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Contradiction Equations in a B Matrix of Vertex Weight Method and Their Correspondence with the k-Summability Property of Vertices | IEEE Journals & Magazine | IEEE Xplore

Contradiction Equations in a B Matrix of Vertex Weight Method and Their Correspondence with the k-Summability Property of Vertices


Abstract:

This note attempts to show that, in a vertex weight method [1], every contradiction equation bears a one-to-one correspondence with the summability pair C1S, C2S, where C...Show More

Abstract:

This note attempts to show that, in a vertex weight method [1], every contradiction equation bears a one-to-one correspondence with the summability pair C1S, C2S, where C1S = {X11, X12, ..., X1k}⊆ C1 C2S = {X21, X22,..., X2k} ⊆ C2 and vector sums of the vertices plz check [Eqa] The vertices, Xki's, K = 1, or 2, are not necessarily distinct, and C1, C2 are two disjoint sets of vertices in En space. As a consequence, the contradiction equation is a necessary and sufficient condition that the homogeneous system, solved for a threshold function of order r, has no solution. This tells that the threshold function is of order greater than r.
Published in: IEEE Transactions on Computers ( Volume: C-21, Issue: 6, June 1972)
Page(s): 606 - 610
Date of Publication: 30 June 1972

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