(military) Material and supply section of an Air Force staff.

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A-4 Sentence Examples

For the quartic (ab) 4 = (aib2-a2b,) alb2 -4a7a2blb2+64a2 bib2 - 4a 1 a 2 b 7 b 2 + a a b i = a,a 4 - 4ca,a 3 +6a2 - 4a3a3+ aoa4 = 2(a 0 a 4 - 4a1a3 +e3a2), one of the well-known invariants of the quartic.

To determine them notice that R = (a6) and then (f, a 5) 5 = - R 5 (k1 +k2+k3) (f, a 4 5) 5 = - 5R5 (m 1 k 1+ m 2 k 2+ m 3 k 3), (f, a352) 5 = -10R5 (m21ke +m2k2+m3k3) three equations for determining k 1, k2, k3.

from the invariant a2 -2a 1 a 3 -2aoa4 of the quartic the diminishing process yields ai-2a 0 a 21 the leading coefficient of the Hessian of the cubic, and the increasing process leads to a3 -2a 2 a 4 +2a i a 5 which only requires the additional term-2aoa 6 to become a seminvariant of the sextic. A more important advantage, springing from the new form of S2, arises from the fact that if x"-aix n- +a2x n-2.

Similarly for the quartic A 4 /z) - -a s z 1 -az4.1 -a2.1-a2z4.1-a3 .1 establishing the 5 ground forms and the syzygy which connects them.

Hence every product of A 1, A2, A3, A4, which contains the product A 4 A 3 disappears before reduction; this means that every seminvariant, whose partition contains the parts 4, 3, is a perpetuant.