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The 'quadratic' property of $Q(p+q)$ and the values $Q(dc)$ on coboundaries are expressed in terms of higher $\\cup_i$ products of Steenrod. 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The 'quadratic' property of $Q(p+q)$ and the values $Q(dc)$ on coboundaries are expressed in terms of higher $\\cup_i$ products of Steenrod. 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