... the
a
(k)
i
are the
roots of A
kk
(z). Similar remarks apply to all appearances of the word “generic” below.
Annals of Mathematics
Isomonodromy
transformations of linear
systems of difference
equations ... p
i
···p
j−1
p
j
j+1
···p
j
i+n−1
p
i,j
i+n+1
···p
i,j
i+2n
p
j
i+2n
···p
j
j+2n
.
Annals of Mathematics, 160 (2004), 1141–1182
Isomonodromy transformation...
... subspace of V
∗
or V as a subspace
Annals of Mathematics
Periodic simple groups of
finitary linear
transformations
By J. I. Hall
PERIODIC SIMPLE GROUPS OF FINITARY LINEAR TRANSFORMATIONS
463
of ... groups
of finitary linear transformations
By J. I. Hall*
In Memory of Dick and Brian
Abstract
A group is locally finite if every finite subset generates a finite...
... VNU Journal of Science, Mathematics - Physics 23 (2007) 201-209
Fully parallel methods for a class of linear partial
differential-algebraic equations
Vu Tien Dung
∗
Department of Mathematics, ... properties of the so called
nonnegative pencils of matrices. In Section 3 we describe two parallel methods for solving linear
PDAEs, whose coefficients found a nonnegative pencil of m...
... 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...
... 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...
... 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...
... result of this section, a multilinear inequality
which builds on the bilinear case of Lemma 3.1. We will use three versions
{ψ
i
}
3
i=1
of the map ψ in the previous lemma, with various values of ... 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 pr...
... 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...
... 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...
... 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...