Prescriptive integration

Recent revisions to the boundary conditions (ice-sheet topography and sea surface temperatures) have added uncertainty to many of the GCM calculations of the past two decades. Moreover, all of these calculations use prescriptions for at least one central component of the climate system, generally oceanic heat transport and/or sea surface temperatures. This limits the predictive benefit of the models. Nonetheless, these models are the only appropriate way to integrate physical models of diverse aspects of the Earth systems into a unified climate prediction tool. 

We note that the integrand in Eq. 40 does not depend on k , whose integration gives the density of states at the Fermi surface, and the it prescription is consistent with the Feynman propagator. The pole occurs at... 

This equation will prove useful later on, but it is worth noting at this point that it also offers a prescription for determining the molecular energy. With a wave function in hand, one simply constructs and solves the integral on the left (where i and j are identical and index the wave function of interest). Of course, we have not yet said much about the form of the wave function, so the nature of the integral in Eq. (4.8) is not obvious. .. although one suspects it might be unpleasant to solve. 

Here C is another integration constant to be determined from matching with the transition layer solution (5.5.20). This matching may be achieved, following the standard prescription of matched asymptotics [15], by introducing the intermediate variable... 

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