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The Balanced States of a Proportioning Network

A. H. Zemanian
SIAM Journal on Applied Mathematics
Vol. 34, No. 3 (May, 1978), pp. 597-610
Stable URL: http://www.jstor.org/stable/2100957
Page Count: 14
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The Balanced States of a Proportioning Network
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Abstract

Proportioning networks that need not be bipartite arise as models of certain hypothetical marketing systems. This work examines the balanced states of such networks. Necessary and sufficient conditions for the existence of at least one balanced state as well as for the existence of more than one balanced state are given. The dimension of the linear space of all homogeneous states for a given network is also determined.

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