Parameters’ value

If this criterion is based on the maximum-likelihood principle, it leads to those parameter values that make the experimental observations appear most likely when taken as a whole. The likelihood function is defined as the joint probability of the observed values of the variables for any set of true values of the variables, model parameters, and error variances. The best estimates of the model parameters and of the true values of the measured variables are those which maximize this likelihood function with a normal distribution assumed for the experimental errors. 

The addition of components to this set of 92, the change of a few parameter values for existing components, or the inclusion of additional UNIQUAC binary interaction parameters, as they may become available, is best accomplished by adding or changing cards in the input deck containing the parameters. The formats of these cards are discussed in the subroutine PARIN description. Where many parameters, especially the binary association and solvation parameters are to be changed for an existing... 

The values of common hydrocarbon solubility parameters vary between 300 and 600 (kJ/m3) /2 Several tables are available where the solubility parameters are shown as (cal/cm ) / Jq convert these values, it is necessary to multiply by 64.69. Thus a solubility parameter value of 10 (cal/cm ) / jg equal to 646.9 (kJ/m ) / ... 

In practice, it is nontrivial to manually select the parameter values to obtain successful results. Moreover, it is not obvious how to measure the quality of the results. Therefore, a well defined performance measure and an efficient parameter optimization method are desired. 

By means of the performance measure H x) described above, systematic and iterative search for good parameter values can be performed. In this work, one systematic and two iterative search methods were explored. 

In the systematic approach, the contaminated signal was processed using transients with parameters selected from a uniformly sampled grid in the parameter space. For each parameter value, the quality of the processed signal was computed. An example result is presented in Figure 2 which shows the performance as a function of the two parameters and / p. The parameter values /, and which yielded the lowest entropy were selected for processing. 

The Channel area contains controls which affect each of the channels (detection and coupling) independently. The parameter values displayed refer to the channel currently selected for dis-play-... 

The reactant P is again taken as a pool chemical, so the first step has a constant rate. The rate of the second step depends on the concentration of the intennediate A and on the temperature T and this step is taken as exothennic. (In the simplest case, is taken to be independent of T and the first step is thennoneutral.) Again, the steady state is found to be nnstable over a range of parameter values, with oscillations being observed. 

For certain parameter values tliis chemical system can exlribit fixed point, periodic or chaotic attractors in tire tliree-dimensional concentration phase space. We consider tire parameter set... 

To gain some idea of the meaning of this shaded area, consider the straight line OA of slope a/q shown in Figure 25.4. The line enters the region of stable motion at P and leaves it at Q. For typical values of U (1000 V), V (6000 V), co (1.5 MHz), and r (1.0 cm). Equation 25.2 predicts that point P corresponds to an ion of m/z 451 and Q to m/z 392. Therefore, with these parameter values, all ions having m/z between 392 and 451 will be transmitted through the quadmpole. 

Antioxidants have been shown to improve oxidative stabiHty substantially (36,37). The use of mbber-bound stabilizers to permit concentration of the additive in the mbber phase has been reported (38—40). The partitioning behavior of various conventional stabilizers between the mbber and thermoplastic phases in model ABS systems has been described and shown to correlate with solubiHty parameter values (41). Pigments can adversely affect oxidative stabiHty (32). Test methods for assessing thermal oxidative stabiHty include oxygen absorption (31,32,42), thermal analysis (43,44), oven aging (34,45,46), and chemiluminescence (47,48). 

The isolation and/or identification of nonpolymerics has been described, including analyses for residual monomers (90,102,103) and additives (90,104—106). The deterrnination of localized concentrations of additives within the phases of ABS has been reported the partitioning of various additives between the elastomeric and thermoplastic phases of ABS has been shown to correlate with solubility parameter values (41). 

As computing capabiUty has improved, the need for automated methods of determining connectivity indexes, as well as group compositions and other stmctural parameters, for existing databases of chemical species has increased in importance. New naming techniques, such as SMILES, have been proposed which can be easily translated to these indexes and parameters by computer algorithms. Discussions of the more recent work in this area are available (281,282). SMILES has been used to input Contaminant stmctures into an expert system for aquatic toxicity prediction by generating LSER parameter values (243,258). 

The parameter values for the curves of Fig. 14-14 originally were defineci from film theory as (Dg/D )(B /vCi) but later were refined by the results of penetration theory to the definition (( ) — 1), where... 

Preliminary Analysis The purpose of the preliminary analyses is to develop estimates for the model parameter values and to estabhsh the model sensitivity to the underlying database and plant and model uncertainties. This will estabhsh whether the unit test will actually achieve the desired results. 

The hurdles to arriving at a unique set of parameter values are large. 

The measurements do not close the constraints. Estimation of the parameter values against the actual measurements results in parameter values that are not unique. 

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