Since this form of dissipation is special mathematically (forming a group), we argue it must be special physically too.
While mathematically appealing, the uniqueness of solutions in this approach is still an open question.
Many theories have been formulated mathematically in fields which were earlier thought to be outside the scope of mathematical reasoning.
In a game theory model, the outcome of the model can be represented as a set of mathematically specified equilibria.
The same approach evidently applies to mathematically equivalent problems of flows through porous media.
The model assumes that, initially, both aphids and natural enemies coexist at low densities (mathematically, at a stable equilibrium).
In other words, the result concerning the eectiveness of the relevance feedback process can be mathematically proven.
It is worth pointing out that our results even apply to such mathematically unwieldy structures as term models for full-scale programming languages.
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