A Property Which Characterizes Continuous Curves by Wilder R.L.

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By Wilder R.L.

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First, the variables in the projection are limited to those in X , so none of the variables in X\X appear in the projection. Some or all of the assumptions in Xp may appear in the projection; the user only specifies X , and the necessary assumptions are determined by the definition. Second; the projection (and therefore its adjacency matrix) represents all relationships among the variables in X and αij∗ = ∅ iff αij = ∅ (where A is the adjacency matrix of the projection). The first observation implies that the decision maker needs only to specify the relevant variables over which the projection is desired, and the operation then generates the relevant assumptions for each projected relationship.

In our second example, the sum of the higherlevel views of the life cycle costing calculations and of the cost estimating relationships was equivalent to a single view constructed directly from both sets of calculations. At the same time, the ways in which these relationships were presented to the user were different in two respects. First, the sum of the high-level views contained redundant information, in the form of dominated metapaths. For example, the sum of the views disclosed that miles driven, fuel cost, and annual cost of preventive maintenance are sufficient to calculate annual operation and support cost, but it also disclosed that miles driven is sufficient to calculate annual operation and support cost.

There is at least one metapath M(V , W ) in S from V ⊆ X to W ⊆ X . Consider the set of all such metapaths {M, (V , W ), M2 (V , W ), . }. Since there can be only one such set, C(e ) is unique. Therefore, for each e , C(e ) is unique. An interesting property of projections that does not apply to metagraphs in general, is that in a projection, there can be no simple paths of any length between two elements unless there is an edge in the projection connecting the elements. 2. Given a metagraph S = X, E with adjacency matrix A and closure A∗ , and its projection S = X , E over X ⊆ X with adjacency matrix A and closure A ∗ , aij = φ iff aij∗ = φ for any xi , xj ∈ X .

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