Triangulation method

Figure 3 describes schematically the algorithm used for determination of d ss by the triangulation method. The square... 

Figure 3. Process of determination of the self-similar fractal dimension of the three-dimensional surface by the triangulation method.

Figure 9. Dependence of the scaled length SL on the projected segment size SS on a logarithmic scale obtained from the self-affine fractal profiles in Figure 7 by using the triangulation method for Euclidean two-dimensional space. Flere, S means d In SL / d In SS. Reprinted from H. -C. Shin et al., A study on the simulated diffusion-limited current transient of a self-affine fractal electrode based upon the scaling property, J. Electroanal. Chem. 531, p. 101, Copyright 2002, with permission from Elsevier Science.

Fractal Dimensions of the Profiles h(x) at Various Morphological Amplitudes rj in h(x) = 77/wsCv) Determined by the Current Transient Technique (2nd Column) and the Triangulation Method (3rd Column). Here, /ws(-v) Means the Weierstrass Function with a Self-Affine Fractal Dimension t/Fsa = 1.5 ... 

XsNv dp df Determined by the current transient technique dF.ss Determined by the triangulation method... 

From the above results, it is noted that the self-similar scaling property investigated by the triangulation method can be effectively utilized to analyze the diffusion towards the self-affine fractal interface. This is the first attempt to relate the power dependence of the current transient obtained from the self-affine fractal curve to the self-similar scaling properties of the curve. 

In summary, from the above theoretical and experimental results, it is concluded that ionic diffusion towards self-affine fractal electrode should be described in terms of the apparent selfsimilar fractal dimension rather than the self-affine fractal dimension. In addition, the triangulation method is one of the most effective methods to characterize the self-similar scaling property of the self-affine fractal electrode. 

Several algorithms have been used to determine surface fractal dimension from SPM images. The most popular ones are the power-spectrum method,1 2 68"71 the triangulation method,10 37 ... 

The manual triangulation method used to measure peak areas is no longer in use. However, it is useful to remember that for a Gaussian eluting peak, the product of its width at half height by its height corresponds to approximately 94% of the total area of the peak. 

Rieger and Ballschmiter [43] developed a low resolution method for PCA analyses, based on GC/ECNI-MS in the SIM mode. Their method of quantifying PCAs in environmental samples was based on a triangulation method previously developed in their laboratory for the analysis of toxaphene [56], For PCAs, typically four ions,known to be prominent in the external standard, were monitored in separate injections of a known amount of standard and in the sample, and the areas of the broad PCA peak were then compared. The choice of external standard used was based on pattern matching, i.e., visually comparing the elution time and signal structure of the sample to those of a number of in-house standards [57],... 

Please note that values of sea level in Table 2 for some years may be overestimated or underestimated as compared with real ones. For example, the direct measurements made in November 2002 [12,13] and October 2003 [14] (see also [15]) at the point 45°05.6 N, 58°20.2 E, using the geodesic triangulation method, yielded practically the same values - 30.47 and 30.50 m, respectively, which is about 1.5 m less than estimated values in Table 2 for these years. This overestimating of the sea level values can be the result of inaccurate determination of sea area based on satellite images. 

Figure 20-54. Triangulation method to measure peak areas of unsymmetrical peaks.

Studies have also been conducted in this laboratory on this subject with panels of trained tasters using the triangulation method. The findings, summarized in Table I, again emphasize the fact that the effect of one taste factor upon another is a function not only of the tastes themselves but of their concentrations. 

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