Formally principal homogeneous

Let G be an affine group scheme over a ring k, and let AT be a representable functor on which G acts (3.1). Following the usual definition for groups, we say the action is simply transitive, or X is formally principal homogeneous, if for each pair of points in there is a unique element in G(R) taking the second to the first. In other words, the map G x X - X x X sending (g, x) to (gx, x) should be bijective. 

Since the many-point density formalism in its practical applications assumes macroscopically homogeneous system, we will restrict ourselves to a particular class of microscopically self-organized autowave processes. Without investigating in Chapter 8 all possible kinds of autowave processes, we are aimed to answer a principal question - whether these two models under question could be attributed to the basic models useful for the study of autowave processes. 

Classical chemical engineering has been intensively developed during the last century. Theoretical backgrounds of momentum, mass, energy balances, and equilibrium states are commonly used as well as chemical thermodynamics and kinetics. Physical and mathematical formalisms are related to heat, mass, and momentum transfer phenomena as well as to homogeneous and heterogeneous catalyses. Entire object models, continuum models, and constrained continuum models are frequently used for the description of the events, and for equipment designing. Usual, principal. 

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