A New Kind of Test of the Correspondence Principle Based on by Tolman R.C., Badger R.M. PDF

By Tolman R.C., Badger R.M.

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Extra resources for A New Kind of Test of the Correspondence Principle Based on the Prediction of the Absolute Intensities of Spectral Lines

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1. A conditional metagraph is a metagraph S = Xp ∪ Xv , E , in which Xp is a set of propositions and Xv is a set of variables, and: 1. ∀e ∈ E, Ve ∪ We = ∅; 2. X = Xv ∪ Xp with Xv ∩ Xp = ∅ such that ∀p ∈ Xp , ∀e ∈ E, if p ∈ We , then We = {p}. Note that a metagraph as defined in Chapter 2 is a specialization of a conditional metagraph in which Xp = ∅. Where significant, we can refer to such a metagraph as a simple metagraph. 56 A. W. Blanning Thus, conditional metagraphs must meet two constraints in addition to the requirement that the generating set be partitioned into variables and propositions.

Since in practice this set is not large (otherwise, the benefit of constructing the projection is lost), the procedure is still practical. 3. 4. Two propositions, cadv and mkt, do not appear in the projection. The reason is that cadv appears only in the invertex of e2 and mkt appears only in the invertex of e6 , and neither of these edges is a member of a dominant metapath corresponding to the edge e1 in the projection. We now consider the issue of combining projections and contexts. More specifically, we address the following questions: 1.

The projection itself can be computed using the A∗ matrix of the underlying metagraph. Although the complexity of the procedure is exponential in the number of triples in the relevant portion of the A∗ matrix, the size of this portion depends upon the projection set (the elements in the generating set that define the projection). Since in practice this set is not large (otherwise, the benefit of constructing the projection is lost), the procedure is still practical. 3. 4. Two propositions, cadv and mkt, do not appear in the projection.

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A New Kind of Test of the Correspondence Principle Based on the Prediction of the Absolute Intensities of Spectral Lines by Tolman R.C., Badger R.M.


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