An Extension of the Nested Partitions Method
EBERT BREA
Definition 6 (Depth vector)
d(k)
u
(1)
σ(k)
(1)
σ(k),...,u
(n+m)
σ(k)
(n+m)
σ(k)
t
,∀k ∈−N.
(4)
Note
SM
i=1
Finally,
b.
REGION
We
Proposition 1
(j)
σ
(j)
σ
be
σ
(j)
1
σ
≤−x ≤−
σ
};
(5a)
σ
σ
σ
},
(5b)
where
(j)
σ
(j)
σ
(j)
σ
line
(j)
σ
(j)
σ
Proof. We
As
(j)
1
σ(j)(k)
(j)
1
(j)
2
partition
Proposition 2
(j)
σ
(j)
be
promising
[¯lσ(j),δ(j)]
(j)
σ
[¯lσ(j),⌊δ(ℓ)⌋]
(j)
σ
6
(6)
where
σ(j)
(j)
σ
(j)
σ
line
(j)
σ
(j)
σ
Proof.
the
can
(j)
1
2
1
(j)
σ
are
(j)
1
(j)
2
σ¯1
(j)
(j)
then
(j)
1
(j)
σ
and
(j)
2
(j)
σ
σ¯
(j)
1
(j)
2
(j)
1
(j)
2
Based
As
{ℓ}Mℓ=1σ
SM
Semestre
ISSN
ISSN:
121