Merging algebras

The merging of mathematical graph theory with chemical theory is the formalization of what most chemists do in a more or less intuitive mode. Chemists currently use graphical images to embody chemical information in compact form which can be transformed into algebraic sets. Chemical graph theory provides simple descriptive interpretations of complicated quantum mechanical calculations and is, thereby, in-itself-by-itself an important discipline of study. 

The so(4) subtowers are all linked together at the top through the action of T+ so that successive application of T+ to the top state of a subtower produces the top state of the next subtower. Thus, by merging so(4) and so 2,1) we should be able to find a larger Lie algebra for which all hydrogenic bound states are contained in a single unirrep. 

Based on these requirements, the outcome of the merge is a set of relations, where each of the relations of the first three types of constraints (i.e., all but containment constraints) mean that the relations are combined, with all of their attributes present in the global schema. For containment constraints, the two relations are left separate, since there can be no way of determining what relational algebra operator to use. 

Several resent studies indicate that algebraic slip models are sufficient modeling the flow pattern in bubble columns [14, 21, 118, 157], as the pressure and steady drag forces only dominate the axial component of the gas momentum balance. Therefore, the population balance model can be merged with an algebraic slip model to reduce the computational cost required for preliminary analysis [14]. Furthermore, adopting this concept the restriction used in the two-fluid model assuming that all the particles have the same velocity can be avoided. This means that only one set... 

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