Transformed triangle sections

Solution 3.2 Figure 3.6 shows the plots one should obtain from the program. Note that the plots shown include dashed, straight lines which trace the movement of pinch points. Collectively these lines produce a triangle, known in the context of CPMs as a transformed triangle (TT). The importance and use of the TTs are discussed in greater detail in Section 3.6.5. 

It is instructive to consider a specific example of the method outline above. The triangle fimction (l/l) a (x/l) was discussed in Section 11.1.2. It was pointed out there that it arises in dispersive spectroscopy as the slit function for a monochromator, while in Fourier-transform spectroscopy it is often used as an apodizing function. Its Fourier transform is the function sine2, as shown in Fig. (11-2). The eight points employed to construct the normalized triangle fimction define the matrix... 

It is not immediately clear from the form in which these are written that they are equivalent functions, that is, differ only in their orientation, but it is easily confirmed that they do transform into each other if the axes are rotated through 120°. Again it can be shown that the determinant of -functions has the same value as (18). One other point about this set of equivalent orbitals is that there appears to be no preferential direction in which any one of the vertices of this triangle may be chosen. The choice is, in fact, arbitrary and any set of three equivalent directions perpendicular to the z direction would suffice. This only applies for an atomic wave function, of course. In molecules (such as planar XY3) there may be a preferred choice of axes on account of symmetry. This will be clear from some examples considered in the next section. 

Figure 3.24 Estimation of fraction transformed for sample heat capacity change correction. A straight line is drawn between baselines at onset and termination of the endotherm, forming a triangle. After area determination based on the upper baseline, the triangle is subtracted (see section 4.1).

These terms may also be calculated from the j1,-,- s in the MO description. As mentioned in Section XXVII-C, the relative importance of the pairs, Eq. (173), to the triangles, Eqs. (175) and (176), part should be greater in the rj description than in the MO one, Eq. (171). Nevertheless, owing to the simpler transformations of some pairs, as in Eq. (168), some of the MO triangles may correspond directly to Rm and possibly simplify its calculation. Further work is needed along these lines (see Note Added in Proof at the end of this article). 

Figure 6.7 shows for comparison the trajectories of quasisharp (a) and sharp (b) reversible distillation in the intermediate section for ideal mixture (Ki > K2> K3). This figure shows that, at movement of pseudoproduct point from the vicinity of continuation of side 1-3 to this continuation itself, there is transformation of reversible distillation trajectory it disintegrates into two parts - into one that lies inside the triangle and into the part that lies at side 1-3. We note that similar transformation also takes place at passage from quasisharp distillation to sharp one for the top and bottom sections. The stationary point Sm at this transformation stays at the internal part of reversible distillation trajectory. Point N+ passes to side 1-3. Point N passes from vertex 3 to its vicinity at side 1-3. 

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