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Spectral shapes are quantified with one simple fitting parameter of a generalized fit to the autocorrelation function (=Fourier transform of the Doppler spectrum).
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The generalized Fitting subgroup (F^(G)) of (G) is the unique maximal normal quasinilpotent subgroup of (G).
The following well-known facts about the generalized Fitting subgroup of a group G will be used in our proofs (see [[6], Chapter X] and [[7], Lemma 4]).
Suppose that every non-cyclic Sylow subgroup (P) of (F^(E)) has a subgroup (D) such that (1<|D|<|P|) and every subgroup (H) of (P) with order (|H|=|D|) or with order (2|D|) (if (P) is a nonabelian 2-group and (|P D|>2)) is weakly (s -permutable in (G), where (F^(E)) is -permutableined FittinG subgroup of (E).
Recall that a group G is called quasinilpotent if given any chief factor H / K of G, every automorphism of H / K induced by an element of G is inner; the generalized Fitting subgroup F ∗ ( G ) of G is the product of all normal quasinilpotent subgroups of G.
In fact, the main result established in this paper provides a new criterion, in terms of the λ-supplemented cyclic subgroups of order prime or 4 contained in the generalized Fitting subgroups, for a group to be contained in a saturated formation containing all supersoluble groups.
Suppose that every non-cyclic Sylow subgroup (P) of (F^(E)) has a subgroup (D) such that (1<|D|<|P|) and every subgroup (H) of (P) with order (|H|=|D|) or with order (2|D|) (if (P) is a nonabelian 2-group and (|P D|>2)) is either (s -semipermutable or (s -semipermutablen (G), where (F^(E)) is the generalized Fitting subgrorp of (E).
He had a series of generalized fits within 5 hours of admission.
The final alignment of landmark configurations in the generalized Procrustes fit is obtained by an ordinary Procrustes fit of each configuration to the consensus shape [ 49].
Df: degrees of freedom Wing shape was extracted from the landmark coordinate data with a generalized Procrustes fit [ 35].
Then, a generalized Procrustes fit superimposes all configurations and produces an overall mean shape [e.g. [ 28, 29]].
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