Conditional models independence model

The stoichiometric relationship between chlorine dioxide added and color removed during bleaching is nonlinear, but it is independent of temperature, pH, and pulp concentration under conditions normally used. Models used to explain the kinetics and stoichiometry show a strong dependence on chromophore concentration that probably results from differences in the reaction rates of the various chromophores present in the pulps (80). 

The initial conditions for the sensitivity coefficients are usually taken as zero. At the initial condition of the model problem there is no sensitivity to the parameter values, since the initial conditions are usually specified independently of the parameters. 

Table A.2 Predictions from nine different independent models with same material properties and operating conditions for a cross SOFC.

The Wicke and Eigenberger models are models for an ideal adsorption layer. They have been examined at the Institute of Catalysis, Siberian Branch of the U.S.S.R. Academy of Sciences [93-104,108,109] independently of Wicke and Eigenberger (the first publications refer to 1974). It was shown [93-96] that, for the detailed mechanisms of catalytic reactions either with the steps that are linear with respect to intermediates or with non-linear steps (but containing no interactions between various intermediates), the steady state of the reaction is unique and stable (autocatalytic steps are assumed to be absent). Thus the necessary condition for the multiplicity of steady states is the presence of steps for the interaction between various intermediates in the detailed reaction mechanism [93-100]. Special attention in these studies was paid to the adsorption mechanism of the general type permitting the multiplicity of steady states [102-104]... 

The double summation is used to take each of the models as a reference in order to avoid mislocations of optimal discrimination conditions Since the model adequacy criteria and the design criterion are independent of each other, any type of design criterion can be used An alternative one is [9] given by eq 59... 

Under steady-state conditions (and assuming that the inlet condition is independent of time), this two-mode model can be further simplified to... 

In order to determine the influence of various discharge processes on laser characteristics, gas temperature, electron density, and average electron energy were taken as independent modeling parameters [8]. In reality this cannot be achieved under ordinary dc discharge conditions. However, by using this approach it is possible clearly to identify the discharge parameters that have major influence on laser performance characteristics. 

It is essential that while setting the conditions for the differential mass-balance equation we did not define the function of the excess adsorption isotherm. We can now use the expression (2-46) for measurement of the model independent excess adsorption values. It is convenient to use it for the study of the adsorption behavior of binary eluents [22]. 

A remarkable feature of the model (4.1) of size-structured competitors is that the average individual length and the average individual surface area of the /th population at time t approaches a constant value as / ->oo, and this value is independent of initial conditions and independent of whether or not a competing population is present. In order to see this, let... 

When more than one set of experimental results is available, the unknown form of the conversion function f(a) or g(ar) may be eliminated by comparing measurements made at a common value of a under the two (or more) sets of different conditions. These isoconversional methods are thus model independent, or nondiscriminating methods of estimating the Arrhenius parameters [14,42,43]. 

Approaching equilibrium from the other side, In the topmost picture, the same model of the vessel is filled with 2 mol HI molecules. After some time, measurable amounts of H2 and l2 are discovered (middle). When equilibrium has been reached, the composition of the vessel contents remains constant one finds the same equilibrium concentrations as before, namely, 0.22 mol H2, 0,22 mol l2 and 1,56 mol HI per 10 L. The equilibrium conditions are independent of the direction from which the equilibrium is approached. 

Validation of models such as the second-order and multireaction model requires model parameters to be estimated independently. Such a validation should be carried out prior to model adoption for prediction of retention and mobility of heavy metals in soils. This validation is also necessary for the use of a model for different soils and for a wide range of conditions. This requirement is not always achieved because independent parameters are not often available, however. As a result, evaluation of a model is sometimes restricted to goodness of fit of the model results to experimental measurements. 

In the model presented above, the R matrix elements, or matrix of within-subject errors, are uncorrelated and of constant variance across all subjects. When this is the case, Eq. (6.15) is sometimes called the conditional independence model since it assumes that responses for the ith subject are independent of and conditional on the U s and (3. At times, however, this may be an unrealistic assumption since it seems more likely that observations within a subject are correlated. For example, if the model were misspecified, then parts of the data over time would be more correlated than other parts (Karls-son, Beal, and Sheiner, 1995). Hence, it is more realistic to allow the within-subject errors to be correlated. 

We do not mean to imply that Equation 3 is appropriate as a model only because it can be solved analytically. But in fact, under certain conditions it is possible to obtain anaytical solutions to the first order PDE which results when the diffusive terms are neglected in Equation 1. Under these condtions this model predicts single pass concentration profiles accurately and, when applied to the RCFE it yields values for the flip point, i.e. S=-L yE/, which are identical to those predicted in the low Peclet number limit, suggesting that this condition is independent of both molecular diffusion and the electroosmotic flowrate for all values of the Peclet number. It is therefore expected that Equation 3 will yield accurate predictions of both the flip point and the flux profiles in the RCFE. 

---