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Box 5.2 Basic notation for network environ analysis

Flows: fj = within system flow directed from j to i, comprise a set of transactive flows.

Boundary transfers: zj = input to j, yt = output from i. Storages: Xj represent n storage compartments (nodes). Throughflow: T^ = zt + Z f

Non-dimensional, intercompartmental flows are given by g j = fj /Tj Non-dimensional, intercompartmental utilities are given by d j = ("f-j/T. Non-dimensional, storage-specific, intercompartmental flows are given by pj = Cj A^ wtei-e for i#j, Cij =fj/xp and for i =j, pii = 1 + c an where Cii = -Ti/xi.

Non-dimensionless integral flow, storage, and utility intensity matrices, N, Q, and U, respectively can be computed as the convergent power series:

N = G0 + G1 + G2 + G3 + K + Gm +... = (I - G)-1 Q = P0 + P1 + P2 + P3 + ... + Pm +K = (I - P)-1 (1)

The mth order terms, m = 1,2, k, account for interflows over all pathways in the system of lengths m.

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