Manuscript II-B@1 · II-B-v1.tex · proposition · bfd2eb3c

Proposition: Reference response

The frozen response problem › Ward reduction and the target function · lines 684–704 · proof included or linked

II-B@1#prop:reference, II-B@1#eq:F

The single-longitudinal reference response is

F (d) = (D_{s} - D) W_{2} + (D_{t} - D) W_{3} + (D_{u} - D) W_{4} .

Proof. Equations (eq:ward3) and Lemma lem:inverse give, channel by channel,

v_{3} (G_{ζ}, u, D J (v, w)) = - v_{3} (R_{ζ} u, v, w) .

The tree minus sign therefore makes the exchange contributions $D_{s} W_{2} + D_{t} W_{3} + D_{u} W_{4}$ . The quartic contributes $- D (W_{2} + W_{3} + W_{4})$ by (eq:ward4).

Displayed formulas in this passage

II-B@1#eq:F · line 687
$F (d) = (D_{s} - D) W_{2} + (D_{t} - D) W_{3} + (D_{u} - D) W_{4} .$
unlabeled · line 697
$v_{3} (G_{ζ}, u, D J (v, w)) = - v_{3} (R_{ζ} u, v, w) .$

Nearby in this section

section: Ward reduction and the target function
section: Ward reduction and the target function