Manuscript Em01-C@3 · Em01-C-v3.tex · section · f0953702

Response-normal density

Density and vertex audits › Response-normal density · lines 2310–2335

With $q = q_{R}$ ,

u = \frac{q}{4 β} .

The ambient density becomes

\frac{( β - q / ( 4 β ) ) ^{2}}{β} d^{4} a d Ω d α d β d^{4} r d q d v d^{2} ξ .

Its $q = 0$ factor is $β > 0$ .

For a smooth factor $J (q, τ)$ , use $J Ψ$ as the scalar test. The inverse-scale coefficient becomes $J (0, τ) c_{1}$ . The finite distribution is multiplied by $J$ ; in particular,

J \partial_{q} δ_{o} = J (0, τ) \partial_{q} δ_{o} - \partial_{q} J (0, τ) δ_{o} .

The derivative of $J$ changes the finite part, not the inverse-scale coefficient.

Displayed formulas in this passage

unlabeled · line 2313
$u = \frac{q}{4 β} .$
unlabeled · line 2317
$\frac{( β - q / ( 4 β ) ) ^{2}}{β} d^{4} a d Ω d α d β d^{4} r d q d v d^{2} ξ .$
unlabeled · line 2327
$J \partial_{q} δ_{o} = J (0, τ) \partial_{q} δ_{o} - \partial_{q} J (0, τ) δ_{o} .$