Graph theory proved to be a quite powerful mathematical tool to model several problems in a discrete setting. In this paper the authors illustrate how a general graph framework can be used to model multi-dimensional alternatives decision processes in three different contexts: social choice, judgment aggregation and automata decisions.
Ester formation during production of beer was much affected by the degree of the aeration of wort during fermentation.Thus, the quantification and control of ester formation could be related to the total amount of dissolved oxygen consumption (TDOC) by yeast, which was defined and measured by the authors in the previous report (S. MITSUI et al.: MBAA Tech. Quart., 28, 119 (1991)), as a new index for fermentation control.It was comfirmed that maximum ester formation was directly related to TDOC, and the optimum level of TDOC necessary to produce and optimum ester production could be determined.It was possible to prevent high ester formation quantitatively during high gravity brewing by controlling TDOC.
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