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We present a fast algorithm for the subset convolution problem:given functions f and g defined on the lattice of subsets of ann-element set n, compute their subset convolution f*g, defined for S⊆ N by [ (f * g)(S) = [T ⊆ S] f(T) g(S/T),,]where addition and multiplication is carried out in an arbitrary ring. Via Möbius transform and inversion, our algorithm evaluates the subset convolution in O(n2

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This paper treats the problem of calculating the macroscopic effective properties of dielectric mixtures where both the inclusions and the background medium can be anisotropic. For this homogenization process, the Maxwell Garnett -type approach is used where the inclusions are assumed to be spherical and embedded in a homogeneous background medium. The anisotropy of the background medium has to be