Representations, completely reduced reduction

Figure 9.3. Simplified representation of the state of the system during discharge of an organic-electrolyte Li-S battery (a) charged state (b) during discharge, (c) discharged state). The dissolution of the active material occurs at the beginning of discharge, whereas the completely reduced product - Li - is insoluble. During the reduction, the metal lithium electrode is, for its part, partially consumed...

When such a complete reduction has been achieved, the component representations rF),r(2 are called the irreducible representations of the group G and the representation T is said to be fully reduced. An irreducible representation may occur more than once in the reduction of a reducible representation T. Symbolically... 

The problems considered so far were one-dimensional in essence. Here, a two-dimensional problem will be considered. It should be also noted that no reduction of any term of the complete Navier—Stokes equations was made yet. This means that no groundless assumptions were employed apart from the representation of EPR by a distributed force. In contrast, the Navier—Stokes equations reduced to the boundary-layer approach (1.4), (1.5) were employed by meteorologists. 

Further effort established that both eigenvalue trends are related to a defective analytic representation of the capture in the 1-eV °Pu resonance. Normalization of this capture rate to that determined by MONTE CARLO calculations which have been completed together with a reduction in the value 2.89, used as the number of fission neutrons per Pu fission is expected to reduce the scatter and to adjust the magnitude of the plutonium eigenvalues to those associated with uranium criticals. 

Because we have assembled the reducible representations for complete sets of orbitals, the character totals obtained are independent of the choice of symmetry elements or operations from each class in the point group. We can now proceed to using the reduction formula to find the irreducible labels for p- and d-orbitals in O. For the p-orbitals, inspection of the standard character table from Appendix 12 shows that... 

Table 6.16 The application of the reduction formula to the reducible representation for the vibrational modes of benzene (Table 6.15). The classes with zero in P are omitted as they will not contribute to the summation. However, the order of the group h is set by the total number of operations in the complete Deh character table.

After reduction F = 2F4 + Fs.s, which corresponds to two doubly degenerate levels with symmetry F4 and two degenerate levels with symmetries F5 and Fe, consistent with an overall sixfold degeneracy which is not completely lifted by the crystal field, as Yb(III) is a Kramers ion. Analogously, the transforms as the reducible representation F,.= 3F4 + F5 6. 

---