Generating relations

Synthesized libraries of compounds such as Optiverse are not the only source of new leads. Natural products also play an important role in lead discovery. There are numerous examples where natural products have led to the discovery of new drugs. It is also clear that they represent an inexpensive source of nature s molecular diversity in a lead discovery program. However, a key limitation that must be overcome if leads are to be developed into drugs is they are usually difficult to synthesize, thereby making it more resource-intensive to generate related compounds with better properties. 

With rich luminescent properties, long-lived CT excited states and a variety of bimolecular photochemical reaction pathways, the mixed-ligand square-planar diimine dithiolene complexes of d8 metal ions show great promise for solar-energy conversion, as luminescent probes or in photocatalytic applications. Complexes of this type have also received attention for the nonlinear optical properties, such as second harmonic generation, related to the MMLL CT excited state (14, 129). 

When we decide to work with an EEE plan and when we have more than three factors, a new problem appears because we then have more possibilities to build the plan. Eor an answer to the question that requires a choice of most favourable possibility, we use the resolution power of each one of the options. So we generate the first possibility for an EEE plan by choosing the production (generation) relation. We can then go on with the contrast relation through which we obtain all the actual relations that are similar to those given in (5.107). 

Exercise 4.12. The confounded effects in a certain contrast are determined by the generating relations of the factorial and by all their possible products. For the 2 and 2 " designs there was only one generating relation, and for this reason only two effects were confounded in each contrast. In the 2 design there are two generators and we need to consider three equations the two defining relations, I = 1234 and 125, and their product, (I)(I) = I = (1234)(125) = 345. Each effect will thus be confounded with three others, (a) Use these relations to show that main effect 1 is confounded with the 25, 234 and 1345 interactions (b) which interactions are confounded with main effect 5 ... 

Exercise 4.14. In the 2 " fractional factorial each main effect is confounded with 15 interactions. To discover which terms are confounded we must use, in addition to the four generating relations, their six binaiy products, their four ternary products and the product of aU four relations. Determine which interactions are confounded with the main effect that represents the side of the tennis court. 

Exercise 4.17. Use the generating relations given in Table 4.15 and find the three-... 

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