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Fig. 2. Illustration of calculating remaining uncertainty and misinformation, given a predicted annotation graph P and a graph of true annotations T. Graphs P and T are uniquely determined by the leaf nodes p 1, p 2, t 1, and t 2, respectively.
(see graph, p. XXXX).
"For any graph P, let '{P}' denote the place of P" (Roberts 1973: 38).
The average Lefschetz number is 1. (3) Let G be the discrete graph P n.
Still, in the last five years Travelers' stock has returned an annual average of 7%, more than the shares of Goldman Sachs, JPMorgan Chase & Co. and Berkshire Hathaway (see graph, p. 77).
It is easy to see that 2 is an eigenvalue of each oriented graph P 0, l 1, l 2, 0 − − v. Thus, 2 is an eigenvalue of P 0, l 1, l 2, 0 − with multiplicity 2. □.
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Process graph (P-graph) approach has been extended gradually to provide a friendly and fast optimum result for PNS problem.
The process graph (P-graph) framework was introduced in the early 1990s as a graph theoretic approach to Process Network Synthesis PNSS) problems in chemical engineering.
Kinship relations can be represented as Ore graph, p-graph or bipartite p-graph (White et al. 1999; Batagelj and Mrvar 2008).
We present an intelligent system that addresses these by integrating different process systems engineering methodologies – process graph (P-graph), hierarchical design strategy, water reuse method, and multi-objective stochastic optimization.
In this paper, we describe how such educational strategies can be used to improve learning outcomes through the use of the process graph (P-graph) framework for the synthesis of polygeneration systems, in addition to conventional approaches using lectures and drills.
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