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 t...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.展开更多
文摘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.
