Apparent mirror position

CLA was observed to have an oncostatic, cell-cycle inhibitory effect on estrogen-receptor (ER) positive MCF-7 breast cancer cells, whereas the parent Unoleic acid had the opposite effect (e.g., protumorigenic and proUferative) (35). In contrast to MCF-7 cells, the ER negative MDA-MB-231 breast cancer cells were unresponsive to CLA. The responses of the different cell types to CLA treatment were apparently mirrored by the observed decrease in c-myc expression, a major cell cycle regulatory oncogene, in MCF-7 but not MDA-MB-231 breast cancer cells. 

It is apparent that we can always get a set of 3 x 3 matrices, which form a representation of a given point group, by consideration of the effect that the symmetry operations of the point group have on a position vector. Why this works is shown pictorially in Fig. 5-3.2 for the a = a TCt operation of, T. The symmetry operation C8 on the position veotor p followed by a r on p produces a vector p which is coincidental with the one produced by the operation o on p. The matrices D(Ct), D(a r), X>(o ) then simply mirror what is being done to the point vector. The general mathematical proof that, if symmetry operations R, S, and T obey the relation SR — T, then the matrices D(R), D(S), and D(T), found as above, obey the relation... 

The simplest type of stereoisomerism for hexacovalent systems occurs in cases where four of the six substituents on a complex are the same. The remaining two, which may or may not be different from each other, may occupy either cis or irans positions (Fig. 22-14). Both of these complexes are superimposable on their mirror images and cannot be separated into enantiomorphic forms. This can be checked by imagining the complexes to be reflected in a mirror (as was done in Fig. 22-7), or it may be noted that both complexes have at least one plane of symmetry (that is, that there is at least one way in which a plane can bisect the complex into two mirror-image halves). The presence of a plane of symmetry is a convenient indication of the nonresolvability of a complex. The apparent absence of such a plane, however, should be regarded with reserve, for without considerable experience or a good sense of spatial... 

Since the diagram 13.11 has mirror symmeMy about A = 0 it will suffice just lo use one-half of this diagram. We choose the right-hand half, that corresponding to positive A. The index A is called the wavevector. The variation in energy as a function of the wavevector A is called the dispersion of the band. In three-dimensional situations the vector nature of the wavevector becomes apparent and we will write it as k. 

---