We obtain a general formula for the late terms in the perturbation expansion of the energy levels of a periodic potential and compare it with the computed values for the first one hundred terms.

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This paper proposes a low complexity n-dimensional (nD) FastICA algorithm and architecture by introducing the concept of co-ordinate rotation where n ≥ 2. The proposed algorithm can merge the two key steps of Conventional FastICA -Preprocessing and Update and is therefore capable of reducing the hardware complexity of the conventional FastICA significantly as demonstrated in this paper. Hardware implementation can further be simplified due to the recursive nature of the proposed algorithm where the same 2D hardware module can be used as the fundamental core to implement nD architecture. Together with the algorithm formulation, its functionality is also validated and hardware complexity is analyzed and compared with the conventional nD FastICA.

Correlation-function exponents ijj. and r\\\ appropriate to the free-surface problem have been obtained by renormalization-group calculation to order £ 2 . By using the scaling relations 71 = ^(2 -T/ ± ) and y n = v{l -T?U), expansions for y t and y^ are obtained. These expansions are in agreement with the surface scaling relation 2y 1 -y 11 =y+^, but disagree with the relation y n = v-1 due to Bray and Moore.