Tài liệu Đề tài "Gr¨obner geometry of Schubert polynomials " ppt
Tài liệu Đề tài "Gr¨obner geometry of Schubert polynomials " ppt
... Cohen–Macaulayness of the initial
scheme L
w
as part of our evidence for the naturality of Gr¨obner geometry
for Schubert polynomials, and the generality of subword complexes allows our
simple proof of their ... multidegree of X equals
the sum of multidegrees of components of Y that happen also to be compo-
nents of X. By hypothesis, the multidegrees of X and Y coin...
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 ... an
GEOMETRY OF THE UNIFORM SPANNING FOREST
477
arbitrary ordering of the vertices of a transient graph G. Let X
1
be a simple
random walk started from v
1
. Let F
1
den...
Tài liệu Đề tài " Decay of geometry for unimodal maps: An elementary proof " doc
... 12.2
of [13]. We note that these proofs of the starting condition make elaborate use
of “complex” methods and do not seem to work for the case <2.
In this paper, we shall prove the decay of geometry ... µ +2
2µ
≥
2
√
2+1
2
> 1.9.(4.7)
Annals of Mathematics
Decay of geometry for
unimodal maps:
An elementary proof
By Weixiao Shen
DECAY GEOMETRY
401
Moreover...
Tài liệu Đề tài " Pair correlation densities of inhomogeneous quadratic forms " pdf
... is of index three in Γ
k
.
Proof. It is well known [9] that Γ
θ
is of index three in SL(2, ) and
SL(2,
)=
2
j=0
Γ
θ
0 −1
11
j
.
By virtue of the group isomorphism employed in the proof of ... measure of G
k
.
This theorem is a special case of Shah’s more general Theorem 1.4 in
[27] on the equidistribution of translates of unipotent orbits. Because of the
simple structu...
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 ... 2002)
Annals of Mathematics
Hausdorff dimension of the set
of nonergodic directions
By Yitwah Cheung
Annals of Mathematics, 158 (2003), 661–678
Hausdorff di...
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
... 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, but also allows ... quadratic
endomorphism rings.
Proof. The proof of Theorem 2 shows that an element (A, B) uniquely
determines the multiplication table of R, in terms of some basis 1,ω,θ. Ele...