Tài liệu Đề tài " On the K2 of degenerations of surfaces and the multiple point formula " pptx
Tài liệu Đề tài " On the K2 of degenerations of surfaces and the multiple point formula " pptx
... which is the composition of
blow-ups at points of the central fibre, such that X
is smooth.
Annals of Mathematics
On the K2 of
degenerations of surfaces
and the multiple point
formula ... component of type (i), then the intersection in codimension
one of any two distinct components can only be a line.
If there is no component of type (i), then t...
Tài liệu Đề tài " On the volume of the intersection of two Wiener sausages " ppt
... second
term on the right-hand side of the analogue of (2.93).
4. Proof of Theorem 3
In Sections 4–6 we prove Theorems 3–5. The proof follows the same line
of reasoning as in [3, §5], but there ... N-boxes), and therefore the
estimate in (2.63) implies that most of the intersection volume is unaffected
by the reflections.
8. Before giving the proof of Propositions...
Tài liệu Đề tài " On the holomorphicity of genus two Lefschetz fibrations " pptx
... for the size of
the neighbourhood V of the singular set on noncontracted components is the
diameter of ϕ(V )inM; on contracted components one may take the smallest
ε with V contained in the ε-thin ... if and only if |C| is smooth and m(C) = 0 if and only if C has no
multiple components.
The definition of the C
0
-topology on the space of pseudo-holomor...
Tài liệu Đề tài " On the complexity of algebraic numbers I. Expansions in integer bases " ppt
... to the proof of Theorem 5. Keep the notation and the
assumptions of this theorem. Assume that the parameter w>1 is fixed,
as well as the sequences (U
n
)
n≥1
and (V
n
)
n≥1
occurring in the ... get, on
the one hand, that
|U
n
|
|V
n
|
≤
|W
1
|
1+|W
2
|
≤ r − 1
and, on the other hand, that σ
n
(u) is a prefix of V
n
of length at least 1/r
times the length o...
Tài liệu Đề tài " Hausdorff dimension of the set of nonergodic directions " ppt
... Diophantine.
The construction of this Cantor set is based on Lemma 1.1 and is presented in
Section 2. The proof of Theorem 2 is completed in Section 3 if we assume the
statement of Theorem 3, whose proof ... integer satisfies the hypothesis of Theorem 1.
Some generalizations of Theorem 1 are mentioned in Section 2. For the
class of Veech billiards (see [V2]) the set...
Tài liệu Đề tài " Higher composition laws II: On cubic analogues of Gauss composition " ppt
... HIGHER COMPOSITION LAWS II
873
The proof of Theorem 2 not only gives a complete description of the
nondegenerate orbits of the representation of Γ on Z
2
⊗ Z
3
⊗ Z
3
in terms of
cubic rings, ... of Sections 2.3 and 3.1.
As shown in Section 2.3, the GL
2
factor of L acts on the basis of a cubic
ring R, while the two SL
3
factors act on the bases of two i...
Tài liệu Đề tài " Geometry of the uniform spanning forest: Transitions in dimensions 4, 8, 12, . . . " pptx
... further condition on the occurrence
of S, then we should also contract the edges in K
1
and delete the edges in K
2
.
Therefore, conditionally on Υ
R
and the occurrence of S, the path γ
R
has the
distribution ... be the USF on Z
d
, and denote by Γ
D
the event that there are no oriented
edges in F from D
c
to D. Then the distribution of F ∩
D
c
conditione...
Tài liệu Đề tài " The space of embedded minimal surfaces of fixed genus in a 3-manifold III; Planar domains " doc
... ˜σ
1
|
[a,b]
is noncontractible, then we are done. Otherwise, if
˜σ
1
|
[a,b]
bounds a disk, then we apply the Gauss-Bonnet theorem to see that
˜σ
1
|
(a,b)
contains a break and proceed as in the proof of ... .(II.1.14)
Proof. Following the first two steps of the proof of Lemma II.1.11 (with
the obvious modifications), we get a simple closed broken geodesic ˜σ
1
which is
nonco...
Tài liệu Đề tài " Statistical properties of unimodal maps: the quadratic family " pptx
... ∈
Ξ
i
(C
d
i
) ∩F
κ
then Ξ
i
(C
d
i
)=J
i+1
[g].
We will concentrate on the analysis of the regularity of Ξ
i
for the spe-
cial class of simple maps f: one of the good properties of the class of simple
maps ... describe the general
strategy behind the proofs of Theorems A and B.
(1) We consider a certain set of nonregular parameters of full measure
and de...
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