Tài liệu Đề tài " Pair correlation densities of inhomogeneous quadratic forms " pdf
Tài liệu Đề tài " Pair correlation densities of inhomogeneous quadratic forms " pdf
... limit
lim
i→∞
ρ
t
i
(F ◦Ψ
s
)=ν(F ◦ Ψ
s
)
Annals of Mathematics
Pair correlation densities of
inhomogeneous quadratic forms
By Jens Marklof
INHOMOGENEOUS QUADRATIC FORMS 437
exists, and we know ... γ
x
y
=
ax + by
cx + dy
.
Annals of Mathematics, 158 (2003), 419–471
Pair correlation densities of
inhomogeneous quadratic forms
By Jens M...
Tài liệu Đề tài " Hypersurface complements, Milnor fibers and higher homotopy groups of arrangments " ppt
... the discussion after the proof of Theorem 3.
2. Polar curves, affine Lefschetz theory
and degree of gradient maps
The use of the local polar varieties in the study of singular spaces is
already ... there.
Proof of Theorem 1. In view of Hamm’s affine Lefschetz theory, see
[H, Th. 5], the only thing to prove is the equality between the number k
n
of n-cells attached and the degree of...
Tài liệu Đề tài " Moduli spaces of surfaces and real structures " doc
... form is even: then S is a connected sum
of copies of P
1
C
× P
1
C
and of a K3 surface if the signature is negative,
and of copies of P
1
C
× P
1
C
and of a K3 surface with reversed orientation
if ... contradiction assuming the existence of an anti-
holomorphic automorphism σ of C.
Step I. G = A, where A is the group of holomorphic automorphisms
of C, A := Bihol(C, C).
Pro...
Tài liệu Đề tài " Hochschild cohomology of factors with property Γ " doc
... joint continuity of Corollary 4.5.
We now come to the main result of this section, the vanishing of cohomol-
ogy for property Γ factors with separable predual. The heart of the proof is to
show ... verify that the infinite tensor product of an arbi-
trary sequence of type II
1
factors has property Γ, using the ·
2
-norm density
of the span of elements of the form x
1
⊗x
2
⊗...
Tài liệu Đề tài " Hausdorff dimension of the set of nonergodic directions " ppt
... completes the proof of Lemma A.1.
A.3. The completion of the proof
Let H beaseparable Hilbert space. Denote by L(H) the Banach algebra
of bounded linear operators on H, and by U(H) the subset of unitary ... 1963.
[KMS]
S. Kerckhoff, H. Masur, and J. Smillie, Ergodicity of billiard flows and quadratic
differentials, Ann. of Math. 124 (1986), 293–311.
[Ma]
H. Masur, Hausdorff dimensi...
Tài liệu Đề tài " On the volume of the intersection of two Wiener sausages " ppt
... yields the claim in (2.80). This completes the proof of
Lemma 6.
This completes the proof of Proposition 4 and hence of Theorem 1.
3. Proof of Theorem 2
In this section we indicate how the arguments ... side of the analogue of (2.86). The integral on the right-hand
side of (3.9) is of order
1/2
log(1/). Hence we get C
5/6
log(1/) for the second
term on the right-hand side...
Tài liệu Đề tài " Higher composition laws II: On cubic analogues of Gauss composition " ppt
... laws of composition. These com-
position laws are defined on 1) pairs of ternary quadratic forms, and 2) pairs
of senary (six-variable) alternating 2 -forms. In the case of pairs of ternary
quadratic ... Det(Ax − By)=ax
3
+ bx
2
y + cxy
2
+ dy
3
for this pair (A, B).
3.2. Composition of pairs of ternary quadratic forms. Define a pair
of ternary quadratic forms (A...
Tài liệu Đề tài " Geometry of the uniform spanning forest: Transitions in dimensions 4, 8, 12, . . . " pptx
... clearly
unaffected by the removal of D from Z
d
.
5. Proofs of main results
Proof of Theorem 1.1. Denote m =
d−1
4
. By applying Corollary 3.4
to m + 1 independent copies of the USF relation, and invoking ... satisfies
the correlation inequality (2.2) with γ in place of α, and completes the proof.
3. Tail triviality
Consider the USF on Z
d
. Given n =1, 2, , let R
n
be the relati...
Tài liệu Đề tài " Classification of local conformal nets. Case c doc
... classification of Q-systems up to equivalence when a
system of endomorphisms is given and ρ is a direct sum of endomorphisms in
the system.
2.5. Classification of local extensions of the SU(2)
k
net. ... desired.
Remark 2.5. The proof of uniqueness for the E
8
case in [41, Sec. 6] uses
vertex operator algebras. Izumi has recently given a direct proof of uniquenss
of the Q-system...
Tài liệu Đề tài " The space of embedded minimal surfaces of fixed genus in a 3-manifold III; Planar domains " doc
... curvature and area of
stable sectors. A stable sector in the sense of [CM3], [CM4] is a stable subset
of a minimal surface given as half of a normal tubular neighborhood (in the
surface) of a strictly ... each r
x
can be replaced by any r
x
≤ r
x
. This will be
used freely in the proof of Theorem 0.1 below.
Proof of Theorem 0.1. Let x
k
,g
k
,R
k
,R
k,j
and r
x
be from Lemma I...
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