Manuscript En03-A@1 · En03-A.tex · definition · 5398614e

Definition: Schedule past

Kinematics and causal cuts on a prescribed schedule › Scheduled blocks · lines 634–653

En03-A@1#def:schedule-past, En03-A@1#eq:cone, En03-A@1#eq:schedule-past

For $Y \subseteq X$ and $0 \leq s \leq t \leq T$ , set

N_{t, t} (Y) N_{s, t} (Y) = Y, = ⋃ {B \in B_{s + 1} : B \cap N_{s + 1, t} (Y) \neq = \emptyset}, s < t,

and

J_{sched}^{-} (Y, t) = {(x, s) : 0 \leq s \leq t, x \in N_{s, t} (Y)} .

Displayed formulas in this passage

En03-A@1#eq:cone · line 637
$N_{t, t} (Y) N_{s, t} (Y) = Y, = ⋃ {B \in B_{s + 1} : B \cap N_{s + 1, t} (Y) \neq = \emptyset}, s < t,$
En03-A@1#eq:schedule-past · line 648
$J_{sched}^{-} (Y, t) = {(x, s) : 0 \leq s \leq t, x \in N_{s, t} (Y)} .$