Parabolic Function Method

Harris et al. also employed a less-known CCK procedure, which Meehl and Yonce (1996) named SQUABAC, but the authors referred to as the Parabolic Function Method. Two SQUABAC analyses were performed, one with the PCL-R total score as the input variable and criminal recidivism as the output variable, and another with adult criminal history and recidivism as input and output variables, respectively. Recidivism history was paired with the two potential taxon indicators because it is a conceptually related but distinct variable. It is expected to be a valid indicator of the taxon, but it is not redundant with other indicators, thus nuisance correlations should not be a problem. 

Ideally, this method would be fairly simple to implement on flat specimens. However, all the specimens tested contained significant degrees of warp due to the effects of a vacuum-pressure exposure test. In many specimens, the magnitude of this distortion was several times that of the surface irregularities. Therefore, it was necessaiy to flatten the bondline by fitting a parabolic function to the cup and then subtract the fit from the raw data. Next, the data were sorted in ascending order to produce a cumulative distribution for all measured surface displacements. A thickness tolerance could then be specified to define the bondline region as well as a depth... 

Specimen 5 was particularly problematic because it contained significant distortion (both cup and bow). This specimen had obvious regions of bondline voids that should have been readily detected by the laser-scanning method- but were instead obscured by the specimen distortion. For this specimen, fitting a parabolic function to a single scan and subtracting it from all the scans was not sufficient to reproduce a flat bondline. Rather, to improve the analysis, it may have been useful to initially fit a bi-quadratic function to the data to completely remove all surface distortion, and then apply the relevant tolerance to better resolve these surface features. 

A method frequently used to evaluate energy derivatives with respect to the number of electrons consists in writing E(N) as a parabolic function of... 

Now we undertake to find approximate solutions using the several variations of weighted residuals. Central to all methods is the choice of the trial solution, y . By noting the boundary conditions at x = 0 and ac = 1, a parabolic function seems to be a good choice so we write our first guess as... 

With this approach, accurate descriptions of peaks showing large asymmetries can be obtained, including those showing deformation either to the right or to the left. Also, eq. 8.48 with a linear or a parabolic function can be applied to refine peak parameters, such as the efficiency and asymmetry factor, estimated by direct measurement of the chromatographic signal. The method of Powell can be used to fit the experimental data to the nonlinear functions [28]. 

In the upwind Galerkin method, the weighting function L/ = Nj + Fj, Fj is parabolic function of Ni, and they can be found in Appendix 1. Substitution of expression (9) into equation (8), and standard Hnite element procedure such as... 

In reality, as the barrier becomes narrower, it deviates from the square shape. One often used model is the parabolic barrier (dashed line in Fig. 1). When the barrier is composed of molecules, not only is the barrier shape difficult to predict, but the effective mass of the electron can deviate significantly from the free-electron mass. In order to take these differences into account, a more sophisticated treatment of the tunneling problem, based on the WKB method, can be used [21, 29-31]. Even if the metals are the same, differences in deposition methods, surface crystallographic orientation, and interaction with the active layer generally result in slightly different work functions on either side of the barrier. 

The use of sterlo parameters such as and of methods such as the branching equations to represent sterlo effects on bio-activity Is Justified. Transport parameters are composite they are a function of differences In Intermolecular forces. The function of bulk and area parameters Is to provide the proper mix of Intennol-eoular forces required by a particular mode of bloaotlvlty. In the absence of parabolic or bilinear behavior bloactlv-Ity can be modeled by an equation based on Intermolecular forces and steric effects. 

This momentum equation is a linear parabolic partial differential equation (for constant p) that can be solved by the method of separation of variables. In this approach the solution can be found to be a product of two functions as w(t, r) = f t)g r). The solution is represented as an infinite series that can be readily evaluated at any time or value of r. Such a solution is available for a variety of boundary conditions, including time-oscillating rotation rates. At this point, however, we choose to proceed with a numerical solution. 

Fig. 12. 53. Experimental coverage-potential relation for n-valeraldehyde on platinum as a function of electrode potential. Two things should be noted First, adsorption-potential plots are roughly parabolic. Second, there is medium-good agreement between two entirely different methods, one based on the interpretation of ellipsometric data and the other on FTIR measurements. (Reprinted from J. O M. Bockris and K. T. Jeng, J. Electroanal-chem. 330 553, copyright 1992, with permission from Elsevier Science.)...

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