For a Riemannian manifold with dimension at least six, we prove that the existence of a conformal metric with positive scalar and Q curvature is equivalent to the positivity of both the Yamabe invariant and the Paneitz operator.
Conformally variational Riemannian invariants (CVIs), such as the scalar curvature, are homogeneous scalar invariants which arise as the gradient of a Riemannian functional. We establish a wide range of stability and rigidity results involving CVIs, generalizing many such results for the scalar curvature.2010 Mathematics Subject Classification. Primary 53C20; Secondary 53A55, 53C21, 53C24.
This study uses two data sets, Taiwanese export values as the prediction varialbe and its foreign exchange spot rates as the auxiliary variable, to discuss two forecasting issues in the fuzzy time series analysis by using One-and Two-factor models. First, disregarding the length of information period, when window basis is two, a better forecasting result is obtained. Second, the optimum number of partition equal intervals is to select 14 intervals to have the smallest MSE in all models. However, if partitioning the information into more than 14 equal intervals, MSE can not be reduced but presents a waving pattern.
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