I know the right hand side of the above formula is defined to be the pullback of δδ with ff. Let u∈D′(R)u∈D′(R) be a given distribution and φφ a given test function. The pullback f∗uf∗u of uu with (the smooth function) ff is, by definition, the...
JacobianDirac delta functioncoordinate transformationchain rule of partial derivativesWe demonstrate how to make the coordinate transformation or change of variables from Cartesian coordinates to curvilinear coordinates by making use of a convolution of a function with Dirac delta functions whose arguments ...
Due to the complexity of the derivation process needed to calculate the incidence coefficient, the specific formula expression is omitted from this paper and can be referred to in Dang et al. [87]. 3.3. Bivariate LISA Model The bivariate LISA statistic is defined as [72,78]: 𝐵𝐿𝐼...