Cosine Moments and Their Application to ∑ Relationships

Abstract

Abstract: Recent advances In the theory of ∑ relationships lead to the Investigation of moments needed to derive the relavant joint probability densities. These together with the linear theory of relationships, make possible the calcualtion of therelationships from ∑₁ to ∑₂ one by one. The superior performance ofour new ∑₄ and ∑_r relationships, for example, with respect to the older ∑₁ and ∑₃ formulas strongly suggests a deeper study of the pertinent moments. In this paper a new concept, the cosine moment, is introduced which, together with a certain integral theorem, permits the derivation of the relevant joint probability densities. These lead in turn to the derivation of all ∑ relationships valid for all the space groups.

Key words: Consine moment, &sum, relationship, Joint probability density

Guo Dongyao, Guo Shishan. Cosine Moments and Their Application to ∑ Relationships[J]. Chemical Research in Chinese Universities, 1990, 6(1): 62-66.

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Cosine Moments and Their Application to ∑ Relationships

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