Undefined parameters

Experimentally undefined parameters, which have a real physical meaning that is, they reflect an actual physical phenomenon but cannot be determined from the experimental data (even a thought experiment to measure them cannot be conceived) or by a thermodynamic calculation. In isolated cases such parameters can be calculated on the basis of nonthermodynamic models. The equations used for calculations generally contain sums, differences, or other combinations of such parameters that are measurable. The Galvani potential at the interface between two dissimilar conducting phases is an example. 

The electrochemical potential of single ionic species cannot be determined. In systems with charged components, all energy effects and all thermodynamic properties are associated not with ions of a single type but with combinations of different ions. Hence, the electrochemical potential of an individual ionic species is an experimentally undefined parameter, in contrast to the chemical potential of uncharged species. From the experimental data, only the combined values for electroneutral ensembles of ions can be found. Equally inaccessible to measurements is the electrochemical potential, of free electrons in metals, whereas the chemical potential, p, of the electrons coincides with the Fermi energy and can be calculated very approximately. 

Unfortunately, neither the averaging procedure to obtain nor the manner in which pt(AE) is to be evaluated are unambiguously defined. Thus, (41) replaces a single experimental quantity by two undefined parameters and an electronic factor which is difficult to evaluate. 

In defining the harmonic oscillator basis by Eqs. (5.23)—(5.25) the problem of scaling was postponed. Equation (5.27) shows that the three yet undefined parameters, D, E° and a, are interrelated so that they are all determined when anyone has been given a value. A reasonable estimate is most easily obtained for the spacing E°, which should be close to the mean spacing of the levels considered, in order to minimize the dimensions of the Hamilton matrix. Thus, in the present example it was found that with E° = 80 cm-1 the basis could safely be truncated at n = 39 corresponding to matrix dimensions 20 x 20 for the diagonal blocks of H. ... 

With the basic ingredients in hand, the next step is to set up a working force field. It is not necessary at this point to achieve a good fit, but the force field should allow calculations for all stfuctures needed to reproduce the reference data set. This involves choosing functional forms for bonds and angles involving the metal and then guessing reasonable values for all previously undefined parameters. When all of this is accomplished, automatic procedures can vary the param-... 

Probability theory and mathematical statistics had long been considered the only method of dealing with indetermination until the 1960s although in reality there were many undefined parameters. Dealing with optimization problems, one would often find the so-called stochastic programming model formed by those parameters that appeared in the model as random variables [1]. 

Equation (5.149) is a local polarization curve of the cell it includes a yet undefined parameter E. To calculate this parameter we equate two... 

Quantitative thin-layer chromatography (QTLC) measured by direct photometric scanning has been performed for more than forty years. Despite this long period, this procedure has not achieved the reputation of a very reliable quantitative analytical method. Large standard deviations in measurements have often been mentioned as a reason why TLC was supposedly not acceptable for quantitative work. The most important reasons which have kept TLC from being recognized as a quantitative tool were uncertainties and problems in sample applications, development, and scanning. There were many undefined parameters, factors which contributed to the poor reproducibility of TLC. 

As previously stated, both these methods have been utilized to affect the stability of a poly (vinyl chloride) latex. Using the coagulation data obtained, the only undefined parameter in the DLVO theory is found to be the Hamaker constant thus, the constancy of this parameter may be used as a criteria for the validity of their theory. 

Equation 5.128 gives the last undefined parameter, the CCL proton conductivity Gp. Thus, Equations 5.123 and 5.124 and one of Equations 5.127 and 5.128 allow characterizing the CCL from a single low-current impedance curve without fitting. 

From Table 5.11, it can be seen that the expression for the ORR overpotential contains yet undefined parameter, the carbon phase potential of the cathode cj) (the cell potential). The solution to Equation 5.228 must obey the following condition ... 

Undefined parameters appear inside the back cover. 

The Index n = k- ) - M + m is the current variable that indicates the sequence for the beam projections. Exploiting the current measurings y fn) one has to estimate the unknown image parameters a, with undefined conditions about their distribution and the noise FDD function. 

The various restructures of the industry are all planned to address these major issues. Wide-area planning, while undefined, may solve certain issues resulting from the unknown parameters. Divestiture of the industiy into generation, transmission, and distribution companies will strengthen emphasis on the facilities involved. Many of these new structures will move the industiy toward full competition however, coordination of their activities could become more difficult. 

Cultures of Gambierdiscus toxicus have been obtained in several laboratories (14,17-19). These cultures produce large amounts of maitotoxin and low amounts of lipid-soluble CTx-like toxin. However, in most cases, this toxin has not been unequivocally identified as CTx. The only firm evidence that cultures of Gambierdiscus toxicus produce CTx was provided by Baden et al. (20) who used radioimmunoassays and electrophysiological experiments to characterize the toxin. It is possible that cultured Gambierdiscus toxicus produce only trace amounts of CTx and that levels of production comparable to those found in natural populations are dependent on yet undefined environmental parameters. 

Positioning the EM techniques reviewed in this chapter into a research map (Figure 5) that has manufacturing level and decision timescale as its axes reveals almost intuitive results. The more focused (lower manufacturing level) an EM technique, the shorter the timescale on which decisions can be made adjusting machine setup parameters (turret level) can be done by one person in a few minutes, whereas reconfiguring a supply chain (enterprise level) will take a team of people months or even years. In the research map, this correlation seems linear, but since the x-axis is not continuous and the y-axis is not quantitatively scaled, a strict correlation is undefinable and inappropriate. Nonetheless, there are clear areas of the map that are not occupied by any of the reviewed EM techniques, and it is therefore suggested that there is a need for research to be undertaken to address these areas. 

In pure circuit theory, the velocity of circulation can be regarded as too orthodox a concept, partly due to the unrealistic quantity theory assumption that it is a stable parameter. However, in an implicit defence of the velocity concept, Graziani (2003 12) has denigrated the extreme case of an undefined, infinite velocity as being associated with a quasi-barter economy in which money did not exist . 

Since most synthetic and natural gas systems will contain some amount (however small) of heavy undefined components, we have been searching for improved methods of predicting critical properties and an equation of state which does not use critical constants (or quasi critical constants) to determine the parameters for the equation. Development of improved critical property prediction methods appears to be a waste of time. Wilson and Cunningham (6) have presented an equation—the Parameters From Group Contributions (PFGC) equation of state which satisfies our needs. As the name implies, the parameters in this equation of state are estimated by group contribution rather... 

Since the electrolyte may contain associated species, we choose to define the general term current fraction as Is /Io, assuming that interfacial resistances, which may change during the course of an experiment, have been allowed for. Because the steady state current is not a linear function of the applied potential difference above some undefined potential, the above parameter is generally potential-dependent. However, because electrolytes display a linear, steady state, current-applied potential difference response up to at least 20 mV we may define a limiting current fraction, f+, as... 

The variance of residuals = SSJDF, is undefined the data set contains two values (n = 2) but one degree of freedom has been lost for each of the two parameters Pq and p,. Thus, DF, = 2-2 = 0 and there are no degrees of freedom available for calculating the variance of residuals. 

In a long-term study ( 20 years) of about 200 ethylbenzene production workers exposed to an undefined concentration of this compound, none of the workers showed changes in haematological parameters or serum enzyme levels as a measure of liver function (Bardodej Cirek, 1988). 

The specific activity of a debris sample will depend upon the thermal history experienced by the sample, the time after fission when the melted or heated soil was exposed to the fission product vapors, the time-temperature history of the exposure, and a number of undefined and complex parameters. 

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