Symmetry hyperplane

To obtain control, we choose the intermediate state Z 3) to be symmetric andfte intermediate state E2) to be antisymmetric, with respect to reflection in the a hypei-plane. Hence we must first demonstrate that it is possible to optically excite, i taneously, both the symmetric i 3) and antisymmetric E2) states from the grouji state i). Using Eq. (3.75) we see that this requires the existence of botj symmetric dipole component, denoted dJ5 and an antisymmetric component, de da, with respect to reflection in the a hyperplane because, by the symmetry ] ties of fs3) and E2),... 

Let us now transform this chain tail by symmetry with respect to the hyperplane x = xffi. Thus, we generate a new self-avoiding chain with N links and the extension Xt + X2. For this new chain, we can define an index X2 corresponding to a value x 2 defined as above. 

We now ask when does the left side of (18) vanish, i.e. when a point, which is displaced with respect to A, stays in the same hyperplane. Due to the skew symmetry of (pij this clearly happens when... 

Taking into consideration the symmetry of these sphts, we confine the discussion to the direct split. In the mode of minimum reflux, point x/ should coincide with the stable node A +, and point x/ i should belong to rectifying minimum reflux bundle 5 - Nf (Fig. 5.30). Along with that, Eq. (5.18) should be valid. The search for the value (L/ F) is carried out in the following way at different values (L/V)r, he coordinates of point X/ = Nf are determined by means of the method tray by tray for bottom section and then the coordinates of point x/ i are determined by Eq. (5.18). At(L/F), < (L/F) , points X/-1 and xd are located on different sides from the plane or hyperplane - Nf and, at (L/ V)r > (L/ y)f", these points are located on one side. That finds approximate values (L/ F) (not taking into consideration curvature of bundle 5 - Nf) and approximate coordinates of points X/ i and x/. To determine exact values (L/ F) and coordinates X/-1 and Xf, one varies the values of (LjVjr in the vicinity of found approximate value (L/V)f. Then one realizes trial calculations of top section trajectories by means of the method tray by tray from feed cross-section to the product. If at... 

More generally, one may apply to any lattice symmetry operation that leaves ujk and uji invariant or any lattiee symmetry operation that interchanges u>k and uji, followed by the inversion (2.80). Such symmetry operations exist if uji - ujk lies on certain axis or diagonal hyperplanes. 

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