values and standard deviations were obtained k,=0.0037838 0.000057 and k2=27643 461. 

Ip when the SNR value is reduced. Finally, they tested the effect of the number of sampling points from 2 to 2 °. The deviations in Ep and Ip are reduced with a higher value of this parameter. The authors concluded that the third-order B-spline wavelet basis, and truncation frequency L = 3, are the optimum parameters for processing voltammetric signals. 

Fig. 3. Definition of the orientation parameter, that is, the deviation, from the optimal angle, of the dipole orientation with respeet to the side-chain N-R bond. The optimum for...

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