Isomorphic designs

Empirical grey models based on non-isothermal experiments and tendency modelling will be discussed in more detail below. Identification of gross kinetics from non-isothermal data started in the 1940-ties and was mainly applied to fast gas-phase catalytic reactions with large heat effects. Reactor models for such reactions are mathematically isomorphical with those for batch reactors commonly used in fine chemicals manufacture. Hopefully, this technique can be successfully applied for fine chemistry processes. Tendency modelling is a modern technique developed at the end of 1980-ties. It has been designed for processing the data from (semi)batch reactors, also those run under non-isothermal conditions. 

Raymond, J. W. and Willett, P. (2002) Maximum common subgraph isomorphism algorithms for the matching of chemical structures. J. Comput.-Aided Mol. Design 16, 521-533. 

Every group is isomorphous to some permutation group. It is easy to find a representation of a permutation group by using a permutation matrix. Each row and column of such a matrix has but one non-zero element and that is unity. The row and column thus designate the initial and final locations of the object permuted. 

Because there is no unique principal axis in D2, the Mulliken conventions are not used in naming the representations of D2. These two groups are isomorphous and the character systems of the four IRs are identical, but corresponding representations are labeled differently, which tends to obscure rather than emphasize the isomorphism. Note that C2x and ox are corresponding elements, and so are C2y and totally symmetric representation in D2). In C2V, the Mulliken designations B and B2 are arbitrary because there are two equivalent improper binary axes normal to z. 

Zeolites and related materials prepared by isomorphous substitution of lattice atoms can also be considered as sohd solutions and yield specifically designed micro- and mesoporous catalysts. 

Table 1 lists the numbers of nonisomorphic 12-, 16-, and 20-run orthogonal designs. (Two designs are called isomorphic if one design can be obtained from another by relabelling runs, relabelling factors, and exchanging factor levels.) For... 

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